DATE DUE

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GAYLORD 'HINTED IN U.S.A.


National Bureau of Standard

TIME AND FREQUENCY:

Theory and Fundamentals

Byron E. Blair, Editor

Time and Frequency Division

Institute for Basic Standards

\J , $ , National Bureau of Standards

Boulder, Colorado -80302

JUL 1 0 1974

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

Issued May 1974
Library of Congress Catalog Number: 73-600299

National Bureau of Standards Monograph 140

Nat. Bur. Stand. (U.S.), Monogr. 140, 4 70 pages (May 1974) CODEN: NBSMA6

^6-19^

For sale by the Superintendent of Documents. U.S. Government Printing Office. Washington, D.C. 20402

(Order by SD Catalog No. C13.44:140). Price $8.65 Stock Number 0303-01202
ABSTRACT

This is a tutorial Monograph describing various aspects of time and frequency (T/F). Included

are chapters relating to elemental concepts of precise time and frequency; basic principles of quartz

oscillators and atomic frequency standards; historical review, recent progress, and current status

of atomic frequency standards; promising areas for developing future primary frequency standards;

relevance of frequency standards to other areas of metrology including a unified standard concept;

statistics of T/F data analysis coupled with the theory and construction of the NBS atomic time

scale; an overview of T/F dissemination techniques; and the standards of T/F in the USA. The

Monograph addresses both the specialist in the field as well as those desiring basic information

about time and frequency- The authors trace the development and scope of T/F technology, its improvement over periods of decades, its status today, and its possible use, applications, and

development in days to come.

Key words: Accuracy; Allan variance; atomic frequency standards; atomic time scales; AT(NBS);

BIH; buffer gases; CCIR; clock ensembles; clocks; crystal aging; Cs frequency standard; dissemination techniques; figure of merit; flicker noise; frequency domain; frequency stability; frequency

standards; frequency/time metrology; hydrogen maser; leap seconds; Loran-C; magnetic reso- nance; masers; NBS-III; NBS-5; NBS/USNO time coordination; Omega; optical pumping; precision; quartz crystal oscillators; radio T/F dissemination; Rb frequency standards; satellite T/F

dissemination; short-term stability; SI Units; TAI; television T/F dissemination; thallium beam

standards; time; time dispersion; time domain; time/frequency statistics; time scale algorithm; time

scales; "unified standard"; URSI; USA standard time zones; UTC(NBS); UTC(USNO).

Preparation of this document was supported in part by the Directorate of Communications Engineering, COMSEC/Data Systems Division, Air Force Communications

Service.

in
FOREWORD

It is indeed fitting that a time and frequency Monograph should appear now. The year 1973

marks the 50th Anniversary of the transmission of standard radio frequencies on a regularly

announced schedule from WWV at Washington, DC; the 25th Anniversary of time and frequency

broadcasts from WWVH in Hawaii; and the 25th Anniversary of the first laboratory operation of an

atomic clock (at the National Bureau of Standards, Washington, DC). That the field of time and

frequency is slowly emerging as a specialty technology is not surprising in today's world of timereferenced measurements and systems such as those required for navigation and communication.

It is paradoxical that time, related centuries ago solely to the daily apparent movement of the sun, water clocks, mechanical instruments, and the like, should be at the center of this complex field. Nevertheless, it is becoming a precise and important scientific discipline, in combination with

elements of physics, chemistry, quantum mechanics, electronics, radio propagation, and statistics to form atomic frequency generators, time scales, and varied techniques of dissemination.

The urgent demands of scientific endeavors, requiring precision measurements in the 1950's, led the National Bureau of Standards (NBS) to publish Handbook 77 — a three volume publication

of Precision Measurement and Calibration; one of these volumes — Electricity and Electronics

contained a small time and frequency section. With the advance in the 1960's of scientific methodology, standards of measures, and complex experimental techniques, NBS published a new

series of Precision Measurement and Calibration in some eleven volumes — Volume V of this Special Publication 300 was devoted entirely to papers on Frequency and Time published in the

1960's. The present Monograph results from recommendations of recent Time and Frequency

Division Advisory Panels to publish current information that would be "basic, understandable, and

practical." The Panels were concerned that the gains and utility of time and frequency techniques

be made readily available to both new and experienced workers in the field in a tutorial and comprehensible manner. That has been the objective of the authors of this Monograph.

The Institute for Basic Standards (IBS), one of four Institutes of the NBS, is given the following

responsibility — it "shall provide the central basis within the United States of a complete and consistent system of physical measurement; coordinate that system with measurement systems of other

nations; and furnish essential services leading to accurate and uniform physical measurements

throughout the Nation's scientific community, industry, and commerce." 1 As such, IBS is at the center of the National Measurement System with a primary goal of compatibility among standards;

i.e., every user in a measurement system expects to obtain the same value of a measurement based

on the same reference, but independent of the means. A person desiring time may listen to WWV by

radio, dial the telephone time number, or record a satellite time signal. The degree of accuracy may

vary but the information is related to a common source and is compatible.

I should emphasize that the major effort of this work is to describe basic principles and practices; it is of little use to maintain and update measurement standards without publicizing their construction, theory of operation, capabilities, and manner of use. We sincerely hope that this Monograph will become a valuable sourcebook of information to the practicing "time and fre- quency" specialist as well as to those new in the field seeking an understanding of compatibility

among National and International time and frequency standards and time scales, telecommunication/navigation systems, and varied dissemination techniques. It is equally important that the

material might stimulate new ideas and applications, which of themselves would broaden the depth

and scope of time and frequency technology.

E. Ambler, Director

Institute for Basic Standards

National Bureau of Standards

May 8, 1973

1 U.S. Department of Commerce, Departmental Organizational Order 30-2B, NBS Mission Statements, June 12, 1972 (see ann. ll.A-chap. 11 ).

IV
PREFACE

"National Bureau of Standards Time . . . This is radio station WWV, Fort Collins, Colorado

broadcasting on internationally allocated standard carrier frequencies of 2.5, 5, 10, 15, 20 and 25

MegaHertz, providing time of day, standard time interval, and other related information . . ." Behind such periodic radio announcements lie a substantive and state-of-the-art technology

which has advanced tremendously the last several decades. It is the objective of this Monograph

to give comprehensive pictures of various aspects of time and frequency standards in terms of the

past, present and future. As such, we trust it will serve as a tutorial reference book by providing a

historical background, the present capabilities, and the future potential of the precise and accurate time-keeping technology.

The subject matter is presented in 11 major chapters of reprinted, updated, and new material

authored by staff members of the NBS Time and Frequency Division and several other agencies,

such as the U.S. Naval Observatory and the U.S. Army Electronics Command. Chapter 1 describes

basic concepts of time, frequency, and time scales including the International Atomic Time (TAI)

scale. Following basic time aspects are chapters describing crystal oscillators, fundamental principles of atomic frequency standards, and both the historical development and recent progress in realizing various types of atomic frequency standards. Chapter 5 details improvements in cesium

beam standards at the National Bureau of Standards (NBS) including a brief description of the new

NBS-5; this frequency standard shows a tentative potential accuracy of 2 parts in 10 13 which is equivalent to a loss of a second in ~ 160,000 years. (Needless to say, a clock will not run such a length of time. However, the current state of the art today requires 6fxs in a year which is the same

relative accuracy.)

Next are two chapters which project one's thinking to future possibilities; one of these de- scribes areas of promise for developing tomorrow's primary frequency standards while the second

relates frequency standards to areas of metrology which might include a unified standard for frequency, time, and length. Chapter 8 presents basic principles of statistics useful for analyzing

time and frequency data and for describing the quality of such measurements. This is followed by

a chapter which depicts in detail both the theory and formation of the NBS atomic time scale AT

(NBS). AT(NBS) is one of seven inputs to the TAI scale maintained by the Bureau International

d'Heure (BIH) in Paris, France.

If a laboratory maintains a state-of-the-art frequency standard and time scale, such standards

are of small value unless they can be made available readily to distant users. Chapter 10 describes

various dissemination techniques for bridging the gap between a frequency standard and varied

classes of time and frequency users. The Monograph concludes with Chapter 11, a joint paper of the NBS and USNO, which depicts the standards of time and frequency in the USA; the chapter

details and compares the timekeeping missions and responsibilities of both organizations. By

mutual agreement, time at both national laboratories is maintained within about ±5/as of each

other. Chapter 11 includes a brief description of international agencies involved with timekeeping

responsibilities as well as the Uniform Time Act of 1966 of the USA given in the U.S. Code.

There has been an earnest attempt to thoroughly document each chapter with a complete

reference listing. In many instances a selected bibliography also has been included to aid a reader

seeking additional information in the given subject areas. We have attempted to be consistent and

complete in listing the references; journal title abbreviations are those given in the 1961 Chemical

Abstracts — Lists of Publications or the 1966 Revised and Enlarged Word Abbreviation List for

USAZI Z39.5-1963 — American Standard for Periodical Title Abbreviations. Many of the biblio- graphic listings can be seen at public or university libraries. NBS Technical Notes and publications

with a USGPO notation may be purchased from:

V
Superintendent of Documents

U.S. Government Printing Office

Washington, DC 20402.

References showing an AD or N accession number and a NTIS notation are available at reproduction costs from the National Technical Information Service as follows:

National Technical Information Service

U.S. Department of Commerce

5285 Port Royal Road

Springfield, VA 22150.

Limited reprints of research articles and reports are available usually from individual authors.

We have tried to maintain consistency in the use of symbols or their equivalents in all chapters;

definitions are given in the Glossary of Symbols — Annex A of Chapter 8. To aid readers unfamiliar

with letter symbols in the time and frequency field, we have added an abbreviation fisting which

follows the subject index.

A rapidly increasing number of technologies and disciplines are employing time and frequency

techniques. Included are areas such as national defense, telecommunications, public safety,

electric utilities, navigation, high speed data-computing networks, etc. There are also indications

that a large number of systems independently generate and disseminate their own time and fre- quency information, largely through use of the radio spectrum. We would point out that the radio

spectrum might be conserved to a large extent if both communication and navigation systems were

designed to include synchronization pulse formats convenient for T/F dissemination without compromising primary system concerns. By the same token, a system designer better can accommodate

a frequency dissemination function through referencing system frequencies to recognized national

frequency standards and choosing convenient subsystem frequencies where feasible. The editor wishes to gratefully acknowledge the cooperation and patience of the many authors

who have contributed to this Monograph. Considerable help and suggestions were given by Dr. Yardley Beers, Mr. Roger Easton, Mr. Donald Hammond, Dr. Richard Klepsynski, Dr. Allan

Mungall, Dr. David Wait, Dr. Bernard Wieder, and many staff members of the Time and Frequency

Division. Credit also must be given both to the NBS Visual Information Group for the many dis- tinctive illustrations in this book and to the NOAA Library personnel for help in locating and

verifying many reference citations. Last but not least special thanks are due Mrs. Sharon Erickson

for her diligence and effort in processing the final copy of this publication.

The authors trust that the Monograph will prove helpful in the understanding of the intriguing

and ever changing field of time and frequency; they would welcome suggestions, comments and/or

questions about the subject material.

Time moves on; the WWV broadcast proclaims "at the tone hours, minutes

Greenwich Mean Time."

Byron E. Blair, Editor

National Bureau of Standards

Boulder, Colorado 80302

April 23. 1973

VI
Contents

Page Abstract 'Ill Foreword IV Ernest Ambler, Director, Institute for Basic Standards, NBS, Washington, DC 20234

Preface V

Byron E. Blair, Time and Frequency Division, NBS, Boulder, CO 80302 CHAPTER 1. BASIC CONCEPTS OF PRECISE TIME AND FREQUENCY 1 James A. Barnes, Time and Frequency Division, NBS, Boulder, CO 80302

Introduction 3 Clocks and timekeeping 3 Basic concepts of time 4 Time scales 4

International Atomic Time (TAI) Scale 10 The concepts of frequency and time interval 10 Uses of time scales 11 Conclusions 13 References 13 Bibliography 14 Annex A— Definitions of the second and TAI 15 Annex B — Standard frequency and time broadcast agreements 29 Annex C — Results of 6th Session of Consultative Committee for Definition of the Second (CCDS) 37 CHAPTER 2. PART A- STATE OF THE ART- QUARTZ CRYSTAL UNITS AND OSCILLATORS 41 Eduard A. Gerber, Electronics Components Laboratory, U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, and Roger A. Sykes, Bell Telephone Laboratories, Inc., Allentown, PA

18103

Introduction 43 Quartz crystal units 44 Frequency stability as a function of Temperature 48 Time (aging) 48

Stress, vibration and acceleration 50

Drive level 50 Nuclear effects 51 Quartz crystal controlled oscillators 52 Conclusions 55 PART B - PROGRESS IN THE DEVELOPMENT OF QUARTZ CRYSTAL UNITS AND OSCIL- LATORS SINCE 1966 57 Eduard A. Gerber, Electronics Technology and Devices Laboratory, U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, and Roger A. Sykes, formerly with Bell Telephone Laboratories, Inc., Allentown, PA 18103

Introduction 59 Quartz crystal units 59 Frequency stability as a function of Temperature 60 Time (aging) 61

Stress, vibration and acceleration 61 Drive level 61 Quartz crystal controlled oscillators 62 Conclusions and possible future developments 62 References 63 CHAPTER 3. THE PHYSICAL BASIS OF ATOMIC FREQUENCY STANDARDS 65

Allan S. Risley, Time and Frequency Division. NBS. Boulder. CO 80302

Introduction 67 Atomic energy levels 67 The interaction between atoms and electromagnetic radiation 71 Choosing a suitable atom 73 The three major examples of atomic frequency standards 78 Summary 83 References 84

Bibliography 84 CHAPTER 4. PART A- A HISTORICAL REVIEW OF ATOMIC FREQUENCY STANDARDS 85 Roger E. Beehler, Frequency and Time Division, Hewlett-Packard Company, Palo Alto, CA 94304 (now with Time and Frequency Division, NBS, Boulder, CO 80302.) Introduction 87 Development of basic techniques 87

Applications of basic techniques to the development of specific types of atomic frequency

standards 93 Conclusions 99 References 99

VII
Page PART B- RECENT PROGRESS ON ATOMIC FREQUENCY STANDARDS 101 Roger E. Beehler, Time and Frequency Division, NBS. Boulder. CO 80302

Introduction 103 Laboratory cesium standards 103 Hydrogen standards 105 Commercial cesium standards 107 Commercial rubidium standards 108 References 108 CHAPTER 5. PART A - IMPROVEMENTS IN ATOMIC CESIUM BEAM FREQUENCY STANDARDS AT

THE NATIONAL BUREAU OF STANDARDS Ill David J. Glaze, Time and Frequency Division, NBS. Boulder, CO 80302

Introduction 113

Modifications to the NBS-III System 113 Accuracy capability of NBS-III (1969) 115 Some immediate goals 116 Conclusions 116 References 117 PART B - THE NEW PRIMARY' CESIUM BEAM FREOUENCY STANDARD: NBS- 5 . . . .

'.

'.

'. 119 David J. Glaze, Helmut Hellwig, Stephen Jarvis, Jr., Arthur E. Wainwright, and David W. Allan. Time and Frequency Division. NBS, Boulder, CO 80302

Introduction 121 The NBS-5 system 121 Preliminary experimental results (status April 1973) 122 References 124 CHAPTER 6. AREAS OF PROMISE FOR THE DEVELOPMENT OF FUTURE PRIMARY FREQUENCY

STANDARDS 125 Helmut Hellwig, Time and Frequency Division, NBS, Boulder, CO 80302

Introduction 127

Effects on frequency: particle interrogation 127

Effects on frequency: particle confinement 129

Effects on frequency: particles and particle preparation 130

Existing concepts for quantum electronic frequency standards 131 Frequency stability for one second averaging 133 Accuracy capability 133 Conclusions 134 References 135 CHAPTER 7. ACCURATE FREQUENCY MEASUREMENTS: RELEVANCE TO SOME OTHER AREAS OF

METROLOGY 137 Helmut Hellwig and Donald Halford, Time and Frequency Division, NBS, Boulder, CO 80302

Introduction 139 Accurate frequency measurements: principles and methods 140 Survey of accurate frequency measurements 142

Significance and impact of accurate frequency measurements 144 Summary 145 References 146

Selected bibliography: future trends in accurate frequency/time metrology 148 CHAPTER 8. STATISTICS OF TIME AND FREQUENCY DATA ANALYSIS 151 David W. Allan, John H. Shoaf, and Donald Halford, Time and Frequency Division, NBS, Boulder, CO 80302

Introduction 153

Definitions and fundamentals 153

Characterization of frequency stability 154 Requirements for a measure of frequency stability 155 Concepts of frequency stability 156 The definition of measures of frequency stability (Second Monert type) 156

Translations among frequency stability measures 159 Examples of applications of previously developed measures 161 Measurement techniques for frequency stability 162 Summary of frequency stability measures 165

Practical applications of frequency stability specification and measurements 165 Terminology for specification of frequency stability 165 Comparison of measurement techniques 167

Operational systems for measurement of frequency stability at NBS (high frequency region) 168

Operational systems for measurement of frequency stability at NBS (microwave region) 171 Conclusions/summary 175 References 175 Annex A— Glossary of symbols 176 Annex B — Translation of data from frequency domain to time domain using the conversion chart

(table 8.1) 178 Annex C — Spectral densities: frequency domain measures of stability 178

VIII
Pane Annex D — A sample calculation of script =Sf 180 Annex E — A sample calculation of Allan Variance, o-^(t) 181 Annex F— Computing counter program using an efficient overlapping estimator for (o-'^(/V = 2, T, r,fh)) il2 182 Annex G — Selected frequency stability references: bibliography 182 Annex H — Detailed procedure for calibrating microwave (frequency stability) measurement

system 187 Annex I — Measurement procedure for determining frequency stability in the microwave region... 188 Annex J — Tables of bias function, B\ and B > . for variances based on finite samples of processes

with power law spectral densities 190 Table 8.1 — Stability measure conversion chart 166 CHAPTER 9. THE NATIONAL BUREAU OF STANDARDS ATOMIC TIME SCALE: GENERATION,

STABILITY, ACCURACY, AND ACCESSIBILITY 205 David W. Allan, James E. Gray and Howard E. Machlan, Time and Frequency Division, NBS,

Boulder. CO 80302

Introduction .- 207

Basic time and frequency considerations 208 Clock modeling 208 The AT(NBS) time scale system 214 The UTC(NBS) coordinated scale 220 UTC(NBS) accessibility 221 The International Atomic Time Scale (TAI) 223

Conclusions 223 References 224 Annex A — Optimum filters for various noise processes (Eq (9.19)) 225 Annex B — Time dispersion with recursive filter applied to flicker noise FM 226 Annex C — Mini-computer program for first order time scale algorithm 227 Annex D — Selected bibliography on time scales and their formation 230 CHAPTER 10. TIME AND FREQUENCY DISSEMINATION: AN OVERVIEW OF PRINCIPLES AND

TECHNIQUES 233 Byron E. Blair, Time and Frequency Division, NBS, Boulder, CO 80302

Introduction 235

Dissemination concepts 235 Radio dissemination of time and frequency 239

Dissemination of time and frequency via portable clock 290 TFD via other means 294 T/F user and system evaluation 299

Conclusions 302 References 303. Annex A — Characteristics of radio frequency bands 4 through 10 310a Annex B — Characteristics of standard frequency and time signals in allocated bands 311 Annex C — Characteristics of stabilized frequency and time-signal emissions outside allocated frequency assignaments 312 Annex D — Characteristics of frequency stabilized navigation systems useful for time/frequency

comparisons 313 CHAPTER 11. THE STANDARDS OF TIME AND FREQUENCY IN THE USA 315 James A. Barnes, Time and Frequency Division, NBS, Boulder, CO 80302, and Gemot M. R. Winkler, Time Service Division, USNO, Washington, DC 20390

Introduction 317 Time scales — terms of reference 317 Time and frequency (T&F) activities of the National Bureau of Standards and the U.S. Naval

Observatory 318

International organizations involved in standard time and frequency 323 The legal definition of "standard time" 325 Summary 325

References 325 Annex A — NBS enabling legislation 329 Annex B — USNO authorizing documents 347 Annex C — NBS time and frequency responsibilities 359 Annex D — USNO precise time and time interval (PTTI) responsibilities 363 Annex E — NBS/USNO time coordination/services 377 Annex F— Treaty of the meter 385 Annex G— Legal documents concerning "standard time" 389

Subject Index 415 Time and Frequency Abbreviation Listing 458

CHAPTER 1

BASIC CONCEPTS OF PRECISE TIME AND FREQUENCY*

James A. Barnest

Contents

Page 1.1. Introduction 3

1.2. Clocks and Timekeeping 3

1.3. Basic Concepts of Time 4

1.4. Time Scales 4

1.4.1. Universal Time (UTO) 5

1.4.2. Universal Time 1 (UT1) 6

1.4.3. Universal Time 2 (UT2) 6

1.4.4. Ephemeris Time (ET) 6

1.4.5. Atomic Time (AT) 7

1.4.6. Coordinated Universal Time (UTC) Prior to 1972 8

1.4.7. The New UTC System 8

1.4.8. Comparisons of Time Scales 9

1.4.8.1. Reliability and Redundancy 9

1.5. International Atomic Time (TAI) Scale 10

1.6. The Concepts of Frequency and Time Interval 10

1.6.1. Time Interval and Time Scales 11

1.7. Uses of Time Scales 11

1.7.1. Time Scales for Systems Synchronization Uses 11

1.7.2. Time Scales for Celestial Navigation and Astronomical Uses 11

1.8. Conclusions 13

1.9. References 13

1.10. Bibliography 14

Annex l.A. Definition of the Second and TAI 15

Annex l.B. Standard Frequency and Time Broadcast Agreements 29

Annex l.C. Results of 6th Session of Consultative Committee for Definition of the Second

(CCDS) 37

•Manuscript received January 9, 1973. tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302.

1
"What is time? The shadow on the dial, the striking of the clock, the running of the sand, day and night, summer and winter, months, years, centuries — these are but arbitrary and outward signs, the measure of time, not time itself . . ."

Longfellow, Hyperion, Bk. ii, Ch. 6.

This chapter describes some elements of timekeeping and gives basic concepts of time and

frequency such as date, time interval, simultaneity and synchronization. This chapter details characteristics of numerous time scales including astronomical, atomic, and compromises of both. The uni- versal time scales are based on the apparent motion of the sun in the sky. while atomic time scales are based on the periodic fluctuations of a radio signal in resonance with a certain species of atoms. The chapter includes a description of the UTC time scale both before and after January 1, 1972, and

delineates requirements of an International Atomic Time scale.

Key words: Atomic time; clocks; ephemeris time; frequency; navigation/time; TAI scale; time; time

interval; time scales; universal time; UTC system.

2
1.1. INTRODUCTION

The measurement of time is a branch of science

with a very long history [1, 2, 3]. 1 For this reason, it is difficult to understand the current operations of

time and frequency measurements without some

background. This chapter presents a brief history

of the scientific and engineering aspects of time and

frequency. The discussion commences with a basic

consideration of clocks and concepts involved in time measurements. Time scales are described and

delineated as either astronomical, atomic, or compromises thereof. Universal time scales are based

on the apparent motion of the sun in the sky, while

atomic time scales are related to periodic fluctuations of a radio signal in resonance with a certain

species of atoms. This chapter includes a description of the UTC system which commenced Jan- uary 1, 1972. Characteristics and requirements of an International Atomic Time (TAI) 2 scale indicate

that the atomic time scale of the Bureau Inter- national de l'Heure (BIH) is a logical choice. However, the TAI scale will not replace some of the

needs for astronomical time scales which are necessary for earth position. The reader is referred to Chapter 9 for details of constructing and maintaining an atomic time scale.

10

100

1. ) PRIMARY DATA FROM WARD[41

,

MARRIS0N[5] , & FRASER[ 1 2]

.

2. ) INTENT IS TO SHOW BENCHMARKS OF PROGRESS . VARIOUS

CLOCK TYPES CAN SHOW IMPR0VE0 ACCURACIES.

3 . ) PRIOR TO 1000 A.D. VAR I ED TIMEKEEPERS WERE USED

SUCH AS MECHANICAL

WATER CLOCKS, N0CTURNIALS,

SUNDIALS, TIME CANDLES

,

ETC. , OF LITTLE KNOWN ACCURACY.

CESIUM CESIUM

ATOMIC | ATOMIC (IMPR0VED«(NBS-5 EST) NBS III) I

BAROMETRIC COMPENSATION

(ROBINSON)

PENDULUM (HUYGEN • IMPROVED ESCAPEMENT

( GRAHAM

)

CROSS-BEAT

ESCAPEMENT

(BURGI

)

VERGE S F0LI0T

BALANCE CLOCKS

1400 1600 CALEN0AR YEARS , A.D.

Fig. 1.1. Progress in timekeeping accuracy.

1.2. CLOCKS AND TIMEKEEPING

In early times, the location of the sun in the sky was the only reliable indication of the time of day.

Of course, when the sun was not visible, one was

unable to know the time with much precision. People developed devices (called clocks) to interpolate

between checks with the sun. The sun was sort of

a "master clock" that could be read with the aid of a

sundial. An ordinary clock, then, was a device used

to interpolate between checks with the sun. The dif- ferent clock devices form an interesting branch of

history; we will not review them to any extent here

except to point out their gain in accuracy over a period of years as shown in figure 1.1 and to refer the reader to the works of Ward, Marrison, and Hood

[4, 5, 6]. (Timekeeping has shown nearly 10 orders

of magnitude improvement within the last 6 centuries with about 6 orders occurring within 70 years

of the 20th century.) Thus, a clock could be a "primary clock" like the position of the sun in the sky, or

it could be a secondary clock and only interpolate

between checks with the primary clock or time

standard. Historically, some people have used the

word "clock" with the connotation of a secondary

time reference but today this usage would be too

restrictive.

1 Figures in brackets indicate the literature references at the end of this chapter.

2 The 6th Session of the Consultative Committee for the Defintion of the Second recommends that International Atomic Time be designed by TAI in all languages (July

1972).

When one thinks of a clock, it is customary to think of some kind of pendulum or balance wheel

and a group of gears and a clock face. Each time the

pendulum completes a swing, the hands of the clock

are moved a precise amount. In effect, the gears and

hands of the clock "count" the number of swings of the pendulum. The face of the clock, of course, is not marked off in the number of swings of the pen- dulum but rather in hours, minutes, and seconds.

One annoying characteristic of pendulum-type

clocks is that no two clocks ever keep exactly the same time. This is one reason for looking for a more

stable "pendulum" for clocks. In the past, the most

stable "pendulums" were found in astronomy. Here

one obtains a significant advantage because only one universe exists — at least for observational pur- poses, and time defined by this means is available to anyone — at least in principle. Thus, one can obtain

a very reliable time scale which has the property of universal accessibility. In this chapter, time scale

is used to refer to a conceptually distinct method of assigning dates to events. In a very real sense, the pendulum of ordinary,

present-day electric clocks is the electric current supplied by the power company. In the United

States the power utilities generally synchronize their generators to the National Bureau of Standards

(NBS) low frequency broadcast, WWVB [7]. Thus,

the right number of pendulum swings occur each
day. Since all electric clocks which are powered by

the same source have, in effect, the same pendulum,

these clocks do not gain or lose time relative to each

other; i.e., they run at the same rate. Indeed, they

will remain fairly close to the time as broadcast by

WWVB (±5 seconds) and will maintain the same

time difference with respect to each other (±1 milli- second) over long periods of time.

It has been known for some time that atoms have

characteristic resonances or, in a loose sense, "characteristic vibrations." The possibility therefore

exists of using the "vibrations of atoms" as pendulums for clocks. The study of these "vibrations" has

normally been confined to the fields of microwave

and optical spectroscopy. Presently, microwave res- onances (vibrations) of atoms are the most precisely determined and reproducible physical

phenomena that man has encountered. There is ample evidence to show that a clock which uses

"vibrating atoms" as a pendulum will generate a time scale more uniform than even its astronomical

counterparts [8, 9, 10].

But due to intrinsic errors in any actual clock sys- tem, one may find himself back in the position of

having clocks which drift relative to other similar

clocks. Of course, the rate of drift is much smaller

for atomic clocks than the old pendulum clocks, but

nonetheless real and important. If at all possible, one would like to gain the attribute of universal accessibility for atomic time also. This can be accomplished

only by coordination between laboratories generating atomic time. Both national and international

coordination are in order.

1.3. BASIC CONCEPTS OF TIME

One can use the word "time" in the sense of date. (By "date" we mean a designated mark or point on a time scale.) One can also consider the concept of

time interval or "length" of time between two

events. The difference between these concepts of

date and time interval is important and has often

been confused in the single word "time". This section explores some basic ideas inherent in the various

connotations of time.

The date of an event on an earth-based time scale

is obtained from the number of cycles (and fractions

of cycles) of the apparent sun counted from some

agreed-upon origin. Similarly, atomic time scales are obtained by counting the cycles of a signal in reso- nance with certain kinds of atoms. (Several atomic

time scales [9] have chosen the "zero point" at zero hours January 1, 1958 (UT-2), but this is not uni- versal among all atomic time scales in existence

today.) One of the major differences between these

two methods is that the cycles of atomic clocks are much, much shorter than the daily cycles of the

apparent sun. Thus, the atomic clock requires more

sophisticated devices to count cycles than are

required to count solar days. The importance of

this difference is a matter of technological con- venience and is not very profound. Of technological

significance are the facts that atomic clocks can be

read with much greater ease and with many thousands of times the precision of the earth clock. In

addition the reading of an atomic clock can be pre- dicted with almost 100,000 times better accuracy

than the earth clock. In the U.S. literature on navigation, satellite tracking, and geodesy, the word "epoch" is sometimes

used in a similar manner to the word "date." However, dictionary definitions of epoch show gra- dations of meanings such as time duration, time

instant, a particular time reference point, as well as a geological period of time. Thus, epoch often simultaneously embodies concepts of both date and duration. Because of such considerable ambiguity in the

word "epoch," 3 its use is discouraged in preference

to the word "date," the precise meaning of which is neither ambiguous nor in conflict with other, more

popular usage. Thus, the date of an event might be: 30 June 1970, 14 h, 35 m, 37.278954 s,UTC, for example, where h, m, s denote hours, minutes, and sec- onds. (The designation UTC, meaning Universal

Time Coordinated, will be discussed later.) On the

other hand, "date" should not be interchanged indis- criminately with "epoch" or "time."

Another aspect of time is that of simultaneity; i.e., coincidence in time of two events. For example, we

might synchronize clocks upon the arrival of portable clocks at a laboratory. Here we introduce an

additional term, synchronization, which implies that the two clocks are made to have the same reading in some frame of reference. Note that the clocks need

not be synchronized to an absolute time scale. As an example, two people who wish to communicate with

each other might not be critically interested in the

date, they just want to be synchronized as to when

they use their communications equipment. Many

sophisticated electronic navigation systems (and

proposed collision avoidance systems) do not depend

on accurate dates but they do depend upon very accurate time synchronization. Even ordinary tele- vision receivers require accurate time synchronization. We thus see some of the complexities involved

in concepts of time and how varied combinations of time aspects are embodied in and influence various

time-related activities.

1.4. TIME SCALES

A system of assigning dates to events is called a time scale. The apparent motion of the sun in the

3 This suggestion awaits definitive recommendations or statement of terms by parties such as the CCIR Study Group 7, Interim Working Party 7/2 on "Forms of Expression

for Use of the Standard-Frequency and Time Signal Service"; International Council of

Scientific Unions; and the IEEE Standards Committees, among others. 4
sky constitutes one of the most familiar time scales

but is certainly not the only time scale. Note that to completely specify a date using the motion of the sun

as a time scale, one must count days (i.e., make a calendar) from some initially agreed-upon beginning.

In addition (depending on accuracy needs) one measures the fractions of a day (i.e., "time of day")

in hours, minutes, seconds, and maybe even frac- tions of seconds. That is, one counts cycles (and even fractions of cycles) of the sun's daily apparent

motion around the earth. There are both astronomical time scales [11] and

atomic time scales [9] which can provide a basis for precise synchronization. A sensible use of the

unqualified word "time" is the use which embodies

all of these various aspects of time scales, time

measurement, and even time interval (or duration).

This is totally consistent with the dictionary defini- tion of the word. Thus, the study of synchronization

would be properly said to belong to the broader

study of time in general. Thus, it is not only misleading but wrong to say that "time" is only determined

by astronomical means. Indeed, there are many

classes of time — astronomical time, biological time,

and atomic time, to name a few [12].

Time derived from the apparent position of the sun in the sky is called apparent solar time. A sundial can indicate the fractions of cycles (i.e., time

of day) directly [13J. Calendars, like the Gregorian

Calendar, aid in counting the days and naming them.

Copernicus gave us the idea that the earth spins on its axis and travels around the sun in a nearly cir- cular orbit. This orbit is not exactly circular, however, and, in fact, the earth travels faster when

nearer the sun (perihelion) than when further from

the sun (aphelion). The details of the earth's orbit and Kepler's law of "equal areas" allows one to see

that apparent solar time cannot be a uniform time

[14]. There is also an effect due to the inclination of the earth's axis to the plane of its orbit (ecliptic

plane). A pictorial diagram of the sun-earth-moon

relationships is shown in figure 1.2.

1.4.1. Universal Time (UTO)

It is possible to calculate these orbital and incli- nation effects and correct apparent solar time to obtain a more uniform time — commonly called mean

solar time. This correction from apparent solar time

MAR 21 VERNAL EQUINOX

APHELION

JUL 5, 1966

PATH

PERIHELION

JAN 3, 1966

LUNAR ORBIT NODAL LINE PERIOD = 27 .32 DAYS

INCLINATION OF EARTH'S

EQUATOR TO ITS ORBIT

( 23 .45°)« 20° TO 26° INCLINATION OF LUNAR ORBIT TO EARTH'S EQUATOR

18.06° TO 28.1°

5° INCLINATION OF LUNAR EQUATOR TO ITS ORBIT PERIGEE = 3 .64 x 1

0

8 m

-EARTH-MOON APSIDE LINE „ APOGEE = 4.06 x 10 m

Fig. 1.2. Sun, earth, moon relationships. (Courtesy of A. D. Watt)

5
to mean solar time is called the Equation of Time

and can be found engraved on many present-day

sundials [13]. If one considers a distant star instead of our star

the sun — to measure the length of the day, then the

earth's elliptic orbit becomes unimportant and can be neglected. This kind of time is the astronomer's

sidereal time and is generically equivalent to mean

solar time since both are based, ultimately, on the

spin of the earth on its axis — the second of sidereal

time being just enough different to give a sidereal

year one more "day" than that of a solar year. In actual practice, astronomers usually observe side- real time and correct it to get mean solar time. Universal Time (UTO) is equivalent to mean solar time

as determined at the Greenwich Meridian, sometimes called Greenwich Mean Time (GMT).

Time, of course, is essential to navigation in deter- mining longitude [15]. In effect, a navigator using a sextant measures the angle between some distant

star and the navigator's zenith as shown in figure 1.3.

It is apparent that for a given star there is a locus of

points with the same angle. By sighting on another

star, a different locus is possible and obviously the

position of the navigator is at one of the intersections

of the two loci. (A third sighting can remove the

ambiguity.) The position of this intersection on the

earth obviously depends on the earth's rotational

position. It is important to emphasize that celestial navigation is basically connected to earth position

and only to time because the earth also defines a useful time scale.

LOCAL

Fig. 1.3. Principle of celestial navigation.

1.4.2. Universal Time 1 (UT1)

In order for the navigator to use the stars for navigation, he must have a means of knowing the earth's position (i.e., the date on the UT scale). Thus, clocks

and sextants together became the means by which

navigators could determine their locations. With

navigation providing a big market for time and for

good clocks, better clocks were developed, and

these began to reveal a discrepancy in Universal

Time measured at different locations. The cause of

this was traced to the fact that the earth wobbles on

its axis; the location of the pole as it intersects the

earth's surface is plotted for 1964-69 in figure 1.4. In effect, one sees the location of the pole wandering

over a range of about 15 meters. By comparing astro- nomical measurements made at various observatories spread over the world, one can correct for

this effect and obtain a more uniform time — denoted

UT1 [16].

Fig. 1.4. Path of earth's pole 1964-1969.

1.4.3. Universal Time 2 (UT2)

With the improvement of clocks — both pendulum

and quartz crystal — it was discovered several years ago that UT1 had periodic fluctuations (of unknown

origin) with periods of one-half year and one year. The natural response was to remove these fluctua- tions and obtain an even more uniform time — UT2.

Thus, there exists a whole family of Universal Times

based on the spin of the earth on its axis and various

other refinements as diagrammed in figure 1.5. In

this historical progression, one notes that UT1 is the true navigator's scale related to the earth's angular

position. UT2 is a smoothed time and does not reflect the real, periodic variations in the earth's angular

position.

1.4.4. Ephemeris Time (ET)

At this point it is desirable to go back in time —

near the turn of the century — and trace some other

astronomical studies. In the latter 19th century,

6
UNIVERSAL TIME FAMILY

APPARENT SOLAR TIME

CORRECTED BY EQUATION OF TIME | MEAN SOLAR TIME T

[UTO]

CORRECTED FOR MIGRATION OF POIES At - 0 05sec f

UT1

CORRECTED FOR KNOWN PERIODICITY At O.05sec m UT2

Fig. 1.5. Universal time family interrelationships.

Simon Newcombe compiled a set of tables, based on Newtonian mechanics, which predicted the posi- tions of the sun, the moon, and some planets for the

future. A table of this sort is called an ephemeris. It was discovered that the predicted positions gradually departed from the observed positions in a fashion too significant to be explained either by

observational errors or approximations in the theoryIt was noted, however, that if the time were some- how in error, all the tables agreed well. At this point

it was correctly determined that the rotational rate

of the earth was not constant. This was later con- firmed with quartz clocks and atomic clocks [17, 18,

19]. The astronomers' natural response to this was,

in effect, to use Newcombe's tables for the sun in reverse to determine time — actually what is called Ephemeris Time. Ephemeris Time is determined by

the orbital motion of the earth about the sun (not by

rotation of the earth about its own axis) and should

not be affected by such things as coremantle slippage or other geometrical changes in the shape of

the earth.

•1 00

1700 1800 1900 CALENDAR YEARS, A.D.2000

Fig. 1.6. Trend of UT-ET for over three centuries (data from Brouwer [20]).

The variations in UT scales or earth rotation rates have been studied extensively by Brouwer and many

others [20, 21, 22]. In this chapter, we need only

point out the general nature and size of the varia- tions which have been observed. Brouwer's study

covered a long period of time; the curves shown in figure 1.6 summarize much of his data and analysis.

They reflect the random behavior [23 J of UT, marked

on occasion by sudden erratic changes such as seen

in 1963 [24J. The abscissas in figure 1.6 are proportional to the astronomical time scale, ET. At present

ET can be considered uniform with respect to AT

[25J and is a good comparison scale to be used in detecting long-term (gross) properties of a time

scale. It is of value to recognize that Brouwer deter- mined that the random processes which affect the

rotation of the earth on its axis caused the rms fluc- tuations in Universal Time to increase as t 312

, for t greater than one year. For periods of the order of a year or less it appears that the variations in the UT2

time scale cause the rms fluctuations to increase as the first power of t (flicker noise frequency modulation) [26J. The coefficient of this linear term is about

2 X 10~9 or almost a factor of 105 worse than some

cesium clocks. The present means of determination

of ET are not adequately precise to allow definitive statements about possible systematic variations of

ET [11].

1.4.5. Atomic Time (AT)

As was pointed out previously, the date of an

event relative to the Universal Time Scale is obtained from the number of cycles (and fractions of

cycles) of the apparent sun counted from some

agreed-upon origin. (Depending on the need, one may have to apply corrections to obtain UTO, UT1, or UT2.) Similarly, atomic time scales are obtained by

counting the cycles of a signal in resonance with

certain kinds of atoms.

In the latter part of the 1940's, Harold Lyons at the National Bureau of Standards announced the

first Atomic Clock [27]. During the 1950's several

laboratories began atomic time scales [28. 29. 30]. The Bureau International de l'Heure (BIH) has been

maintaining atomic time for some years now, and

this time scale received the official recognition as International Atomic Time (TAI) of the General Conference of Weights and Measures (CGPM) in October 1971 [31] (see ann. l.A). Beginning 1 January

1972, this atomic time scale has been broadcast

(with some modifications) by most countries (see

"The new UTC system" in sec. 1.4.7). In review, we have discussed three broad classes

of time scales as illustrated in figure 1.7. The Universal Time family is dependent on the earth's spin on its axis; Ephemeris Time depends on the orbital motion of the earth about the sun; and Atomic Time,

which depends on a fundamental property of atoms,

is very uniform and precise. Because of the "slow"

7
UNIVERSAL TIME 4

(UTO, UT1, UT2) T

MEASURED TO 3ms IN 1 DAY

EPHEMERIS TIME ^

(ET) V

MEASURED TO 50ms IN 9 YEARS

ATOMIC TIME & MEASURED TO <0.1 Ms IN 1 min T (DIFFUSION RATES OF 0.1 F

s/day FOR ENSEMBLES OF CLOCKS]

Fig. 1.7. Classes of time scales with typical accuracies.

merit [33J. UTC was supposed to agree with UT2 to within Vio second (V20 second before 1963). On

occasion it was necessary to reset the UTC clock by

Vio second (V20 second before 1963) in order to stay

within the specified tolerances as shown in fig- ure 1.8. Also, by international agreement [33J. the

offsets in clock rate were constrained to be an inte- gral multiple of 5 parts per billion (1 part per billion before 1963). In addition, a few stations (e.g., WWVB) broadcast a Stepped Atomic Time (SAT)

signal which was derived directly from an atomic

clock (no rate offset) but which was reset periodically (more often than UTC) to maintain SAT within

about Vio second of UT2 [34J.

orbital motion of the earth (1 cycle per year), meas- urement uncertainties limit the realization of accurate ephemeris time to about 0.05 second for a 9-year average, while UT can be determined to a few thousandths of a second in a day, and AT to a few billionths of a second in a minute or less.

1.4.6. Coordinated Universal Time (UTC)

Prior to 1972

From 1960 through 1971 many broadcast time sig- nals (e.g., MSF, WWV, CHU) were based on a time

scale called Coordinated Universal Time (UTC) [32]. The rate of a UTC clock was controlled by atomic

clocks to be as uniform as possible for 1 year, but

this rate could be changed at the first of a calendar

year. The yearly rate was chosen by the BIH.

Table 1.1 lists the fractional offsets in rate of the

UTC scale relative to a pure atomic time scale.

Table 1.1. Frequency Offsets of UTC from 1960 to 1972

Offset rate of Year UTC in parts per 1010

1960 -150

1961 -150

1962 -130

1963 -130

1964 -150

1965 -150

1966 -300

1967 -300

1968 -300

1969 -300

1970 -300

1971... -300

1972^ future 0

The minus sign implies that the UTC clock ran slow

(in rate) relative to atomic time. The offset in clock

rate was chosen to keep the UTC clock in reasonable agreement with UT2. However, one could not exactly predict the earth's rotational rate and dis- crepancies would accrue. By international agreeCOORDINATED UNIVERSAL TIME (UTC)

[PRIOR fO 1 972) YEARS

UTC-AT

UI2-AI

ff = n » (50 » lO"")

it = 1/10 sec

Fig. 1.8. Relationship between UTC and UT2 time scales — prior

to 1972.

1.4.7. The New UTC System

The facts that the clock rate of UTC have been

offset (see table 1.1) from the correct (atomic) rate and that this offset changed from time to time necessitated actual changes in equipment and often inter- rupted sophisticated systems. As the needs for reliable synchronization have increased, the old UTC system became too cumbersome. A new compromise system was needed to account better for the

ever-growing needs of precise time synchronization.

A new UTC system was adopted by the Inter- national Radio Consultative Committee (CCIR) in Geneva in February 1971 [35, 36] and became effec- tive 1 January 1972 (see ann. LB). In this new sys- tem all clocks run at the correct rate (zero offset). This leaves us in a position of having the clock rate not exactly commensurate with the length of the day.

This situation is not unique. The length of the year

is not an integral multiple of the day. This is the

origin of "leap year." In this case, years which are

divisible by 4 have an extra day — February 29 —

unless they are also divisible by 100, and then only

if they are not divisible by 400. Thus, the years 1968,

1972,' 1976, and 2000 are leap years. The year 2100

8
will not be a leap year. By this means our calendar

does not get out of step with the seasons. With this as an example, it is possible to keep the

clocks in approximate step with the sun by the infre- quent addition (or deletion) of a second — called a "leap second." Thus, there may be special situations

where a "minute" contains 61 (or 59) seconds

instead of the conventional 60 seconds. This should

not occur more often than about once a year. By

international agreement, UTC will be maintained

within about 0.7 second of the navigators' time scale,

UT1. The introduction of leap seconds allows a good clock to keep approximate step with the sun. Because of the variations in the rate of rotation of

the earth, however, the occurrences of the leap

seconds are not predictable in detail.

1.4.8. Comparisons of Time Scales

It is of value in comparing time scales to consider

four significant attributes of some time scales:

a. accuracy and precision,

b. reliability,

c. universal accessibility,

d. extension.

In the areas of accuracy and precision, atomic

time scales have a clear advantage over their astro- nomical counterpart. Atomic clocks may be able to make a reasonable approach to the reliability and

accessibility of astronomical clocks, however, astro- nomical time scales are based on a "single" clock

which is available to everyone (i.e., only one solar system is available for study). Also, many atomic

clocks can show disagreements, an impossibility

with only one clock. The extension of dates to past events (indeed, remote, past events) is a feature

which atomic clocks will never possess. Their utility for future needs, however, is quite another matter. The needs of the general scientific community and,

in particular, the telecommunications industries are making ever greater demands on accurate and precise timing covering longer time intervals. Often

these needs cannot be met by astronomical time.

However, the continued motion of the solar system

gives a reliability to astronomical time scales which

atomic clocks have not yet attained.

One can imagine synchronizing a clock with a hypothetically ideal time scale. Some time after this synchronization our confidence in the clock reading

has deteriorated. Figure 1.9 shows the results of some statistical studies which indicate the probable

errors of some important clocks after synchronization. There are really two things of significance to note in figure 1.9: First, Atomic Time (state of the

art, 1964) is about 10,000 times more uniform than

Universal Time, and second, measurement uncertainty totally limits any knowledge of statistical fluctuations in Ephemeris Time.

PROBABLE CLOCK ERRORS

(NON-UNIFORMITY)

Fig. 1.9. Probable errors of 3 clock types after synchronization.

1.4.8.1. Reliability and Redundancy

In the past, reliable operation of atomic frequency

standards has been a significant problem. Presently,

however, commercial units with a Mean Time

Between Failure (MTBF) exceeding 1 year are not uncommon [37]. Finite atom source lifetime pre- vents unlimited operation without interruption,

however.

It is true that a MTBF exceeding 1 year reflects significant engineering accomplishments, but this is far from comparable to the high reliability of astro- nomical time. The obvious solution is to introduce

redundancy in the clock system. One can use several atomic clocks in the sytem and this should

certainly be the best approach in the sense of

accuracy and reliability — it is expensive, however.

Suppose the synthesizer-counter subsystem of a clock system should jump a small amount and cause

a discontinuity in its indicated time. It is possible

that such a transient malfunction could occur with no outwardly apparent signs of malfunction of the

apparatus. It is also apparent that if only two clocks

are available for intercomparison, it is impossible to decide which clock suffered the transient malfunction. Thus, three clocks (not necessarily all atomic)

constitute an absolute minimum for reliable operation. If one or more of these has an extended probable down time (e.g., while the atom source is replenished) then 4 or 5 clocks become a more workable minimum.

9
It should be noted here that one could assemble a large group of clocks into one system and the system

MTBF calculated from the ' individual MTBF's

might extend into geologic time intervals. This sys- tem MTBF is undoubtedly over-optimistic due to neglect of the possibilities of catastrophes or operator errors. Nonetheless, with various atomic clocks

spread over the earth, it should be possible to maintain an atomic time scale with a reliability that could

satisfy almost any future demand.

1.5. INTERNATIONAL ATOMIC

TIME (TAI) SCALE

In recent years the General Conference of Weights

and Measures (CGPM) has been encouraged to adopt an International Atomic Time (TAI) scale [38] (see ann. l.A). For such a scale to be of value the

following attributes are required:

a. It must provide greater accuracy and convenience than the astronomical counterparts.

b. It must be highly reliable with almost no

chance of a failure of the clock system. (This can be accomplished by using many clocks dis- persed over the world but which can be inter- compared accurately.)

c. The atomic time scale must be readily available

everywhere.

Indeed, all of these points appear to be more than

adequately covered by the atomic time scale of the

BIH. In October 1971 the CGPM endorsed the BIH

atomic time scale as the International Atomic Time

scale [31] (see ann. l.A) defined as follows:

"International Atomic Time is the time reference coordi- nate established by the Bureau International de l'Heure on

the basis of the readings of atomic clocks functioning in various establishments in accordance with the definition of the second, the S.I. Unit (International System of Units) of time." The Atomic Time (AT) scales maintained in the

U.S. (by both NBS and USNO) constitute ~37Ya

percent of the stable reference information used in maintaining a stable TAI scale by the BIH [39]. The

question of the accuracy of rate of the TAI scale is not now completely specified [40]. There is a question of formal averaging procedures for correcting

TAI. A special meeting of the Consultative Committee for the Definition of the Second (CCDS) was held

in Paris, France, July 1972, to consider the status of

atomic frequency standards and improved realiza- tion of the TAI, among other pertinent questions.

Recommendations of this committee (6th Session of

CCDS) are given in Annex l.C. Dr. Guinot, Director of the BIH, recommended a new method of calculation of TAI. By using individ- ual clock data in place of local time scales from var- ious laboratories, improved weighting of clock data

is anticipated [40]. Some advantages of the individ- ual clock procedure he pointed out are as follows:

"1. Most of the local time scales are based on a small number of clocks. Irregularities of TAI are due to changes of frequencies of certain TA(i) which cannot be seen at the local

level when the number of standards in effective use has to be

less than 3. This happens frequently. In a global treatment, such irregularities would be visible.

2. Isolated standards could be employed. For example, at least 12 cesium standards conveniently available and compared to the Loran C pulses or TV pulses are available in Europe, not including those at the Loran C stations.

3. The treatment of all the standards would be unified, described in detail, and understood by all. At present, it is practically impossible to understand how TAI is calculated

since it is necessary to understand the methods of each

participating laboratory, methods which are not always

published.

4. The direct calculation of TAI would allow a complete freedom to the laboratories in order to establish the TA(i), according to their criteria, without which they have to be

preoccupied with the criteria adopted by TAI." A tentative schedule for work of the BIH for improving TAI is given in Annex l.C. A complete

description of the construction of a local atomic

time scale is treated by D. Allan et al. in chapter 9. The UTC scales of the USA are coordinated with

UTC(BIH) to within a tolerance of about ± 10 fxs. All of the UTC scales are supposed to agree with

UTC(BIH) to ±1 millisecond by International

Radio Consultative Committee (CCIR) agree- ment [36]. For those desiring accurate UT information, corrections are encoded into standard time

broadcasts [36]. Yet, even with the existence of an

International Atomic Time scale, one must recognize that there will be continued need for the

astronomical time scales. A person doing celestial navigation, for example, must know earth position

(UT1).

1.6. THE CONCEPTS OF FREQUENCY AND TIME INTERVAL

The four independent base units of measure- ment currently used in science are length, mass,

time, and temperature. It is true that, except for

fields of science such as cosmology, geology, and

astronomy, time interval is the most important

concept, and (astronomical) date is of much less importance to the rest of science. This is true be- cause the "basic laws" of physics are differential

in nature and only involve small time intervals. In essence, physical "laws" do not depend upon when

(i.e., the date) they are applied.

Based on these laws and extensive experimentation, scientists have been able to demonstrate that frequency can be controlled and measured with the

smallest percentage error of any physical quantity.

The frequency of a periodic phenomenon is the

number of cycles of this phenomenon per unit of

time (i.e., per second). The name of the unit of fre- quency is the hertz (Hz) and is identical to a cycle

per second (cps). Since most clocks depend upon some periodic phenomenon (e.g., a pendulum) in order to "keep time," and since one can make reli- able electronic counters to count the "swings" of

10
the periodic phenomenon, we can construct clocks

with timekeeping accuracy (rate accuracy) equal

to the accuracy of the frequency standard.

In terms of the advancement of time scales, the

history of the definition of the second can be

expressed very briefly. Prior to 1956, the second was defined as the fraction 1/(86,400) of a mean solar day; from 1956 to 1967 it was the ephemeris second

denned as the fraction 1/(31 556 925.9747) of the

tropical year at OOh 00m 00s 31 December 1899, and

since 1967, in terms of a resonance of the cesium

atom [41] (see ann. LA). The present definition of the second states:

"The second is the duration of 9 192 631 770 periods of the

radiation corresponding to the transition between the two

hyperfine levels of the ground state of the cesium — 133 atom". (13th CGPM (1967), Resolution 1), [42]. Today's most precise and accurate clocks incorporate a cesium atomic beam as the "pendulum" of the clock.

1.6.1. Time Interval and Time Scales

One should note sources of confusion which can

exist in the measurement of time and in the use of

the word "second." Suppose that two events occurred at two different dates. For example the

dates of these two events were 15 December 1970,

15h 30m 00.000000s UTC and 15 December 1970,

16h 30m 00.000000s UTC. At first thought one would

say that the time interval between these two events was exactly 1 hour = 3600.000000 seconds, but this

is not true. (The actual interval was longer by

about 0.000108 seconds [3600 secondsX300X 10" 10

]. See table 1.1.) Recall that the UTC time scale (like

all the UT scales and the ET scale) was not defined

in accordance with the definition of the interval of time, the second. Thus, one cannot simply subtract

the dates of two events as assigned by the UTC

scale (or any UT scale or the ET scale) in order to obtain the precise time interval between these

events. Historically, the reason behind this state of

affairs is that navigators need to know the earth's position (i.e., UT1) — not the duration of the second.

Yet, many scientists need to know an exact and

reproducible time interval. Note that this might

also be true of the new UTC system if the particular

time interval included one or more leap seconds.

It is also confusing that the dates assigned by the

UT, ET, and UTC scales involve the same word as the unit of time interval, the second. For accurate and precise measurements, this distinction can be

extremely important.

1.7. USES OF TIME SCALES

The study of time scales can be divided into the

study of time scales used for systems synchronization and time scales used for celestial navigation

and astronomy.

1.7.1. Time Scales for Systems Synchronization Uses

Long ago people were simply content to let the sun govern their fives. Sunrise indicated time to arise and begin work; sunset signalled the day's end.

With the advancement of civilization, growth of commerce and city life and technological gains,

communities were established which instituted

clocks set to agree roughly with the apparent

movement of the sun. Thus developed the idea of

local time and each community could have its own

local time. Clearly, when almost all communications

and business transactions occur within a given community or locale, this is a workable solution. With

the advent of railroads and hence more rapid communications, this "crazy-quilt" maze of individual

local times had to end. The railroads are generally

credited with unifying the various local times into time zones in the continental U.S., resulting in a much more workable national time system. In 1884 an international conference recommended that the

meridian of Greenwich, England be the standard

reference meridian for longitude and time [43]. Longitude meridians, each 15°, represent 1 hour

time-zone differences ± 12 hours east and west of

Greenwich. Figure 1.10 shows the standard time zones of the world in effect today.

This brief historical sequence illustrates that, as communications become more rapid and more far- reaching, the greater are the demands on an all- pervasive and unifying convention of synchronizing

clocks with each other. That is, this convention is a matter of convenience and there is nothing sacred

or absolute about what our clocks read; it's just

important that they read the same time (or have a well-defined time difference as between the time

zones). In the days when the railroads were the

primary means of transportation across the North

American continent, an accuracy of a few seconds

of time was important and sufficient. Nowadays,

with the existence of sophisticated telecommunications equipment capable of sending and receiving

several million alphanumeric characters each

second, there are real needs for clock synchronizations at accuracy levels of a millionth of a second

and better.

1.7.2. Time Scales for Celestial Navigation

and Astronomical Uses

As pointed out previously, time is essential for celestial navigation. If one knows what time it is

(i.e., solar time) at some reference point — say the

Greenwich Meridian — and also his local time as indicated by a sundial — one can figure his longitude.

11
o o oooooo

12
since the earth makes one complete revolution

(360°) on its axis in about 24 hours. For example,

noon Greenwich Mean Time is 0200 Hawaiian Standard Time or 10 hours different. Thus, one can easily calculate that Hawaii is about 10/24 of the way

around the world from Greenwich, England —i.e., about 150° west of the Prime Meridian. If this person were to measure the actual position of the sun in the sky using, say, a navigator's sextant,

then he could get a rather accurate determination

of local solar time. The key problem is knowledge

of correct time on the Greenwich Meridian.

Nearly 200 years ago, a man in England named

Harrison was awarded £20,000 for designing and

building a chronometer which would allow the accurate determination of longitude while at sea

(less than 1 minute error after 5 months at sea [44]). Until radio signals were available in the early 1900's,

navigation at sea was totally dependent upon good

clocks. Today, there are many standard time broadcast stations in the world which can provide time

signals accurate to better than 1 second of earth

time, UT1 [45]. If astronomical time could be measured with

sufficient accuracy and convenience, then astro- nomical time could be used for system synchronization uses also. In actuality, astronomical time is difficult to measure, and accuracies of a few

thousanths of a second may be realized only after the averaging of a whole evening's sightings by a sophisticated and well-equipped observatory. The

accurate determination of UT1 involves measure- ments at, at least, two observatories widely separated in longitude.

1.8. CONCLUSIONS

Two very different uses for time have been dis- cussed. The first is a convention which, when

universally accepted, allows both rapid and efficient communications systems to function. The needs

here are for extremely precise and uniform meas- urements of time. The second use is for celestial navigation and astronomical observations. Here

there is not the need for highly precise time, at least not to the same degree as the first mentioned use. Because of the conflicting requirements imposed

on time scales by these two categories of time scale

users, there has been a great deal of effort to obtain

a compromise time scale which adequately reflects the relative importance of these two user groups. As one might well imagine, with the growing

importance and sophistication of communications

systems and the implementation of electronic

navigation systems (to replace celestial navigation),

the trend in the compromise time scales has been

away from time scales based on the earth's rotation

(i.e., astronomical time scales) and toward a pure

atomic time scale.

In this compromise scale, UTC, one finds himself

in a rather familiar situation. There is not a whole

number of days in the year and one doesn't want the

calendar to get badly out of step with the seasons.

Similarly, there is not a whole number of seconds

in a solar day and one doesn't want our clocks to get badly out of step with the sun. The solution

(as noted above) is analogous to the leap year with

its extra day; we have an extra second — a leap

second which must be added or deleted on occasion.

1.9. REFERENCES

[1] Needham, J., Ling, W., and de Solla Price, D. J., Heavenly

Clockwork, 254 pages (The University Press, Cambridge,

London, England, 1960).

[2] Jones, H. Spencer, "The measurement of time," Reports on

Progress in Physics, 4, pp. 1-26 (1937) (The University

Press, Cambridge, London, England, 1938).

[3] Mueller, I. I., Spherical and Practical Astronomy as Applied

to Geodesy, pp. 319-400 (Frederick Ungar Publishing Co., New York, N.Y. 10003, 1969).

[4] Ward, F. A. B., Time Measurement, Pt. 1 - Historical Review, 60 pages (H.M.S.O., William Clowes and Sons Ltd., London, England, 1961).

[5| Marrison, W. A., "The evolution of the quartz crystal clock," Bell Sys. Tech. J., 27, No. 3, pp. 510-588 (July

1948).

[6] Hood, P., How Time is Measured, 64 pages (Oxford University Press, London, England, 1955).

[7] Cohn, N., "Power systems- time and frequency," Leads and

Northrup Tech. J., No. 7, pp. 3-11 (Fall 1969).

[8] Lyons, H., "Atomic clocks," Scientific American, 196,

No. 2, pp. 71-82 (February 1957).

[9] Essen, L., "Time scales," Metrologia, 4, No. 4, pp. 161-165

(July 1969).

[10] Becker, G., "Von der Astronomischen zur Atomphysikali- schen Definition der Sekunde," (From the astronomical to the atomic definition of the second.) PTB-Mitteilungen,

76, No. 4, pp. 315-323 and No. 5, pp. 415-419 (August/ October 1966) (in German).

[11] Kovalevsky, J., "Astronomical time," Metrologia, 1, No. 4, pp. 169-180 (October 1965).

[12] Fraser, J. T., Voices of Time, pp. 281, 296, 312, 401 (George

Braziller, Inc., One Park Avenue, New York, N.Y.

10016, 1966).

[13] Cousins, F. W., Sundials— A Simplified Approach by Means

of the Equatorial Dial, 249 pages (Universe Book, Inc., New York, N.Y. 10016, 1970).

[14] Mueller, I. I., see Ref. [3], pp. 141-145.

[15] Mueller, I. I., see Ref. [3], pp. 476-518.

[16] Guinot, B., Feissel, M., and Granveaud, M., Bureau Inter- national de I'Heure Annual Report for 1970, pp. 37-62

(BIH, Paris, France, 1971).

[17] Scheibe, A., and Adelsberger, U., "Die Technischen

Einrichtungen der Quarzuhren der Physikalisch-Tech- nischen Reichsansalt," (Technical development of quartz

clocks of the PTR) Hochfrequenz-technik und Elektroakustic, 43, pp. 37-47 (February 1934) (in German).

[18] Essen, L., Parry, J. V. L., Markowitz, W., and Hall, R. G., "Variation in the speed of rotation of the earth since 1955," Nature {Lett.), 181, No. 4615, p. 1054 (April 12, 1958).

[19] Essen, L., Parry, J. V. L., and Steele, J. McA., "Frequency

variations of quartz oscillators and the earth's rotation in terms of the N. P. L. cesium standard," Proc. Inst. Elec. Eng. (England), 107, Part B, No. 33, pp. 229-234 (May

1960).

[20] Brouwer, D., "A study of the changes in the rate of rotation of the earth," Astron. J., 57, No. 5, pp. 125-146 (September 1952).

13
[21] Munk, W. H., and MacDonald, G. D. F.. The Rotation of the Earth, Chap. 8 (Cambridge University Press, London,

England, 1960).

[22] Sidorenkov, N. S., "Neravnomervost' vrashscheniya zemli podannym astronomicheskikh noblyudeniy za period 1955.5-1965.0 gg," (Non-uniformity in the rotation of the earth according to the data of astronomic observations

for the period 1955.5- 1965.0), Astronomicheskiy J. (USSR),

44, No. 3, pp. 650-662 (1967-English translation, NTIS,

AD 667076, January 1968).

[23] Blackman, R. B., and Tukey, J. W., The Measurement of Power Spectra, pp. 151-159 (Dover Publications, Inc., New York, N.Y. 10014, 1958).

[24] Iijima, S., Matsunami, N., and Okazaki, S., "On the abrupt

change in the earth's rotation at the beginning of 1963," Ann. Tokyo Astron. Observatory, 2nd series, VIII, pp. 207-217 (August 1964).

[25] Nicholson, W., and Sadler, D., "Atomic standards of fre- quency and the second of ephemeris time," Nature

{Lett.), 210, No. 5032, p. 187 (April 9, 1966).

[26] Barnes, J. A., and Allan, D. W., "An approach to the prediction of coordinated universal time," Frequency, 5, No. 6, pp. 15-20 (November—December 1967).

[27] NBS, "The atomic clock — an atomic standard of frequency and time," Nat. Bur. Stand. (U.S.) Tech. News Bull., 33,

No. 2, pp. 17-24 (USGPO, February 1949).

[28] BIH, Bulletin Horaire, Ser. J., No. 7. p. 2 (BIH, Paris, France, January/February 1965).

[29] Markowitz, W., "The atomic time scale," IRE Trans, on

Instrum., 1-11, Nos. 3 and 4, pp. 239-242 (December

1962).

[30] Bonanomi, J., Kartaschoff, P., Newman, J., Barnes, J. A., and Aktinson, W. R., "A comparison of the TAj and the NBS-A atomic time scales," Proc. IEEE {Carres.), 52,

No. 4, p. 439 (April 1964).

[31] CGPM, Comptes Rendus des Seances de la Quatorzieme

Conference Generale des Poids et Mesures (Proceedings

of the Sessions of the 14th General Conference of Weights and Measures) (Paris, France, October 4-8, 1971), pp. 49-52; 77-78 (BIPM, Sevres, France, 1972) (in French — see ann. 1.A.3).

[32] Essen, L., "The international co-ordination of time scales and standard frequency transmissions," Nature {Lett.), 187, No. 4736, pp. 452-453 (August 6, 1960).

[33] CCIR, "Standard frequency and time signal emissions,"

Recommendation 374-1, Documents of the XIth Plenary

Assembly (Oslo, Norway, 1966), III, pp. 281-282 (ITU, Geneva, Switzerland, 1967).

[34] Hudson, G. E., "Some characteristics of commonly used

time scales," Proc. IEEE, 55, No. 6, pp. 815-821 (June

1967).

[35] CCIR, "Standard-frequency and time-signal emissions,"

(Recommendation 460), in Xllth Plenary Assembly CCIR,

(New Delhi, India, 1970), III, p. 227 (ITU, Geneva,

Switzerland, 1970) (see ann. l.B.l).

[36] CCIR, "Detailed instructions by Study Group 7 for the implementation of Recommendation 460 concerning the improved coordinated universal time (UTC) system, valid from 1 January 1972," in Xllth Plenary Assembly CCIR,

(New Delhi, India, 1970) III, p. 258 a-d (ITU, Geneva,

Switzerland, 1970) (see ann. 1.B.2).

[37] Hyatt, R., Throne, D., Cutler, L., Holloway, J. H., and

Mueller, L. F., "Performance of newly developed cesium beam tubes and standards," Proc. 25th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 26-28. 1971), p. 316 (NTIS,

AD 746211, 1971).

[38] CCDS, "Recommendations du comite consultatif pour la definition de la seconde ..." (Recommendations of the Consultative Committee for the definition of the second . . .) Comite Consultatif pour la Definition de la seconde, (CIPM, 5

e Session, Paris, France, June 18-19,

1970), pp. S21-S23 (BIPM, Sevres, France, 1971) (in French — see ann. 1.A.2).

[39] Guinot, B.. Feissel, M., and Granveaud, M., see Ref. [16],

p. 28.

[40] Guinot, B., (Reporter), "Sixieme rapport du comite consultatif pour la definition de la seconde au comite inter- national des poids et measures," (Minutes of 6th session

consultative committee for the definition of the second)

(CIPM, 6

e Session, Paris, France, July 6-7, 1972) (BIPM,

Sevres, France, 1972) (in French — see ann. l.C).

[41] Smith, H. M., "International time and frequency coordination," Proc. IEEE, 60, No. 5, pp. 479-487 (May 1972).

[42] CGPM, Comptes Rendus des Seances de la Treizieme Conference General des Poids et Mesures (Proceedings

of the Sessions of the 13th General Conference of Weights

and Measures) (Paris, France, October 1968), p. 103

(Gauthier-Villars, Paris, France 1968) (in French — see

ann. l.A.l).

[43] IMC, International Meridian Conference, Washington, for

the Purpose of Fixing a Prime Meridian and a Universal Day (Gibson Bros., Washington, DC, 1884).

[44] Ward, F. A. B., see Ref. [4]. pp. 29-31.

[45] CCIR, "Standard frequency and time signals." (Study

Group 1) Xllth Plenary Assembly (New Delhi. India, 1970),

III, pp. 229-240 (ITU, Geneva, Switzerland 1970).

1.10. BIBLIOGRAPHY

[Bl] Barnes, J. A., "The development of an international atomic time scale," Proc. IEEE, 55, No. 6, pp. 822-826 (June

1967). [B2] Brouwer, D., "The accurate measurement of time,"

Physics Today, 4, No. 8, pp. 6-15 (August 1951). [B3] Davey, W. R., "A review of studies made on the decade

fluctuations in the earth's rate of rotation," Nat. Bur. Stand. (U.S.), Tech. Note 358, 16 pages (USGPO,

October 1967) [Note: Contains many pertinent references on earth rotation variations.] [B4] Decaux. B., and Guinot, B., La Mesure du Temps (The measure of time), 126 pages (Presses Universitaires de

France, 108, Boulevard Saint-Germain, Paris 1969)

(in French).

[B5] Guinot, B., "Characteristics of a scale of time," Alta Frequenza, 40, No. 8, pp. 320E-322E (August 1971)

(in English).

[B6] HMSO/USNO, Explanatory Supplement to the Astro- nomical and the American Ephemeris and Nautical Almanac, prepared jointly by the Nautical Almanac

Office of the United Kingdom and the United States

of America — USNO (Her Majesty's Stationary Office, London, England, 1961). [B7] Jones, H. Spencer, "Variations of the earth's rotation," Physics and Chemistry of the Earth, 4, Chap. 4, pp. 186-210 (Pergamon Press, London, England, 1961). [B8] Lewis, F. D., "Frequency and time standards," Proc. IRE, 49, No. 9, pp. 1046-1068 (September 1955). [B9] Markowitz, W., Hall, Glenn R., Essen, L., and Parry,

J. V. L., "Frequency of cesium in terms of ephemeris

time," Phys. Rev. Lett., 1, pp. 105-108 (August 1958). [B10] Markowitz, W., "Variations in the rotation of the earth,

results obtained with the dual rate moon camera and

photographic zenith tubes," Astron. J., 64, No. 1268,

pp. 106-113 (April 1959). [Bll] Milham, W. I., Time and Timekeepers, 616 pages, (Macmillan Co., New York, N.Y. 10022, 1941). [B12] Mungall, A. G., "Atomic time scales," Metrologia, 7, No. 4, pp. 146-153 (October 1971). [B13] Richardson, J. M., and Brockman, J. F., "Atomic standards

of frequency and time," The Physics Teacher, 4, No. 6, pp. 247-256 (September 1966). [B14] Smith, H. M., "The determination of time and frequency,"

Proc. Inst. Elec. Eng. (England), 98, Pt. II, pp. 143-153

(April 1951). [B15] Woolard, E. W., and Clemence, G. M., Spherical Astron- omy, 453 pages (Academic Press, New York, N.Y.

10003, 1966).

14
ANNEX l.A

t

DEFINITION OF THE SECOND AND TAI

Contents

Page l.A.l. Definition of the Second 17

l.A.2. Recommendations of the 5th Session of the Consultative Committee forithe Definition of the Second 19

l.A.3. Some Results of the 14th General Conference of Weights and Measures (CGPM)

in October 1971 25

l.A.3. a. Unit of Time and Time Scale; Arrangements with the BIH presented by CCDS... 26

l.A.3. b. Resolutions Adopted by the 14th General Conference of Weights and Measures

(CGPM) in October 1971 26

tOriginal language versions in French are followed with English translations.

15

l.A.l. Definition of the Second *

RESOLUTIONS ADOPTfiES

PAR LA 13* CONFERENCE GENERALE

Systeme International d 'Unites (SI)

Unite de temps (seconde)

Resolution

La Treizieme Conference Generate des Poids el Mesures,

CONSIDERANT

que la definition de la seconde decidee par le Comite International des Poids et Mesures

a sa session de ig56 (Resolution 1) et ratifiee par la Resolution 9 de la Onzieme Conference

Generate (i960), puis maintenue par la Resolution 5 de la Douzieme Conference Generale (1964) ne suffit pas aux besoins actuels de la metrologie,

qu'a sa session de 1964 le Comite International des Poids et Mesures, habilite par la Resolution 5 de la Douzieme Conference Generate (1964), a designe pour repondre a ces besoins un etalon atomique de frequence a cesium d employer temporairement,

que cet etalon de frequence est maintenant suffisamment eprouve et suffisamment precis

pour servir a une definition de la seconde repondant aux besoins actuels,

que le moment est venu de remplacer la definition actuellement en vigueur de I'unite de

temps du Systeme International d' Unites par une definition atomique fondee sur cet etalon,

DECIDE

i° L' unite de temps du Systeme International d' Unites est la seconde definie dans les termes suivants :

« La seconde est la duree de 9 192 63 1 770 periodes de la radiation correspondant a la transition entre les deux niveaux hyperfins de t'etat fondamenlal de Vatome de cesium 133 ».

2

0 La Resolution 1 adoptee par le Comite International des Poids et Mesures a sa session

de ig56 et la Resolution 9 de la Onzieme Conference Generate des Poids et Mesures sont abrogees.

*CGPM. Comptes Rendus des Seances de la Treizieme Conference Generate des Poids et Mesures (Proceedings of the Sessions of the 13th General Conference of Weights and Measures) (Paris, France, October 1968), p. 103 (Gauthier-Viliars, Paris, France 1968) (in French).

17
l.A.l. Definition of the Second *t

Resolutions Adopted by the 13th General

Conference

International System of Units (SI)

Unit of Time (Second)

Resolution

The 13th General Conference of Weights and

Measures,

CONSIDERING

that the definition of the second decided by the

International Committee of Weights and Measures

at its session of 1956 (resolution 1) and ratified by

Resolution 9 of the 11th General Conference 1960,

then maintained by the 5th Resolution of the 12th

*CGPM. Comptes Rendus des Seances de la Treizieme Conference Generate des Poids el Mesures (Proceedings of the Sessions of the 13th General Conference of Weights and Measures) (Paris. France, October 1968), p. 103 (Gauthier-Villars, Paris, France 1968) (In French). tEnglish translation. 11

General Conference 1964, does not satisfy the actual

needs of metrology.

that at its session of 1964 the International

Committee of Weights and Measures, enabled by

the 5th Resolution of the 12th General Conference

1964, in order to respond to these needs designated

a cesium atomic frequency standard to be employed temporarily.

that this frequency standard is now sufficiently

proven and sufficiently precise to serve as a defini- tion of the second responding to actual needs.

that the moment has now come to replace the

actual definition in force for the unit of time of the

International System of Units by an atomic defini- tion based on this standard.

DECIDES

1. The unit of time of the International System

of Units is the second defined in the following terms: "The second is the duration of 9 192 631 770

periods of the radiation corresponding to the transi- tion between the two hyperfine levels of the ground

state of the cesium 133 atom."

2. Resolution 1 adopted by the International

Committee of Weights and Measures at its session

of 1956 and Resolution 9 of the 11th General

Conference of Weights and Measures are annulled.

18
I.A.2. Recommendations of the 5th Session of the Consultative

Committee for the Definition of the Second*

Recommandations ( 2

) du Comite Consultatif pour la Definition de la Seconde

presentees

au Comite International des Poids et Mesures

Proposition d'adoption d'une echelle de Temps Atomique International

Recommandation S 1 (1970)

Le Comite Consultatif pour la Definition de la Seconde,

CONSIDERANT

1° Le desir general de synchroniser ou de coordonner I' ensemble des emissions de signaux horaires diffuses dans le monde

;

2° le besoin d'une reference de temps uniforme pour Vetude de la dynamique des systemes et, en particulier, pour Vetude des mouvements des corps

celestes naturels et artificiels

;

(*) Note du B.I. P.M. — Les representants des laboratoires japonais ont fait savoir,

par lettre du 12 aout 1970, leur accord general avec les vues exprimees par le C.C.D.S. En particulier, ils soulignent l'importance de la Recommandation S 3 et des regies

pour la mise en pratique du Temps Atomique International, et ils approuvent les propositions d'aide flnanciere au B.I.H.

(

2) Les numeros initialement attribues a ces recommandations ont ete changes

apres l'examen par les membres du C.C.D.S. du projet du rapport de la session : — La Recommandation S 1 correspond a l'ancienne Recommandation S 1 amputee

du considerant 4°; ce paragraphe est reporte en remarque finale de l'ensemble des

Recommandations adoptees. — La Recommandation S 2 est inchangee. — La Recommandation S 3 correspond a l'ancienne Recommandation S 4. — La Recommandation S 4 correspond a l'ancienne Recommandation S 5. — Les regies pour la mise en pratique du Temps Atomique International corres- pondent a l'ancienne Recommandation S 3.

Ces Recommandations ont ete approuvees par le Comite International des Poids

et Mesures a sa 59 e session (octobre 1970).

*CCDS, "Recommendations du comite consultatif pour la definition de la seconde . . ." (Recommendations of the Consultative Committee for the definition of the second . . .)Comite Consultatif pour la Definition de la Seconde (CIPM. 5" Session, Paris, France, 18-19 June 1970), pp. S21-S23 (Bur. Internat. des Poids.et Mesures, Sevres. France, 1971) (in French).

19
— S 22 —

3° I'utilite d'une echelle de temps aussi uniforme que possible pour servir

de base a la comparaison des etalons de frequence operant en des lieux et a des

instants differents

;

recommande Vadoption d'une echelle de Temps Atomique International.

Proposition de definition du Temps Atomique International

Rf.commandation S 2 (1970)

Le Comite Consultatif pour la Definition de la Seconde propose de definir

le Temps Atomique International (TAI) comme suit:

« Le Temps Atomique International est la coordonnee de reperage temporel

etablie par le Bureau International de I'Heure sur la base des indications

d'horloges atomiques fonctionnant dans divers etablissements conformement a

la definition de la seconde, unite de temps du Systeme International d' Unites ».

Poursuite des recherches sur les etalons atomiques de frequence et sur les methodes devaluation du Temps Atomique International

Recommandation S 3 (1970)

Le Comite Consultatif pour la Definition de la Seconde,

considerant que le nombre des etalons primaires de frequence et leur

exactitude sont a peine suffisants pour controler le maintien d'une duree constante de I'intervalle unitaire de I'echelle de Temps Atomique International,

recommande aux organismes competents d'entreprendre ou de poursuivre

activement les recherches en vue d'une realisation plus exacte de la seconde du

Systeme International d' Unites.

Recommandation S 4 (1970)

Le Comite Consultatif pour la Definition de la Seconde,

considerant que V experience acquise n'est pas suffisante pour que I'on puisse des maintenant fixer les regies de ponderation des indications des

horloges atomiques contribuant a I'etablissement de I'echelle de Temps Atomique

International,

recommande que cette question soit etudiee activement.

20
— S 23

M [SI. EN PRATIQUE DU TEMPS AtOMIQUE INTERNATIONAL

Le Comite Consultatif pour la Definition de la Seconde propose les regies

suivantes pour la mise en pratique de Vechelle de Temps Atomique International

pendant les quelques annees a venir

:

1° La duree de I'intervalle unitaire de Vechelle de Temps Atomique Inter- national est determinee par le Bureau International de VHeure (B.I.H.) de

fagon qu'elle soit en accord etroit avec la duree de la seconde du Systeme Inter- national d' Unites rapportee a un point fixe de la Terre au niveau de la mer.

2° La duree de I'intervalle unitaiie de Vechelle de Temps Atomique Inter- national est maintenue aussi constante que possible. Elle est frequemment

comparee a la duree de la seconde du Systeme International d' Unites telle qu'elle est obtenue a Vaide des etalons primaires de frequence de divers etablissements. Les resultats de ces comparaisons sont portes d la connaissance du

B.I.H.

3° La duree de I'intervalle unitaire de Vechelle de Temps Atomique Inter- national n'est changee intentionnellement que si elle differe d'une fagon significative de la duree de la seconde specifiee en 1°. Ces ajustements n'auront

lieu qu'd des dates convenues d Vavance et annoncees par le B.I.H.

4° L'origine de Vechelle de Temps Atomique International est definie

conformement aux recommandations de V Union Astronomique Internationale

(XIIIe Assemblee Generate, Prague, 1967^, c'est-d-dire que cette echelle s'accorde approximativement avec le TU2 d 0 heme le l

er janvier 1958.

5° Le procede par lequel le Temps Atomique International est actuellement

porte a la connaissance des usagers, c'est-d-dire par la publication mensuelle

des ecarts des echelles locales, est considere comme satisfaisanl.

Le Comite Consultatif pour la Definition de la Seconde note que les Recommandations et propositions ci-dessus vont dans le sens des demandes

approuvees par le Comite Consultatif International des Radiocommunications (C.C.I.R.) a sa 12 e Assemblee Pleniere (New Delhi, 1970) et par

l'Union Radioscientiflque Internationale (U. R.S.I.) a sa 16 e Assembled

Generale (Ottawa, 1969, Resolution 1.4).

21
I.A.2. Recommendations of the 5th Session

of the Consultative Committee for the

Definition of the Second

presented to

the International Committee of Weights and

Measures*t

Proposition for Adoption of International Atomic

Time Scale

Recommendation S 1 (1970)

The Consultative Committee for the Definition

of the Second,

CONSIDERING

1. The general desire to synchronize or to coor- dinate the ensemble of time signal broadcasts

disseminated within the world;

2. The need of a uniform time reference for the

study of the dynamics of systems and, in particular,

for the study of the movements of natural and

artificial celestial bodies;

3. The utility of a time scale as uniform as possible

to serve as the basis of comparison of frequency

standards operating in different places and at different times;

RECOMMENDS the adoption of an International

Atomic Time Scale.

Proposition for the Definition of International

Atomic Time

Recommendation S 2 (1970)

The Consultative Committee for the Definition

of the Second proposes to define International

Atomic Time (TAI) as follows: "International Atomic Time is the time reference

coordinate established by the International Time

Bureau on the basis of atomic clock readings

functioning in various establishments conforming

to the definition of the second, unit of time of the

International System of Units."

Pursuit of research on atomic freque'ncy standards

and on the method of evaluation of International

Atomic Time.

Recommendation S 3 (1970)

The Consultative Committee for the Definition

of the Second,

CONSIDERING

That the number of primary frequency standards

and their accuracy are scarcely sufficient to control

the continuation of a constant duration of the unit interval of the International Atomic Time Scale,

*CCDS. "Recommendations du comite consultatif pour la definition de la seconde . . ." (Recommendations of the Consultative Committee for the definition of the second . . .) Comite Consultatif pour la Definition de la Seconde, (CIPM, 5

e Session, Paris, France, 18-19 June 1970), pp. S21-S23 (Bur. Internal, des Poids et Measures, Sevres, France, 1971) (In French).

t English translation.

RECOMMENDS

To competent organizations to undertake or to pursue actively research in view of a more accurate

realization of the second of the International

System of Units.

Recommendation S 4 (1970)

The Consultative Committee for the Definition

of the Second

,

CONSIDERING

That the experience acquired is not sufficient to permanently fix the rules for weighting of clock

readings contributing to the establishment of the

International Atomic Time Scale,

RECOMMENDS

That this question be studied actively.

Mise en Pratique (Putting into Practice) of

International Atomic Time

The Consultative Committee for the Definition

of the Second proposes the following rules for the

Mise en Pratique of the International Atomic

Time Scale during the next few years:

1. The duration of the unit interval of the Inter- national Atomic Time Scale is determined by the

Bureau International de l'Heure (BIH) such that it be in close agreement with the duration of the

second of the International System of Units relative

to a fixed point on the earth at sea level.

2. The duration of the unit interval of the Inter- national Atomic Time Scale is maintained as constant as possible. It is frequently compared to the duration of the second of the International System of Units as it is obtained from the primary fre- quency standards of various establishments. The

results of these comparisons are published bv the

BIH.

3. The duration of the unit interval of the Inter- national Atomic Time Scale is intentionally changed

only if it differs in a significant fashion from the

duration of the second specified in 1. These adjustments will take place only at dates agreed upon in advance and announced by the BIH.

4. The origin of International Atomic Time is defined in conformance with the recommendations

of the International Astronomical Union (13th

General Assembly, Prague, 1967) that is, this scale was in approximate agreement with 0 hours UT2

January 1, 1958.

5. The process by which International Atomic

Time is brought to the awareness of users, that is by the monthly publication of differences of time

scales, is considered as satisfactory.

The Consultative Committee for the Definition

of the Second notes that the recommendations and

the propositions above are in essential agreement

to the requests approved by the CCIR at its 12th

Plenary Session, New Delhi, 1970, and by URSI at

its 16th General Assembly, Ottawa, 1969, Resolution 1.4.

22
I.A.3. Some Results of the 14th General Conference of Weights and

Measures (CGPM) in October 1971 *

l.A.S.a Unit of Time and Time Scale; Arrangements with the BIH presented by CCDS

9. Unite de temps et echelles de temps; arrangements avec le Bureau

International de l'Heure

Mr Dunworth, president du Comite Consultatif pour la Definition de

la Seconde (C. C. D. S.), presente le rapport suivant : La mesure du temps et de l'intervalle de temps est lite dans l'esprit de la plupart des

gens aux mouvements apparents du Soleil et des etoiles. Au cours des siecles, le perfectionnement par les astronomes et les navigateurs des mesures qui s'y rapportent a fourni un systeme qui satisfait la plupart des besoins, meme ceux d'une societe ayant un degre

eleve de technicite. La decouverte de la radio vers le debut de ce siecle et de la « valve

thermo-ionique » au cours de la Premiere Guerre mondiale conduisirent il y a une cin- quantaine d'annees a la creation d'une nouvelle technique, celle de l'electronique. Cette technique a permis d'obtenir avec une relative simplicite et stabilite une oscillation elec- trique qui pouvait constituer la base d'une mesure precise de l'intervalle de temps.

A l'origine, les dispositifs utilisaient les propri£tes du quartz, un materiau que vous

connaissez tous. Des avant la Seconde Guerre mondiale on a couramment utilise des

oscillateurs a lampes controles par quartz pour maintenir avec precision les frequences

des emetteurs de radio aux valeurs qui leur etaient attributes par accord international.

Plus r£cemment, on a toutefois eu la possibilite d'utiliser les proprietes des atomes individuels de substances appropriees au lieu du quartz. Cela eut comme resultat de pouvoir

obtenir une base pour la frequence, et par consequent pour l'intervalle de temps, encore

plus stable, plus precise et plus facilement reproductible. On a appele l'horloge ainsi obtenue une « horloge atomique ». La comparaison des resultats de fonctionnement

d'horloges de ce type avec le mouvement apparent des etoiles et du Soleil a rtvele des

irregularites. Les savants pensent que ces irregularites sont dues a de petites variations,

erratiques, dans la vitesse de rotation de la Terre, plutdt qu'a des irregularites systematiques dans toutes leurs horloges atomiques.

•CGPM, Comples R^ndus des Seances de la Qualorzieme Conference Generate des Poids et Mesures (Proceedings of the Sessions of the 14th General Conference

of Weights and Measures) (Paris, France, October 4-8, 1971), pp. 49-52 (BIPM, Sevres, France, 1972) (in French).

23
La definition de la frequence et de son inverse — l'intervalle de temps — est depuis

longtemps Tune des preoccupations du Gomite International des Poids et Mesures. Une

definition d'une unite d'intervalle de temps atomique a ete adoptee par la 13 e Conference

Generale (1967). Toutefois il faut faire une difference entre « temps » et « intervalle de

temps ». Une facon simple de faire cette difference est de considerer d'une part un chronometre pour mesurer le temps mis par un athlete pour courir cent metres, et d'autre

part une horloge qui nous dit quand partir travailler. Pour bien des utilisations, le temps

astronomique est tres commode ou necessaire, comme par exemple en navigation ou dans

notre vie quotidienne. Toutefois, pour certaines utilisations scientifiques ou techniques

pour lesquelles l'heure du jour en termes astronomiques est sans importance, il y a un

avantage a avoir une horloge qui conserve un degre eleve d'uniformite de l'intervalle de temps sur une longue periode. De plus, l'utilisation simultanee d'horloges de ce type

en differents lieux peut etre essentielle. Depuis de nombreuses annees, des echelles de

temps atomique de cette nature sont disponibles dans les pays les plus industrialises.

Le Bureau International de l'Heure, dont le siege est a Paris et qui s'occupe depuis

longtemps du temps astronomique, joue depuis quelques annees le role de centre inter- national pour la diffusion, a titre d'essai, du temps atomique. Gette tache supplementaire

a ete rendue possible par l'aide genereuse fournie par le personnel de l'Observatoire de

Paris, par le pret d'appareils fournis par des organismes americains et par la cooperation

des differents pays deja interesses par le temps atomique. Recemment, l'Union Astro- nomique Internationale, l'Union Radioscientifique Internationale et le Gomite Gonsultatif

International des Radiocommunications ont demande au Gomite International des Poids

et Mesures de recommander a la presente Conference Generale l'etablissement d'une

Echelle de Temps Atomique. Le Comite International a reconnu quatre points importants en repondant a cette demande :

1° II y aura, dans un futur previsible, de nouveaux progres dans la facon precise

de traiter le probleme de l'echelle de temps atomique.

2° Ces progres interviendront d'autant plus surement que Ton etablira de facon

officielle des maintenant une echelle de temps atomique.

3° On aura encore besoin d'une echelle de temps liee a la rotation de la Terre

et il sera indispensable de maintenir une liaison etroite avec le Bureau

International de l'Heure qui continuera a fournir une telle echelle. 4° II serait tres couteux pour le Bureau International des Poids et Mesures d'etablir une echelle de temps atomique avec ses propres instruments et son propre personnel.

En consequence, le Comite International des Poids et Mesures a etudie la possibilite

de convaincre le Bureau International de l'Heure de mettre officiellement ses realisations

actuelles en association avec le Comite International. J'ai le grand plaisir de vous informer

que le Bureau International de l'Heure repondra selon toute vraisemblance de facon

favorable a une telle invitation qui ne represente qu'une modeste charge annuelle sur

les fonds du Gomite International. D'autre part, des discussions approfondies ont eu

lieu entre des representants du Comite International et les differents organismes internationaux qui s'occupent du temps et dont j'ai parie plus haut. Toutes ces discussions

ont conduit aux propositions presentees au point 9 de la Convocation a cette Conference

(voir p. 16). Les details techniques precis qui sont a la base de ces propositions sont complexes; beaucoup d'entre vous les connaissent deja et je n'essaierai pas d'en parler

ici. Si la Conference Generale approuve ces propositions, il est prevu que les nouvelles

dispositions entreront en vigueur le l

er janvier 1972, a la condition qu'un accord satis- faisant soit conclu avec le Bureau International de l'Heure.

Au nom du president et des membres du Comite International des Poids et Mesures,

je vous recommande vivement ces propositions et vous invite a approuver les projets

de resolutions qui vous sont soumis.

24
I.A.3. Some Results of the 14th

General Conference of Weights and

Measures (CGPM) in October 197 1 * t l.A.3.a. Unit of Time and Time Scale;

Arrangements with the BIH presented by

CCDS

9. Unit of time and time scales; arrangements with the

International Time Bureau

Mr. Dunworth, President of the Committee

Consultative for the Definition of the Second

(CCDS), presented the following report:

The measurement of time and of time interval is based in principle for most people on the apparent

movements of the sun and stars. Through the course

of centuries, the perfection of time measures by

astronomers and navigators has furnished a system

which satisfied most of the needs, even those of the society having a high level of technology.

The discovery of radio toward the beginning of the

century and of the thermionic tube during the course

of the 1st World War 50 years ago led to the creation of a new technique — that of electronics. This

technique has permitted the design of a relatively

simple and stable electronic oscillator which can

constitute the basis of a precise measure of time

interval. Initially, the devices used the properties

of quartz, a material which you all know well. From the beginning of the 2d World War one com- monly used vacuum tube oscillators controlled by

quartz to maintain the frequencies of radio trans- mitters precisely to the values which they were

assigned by international agreement. More recently, one even has had the possibility of using the properties of individual atoms of appropriate substances

in place of quartz. This has resulted in the capability of a new basis for frequency and, by conse- quence, for time interval even more stable, more

precise, and more easily reproducible. We have

called such a clock an atomic clock. Comparison

results of such clocks with the apparent movement

of the stars and of the sun has revealed irregularities. Experts think that these irregularities are due

to small erratic variations in the velocity of the

rotation of the earth, rather than those of systematic

irregularities in all of their atomic clocks. The definition of frequency and its inverse, time

interval, has for a long time been one of the pre- occupations of the International Committee of

Weights and Measures. A definition of a unit

of atomic time interval has been adopted by the

13th General Conference (1967). However, it is necessary to note a difference between time and

time interval. A simple way to make this judgment is to consider, on one hand, a chronometer which

measures the time taken by an athlete to run

100 meters and, on the other hand, a clock which

*CGPM, Comptes Rendus des Seances de la Quatorzieme Conference Generate des Poids el Mesures (Proceedings of the Sessions of the 14th General Conference of Weights and Measures) (Paris, France, October 4-8, 1971). pp. 49-52 (BIPM, Sevres, France, 1972) (in French).

t English translation.

tells us when to leave for work. For most uses, astronomical time is very convenient or necessary as for example in navigation or in our daily

life. Yet, in certain scientific or technical uses

the hour of the day in terms of astronomy is unimportant, there still is an advantage to having a clock

which maintains a high degree of uniformity of time

interval over a long period. Further, the simultan- eous use of clocks of this type in different places can be essential. For many years atomic time scales

of this nature have been available in the more industrial countries. The International Time Bureau,

located in Paris and concerned for a long time with

astronomical time, has played the central inter- national role for the distribution of atomic time for many years by virtue of its tested capability. This

supplementary duty has been made possible by the

generous aid furnished by the personnel of the

Paris Observatory, by the availability of apparatus

furnished by American organizations, and by the

cooperation of different countries already interested

in atomic time. Recently, the International Astro- nomical Union, the International Scientific Radio

Union, and the International Radio Consultative

Committee have asked the International Committee

of Weights and Measures to recommend to the pres- ent General Conference the establishment of an

atomic time scale. The International Committee

has recommended four important points in responding to this request:

1. In a foreseeable future there will be new prog- ress in the precise method of treating the

problem of the atomic time scale.

2. These advances will take place even more

surely if one will establish an atomic time

scale of an official nature now.

3. One will still have need of a time scale based on

the rotation of the earth; it will be absolutely

essential to maintain a close relation with the

International Time Bureau which will continue

to furnish such a scale.

4. It would be very costly for the International

Bureau of Weights and Measures to establish an atomic time scale with its own instruments

and personnel.

As a consequence, the International Committee

of Weights and Measures has studied the possibility of convincing the International Time Bureau

by virtue of its capability to officially seek association with the International Committee. I have the

great pleasure to inform you that, most assuredly,

the International Time Bureau will respond, in a a favorable fashion to such an invitation; such action

represents only a modest annual charge on the funds

of the International Committee. On the other hand, some thorough discussions have taken place

between the representatives of the International

Committee and the international organizations

25
which are concerned with time and of which I have spoken above. All these discussions have led

to the propositions presented in point 9 of the

Convocation of this Conference (see p. 16). The

precise technical details which are fundamental to these propositions are complex. Many among you

already known this, and I will not try to speak of

it here. If the General Conference approves these

propositions it is seen that the new arrangements

will enter in force 1 January 1972 under the condition that a satisfying accord be concluded with the

International Bureau of Time.

Under the name of the president and the members

of the International Committee of Weights and

Measures I strongly recommend these propositions

to you and invite your approval of the resolutions

which are submitted to you.

l.A.3.b. Resolutions Adopted by the 14th

General Conference of Weights and

Measures (CGPM) in October 1971 *

Resolutions Adopted by the 14th General

Conference*

International Atomic Time

Role of the International Committee of Weights

and Measures concerning International Atomic

Time.

Resolution 1 The 14th General Conference of Weights and

Measures,

CONSIDERING

that the second, unit of time of the International

System of Units, has been defined since 1967

according to a natural atomic frequency and no

longer according to time scales furnished by astro- nomical movements;

that the need of an International Atomic Time

Scale TAI is a consequence of the definition of

the atomic second;

that many international organizations have as- sured and continue to assure with success the es- tablishment of time scales based on astronomical

movements, particularly by grace of the permanent

services of the International Time Bureau (BIH);

that the BIH has begun to establish an atomic

time scale of which the qualities are recognized

and which have proven its utility; that the atomic frequency standards serving as the realization of the second have been considered

and should continue to be by the International

Committee of Weights and Measures assisted by a

consultative committee and that the unit interval

of the International Atomic Time Scale ought to be the second realized in conformance with its atomic definition; that all the competent international scientific organizations and the active national laboratories

in this domain have expressed the desire that the

International Committee and the General Conference of Weights and Measures give a definition of International Atomic Time and contribute to the

establishment of the International Atomic Time

Scale;

that the utility of International Atomic Time necessitates a close coordination with the time scales

based on astronomical movements asks of the Inter- national Committee of Weights and Measures

1. to give a definition of International Atomic

Time*.

2. to take the necessary steps in accord with the

interested international organizations in order

that the scientific competence and the means

of action existing be best utilized for the reali- zation of the International Atomic Time Scale,

and in order that the needs of users of TAI be

satisfied. Arrangements with the Bureau International

de l'Huere concerning International Atomic Time.

Resolution 2

The 14th General Conference on Weights and

Measures,

CONSIDERING—

that an International Atomic Time Scale

ought to be placed at the disposition of users;

that the Bureau International de l'Heure has

proven that it is capable to assure this service;

EXPRESSES HOMAGE to the Bureau Inter- national de l'Heure for the work it has already

accomplished;

ASKS of national and international institutions of good will to continue and, if possible, augment the

aid that they have given to the Bureau International

de l'Heure for the benefit of the international

scientific and technical community;

AUTHORIZES the International Committee of

Weights and Measures to conclude with the Bureau

International de l'Heure the arrangements necessary

for the realization of the International Atomic Time

Scale as defined by the Committee International.

*CGPM, Comples Rendus des Seances de la Quatorzieme Conference Generate des Poids el Mesures (Proceedings of the Sessions of the 14th General Conference of Weights and Measures) (Paris, France, October 4-8, 1971), pp. 77-78 (BIPM, Sevres, France, 1972) (in French, see page 27). tEnglish translation.

* In anticipation of this request, the International Committee of Weights and Measures has charged the Consultative Committee for the Definition of the Second to prepare a definition of International Atomic Time. This definition, approved by the

International Committee at its 59th Session, October 1970, is as follows: "International Atomic Time is the time reference coordinate established by the Bureau International de l'Heure on the basis of atomic clock readings functioning in diverse establishments conforming to the definition of the second, unit of time of the International System

of Units."

26
l.A.3.1). Resolutions Adopted by the 14th General Conference of Weights and

Measures (CGPM) in October 1971*

RESOLUTIONS ADOPTEES

PAR LA 14« CONFERENCE GENERALE

Temps Atomique International

R61e du Comite International des Poids et Mesures concernant le Temps Atomique

International

RESOLUTION 1 La Quatorzi&me Conference Ginirale des Poids et Mesures,

CONSIDERANT

que la seconde, unite de temps du Systeme International d' Unites, est dtfinie depuis 1967

d'apres une frequence atomique naturelle, et non plus d'apres des echelles de temps fournies

par des mouvements astronomiques,

que le besoin d'une echelle de Temps Atomique International (TAI) est une consequence

de la definition atomique de la seconde,

que plusieurs organisations internationales ont assure et assurent encore avec succes I'eta- blissement des echelles de temps fondees sur des mouvements astronomiques, particulierement

grace aux services permanents du Bureau International de VHeure {B. I. H.),

que le Bureau International de VHeure a commence a etablir une echelle de temps atomique

dont les qualites sont reconnues et qui a prouve son utilite, que les etalons atomiques de frequence servant a la realisation de la seconde ont ete considires et doivent continuer de I'elre par le Comite International des Poids et Mesures assisle d'un Comite Consultatif, et que I'intervalle unitaire de I'echelle de Temps Atomique Inter- national doit etre la seconde realisee conformement a sa definition atomique,

que toutes les organisations scientifiques internationales competentes et les laboratoires

nationaux actifs dans ce domaine ont exprime le desir que le Comite International et la Conference Generate des Poids et Mesures donnent une definition du Temps Atomique

International, et coniribuent a Vetablissement de I'echelle de Temps Atomique International,

que I'utilite du Temps Atomique International necessite une coordination etroite avec les ichelles de temps fondees sur des mouvements astronomiques,

demande au Comite International des Poids et Mesures

1° de donner une definition du Temps Atomique International (');

(') En provision de cette demande, le Comite International des Poids et Mesures avait charge son Comite Consultatif pour la Definition de la Seconde de preparer une definition du Temps Atomique

International. Cette definition, approuvee par le Comite International a sa 59 e session (octobre 1970),

est la suivante :

« Le Temps Atomique International est la coordonnie de reperage temporel etablie par le Bureau

International de VHeure sur la base des indications d'horloges atomiques fonctionnant dans divers itablissements conformement a la definition de la seconde, unite de temps du Systeme International

d' Unites. »

*CGPM, Comptes Rendus des Seances de la Quatorzieme Conference Generate des Poids et Mesures (Proceedings of the Sessions of the 41th General Conference of Weights and Measures) (Paris, France, October 4-8, 1971), pp. 77-78 (BIPM, Sevres, France, 1972) (in French). 27
78 QUATORZIEME CONFERENCE GENERALE DES POIDS ET MESURES

2° de prendre les mesures necessaires, en accord avec les organisations internationales

intiressies, pour que les competences scientiftques et les moyens d'action existants soient

utilises au mieux pour la realisation de Vechelle de Temps Atomique International, et pour

que soient satisfaits les besoins des utilisateurs du Temps Atomique International.

Arrangements avec le Bureau International de 1'Heure concernant le Temps

Atomique International

Resolution 2

La Qualorzieme Conference Generate des Poids et Mesures,

considerant

qu'une echelle de Temps Atomique International doit etre mise a la disposition des uti- lisateurs,

que le Bureau International de 1'Heure a prouve qu'il est capable d' assurer ce service; rend hommage au Bureau International de 1'Heure pour I'ceuvre qu'il a deja accomplie;

demande aux institutions nationales et internationales de bien vouloir continuer, et si possible augmenter, I'aide qu'elles donnent au Bureau International de 1'Heure, pour le bien de la communaute scientifique et technique internationale;

autorise le Comite International des Poids et Mesures a conclure avec le Bureau Inter- national de 1'Heure les arrangements necessaires pour la realisation de Vechelle de Temps

Atomique International a definir par le Comite International.

28
ANNEX I B

STANDARD FREQUENCY AND TIME BROADCAST AGREEMENTS

Contents

Page l.B.l. CCIR Recommendation 460 31

l.B.2. CCIR Report 517 32

29

I.B.I. CCIR Recommendation 460

RECOMMENDATION 460

STANDARD-FREQUENCY AND TIME-SIGNAL EMISSIONS

(Question 1/7)

The C.C.I.R., (1970)

CONSIDERING

(a) the desirability of eliminating all offsets from nominal values in the carrier frequencies and in the time signals;

(b) the desirability of disseminating on a world-wide basis precise time intervals in conformity

with the definition of the second (SI), as adopted by the 1 3th General Conference of Weights

and Measures (1967);

(c) the continuing need of many users for Universal Time (UT);

UNANIMOUSLY RECOMMENDS

1. that, from a specified date, carrier frequencies and time intervals should be maintained

constant and should correspond to the adopted definition of the second

;

2. that the transmitted time scale should be adjusted when necessary in steps of exactly one

second to maintain approximate agreement with Universal Time (UT);

3. that the standard-frequency and time-signal emissions should contain information on the

difference between the time signals and Universal Time (UT)

;

4. that detailed instructions on the implementation of this Recommendation be adopted by

Study Group 7 after consideration of the report of Interim Working Party 7/1

;

5. that the standard-frequency and time-signal emissions should conform to §§ 1, 2, 3 and 4

above from 1 January 1972, 0000 h UT;

6. that this document be transmitted by the Director, C.C.I.R., to all Administrations Members

of the I.T.U., to the Scientific Unions (I.A.U., I.U.G.G., U.R.S.I., I.U.P.A.P.), and other

organizations such as B.I.H., C.I.P.M., I.C.A.O. and I.M.C.O.

•CCIR, "Standard-frequency and time-signal emissions." (Recommendation 460). in Xlllh Plenary Assembly CCIR. (New Dehli. India. 1970), III. p. 227 (ITU. Geneva. Switzerland. 1970).

31
I.B.2. CCIR Report 517t

REPORT 517*

STANDARD-FREQUENCY AND TIME-SIGNAL EMISSIONS

Detailed instructions by Study Group 7 for the implementation

of Recommendation 460 concerning the improved Coordinated Universal Time (UTC) System,

valid from 1 January 1972

(Question 1/7, Resolution 53)

(1971)

1. The Xllth Plenary Assembly of the C.C.I.R. adopted unanimously Recommendation 460. According to § 4 of this Recommendation, Study Group 7 was entrusted with the task of

formulating the detailed instructions for its implementation on 1 January 1972. Study Group 7 met from 17-23 February 1971 and adopted the following text for this purpose

2.

2.1 A special adjustment to the standard-frequency and time-signal emissions should be made

at the end of 1971 so that the reading of the UTC scale will be 1 January 1972, Oh 0m 0s at the instant when the reading of Atomic Time (AT) indicated by the Bureau international de

l'Heure (B.I.H.) will be 1 January 1972, Oh 0m 10s. The necessary adjustments to emissions

which are in accordance with Recommendation 374-2 will be specified and announced in advance by the B.I.H.

2.2 The departure of UTC from UT1 should not normally exceed 0-7 s**.

2.3 Inserted seconds should be called positive leap seconds and omitted seconds should be called negative leap seconds.

2.4 A positive or negative leap second, when required, should be the last second of a UTC

month, preferably 31 December and /or 30 June. A positive leap second begins at 23 h 59 m

60s and ends at 0 h 0m 0s of the first day of the following month. In the case of a negative

leap second, 23h 59 m 58s will be followed one second later by Oh 0TM 0s of the first day of

the following month. (See Annex I).

* This Report was adopted unanimously.

** Universal Time

In applications in which errors of a few hundredths of a second cannot be tolerated, it is necessary to specify the form of Universal Time (UT), referred to in Recommendation 460, which should be used. UT1 is a form of UT in which corrections have been applied for the effects of small movements of the Earth relative to the axis of rotation. UT2 is UT1 corrected for the effets of a small seasonal change in the rate of rotation of the Earth. UT1 correspond directly with the angular position of the Earth around its axis of rotation, and is used

in this document. GMT may be regarded as the general equivalent of UT1.

tCCIR, "Detailed instructions by Study Group 7 for the implementation of Recommendation 4*0 concerning the improved coordinated universal time (UTC) system, valid from 1 January 1972" in Xllth Plenary Assembly CCIR, (New Dehli, India, 1970) III, p. 258 a-d (ITU, Geneva, Switzerland, 1970).

32
— 258b —

2.5 The B.I.H. should decide upon and announce the occurence of a leap second; such an an- nouncement is to be made at least eight weeks in advance.

2.6 The time signals of standard-frequency and time-signal emissions should be kept as close

to UTC as possible, with a maximum deviation of one millisecond.

3.

3.1 The approximate value of the difference UT1 minus UTC, as disseminated with the time

signals should be denoted DUT1,

where DUT1 & UT1-UTC.

DUT1 may be regarded as a correction to be added to UTC to obtain an approximation

of UT1.

3.2 The values of DUT1 should be given in integral multiples of OT s. The B.I.H. is requested to determine and to circulate one month in advance the value of DUT1. Administrations and

organizations should use the B.I.H. value of DUT1 for standard-frequency and time-signal

emissions whenever possible, and are requested to circulate the information as widely as possible in periodicals, bulletins, etc.

3.3 Where DUT1 is desseminated by code, the code should be in accordance with the following

principles

:

— the magnitude of DUT1 is specified by the number of emphasized seconds markers and

the sign of DUT1 is specified by the position of the emphasized seconds markers with

respect to the minute marker. The absence of emphasized markers indicates DUT1 = 0; — the coded information should be emitted after each identified minute.

Full details of the code are given in Annex II.

3.4 Alternatively DUT1 may be given by voice announcement or in morse code.

3.5 In addition, UT1-UTC may be given to the same or higher precision by other means, for example, in morse or voice announcements, by messages associated with maritime bulletins,

weather forecasts, etc.; announcements of forthcoming leap seconds may also be made by

these methods.

3.6 The B.I.H. is requested to continue to publish in arrears definitive values of the differences

UT1-UTC, UT2-UTC and AT (B.I.H.)-UTC.

33
— 258c —

ANNEX I

DATING OF EVENTS IN THE VICINITY OF A LEAP SECOND

(Taken from § 2.4 of the Report)

A positive or negative leap second, when required, should be the last second of a UTC

month, preferably 31 December and/or 30 June. A positive leap second begins at 23 h 59 m 60s

and ends at Oh 0 m 0s of the first day of the following month. In the case of a negative

leap second, 23h 59m 58s will be followed one second later by 0 h 0m 0s of the first day

of the following month.

Taking account of what has been said in the preceding paragraph, the dating of events in the vicinity of a leap second shall be effected in the manner indicated in the following figures:

event

I I i I I 56 57 58 59 60

30 June, 23h 59m

leap second

1 July, Oh 0m

Designation of the date of the event

30 June, 23h 59TM 60 -6* UTC

Figure 1

Positive leap second

30 June, 23h 59m

event

1 July, Oh 0m

Designation of the date of the event

I I I jl I I I I I I 56 57 58 0 1 2 3 4 5 6 30 June, 23h 59m 58 . 9s UTC

Figure 2

Negative leap second

34
— 258d —

ANNEX II

CODE FOR THE TRANSMISSION OF DUT1

A positive value of DUT1 will be indicated by emphasizing a number (n) of consecutive

seconds markers following the minute marker from seconds markers one to seconds marker

(n) inclusive; (n) being an integer from 1 to 7 inclusive. DUTl = (n x 0-1 )s A negative value of DUT1 will be indicated by emphasizing a number (m) of consecutive

seconds markers following the minute marker from seconds marker nine to seconds marker

(8 + m) inclusive; (m) being an integer from 1 to 7 inclusive. DUTl = -(m x 01)s

A zero value of DUT1 will be indicated by the absence of emphasized seconds markers.

The appropriate seconds markers may be emphasized, for example, by lengthening,

doubling, splitting, or tone modulation of the normal seconds markers.

Examples:

Minute

marker Emphasized seconds markers

/ ^

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | 16 Limit of coded sequence

j Figure 3 DUTl = +0-5s

Minute

marker Emphasized seconds markers

JTjTJlJTJTJlJiri^ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

j 16

Limit of coded sequence i Figure 4

DUTl=-0-2s \

35

ANNEX l.C

RESULTS OF 6TH SESSION OF CONSULTATIVE COMMITTEE

FOR DEFINITION OF THE SECOND (CCDS)*

Contents

Page l.C.l. Recommendations of the 6th Session of CCDS 39

l.C. 2. The Work of the Bureau International de l'Heure for the Improvement of Inter- national Atomic Time (TAI) 39

*Cuinot. B., (Reporter), "Minutes of 6th Session Consultative Committee for the Definition of the Second, SLtieme rapport du comite consultatif pour la definition de la seconde au comite international des poids et mesures (CIPM, 6

e Session, Paris, France, July 6-7, 1972) (Bur. Internat, des Poids et Mesures. Sevres, France, 1972) (in French).

37

l.C.l. Recommendations of the 6th Session

of CCDS*

Recommendations of the Consultative

Committee for the Definition of the Second

presented to the

Internationa] Committee of Weights and

Measures

Sending to the Bureau International de l'Heure

Information concerning the individual clocks

Recommendation S-l (1972)

The Consultative Committee for the Definition

of the Second,

CONSIDERING that the Bureau International

de l'Heure (BIH) would be able to improve the uni- formity of International Atomic Time (TAI) if

it received more complete information.

RECOMMENDS that the organizations concerning themselves with the establishment of time

scales furnish to the BIH at its request and in the form which it will specify the results of comparisons of individual atomic clocks as well as all perti- nent information.

Consequence of the adoption of International

Atomic Time for time scales used in current life Recommendation S-2 (1972)

The Consultative Committee for the Definition of

the Second,

CONSIDERING

1. That the scale of international atomic time

(TAI) implies a counting of seconds from its origin

(January 1958).

2. That the scales of time in use for the current

life which are based on the second of SI will continue to involve years, months, days, hours, and

minutes,

PROPOSES

That these questions be studied in collaboration

with interested organizations, in particular the Inter- national Astronomical Union.

Declaration of the Consultative Committee

for the Definition of the Second

presented to the

International Committee of Weights and

Measures

On the legal usage of Universal Coordinated Time

* English translation.

The Consultative Committee for the Definition

of the Second,

CONSIDERING the recommendations of the In- ternational Radio Consultative Committee (CCTR)

and of the International Astronomical Union

(IAU) for an improved system of Coordinated

Universal Time serving for broadcast of time signals.

TAKES NOTE that the quasi universal ac- ceptance of UTC can furnish a solid basis to a future recommendation of the General Conference

of Weights and Measures on the time system ac- ceptable internationally.

l.C. 2. The Work of the Bureau International

de l'Heure for the Improvement of International Atomic Time (TAI)*

1. Current determination of TAI

During the time of studies mentioned above,

TAI will continue to be established by the method

currently in use. In the eventuality where other

local time scales become usable, they will be in- corporated with the weight unity.

2. Preparation to employ the data of individual

clocks

This operation will be described as follows:

a. About October 1972 inquests on the conditions of use of clocks within the time services (the

BIH will reserve the right to use only the clocks

exploited in satisfactory condition). Requests by

the BIH of comparisons of clocks for all the year 1972 in a specified format (punched cards and

perforated tapes would be able to be used).

b. End of 1972, beginning of 1973. Reduction of

the data of clocks with the method called ALGOS

which contains a weighting of clocks according to their mean bimonthly rate.

c. Beginning of 1973. Comparative study of the current results and of the results of ALGOS.

Balance sheet on the time of exploitation of ALGOS.

d. April-May 1973. Presentation of results of the

study to the President of CCDS, the President of the Directing Board of the BIH. as well as to con- cerned laboratories. If the new method appears to improve TAI, which is very probable according to the studies which have already been made, its adoption will be proposed with immediate appli- cation. It seems thus possible that the new method

be adopted within about 1 year. NOTE: — The calendar proposed is approximate. — In that which preceded, one will not intentionally modify the duration of the unit interval of TAI.

One will insure that this duration will not be modified during the passage from one method to the

other. — One will propose later a method designed to in- sure simultaneously the stability in mean term

(a few years) and accuracy.

39
— In the new method, the results will be presented

in the same form as at present. That is to say, that one will give every 10 days the values of TAI-TA(i)

and TUC-TUC(i); and that these results will

appear only every two months. Further, one will furnish to the concerned laboratories the mean

frequencies relative to TAI and the weights of each

of the clocks.

40
CHAPTER 2 -PART A

STATE OF THE ART— QUARTZ CRYSTAL UNITS AND OSCILLATORS

Eduard A. Gerber,t IEEE Fellow and Roger A. Sykes,* IEEE Fellow

Contents

Page 2A.1. Introduction 43

2A.2. Quartz Crystal Units 44

2A.2.1. Equivalent Circuit 44

2A.2.2. Vibrator Types 44

2A.2.3. Enclosures 44

2A.2.4. Quartz Material 45

2A.2.5. Modes of Motion 46

2A.3. Frequency Stability as a Function of: 2A.3.1. Temperature 48

2A.3.2. Time (Aging) 48

2A.3.3. Stress, Vibration and Acceleration 50

2A.3.4. Drive Level 50

2A.3.5. Nuclear Effects 51

2A.4. Quartz Crystal Controlled Oscillators 52

2A.4.1. General Purpose Oscillators 52

2A.4.2. Temperature Compensated Oscillator 52

2A.4.3. Voltage Controlled Oscillator 52

2A.4.4. Oscillators for Severe Environment 52

2A.4.5. Precision Oscillators 52

2A.4.6. Short-Term Stability 54

2A.5. Conclusions 55

2A.6. References 55

t Electronics Components Laboratory, U.S. Army Electronics Command, Ft. Monmouth, NJ 07703. tBell Telephone Laboratores, Inc., Allentown, PA 18103.

41
"Arts and sciences are not cast in a mould, but are found and perfected by degrees, by often handling and polishing . . ." Montaigne,

Essays, Bk.ii. Ch. 12

The paper discusses progress made in the field of quartz crystal units and quartz crystal controlled oscillators over the past few years. The field is reviewed in general, but several accomplishments

which are thought to be of special importance, are discussed in detail. These subjects include, among

others, quartz vibrator characteristics and enclosures, modes of motion including the "trapped energy"

concept and long-term drift (aging) of crystal units. The characteristics of various types of oscillators are reviewed including temperature compensated and high precision types, and the problem of short- term stability of crystal controlled oscillators is discussed. Precision oscillators are available today with

a daily drift rate as low as a few parts in 10" and a short time stability better than a few parts in 1010 for a time period of one millisecond.

Key words: Aging (time); crystal material; crystal modes of motion; crystal vibration effects; frequency

stability; oscillator drift; precision quartz oscillators; quartz crystal oscillators; short term stability; temperature compensated oscillator.

42
2A.1. INTRODUCTION

THE QUARTZ CRYSTAL controlled oscillator was developed with the advent of radio broadcasting in the early 1920's, giving for the first time a highly stable radio-frequency source. Similar to

all mechanical vibrators in this period, there were many

factors that controlled the stability of such oscillators,

including the electrical circuit and amplifying device in which the quartz crystal unit was the principal fre- quency controlling element. Early developments involving quartz crystals to improve frequency stability were

centered around the low-frequency types, since they

were the best cases for known analytical methods. In

order of their development they were: the second over- tone of an X-cut extensional bar, the ring vibrator,

and the GT-cut quartz plate, all of which operated at 100 kHz. Progress in these developments is best illus- trated by the fact that early experimental data on

crystal controlled oscillators showed the variation of a pendulum clock due to the gravitational effects of the moon and, later, minor irregularities in the earth's

rotational period.

Following the development of the high-frequency

plated crystal units during the latter part of World

War II, an attempt was made to determine the stability

and drift rates of these crystal units by employing in their design and fabrication all the known techniques

of the 100-kHz GT. This development, initially started

for the Air Force on the NAVARHO project and continued mainly under sponsorship of the II. S. Army,

resulted in a high-precision glass enclosed fifth overtone AT crystal plate at 5 and 2.5 MHz for use in precision

oscillators [l], [2]. Most of this work was done in the

ten-year interval, 1950 to 1960. Associated with the

crystal development was the corresponding temperature

control and circuit development to give a net improvement in frequency stability and, in particular, low, long- term drift rate. Immediately following the R and D

program, the U. S. Army initiated several manufacturing development contracts to make these types of crystal units available to the industry for improved preci- sion oscillators. This last step made it possible to obtain

commercial precision oscillators having low drift rates and high stability. One can obtain on the market

today precision oscillators capable of daily drift rates as low as a few parts in 10 11

, with a short time stability better than a few parts in 10 10 for time periods as small

as one millisecond. A stabilization period of one to six weeks is often required to achieve these low drift rates. Recent developments utilizing thermocompression bonds

for the vibrator mounting and cold welded metal enclo- sures have indicated that a further material reduction in the stabilization period is possible.

It is important to point out that the above state- ments with reference to drift rate and stability apply to specially designed oscillators and crystal units, when

continuously operated in controlled environments.

There are, of course, needs for the generation of fre- quencies in the low-frequency end of the spectrum

where the thickness shear mode obviously cannot be

used, as well as in the very-high-frequency region where

factors neglected in the 2.5- and 5-MHz units become

of major importance. In addition, precision oscillators are required which must operate in severe mechanical

and temperature environments, where the techniques

and size employed in the 2.5- and 5-MHz units are not

applicable.

Except for long-term nonperiodic fluctuations of continuously operating oscillators, the principal contributions to medium- and long-term stability are made by

the particular crystal unit used. Therefore, most of the emphasis in this discussion will be concentrated on the

characteristics and performance of the various types

and designs of crystal units currently employed for fre- quency control. The reason for this is that the very low

coupling, together with the high Q's attainable with precision crystal units, have made it possible to reduce the

effects of other circuit components on the frequency of

oscillation to a negligible level when the best available

components and circuit designs are employed. Cases

in which this is not strictly true will be discussed in the

section on oscillators. 43
Fig. 1. Equivalent circuit of a quartz crystal unit.

2A.2. QUARTZ CRYSTAL UNITS

2A.2.1. Equivalent Circuit

The electrical equivalent of a quartz crystal unit is shown in Fig. 1 [3], where the motional parameters of the crystal vibrator are Li, C\, and R\, and the capaci- tance of the electrodes with quartz as a dielectric is shown as Ce

. The other capacitances shown, Cu, Cu,

and dz, are of a distributed nature as well as that be- tween the electrodes and surrounding ground such as a metal holder. When shown as a two-terminal network,

as in most specifications, the shunt capacitance of a

crystal unit is normally designated Co- It is obvious in this case how C0 would be defined once the connection

of the crystal unit in a particular circuit has been deter- mined. The assignment of the distributed capacitances

and how they are combined with the rest of the elements

of a circuit in which the crystal unit is used has led to considerable misunderstanding, as well as to a lack of correlation in the measurement of the ratio of capaci- tances or inductance [3].

2A.2.2. Vibrator Types

Figure 2 illustrates the modes of motion that are used

in practically all crystal units on the market today. To

cover a wide frequency range from a few hundred hertz

to over 200 MHz, quartz bars or plates are used in the

flexural, extensional, and shear modes of motion. At 1

is shown the lowest frequency of flexure mode in which

the motion can be in the length-thickness or the lengthwidth plane, and can be used at frequencies as high as 100 kHz. Essentially the same form of bar, but in the

extensional mode, is shown at 2, where it is used at fre- quencies as low as 60 kHz and as high as 300 kHz. A face shear mode is shown at 3 and 4 in which at 3 a square and sometimes circular plate is used, and at 4 a rec- tangular plate is used with critical ratios of the width to

length. The shear mode shown at 4 is often referred to as width shear. The shear mode shown at 5 is a thick- ness shear. This mode is used over the frequency range

from 0.5 MHz to 20 MHz, where overtones of this same

mode, as shown at 6, for the third overtone case, will operate over the frequency range normally from 10 to 250 MHz. In some particular cases, the low-frequency

types illustrated at 1 and 2 are used at higher mechanical overtones. To obtain the best characteristics and,

in particular, those as a function of temperature, cer- tain orientations with respect to the crystallographic

3 4

5 6

Fig. 2. Basic modes in quartz crystal vibrators. J_ Flexure mode. 2

Extensional mode. 3 and 4 Face shear modes. 5 and 6 Thickness

shear modes.

TABLE I Designation of "Quartz Vibrators"

Vibrator

Designation

Usual

Reference Mode of Vibration Frequency Range

A AT cut Thickness Shear 0.5 to 250 MHz

B BT Thickness Shear 1 to 30 MHz

C CT Face Shear 300 to 1000 kHz

D DT Face or Width Shear 200 to 750 kHz

E +S°X Extensional 60 to 300 kHz

F -18°X Extensional 60 to 300 kHz

G GT Extensional 100 to 500 kHz

H +5°X Length-Width Flexure 10 to 100 kHz

J +5°X Duplex 1 to 10 kHz

(2 plates) Length-Thickness Flexure M MT Extensional 60 to 300 kHz

N NT Length-Width Flexure 10 to 100 kHz

K X-Y bar Length-Width Flexure or 2 to 20 kHz

Length-Thickness Flexure

axes of quartz have been developed, and are shown in Table I [4]. A designation system has been established

to give these various quartz vibrators a convenient

"handle" for further discussion.

2A.2.3. Enclosures

The characteristics and performance of the various

crystal vibrators are controlled largely by the mounting

system used, together with the enclosure. The types of holders that are now in common use, together with those

recently developed, are shown in Fig. 3. The holders HC-6, HC-13, and HC-18, developed during and after World War II, are of such size that crystal vibrators as 44
Fig. 3. Quartz crystal unit holders.

shown in Table I may be mounted within them to provide frequency coverage from a few kilohertz to 200

MHz. For crystal units of moderate precision, these holders have served to meet the bulk of the requirements since about 1948, and even today represent most

of the crystal units produced. The major problem with

this type of holder has been the sealing of the cover to the base by soldering. During this sealing process, a

small amount of contamination is introduced within

the enclosure even with the introduction of a breather

hole that is later sealed. To overcome this difficulty, all- glass holders of the HC-6 and HC-18 dimensions have

been developed and are shown as HC-26 and HC-27 [5]. They are used principally for the high-frequency thick- ness shear-type crystal units. In addition, the HC-30

and its larger counterpart, T-ll, are all-glass holders used for high-frequency overtone precision type crystal

units [l], [6]. They are the same as those used in the vacuum tube industry, and are of the drop seal type

using the T-5£ and T-ll glass bulbs. The principal dif- ference between these various glass types is that, with

the drop seal design, eutectic solder may be used in the mounting system for the quartz vibrator, whereas in the case of the HC-26 and HC-27 enclosures, high temperature bonding agents such as silver paste and ce- ments must be used. Also with the vacuum tube types, more appropriate annealing procedures to reduce glass

strain may be employed. The vacuum tube-type structure, however, can never be reduced to the small space needed for compatibility with equipment using HC-6

and HC-18 metal types. The principal advantage of any

of the glass types is that they are more amenable to cleaning techniques. As a result, with normal processing, there will usually be lower contamination within the

enclosures. Glass types have been developed to high

perfection and are being used for medium precision

applications in single sideband equipment, both temperature controlled and temperature compensated.

Some experiments performed a few years ago with special control of the process on HC-6 and HC-18 type

enclosures indicated that nearly as good stability might

be obtained with the metal enclosure. The principal

problem would be maintenance of control of process. Recent developments employing cold welding and utiliz- ing sizes compatible with transistor enclosures are also shown in Fig. 3 [7]. The particular advantage of these holders is in their ability to be used with any of the crystal vibrators shown in Table I, making use of soldered mounting systems, and yet be sealed at low temperaby the cold welding process, thus yielding less contamination within the enclosure and maintaining high reli- ability of seal. For vibrators requiring greater height,

longer cans are used on the bases shown. Also, in at- tempts to miniaturize the enclosure as much as possible, there have been recent developments to produce holders

similar to the TO-5 transistor enclosure, as shown in Fig. 3, but having a diameter of 0.250 inch and height

of 0.070 inch. The seal is made by the electron beam

welding process [8]. 2A.2.4. Quartz Material

During the past few years, synthetic quartz has be- come available from a number of commercial sources. The proper choice of seeds and growth pattern enables

the manufacturer to cut vibrator plates with a mini- mum of waste [9]. Recently, much effort has gone into the attempt to improve the Q obtainable from synthetic

quartz. The maximum Q value obtainable is limited by

the internal friction of the material. Figure 4 shows some

early measurements of the internal friction of natural quartz over a wide temperature range obtained by

measurement of the Q of a 5-MHz fifth overtone glass enclosed A vibrator [10], [ll]. This particular crystal unit construction has been used for the measurement of the Q of synthetic and natural quartz because its unique

construction suggests that most of the measurable loss

is in the vibrator material, and not in the mounting sys- tem. There is a sharp relaxation peak at 50°K plus a

general background which has a maximum at 20°K. It has been shown [l2]-[l4] that the peak of 50°K is due

to a sodium impurity. This peak varies with different specimens of material and can be removed by electrolytically "sweeping out" the impurity or replacing it by

lithium [15] in the growing solution. It has been shown

that the Q of synthetic quartz can thus be improved to a value equivalent to natural quartz [16], [17]. Causes

of the impurity peaks and -the role which sodium and

lithium play have been very well explained by setting

up a model for this effect [18]. The background relaxation shown in Fig. 4 has been explained as being a phonon-phonon loss; i.e., a direct conversion of acoustic waves into thermal energy [ll]. Further work in the

field of quartz material has been accomplished; on the

specific problems of the change of elastic constants as a function of an applied dc field [19], [20], the variation

of dielectric constants as a function of temperature over

a range from 20 to 70°C [21 ], and the anomalous weakness of synthetic quartz whose strength drops rapidly

at 400°C [22]. The origin of oscillations which have

been experienced during quartz electrolysis and the

45
2-0 P£l

1

1

-k I

j.—

| I

/

i 4\$\

\ I 1 **L.

\\ r

ii V

i -\

\

<

0 10 20 30 40 50 60 70 80 90 100 110 120 TEMPERATURE IN DEGREES KELVIN

Fig. 4. Friction losses in quartz solid curve represents measured

internal friction consisting of relaxation peak and background

loss (dashed curves).

study of the mechanism of electrical conductivity in quartz has been the object of further studies [23], [24]. Recent correlation between the infrared absorption in synthetic quartz and its acoustic loss has been a material aid in rapidly determining the Q of newly grown

material [25]. Since the acoustic loss in the vibrator is inversely

proportional to the elastic constant, a B vibrator, with

its elastic constant more than twice as high as that of an A vibrator, offers higher Q values. A Q of 1 • 10 6 has been

measured at 15 MHz [26].

2A.2.5. Modes of Motion

Over a number of years, the resonance pattern of both

low- and high-frequency-type crystal vibrators has been

measured experimentally to determine the types of motion in bars and plates to obtain a better understanding of the cbHlblex resonance phenomena observed in specific crystal units. This background of work has

enabled the mathematicians tb set up the boundary

conditions to solve this complex problem. Tremendous

progress has been made, especially at Columbia University, in calculating the various modes of motion in crystal plates and determining their amplitude distribution. A comprehensive theory of vibration of crystalline

bars and plates and, concurrently, of the mathematical

methods and tools for dealing with the solutions of these equations has been developed. A study of three refer- ences [27 ]— [29 ] will give a good indication of what has

been accomplished in this field to date. The results of these studies at Columbia University are closely tied to many of the practical problems we have today; e.g., the

suppression of unwanted responses in crystal units for

filters by contouring or by control of electrodes for "energy trapping" [30 ]. The concept of energy trapping means that containment of the vibrator energy in the electroded region of the crystal plate is due to a cutoff

phenomenon. If the outer portion has a frequency higher

than that of the plated portion, the resulting energy of the vibrator is principally confined to the plated portion, and decreases exponentially with distance from

the plated electrode. This energy containment concept

is the basis for the design of singly resonant crystal units

for application in filters at high frequencies [31 ]— [33 ]

.

Since the energy is confined principally to the electroded

portion, several vibrators may be included on a single substrate of quartz. Critical parameters for applying

the trapped energy concept are the diameter and thick- ness of the electrode relative to the thickness of the quartz plate. In general, when larger diameters are used

with thinner electrodes, there is a less rapid decrease in energy away from the edge of the electrode. This allows low impedance units to be designed which have but a

single response, and the limit is reached when the ohmic

loss of the electrode materially affects the Q. In the case

of high-frequency plates, a number of single electrode vibrators may be used in parallel on the same substrate

to develop lower impedances. Mesa designs of crystal

plates and tuning with insulating layers have been pro- posed [31 ] to simplify the frequency adjustment pro- cedure. An illustration of the reduction in unwanted

responses by the energy trapping principle is shown in Figs. 5(a) and 5(b) [32]. Similar degrees of suppression can be obtained for fundamental crystals as low as 6 or 7 MHz by electrode control; however, contouring in addition to electrode control may be necessary at lower

frequencies.

Precise experimental methods have been devised to measure the distribution of amplitude or stress in a vi- brating quartz plate. One of these has been the measure- ment of the degree of modulation of a light beam which

is reflected from an area of selective reflection on a quartz crystal vibrating in thickness shear [34]. Methods of obtaining a picture of the amplitude distribution by using electrical probe techniques have yielded results which check very well with theory [35]. Visual observations have been accomplished by using the rotation of the optical index ellipsoid of a quartz crystal by its resonant modes [36]. Phenomenological theory in describing the effects of unwanted modes in quartz crystal units has been developed [37]. Material success has

been achieved recently with the use of X-rays to study

strain or displacement in vibrating crystal plates. This

technique also shows imperfections in the material which

result in lattice distortions [6], [38], [39]. Any motion

resulting in a curvature of the lattice can easily be de- tected by the topographic X-ray method; Fig. 6 illus- trates the degrees of sensitivity that may be obtained.

This figure shows the various modes of motion of a 3.2-MHz contoured thickness shear vibrator with their

relative responses. Each photograph of the crystal plate

is of the same plate being driven at the various responses

directly above and including the principal response at

3.2 MHz. Along the line marked -20 dB are those 46
47
responses that are functions primarily of the X-axis

direction. Those along the 0-dB line are responses de- pendent upon Z', where the group at the top of the

figure are responses dependent upon both X and Z' . It will be noted that the same crystal imperfections show

up in all photographs, indicating that the same plate was used. Also of interest are the dissymmetric modes

shown at 3.256, 3.652, and 3.802 MHz, which piezoelectrically should not be driven with a single pair of electrodes. This can be accounted for only by imbalance

in the drive mechanism or sufficient dissymetry in the

lattice. Strain patterns resulting from baked-on silver cement for the terminal connections are evident at three places on the periphery in each picture. All of the ob- served responses are shown in this figure, which means

there is an abrupt termination of these responses above

3.852 MHz. This indicates that an energy-trapping

mechanism is in operation here due to a combination of, the electrode diameter and mass, as well as contour of the crystal plate. Using this technique, strain distribu- tion in vibrating quartz plates is easily and quickly observed. Further experiments of this nature should

greatly assist in obtaining a more complete mathematical solution to the various resonances observed in

all types of quartz crystal vibrators. In addition, there

is the source image distortion technique by X-rays [39] which clearly shows surface strain which is produced by

various adherent platings with differing temperature

coefficients from that of quartz as well as those strains produced by baked-on silver cements.

All of the high-frequency crystal units previously described and shown in Table T are excited by an electrical

field Y' which is perpendicular to the major surfaces of the crystal plate. In A and B vibrators an electrical

field parallel to the major surface may be used to couple

to the thickness shear mode [40]- [42]. This may be

accomplished by the deposition of electrodes which do

not cover the central portion, the principal frequency

determining part of the quartz plate. Since the most

active central area of the crystal vibrator is not covered

by any metal, a higher Q value and a better behavior

with regard to sudden temperature changes are obtained. This will be discussed in more detail in the next

section. The parallel field design results in a high impedance, low coupling device that is difficult to use for feedback control in an oscillator; however, a "composite

field" arrangement [41 ] permits the lowering of the impedance of the crystal units. 2A.3. FREQUENCY STABILITY AS A

FUNCTION OF:

2A.3.1. Temperature

The principal change in frequency of most crystal units is that resulting from ambient temperature

changes. The temperature characteristics of some of the

vibrators shown in Table I are shown in Fig. 7. Except

for the A and G vibrators, the temperature behavior is parabolic in nature. While the curves shown have a

-iu —

G

A "

G

/

V

T

-50-40 i i-30 i-20 -10 V 0 10 202530 40 50 60 70 80 90 100 TEMPERATURE *C

Fig. 7. Frequency-temperature characteristics of various quartz

vibrators (for the explanation of letters ascribed to curves see Table I).

common inflection point near room temperature, in most cases the temperature for zero coefficient can be

placed almost anwhere in the usable temperature range

by change in orientation of the quartz plate with respect

to the crystallographic axes. The G vibrator is unique in that its temperature characteristic may be altered after the plate has been cut to a given orientation, by proper

choice of the length and width dimensions. The A

vibrator characteristic is completely controlled by the

orientation of the quartz plate. The two points of zero

coefficient are nearly symmetric about room temperature. Therefore, an orientation may be chosen for small temperature ranges yielding a small overall frequency

change. For wide temperature ranges such as — 55°C to + 105°C, a total frequency shift of ±0.002 percent will result. By temperature compensation methods, the

overall change in frequency may be reduced materially

for most of the vibrators shown in Fig. 7. This will be

covered in more detail in Section IV.

2A.3.2. Time (Aging)

The change in frequency of quartz crystal units with

time, termed aging or long-time drift, has received much

attention and accounts for a great deal of the development effort on improving stability. Great strides have

been made in the past years to isolate the various physical and mechanical processes which contribute to aging

of thickness shear vibrators and to develop crystal units with improved frequency stability. Little attention has been paid, however, to wire- mounted low-frequency types. First improvements in these types were noted in measurements of width-shear

vibrators. The apparent reason for improved long-time

stability of this type of wire mounted crystal unit is that

the support and electrical connection covers only a part

of the nodal area of the plate; consequently, less dissipa- tion and influence on frequency is produced where the supports undergo a shearing action. In other types of

48
10 TIME IN DAYS

Fig. 8. Aging characteristics of low-frequency

wire mounted crystal units.

extensional modes and square face shear types, the node

is a point, and thus the energy lost and long-time strain relaxation at the connection is greater. This probably

helps to explain why some flexure types of crystal units have low aging. The suspension system connected to the

nodal points is subject to rotary motion instead of compression and extension. While none of the present low- frequency types including flexure or width-shear possess

the low drift rates obtained by the high-frequency thick- ness shear types, it is probable that many improvements

can be made by employing less dissipative and lower

strain mounting systems. Figure 8 shows typical aging

rates for low-frequency type crystal units produced

under careful control of processes and enclosed in the

cold weld holders described previously. It is apparent

from these data that, of the low-frequency types, the width-shear vibrator possesses the lowest aging rate. Flexure vibrators are next, and the square face shear as

well as extensional units have the highest aging rate. It

is also obvious that, for a given vibrator, a lower fre- quency or more massive plate has a lower aging rate. Obviously, a given mounting system will have less effect, because it represents a smaller amount of the total vibrating system. The figure shows the aging of crystal

units linear with logarithmic time, and this is probably

true only during the first year. One would expect the

rate to decrease over long periods of time. The aging rates of high-frequency thickness shear

vibrators such as the A and B types have been reduced

during the past few years to exceptionally low rates, particularly those of the so-called precision type. Some

general statements may be made, however, about the aging of the general-purpose, high-frequency crystal

units as governed by the type of construction and the

control of processes. In solder sealed metal holders,

aging rates could be as high as 5 parts per million per month for the first year, and as low as 1 to 2 parts per

million per year for the first two years. The high value

represents lack of process control, poor design of the mounting system with high strain, and excess contamination through improper solder sealing of the enclosure. The lower value represents what can be done with good

METAL ENCLOSED UNITS GLASS ENCLOSED UNITS

2^

HIGH TEMR BONDED 4^~METAL ENCLOSED UNITS

10 15 20

TIME - DAYS

"50

Fig. 9. Aging of metal and glass enclosed 5-MHz crystal units.

design and careful control even in solder sealed metal

holders. The use of glass holders makes it necessary to use clean processes; as a material, glass is easier to

clean, thus resulting in aging rates as low as and often lower than the best for metal holders. The cold welded

metal holders, together with mounting systems that

will allow high temperature bakeout prior to sealing,

have yielded the lowest aging. Figure 9 illustrates what

has been done in recent years, including the addition of getters, for a particular case [7]. According to the latest results, aging of thickness shear crystal units is caused mainly by four processes.

1) Temperature gradient effects lasting several minutes to several hours after a thermal disturbance.

2) Stress relief effects as a function of previous

thermal history lasting three days Xp three months.

3) Change of mass effects caused by gain or loss of mass of the crystal plate surface, and mostly due to adsorption or desorption of gases, lasting over a period

of several weeks to several years.

4) Structural changes in the quartz due to imperfections in the crystal lattice. These will also be long-time

effects [6], [14], [42]. They may be caused by a density change due to the exit of excess vacancies to the

crystal surface [43]. The frequency-time performance of precision quartz

vibrators seems to be divided into two distinct parts:

1) an initial stabilization period in which there may be

frequency changes as much as 1 pp 10 8 for a period of three to five weeks, and 2) a much slower drift rate in which the total frequency change may be the order of 1 to 3 pp 10 10 per month. It has been shown experimentally

that the effects of adsorption and desorption of residual gas and the relaxation of temperature-induced stress may compensate one another to a certain extent [6]. Short-term frequency changes are also caused by

either adsorption and desorption of gases or by strains

set up between the crystal and its electrodes. Figure 10 shows the effect of a seven day oven shutoff and the

effect of stopping the quartz plate vibration for 14 days

[6]. From the similarity of these effects and from the

fact tha^ gettering or high temperature vacuum baking

reduces these effects to a large extent, it must be con49
-EF

1 "FECT

.VEN D

3F -

. 01JAR

LAI OA

T2

v-

\ SE AY «^

p

VI c rEnor PEC

-*-

t UVLIN SHUTOFF /

STOP f\ /

I1

/

I -»- /

I -»- fcEFF ECT OF

1

1 STOPPING

JARTZ PLATE

IBRATIONS /

-0

V

\1

i t FOU UK

RT

AY

I •EN

C

C UARTZ PLATE

»

v i ortM i iun: commence:

I 10 20 30 40

TIME IN DAYS 50 60 70

Fig. 10. Frequency change in precision quartz crystal units due to stopping quartz plate vibrations and interruption of oven

control.

50° C | 51° C

/ y

/ 1.5 MHz.n = 1, PARALLEL FIELD

/ 2. 5 MHz,n = 1, PERPENDICULAR FIELD

/ 3. 5 MHz.n =5,PERPENDICULAR FIELD

10 15 TIME IN MINUTES

Fig. 11. Change in frequency of perpendicular and parallel field crystal vibrators due to a 1°C change in temperature.

eluded that the frequency deviation is due to the sorption of minute quantities of gas on the crystal surface during an oven or oscillator shutdown. Figure 11 shows

the effect of small abrupt temperature changes for per- pendicular and for parallel field vibrators [42]. It can

be seen that the transient frequency excursion due to the 1°C thermal shock is decreased by over an order of magnitude in the parallel field vibrator, the reason probably being that no strain can be set up between the

active part of the crystal and the electrode, since the

center of the vibrator is free of any metal plating.

Recently, a study of the effects of impurities in quartz

along with an examination of the role of sorption phe- nomena and thermally induced strains has been initiated toward the goal of a non-aging quartz crystal, i.e., the production of a crystal unit whose frequency change

with time is less than a few parts in 10 11

. Three crystal

vibrators were used in a common vacuum system to

differentiate thermal and mass effects [44]. Evidence of the role of impurities, particularly alkali ions, was noted. Hydrogen can be the reason for short-time instability

because, in the presence of this gas, the frequency re- cording was broadened from 1.5 to 12 parts in 10 10

. The

presence of carbon monoxide also influences frequency

stability. This effect may be diminished by using the

parallel field vibrator. Short-term frequency fluctuations, however (with a sampling time of one second or less), are generally

caused by the entire oscillator and will be discussed in Section IV.

2A.3.3. Stress, Vibration and Acceleration

Requirements exist where a crystal unit must maintain its frequency stability when vibrated and accel- erated. A radio set, for instance, must operate when

transported in a truck over a rough terrain. To avoid

deterioration of the frequency stability by mechanical

vibration, a mounting structure can be provided whose

resonances are above the mechanical vibration frequencies. It has been shown in the case of a 100-MHz

vibrator mounted on ribbons and sealed in a TO-5

transistor cold-weld enclosure that the bandwidth

measured at X-band can be reduced from 2400 Hz, as exhibited by a vibrator mounted in the standard HC-18

metal container, to 70 Hz in the case of the ribbon

mounted unit [45]. Insensitivity to static acceleration is more difficult to achieve. Experiments with a centrifuge showed that it is possible to design crystal units which have a frequency

acceleration coefficient of 10~ 10 /g in one preferred direction. For acceleration forces applied in all directions, the frequency stability obtainable is approximately

10~9/g [46]. The behavior of the vibrating crystal

plate under various types of external forces and stresses has been investigated experimentally and theoretically.

The results are rather complicated and defy, so far, a complete theoretical explanation [47]. Specifically, it

is rather difficult to separate the various stresses from

one another, with the possible exception of the tensile

stress. In this case, the frequency change has been

proven to be always linear with the tensile force. Figure

12 gives an example chosen from many measurements

[47]. It shows how the frequency change depends not only upon the amount and orientation of the force, but

upon the point of attack as well. Tensile and compressional forces also change with the azimuth angle from +

to — in A-type vibrators and have been used to obtain

compensation of the frequency-temperature drift [48]. As far as the solution to these problems is concerned, it seems that the nonlinear theory will provide better answers than the perturbation theory [47].

2A.3.4. Drive Level

In a precision oscillator, another disturbing effect to be considered is the dependence of frequency upon the amplitude of vibration which, in turn, is proportional

to the crystal current. Two typical curves are shown in Figure 13. Instead of amplitude or current, its square,

50
n i

i r 200 300 400 500

TOTAL TENSILE FORCE IN gm < 600 700

TENSILE FORCE APPLIED THROUGH MULTI-WIRE MOUNTINGS

AT-CUT PLATE 0 500 IN X 0 500 IN CIRCULAR ELECTRODE DIA. = 0.250 IN

DRIVEN AT FUNDAMENTAL

Fig. 12. Change in frequency of A-type vibrators due to external

forces. The squares represent the crystal plates; the arrows in the squares indicate the direction of the X-axis, and the arrows outside indicate the applied tensile forces.

POWER IN MICRO WATTS

Fig. 13. Change in frequency with power dissipation

in two typical 2.5-MHz crystal units.

TABLE II Pulsed Nuclear Radiation Tests

Crystal Type

Nuclear

Source

Dose Observed Effects

Gamma Fast Neutrons Permanent Frequency

Change pp 108 Post-Irradiation Aging 10-8 /Week

5-MHz

HC-27/U Holder Triga* Reactor 10s R 4.6X1012 NVT -7.6 to +16 -1.4 to +1.2

19-MHz, Third Overtone Nuclear Burst 8.5X103 R 4.6X10" NVT + 40 max. -3.2 to +1.6

HC-27/U Holder 16-MHz, Third Overtone Nuclear Burst 8.6X104 R 1 .4X1012 NVT -165 to -970 +8 to +54

HC-27/U Holder

* Training, Research and Isotope Production Reactor, General Atomics.

which is proportional to the power dissipated in the

crystal, is plotted as abscissa [49]. The upper portion

of the curve ranging from 10 microwatts to 1 milliwatt

is linear with power and has been interpreted as due to

a thermal gradient between the vibrating region and the periphery of the crystal plate. A second possible ex- planation is a change of the stress-strain relationship in the material. Since the response time of the frequencyamplitude effect was measured to be 0.12 second, the

effect seems to be related to the time required to build

up the amplitude of vibration to the steady-state value

and is rather short to be explained on the basis of a thermal gradient. Obviously, it is advisable to operate

high precision crystal units at the lowest possible drive

level. A change in crystal current (or vibrational amplitude) in 5- and 2.5-MHz fifth overtone crystal units

also changes the aging behavior. An increase in current from 75 ^A by one order of magnitude changes the monthlv aging from 1 part in 10 10 to 1.5 parts in 10 9

[50]. 2A.3.5. Nuclear Effects

There are applications where crystal units are ex- posed to a nuclear environment. The results of the influence on frequency of the exposure to steady state radiation as found in the Van Allen belt have been de- scribed in a previous review article [51 ]. In addition, it has been found that, when exposed to massive doses of gamma radiation, crystal units fabricated from "swept"

synthetic quartz exhibit lower permanent frequency

change than units made from natural quartz [52]. Table II shows the behavior of crystal units under

pulsed nuclear radiation [53]. The permanent frequency

change and the post-irradiation aging which occurs

after the exposure to a nuclear burst are plotted to- gether with the doses. The effects on the 16-MHz third overtone unit are quite extensive. For comparison, similar data obtained with a TRIGA reactor on a 5-MHz

vibrator enclosed in the same type of holder are shown.

In spite of the fact that the dose is similar to the 16- MHz experiment, the permanent frequency change and

the post-irradiation aging are much lower. This is probably due to the fact that the 16-MHz unit could not be

removed immediately from the nuclear environment

after the actual test was over. Further studies of the

effects on crystal units in a nuclear environment are re- quired to provide statistical validity to the data obtained from previous tests.

51
2A.4. QUARTZ CRYSTAL

CONTROLLED OSCILLATORS

2A.4.1. General Purpose Oscillators

The simplest and most general purpose oscillator is that shown in Fig. 14, where the principal control ele- ment is the quartz crystal unit. An amplifier, either vacuum tube or transistor type, is employed with some

degree of selectivity dependent upon the type of crystal

unit used. The degree of isolation from the load is de- pendent upon the output requirements and amount of stability required. In this case the main control of stability is temperature; therefore, with reasonable

design, using high-frequency crystal units with A-type

vibrators, one can expect a frequency stability of + 0.002 percent over the temperature range of — 55°C.to

+ 105°C, and ±0.0005 percent over the restricted range

of — 20°C to +70°C. Crystal unit aging or drift is not a problem with the simple form of oscillator, since it is small compared with the change due to temperature and

is easily absorbed by periodic readjustment of the cir- cuit phase. Even though the drift rate is higher for low- frequency wire mounted units, the same reasoning can

be applied because the frequency temperature characteristics are mainly parabolic and, hence, greater

tolerances must be assigned over wide temperature

ranges.

2A.4.2. Temperature Compensated Oscillator

Since temperature is the limiting factor in the stabil- ity of simple oscillators, it has been common practice to add a temperature controlling oven. Recently, there has

been a trend to use temperature compensation because

of the availability of stable thermistors. This principle

is shown in Fig. 15. For improved stability, some measure of limiting is used as well as isolation. There are three definite advantages to temperature compensation.

Little or no additional power is required, the aging rate

of the crystal unit is less since it is always at the ambient

temperature, and no warmup time is required. Figure 16 shows a simple compensation circuit [54]. As an ex- ample, it has been possible to reduce the frequency

deviation of a 30-MHz third overtone A-type unit to 1 part in 106 for the temperature range from —30° to + 60°C. With a more sophisticated design of the sensing

network, 1 part in 10 7 over the temperature range -30°Cto +50°Cat 3-MHz has been reported [55]. For

this high precision in compensation, no standard compensation network is possible, but computer synthesis

has been proven to be feasible. Somewhat less than 1 part in 106 has been obtained by using only an inductorcapacitor-thermistor network which does not need bias voltage [56]. Figure 17 shows the frequency-temperature curve for an uncompensated and, for comparison, a compensated 25-MHz crystal unit. Other approaches to frequency compensation have been the use of temperature dependent mechanical forces on various parts of the

crystal plate and a temperature dependent capacitor

[48], [54]. These two approaches would also provide a

unit which could be a direct replacement for standard

crystal units since no dc voltage is required. The elec- tronic approach seems to be superior because it shows

promise of increased accuracy and a wider temperature

range.

2A.4.3. Voltage Controlled Oscillator

When it is desired to stabilize a crystal controlled

oscillator to a more precise source or to link it to a voltage controlled servo, a similar circuit is used, as shown in Fig. 18. These are often referred to as VCXO

(Voltage Controlled Crystal Oscillators). It is only

necessary to replace the temperature sensing network

with one that shifts the frequency of the crystal unit as

a result of voltage changes. Stability in this case is de- termined by the control mechanism. A typical VCXO

has a short-term stability of a few parts in 10 9 for one

second averaging [57]. 2A.4.4. Oscillators for Severe Environment

Stable frequency sources that are subject to high

shock and vibration such as experienced in missile and

space applications present a somewhat different problem. Phase coherence and spectral purity are of prime

importance. Figure 19 represents this case where an oven is usually used to obtain the thermal stability re- quired. All the component parts of these oscillators must be able to withstand the rugged environment imposed, and particular attention must be paid to the assembly. Foamed mounting is often used. The crystal unit design problem here is one of compromise. For

greatest stability, the vibrator must be held in a strainfree condition, but this environment requires a moderately rigid support. The g forces are transmitted to the vibrator, resulting in a frequency shift. Also, the

rigidity of the support relaxes with time, contributing to a higher aging rate. Of the various high-frequency crystal unit designs, the triple ribbon supported vibrator in the TO-5-type transistor enclosure has been found

suitable for this class of service. For frequencies of 10- MHz and up, stability is in the order of 1 part in 1010 per g if the shock and vibration frequencies are less than the mechanical resonance of the crystal vibrator

mounting system. From strain relaxation considerations, the aging or drift rate will vary with frequency,

being greater at the higher end. Typical examples are

1 part in 1010 per day at 10-MHz, increasing to 1 part

in 10 8 per day at 150-MHz. Short-term frequency in- stability measurements on a crystal controlled X-band

source made under a vibration environment showed that the contribution due to the oscillator can be reduced to the level of other signal contaminating sources, if a •ribbon-mounted cold welded crystal unit is used [45],

[58]. 2A.4.5. Precision Oscillators

If one is to obtain the greatest stability and lowest
Fig. 14. General purpose crystal controlled oscillator.

TEMP SENS

REACTANCE

LIMITER ISOL.

Fig. 15. Temperature compensated crystal controlled oscillator.

THERMISTOR W\ •— |Q| o

Fig. 16. Temperature compensation circuit containing one variable capacitance diode and two thermistors.

THERMAL STABILIZER

L.

AMP ISOL

.J

Fig. 19. Oscillator for severe mechanical and temperature environments.

INNER OVEN CONTROL

HEATER T

5

CRYSTAL NETWORK

| OVE_N

j HEATER T, L--|fU^rV£|___i

OSCILLATOR

AMPLIFIER OUT

AGC

OUTER OVEN

CONTROL

Fig. 20. Precision crystal controlled oscillator.

TEMP IN °C

Fig. 17. Effect of compensation on the frequency of a 25-MHz

crystal unit by using an inductor-capacitor-thermistor network.

CONTROL VOLTAGE

( VCXO)

Fig. 18. Voltage controlled crystal oscillator (VCXO).

drift rate of which the best precision crystal units are capable, detailed attention must be given to the design

of the oscillator circuit. Figure 20 shows the necessary

controls that must be used, and is typical of most preci- sion oscillators on the market today [2]. Not only must

the temperature of the crystal unit be held constant,

but also there must be no gradients in the quartz plate.

Therefore, a double oven is employed and proportional

control is usually used. In some cases the oscillator cir- cuit is located within the outer oven to stabilize its component parts. As mentioned previously, one factor governing the stability of a crystal unit is that of amplitude of vibration; therefore, a large amount of negative feedback is used in the amplifier as well as A.G.C.

to maintain a constant level in the oscillator circuit. Because of the advances made in temperature control and circuit development, as well as the very low coupling

provided by the 2.5- and 5-MHz fifth overtone crystal unit design, the performance of these precision oscil- lators is determined by that of the particular crystal

unit used. Presently available vacuum-tube glass- enclosed types, after a stabilization period of one to three months, show remarkably low aging or drift rates. Oscillators using the 2.5-MHz units used for stabilizing some of the Navy VLF transmitters as well as those used at the U. S. Naval Observatory have average daily

drift rates as low as a few parts in 10" with a probable average for oscillators of this type of 10~u daily drift

53
6

STAB 1 LIZATION

0 5 10 15 20

TIME IN DAYS

A

DRVERAt

1 FT R/;ekTE

180 185 190 195 200

TIME IN DAYS

Fig. 21. Initial stabilization period and drift rate

of 2.5-MHz precision oscillators.

LOG (SAMPLING TIME T)

Fig. 22. Short-term stability of crystal controlled oscillators as a function of sampling period.

rate. After three weeks of operation, the aging is less than 10-9 per week. The data are based on optimum

environments and continuous operation. Typical initial stabilization and drift rate after 180 days are shown in Fig. 21. As mentioned before, after continuous operation for a period, a temporary shutdown of the oscil- lator or of the oven will produce a change in frequency,

and a new stabilization period is again required. This

effect varies with particular units, but an average change

will take place as previously discussed and shown in Fig. 10. When fifth overtone A vibrators are mounted in transistor-type cold weld enclosures by thermocompression to the support ribbons, a material improvement

in oscillator stability is noted, and in particular, in the oven shutdown experiment. About five hours are re- quired for temperature stabilization, and at the end of

this period, the frequency is within less than 1 part in 10 9 of that before oven shutdown. Comparison with the

results shown in Fig. 10 indicates the advantage of the high temperature vacuum bakeout and large thru-put

capability of this design. When this type of crystal unit

is employed, one to two orders of improvement may

be available in precision quartz crystal controlled

oscillators. Other precision crystal controlled oscillators are described in the literature [59], [60 ], and the influ- ence of supply voltage changes on frequency stability

is discussed [60 ].

2A.4.6. Short-Term Stability

Practical oscillators appear to have three main sources

of noise contributing to frequency fluctuations [61 ]- [63]:

1) thermal and shot noise within the oscillator itself which actually perturbs the oscillation,

2) additive noise associated with accessory circuits which do not perturb the oscillation, but merely add to the signal, and

3) fluctuations of the oscillator frequency due to either the crystal unit or circuit parameter changes.

Figure 22 shows the various calculated contributions

to oscillator frequency fluctuations as a function of the sampling time t. As can be seen, the noise from within

the oscillator varies with \/\/t for low and high integration times. During the transition of the 1/ y/r noise from

a higher to a lower level, the slope changes to 1/r during

this period. The contribution of the second component

varies with 1/r and depends on the properties of an out- put filter. Unless the effective quality factor of this

filter is very high, it is this second component which

dominates the short-term frequency stability of the

oscillator. The frequency fluctuations due to the last mentioned source appear to have a 1// power spectral

density. The mechanism involved probably differs in various oscillators depending upon the type of crystal unit and circuitry used. Measurements on a high precision 5-MHz crystal controlled oscillator show, in fair agreement with theory, a linear increase of stability with increase of the sampling time, namely from 2 parts in 10 9 for one milli- second to 3 parts in 1012 for one second [61 ]. Finally, it may be stated that while the quality factor

of the vibrator is most important in improving the fre- quency stability with respect to incidental variations in circuit parameters, the short-term stability of the

oscillator is directly determined by the vibrator Q only

when the additive noise components are sufficiently suppressed by narrow-band filters in the output stage. Whereas first-order theories predict an ever increasing

improvement with signal power in the signal-to-noise

ratio of the oscillator output, higher order effects impose limitations, the onset of which must still be de- termined experimentally.

54
2A.5. CONCLUSIONS

There exists a large number of applications where the average drift rate of commercially available precision

crystal units is satisfactory. With the use of atomic and

molecular frequency standards or calibration by VLF,

those applications requiring lower drift rates can be

satisfied so that further improvements in drift characteristics of high precision crystal controlled oscillators are no longer of primary concern. The areas where these

precision crystal units could be improved is in reduced

initial stabilization period and obtaining reproducible

drift rates. Additionally, a need exists in improving the short-term stability of crystal units and oscillators for applications such as Doppler radar, high-speed data

transmission, and systems requiring phase coherence. Since many atomic and molecular standards employ

crystal controlled oscillators, the short-term stability

of the entire standard is dependent only upon the

crystal controlled oscillator. When crystal units outside

of the 2- to 10-MHz range are required, material improvements are needed to reduce the long-term drift

rate, in particular, for miniaturized communication

equipment in the field. In addition, more work is neces- sary in order to explore the influence of adverse environ- ments such as shock, vibration, acceleration, and nuclear

radiation. 2A.6. REFERENCES

[1] A. W. Warner, "Design and performance of ultraprecise 2.5 Mc

quartz crystal units," Bell Sys. Tech. J., pp. 1193-1217, September I960.'

[2] R. A. Sykes, W. L. Smith, and W. J. Spencer, "Performance of precision quartz-crystal controlled frequency generators," IRE

Trans, on Instrumentation, vol. I- 1 1 , pp. 243-247, December 1962.

[3] "IRE standards on piezoelectric crystals—the piezoelectric vibrator: definitions and methods of measurement, 1957,"

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[5] D. M. Eisen, "New developments in glass enclosed crystal

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[7] R. J. Byrn&and R. L. Reynolds, "Design and performance of a new series of cold welded crystal unit enclosure," 1964 Proc. 18th Annual Symp. on Frequency Control, pp. 166-180.

[8] W. G. Stoddart, "A new design for microminiature crystals,"

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[9] J. M. Stanley, "The Signal Corps synthetic quartz program," IRE Trans, on Military Electronics, vol. MIL-4, pp. 438-447, October 1960.

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[11] W. P. Mason, "Developments in ultrasonics," 1964 Proc. 18th Annual Symp. on Frequency Control, pp. 12-42.

[12] J. C. King, "The anelasticity of natural and synthetic quartz at low temperatures," Bell Sys. Tech. J., vol. 38, pp. 573-602, 1959.

[13] D. B. Fraser, informal presentation at 1964 19th Annual Symp.

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[14] J. M. Stevels and J. M. Yolger, "Further experimental in- vestigations on the dielectric losses of quartz crystals in relation

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314, June 1962.

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July 1962.

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17} A. A. Ballman and D. VV. Rudd, "The doping of cultured

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Solids, vol. 26, pp. 673-686, April 1965.

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1951.

[28] R. D. Mindlin and D. C. Gazis, "Strong resonances of rectan- gular AT-cut quartz plates," 1962 Proc. 4th U.S. Nat'l Congress Appl. Mech., pp. 305-310.

[29] R. D. Mindlin and P. C. Y. Lee, "Thickness-shear and fiexural vibrations of partially plated crystal plate," Dept. of Civil Engrg. and Engrg. Mechanics, Columbia University, New York, N. Y., Contract DA36-039 AMC-00065(E), Tech. kept. 2, June

1965.

[30] W. Shockley, D. R. Curran, and D. J. Koneval, "Energy trap- ping and related studies of multiple electrode filter crystals," 1963 Proc. 17th Annual Symp. on Frequency Control, pp. 88-126.

[31] D. R. Curran and D. J. Koneval, "Factors in the design of VHF

filter crystals," 1965 19th Annual Symp. on Frequency Control, pp. 213-286.

[32] , "Energy trapping and the design of single and multielectrode filter crystals, 1964 Proc. 18th Annual Symp. on Fre- quency Control, pp. 93-119.

[33] R. Bechmann, T. J. Lukaszek, and H. P. Wasshausen, "Im- provements in HF and VHF quartz filter crystals," Proc. IEEE,

vol. 53, pp. 1160-1161, August 1965.

[34] G. Sauerbrey, "Messung von Plattenschwingungen sehr kleiner Amplitude durch Lichtstrommodulation," Z. Phys., vol. 178, pp. 457-471, April 1964.

[35] I. Koga, "Radio-frequency vibration of rectangular AT-cut

quartz plates," /. Appl. Phys., vol. 34, pp. 2357-2365, August

1963.

[36] A. J. DeMaria and G. Barnard, "Visual observations of piezoelectric modes," /. Appl. Phys., vol. 34, pp. 2296-2297, August

1963.

[37] M. Onoe, "Analysis and detection of unwanted modes in quartz

crystal units for oscillators," J. Inst. Elec. Commun. Engrs. (Japan), vol. 47, pp. 38-47, January 1964.

[38] W. J. Spencer, "Modes in circular AT-cut quartz plates," IEEE Trans, on Sonics and Ultrasonics, vol. SU-12, pp. 1-5, March 1965.

[39] R. A. Young, R. B. Belser, A. L. Bennett, W. H. Hicklin, J. C. Meaders, and C. E. Wagner, "Special X-ray studies of quartz frequency control units," 1965 Proc. 19th Annual Symp. on

Frequency Control, pp. 23-41.

[40] R. Bechmann, "Excitation of piezoelectric plates by use of a

parallel field with particular reference to thickness modes of quartz," Proc. IRE, vol. 48, pp. 1278-1280, July 1960.

[41] W. Ianouchevsky, "High Q crystal units," 1963 Proc. 17th Annual Symp. on Frequency Control, pp. 233-247.

[42] A. W. Warner, "Use of parallel-field excitation in the design of quartz crystal units," ibid., pp. 248-266. _ [43] O. Sh. Grois, "One possible mechanism of quartz aging," Radiotekhnika i Elektronika (USSR), vol. 7, pp. 702-705,

April 1962. For English translation, see Radio Engrg., Electronic Phys., vol. 7, p. 651, April 1963.

[44] A. W. Warner, D. B. Fraser, and C. D. Stockbndge, "Funda55
mental studies of aging in quartz resonators," IEEE Trans, on

Sonics and Ultrasonics, vol. SU-12, pp. 52-59, June 1965.

[45] D. B. Leeson, "Aerospace crystal environmental requirements," 1965 Proc. 19th Annual Symp. on Frequency Control, pp. 49-58.

[46] W. J. Spencer and W. L. Smith, "Precision crystal frequency

standards," 1961 Proc. 15th Annual Symp. on Frequency Control, pp. 139-155.

[47] C. R. Mingins, L. C. Barcus, and R. W. Perry, "Effects of externa! forces on vibrating crvstal plates," Lowell Technological

Inst. Research Foundation, Contract DA36-039 AMC-02239(E),

Final Rept., May 1, 1963 to April 30, 1965.

[48] E. A. Gerber and M. H. Miles, "Reduction of the frequency- temperature shift of piezoelectric resonators by mechanical

stress," Proc. IRE, vol. 49, pp. 1650-1654, November 1961.

[49] D. L. Hammond, C. Adams, and L. Cutler, "Precision crystal

units," 1963 Proc. 17th Annual Symp. on Frequency Control, pp. 215-232.

[50] A. Karolus and D. Aus Dem Bruch, "On the aging of harmonic

quartz crystals of 2 and 2.5 Mc/s" (in German), Z. Instru- mentenkunde, vol. 72, pp. 229-232, August 1964.

[51] R. B. Belser and W. H. Hicklin, "Aging characteristics of quartz

resonators with comments on the effect of radiation, " 1963 Proc.

17th Annual Symp. on Frequency Control, pp. 127-175.

[52] G. K. Guttwein, "Quartz crystals and quartz oscillators," 1964

Proc. Internal'I Conf. on Chronometry, pp. 30-51.

[53] J. M. Stanley, "Effects of transient radiation on frequency control devices," in Transient Radiation Effects on Electronics. Battelle Memorial Inst. Handbook, 1965, pp. L-l to L-ll.

[54] D. E. Newell, H. Hinnah, and R. Bangert, "Advances in crystal

oscillator and resonator compensation," 1964 Proc. 18th Annual

Symp. on Frequency Control, pp. 487-534.

[55] R. Bangert, H. Hinnah, and D. E. Newell, "Recent develop- ments in crystal oscillator temperature compensation," 1965

Proc. 19th Annual Symp. on Frequency Control, pp. 617-641.

[56] S. B. Boor, W. H. Horton, and R. B. Angove, "Passive temperature compensation of quartz crystals for oscillator applications,"

ibid., pp. 105-124.

[57] R. L. Kent, "The voltage-controlled crystal oscillator (VCXO),

its capabilities and limitations," ibid., pp. 642-654.

[58 1 J. R. Buck and D. J. Healey, "Short term frequency stability measurement of crystal controlled X-band source," 1964 Interim

Proc. Symp. on Definition and Measurement of Short-Term Fre- quency Stability, pp. 1 1 1-9 1 to 111-120.

[59] E. V. Dvornikov, E. A. Mavrin, and N. V. Morkovin, "A highstability transistorized crystal oscillator," Pribory i Tekhn. Eksperim. ( USSR), no. 4, July-August 1963. For English translation see Instr. Exper. Tech. (USSR), pp. 672-674, JulyAugust 1963.

[60] P. J. Baxandall, "Transistor crystal oscillators and the design

of a 1-mc/s oscillator circuit capable of good frequncy stability,

Radio Electronic Engrg. (GB), vol. 29, pp. 229-246, April 1965.

[61] L. S. Cutler, "Some aspects of the theory and measurement of frequency fluctuations in frequency standards," 1964 Interim

Proc. Symp. on Definition and Measurement of Short-Term Fre- quency Stability, pp. 11-73 to 11-104.

[62] E. Hafner, "The effects of noise on crystal oscillators," ibid., pp. 11-157 to 11-204.

[63] W. A. Edson, "Progress and problems in short term stability," 1965 Proc. 19th Annual Symp. on Frequency Control, pp. 43-48.

Reprinted from the PROCEEDINGS OF THE IEEE

VOL. 54, NO. 2, FEBRUARY, 1966

Pp. 103-116

Copyright 1966, and reprinted by permission of the copyright owner PRINTED IN THE U.S.A.

Manuscript received November 15, 1965; revised November 29. 1965. NBS Editors Note: The symbol,/, used in Chapter

2A (figs. 7, 8, 9, 12, 21, and 22) is equivalent to, v, shown in the glossary of Chapter 8; thus:

A / = ov: —r = y = —

,

/ Vq

where vo is the nominal frequency.

56
CHAPTER 2 — PART B

PROGRESS IN THE DEVELOPMENT OF QUARTZ

CRYSTAL UNITS AND OSCILLATORS SINCE 1966*

Eduard A. Gerbert and Roger A. Sykest

Contents

Page 2B.1. Introduction 59

2B.2. Quartz Crystal Units 59

2B.2.1. Equivalent Circuit 59

2B.2.2. Vibrator Types 59

2B.2.3. Quartz Material 59

2B.2.4. Modes of Motion 59

2B.3. Frequency Stability as a Function of: 2B.3.1. Temperature 60

2B.3.2. Time (Aging) 61

2B.3.3. Stress, Vibration and Acceleration 61

2B.3.4. Drive Level 61

2B.4. Quartz Crystal Controlled Oscillators 62

2B.4.1. Short-Term Stability 62

2B.5. Conclusions and Possible Future Developments 62

2B.6. References 63

* Manuscript received October 9, 1972.

t Electronics Technology and Devices Laboratory, U.S. Army Electronics Command, Ft. Monmouth, NJ 07703.

t Formerly with Bell Telephone Laboratories, Allentown. PA 18103.

57
"And step by step, since time began, I see the steady gain of man."

Whittier, The Chapel

of the Hermits.

This chapter highlights progress in the field of quartz crystal units and oscillators since publication of similar material in 1966 (see chap. 2A). The organization of the chapter follows Part A. Specific

subjects described include: (1) Quartz crystal units — equivalent circuits, vibrator types, quartz material, and modes of motion. (2) Frequency stability in terms of temperature, aging, stress, vibration, acceleration, and drive level. A small fundamental-mode crystal unit has been designed in the range of 15-23 MHz which can survive shock acceleration of 15,000 g's or more. (3) Short-term stability of crystal

oscillators is discussed with reference to aspects of noise and fluctuations of various types of precision

oscillators. The chapter ends with a view towards future developments and technical possibilities in the field of crystal oscillators.

Key words: Crystal aging; crystal characteristics; crystal oscillators; frequency stability; quartz crystals; quartz material; precision frequency sources; short-term stability.

58
2B.1. INTRODUCTION

Part B discusses progress in the state of the art of quartz crystal units and oscillators since 1966.

It includes subjects covered earlier in similar

papers [1, 2] 1 and follows the format of Part A.

2B.2. QUARTZ CRYSTAL UNITS

In this section we consider a general equivalent

circuit, vibrator types, quartz material, and modes

of motion recently evaluated in quartz crystal

units.

2B.2.1. Equivalent Circuit

A more general equivalent circuit has been

derived [3] that is valid at any frequency up to and

including the lower UHF ranges but reduces to the

conventional circuit (fig. 1 in chap. 2A) if the

parameters are properly redefined. The characteristics are illustrated with the aid of crystal impedance

and admittance diagrams. Recently, the equivalent

circuit has been further expanded by using trans- mission fines in addition to lumped elements. It can thus represent a stack of thickness mode

crystal vibrators [4].

2B.2.2. Vibrator Types

Lately, more effort has gone into bridging the

gap between face shear and thickness shear vibrators. A width-shear quartz resonator has been

developed for applications between 0.8 and 3

MHz [5]. It has an unusually high length-to-width

ratio of 25 and is symmetrically bevelled on one of

its major edges.

2B.2.3. Quartz Material

The anelastic effects of sodium, lithium, and po- tassium impurities have been studied from liquid

helium temperatures to near the quartz inversion

point at 573 °C [6]. Recent work has shown that the

major source of acoustic loss in the normal operating

temperature range is due to the hydrogen bonded

OH content in the crystal. It also was shown that

this H-bonded OH-content causes characteristic

absorption of light in the near-infrared region,

affording a rapid evaluation of the OH content and

hence of Q in newly grown material [7]. Specific curves are given for the sodium hydroxide and

sodium carbonate growth process which relate the

extinction coefficient at 3500 cm -1 with the Q measured on 5 MHz (5th overtone) high precision resonators [8, 9]. It should be noted that the absorption

measurement method must be made in an exact and precise manner for Q's in excess of 1 million.

' Figures in brackets indicate literature references at the end of this chapter.

The Na2 CO.-) method leads to crystals of small

hydrogen content and yields Q values in the order of 2 to 3 million at 5 MHz [10J. The more rapid growth

in the NaOH process initially led to Q values much

below one million, but Q in the order of one to two

million may be obtained by using additives in the

solution [11]. Correlation between the density of dislocations, the distortion of the crystal structure,

and the half-width of X-ray diffraction was estab- lished with the Q-value obtained through the infrared

absorption method [12].

2B.2.4. Modes of Motion

Progress has continued in determining motion

types in plates as well as improving mathematical

analysis of the complex phenomena in specific resonators. Figure 2B.1 compares theoretical and

experimental results of flexure and shear modes in high frequency crystal resonators, including those

due to a twist in the third dimension. It illustrates the progress that has been made in identifying and

describing the more complex forms of the thick- ness shear and flexure modes [13]. The various

modes are shown in figure 2B.2 [13]. As can be seen,

the mode shape comprises phase reversals across

the width of the plate which result in a twisting

deformation across the width. Recently, the thickness-shear and shear-flexure-twist vibrations in rectangular AT-cut plates with partial electrodes

have been analyzed; the results were compared

with x-ray topographs [14, 15]. At the lower end of the vibrational spectrum of quartz plates, closed

a/b (WIDTH TO THICKNESS RATiO)

Fig. 2B.1. Computed and measured resonance for rectangular AT-cut quartz plates with a length to thickness ratio of 20.

59
Fig. 2B.2. Mode shapes in quartz plates.

form solutions of coupled extensional, flexural,

and width-shear vibrations have been obtained for thin rectangular plates with free edges. These

solutions check very well with experimental results

[16]. The theory of crystalline body vibration, de- veloped at Columbia University and elsewhere,

formed the basis for hypothesizing the phenomenon

of "energy trapping" [17, 18]. The dispersion curve

for thickness shear and flexural waves in an infinite plate, propagated in the X-direction, is shown in figure 2B.3; this demonstrates the criticality of the

electrode dimensions. Dimensionless frequency is plotted as ordinate and lateral wave number as

abscissa. The upper curves are the dispersion curves for the uncoated and the lower ones for the

coated part of the plate. The amount of frequency

decrease is dependent upon the piezoelectric

coupling in addition to the mass of the electrode.

To the left of zero, the wave number is imaginary,

and the waves are non-propagating. At frequencies

between the two cut-off frequencies, the thicknessshear motion in the plated part is propagating;

in the unplated portion, however, there is non- propagation so that the amplitude decreases exponentially outside of the plated portion. Above the

cut-off frequency of the unplated portion both waves

are propagating over the entire plate. If the x- dimension of the plating is short enough, the lateral wavelength of the first anharmonic overtone would

^(LATERAL WAVE NUMBER)

Fig. 2B.3. Dispersion curves for thickness shear and flexure in a quartz plate; the upper curves are the dispersion curves for the uncoated and the lower ones for the coated part of the

plate.

have to be — 2/3 the length of the plating; the wave number then would be high, and the frequency of

the anharmonic overtone would be above the cutoff frequency in the unplated portion. This would

result in the first and all higher overtones propagating out. Thus, the critical length of plating for a given thickness will be inversely proportional to the wave number in the plated portion at the cut-off frequency of the unplated portion of the plate.

The reader is referred to the literature [13, 19] for detailed study of electrode dimension relations

for trapped energy resonators. Studies have continued on strain or displacement

in vibrating crystal plates through x-ray topographic

methods. This technique shows both imperfections

in the material (which result in lattice distortions)

[20] and strain from the thin metal films on quartz

[21, 22].

2B.3. FREQUENCY STABILITY AS

A FUNCTION OF:

2B.3.1. Temperature

The development of a new type of double-rotated

crystal plate, the FC-cut, may prove to be a superior

alternative to the AT-type in many applications;

examples are 1) oven controlled units at elevated

temperature, 2) temperature compensated oscilla- tors at discreet temperature ranges, and 3) fast warm-up applications [23]. The "flatness" of the

turning point of an FC-cut at 80 °C is equivalent to the "flatness" of the turning point of an AT-cut in the region of 40 °C (see fig. 7 in chap. 2A).

60
50

40

SOLDER BONDING,

GLASS ENCAPSULATIOI

THERMOCOMPRESSION BONDING, '

j HIGH TEMPERATURE PROCESSING

30 40

TIME, days

70

Fig. 2B.4. Frequency change in precision quartz crystal units from stopping quartz plate vibrations and interrupting oven control.

2B.3.2. Time (Aging)

Short-term frequency changes can be caused by

either adsorption and desorption of gases or by

strains set up between the crystal plate and its electrodes [24]. Figure 2B.4 shows the effect of

shutting off the oven and stopping the quartz plate

vibration for three days. As can be seen, the re- covery from temperature control or power supply

interruptions can be greatly improved by using both

a mounting system for the quartz plate (that may be

vacuum-baked) and cold-welded metal enclosures.

The mounting system that supports the quartz

vibrator in the metal enclosure makes use of

higher temperature bonding alloys than for the glass

units; thus, the complete unit may be high-temperature, vacuum-baked in an oil-free system and then

cold-welded while under vacuum. This results in less contamination and strain in the mounting,

with a consequent shortening of the initial stabiliza- tion time.

2B.3.3. Stress, Vibration and Acceleration

Progress has been made in designing small

fundamental-mode crystal units, in the frequency

range of 15 to 23 MHz, which will survive shock

acceleration amplitudes of 15,000 g's and more. The

quartz resonator is bonded to the support, using

electroplated nickel films of thicknesses about

10 /Am [25].

2B.3.4. Drive Level

It has been known for some time that the resonance resistance in some At-cut quartz units increased considerably for very low drive levels. This large crystal-unit resistance can prevent initial oscillations. It has been found that small metal

particles, sticking on active quartz surfaces, cause

the current dependency of the resistance, and other constants as well [26].

61
2B.4. QUARTZ CRYSTAL CONTROLLED OSCILLATORS

A major advance in quartz crystal controlled

oscillators has been short-term stability; this is described in the following section.

2B.4.1. Short-Term Stability

The importance of the problem of short-term

frequency stability is evidenced by the large number

of papers devoted to the subject. It can be touched

on only very briefly within the framework of this review. Figure 2B.5 shows the phase noise of a 5- MHz precision oscillator (referred to a 1-Hz bandwidth) within the frequency range of 100 Hz to 5 kHz [27]. It should be noted that the noise is ap- proximately 8 dB lower for a field effect transistor

(2N3823) than for a silicon planar transistor (2N2222)

used in the oscillator and amplifier stages. Phase

noise under vibration is somewhat higher than in the quiescent state. A state-of-the-art advance of more than 10 decibels was reported recently for 5-MHz quartz oscil- lators [28]. This was achieved by selection of

transistors for the lowest possible flicker of phase

and DC flicker noise, and by utilizing massive negative feedback. Similar results are reported in [29]. A more general review of the fundamentals

and aspects of noise and fluctuation on signals,

which lead to characteristics of various types of

precision signal sources, can be found in reference

[30]. Reference should also be made to the

IEEE-NASA Symposium on Short-Term Frequency

Stability [31] and to the special issue of the Proceedings of the IEEE on Frequency Stability [32]. Finally, an overview of the state-of-the-art in short-term stability of high precision frequency

sources, as it existed at the time of this report, is

FREQUENCE , Hz

Fig. 2B.5. Oscillator output phase noise referred to 1-Hz band.

10" 9

1 SEC 1 DAY 1M0 1 YR

Fig. 2B.6. Stability values of frequency standards, indicating the margin between specified data and performance of selected

units.

given in figure 2B.6 [33]. In each case, some

spread in the data has been allowed for. The better

values correspond to measurements on selected

units, whereas the more-conservative limit corre- sponds to data specified in manufacturers' data

sheets.

2B.5. CONCLUSIONS AND POSSIBLE FUTURE DEVELOPMENTS

During the past 6 years, the technical possibilities and future trends have become more

evident. For communications, we have analog and

digital systems, both of which are dependent upon

an accurate frequency source. In the digital case, we need a clock which in many cases must be

regenerated or phase locked with a transmitting or

central clock. In analog systems, in addition to the

frequency generator or clock, we need a precise

filter to select one channel from another. With the

present progress in integrated circuitry, frequencies can be generated very simply and synthesized to place them anywhere as needed in the frequency

spectrum. All that is required is one precise generator. Very probably there will be fewer crystal

units produced for these systems, but they will have

higher accuracy. There should be a material size reduction in the higher frequency units. Present

10 MHz crystal units can be produced with crystal

plates 7.5 mm in diameter or less. At 30 MHz

they should be 2.5 mm or less. It is inconceivable

that any of these plates would be put in present

holders. They probably will be in the form of thin

enclosures not over 30-50 mils thick and will have

beam leads. It is believed that if we take a look at the progress that has been made in integrated circuit technology and apply some of those techniques to the present crystal design and developments, we

would be far ahead. For example, batch processing

becomes feasible for smaller size plates and,

62
except for final adjustment, 100 vibrators can be

processed from a 1-in (2.54 cm) square plate.

There should be standardization of generator

frequencies to make them off-the-shelf items for applications to digital and analogue, wire, and radio

transmission systems. In the future there will be more and more use of mobile and marine radio

equipment. With developments in active solid

state devices moving in the direction of performing

functions, it is inconceivable that elements for frequency control and selection would not follow

this same trend. Some solid state designs have

already started, but presently available VCXO's

(voltage controlled crystal oscillators) and filters resemble little the advancements in integrated

circuitry. What is envisioned is a completely inte- grated series of functions utilizing crystal resonators

to produce frequency generators, synthesizers,

translators and modulators; narrow band amplifiers

for SSB, AM and FM systems; and discriminators

for FM systems. These functional devices should

be compatible with other equipment components

in both size and performance to form integral parts

of a system.

2B.6. REFERENCES

[I] Gerber, E. A., and Sykes, R. A., "Quartz frequency stand- ards," Proc. IEEE, 55, No. 6, pp. 783-791 (June 1967).

[2] Gerber, E. A., and Sykes, R. A., "Quarter century of progress in the theory and development of crystals for frequency control and selection," Proc. 25th Ann. Symp.

on Frequency Control (U.S. Army Electronics Command,

Ft. Monmouth, NJ 07703. April 26-28, 1971), pp. 1-45

(NTIS, AD 746211, 1971).

[3] Hafner, E., "The piezoelectric crystal unit — definitions and methods of measurement," Proc. IEEE, 57, No. 2, pp. 179-201 (February 1969).

[4] Ballato, A., "Transmission-line analogs for stacked piezoelectric crystal devices," Proc. 26th Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 86-91 (Electron. Ind. Assn., Washington, DC 20006,1972).

[5] Royer, J. J., "A new DT quartz resonator," IEEE Trans, on

Sonics and Ultrasonics, SU-17, No. 1, pp. 18-22 (Jan- uary 1970).

[6] Fraser, D. B., "Anelastic effects of alkali ions in crystalline quartz," J. Appl. Phys., 35, No. 10, pp. 2913-2918

(October 1964).

[7] Byrne, R. J., and Reynolds, R. L., "Design and perfor- mance of a new series of cold welded crystal unit en- closure," Proc. 18th Ann. Symp. on Frequency Control

(U.S. Army Electronics Labs., Ft. Monmouth, NJ 07703, May 4-6, 1964), pp. 166-180 (NTIS, AD 450 341, 1964).

[8] Fraser, D. B., Dodd, D. M., Rudd, D. W., and Carroll, W. J., "Using infrared to find the mechanical Q of a-quartz," Fre- quency, 4, No. 1, pp. 18-21 (January- February 1966).

[9] Sawyer, B., "Q capability indications from infrared absorption measurements for Na2C03 process cultured

quartz," IEEE Trans, on Sonics and Ultrasonics, SU- 19,

No. 1 , pp. 41-44 (January 1972).

[10] Sawyer, B., "Pilot plant production of cultured quartz," Sawyer Research Products, Inc., Eastlake, Ohio, Final

Report Contract DA 36- 039-sc-8I245 (January 1964).

[II] BaUman, A. A., Laudise, R. A., and Rudd, S. W., "Synthetic

quartz with a mechanical Q equivalent to natural quartz," Appl. Phys. Lett., 8, No. 2, pp. 53-54 (January 1966).

[12] Asahara, J., and Taki, S., "Physical properties of synthetic quartz and its electrical characteristics," Proc. 26th

Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 93-96 (Electron. Ind. Assn., Washington, DC 20006,

1972).

[13] Mindlin, R. D., and Spencer, W. J., "Anharmonic, thick- ness-twist overtones of thickness-shear and flexural vibra- tions of rectangular, AT-cut quartz plates," J. Acoustical

Soc. Am., 42, No. 6, pp. 1268- 1277 (December 1967).

[14] Byrne, R. J., Lloyd, P., and Spencer, W. J., "Thicknessshear vibration in rectangular AT-cut quartz plates with

partial electrodes," J. Acoustical Soc. Am., 43, No. 2, pp. 232-238 (February 1968).

[15] Lee, P. C. Y., and Spencer, W. J., "Shear-flexure-twist

vibrations in rectangular AT-cut quartz plates with partial electrodes" J. Acoustical Soc. Am., 45, No. 3, pp. 637-645 (March 1969).

[16] Lee, P. C. Y., "Extensional, flexural, and width-shear

vibrations of thin rectangular crystal plates," Proc. 25th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 26-28, 1971).

pp. 63-69 (NTIS, AD 746211, 1971).

[17] Mortley, W. S., "Energy trapping," Marconi Revieiu, 30,

No. 165, pp. 53-67 (Second Quarter 1967).

[18] Shockley, W., Curran, D. R., and Koneval, D. J., "Trappedenergy modes in quartz filter crystals," J. Acoustical Soc. Am., 41, No. 4 (Part 2), pp. 981-993 (April 1967).

[19] Mindlin, R. D., "Studies in the mathematical theory of

vibrations of crystal plates," Proc. 20th Ann. Symp. on Frequency Control (U.S. Army Electronics Command,

Ft. Monmouth, NJ 07703. April 19-21, 1966), pp. 252-265

(NTIS, AD 800 523,1966).

[20] Spencer, W. J., and Haruta, K., "Defects in synthetic quartz," J. Appl. Phys., 37, No. 2, pp. 549-553 (February

1966).

[21] Haruta, K., and Spencer, W. J., "Strain in thin metal

films on quartz. "J. Appl. Phys., 37, No. 6, pp. 2232-2233 (May 1966).

[22] Haruta, K., and Spencer, W. J., "X-ray diffraction studies of vibrational modes, "Proc. 20th Ann. Symp. on Frequency

Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 19-21, 1966), pp. 1-13 (NTIS, AD 800

523, 1966).

[23] Lagasse, G., Ho, J., and Block, M., "Research and develop- ment of a new type of crystal — the FC-cut," Proc. 26th Ann. Synp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703. June 6-8, 1972). pp. 148-151 (Electron. Ind. Assn., Washington, DC

20006. 1972).

[24] Armstrong, J. H., Blomster, P. R., and Hokanson, J. L., "Aging characteristics of quartz crystal resonators,"

Proc. 20th Ann. Symp. on Frequency Control (U.S. Army

Electronics Command, Ft. Monmouth, NJ 07703, April 19-21, 1966), pp. 192-207 (NTIS, AD 800 523, 1966).

[25] Bernstein, M., "Quartz crystal units for high G environ- ment," Proc. 25th Ann. Symp. on Frequency Control

(U.S. Army Electronics Command, Ft. Monmouth, NJ

07703, April 26-28, 1971), pp. 125-133 (NTIS, AD

746211, 1971).

[26] Nonaka, S., Yuuki. T., and Hara, K., "The current de- pendency of crystal unit resistance at low drive level." Proc. 25th Ann. Symp. on Frequency Control (U.S. Army

Electronics Command, Ft. Monmouth, NJ 07703, April

26-28, 1971), pp. 139-147 (NTIS, AD 746211, 1971).' [27] Pustarfi, H. S., "An improved 5 MHz reference oscillator for time and frequency standard applications," IEEE

Trans. lustrum, and Meas., IM-15, No. 4. pp. 196-202 (December 1966).

[28] Brandenberger, H., Hadom. F., Halford, D., and Shoaf, J. H., "High quality quartz crystal oscillators: frequency do- main and time domain stability," Proc. 25th Ann. Symp.

on Frequency Control (U.S. Army Electronics Command.

Ft. Monmouth, NJ 07703. April 26-28. 1971). pp. 206-230

(NTIS, AD 746211, 1971).

[29] Driscoll, M. M., "Two-stage self-limiting series mode type

quartz crystal oscillator exhibiting improved short-term frequency stability." Proc. 26th Ann. Symp. on Frequency

63
Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 43-49 (Electron. Ind. Assn., Washington, DC 20006, 1972).

[30] Cutler, L. S., "Stability characteristics and application tech- niques for precision frequency sources," Proc. 3rd Ann. DOD Precise Time and Time Interval (PTTI) Strategic

Plan, Meet. (U.S. Naval Observatory, Washington, DC

20390, November 16-18, 1971), pp. 229-253 (USNO, Washington, DC 20390, 1972). (NTIS, AD 758 739)

[31] Chi, A. (Chairman), Proc. IEEE-NASA Symp. on Short- Term Frequency Stability (Goddard Space Flight Center,

Greenbelt, Md 20771, November 23-24, 1964), NASA

Report SP-80, 317 pages (USGPO, 1965).

[32] Chi, A. (Editor), Special Issue on Frequency Stability. Proc. IEEE, 54, No. 2 (February 1966).

[33] KartaschofF, P., and Barnes, J. A., "Standard time and fre- quency generation," Proc. IEEE, 60, No. 5, pp. 493-501 (May 1972).

64
CHAPTER 3

THE PHYSICAL BASIS OF ATOMIC FREQUENCY STANDARDS*

Allan S. Risleyt

Contents

Page 3.1. Introduction 67

3.2. Atomic Energy Levels 67

3.2.1. Four Basic Ideas 67

a. The Electron 67

b. The Nucleus 67

c. The Quantization of the Energy of Atoms 68

d. The Quantization of the Electromagnetic Field 68

3.2.2. The Bohr Model of the Hydrogen Atom 68

3.2.3. Quantum Mechanics 70

3.2.4. Spin — Additional Energy Levels 70

3.3. The Interaction Between Atoms and Electromagnetic Radiation 71

3.3.1. Maxwell's Theory of Electromagnetic Radiation 71

3.3.2. The Dependence of Atomic Transitions upon EM Radiation 71

3.3.3. Transition Probability and Linewidth of Actual Frequency Standards 72

3.4. Choosing a Suitable Atom 73

3.4.1. The Energy Levels of a Many-Electron Atom 73

3.4.2. The Hyperfine Interaction 76

3.4.3. Criteria for Choosing an Atom 77

3.4.4. The Need for State Selection 78

3.5. The Three Major Examples of Atomic Frequency Standards 78

3.5.1. General Considerations 78

a. Common Functions 78

b. Primary versus Secondary Standards 78

3.5.2. The Hydrogen Maser 79

3.5.3. The Cesium Beam 80

3.5.4. The Rubidium Gas Cell 81

3.6. Summary 83

3.7. References 84

3.8. Bibliography 84

'Published as Nat. Bur. Stand. (U.S.) Tech. Note 399, April 1971. tTime and Frequency Division, Institute for Basic Standards. National Bureau of Standards, Boulder, CO 80302.

65
"Science is the labour and handicraft of the mind . . ." Francis Bacon,

Description of the Intellectual Globe, Ch. 1. A tutorial discussion of the physical basis of atomic frequency standards is given. These principles are then related to the conditions under which an atom can be used as the working substance of a stable and accurate frequency standard. The three primary examples of atomic frequency standards — the hydrogen maser, the cesium beam, and the rubidium gas cell— are then discussed in terms of these

principles and conditions. The functions of the fundamental parts of each device become apparent

through this development.

Key words: Atomic frequency standards; cesium beam; energy levels; hydrogen maser; hyperfine

interaction; Rubidium gas cell; transition probability.

66
3.1. INTRODUCTION

Many people have an interest in modern tech- nological developments. For some, these developments relate to their work and for others, such as students, these devices offer evidence of the realiza- tion of basic physical ideas. Atomic frequency

standards are an important example of such devices.

Not only is their application of significance economically but their design is based upon a foundation

of physical theory which is basic to both physics and

chemistry— the idea of atoms and atomic structure. The purpose of this paper is to state the physical

basis of atomic frequency standards and, having

done so, to show how these principles determine the

design of the specific devices.

As the reader will observe, I have taken a his- torical approach in discussing the atomic theory. In

so doing, perhaps some of the excitement and beauty

of physics will be apparent. If I have been successful

in this effort then it may be that some people who

are already familiar with the atomic theory will find

this work stimulating. Whatever his level of education, the reader should find the essentials of atomic

frequency standards given here.

3.2. ATOMIC ENERGY LEVELS

"The only existing things are the atoms and

empty space; all else is mere opinion"— Democritus

(about 400 B.C.).

Today, the atomistic character of matter is taken

for granted by almost everyone who has been raised

in a technological society. And yet, for 2200 years

(from the time of Democritus), a majority of sci- entists, partly on theological grounds, actively

rejected the idea. As foreign as the atomistic concept is to the human

senses, by the early 1800's the study of gases and

of chemical composition had made atoms a compelling idea. Atomic frequency devices are intimately

tied up with the ideas of atoms, atomic energy levels,

and electromagnetic radiation that developed so

rapidly from about 1800 to 1930. A discussion of

these ideas is essential to the understanding of

these devices. These ideas will be discussed in a

historical manner with a secondary goal of suggesting the profound changes that took place in physics

during this period. The major goal will be to give

sufficient detail that the function of the various

parts of each device will be obvious.

3.2.1. Four Basic Ideas

The knowledge upon which atomic frequency

standards are based developed from the study of

the absorption and emission of electromagnetic

radiation by matter. This study, which is a branch

of spectroscopy, has developed a very elaborate

model of the energy level structure of atoms and

of their interaction with the electromagnetic field

in an attempt to account for the great number of

spectroscopic observations. It is an effort which has

been remarkably successful.

a. The Electron

The atom, as a miniature solar system, is a model

which is familiar to many people. As familiar as

this — the Bohr model — is, 100 years of ingenious

experiment and profound change in theoretical

concept were the necessary preliminary to its birth. At first it was not necessary to think of atoms as having structure, of being made up of a nucleus and

electrons. Progress was made in understanding

gases simply by assuming atoms to be spherical

objects with mass and a small but nonzero radius.

Information about the structure of atoms came from

the electrochemical studies of Faraday around 1834. These experiments showed that atoms had electrical charge associated with them; and in fact that the

charge comes only in discrete amounts — it is not

infinitely subdivisible. But neither the mass nor the

charge of individual atoms were separately known;

rather only the charge to mass ratio. These ratios depended on what substance was used in the experiment, but for any given substance the ratio was

constant. The electron itself, however, could not be isolated

by the electrolysis technique, and another 60 years passed before, in 1897, J. J. Thomson conducted an experiment with electric discharges in gases and was able to isolate the electron. This experiment,

sometimes called a cathode ray experiment, measured the deflection of a stream of particles— elec- trons— the particles being deflected by electric and

magnetic fields. Nevertheless, this experiment was

the same as the electrolysis experiment, in the sense

that it gave only the ratio of charge to mass, elm.

Thomson realized that he had discovered a fundamental characteristic of all atoms because the

character of these cathode rays was independent of

the gases and metals he used in his experimental

apparatus. Another thing Thomson found was that the cathode rays were negatively charged.

The results of Faraday and of Thomson suggested

a radically new concept: atoms are normally electrically neutral; they are composed of very light

particles — electrons — which have a negative charge

and a much heavier other part which has a compensating positive charge. Thomson's work was fol- lowed by the Millikan oil-drop experiment in the

year 1910. Here, Millikan measured the absolute

charge on the electron, and, having elm from

Thompson's work, the mass, m, of the electron

became known.

6. The Nucleus

The positively charged "other part" of the atom was not yet pictured as a very small, and therefore,

very dense core — a nucleus. During the period 1909

to 1911, the work of Ernest Rutherford and his

67
colleagues evolved this profound idea. Their experiment was based on letting alpha particles (the nuclei

of helium atoms) coming out of radioactive radium

strike a thin metal film. A quotation from Rutherford

shows his excitement over the result [1]:

1

"... I had observed the scattering of a-particles, and Dr. Geiger in my laboratory had examined it in detail. He found,

in thin pieces of metal, that the scattering was usually small,

of the order of one degree. One day Geiger came to me and

said, 'Don't you think that young Marsden, whom I am train- ing in radioactive methods, ought to begin a small research?' Now I had thought that, too, so I said, 'Why not let him see if any a-particles can be scattered through a large angle?' I may

tell you in confidence that I did not believe that they would be, since we knew that the a-particle was a very fast, massive

particle, with a great deal of [kinetic] energy, and you could show that if the scattering was due to the accumulated effect of a number of small scatterings, the chance of an a-particle's being scattered backward was very small. Then I remember

two or three days later Geiger coming to me in great excitement and saying, 'We have been able to get some of the a-particles coming backward . . .' It was quite the most incredible event

that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized

that this scattering backward must be the result of a single

collision, and when I made calculations I saw that it was im- possible to get anything of that order of magnitude unless you

took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive center carrying

a charge."

c. The Quantization of the Energy of Atoms

Two more ideas were necessary ground work for the Bohr model. These were (1) the quantization of

the energy of atoms and (2) the quantization of the

energy of the electromagnetic (EM) field. The idea of the quantization of the energy states of matter was conceived by Max Planck around the

year 1900. He introduced the idea in his highly

successful theory of black-body radiation. Black-body radiation had been a subject of longstanding interest in the field of thermodynamics as

well as spectroscopy. The first, and partially suc- cessful theoretical attacks upon this phenomena,

were based upon conventional thermodynamic

theory and the exceedingly successful electro- magnetic theory of James Clerk Maxwell. These

approaches were able to give good results for either

the long or the short wavelength ends of the emission spectrum, but no one model satisfied the entire

spectrum.

Planck based his theory on several assumptions:

(1) Matter (as far as thermal radiation is concerned)

is made up of an exceedingly large number of electrically charged oscillators. This collection contains

oscillators at all possible frequencies. (2) Although

all frequencies are represented, any given oscillator has its own specific frequency, say v, and it cannot

radiate any other. (3) He further assumed that the

amounts of energy that a given oscillator could emit

1 Figures in brackets indicate literature references at the end of this Chapter.

were given by En = nhv, where v is the characteristic frequency of the oscillator, n is an integer

(1,2,3,. . .), and A is a constant. The quantity, h, is a fundamental constant of nature and is known as Planck's constant. The third assumption is the third

of the four basic foundation stones of Bohr's theory.

So Planck's ideas succeeded in predicting blackbody radiation, but nobody, including Planck, was

comfortable with them. To quote Holton and Roller

[2]:

"Planck himself was deeply disturbed by the radical character of the hypotheses that he was forced to make, for they set aside some of the most fundamental conceptions of the 19th-century science. Later he wrote that he spent many

years trying to save physics from the notion of discontinuous energy levels, but that the quantum idea 'obstinately with- stood all attempts at fitting it, in a suitable form, into the framework of classical theory . . .' "

d. The Quantization of the Electromagnetic Field

In 1905, Einstein proposed the following relation as an explanation of the photoelectric effect: hv=P+Ek, max where v is the frequency of the elec- tromagnetic radiation striking the surface from

which electrons are emitted, Ek, max is the maximum

kinetic energy of these electrons, P is a property of

the metal being studied, and h is a constant — independent of the metal being studied and of the

frequency v. Eventually, careful measurements

showed that this constant, h, was numerically equal

to Planck's constant, and, with the passage of time,

the two constants have come to be accepted as identical— as representing the same immutable aspect of nature. The idea behind the above equation was that light was quantized — that its energy came in discrete

amounts, hv, that it had a particle-like as well as a wave-like character. This new idea was no more

acceptable to the majority of scientists than was

Planck's proposal that the energy states of matter were quantized. One might have thought, however,

that Planck would have maintained a reserved

silence— after all, Einstein's idea and his own were

so analogous and the two constants appeared to be

numerically equal. But he did not. In 1910 Planck

wrote that, if this new theory of light were accepted

"the theory of light would be thrown back by cen- turies—for the sake of a few still rather dubious

speculations" [3].

3.2.2. The Bohr Model of the Hydrogen Atom

With these four ideas and with the boldness characteristic of these ideas, Niels Bohr, in 1913, pro- posed his now famous model of the hydrogen atom. Before discussing the Bohr model, however, it is necessary to admit that it will not allow us to explain

all the details of atomic frequency standards. One

reason is that the Bohr theory will not correctly

predict the intensities of the absorptions and emissions that an atom can undergo. Even so, the Bohr

68
model is of much more than historical interest. For

one thing, it does incorporate the majority of the

ideas which we need, and it does provide a mechanistic, intuitive picture of the energy levels of an

atom. Bohr was faced with the problem of both acknowledging the idea of the nuclear atom and of predicting

its stability. Precisely what went through Bohr's

mind is something that is not known to us, but the

similarity between his problem and planetary motion

is obvious: In the simplest case there is the sun

(nucleus), a very massive body, and a planet such as the earth (electron). The two bodies attract one

another with a force which is inversely proportional

to the square of their distance of separation.

Bohr knew that the radiation from an atom was

associated with its electrons because in 1897 (just after the discovery of the electron by Thomson)

Zeeman and Lorentz showed that the radiation coming from an atom was due to a charged particle

whose charge-to-mass ratio was the same as that

for the electron. Maxwell's theory predicts that if an electron is moving in a circular path with an

angular frequency, ft, it will radiate electromagnetic

ft energy at a frequency, v = 2^- This is because the

electron is charged and because of the acceleration

experienced in circular motion. The difficulty with

the planetary idea is that, as the electron radiates

away its energy, it slows down and gradually spirals

into the nucleus. Bohr dispensed with the problem of

a nuclear crash by assuming an arbitrary restriction. Bohr's analysis was based on two equations. The

first equates the attractive force between the

nucleus and the electron to the product of the radial

acceleration of the electron and its mass. The sec- ond equation sets the angular momentum of the

electron, mvr, equal to a constant, rc/i/(27r). Here, V

is the magnitude of the velocity of the electron upon

its circular orbit, r is the radius of this orbit, m is the mass of the electron, n is an integer (1, 2, 3, . . .), and h is Planck's constant. This second equation is completely arbitrary and is in fundamental disagreement with Maxwell's electromagnetic theory

because it implies that an electron can travel around

a circular path without radiating.

Bohr solved these two equations for the "allowed"

orbits, i.e., those particular values of the radius

which satisfy both conditions. This results in r=n2 c, (3.1)

where c is a constant. The smallest value of the inte- ger n is 1 (unity), and when the electron is in the orbit corresponding to this radius it is said to be in its ground state. (The definition of "ground state" has to be modified for a many-electron atom.) This result is one of the major successes of Bohr's theory because

if the constant is evaluated it is found that r, for n—1, is approximately equal to 0.5x10" 10 m. This is in good agreement with the size of the hydrogen

molecule as obtained from the kinetic theory of gases. The second important result of Bohr's analysis is the expression of the total energy E of the atom in terms of the integer n. The result is

E = -

n

2 8e2/i2

'

where m and h are as defined above, e is the charge

of the electron, and €o is the dielectric constant of free-space. By taking the difference between the

energies of two orbits, an equation is obtained which

predicts many important observations of optical

spectroscopy. The result is

p _ F , = jn^_ (\_ j_

(3.2;

When energy is absorbed or emitted the electron

makes a corresponding change in orbit — this is commonly called a transition. Figure 3.1 shows the

energy level diagram for the hydrogen atom. The

Fig. 3.1. The energy level diagram of the hydrogen atom as obtained from the Bohr theory. The wavelengths (of the Lyman

Series) are given in nanometers, nm (1000 Angstroms equals 100 nm).

69
vertical lines represent possible transitions. To

understand the experimental results of optical spec- troscopy it was useful to group the various emissions. These groups were given names according to those people who had devoted the most study to them, Lyman, Balmer, etc. For the hydrogen atom,

transitions to the n—1 level involve radiation whose

wavelengths are of the order of 100 nm (1000 Angstroms). This corresponds to a frequency of 3 X 1015 hertz. (A hertz is equal to one cycle per second.)

However, when the effects of the intrinsic magnetic

moments of the electron and the nucleus are included, it turns out that additional levels are avail- able whose spacings are at microwave frequencies

(somewhere between 109 and 10 u hertz). Before dis- cussing these effects, I need to talk about an entirely

different basis for calculating the characteristics of an atom. This approach is essential for obtaining the

probabilities of transitions between the various

levels— a subject which is crucial to atomic fre- quency standards. This theory is called quantum

mechanics.

3.2.3. Quantum Mechanics

It was not just its inability to account for all of

the experimental data that left something to be

desired in the Bohr theory. It was the fact that this theory— just as the black-body theory of Planck

and the photoelectric theory of Einstein — was an

intellectually uncomfortable, ad hoc, combination

of the old ideas of classical physics and the new

idea of quantization. These conceptual difficulties were removed with the advent of quantum mechanics

This new theory was developed separately, and

nearly simultaneously, by Erwin Schrodinger and

Werner Heisenberg about 1926. The work of these

two men, at first sight, seemed quite different; but

it was soon shown that, despite their difference in mathematical form, they were physically equivalent. A brief description of Schrodinger's theory is given here. Schrodinger's theory takes the form of a partial differential equation. Specifically, it is an

equation involving the rate of change of a quantity,

(//, with respect to the variables of space and time. In its original form, this equation was designed to predict the possible values of energy which could

be possessed by a material body. In its generalized

form it is used to calculate any measurable property

of a particle. The quantity if) is usually referred to as a wave function. The physical meaning of this quantity was, at first, quite uncertain. It is now

generally agreed, however, that the square of the

magnitude of «//, at any given point in space, repre- sents the probability of finding the particle at that point in space. This probabilistic interpretation is perhaps the

key feature of the new physics — of quantum me- chanics—which says that particles have a wave-like

aspect. Einstein based his photoelectric theory on

the idea that light had a particle-like property. In

1924, Louis de Broglie turned the cart around by

suggesting that a particle has a wavelength associated with it. In other words, a particle has some of

the characteristics of a wave. In particular he said

that the wavelength, K, of a particle should be given

by \=— where h is Planck's constant and the

product, mv, is the momentum of the particle. To

quote de Broglie [4]: "Determination of the stable motion of electrons in the atom

introduces integers; and up to this point the only phenomena

involving integers in physics were those of interference and of normal modes of vibration. This fact suggested to me the idea

that electrons, too, could not be regarded simply as corpuscles, but that periodicity must be assigned to them."

Schrodinger's equation brings together in a

natural way the localized (what we usually call the

particle aspect) and wave-like aspects of a particle.

This is very clearly seen in the solution of

Schrodinger's equation as applied to the hydrogen

atom. Some of the results of the solution are:

(1) The atom can have only certain discrete values of energy, and these values are associated with an inte- ger, n. This is qualitatively and quantitatively the same result as obtained from the Bohr theory, but,

(2) although for any given energy the electron has a high probability of being found in a restricted region

about the nucleus, it has some chance of being found

anywhere, and certainly it is not to be thought of as being localized on orbits as in the Bohr model.

(3) In solving for the H atom it is found that two more

integers, / and mi, occur as a natural result of the

solution. Thus we get three numbers, n, I, and mi,

each of which are integers. These integers are called

quantum numbers, and they represent the fact that here three properties of the atom are quantized.

They are: The energy, represented by n; the total orbital angular momentum, represented by /; and

the projection of the total angular momentum, along some specified direction, represented by mi. The

importance of these additional quantum numbers

will be discussed in Section 3.4.1.

It is apparent that the theory of matter and elec- tromagnetic energy has gradually become more and more abstract, less and less intuitive. Despite the

fact that quantum mechanics is a profoundly differ- ent concept than that used by Bohr, he was prepared

to accept the increasing abstraction — he wrote [5]:

"To the physicists it will at first seem deplorable that in atomic problems we have apparently met with such a limitation of our usual means of visualization. This regret will, however, have to give way to thankfulness that mathematics in this field, too, presents us with the tools to prepare the way for further progress."

3.2.4. Spin — Additional Energy levels

The spectrum of the hydrogen atom, when looked

at with sufficient precision, is found to have some

significant disagreements with the Bohr model.

70
These discrepancies take the form of shifts in energies of the various levels. Looked at on an even finer

scale, it is found that nearly all of the lines split into two lines so that there are more levels in the actual

spectrum of hydrogen than Bohr predicted. For a time it appeared that if Bohr's theory were generalized to include both elliptical orbits and Einstein's

theory of special relativity (the Bohr-Sommerfeld

theory), the shifts (but not the extra lines) could be

accounted for. Later, however, it became clear that there were inconsistencies in this approach. Then,

in 1925, Uhlenbeck and Goudsmit showed that the

observed shifts in energy could be obtained by

assuming that electrons intrinsically possess angular

momentum and a magnetic moment. In 1924, W.

Pauli had suggested that the properties of intrinsic angular momentum and magnetic moment be attri- buted to the nucleus of an atom as a possible means

of explaining some of the other details of atomic

spectroscopy. It is now commonly accepted that these two properties are as much a part of the

intrinsic character of electrons and nuclei as are those of mass and charge. The two properties of

intrinsic angular momentum and magnetic moment

are inseparable and are often referred to by the

single name-spin.

The existence of the spin properties of the

nucleus and electron means that there are additional

forces between these two particles for which Bohr's

theory did not account. Thus, in the more detailed

theory, the energy level structure is modified. For

our purpose, the result of all this is that there are

additional energy levels, some of which have a separation corresponding to microwave frequencies.

3.3. THE INTERACTION BETWEEN

ATOMS AND ELECTROMAGNETIC

RADIATION

Section 3.2 discussed the idea that any given atom

can only exist in certain discrete states and that each state has a definite energy. If an atom is not

able to interact with other atoms it can only change

its state by absorbing or emitting electromagnetic

(EM) energy. This absorption (or emission) is the means whereby we know that the energy level structure exists. In the case of atomic frequency

standards the EM radiation which causes these

transitions is directly related to the output of the

standard. It is the purpose of this section to show

that the probability of making these desired transi- tions depends upon the frequency and upon the

intensity of the EM field and that the atom must have

a non-zero magnetic moment. In this paper I consider only elemental atoms and not molecules. If the output frequency is to be well defined, it is also necessary to have the atoms interact with the EM

field for a fairly long time.

3.3.1. Maxwell's Theory of Electromagnetic

Radiation

The earliest work in spectroscopy involved look- ing at the various colors of light that were emitted

and absorbed by heated solids, liquids, and gases. The detailed work in this field had begun by the mid18th century. At this time, light was generally held

to be corpuscular in nature, i.e., not a wave. By the

first part of the 19th century, however, the tables had been turned in favor of a wave theory of light.

This was due in major part to the work of Thomas

Young and Augustin Fresnel in studying the phe- nomena of diffraction, interference, and polarization.

The theoretical work of Maxwell and the experimental work of Heinrich Hertz near the end of the

19th century seemed to give the final, irrefutable

evidence in favor of a wave theory as opposed to a corpuscular theory of light.

By the mid-19th century the most important facts of some two centuries of study of electricity and of magnetism were embodied in four equations. It was Maxwell s remarkable contribution to realize that if one of these four relations (Ampere's law) were modified it would resolve a problem in understanding the conservation of charge, and it would

allow the four equations to be combined to form wave equations for both the electric and magnetic

fields. That is to say, these equations predicted

EM radiation. It was only some five years later, in 1888, that Hertz conducted experiments which veri- fied Maxwell's predictions including the prediction

that the wave would propagate with the speed of

light. The obvious conclusion is that light is an

electromagnetic wave!

Maxwell's theory of the EM field says that the

field's intensity can vary continuously from zero to any arbitrary value. In Section 3.2.1.d. , however,

Einstein's studies of the photoelectric effect were

discussed, and his conclusion was that the energy

of a light wave is quantized. (Actually, EM radiation

has both particle-like and wave-like properties. In most experimental situations, however, one aspect

predominates over the other.) Although the particle- like aspect of radiation was important to Bohr in his theory of the atom, for most of our purposes we need

only to make use of the fact that the radiation that causes transitions is electromagnetic in nature and

to treat its energy as continuously variable. (But see

the discussion on particle detection in sec. 3.5.1. a.)

3.3.2. The Dependence of Atomic Transitions

upon EM Radiation

The dependence of the transition probability

upon the EM field was first studied by Einstein. This

work (which was a further examination of blackbody radiation) assumed that there were two

mechanisms for emission of radiation — induced and

71
spontaneous — and, also, that absorption, like in- duced emission, depended on the strength of the

EM field and the duration of the interaction. His

calculations showed that the probability per atom

per unit of time for induced emission Bnn' was

equal to that for absorption B n

< n

Bnn' = Bn'n. (3.3)

This is a very important fact and will be discussed

further in Section 3.4.2. He also found that the

coefficient for spontaneous emission A nn < was related to the coefficient B nn < by A nn > = —-=

Bn n'. In

the microwave region (say W1 ' hertz) — —is a very

small quantity, and hence spontaneous emission —

which causes noise — has, to date, not been a problem in atomic frequency standards. (Noise is any

disturbance that tends to obscure the desired

signal.) It is, however, an important factor in the

infrared and visible radiation regions, as, for ex- ample, in state selection for the rubidium gas cell (see sec. 3.5.4). A quantum mechanical (QM) analysis gives

similar results. The result that the induced emission and absorption probabilities (per atom) are

identical is obtained in both cases. In the QM case

these probabilities again depend on the intensity of

the EM field and upon the duration of interaction, but because it can be more detailed, the QM

analysis produces some new results which are of

particular use in atomic frequency standards. In the Einstein calculation, no explicit dependence

upon the frequency v is obtained for the coefficient Bnn', but the QM result does have an explicit

frequency dependence. In atomic frequency standards the atoms are in a gaseous state at very low

pressure when interacting with the EM field. To a very good approximation, we need only consider the

interaction with a free atom, and, if the QM analysis

is done for this case, the following is obtained:

(IT />„„' = sin 2 0sin2 y (3.4)

Pnn' is the probability of making a transition from

state n to n' after a time interval t if the atom was in state n at the beginning of the interval. The quantity sin 6 is defined as — 2b/a, where

a= [(a0 -n) 2 +(2b) 2 yi2

. Here, CL 0 = ^ (EnEn'), and b is the product of the magnetic moment

of the atom and the strength of the EM field which

is exciting it. The symbol fl is defined as 2irv. One

of the things this result shows is that for Pn n' to be

nonzero, the atom must have a nonzero magnetic

moment when in either state n or n . In figure 3.2, Pnn ' as given by eq (3.4), is plotted versus (Cl—Cl0 )l(2b) for several cases. The dashed

curve shows that if the radiation frequency is equal

to the frequency difference associated with the two

levels, i.e., 2ttv = Qo= {E n —En >) then — after

the time interval t= 77-/ (26) — the atom is sure to have made the transition between state n and state n . The dashed curve assumes that the EM field is interacting with a single atom or a group of atoms

all moving with the same velocity. In a real device the atoms have different velocities; the solid curve shows the result of averaging

eq (3.4) over a Maxwellian velocity distribution. This

curve applies to the specific case of the interaction

time t being equal to 1.27r/(2b). This is the inter- action time for which the transition probability will be largest. The dotted curve gives the transition

probability for t much greater than 7r/(2b). The basic

conclusion from eq (3.4) and figure 3.2 is that for a given value of the interaction time, the transition

probability will be maximized for H = n0 and that

this maximum value depends upon both the magnetic moment of the atom and the strength of the EM

field.

3.3.3. Transition Probability and Linewidth

of Actual Frequency Standards

Until now I have been emphasizing the maximum

value of the transition probability curve— its value

when Cl = Ho. The extent to which this curve spreads

out is also important, and I will now discuss this point.

The purpose of a frequency standard is to provide an output which is as nearly a single frequency as is possible. There are certain features of the real world

that inevitably cause the output of an actual standard to be less than perfect. The nonzero width of the

transition probability curve, as displayed in fig- ure 3.2, is an important example of one of these

degrading features. In an active device — a device

which generates its own EM field — the meaning of

this nonzero width is that the device emits observable energy over a range of frequency. [The line- width of a resonance curve is usually defined to be

the difference (in frequency) between those two fre- quencies at which the intensity is one-half its peak

value.] The intensity of the undesired energy falls off rapidly as its frequency deviates from vo by more

than one linewidth.

A passive device— a device where the EM field is supplied by an external source — also has a nonzero

linewidth.

We are now in a position to see two important

requirements of a high-quality frequency standard.

First, the peak value of the transition probability

must be high enough that the signal can be seen above the noise, and second, the interaction time

must be long enough to make the linewidth suffi- ciently narrow. In Section 3.5, the means by which

these two goals are achieved will be discussed. In the case of atomic frequency standards, there

is a useful relationship between the linewidth, W

,

of the frequency response and the interaction time r.

72
/

V\

/

/ —f

1 /

1 /

I /

/ / y //

// y

/ • V

• V

— — \

ft \

/•) i\

/

1

.7 1

\ \\ \ , s~ •

-~~7

"

1 1

\ N

\ \ 10 12 3 4 5

(n-n0)/2b

Fig. 3.2. Theoretical curves o{Pnn '- The dashed curve is obtained from eq (3.4) by setting t = 7r/(2b). The full curve is obtained from an average over the velocity distribution and with an optimum t(t = 1.27r/(2b)). The dotted curve comes from an

average over the same velocity distribution but with j > ir/(2b). (See text for further details.) (This figure is a modification of

Fig. V.l of Molecular Beams by Norman F. Ramsey, copyright by Oxford University Press, 1956.).

For example, in an ideal cesium beam (monovelocity beam) using "two-cavity" excitation (see

item 4 of sec. 3.5.3), W and t are related by

Wt=1/2. (3.5)

For other high quality atomic frequency standards,

the Wr product is also of the order of unity. Equation (3.5) makes the importance of the parameter t obvious: The linewidth of the atomic resonance improves linearly with increasing t.

3.4. CHOOSING A SUITABLE

ATOM

Sections 3.2 and 3.3 discussed two fundamental

facts of physics, atomic energy levels and the inter- action of atoms with electromagnetic fields. These

facts are the basis for atomic frequency standards. We need now to decide how to choose a

suitable atom.

3.4.1. The Energy Levels of a Many-Electron

Atom

The purpose of this subsection is to describe the

energy level structure of atoms with more than one

electron. In order to understand this structure it is useful to consider a basic experimental result of

spectroscopy.

For simplicity's sake, consider the simplest of

atoms — hydrogen. If a gas made up of hydrogen

atoms is heated to a high temperature, then it will

emit EM energy. This energy is emitted at discrete

frequencies. In the range of visible light, the standard means of observing these radiations is to use an

optical spectrograph. This device causes the energy

at the various frequencies to be split up spatially so

that if it is directed onto a strip of photographic film,

the developed film shows a group of lines known as the Balmer Series. These are so labeled in figure 3.3. The response of the photographic film is limited to visible light but if it could respond to higher and to lower frequencies, additional groups of lines, which

are also shown in figure 3.3, would result. For any

given group, it can be seen that the lines become

very closely spaced towards their high frequency

(short wavelength) end. The terminal frequency for each group is indicated by dashed lines in the figure.

The dashed line for a given group is called the series

limit for that group. The importance of the series

limit is that it tells us about a particular energy level which is common to every line in the group. Now,

the emission spectra of gases of any other kind of

atom are fundamentally the same as that of hydrogen. This basic characteristic is often hard to see in the other atoms because there are more energy

levels involved and sometimes the various series

(groups) overlap. Nevertheless the spectra of any

atom is composed of an infinite number of these

series (groups) of lines. Because of this, the fre- quency of any line of any series in any atom can be

obtained from an equation of the same form as eq (3.2). The equation has the general form:

v=T2 -Tl . (3.6)

T2 and 7\ are called spectroscopic terms. T2 is the

generalized common term of a given series of lines. As spectroscopists began to look more closely at the spectrum of atomic hydrogen, they found that most of the lines of the spectrum, which had previously appeared to be single, were actually double.

Before having discovered these double lines, they

had found that to classify all the lines in the spec- trum unambiguously, they needed two (not one)

quantum numbers, n and /. Now, with double the

number of lines, four quantum numbers were necessary. The extra numbers that are needed are s, the

quantum number of the spin of the electron, and j, the quantum number of the total angular momentum

of the electron. The spectra of all other atoms also require four quantum numbers to characterize each

line (energy level). (I should state here that I am

temporarily ignoring the extra complication of the

interaction of the atom with an externally applied

dc field.) At first these four numbers were just an

empirical scheme for specifying the levels, but in time they were given meaning in terms of the struc- ture of the atom. The lables used are the principle

number n — which is analogous to the n of the Bohr

theory; the total orbital angular momentum number L; the total electron spin number S and the total angular momentum number J.

73
03 5000

2000

1000

500 -

250 -

200

150-

125

100 -

mi

PFUND SERIES

BRACKETT SERIES

RITZ-PASCHEN SERIES

^BALMER SERIES

LYMAN SERIES

Fig. 3.3. Schematic diagram of the emission spectrum of the hydrogen atom. The intensity of the emission is roughly

indicated by the thickness of the lines. The dotted lines are

series limits. The wavelength scale is in nanometers. (This

figure is a modification of Fig. 8 of Atomic Spectra and Atomic

Structure by Gerhard Herzberg, copyright by Dover Publications, 1944.)

In atoms with more than one electron, there is not only the electrostatic force between an electron

and the nucleus, and the force between the orbital and intrinsic moments of an electron, but also the

electrostatic and magnetic forces between electrons. These forces determine the energies and therefore

the frequencies corresponding to the possible transi- tions between states. An important reason for using

n, L, S, and J in labeling the levels is that each of these quantities is usually important in characterizing the energies of the levels. The quantity L is formed by means of certain quantum mechanical

rules from the /'s of the individual electrons. The

quantity S is formed in a similar manner. The number J is then formed from L and S, again, using the

appropriate quantum mechanical rules. Now, you

may ask, "Why were all the /'s combined to form L

and s's to form S, why not combine the individual /'s and s's to form /s (the total angular momentum for individual electrons) or even some intermediate

scheme?" The method used here implies that the

coupling of the individual orbital momenta and the

individual intrinsic momenta is very strong with

respect to the coupling of the orbital and intrinsic momenta of a given electron. This is commonly

called Russell-Saunders coupling and usually

applies to the ground state of any atom; this is the

state of interest to us. To gain insight into the quantum number n, and

as a general aid in understanding the energy level structure of an atom, the Pauli Exclusion Principle

is extremely useful. One of the most prominent features of nature is the periodic behavior of the elements. This periodicity expresses itself in the emission (and absorption)

spectra we have been discussing and in the chemical

behavior of the elements as first summarized in 1896

by Dimitri Mendeleev. The periodicity is explaim

able by the Pauli Principle. This principle is to be

taken as a postulate, as fundamental as the concepts

of mass and charge. Wolfgang Pauli, in 1925, pro- posed this principle as a hypothesis based upon his observations of the spectra of the alkali metals. The

principle says: "In an atom there never are two elec- trons having the same group of four quantum numbers." The numbers referred to are n, l,j, and rrij. (The values of m} are the projections of j along a dc

magnetic field.) In his book on quantum mechanics,

Persico [6] says: "It may be said that the entire

theoretical interpretation of spectra is based upon

this principle and constitutes an impressive confirmation thereof." Using Pauli's Principle as a theoretical guide, calculations show that, roughly

speaking, the electrons gather into localized groups

called shells. Figure 3.4 displays this result. These

shells are analogous to the orbits of the Bohr theory

and are labeled by the quantum number n. To be

rigorous about the interpretation of figure 3.4 would

require a much deeper discussion of quantum

mechanics than the purpose of this article allows. The point, however, is that the Pauli Principle

determines the number of electrons that can be

74
0.2 0.4 0.6 0.8 1.0 1.2

r (10" 1 °m)

Fig. 3.4. Charge distribution for the ground states of H, Li+, Na+

, and K+

. The concentrations of charge (corresponding to the maxima) in these distributions are analogous to the orbits of the Bohr theory and are called shells. The area under the curves is proportional to the number of electrons in the atom. The vertical axis is equal to r^i//* where r is in meters. (This

figure is a modification of Fig. 54 of Atomic Spectra and Atomic

Structure by Gerhard Herzberg, copyright by Dover Publications, 1944.)

located in each shell. The letters K, L, and M are

the traditional labels of the first three shells. Another

noteworthy thing observable in this figure is that the

radius of the K shell (and the L shell) decreases

markedly as we go to atoms with more electrons. The reason for this is that the heavier atoms have a nucleus with a larger charge and therefore the

attraction on the electrons in the inner shells is larger.

At this point the discussion can be considerably

simplified by admitting that we are not interested

in the most general energy states of an atom that could possibly occur but rather in those that have

to do with an atom's emission electrons. In atoms

other than the noble gases, there are one or more

electrons which are much more easily caused to go

into an excited state than are the rest. These elec- trons are called emission electrons because the

emission spectra of an atom is usually due to them.

These emission electrons lie outside the filled shells and, to a first approximation, the rest of the atom

(the nucleus and nonemission electrons) appears as

a point charge to these electrons. Now, in the usual case there is more than one emission electron and

the energy of these electrons depends not only upon

their quantum number n (they are usually in the same shell), but upon the "sum", L, of the /'s of the emission electrons and also upon their S and J

values. The values that L, S, and J can assume are

restricted by the Pauli Principle.

To sum up, any given term (energy level) is labeled

by the four quantum numbers, n, L, S, and J. Figure 3.5 is an energy level diagram for the single

emission electron of potassium. This figure makes

use of the quantum numbers. The number n identifies the shell (see the discussion of the Pauli

Principle for the meaning of the word shell). The

capital letter that heads each column represents the

total orbital angular momentum L. The letter S

(not the quantum number S) means an L value of 0; P means an L of 1; D means an L of 2; and F means

Fig. 3.5. The energy level diagram for the emission electron of the potassium atom. The dependence of energy upon the principle quantum number n; the total orbital angular momentum; and

the total angular momentum is shown. The figure gives the wavelengths (in nm) for some of the transitions. See the text for an explanation of the labeling of the levels. (This figure is a modification of Fig. 28 of Atomic Spectra and Atomic Structure by Gerhard Herzberg. copyright by Dover Publications. 1944.)

75
an L of 3. The superscript is equal to 2S + 1. (I am

now talking of the quantum number S.) For potassium, S = i, therefore, 2S+ 1 = 2. The subscript is the J value of the energy level. For S =i there are only two possible values for J, L + i and L — \ (except

that for L = 0, J can only be equal to \)

.

For small values of n there is an observable vertical separation (an energy difference) between the 2P3/2

and 2 Pi/2 states. The amount of separation between

levels with different J value depends upon L as well as upon n, and it can be seen that levels 2D5 / 2 ,3/2 and levels 2 F7/2,5/2 are so close in energy that they

can't be distinguished on this plot. Thus, they are

not separately displayed. From figure 3.5, it is not apparent that it is necessary to specify S. But in spectra where S also changes, then the need for the extra quantum number becomes apparent. Note

that the ground electronic state of the emission

electron is 4

2 Si/2 where the 4 represents the

fourth shell.

3.4.2. The Hyperfine Interaction

The magnetic interaction between the nuclear

spin— which is symbolized by the letter /—and the

spin of an electron is called a hyperfine interaction.

It is this interaction which causes the desired

spacing between the pair of energy levels used in several important frequency standards. Figure 3.6(a)

shows how the ground electronic state 2 Si/ 2 of the

hydrogen atom is split into two states by the hyperfine interaction. One of these two states (the F=l

state) is then further split by the dc magnetic field, H. This figure also shows the dependence of the

energies of each level upon H.

The letter F labeling the ordinate in figure 3.6(a)

represents the quantum number of the total angular

momentum of the entire atom. This number is formed from J and / just as J is formed from L and

S. That is, Fmax = J + I and Fmin =\J —1\. Every

integer value in between Fmax and Fmin is also al- lowed. The nuclear spin has only one possible value,

and, because we are interested only in the 2 Si/2

state, J has only the one value, 1/2. Thus, for the

hydrogen atom, which has an / value of 1/2, there

are only two possibilities for F. Here, F max = 1 and

^min = 0> ar»d no intermediate values are possible

(see fig. 3.6(a)). I have restricted the atom to be in the 2 Si/2 electronic state for reasons to be discussed

in Section 3.4.3. To deal with an external magnetic field we need

yet another quantum number nip. This new number

76
refers to the possible projections of F along the

direction of H. Quantum mechanics allows F ^

ttif = —F. Therefore, for F= 1, the possible values

of mp are 1, 0, and —1. For the hydrogen atom,

figure 3.6(a) shows that the two energy levels be- tween which we want transitions to take place are

the F — l, mF = 0, and F = 0, mF = 0. This is so because these are the levels which have the least dependence on H for low values of the field (see

item (f) of sec. 3.4.3). [This transition is sometimes

symbolized by F, mF —l, 0 <^ 0, 0.

]

3.4.3. Criteria for Choosing an Atom

I can now list those characteristics that are desired in an atom for the purpose of a frequency

standard and then, based on the Pauli Principle

and the spectroscopic information discussed above,

decide which atoms are most suitable. The following are criteria for choosing a suitable atom:

(a) There should be a high probability of finding

the atom in the desired state.

(b) The transition frequency should be in a useful

range.

(c) The magnetic moment should be large enough

for a useful interaction with the EM field and

also for the purpose of state selection.

(d) The atom should be quite inert to interaction

with like atoms or with any container in which

it is stored.

(e) The atom should have a low ionization potential if the transition is to be sensed by means

of ionized particle detection.

(f) The energy levels between which the desired

transition occurs should have as little depend- ence as possible upon H.

As each of these items is discussed it will become

apparent that several of these requirements are mutually contradictory, and a compromise has to be

reached.

Item (a) basically requires that the desired transi- tion be due to the ground electronic state of the

emission electron and that the first excited state of

this electron should be significantly higher in energy. Hydrogen, rubidium, and cesium are the

three atoms that have seen most use for frequency

standards, and one reason is that the ground elec- tronic state in each case is 2 Si/2. This type of state has, in general, the highest possible separation from

the first excited state. The question of what is a useful range for the

transition frequency— item (b)— involves many

things. The one aspect of this question which

properly belongs in this article was discussed above.

This subject is the hyperfine interaction. The reader

should be reminded, however, that a study of atomic

frequency standards is incomplete if these other

topics are not considered. For example, in masers,

the absolute value of the transition frequency influ- ences the ease of detecting the maser output. In passive devices, such as the cesium and rubidium

machines, the spectral purity of the external micro- wave signal depends upon the transition frequency.

For a discussion of these and other points, see refer- ence [7]. When all the considerations are taken into account, it turns out that a transition frequency lying

in the microwave range is quite desirable. The

hyperfine interaction often produces energy level spacings in this region.

The importance of the magnetic moment of the

atom — item (c)— was discussed in Section 3.3.2. It was pointed out that if a frequency standard is based

upon a magnetic interaction, and the highest quality

devices are (I continue to restrict myself to devices

based on atoms and not molecules, but see the summary), then the net magnetic moment must be nonzero. State selection, to be discussed in Section 3.4.4, also requires that the net magnetic

moment be nonzero. In the most general case, the net moment is made up of contributions from the orbital and spin magnetic moments of the electrons and

from the magnetic moment of the nucleus. The

hyperfine interaction (which determines the transi- tion frequency) is crucially dependent upon the

nuclear moment, but, because the nuclear moment

is about 1000 times smaller than that due to the elec- trons, it can be ignored in calculating the net magnetic moment. If the net magnetic moment is too

large, then the interaction of the atoms with themselves and with their container will result in broadening the linewidth, W, and in a frequency shift. It turns out that the parameters involved in practical

frequency standards are such that an atom in the

2 Si/2 state (hydrogen and the alkali metals, Li, Na,

K, Rb, Cs, and Fr) will satisfy the magnetic moment

requirements. This is fortunate because an atom in

this state also best fits the requirement of item (a). It can be seen that the desirability of being inert —

item (d)— is in conflict with item (c). The noble gases

best fit the inert requirement, but, because their

ground state is ! So, they have zero net magnetic

moment. Atoms whose ground state is 2Si/2 (such

as H, Rb, and Cs) form a reasonable compromise

because they satisfy items (a), (b), and (c) and yet

have a very small magnetic moment.

But the alkali metals are surely not chemically

inert — they are among the most chemically active of

all of the elements — and a large price is paid in the

accuracy of the hydrogen maser (see sec. 3.5.2)

because of this. Item (e) points up again the conflict between the

various requirements. One way of sensing that the

desired transition is occurring is to collect the atoms

which have made the transition. This is done by

ionizing those atoms and collecting the charged particles thus generated. If an atom is to be ionized

efficiently then its ionization potential must be fairly low. But a low ionization potential guarantees high

chemical activity so, again, there is a conflict. The

alkali metals all have low ionization potentials, and

cesium is particularly good in this regard.

An external dc magnetic field — item (f) — is another source of frequency shift. For example, even

77
using the F = 1 , mF = 0 and the F = 0, mf =0 energy

level pair in hydrogen, several layers of magnetic

shielding are required if this shift is to be reduced to a tolerable level.

3.4.4. The Need for State Selection

In order for any atomic frequency standard to work, it is necessary to have a difference in population between the two energy levels of interest. That

is, there need to be more atoms in one energy level than in the other. The reason for this is that the

absorption probability, Bn 'n, is equal to the induced

emission probability, Bn n' (see sec. 3.3.2). Thus, if there are the same number of atoms in the upper

and lower states, then energy is absorbed by atoms

in the lower state as fast as it is emitted by those in the upper state. In a maser, there must be more

atoms in the upper than in the lower state. It is this excess in the upper state that provides the energy for the emission of EM energy. In the passive devices, a population imbalance is required because, if the

upper and lower states are equally populated, there

is no net response to the externally applied radiation.

About 1860, James Clerk Maxwell and Ludwig

Boltzmann considered the problem of the relative population of the energy levels of a system with

many possible levels. Equation (3.7) gives the result applicable to our case.

n \ —{En -En'Y\ , 0 ^

=eXP [ kf J" (3 - 7)

Here, n is the number of atoms in the upper

energy state whose energy is En , and n' is the number in the lower state whose energy is E„>. The absolute temperature is given by T, and k is Boltzmann's

constant. For hydrogen, the energy difference between the

upper state (F=l, mF = 0) and the lower state (F — 0, nif — 0) is so small that the ratio n/n' is greater than 0.99. That is to say, for all practical

purposes, there are the same number of atoms in each state. Under these conditions the maser will not operate. The atoms in the lower state must be

removed from the beam of incoming atoms (see

sec. 3.5.2).

Any transition in the microwave region will have

n/n' ~ 1, and so state selection will also be required

in the cesium beam and rubidium gas cell.

3.5. THE THREE MAJOR EXAMPLES OF ATOMIC FREQUENCY

STANDARDS

3.5.1. General Considerations

The prime emphasis of this section will be upon

the relationship of the major parts of each device to the physical principles discussed in the preceding

sections. Some comment will be made on the per- formance characteristics of the devices, but a

detailed discussion is beyond the scope of this

article.

a. Common Functions

There are three functions that each device must

perform. First, the atoms must be in the proper condition to emit EM energy (active device) or to be

responsive to an external source of EM energy (passive device). Second, the atoms must be kept in interaction with the EM field long enough that the

transition linewidth is acceptably narrow. (The EM

field configuration must, of course, be such that an

interaction with the atoms can occur.) Third, some

means of detecting that transitions are occurring

must be provided.

For the hydrogen, cesium, and rubidium devices,

the transition' frequencies are in the microwave

region, and, therefore, to place the atoms in a proper

condition, state selection is necessary. These ideas

are discussed in Section 3.4.4. The means by which the H, Cs, and Rb devices

achieve long interaction times are clearly evident

in their mechanical construction, and this construction has a strong effect on their performance

characteristics.

Of the three devices, the hydrogen maser is the

only active one, and the fact of its oscillation is evidence that transitions are occurring.

If we define the word particle in a general sense, then particle detection describes the means by

which transitions are detected in each of the other

two devices. The collection of ionized atoms, as dis- cussed in Section 3.4.3 (item e), is the usual and

obvious examples of particle detection. But, as mentioned in Section 3.2. l.d, electromagnetic energy has

a particle-like as well as a wave-like character.

When the frequency of the EM radiation is high

enough then the radiation can be detected by means

of a photocell. The radiation is collected at the detector as discrete events. That is, instead of the radia- tion appearing to be continuously there — as, in fact,

it appears to be, at lower frequencies — it occurs in bursts. In this sense, it behaves as we normally

think of particles as behaving. When the particlelike behavior of the EM field is prominent, it is common to refer to it as a photon field and to an

individual event at the detector as the detection of

a photon. In the rubidium gas cell, photons are detected as evidence for the occurrence of

transitions.

6. Primary versus Secondary Standards

The ideal transition frequency of a frequency

standard is that frequency which its atoms would

have if they were completely removed from all sur- roundings including interactions with each other. This is called the free atom frequency. But, in an

actual device, the atoms interact with each other,

and with the rest of their environment, and the

78
resulting transition frequency is displaced from the

free atom frequency. From both experimental and

theoretical studies, some (and hopefully all) of the

factors which cause significant disturbances can

be identified. Furthermore, by means of experiment

and theory, quantitative estimates of each disturb- ance can be obtained. But these estimates are just

that, estimates, and there is an uncertainty asso- ciated with each of them. Those standards whose

net uncertainty is the smallest — whose accuracy is highest — are often called primary standards. Those

other standards whose precision (i.e., stability in time) is also high but whose accuracy is inferior are

often called secondary standards.

3.5.2. The Hydrogen Maser

Figure 3.6(b) is a simplified schematic of the

hydrogen-atom maser. It has six fundamental parts:

(1) a vacuum envelope,

(2) a source of hydrogen atoms,

(3) a state selecting magnet,

(4) a microwave cavity,

(5) a storage bulb, and

(6) a magnetic shield with an associated "C" field

coil. A detailed discussion of these six parts follows:

(1) In this device, as in all of the devices, the gas- eous environment of the desired atoms (in this case hydrogen) must be controlled. If a hydrogen atom in the desired F=l, mF — 0 state collides with a for- eign atom (such as an oxygen atom), then there is a good chance that it will decay to the F = 0, mF = 0

state without having made the desired contribution

to the field in the cavity.

(2) Hydrogen enters the source chamber in the

form of H2 molecules. By means of electrodes placed

across the source, the molecules are dissociated into atoms. A small-diameter, elongated hole at the top

of the source collimates the atoms into a beam as they escape from the source.

(3) When the atoms leave the source they are

nearly equally distributed among the 4 states shown

in figure 3.6(a). The state selecting magnet removes

most of the F — 0, mF = 0 (and F= 1, mF = —1) atoms

so that the beam entering the storage bulb is in a condition for a net emission of energy. By considering figures 3.6(a) and 3.6(b), a simple explanation of

this type of state selection can be obtained.

Figure 3.6(c) shows an end view of a six-pole

magnet. The beam of atoms is directed roughly

along the axis of the small hole in the center of the

magnet. The magnetic field intensity is zero on the

axis of this hole but is of the order of several

thousand gauss at the pole tips. From figure 3.6(a)

it can be seen that for the states F = I, mF = — 1 and F = 0, mF = 0, the energy decreases with in- creasing H. Because of the tendency for a system

to take up the lowest possible energy configuration,

the atoms in these states move towards the pole

tips thereby being defocused. By a similar argument,

the other states are focused. Only the F = 1 , mt = 0

state is wanted in the storage bulb, since the other

state can degrade the performance of the maser,

but if H is adjusted to a few times 10~2 ampere/

meter (a few hundred microoersteds) then the effect of atoms in the wrong state can be kept to a tolerable

level.

(4) Masers work on the principle of self-stimulated

emission. The purpose of the cavity is to obtain a higher field intensity— and, therefore, an increased

transition probability— from a small amount of input

power. The input power, which is supplied by an

excess of atoms in the F = 1, mF = 0 state, must be

greater than the internal power losses. By internal

losses I mean such things as escape of atoms

through the entrance of the storage bulb before

they have made the transition to the F = 0, mF = 0

state and decay to this state without radiating

because of collisions with foreign atoms. There is a minimum flux of atoms, in the correct

state, needed in order for any given maser to oscillate. Above this level a small amount of energy is stored in the cavity in the form of EM energy in the

TEon mode (the cavity is a circular cylinder). A

small fraction of this energy is coupled out and is the output of the maser. Its frequency is about

1420 MHz. (Actually, the usual output of the maser

is at a frequency of 5 MHz and is obtained from a quartz crystal oscillator which has been phase

locked to the 1420-MHz signal. Thus, the frequency

stability of the 1420-MHz signal is partially trans- ferred to the 5-MHz signal. The details of this phase

locking and the purpose of using the quartz oscillator

fall outside the scope of this article. (But see the

discussion of item b in sec. 3.4.3.)

(5) The storage bulb is usually a hollow, thin- walled, quartz sphere about 0.15 meter (about 6

inches) in diameter. It is coated on its inside with

polytetrafluoroethylene. There is a neck attached to the sphere, and the incoming flux of atoms enters through a small hole along the axis of this neck.

On the average, the atoms are stored for about one second within the bulb before they chance to escape

out the hole through which they entered.

This long storage time results in a very narrow

linewidth for the atomic resonance. It should be said

in addition, that were it not for this long storage

time the maser would not oscillate — the losses would

be too high. On the other hand, the bouncing of the

atoms off the walls perturbs the atoms with the

result that (for a bulb 0.15 meter in diameter at room temperature) the frequency incurs a fractional

shift of about 2 parts in 10". The fractional un- certainty in knowing this shift (see sec. 3.5. l.b)

is about 2 parts in 1012 and constitutes the biggest

single factor in the inaccuracy of the H maser [8]. (6) The intensity of the earth's magnetic field is typically about 40 ampere/meter. In addition, this

field is spatially nonuniform, and the nonuniformity

would prevent the maser from oscillating. The

magnetic shield (there are usually three layers of

79
shielding) reduces the intensity and improves the

uniformity of H in the region of space where the

storage bulb is located. The "C" field coil produces a

static field opposing that due to the residual field of the earth. The "C" field is typically adjusted to give a net H of a few times 10 2 ampere/meter.

The magnitude of this field and, therefore, the

resultant frequency shift (see item f of sec. 3.4.3.) can be measured quite accurately by taking ad- vantage of the other two F=l energy states. This

is done by equipping the cavity with a pair of Helmholtz coils which apply an audio frequency field at right angles to H. (The microwave field, in the

region of the storage bulb, is parallel to H which is parallel to the axis of the cavity.) The audio frequency

field (whose frequency is typically a few hundred

hertz) causes transitions between the F=l, m = 0

level and the other two F—l levels. These transi- tions are detected as a decrease in the output power

of the maser, and the frequency necessary to cause

these transitions depends on the magnitude of H.

The accuracy of this measurement is sufficiently

high that the error in the maser frequency due to this source is much less than that due to the wall shift discussed above.

The uncertainties in determining the perturbations to the free H atom frequency are small enough

that the H maser is used in several of the world's

laboratories as a primary standard.

3.5.3. The Cesium Beam

Figure 3.7 shows a schematic diagram of the

cesium beam. It consists of eight major parts:

(1) a vacuum envelope,

(2) a source of cesium atoms,

(3) an "A" magnet,

(4) a microwave cavity,

(5) a "C" field region,

(6) a "B" magnet,

(7) a detector, and

(8) an external source of microwave power.

A detailed discussion of these eight parts follows:

(1) The vacuum envelope performs the same function here as it does in the H maser.

(2) Because, at room temperature, the rate of

evaporation of cesium is too low, the source is a chamber which is heated to about 373 kelvin (100

degrees Celsius). At this temperature, a sufficient number of cesium atoms diffuse through a small,

elongated hole and are collimated as in the H maser.

(3) The purpose of the "A" magnet is to select certain atoms for exposure to the EM field. The

EXTERNAL

MICROWAVE

SOURCE

Fig. 3.7. A simplified schematic of the cesium beam.

80
desired atoms are those which must undergo a

transition in the EM field in order that the "B"

magnet later will focus them onto the detector. The

basic purpose of the "A" and "B" magnets is to create a condition wherein it is possible to deter- mine if the frequency of the microwave source is equal to the transition frequency. In the cesium

beam, just as in the H maser, the two states be- tween which transitions are to take place are essentially of equal population. Thus, the cesium beam

also requires state selection but here it does not matter whether the atoms are primarily in the upper

state or primarily in the lower state because

Bnn' — Bn'n (see sec. 3.3.2.). (In fact, it turns out that

if the state selecting magnet is of the dipolar type,

atoms in both states can be used.)

(4) The cavity serves four purposes. First, it enhances the strength of the EM field for a given

amount of input. This input is supplied in the form

of microwave energy from an external source. Second, it results in a fairly long interaction time

with the EM field. This gives the narrow linewidth

which is desired. Third, it defines a definite region

of interaction and fixes the direction of the EM field with respect to the "C" field. Fourth, it allows the

atoms to experience only a standing-wave EM field (any running wave component could, if not trans- verse to the cesium atoms motion, cause a first- order Doppler shift). Combined with a fairly large value of the inter- action time t, the field enhancing effect of the

cavity easily permits an optimum value of the

product br to be obtained (see sec. 3.3.2). Figure

3.7 shows a horseshoe-shaped cavity. The beam

passes first through one end of the horseshoe and

then, after a time r, through the other. The reason

for using the horseshoe cavity is that the atoms

behave somewhat as if they were in a single, very

large cavity. This increases the interaction time.

If this scheme is to work perfectly then the EM fields

at either end of the horseshoe must be exactly in phase with one another. This condition is difficult to achieve, and the failure to do it perfectly results in the largest single inaccuracy in many cesium beams.

(5) The two states between which transitions are desired are the F — 4, = 0 and the F = 3, mF = 0. (To be specific, I am talking about Cs133 whose

nuclear moment is 7/2. There are actually nine

F = 4 states and seven F — 3 states, and they all have different energies in the presence of a nonzero H (see sec. 3.4.3). These are the two states with

the least dependence on H. (See item / of sec.

3.4.3.) But, just as in the H maser, the dependence

is strong enough that, in the EM field region, the

atoms must be shielded from the earth's field. Again, as in the H maser, a second function of the

shielding is to cause the residual field of the earth

to be spatially uniform in the region of interaction

with the EM field. This is a particularly severe requirement here because the field must be uniform

throughout the entire path of the atoms between

the two cavities. If it is not, an error is introduced

which is equivalent to that due to inequality in phase

between the two ends of the cavity.

(6) The "B" magnet can be identical to the "A"

magnet. Its function is to focus, onto the detector,

those atoms which have made a transition and to defocus those which have not.

(7) Those atoms which have made the desired

transition impinge on the collector and are ionized.

The detector, in laboratory cesium beams, is usually

made of tungsten or a platinum-iridium alloy. When

the detector is heated to about 1200 kelvin, almost

all of the atoms hitting the collector are ionized.

(8) The external source of microwave energy in a cesium beam is usually supplied by a quartz crystal

oscillator whose frequency has been multiplied up

to the cesium transition frequency— about 9192

MHz. As in the H maser, the usual output frequency

is not in the microwave region but rather at 5 MHz.

The quartz oscillator takes on the long term stability

of the cesium transition by being servoed to it. This is done by automatically adjusting the fre- quency of the external source to, in effect, maximize the number of atoms collected at the detector. Those parameters which, in the cesium beam,

alter the transition frequency from its free atom

value have been thoroughly studied [9]. The uncertainties in their determination are quite small,

and the cesium beam is used as a primary standard

in many laboratories. The high accuracy capability

resulted (in October of 1964) in the declaration of the

International Committee of Weights and Measures

that the physical measurement of time be based on

the F, mF = 4>, 0<->3, 0 transition in Cs 133

. The

world's highest quality cesium beams — such as NBS-III at the National Bureau of Standards in Boulder, Colorado; the machine at the National

Research Council of Canada; and the machine at the Physikalisch-Technische Bundesanstalt in Germany— have an evaluated accuracy (one sigma)

of about 5 parts in 10 13. This is a greater proven

accuracy than for any other type of device known [9].

3.5.4. The Rubidium Gas Cell

A schematic diagram of the rubidium gas cell is given in figure 3.8. It has five major parts:

(1) a gas cell containing Rb87 gas,

(2) a Rb87 light source (and associated filter) for state selection,

(3) a microwave cavity,

(4) an external source of microwave energy, and

(5) a photocell detector. A detailed discussion of these parts follows:

(1) Rb87 atoms at a partial pressure of about 10 -4 newtons/meter2 (about 10 -6

torr) are contained in an optically transparent cell. The two levels of

interest are the F — 2, mF = 0 and F—l, mF = 0

states of the ground electronic state. (Rb87 has a nuclear moment of 3/2, and the ground electronic

state is 2 Si/2; therefore, the two possible values of

81
(WITH BUFFER GAS)

RF SIGNAL

IN (6835 MC)

Fig. 3.8. A simplified schematic of the rubidium gas cell.

F are 2 and 1.) The transition frequency is about

6835 MHz.

In addition to Rb87

, the cell contains a buffer gas (which is usually a mixture of neon and helium, at a

partial pressure somewhere between 1 X 102 and

2 X 104 newtons/meter2

). This buffer gas performs

for the rubidium cell the same function that the

storage bulb performs for the H maser and the horseshoe cavity performs for the cesium beam: It increases, by several orders of magnitude, the

interaction time with the EM field, thereby resulting

in a narrower linewidth.

Unlike the H maser and the cesium beam, the

atoms are used over and over again. This is possible

because state selection is done within the gas cell

itself. (2) The method of state selection employed here

is called optical pumping. A simplified explanation

of this technique can be obtained from figure 3.9. This technique involves, in essence, three energy

levels. In figure 3.9, the levels labeled B and C are, respectively, the F=2, mF = 0 and the F— 1, m = 0

levels between which we want transitions to occur.

Level A is a level which is energetically far removed

from levels B and C. The frequency corresponding

to the spacing between level A and the other two

levels is about 3.8 X 10 14 Hz. This means that almost

all of the atoms will be equally distributed between

states B and C, and hardly any will be in state A

(see sec. 3.4.4). Before the light is turned on, almost all of the

atoms are in levels B and C. This is shown in part 1 of the figure. When the light is turned on, many of

the atoms absorb energy from the light beam and

are excited to level A. This is shown in part 2 of the

figure. But, for atoms in state A, it is very likely they

will spontaneously decay to either state B or C

(see sec. 3.3.2.). Decay to states B and C is about

equally probable. Part 3 of the figure shows the

situation. Because the spontaneous emission probability from state B to C is very low, the net result of

this pumping is that the number of atoms in state B is built up at the expense of state C. Thus, the

population imbalance required so that the atoms will be responsive to the external source has been

achieved. The reader should note that the rubid82
-6- -6-

•—

0—

Fig. 3.9. A simplified explanation of optical pumping as applied to the rubidium gas cell. Part 1 is the condition before the pumping light

is turned on. The black circles represent the fact that atoms are in certain of the possible energy states. Part 2 shows the change upon turning the pumping light on. The open circles with arrows indicate that some atoms that were in state C are now in state A. Part 3 shows the tendency of spontaneous emission to depopulate state A. It also indicates the nearly equal probability to make transi- tions to state B or state C.

ium cell is a passive device and that an excess

population in state B is not required — an excess in state C would work just as well. The condition is as

it is because of the state selecting method.

(3) The purpose of the microwave cavity is field enhancement.

(4) The external microwave energy is again supplied by a quartz oscillator and a frequency multiplier chain. If the external source is at the proper

frequency, some of the atoms in state B make transi- tions to state C. This is detected at the photocell as

a decrease in the received light. By servoing the

frequency of the quartz oscillator to minimize the

light at the photocell, the quartz oscillator is kept

on frequency.

(5) There is a great advantage to using a photocell

to detect the fact that transitions are occurring.

The reason is that each photon at the light frequency

has a great deal of energy, and a small change in the number of photons arriving at the detector is quite noticeable.

The buffer gas used in the gas cell causes the

transition linewidth to be quite narrow because it increases the interaction time of the atoms with the

EM field. Unfortunately, it also produces a very

large shift in frequency, just as collisions with the

Teflon coating of the storage bulb produce a net frequency shift in the H maser. The uncertainty in the determination of the shift due to the buffer gas

is quite large, and, consequently, the rubidium cell serves only as a secondary standard.

3.6. SUMMARY

The reason for the use of atoms for frequency

standards is that they have well defined energy

states. In an atom which is useful as a frequency

standard, the desired energy level pair is quite

insensitive to the atom's environment, and, hence,

the energy difference between this pair has the

required high stability.

The energy level pair is used by observing transi- tions from one level of the pair to the other. In an

active type of device — a maser— the atoms emit

electromagnetic (EM) energy by making the

transition from the upper to the lower of the two

states. In a passive device — such as a cesium

beam — an external source of EM energy causes

transitions. Devices are built where the transitions are from the lower to the upper state or vice versa;

in fact, devices are sometimes built where both

processes are used simultaneously. Be the device

active or passive, the central point is that it is the

EM field which causes transitions. There are three basic functions which any atomic

frequency standard must perform. First, the atoms

must be put in a condition in which they will emit

EM energy (active device) or be responsive to an

external source of EM energy. The most commonly

used transitions are in the microwave region, and,

for those transitions, state selection is required.

Second, the atoms must be kept in interaction with

the EM field long enough that the transition line- width is acceptably narrow. The means by which

this long interaction time is achieved in the H, Cs,

and Rb devices has a detrimental side effect upon

the accuracy of each of the devices. Third, some means of detecting that transitions are occurring

must be provided. In the hydrogen maser, its oscil- lation is evidence for the occurrence of transitions. Given the broad definition of particles discussed in the text, the Cs and Rb devices sense transitions by

particle detection.

For a device to adequately perform these three

functions, the type of atom which is used must be

carefully selected. A list of criteria for choosing an atom was given, and it was seen that several of these

criteria tended to conflict. An atom whose electronic

ground state is 2 Si/2 is a good compromise in meeting these criteria, and the reasons for this were

given. All of tne frequency standards described in

this article cause their atoms to be in a very rarified

83
gaseous state when interacting with the EM field. (The buffer gas in the Rb gas cell is at a fairly high

pressure. This gas, however, is not the working

substance; its purpose is the same as that of the

Teflon coating in the hydrogen maser.) This is an

important technique in achieving a stable and

accurate output frequency.

In this paper, I have confined the discussion to devices which use atoms, rather than molecules, as

their working substance. This was done because

these usually have been the more stable and

accurate devices. There is, however, at least one

case — the methane saturated absorption cellwhere the stability (and, perhaps, the accuracy

capability) is extremely high [10]. Even though

molecules are used rather than atoms, the physical

basis is still a well defined energy level pair and an

appropriate interaction with the EM field. The theory of atomic structure and of the inter- action of an atom with the EM field has become

quite elaborate and abstract. Atomic frequency

standards provide concrete examples of a great

many of these ideas.

ACKNOWLEDGEMENTS

I want to thank Dr. Donald Halford, Dr. David

Wait, and Mr. Roger Beehler of the National

Bureau of Standards, Boulder, for many helpful

criticisms of this paper. I also wish to thank Mrs. Eddyce Helfrich for her diligent efforts in typing

the manuscript.

3.7 REFERENCES

[1] Holton, G., and Roller, D. H. D., Foundations of Modern

Physical Science, p. 615 (Addison-Wesley Publishing Co.,

Inc., Reading, MA, 1958).

[2] Ibid., p. 581.

[3] Ibid., p. 591.

[4] Oldenberg, O., Introduction to Atomic Physics, p. 335 (McGraw-Hill Book Co., Inc., New York, NY, 1949).

[5] Holton, op. cit., p. 651.

[6] Persico, E., Fundamentals of Quantum Mechanics, trans- lated by G. M. Temmer, p. 454 (Prentice-Hall, Inc., New

York, NY, 1950).

[7] Cutler, L. S., and Searle, C. L., "Some aspects of the theory and measurement of frequency fluctuations in frequency

standards," Proc. IEEE, 54, No. 2, pp. 136-154 (February

1966).

[8] Hellwig, H., Vessot, R. F. C, Levine, M. W., Zitzewitz,

P. W., Allan, D. W., and Glaze, D. J., "Measurement of the unperturbed hydrogen hyperfine transition frequency," IEEE Trans, on Instrum. and Meas., IM-19, No. 4, pp. 200-209 (November 1970).

[9] Beehler, R. E., Mockler, R. C, and Richardson, J. M., "Cesium beam atomic time and frequency standards,"

Metrologia, l,No. 3, pp. 1.14-131 (July 1965).

[10] Barger, R. L., and Hall, J. L., "Use of laser-saturated absorption of methane for laser frequency stabilization," Proc. of the 23rd Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, May 6-9, 1969), p. 306 (NTIS, AD 746209, 1969).

3.8 BIBLIOGRAPHY

Background

[Bl] Holton, G., and Roller, D. H. D., Foundations of Modern

Physical Science (Addison-Wesley Publishing Co., Inc., Reading, MA, 1958). [B2] Oldenberg, O., Introduction to Atomic Physics (McGrawHill Book Co., Inc., New York, NY, 1949). [B3] Persico, E., Fundamentals of Quantum Mechanics, trans- lated by G. M. Temmer (Prentice-Hall, Inc., New York,

NY, 1950). [B4] Ramsey, N. F., Molecular Beams (Oxford University Press, Amen House, London E.C.4, 1956). [B5] Herzberg, G., Atomic Spectra and Atomic Structure, trans- lated by J. W. T. Spinks (Dover Publications, New York,

NY, 1944). Devices

[B6] Kleppner, D., Goldenberg, H., and Ramsey, N. F., 'Theory

of the hydrogen maser," Phys. Rev., 126, No. 2, pp. 603-

615 (April 1963). [B7] Beehler, R. E., Mockler, R. C, and Richardson, J. M., "Cesium beam atomic time and frequency standards,"

Metrologia, 1 , No. 3, pp. 114-131 (July 1965). [B8] McCoubrey, A. O., "A survey of atomic frequency stand- ards," Proc. IEEE, 54, No. 2, pp. 116-135 (February

1966). [B9] Hellwig, H., "Areas of promise for the development of future primary frequency standards," Metrologia, 6, No. 4, pp. 118-126 (October 1970). (See chap 6).

84
CHAPTER 4 -PART A

A HISTORICAL REVIEW OF ATOMIC FREQUENCY STANDARDS

Roger E. Beehler t

Contents

Page 4A.1. Introduction 87

4A.2. Development of Basic Techniques 87

4A.2.1. Atomic Beam and Magnetic Resonance Techniques 87

4A.2.2. Optical Pumping Techniques 89

4A.2.3. Buffer Gas Techniques 91

4A.2.4. Storage Techniques for Increasing Interaction Times 91

4A.2.5. Maser Techniques 92

4A.3. Application of Basic Techniques to the Development of Specific Types of Atomic

Frequency Standards 93

4A.3.1. Development of the World's First "Atomic Clock" 93

4A.3.2. Development of Atomic Beam Standards Utilizing Cesium or Thallium 93

4A.3.3. Development of Practical Gas Cell Frequency Standards 96

4A.3.4. Development of the Atomic Hydrogen Maser 97

4A.4. Conclusions 99

4A.5. References 99

tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302. (Written when author was with Frequency

and Time Division, Hewlett-Packard Company, Palo Alto, CA.)

85
"A thing is not brought to perfection at once from the outset but through an orderly succession of time . . ."

St. Thomas Aquinas, 1. 279 An attempt is made to trace the historical development of the leading contenders in the atomic frequency standards field — cesium and thallium atomic beam devices, rubidium gas cell standard, and the hydrogen maser. Many of the important experiments leading to the development of tech- niques basic to the various types of standards, such as the magnetic resonance method, optical pumping, buffer gases and wall coatings, and maser techniques are briefly described. Finally, the application of these basic techniques to the development of the specific types of atomic standards is discussed. Key words: Ammonia clock; atom storage techniques; atomic clock; atomic frequency standard;

buffer gases; cesium beam; gas cells; ground states; hydrogen maser; magnetic resonance; optical pumping; storage bulbs; thallium beam; wall shift.

86
4A.1. INTRODUCTION

A LTHOUGH the exploitation of atomic frequency

f-\ standards on a large scale dates back to less than 10 years ago when they came into general use as basic reference standards in many laboratories, some of the basic techniques involved had been developed almost fifty years

ago. It is the purpose of this paper to review some of the

early experiments and outline the subsequent development

of basic techniques which have led to the present atomic

frequency standards. The discussion will be confined to those standards which are presently available commercially

to the general user or are at least under active development

by several commercial or national standards laboratories

namely, cesium and thallium atomic beam devices, rubid- ium gas cell devices, and hydrogen masers. Because of the scope of the subject, it will often be impossible to include many details of the principles of operation of equipment, measurement procedures, and general performance results. However, an attempt will be made to give adequate ref- erences in all cases. The historical development of the most

important basic techniques will first be described without

regard to specific frequency standards, followed by a dis- cussion of the later application of these basic techniques to the development of specific types of atomic standards. For

an analysis of the relative merits of the different types of atomic standards discussed here and for an up-to-date

status report of their performance achievements reference

is made to the article by A. McCoubrey in this issue [1 ].

4A.2. DEVELOPMENT OF BASIC

TECHNIQUES

4A.2.1. Atomic Beam and Magnetic

Resonance Techniques

The first experiments using atomic or molecular beams

were those of the French physicist A. L. Dunoyer in 1911

[2]. Dunoyer's apparatus, shown schematically in Fig. 1, consisted simply of a 20-cm-long glass tube with three separately evacuated chambers which served as source, collimation, and observation chambers. He observed that when

sodium was heated sufficiently in A, a deposit was formed in C whose distribution could be explained by the assumption

that the sodium atoms traveled in straight lines.

Nine years later at the University of Frankfurt in Ger- many, Otto Stern became the first to use a molecular beam

technique for making physical measurements. In these ex- periments to measure directly the speed of gas molecules, a source of silver atoms at the center of an evacuated jar pro- duced a beam of atoms which was collimated by a narrow

slit and detected by deposition on a glass plate near the jar's surface. The principal parts were mounted such that they

could be rotated about a vertical axis inside the bell jar at speeds of 1500 rpm. Stern observed, in agreement with the

results of Dunoyer's experiments, a narrow sharp deposit

explainable by straight line atomic trajectories as long as the apparatus was stationary. However, for rotational speeds

of 1500 rpm the deposited pattern was shifted slightly and

also appeared fuzzy. From the amount of the shift Stern could calculate the average velocity of the atoms, which

— TO PUMP

— TO PUMP

Fig. 1 . Schematic diagram of Dunoyer's original atomic beam apparatus [2].

87
turned out to agree with the predictions of kinetic theory to within a few percent. The fuzziness of the deposit showed

thnt a distribution of speeds existed in the beam.

Less than two more years elapsed before Stern and a colleague, Walther Gerlach, performed their celebrated "Stern-Gerlach experiment" [3] which was to have a most

profound effect on the development not only of molecular

beam techniques but also of quantum mechanics in general.

The results of this experiment supported the concept of

spatial quantization—i.e., the seemingly unlikely idea that the magnetic moment of an atom in an external magnetic

field can have only a few possible discrete orientation angles

with respect to the external field lines. If the atom is considered to behave as a small bar magnet of magnetic moment n in an external field, //, its change in energy, when

placed in the field, would be given by AE= ixH cos 0, where

9 is the angle between the magnet and the field lines. Until

the performance of the Stern-Gerlach experiment, it was

generally believed that a large number of such atoms in a

field would show a random distribution of the angle 8, and

hence would have energy values anywhere between +

and —fiH. An opposing view, however, was suggested by

observations made as early as 1896 by the Dutch physicist

Pieter Zeeman that certain spectral lines split into two or more sharp lines when the radiating atom is placed in an

external magnetic field. This effect could be explained by

postulating that the energy of atoms in a magnetic field is quantized, resulting in the observed spectral emission lines produced by transitions between these discrete energy levels being limited to a few sharply defined frequencies through

the relation Et —E2 = hv, where Ex and E2 are the energies

of the two levels involved in the transition, h is Planck's

constant, and v is the frequency of the emitted spectral line. If the atoms could have random orientations, and hence

energies, in the field, one would expect to observe a blurred

spectral line corresponding to a spread in energy of the

levels of 2/i//, contrary to the experimental evidence.

In 1921 Stern conceived an experiment for testing for space quantization using a beam of silver atoms. He realized that the force exerted on a silver atom with magnetic moment fx by a magnet designed to produce a field with a

large gradient dH/dz across the gap would be given by — fx(dH/dz) cos 0 and would thus vary continuously from + {i(dH/dz) to —fi(dH/dz) if atoms were oriented ran- domly. On the other hand, if space quantization existed, the force on silver atoms would be either — fi(8H/dz) or + n(8H/dz). By shooting a beam of silver atoms between

the poles of such a magnet and observing the deflection pattern produced, one should observe either a single broad

fuzzy line (if random orientations are possible) or two dis- crete sharp lines (if space quantization exists). Performing

the experiment with Gerlach, who had a magnet of the proper design. Stern did indeed observe two separated

lines in the deflection pattern.

1 As we shall see shortly,

' Because the existence of electron spin with its effect on effective magnetic moments was not yet known in 1921. Stern actually expected to observe three discrete lines instead of two. Thus, while this experiment sup- ported the concept of space quantization an additional mystery was intro- duced which was not resolved until 1925.

magnets similar to that used in the Stern-Gerlach experiment are a basic component of today's atomic beam fre- quency standards, being useful for obtaining a beam of atoms in a specific energy state. In 1923 Stern became head of the Department of Physical Chemistry at the University of Hamburg. During the next 10-year period he and his students published a series of some 30 papers which served to establish many of the basic

principles and techniques used in today's atomic beam devices. Particular emphasis was placed upon the development of atomic beam methods for greatly improved measurements of magnetic moments.

In 1932 O. Frisch and E. Segre used an atomic beam tech- nique with potassium to detect transitions produced by

subjecting the atoms to a sudden variation in the direction of a static magnetic field located between two Stern- Gerlach magnets [4]. The first magnet acted as a polarizer,

separating the atomic beam into two beams differing in magnetic state. One of these beams was then blocked by the obstruction of part of the magnet gap, producing a beam

with atoms only in the desired state. These remaining atoms

were then passed through a second Stern-Gerlach magnet

which acted as an analyzer to detect whether the magnetic

state had been changed in the region between the magnets.

When the static field with its rapid reversal in direction was

applied in the center region, a change was noted in the number of atoms reaching the atomic beam detector located

after the second magnet. This indicated that some of the atoms had made transitions to different energy states (and

thus had their magnetic moment reversed in direction), pro- ducing a change in their deflection by the second magnet.

This apparatus, used some 35 years ago, differed primarily

from present atomic beam tubes only in the method of pro- ducing the transitions between the atomic energy levels. Six years later in 1938 at Columbia University, 1. 1. Rabi, one of Otto Stern's former students, made the next major

advance in atomic beam techniques by developing his magnetic resonance method, which permitted the detection of

transitions between the closely spaced energy levels result- ing from the interaction of an external magnetic field with an atom or molecule [5]. Rabi's apparatus, shown sche- matically in Fig. 2, was similar to that used by Frisch and

Segre, except that transitions between the magnetic states of an atom or molecule were produced by applying an

oscillating RF field of proper magnitude and direction and

whose frequency satisfied the resonance condition, Wl — W2 = hv, for the two energy levels of interest. Although the field directions in the A and B Stern-Gerlach

magnets were the same, the field gradients were arranged

to be in opposite directions, so that, in the absence of transi- tions in the C region, molecules from the source O would

undergo equal and opposite deflections by the two magnets

and therefore strike the detector D. Application of the proper frequency RF field in the region R, however, pro- duced a change from one energy state to another, such that (he resultant change in magnetic moment produced a

sufficiently different deflection in the B magnet to cause the molecule to miss the detector. The surface-ionization type

88
Un n rTM i r

5

1 "A" MAGNET

PUMPS PUMP

"B" MAGNET

PUMP

Fig. 2. Schematic diagram of Rabi's magnetic resonance apparatus [.")].

detector used by Rabi ionized nearly all of the molecules

striking the 0.001 -inch wide surface and thus produced an

electrical signal proportional to the number of molecules

striking the wire per second. As the excitation frequency was varied through the resonance value for a particular transition between two energy states, Rabi observed a sharp decrease in the detector output signal. 2 The first resonance

curve ever observed by this magnetic resonance technique is shown in Fig. 3. It was published by Rabi and his colleagues

in February, 1938, and represents a resonance between two

spatial quantization states of the lithium nucleus obtained

with a beam of LiCl molecules in a strong enough C field to decouple completely the nuclear magnetic moments

from one another and from the molecular rotation [5]. From the measured values of the frec/.iency at resonance and the static C field in which the transition occurred, Rabi was able to calculate much improved values for several nuclear magnetic moments.

Soon thereafter another member of the Columbia group,

P. Kusch, extended the new atomic beam magnetic reso- nance technique to measurements of separations of the

closely spaced hyperfine structure levels in the ground state of atoms [6]. Hyperfine-structure level separations in several isotopes of lithium and potassium were measured to a

precision of 0.005 percent. Relative to earlier hyperfinestructure measurements by optical means, the atomic beam

magnetic resonance results were simpler to interpret, much

more accurate, and of much higher resolution. A further refinement in the atomic beam magnetic reso- nance technique, which proved to be of extreme importance

in the application of the technique to frequency standards, was introduced by N. F. Ramsey at Harvard University in 1950 [7]. In the conventional atomic beam apparatus at

that time the oscillating RF field for producing transitions

in the beam was applied over a relatively short region, being

limited by th? requirements of maintaining uniform phase

and uniform static magnetic field (C field) over the entire region of interaction between the atoms and the RF field. A lengthened interaction region is desirable for many ex- periments, however, because the longer the interaction

time, the more sharply defined are the atomic energy levels and thus also the resonance frequencies associated with

transitions among them. Ramsey developed a method which

increased the effective interaction time without adversely

2 In the early experiments described here the transition frequencies of

interest depended linearly on the magnitude of the static magnetic field provided in the C region. For reasons of exp imental convenience reso- nance curves were actually obtained by keeping the frequency fixed and

sweeping the field through the corresponding resonance value.

IOO_

75

IIO

•

115 120 MAGNET CURRENT IN AMPERES

Fig. 3. First published resonance curve using Rabi's magnetic resonance technique [5].

affecting the phase and field uniformity requirements. He

replaced the usual single oscillating field region with two

such regions separated by a relatively large distance and

showed that the effective interaction time was now the entire length separating the two RF regions. Moreover, the observed resonance width under these conditions is 40 per- cent less than that for a single Rabi-type excitation of

length equal to the separation of the two Ramsey fields and the C field uniformity requirements are actually less severe for the Ramsey case. Application of this technique

to atomic beam frequency standards has resulted in reso- nance linewidths of less than 50 Hz at 9192 MHz.

Before discussing the specific development of cesium and

thallium atomic beam frequency standards based upon the basic techniques described up to this point, let us first consider the historical evolution of some other methods and

techniques which led to other types of atomic standards,

such as the optically pumped gas cell devices and the hydrogen ma^sr.

4A.2.2. Optical Pumping Techniques

Optically pumped gas cell frequency standards, such as the Rb87 gas cell devices currently available commercially,

represent a completely different approach to the problem of

detecting a condition of resonance in the hyperfine struc- ture levels of the ground state of an atom. In the atomic

beam devices, as we have seen, the occurrence of transitions excited by RF resonance radiation is detected by observing

resultant changes in the trajectories of the atoms comprising

the beam. In gas cell devices, on the other hand, a double

resonance technique is used in which the RF resonance

89
Fig. 4.

6' S 0

Simplified energy level diagram for mercury showing slates used

in curly double resonance experiments [12].

condition is detected by the resultant changes in the in- tensity of transmitted optical radiation at the proper fre- quency to produce transitions between the ground and

first excited states of the atom. The development of the optical pumping and double

resonance techniques, which are basic to the operation of

gas cell standards, can be traced back to 1949 when Prof.

F. Bitter at the Massachusetts Institute of Technology

showed that the frequency, intensity, and polarization of

optical radiation emitted by an atom in a

2 P-* 2 S (ground

state) transition are all altered if the atom is simultaneously

subjected to a weak oscillating RF held whose frequency is near resonance for the hyperfine levels of one of the energy

states involved in the optical radiation process [8]. About

this same time A. Kastler and J. Brossel of the Ecole Normale Superieurt in Pans suggested a double resonance

technique as a sensitive means of gaining information about

the structure of energy levels [9]. The first application of this technique was to one of the excited states of the mercury

atom by Brossel and Bitter in 1950 [10]. As an aid to understanding the way in which the double

resonance technique was first used, consider the simplified energy level diagram for mercury shown in Fig. 4. The levels indicated are the 6

1 S0 ground state and the three Zeeman

levels of the 6

3 P{ excited state. If mercury vapor is illumi- nated by optical resonance radiation at 2537 A, transitions

will occur from the ground state to one of the excited-state

levels, the particular one depending on the polarization of

the radiation. In the experiment of Brossel and Bitter a

polarization (labeled n in Fig. 4) was used which selectively

populated the m = 0 level of the triplet. Under these cir- cumstances the emitted light from spontaneous transitions back to the ground state also contains only n radiation.

If now an RF field is applied perpendicular to the static magnetic field producing the Zeeman splitting and its fre- quency is adjusted to the proper value for resonance be- tween the m = 0 ant ibe m= + 1 levels, transitions will be induced to the m = + 1 states. Decay from these levels back

to the ground state will now cause Z components to appear

in the emitted light. Since the intensity and polarization of

the emitted light are thus altered in the process, a means is available for optically detecting the occurrence of the RF

resonance. A set of RF resonance curves for mercury ob144 MHz

L_

- 1 \

67 68 69 70 71 H, GAUSS

Fig. 5. Set of RF resonance curves obtained with double resonance

technique for mercury [10],

(o) (b) (c)

Fig. 6. Simplified optical pumping method.

tained in this manner by Brossel and Bitter is shown in Fig.

5. Each curve corresponds to a different amplitude of the RF field. The development of the method of optical pumping as applied to the building up of the population of one certain

level at the expense of others in the ground state of atoms is due primarily to Kastler [11], [12]. Consider the much

simplified energy level diagram shown in Fig. 6, where A

and B represent two closely-spaced energy states in the hyperfine structure of the ground state of an atom and C

represents one of the levels of the first excited state. Transitions A->C and B-+C occur at optical excitation fre- quencies, while transitions A<^>B are in the RF range. Before

application of any excitation radiation to the system, atoms

are equally distributed between levels A and B of the ground

state as in Fig. 6(a). If optical resonance radiation from

which the B-*C component has been removed by some

means such as filtering is now used to illuminate the system,

atoms in level A absorb an optical photon and make transi- tions to C, as indicated in Fig. 6(b). Since lifetimes in the

excited state are very short, however, the atoms in C sponta90
neously re-emit a photon and fall either to level A or B with

approximately equal probabilities. As shown in Fig. 6(c), the net effect at this point has been to increase the population

of B at the expense of A . Now, since there are still atoms in A

which can be excited to C by the optical resonance radiation, the cycle is repeated until (ideally) all the atoms end

up in level B. This is then the process of optical pumping

for changing the population distribution among the ground

state levels. If an RF excitation is now applied which is adjusted in frequency to the resonance value corresponding to the fre- quency separation of A and B, the pumped atoms in B will be stimulated to make transitions back to A, at which point

the optical pumping process resumes. In 1956 H. G. Dehmelt at the University of Washington developed the tech- nique of monitoring the intensity of the light transmitted through the sample as a means of detecting the occurrence

of the RF transitions [13]. Using a photocell detector, one

observes an output current which increases to a constant maximum value (maximum transparency of the sample) for the condition in Fig. 6(c), since at that point no atoms are

available to be pumped A-+C by absorbing part of the incident light. As the RF signal is swept through resonance, however, atoms transfer to A where optical absorption

again takes place, producing a sharp drop in the transmitted

light. The detection of RF resonances by this means is ex- tremely sensitive. For example, a sample of vapor at a pressure of only 10" 7 torr can reduce the intensity of the transmitted light by 20 percent when the correct RF is applied. A very large effective energy gain occurs with the

optical detection technique, since the optical photon detected has an energy approximately 104 to 10 5 times greater

than the energy of the RF photon involved in the micro- wave transition. As we shall see in more detail later, the use of optical pumping and optical detection with atomic

systems of Na23

, Cs 133

, and Rb87 has made possible the development of extremely compact atomic frequency stan- dards relative to the atomic beam devices.

4A.2.3. Buffer Gas Techniques

While the optical pumping technique as briefly described

in the preceding section will, in principle, produce a large

population buildup in level B of Fig. 6, collisions of atoms

in the sample with each other and with the walls of the containing vessel actually provide a relaxation mechanism

whereby atoms can "leak" back to level A without the application of RF. Even in very dilute samples atoms make

about 10 000 collisions per second with the walls. Since this

is usually greater than the number of optical photons which

the atom can absorb per second for repumping to level B,

the pump effectively becomes very leaky and at best only

weak RF resonances can be observed.

In 1955 in the laboratory of A. Kastler a fortunate acci- dent occurred during some experiments with sodium vapor

in highly-evacuated glass bulbs which was to provide the key for significantly improving the efficiency of the optical

pumping process. When a vacuum system failure allowed

hydrogen gas to be introduced into one of his sodium bulbs, Kastler and his colleagues were amazed to find that the

optical pumping was greatly increased! The foreign gas introduced was found to act as a buffer between the sodium atoms and the walls where disorienting collisions take place.

It was found in later experiments that, because of collisions between atoms of the sample and those of the buffer gas, the average diffusion time to the walls could be increased from

10" 4 second (without buffer gas) to nearly a second. It is, of

course, necessary to use a buffer gas which does not itself disorient the sample atom's magnetic state during collisions. In general, use of sample atoms in a

2 S1/2 ground state with

its spherical symmetry appears to be the best way to insure minimum interaction during buffer gas collisions. In addition to producing an enhancement of the optical

pumping process by increasing the effective time during

which RF transitions can be excited, the use of buffer gases

also causes a reduction in the observed resonance linewidth

as compared to the normally observed Doppler broadened

value. This "collision-narrowing" effect in a buffer gas was

first predicted by R. H. Dickein 1953 [14] and was observed

experimentally by J. Wittke and Dicke at Princeton University in 1954 [15]. Measuring the hyperfine splitting in the ground state ofatomic hydrogen by a microwave absorption

technique, they found that atomic hydrogen at a pressure of

5 x 10" 4 torr in a buffer gas of clean molecular hydrogen

at 0.2 torr produced a resonance width of only 3 kHz or

one-sixth of the normal Doppler width.

In 1956 H. G. Dehmelt performed optical pumping ex- periments with sodium in argon buffer gas and observed

relaxation times of up to 0.21 second which corresponds to an amazing 10 8 sodium-argon collisions occurring before

disorientation of the sodium atom [13]. Dehmelt pointed out at that time that such long relaxation times (0.2 1 second)

used in future RF resonanceexperiments with optical pumping would provide extremely narrow linewidths. Even longer

relaxation times (up to 2 seconds) were obtained by Dehmelt's group by replacing the buffer gas with a solid buffer wall coating chosen to have minimum magnetic interaction with colliding rubidium atoms [16]. Using eicosane

(C20 H42 ), they obtained strong resonances in rubidium and

found that at least 600 collisions occurred before appreciable disorientation. W. Hawkins, working at Yale University, also obtained favorable results with wall surfaces of

absorbed air molecules on Apiezon L grease and on copper

[17]. Several years later, however, during '.he early development phase of commercial gas cell standards, R. M. Whitehorn at Varian Associates concluded that use of solid buffer coatings for commercial applications presented too many

technical problems [18]. To date, all commercial gas cell standards have used buffer gases.

4A.2.4. Storage Techniques for Increasing

Interaction Times

The advantages to be gained in terms of narrower reso- nance lines by increasing the interaction time between an

atomic beam and the applied RF resonance radiation have

already been mentioned briefly in connection with the de91
Fig. 7. Schematic diagram of "broken-beam" apparatus [21].

velopment of Ramsey's separated oscillating fields tech- nique. In 1957 Ramsey pointed out that it should be possible

to further increase the interaction time in such an experiment by "storing" the atoms in a bounce box having a suitable non-disorienting wall coating and located between

the two RF field regions of an atomic beam apparatus [19]. If the collisions with the walls of the bounce box do not appreciably affect the magnetic state of the atom, an effec- tive increase in the separation of the two fields is realized without physically lengthening the apparatus.

Kleppner, Ramsey, and Fjelstadt reported in 1958 the

first successful results using this "broken-beam"1 technique

[20]. The bounce box was designed so that an atom had to make at least two collisions in order to pass through and

contribute to an observed resonance. Employing a beam

of atomic cesium, they were able to observe resonances be- tween the hyperfine states for wall coatings of teflon heated

to 100 'C, eicosane, and polyethylene. The authors at this time stated their intention to test other substances for wall coatings for application in a "high-precision atomic clock incorporating both the storage box and maser principles."

Further experiments with a cesium beam and a variety of

wall coatings, using the apparatus shown schematically in Fig. 7, were reported in 1961 by Goldenberg, Kleppner,

and Ramsey [21]. For storage bulbs coated with "Paraflint" (a mixture of long chain paraffins), resonance widths

of only 150 Hz were obtained as compared with 2 kHz

without the storage bulb. This result implied that at least 200 collisions could occur before relaxation of the hyperfine states became a problem. One unfavorable feature of

the experimental observations was a rather large shift of

several hundred Hz in the resonance frequency resulting

from slight displacements of the energy levels during each

collision process. This type of shift was minimized later in the hydrogen maser applications because of the much lower

polarizability of the hydrogen atom compared to cesium.

CAVITY ELECTRODES

MASER FREQUENCY STANDARD

Fig. 8. Diagram of an early ammonia beam maser showing arrangement

of components (courtesy of National Bureau of Standards, Boulder,

Colo.).

4A.2.5. Maser Techniques

The development of maser techniques in 1953, initially using ammonia, represented still another approach to the problem of using microwave resonances in atoms or molecules as frequency standards. The maser was invented by

C. H. Townes of Columbia University [22] but was also proposed independently by N. G. Basov and A. M. Prokhorov of the U.S.S.R. [23]. In this device, a collimated beam

of ammonia molecules effuses from a source and then

passes through an inhomogeneous electrostatic field de- signed to spatially separate the two energy states of the inversion spectrum, just as a Stern-Gerlach magnet separates magnetic states of atoms in the magnetic resonance method. The electrostatic state separator applies a radially

outward force to molecules in the lower inversion state, but

a radially inward force on the upper energy state molecules. The upper-state molecules are thus focused into a high-g

cylindrical microwave cavity tuned to the resonance fre- quency for the ammonia inversion transition (7=3, K=3)

at 23 870 MHz. The resulting large excess population of upper energy state molecules in the cavity is then favorable

for stimulated transitions from upper to lower inversion

92
states with an accompanying emission of an RF photon.

Townes was able to get a sufficient flux of molecules into the cavity so that the emitted microwave energy exceeded

the losses involved, and a small amount of excess energy

could be coupled out of the cavity for external use. Operation of the maser in this manner as an oscillator was found

to require a flux of at least 5 x 10 12 molecules per second per square centimeter. Figure 8 shows the physical arrangement

of the components in an ammonia maser, modified for operation with two beams to reduce Doppler effects. Following the first successful operation of a maser in 1953, J. P. Gordon, H. J. Zeiger, and Townes studied in detail the characteristics of the maser oscillation frequency

and found rather strong dependencies of the output fre- quency upon the ammonia source pressure and the voltage

applied to the electrostatic focuser [24]. The strong coupling

between the ammonia beam and the resonant cavity also causes the output frequency to depend significantly on the tuning of the cavity. In spite of intensive research efforts in the United States, the U.S.S.R., Japan, Switzerland, and several other countries during the next few years to develop adequate tech- niques for controlling the critical maser parameters and for achieving a reproducible frequency from one maser to another, it has now become apparent that, except possibly

for its high short-term frequency stability, the ammonia

maser cannot compete with other types of atomic devices

for use as a primary or secondary frequency standard. Its importance is mainly that it led to the development of one

of the present-day leading contenders for the best atomic

frequency standard—the hydrogen maser. 4A.3. APPLICATION OF BASIC

TECHNIQUES TO THE DEVELOPMENT OF SPECIFIC TYPES OF

ATOMIC FREQUENCY STANDARDS

4A.3.1. Development of the World's First

"Atomic Clock"

The first operational complete "atomic clock" system was developed at the National Bureau of Standards (NBS),

Washington, D. C, in 1948-1949 by H. Lyons and his associates [25]. This system consisted basically of a quartz

crystal oscillator, electronically stabilized by the J= 3, K= 3 absorption line in ammonia at 23 870 MHz, together with

suitable frequency dividers for driving a 50-Hz clock from

the stabilized oscillator. This historic accomplishment was

the culmination of many years of experimental interest in the absorption spectrum of ammonia, extending back to 1933 and the remarkable experiments of C. E. Cleeton and

N. H. Williams in which they were able to observe absorption lines in ammonia more than 10 years before the devel- opment of most microwave equipment and techniques [26]. Aided by the rapid development of microwave techniques

for radar applications during World War II, B. Bleaney and

R. P. Fenrose succeeded in observing the rotational fine structure of ammonia in 1946 [27]. About this time R. V. Pound proposed stabilizing a klystron with one of the

ammonia spectral lines [28]. This was accomplished by

W. V. Smith et al. in 1947 [29] and shortly thereafter by

W. D. Hershberger and L. E. Norton at RCA [30]. The NBS system, developed specifically for use as a fre- quency standard, was first operated on August 12, 1948. A

photograph of this first "atomic clock" is shown in Fig. 9. The heart of the system, a 25-foot long waveguide absorption cell filled with ammonia at a pressure of 10-15 microns,

is shown wrapped around the clock mounted on top of the equipment cabinets. The 7=3, K=3 absorption line obtained by sweeping the excitation frequency through the molecular resonance can be seen displayed on the oscillo- scope in the photograph. A block diagram of the complete

atomic clock system (in a somewhat modified form from

Fig. 9. Original NBS ammonia clock (courtesy of National Bureau

of Standards, Boulder, Colo ).

that shown in Fig. 9) is presented in Fig. 10. Two versions of the NBS ammonia clock were built with demonstrated

long-term stabilities of 1 x 10" 7 and 2x 10" 8

. Work on a

third version was eventually halted when it became ap- parent that atomic beam techniques offered more promise

for frequency standard development.

4A.3.2. Development of Atomic Beam Standards Utilizing Cesium or Thallium

According to Hershberger and Norton [30], I. I. Rabi

made the specific suggestion of using atomic or molecular

transitions in an atomic clock in his January, 1945 Richt- myer lecture before the American Physical Society. Four

and one-half years later a program was initiated at the National Bureau of Standards to develop an atomic beam

frequency standard utilizing cesium, which would hopefully avoid the problems of collision and Doppler broadening encountered in the ammonia absorption cell work.

93
CRYSTAL

HARMONIC

23870 4 ± 0.96 MC ABSORPTION CELL

23,870.1 MC

CRYSTA L GENERATOR

X 8 DETECTOR

PHASE MOD. KLYSTRON FREQUENCY

MULTIPLIER

X II

13.8 ± 0.12 MC FREQUENCY MODULATED

OSCILL ATOR

270 MC

FREQUENCY

MULTIPLIER

CHAIN

X 2700

SAWTOOTH

GENERATOR

PULSE SHAPE R

13.8 ±0.12 MC

MIXER 8 I 39 MC

TUNED NETWORK

DETECTOR

AMPLIFIER a PULSE SHAPER

DISCRIMINATOR

100 KC CRYSTAL

OSCILLATOR

REACTANCE

TUBE

DC

FREQUENCY

DIVIDERS

1000 CYCLE

CLOCK

50 CYCLE

CLOCK

D.C. VTVM

ERROR VOLTAGE

Fig. 10. Block diagram of NBS ammonia clock (courtesy of National Bureau of Standards, Boulder, Colo.).

The NBS group, led by H. Lyons and J. Sherwood, was

able to obtain the services of Prof. P. Kusch of Columbia

University as a consultant and set out to construct a machine

using Rabi's magnetic resonance technique, with the excita- tion radiation at 9192 MHz being applied to the cesium

beam over a 1-cm path by means of a single short-circuited section of A'-band waveguide. At the 1952 New York meeting of the American Physical Society, J. Sherwood reported

the first successful observation of the (F=4, mF = 0) *->(F= 3, mF = 0) microwave transition [31]. A photograph

of the original apparatus involved is shown in Fig. 11. Shortly thereafter, this apparatus was modified for operation with the Ramsey technique of separated oscillating

fields. Using a separation of 50 cm, a Ramsey resonance was observed with a line Q of 30 million, which corresponds

to a linewidth of the central peak of the Ramsey resonance

pattern of only 300 Hz at 9192 MHz [32]. Based on these

results, Lyons predicted an eventual accuracy capability of

1 x 10" 10. The apparatus was soon thereafter disassembled

completely and moved to the new NBS site at Boulder,

Colo., where, under the direction of R. Mockler, it was

eventually reassembled with many new components and im- proved electronics and used to thoroughly evaluate the

precision and accuracy capabilities of cesium beam fre- quency standards [33]. It was not until the 1958 1959

period that this first cesium beam standard was used to

Fig. 1 1. First operating cesium beam frequency standard—NBS I (courtesy of National Bureau of Standards, Boulder, Colo.).

more or less routinely calibrate the frequencies of the NBS

working standards. Meanwhile, L. Essen and his associates at the National

Physical Laboratory (NPL) in Teddington, England, had

placed a similar cesium beam apparatus with a Ramsey line- width of 340 Hz and an accuracy of 1 x 10" 9 into operation

in June, 1955 [34]. This standard, a photograph of which is shown in Fig. 12, was the first to be used on a regular basis 94
Fig. 12. Original NPL cesium beam frequency standard—NPL I (courtesy of National Physical Laboratory, Teddington, Englandcrown copyright reserved).

for the calibration of secondary working frequency stan- dards. Frequency measurements made with this standard,

averaged over the 1955-1958 period, were combined with

data from the U. S. Naval Observatory to obtain a determination of the cesium transition frequency (reduced to zero magnetic field conditions) in terms of the astronomical units of time interval [35]. From these measurements resulted the now familiar cesium frequency of 9192.631770 MHz

in terms of the Ephemeris second. More recently, in 1964,

this value was used to define an atomic unit of time interval. Successful operation of another laboratory-type cesium

standard was reported in 1958 by S. Kalra, R. Bailey, and

H. Daams at the National Research Council (NRC) in Ottawa, Canada [36]. They achieved a Ramsey linewidth of 290 Hz, a measurement accuracy of better than 1 x 10 9

, and a measurement precision of 1 x 10" 10

. During the next

year the first cesium standard at the Laboratoire Suisse de

Recherches Horlogeres (LSRH) in Neuchatel, Switzerland was operated by J. Bonanomi, J. de Prins, and P. Kartaschoff [37]. In the case of all these early cesium beam standards de- veloped by the various national standards laboratories, the frequency of the oscillator providing the cesium transition excitation was first adjusted manually to the peak of the resonance curve and then compared with the unknown fre- quency to be measured. Several years earlier, however, in 1954, J. Zacharias, J. Yates, and R. Haun at the Massachusetts Institute of Technology had been able to electronically stabilize the frequency of a quartz oscillator with the

(4, 0)«->(3, 0) transition in cesium [38 ]. By choosing the time

constants of the servo-loop properly, it was possible to combine the superior short-term stability of the oscillator

with the excellent long-term stability of the atomic reso- nance itself in order to achieve optimum overall perfor- mance. The authors suggested that this technique together

with a sealed-off cesium beam tube should make a commercial cesium standard feasible. Building upon these results, R. Daly and others at the National Company, Maiden, Mass., developed the first commercial cesium beam frequency standard, termed the "Atomichron," in 1956 [39]. Utilizing a cesium beam tube about 6 feet in overall length, this instrument had a specified

stability after one-hour warmup of 5 x 10 10 for measuring

periods of greater than 5 seconds for the life of the instru- ment and an accuracy of 1 x 10

" 9

. These specifications were

later significantly improved as more experience was accu- mulated. A photograph of one of the early Atomichrons is shown in Fig. 13. The relative portability of the Atomichron made it possible in March, 1958 to transport two of these instruments to England for direct comparisons with the National Physical

Laboratory cesium standard of L. Essen [40]. The results showed that the two Atomichrons agreed to within 1x10" 10 but differed from the NPL standard by

2.2xl0" 10

. The measurement uncertainties were considered to be ± 5 x 1 0

" 1

1

. The relatively close agreement observed, considering the state-of-the-art at that time, was

even more remarkable in view of the wide differences exist- ing in terms of the electronics used, the beam optics employed, and the general construction techniques followed

for the commercial and NPL instruments. As new, improved versions of cesium standards evolved

in the various laboratories based on the experiences with the

early instruments, a trend developed in the various national standards laboratories toward very long machines with the

resulting narrow linewidths, while commercial emphasis was directed more toward very short tubes with higherefficiency beam optics, high reliability, and reduced size, weight, and electrical power consumption.

Long-beam instruments, employing separations between

the two oscillating field regions ranging from 2.1 to 4.1 meters, were constructed at NPL in 1959 [41 ], at LSRH in 1960 [37], at NBS in 1963 [42], and at NRC in 1965 [43]. As a result of the long interaction times between the beam

and the RF field, extremely narrow resonance linewidths have been achieved—as low as 20 Hz in the LSRH instru- ment. In all cases, except for NPL, servo systems have been

incorporated in order to stabilize the frequency of a quartz

oscillator with the cesium resonance. Comparisons among

these four long-beam standards by means of the most recent Hewlett-Packard Company "flying clock" experiment [44] (using cesium standards) indicate agreement to within 4 x 10 12

. The best precision and accuracy figures achieved

to date with cesium standards are believed to be ±2 x 10" 13 (one sigma estimate for one-hour averaging time) and + 1.1 x 10" 12 (one sigma estimate), respectively, reported

by Beehler et al., for the NBS standard [45]. Detailed

characteristics and performance results for the various in- dividual standards discussed are given elsewhere, in the

literature.

95
Commercial development of cesium beam standards has proceeded rapidly since 1956 with primary contributions

from National Company, Varian Associates, Pickard and

Burns Electronics, and Hewlett-Packard Company. Recently, the first non-U. S. commercial cesium standard has been introduced by Ebauches, S.A., in Switzerland. These

instruments typically weigh about 60 pounds, require «50

watts of electrical power, use solid-state electronics extensively, and fit into about 9 inches of standard rack space

[46], [47]. Quoted performance characteristics include ± 1 x 10" 1

1

accuracy [46], ± 1 x 10" 1

1

long-term stability 3

[46], and 11 000-hour mean time between failures [48]. Considerable progress [49] has been made in the development of a highly refined 27-inch cesium beam tube and

associated electronics for the U. S. Air Force with a long- term stability specification of + 5 x 10" 14

.

Fig. 1 3. Early model of National Company Atomichron

(courtesy of National Company, Maiden. Mass.).

In parallel with the development of cesium beam devices,

several laboratories have also constructed atomic beam

standards utilizing thallium. Prof. P. Kusch first pointed out in 1957 that thallium should have significant advantages

over cesium in an atomic beam frequency standard in terms

of its higher transition frequency, its much-reduced sensitivity to external magnetic fields, its much simpler atomic

spectrum resulting in the ability to utilize a higher fraction of the atoms comprising the beam with reduced overlap

effects from neighboring transitions, and its lower vapor

pressure [50]. Disadvantages pointed out were the greater

difficulty in detecting the atomic beam and the requirement

for larger deflecting magnets.

In 1962 J. Bonanomi was successful in building a thallium atomic beam standard at Neuchatel Observatory in Switzer3 Total drift for the life of the beam tube.

land [51 ]. A resonance linewidth of 135 Hz, corresponding

to a line Q of 1 .6 x 108

, was obtained. The difficult problem

of detecting thallium atoms was resolved by using the sur- face ionization technique, as with cesium, but with an

oxygenated tungsten detector wire to increase its work function. In assessing the accuracy of the instrument, Bonanomi

concluded that all contributions to inaccuracy from the beam tube itself were too small to be detected. A few months later another thallium standard was placed

into operation by R. Beehler and D. Glaze at the National Bureau of Standards [52]. Experiments there also confirmed the high accuracy potential of thallium standards,

indicating that for similar-length devices, thallium provides

at least as good an accuracy figure as cesium.

Much more recently, R. Lacey at Varian Associates has developed a small (28-inch length), portable thallium beam

tube similar to the sealed-off commercial cesium beam

tubes [53]. This tube makes use of a heated silver tube as a

controllable oxygen leak for continuous oxidation of the tungsten detector ribbon. A novel double-resonance tech- nique, first developed for thallium by J. Bonanomi, was also used by Lacey in order to reduce the size of deflecting magnets needed by making use of atoms which are in states having larger magnetic moments while in the A and B deflection magnet regions of the apparatus. A resonance line- width of only 1 78 Hz was achieved and the observed signal- to-noise ratio implies a frequency stability of less than

1 x 10" 11 for one-second averaging times, provided that shot noise of the beam is the limiting factor. 4A.3.3. Development of Practical Gas Cell

Frequency Standards

The successful incorporation of the double-resonance,

optical pumping, and optical detection techniques into operating frequency standards using alkali metals, such as sodium, cesium, and rubidium, was achieved by a number of

independent laboratories starting in 1958. In that year M. Arditi and T. Carver at the International Telephone and

Telegraph Laboratories [54] and W. Bell and A. Bloom at Varian Associates [55] first used the optical detection tech- nique mentioned earlier to observe the field-independent

hyperfine resonance in Na23. The former, using argon and

neon buffer gases, obtained a linewidth of 400 Hz and were

able to measure shifts of the resonance frequency as a function of the buffer gas pressure. About the same time, P. Bender (NBS), E. Beaty (NBS),

and A. Chi (Naval Research Laboratory) developed a

practical cesium gas cell standard operating on the same

(4, 0)-»(3, 0) hyperfine transition used in the cesium atomic

beam standards [56]. The optical pumping radiation—the A->C component in the simplified scheme of Fig. 6—was

obtained from an argon discharge light source operated in a magnetic field of 5000 gauss so that one of the argon emission lines was Zeeman-shifted to a frequency near that of the desired A^C component. Resonance linewidths of as low

as 40 Hz, corresponding to a Q value of 2 x 108

, were

achieved with neon and helium buffer gases. Extensive data on pressure shifts of various buffer gases with cesium were

obtained both in these NBS experiments and in similar 96
ones conducted by Arditi at ITT Labs [57]. In 1959 Arditi reported some performance results of his cesium gas cell standard [58], including a short-term stability (several sec- onds) of ±2x10 10

, a long-term stability (minutes or

hours) of ± 1 x 10" 10

, and an accuracy of ± 3-4 x 10" 10

. The Rb87 hyperfine resonance had been used in gas cell work as early as 1957 by T. Carver of Princeton University

[59]. Utilizing optical pumping to increase the population

difference within the hyperfine structure of the rubidium

ground state but detecting the microwave transition by observing the microwave absorption, rather than the optical transmission. Carver obtained linewidths of approximately

200 Hz with an argon buffer gas. Shortly thereafter,

P. Bender et al. at the National Bureau of Standards de- veloped a new technique [60] for the optical pumping of Rb87

. A diagram of their experimental apparatus is shown

in Fig. 14. The innovation here was the method used to obtain selective pumping from only one of the hyperfine levels of the ground state up to the excited state. Light from a ru- bidium spectral lamp was filtered by a mixture of Rb85 and

5 cm Hg of argon. The broadening of the Rb85 absorption

lines produced by the argon in the filter cell caused one of

the absorption lines to overlap the lower frequency component (fl->C in Fig. 6) of the Rb87 lamp emitted light. Therefore, the light reaching the sample cell contained

mainly the higher-frequency component (A-+C) and the

optical pumping process proceeded efficiently. This filtering scheme proved so effective that all present commercial Rb

gas cell standards use it. With the apparatus shown. Bender

et al. were able to achieve linewidths of only 20 Hz for Rb87

((2 = 3 x 10 8

). They also reported a precision of 5x 10""

in setting the microwave signal frequency on the center of

the resonance line. With the accumulation of extensive data on cesium and

rubidium gas cell standards from ITT Laboratories. NBS,

Varian Associates, Space Technology Laboratories, and

NPL (England), among others, three main factors which

limited gas cell performance emerged. The first is the nature and density of the particular buffer gas used in the cell. Frequency shifts were found to be directly proportional to buffer gas pressure and were positive for light gases and

negative for heavy gases. By using mixtures of positive and

negative coefficient buffer gases it was found possible to nearly cancel out the effect. The second factor is the linear dependence of the frequency on the temperature of the gas

cell. This effect can also be minimized by proper mixtures

and pressures of buffer gases in the cell, but a single choice of such conditions does not minimize both the pressure and

temperature shifts. R. Carpenter et al. at NBS obtained

temperature coefficients of less than lxl0~"/C with

rubidium as early as 1960 [61]. Both the NBS and ITT

Laboratories groups have published measured temperature and pressure shift coefficients for a variety of buffer gases with cesium and rubidium systems [61 ]. [62]. The third limitation on performance is an observed de- pendence of the frequency on the intensity of the optical

pumping light. This is also a linear shift (at least for low

buffer gas densities) and is reduced by operating at relatively

high buffer gas pressures and gas cell temperatures. A number of other methods have been proposed to reduce this "light shift" and at present manufacturers of commercial

gas cell frequency standards are still devoting much effort to this problem. Data from several laboratories show that if frequency is plotted versus cell temperature for different

light intensities, a series of lines result which converge to a single frequency that agrees within experimental uncertainties with the values determined by atomic beam methods

PHOTOMULTIPLIER

ABSORPTION CELL FILTER BULB

(Pyrex flask containing ( Pyrei flosk containing Rb 67 an d butter gos) Rb 85 ond 5 c m A r)

WAVEGUIDE

TO FREQUENCY

J SOURCE

Fig. 14. Schematic diagram of NBS Rb8 " gas cell frequency standard [60].

(after extrapolation of the gas cell data to zero magnetic

field and zero buffer gas pressure).

Manufacturers of rubidium gas cell standards, such as Varian Associates and General Technology Corporation,

have been able to select and control the important parameters well enough to achieve long- and short-term stabilities of 1 x 10" 11 per month and 1 x 10"" for one second, re- spectively, in extremely compact packages employing solid- state electronics [63]. Because of the frequency dependence on buffer gas the device must be calibrated initially with re- spect to a primary standard. From then on. however, the gas cell performs admirably as a secondary standard with

typical stabilities as quoted above.

4A.3.4. Development of the Atomic

Hydrogen Maser

The atomic hydrogen maser, first developed at Harvard

University in 1960 by N. Ramsey, M. Goldenberg, and

D. Kleppner [64], was an outgrowth of several of the basic techniques discussed earlier, including those involving

buffer gases, atomic beam experiments with stored atoms,

and ammonia maser principles. Maser action had not been

achieved previously with gaseous atoms in the ground state, primarily because of the much smaller values of the relevant magnetic dipole matrix elements as compared to the electric dipole matrix elements characterizing molecular transitions such as the 7=3, K= 3 resonance used in ammonia masers. This difficulty was overcome in the atomic hydrogen maser

by using a "storage bulb" with a non-disorienting wall coating in order to achieve very long effective interaction times

97
of the order of one second. The hydrogen maser developed at Harvard combined in a

single device several outstanding advantages previously

offered in part by a number of different types of atomic fre- quency standards. For example, an extremely narrow line- width of about 1 Hz results from the long interaction time. The spectral line is of very high purity in contrast to the complex structure of the ammonia line. Shifts due to first- order Doppler effect are essentially eliminated by virtue of

the averaging process as the typical atom makes about 104 random bounces off the storage bulb walls before under- going magnetic relaxation from the desired energy state or escapes from the bulb. Finally, the high signal-to-noise ratio characteristic of the maser technique helps to produce the

best short-term frequency stability yet observed with any

atomic frequency standard. A schematic diagram of Ramsey's original apparatus is shown in Fig. 15. Atomic hydrogen from a Wood's dis- charge source first passes through a state separator, just as

in the ammonia maser. However, because the transition of

interest in hydrogen is a magnetic dipole transition, the state separator consists of a hexapole deflecting magnet rather than an electrostatic version. Atoms in the higher energy

state of interest (F= I , mF = 0) are focused into the quartz

storage bulb as indicated by the dashed lines, while the lower-state atoms (F= 0, mF = 0) are defocused. The storage

bulb is centered within a cylindrical resonant cavity tuned

to the frequency of the ( 1 . 0)*->(0, 0) hyperfine transition at 1420 MHz. While bouncing around within the bulb the atoms radiate to the lower energy state and eventually leave the bulb through the entrance aperture after about a second. With the paraffin wall coating first used, at least 104

colli- sions with the walls could occur without seriously perturbing the energy states. Teflon coatings have been found to perform even better. With sufficient beam flux (%4x 10' 2 atoms per second) and high enough cavity Q, maser oscilla- tion was achieved. Not shown in Fig. 15 is a system of Helmholz coils for applying a small dc magnetic field to the cavity region, corresponding to the C field in atomic beam

magnetic resonance devices. A photograph of this first Harvard hydrogen maser is shown in Fig. 16. As in the case of the earlier experiments with buffer gases and wall coatings mentioned previously, the maser oscilla- tion frequency was shown both experimentally and theoretically [65] to depend on the wall coating used. Since the

collision rate is an important factor, the "wall shift" de- pends on the bulb size. For bulb diameters normally used

the shift amounts to a few parts in 10" but appears to be

stable with time. Wall shifts have been measured both at Harvard [66] and by R. Vessot et al. of Varian Associates

[67] by measuring maser frequency for different sizes of

storage bulbs. Work on hydrogen masers was undertaken at Varian

Associates and at LSRH in Switzerland in 1961. C. Menoud

and J. Racine at LSRH [68] and Vessot and Peters at Varian [69] reported successfully operating masers in 1962. The Varian maser has been commercially available for several years and employs many refinements developed for commercial applications, such as elaborate temperature

WOOD'S DISCHARGE SOURCE

,U ^ "i

I t~-~" I STATE

STOp SELECTOR =2N

PARAFFIN LINED QUARTZ BULB TUNED RF CAVITY

Fig. 15. Schematic diagram of Ramsey's original hydrogen maser [64].

Fig. 16. Ramsey's first hydrogen maser (courtesy of N. Ramsey,

Harvard University, Cambridge. Mass.).

control of the resonant cavity to reduce cavity-pulling fre- quency shifts due to mistuning, provision for effective de- gaussing of the three-layer magnetic shielding, use of oil- free ion pumps to reduce the possibility of contaminating

the wall coating and changing the wall shift, and control of

the hydrogen flux by a temperature-controlled palladium

leak. More recently, H. Andresen at the U. S. Army Elec- tronics Command (Ft. Monmouth, N. J.) has developed a servo system for automatically keeping the resonant cavity

tuned to the frequency of the atomic resonance [70]. Further work on hydrogen masers is currently in progress at many laboratories throughout the world. For a summary of the present status of hydrogen maser

performance results the reader is referred to the article by

A. McCoubrey in this issue. It is worth noting, however,

that maser stabilities of 1 x 10" 14 for averaging periods in the vicinity of 30 minutes and absolute inaccuracies of less than 1 x 10" 12 have already been achieved [71 ]. Since 1963,

a number of intercomparisons have been made between

hydrogen masers and cesium beam standards involving

equipment and personnel from five different laboratories in the U. S. and one in Switzerland. The results [45], [71], with one exception in 1963, show that all measured values of the hydrogen frequency in terms of cesium (after application of appropriate corrections to both the hydrogen and

cesium raw data) agree to within the quoted measurement

uncertainties, which ranged from 2 x 10" 1

1

to 1 .2 x 10" 12

. 98
4A.4. CONCLUSIONS

An attempt has been made to at least touch upon the

highlights of the historical development of the better known

types of present atomic frequency standards. A number of other types, or modifications of existing types, of atomic

standards are being investigated in various laboratories and

may eventually prove superior to all those discussed here. In this class would be included the large-bulb (60-inch

diameter) hydrogen maser now under construction at Harvard University for reduction of wall shifts and cavitypulling shifts, the rubidium maser with its extremely high short-term stability, masers using other atoms with optical

pumping, electric resonance molecular beam devices operating at several hundred GHz, and possibly even lasers if the

large frequency gap between RF and the optical region can

be successfully bridged. In view of the large amount of

effort and resources being put into the development of im- proved atomic frequency standards at present in many

countries of the world it seems likely that the performance of atomic frequency standards will continue to improve rapidly

in the foreseeable future. 4A.5. REFERENCES

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- '

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Electronic Engrg.. vol. 68. p. 251. March 1949.

[26] C. Cleeton and N. Williams, "Electromagnetic waves of 1 . 1 cm wavelength and the absorption spectrum of ammonia." Phys. Rev., vol. 45. pp. 234-237. February 1934.

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stabilization of microwave oscillators with spectral lines." J. Appl.

Phys.. vol. 18. pp. 1112-1 115. December 1947.

[30] W. Hershberger and L. Norton. "Frequency stabilization with micro- wave spectral lines." RCA Review, vol. 9. pp. 38-49. March 1948.

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[32] H. Lvons, "Spectral lines as frequency standards." Ann. N. Y. Acad.

Sci.. 'vol. 55. pp. 831-871. November 1952.

[33] R. Mockler. R. Beehler. and J. Barnes, "An evaluation of a cesium beam frequency standard." in Quantum Electronics. A Symposium.

C. H. Townes. Ed. New York: Columbia University Press. 1960. pp. 127-145.

[34] L. Essen and J. Parry, "Atomic standard of frequency and time in- terval," Nature, vol. 176. pp. 280-282. August 1955.

[35] W. Markowitz, R. Hall, L. Essen, and J. Parry. "Frequency of cesium

in terms of ephemeris time." Phys. Rev. Lett., vol. 1. pp. 105-107. August 1958.

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[37] P. Kartaschoff. J. Bonanomi. and J. de Prins. "Cesium frequency

standards: Description and results." Hclv. Phys. Acta. vol. 33. pp. 969-973. 1960.

[38] J. R. Zacharias, J. G. Yates, and R. D. Haun. Jr., "An atomic fre- quency standard," Proc IRE (.Abstract), vol.43, p. 364. March 1955.

[39] W. Mainberger, "Primary frequency standard using resonant cesium." Electronics, vol. 31, pp. 80-85, November 1958.

[40] A. McCoubrey, "Results of comparison : Atomichron-British cesium beam standard," Proc. 12th Annual Frequency Control Svmp.. pp.

pp. 648-664, 1958.

[41] L. Essen and J. Parry, "An improved cesium frequency and time standard," Nature, vol. 184, p. 1791. December 1959.

[42] R. E. Beehler and D. J. Glaze, "The performance and capability of cesium beam frequency standards at the National Bureau of Stan- dards," IEEE Trans, on Instrumentation and Measurement, vol. IM15, pp. 48-55, March-June, 1966.

[43] A. Mungall. H. Daams. and R. Bailey, "The Canadian cesium beam

frequency standard," Proc. 20th Annual Frequency Control Symp..

pp. 436-447. 1966.

[44] L. Bodily. D. Hartke, and R. Hyatt. "World-wide time synchronization. 1966." Hewlett-Packard J., vol. 17. no. 12. pp. 13-20. August

1966.

[45] R. Beehler, D. Halford. R. Harrach. D. Allan, D. Glaze. C. Snider.

J. Barnes, R. Vessot, H. Peters, J. Vanier, L. Cutler, and L. Bodily. "An intercomparison of atomic standards," Proc. IEEE (Letters).

vol. 54. pp. 301-302, February 1966.

[46] Model 5060 Data Sheet, Hewlett-Packard Company. Palo Alto.

Calif.. October I. 1966.

[47] NC 3501 Data Sheet. National Company. Melrose. Mass.

[48] L. Bodily, "Performance characteristics of a portable cesium beam

standard," Proc. 20th Annual Frequency Control Symp.. pp. 448^463.

1966.

[49] J. Holloway and R. Sanborn, "Characteristics of a high performance

cesium beam frequency standard." Proc. 19th Annual Frequency

Control Symp.. pp. 344-368, 1965. 99
[50] P. Kusch. "Precision atomic beam techniques." Proc. 11th Annual

Frequency Control Symp.. pp. 373-384. 1957.

[51 ] J. Bonanomi. "A thallium beam frequency standard." IRE Trans, on

Instrumentation, vol. 1-1 1. pp. 212 215. December 1962.

[52] R. Beehler and D. Glaze. "Experimental evaluation of a thallium beam frequency standard," Proc 17th Annual Frequency Control Symp., pp. 392-407, 1963.

[53] R. Lacey, "A thallium atomic beam tube for frequency control."

Proc. 20th Annual Frequency Control Symp., pp. 416^123. 1966.

[54] M. Arditi and T. Carver. "Optical detection of zero-field hyperfine

splitting of Na 2J ." Plus. Rev., vol. 109. pp. 1012-1013. February

1958.

[55] W. Bell and A. Bloom. "Optically detected field-independent transi- tion in sodium vapor." Phvs. Rev., vol. 109. pp. 219-220. January

1958.

[56] E. Beaty. P. Bender, and A. Chi. "Narrow hyperfine absorption lines of Cs 133

in various buffer gases," Phvs. Rev., vol. 1 12. pp. 450- 451, October 1958.

[57] M. Arditi and T. Carver, "Frequency shift of the zero-field hyperfine

splitting of Cs' 33 produced by various buffer gases," Phvs. Rev., vol. 112. p. 449. October 1958.

[58 ] M. Arditi, "Evaluation of a breadboard gas cell frequency standard,"

Proc. 13th Annual Frequency Control Symp., pp. 655-667, 1959.

[59] T. Carver, "Rubidium oscillator experiments," Proc 11th Annual

Frequency Control Symp., pp. 307-31 7, 1957.

[60] P. Bender, E. Beaty, and A. Chi, "Optical detection of narrow Rb87

hyperfine absorption lines," Phvs. Rev. Lett., vol. I, p. 311-313, November 1958.

[61 ] R. J. Carpenter. E. C. Beaty, P. L. Bender, S. Saito, and R. O. Stone, "A prototype rubidium vapor frequency standard," IRE Trans, on

Instrumentation, vol. 1-9, pp. 132 135. September 1960.

[62] M. Arditi and T. Carver, "Pressure, light, and temperature shifts in optical detection of 0-0 hyperfine resonance of alkali metals," Phys.

Rev., vol. 124, pp. 800-809, November 1961.

[63] Manufacturer's specification sheets.

[64] H. Goldenberg, D. Kleppner, and N. Ramsey, "Atomic hydrogen

maser," Phvs. Rev. Lett., vol. 5, pp. 361-362, October 1960.

[65] D. Kleppner, H. Goldenberg, and N. Ramsey, "Theory of the hy- drogen maser," Phys. Rev., vol. 126, pp. 603-615, April 1962.

[66] S. Crampton, D. Kleppner, and N. Ramsey, "Hyperfine separation of ground-state atomic hydrogen," Phys. Rev. Lett., vol. 11, pp. 338-340. October 1963.

[67] J. Vanier. H. E. Peters, and R. F. C. Vessot, "Exchange collisions, wall interactions, and resettability of the hydrogen maser," IEEE

Trans, on Instrumentation and Measurement, vol. IM-13, pp. 185-188, December 1964.

[68] C. Menoud and J. Racine, "Atomic hydrogen maser. description and

preliminary results," Helv. Phys. Acta. vol. 35, pp. 562-567, Sep- tember-October 1962.

[69] R. F. C. Vessot and H. E. Peters, "Design and performance of an atomic hydrogen maser," IRE Trans, on Instrumentation, vol. I— 11, pp. 183-187, December 1962.

[70] H. Andresen and E. Pannaci, "Servo-controlled hydrogen maser

cavity tuning," Proc. 20th Annual Frequency Control Symp., pp. 402-415. April 1966.

[71 ] R. Vessot. H. Peters, J. Vanier, R. Beehler, D. Halford, R. Harrach, D. Allan. D. Glaze, C. Snider, J. Barnes, L. Cutler, and L. Bodily, "An intercomparison of hydrogen and cesium frequency standards," IEEE Trans, on Instrumentation and Measurements, vol. IM-15. pp. 165-176, December 1966.

Manuscript received January 6, 1967; revised February 16, 1967.

Reprinted from the PROCEEDINGS OF THE IEEE

VOL. 55, NO. 6, JUNE, 1967

pp. 792-805 Copyright © 1967

The Institute of Electrical and Electronics Engineers, Inc. printed in the u.s.a.

100
CHAPTER 4 — PART B

RECENT PROGRESS ON ATOMIC FREQUENCY STANDARDS*

Roger E. Beehlert

Contents

Page 4B.1. Introduction 103

4B.2. Laboratory Cesium Standards 103

4B.3. Hydrogen Standards 105

4B.4. Commercial Cesium Standards 107

4B.5. Commercial Rubidium Standards 108

4B.6. References 108

* Manuscript received June 7, 1973. tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302.

101
"Progress is the activity of to-day and the assurance of to-morrow." Ralph Waldo Emerson

Recent progress on laboratory and commercial atomic frequency standards is summarized for the 1967-1973 period. The discussion is restricted to those devices which are judged to be leading con- tenders in the primary laboratory standards field or which have present or short-term future commercial potential. In the laboratory standards classification a number of cesium beam devices are now

in operation with reported accuracies of 1 X 10" 12 or better and measured stabilities of a few parts in 10 12 for 1-second averaging times. Hydrogen standards, in the maser form, have demonstrated the

best reported stability yet for moderate averaging times (=1000 seconds) of better than 1X10 -14

, although the accuracy potential has not yet proved as good as for the cesium beam devices. Other

forms of hydrogen standards, operating as passive beam devices, are also under investigation and show

considerable promise in both their accuracy and stability characteristics. Commerical activity remains concentrated on cesium beam and rubidium gas cell standards with hundreds of both types having been sold. Commercial cesium standards are achieving both improved

performance — in fact, approaching that of some recent laboratory devices— and a greatly reduced

sensitivity to environmental influences. The major rubidium standards improvements have consisted

of achieving very respectable stabilities under much more severe environmental conditions and in much smaller package sizes.

Key words: Atomic frequency standards; cesium beam standards; hydrogen beam standards; hydrogen

masers; rubidium frequency standards.

102
4B.1. INTRODUCTION

Chapter 4A of this volume describes the historical development of various types of laboratory and commercial atomic frequency standards during the

period ending in 1967. This chapter is intended to summarize further developments in this field which

have occurred in the 1967-1973 period.

Before discussing specific details of some of this more recent progress, it may be of interest to consider briefly the related question of "Why do organizations continue to invest so much time, money, and

energy in pursuing work on atomic frequency standards that already possess almost unbelievable ac- curacy and stability?" The answer— at least in recent years— seems to lie not so much in some

rather nebulous desire to "build a better mousetrap" for the challenge and prestige, but rather in the fact that the atomic standard has proved to a

great many people that it is a most useful device in a wide variety of applications. As important practical

benefits have been realized by the scientific and

technological segments of our society from using

atomic standards, several trends began to develop more or less simultaneously.

First, based on some of the earlier successful

applications of atomic standards in such areas as metrology, navigation, and satellite tracking, sys- tems designers in many other technological areas began thinking in terms of solving their own problems by using time and frequency technology. An

example here would be the conceptual design of an

aircraft collision avoidance system (ACAS) that is based on time and frequency techniques using state- of-the-art atomic standards for frequency and time

reference functions both on board the aircraft and

on the ground.

Second, as these new applications appeared, the

commercial potential of such devices increased

greatly, leading to an intensive development effort to produce better atomic standards in terms of

performance, cost, reliability, and suitability for

field applications in relatively hostile environments.

Third, in response to the increasing availability of atomic standards with continually improving

performance, reduced sensitivity to environmental

conditions, and especially at an acquisition cost reduced from the original price in excess of $50,000

per unit down to under $10,000, the systems de- signers were able to consider even more sophisticated systems and techniques, based on the new

atomic standards and the related time and fre- quency technology. We are now seeing some of the

practical results in the form of advanced navigation

systems, such as Loran-C, Omega, and various

military satellite navigation systems; advanced

communications systems employing synchronized

digital transmissions; and better satellite tracking

systems which make use of cesium or hydrogen maser atomic frequency standards. Also, improved

methods and equipment have been devised for disseminating highly accurate time and frequency

information over large geographical areas using

existing or proposed satellites, television network

facilities, and radio navigation systems. The in- creasing use of atomic standards in scientific applications has already made possible the design and,

in some cases, the performance of new relativity

experiments [l], 1 significant advances in metrology

which may eventually lead to a unified standard

for at least time, frequency, and length \2\; and

greatly improved knowledge of the earth and other

components of our solar system through longbaseline interferometry [3] and satellite-based

measurements. For example, the Goldstone LBI

system, using hydrogen maser frequency and time

references, can already detect relative earth move- ments with a resolution of about 10 cm. Jet Propulsion Laboratory (JPL) personnel would like even

better resolutions in order to study possibilities of predicting earthquakes, but are limited at present

to 10 cm because the maser references "flicker out" at about 7 X 10~15 [4]. This particular application, and the collision avoidance system mentioned

before, are rather interesting because they offer two

examples where important public benefits — that is, safety from air collisions and earthquakes— may

eventually be rather directly dependent on the

existence of atomic standards with state-of-the-art performance.

These interrelated processes that have been

described — namely, the increasing availability of

useful atomic frequency standards making possible new applications and systems with important

benefits to many segments of the population which

in turn generate further demands for still better

atomic standards— seem likely to continue in the

foreseeable future, generating in the process the

motivation needed to insure continued development

of atomic standards.

4B.2. LABORATORY CESIUM

STANDARDS

In discussing now more specifically some of the recent progress in this field, it should be noted that recent improvements already achieved in atomic

standards and those that will be needed in the future

are not confined to better performance, in the sense

only of accuracy and stability. In many applications the accuracy and stability already available

is adequate for the purpose. But, field use may

require greater reliability, less sensitivity to the

environmental conditions, smaller size and weight,

and simpler operation. In other applications, particularly when several standards are needed, re- duced acquisition cost may be the most important

consideration.

During the past few years we have already seen

substantial improvements with regard to many of

1 Figures in brackets indicate literature references at the end of this chapter.

103
these aspects. If we first consider progress from the

laboratory standards point of view, cesium beam

devices continue to serve as the national reference

standards in many nations, based on the 1967

definition of the second in terms of the cesium

resonance frequency. Work is still active on hydrogen masers, however, and new techniques using

hydrogen beams, for example, may eventually

lead to a better absolute standard than cesium.

The state of the art for laboratory cesium beam

standards has now advanced to the point where

documented accuracies for at least three national

laboratory reference standards — those at the

National Research Council (NRC) in Canada, the

Physikalisch-Technische Bundesanstalt (PTB)

in Germany, and the National Bureau of Standards

(NBS) in the United States — have been published

at ±1 X 10~12 or better [5, 6, 7]. Perhaps the extent

of these accomplishments can best be seen by considering the plot in figure 4B.1 showing how published accuracy figures for various laboratory cesium

standards have improved over the past 16-year

period. The plotted points are generally equivalent

to 1-sigma type estimates. While the exact placement of some of the values may be a little uncertain

due to some necessary guessing about confidence

levels of a few of the published estimates, three

conclusions seem fairly clear. First, substantial

steady progress has occurred over a long period in designing, building, and evaluating more accurate

laboratory cesium standards. Second, several of

the present devices have broken the 1 X 10~ 12 barrier. And, third, further improvement to near

the 1 X 10~13 level is already taking place.

The better-than-1 X 10~12 accuracies already

achieved have been made possible largely by careful attention to the three principal sources of

errors identified in several different laboratories

throughout the world as experience was gained

with earlier versions of cesium beam standards.

These primary sources of inaccuracy are associated

with phase shifts in the microwave cavity, uncertainties in the magnetic C-field, and various problems in the excitation electronics.

lxlO" 9 ,-

YEAR

Fig. 4B.1. Accuracy trends in laboratory cesium standards: 1956-1973.

The phase shift problem has been attacked in the recent laboratory standards by providing greatly

improved capabilities for detecting the presence

and the magnitude of any residual phase shift error using techniques that are convenient enough

to permit relatively rapid determinations as often

as desired and precise enough so that the uncertainties in the phase shift error determination can

be much less than 1 X 10"12

. NRC, PTB, NBS,

National Physical Laboratory (NPL) in England,

and the National Research Laboratory of Metrology

(NRLM) in Japan have accomplished this by de- signing standards which allow the direction of the

atomic beam traversal through the microwave cavity

to be reversed, thus reversing the sign of any phase

shift error in the process. In earlier versions,

reversal was accomplished by physically rotating

the cavity structure itself or by physically inter- changing the cesium oven and detector leaving the

cavity undisturbed. Both techniques suffered

somewhat from lack of reproducibility, yielding

measurement uncertainties of near 1 X 10~ 12. The newer standards now in operation at NRC,

NRLM, NPL, and NBS include ovens and detectors at each end of the machines so that frequency

measurements can be made for each beam direction sequentially in a short time and without dis- turbing the microwave cavity or interrupting the vacuum inside the beam tube. This technique,

using repeated measurements, should reduce

uncertainties in the phase shift error correction

in these new standards significantly, provided that

sufficient knowledge is available concerning the

beam velocity distributions and trajectories for each direction of traverse. A different method for measuring phase shift errors at the 1 X 10~ 13 level is used in the present

PTB standard, consisting of making a frequency

measurement at two widely differing mean beam

velocities, which can be selected at will by inter- changing two different sets of focusing magnets,

designed to focus different velocities [8]. Because

any phase shift error is velocity dependent, this technique provides a convenient estimate of the

error. Two other techniques are in use at NBS to evalu- ate possible frequency errors due to cavity phase

shift [9]. Both also make use of the fact that any

cavity phase shift error present will vary with the mean velocity of the atoms contributing to the resonance signal. With the first method frequencies

corresponding to different beam velocities can be

measured by varying the input microwave power,

since the effective mean beam velocity depends on

the power level in the cavity. If the appropriate

velocity distributions are known from other meas- urements (see below) or calculations, the cavity

phase shift, and the resultant frequency bias, can

be computed.

The second, more novel, technique makes use of pulsed microwave excitation to preferentially select

104
only a certain narrow range of atomic velocities,

according to their time of flight between the two

ends of the microwave cavity and the pusle repeti- tion rate [10]. The velocity distribution can be

inferred rather directly, and the measurement of the

standard's frequency at different velocity settings

yields the phase shift bias. C-field errors, due to magnetic field non-uniformities and instabilities, have also been successfully

reduced in most recent standards to below the

1 X 10~ 13 level. The credit belongs primarily to use

of better shielding materials and designs. Several

of the newer lab standards are making use of

longitudinal C-fields, which can be produced with

great uniformity by means of solenoid coils. Electronic problems continue to provide major

difficulties at times in the laboratory cesium beam

standards, but some significant progress has been

made. Frequency multipliers, beam signal processing components, and even crystal oscillators are now becoming available, which have greatly improved phase-noise characteristics. These in- herently more stable circuits, combined with new

modulation schemes, such as the square-wave

modulation systems in use at NRC and PTB, have

resulted in some estimates for inaccuracies contributed by major electronics systems associated

with the standard of only about 1 X 10~13 [9, 11 J. A final area of increasing concern as accuracy

levels below 5 X 10~ 13 are sought is the uncertainty

associated with the correction applied for 2d-order

Doppler shift. Better knowledge of the actual beam

velocity distribution will be needed for each in- dividual standard in order to attain accuracies near

1 X 10-13

. Studies at NBS and NRC indicate some

success in deducing the necessary velocity information from a computer analysis of the experimental

Ramsey resonance curves [9, 12]. The pulsedexcitation method mentioned above in connection

with the phase shift error evaluation also provides

rather directly the velocity information needed for the 2d-order Doppler shift correction.

The stability performance of present laboratory

cesium standards, along with some projections for the near future, is summarized in figure 4B.2 by means of a stability versus averaging time plot.

Recent state of the art is indicated by the upper

band which shows measured 1-second stabilities ranging from 3 X 10" 12 for the PTB standard [13] up to about 1 X 10_n for some of the recent NRC

and NBS devices [7, 11]. The upper dashed line shows the performance expected within the next few months from the NBS-X4 beam tube, developed

jointly by NBS and the Hewlett-Packard Company.

The 1-second stability goal for NBS-X4 is about

1 X 10~ 12 and results from a relatively large beam

flux and an efficient dipole beam optics system.

The lower dashed line shows the anticipated sta- bility for NBS-5, a new long-beam standard that is now in the evaluation phase at NBS [9], as inferred

from beam noise measurements. This performance

results principally from use of a very large beam

, 0

-l 5 I 1 1 1 1 I 1 I 0.1 1 10 10 Z 10 3 10 4 10 5 10 6 AVERAGING TIME (SECONDS)

Fig. 4B.2. Stability performance data for laboratory cesium

standards.

and an efficient beam optics system designed with

the aid of a large digital computer. One motivation

for seeking such high stability is that the large

number of necessary measurements involved in the

accuracy evaluation of such a standard at the

1 X 10"13 level can be performed and repeated in reasonably short time periods.

4B.3. HYDROGEN STANDARDS

Although cesium standards have demonstrated

very impressive accuracy and stability performance

and still seem to have a bright future in the primary

standards area, some old and new competitors are

also attracting considerable interest. The hydrogen

maser, while not yet achieving an accuracy per- formance that exceeds the laboratory cesium

devices, nevertheless has come close, and its stability performance for moderate averaging times

has not been matched by any other type of device.

The main impediment to accuracies better than

about 1 X 10"12 [14, 15, 16] is still the uncertainty

in determining the wall shift caused by the hydrogen atoms bouncing off the walls of the storage

bulb. Several interesting attempts are being tried

to reduce this error source, including the Harvard

large-bulb maser, featuring a 150-cm storage bulb

intended to reduce the number of wall collisions per second and thus the magnitude of the wall

shift by perhaps a factor of 10. The desired accuracy

105
goal has not yet been reached, but some modifications being added to this maser in the form of a deformable storage bulb may permit the wall shift error source to be reduced to about ± 1 X 10~ 14

[17]. This technique involves the use of a deformable

storage bulb built in such a way that the volume of

the bulb can be changed by a large factor without

changing the bulb's surface area [18]. It allows

evaluation of the wall shift without introducing the

uncertainties caused by using a series of different

size bulbs with similar, but not identical, surfaces.

A third method being tried is operation of a maser

at a bulb temperature of about 100 °C, where some

experiments have shown the wall shift goes through

zero [19]. Somewhat on the other side of the coin,

however, is the recent suggestion by Crampton

that two previously unexpected effects involving

hydrogen spin exchange shifts and magnetic field gradients may produce H-maser inaccuracies

amounting to several parts in 1012 [20]. The stability performance of some hydrogen masers at NRC Canada, Jet Propulsion Laboratory

(JPL), NASA Goddard Space Flight Center, and

also at Smithsonian Astrophysical Observatory

(SAO), is summarized in figure 4B.3. Stabilities as good as 6 X 10-15 have been observed for averaging

times in the 100-1000 second range [21, 22].

AVERAGING TIME (SECONDS)

Fig. 4B.3. Stability performance data for hydrogen maser

standards.

The NRC maser is a laboratory device; the JPL

and NASA versions have been developed for long

term, trouble-free operation at NASA tracking

sites; and the SAO maser has been developed

specifically for relativity tests aboard a spacecraft

or rocket vehicle.

Largely because of the wall-shift limitations on

the accuracy potential of the hydrogen maser, two

groups at NBS and NASA-Goddard have been

recently working on other ways for using the simple

hydrogen resonance as a frequency standard which

do not involve the disadvantages associated with maser action. In both cases the intent is to combine

the advantages of the cesium beam and hydrogen maser technologies, while eliminating or reducing some of their disadvantages.

NBS has demonstrated the technical feasibility

of a hydrogen storage beam standard which uses

a hydrogen beam with atom detection as in a cesium

standard, but with the added feature of a storage or bounce box in the beam path [23]. This increases

the atom's interaction time with the rf field, re- sulting in a narrower resonance. The technique

appears to offer reduced cavity-pulling effects and a better way to evaluate the wall shift in the

storage bulb relative to the maser method. Development into a full atomic frequency standard with

potentially superior performance will, however,

require considerable work on a more efficient detector for atomic hydrogen.

A more basic hydrogen beam standard, without

the storage feature, has been built and successfully

operated at NASA-Goddard [24]. The operation is similar to that of a cesium atomic beam machine, but some significant advantages are realized with hydrogen due to its much simpler atomic spectrum.

Figure 4B.4 shows some of the Ramsey resonance

curves obtained at three different C-fields. Because

of the simpler spectrum, no overlap occurs between

the standard frequency transition and others, even

HYDROGEN TRANSITION [M, m=0)—-|F=0, m=0| AT VARIOUS MAGNETIC FIELDS

HBX -1 8/10/71 POWER -OPTIMUM

HORIZ l.llKHz/cm

I-- -i dim n./bWttK L ID K DC COUPLED H-- F 1. : U MHI t

l/c i cv iun | ii C IIRRf NT 1 INCRFA 5E PRESENT AT DETECTOR -h ± SWEEPS L TC R

Fll TFR !C w

f

— -b- ORIfilNAI DATA *> _ 2 j -J- 1

- mA! /K t ~i

... if ... b

e«

-- j

- zL. 1

lc Hi

;, —

—

+- -t r

Fig. 4B.4. Hydrogen transition curves from NASA-GSFC

hydrogen beam standard (courtesy H. Peters, Goddard Space

Flight Center).
at very low C-field values. The Ramsey resonance

width shown here of 1.2 kHz was obtained with room

temperature atoms and some preferential selection

of low-velocity atoms. Although this line Q of about

1.2 X 106 is much lower than for present cesium

standards, a planned cryogenic beam source may

later produce narrower resonances with a resulting

increase in line Q. Dr. Peters of NASA-Goddard

believes the hydrogen beam standard should prove

as stable as the hydrogen maser and is potentially

much more accurate— perhaps at the 1 X 10" 13 level [24]. NBS has also made some preliminary frequency

stability measurements with another variation of a hydrogen storage beam device in which one detects

changes in the microwave signal caused by the

hydrogen resonance rather than detecting the atoms

themselves [23]. An oscillator was locked to the

hydrogen transition frequency using the dispersion

of the resonance. Stabilities of 4 X 10-13 were ob- served for averaging times of 30 seconds and 3

hours, using quartz oscillator and commercial

cesium references, respectively.

Other potential techniques for laboratory fre- quency standards, such as ion storage and saturated

absorption in methane or other gases are being

investigated at several labs [25, 26, 27](see chap. 6). 4B.4. COMMERCIAL CESIUM

STANDARDS

The remainder of this paper will attempt to summarize what has been happening recently in the commercial frequency standard field. As has

been the case for some time now, recent commercial

efforts have been concentrated on cesium and

rubidium devices. Hundreds of both types have been

sold and new improved versions are appearing on

the market in response to the development of new

and expanding application areas. Commercial cesium standards are designed

primarily for high stability; reasonable accuracy;

small size and weight; moderate electrical power

requirements; high reliability; and insensitivity to environmental effects. Presently existing models,

and expecially some newer versions under active

development, show significant advances in each of

these areas. Figure 4B.5 summarizes stability performance

for various commercial cesium standards which are

either presently available or which are in an ad- vanced stage of development. The upper band,

labeled intermediate-performance standards, in- cludes the great majority of commercial cesium

standards now in use and some new versions being

developed for field applications where small size and weight and intermediate stability performance

over a wide range of environmental conditions are

the most important design considerations. For

example, one manufacturer has succeeded in maintaining this intermediate-level stability per- formance in a package one-third the size and oneAVE RAGING TIME (SECONDS)

Fig. 4B.5. Stability performance data for commercial cesium

half the weight of earlier versions [28]. This achievement is made possible largely through use of a recently developed 15-cm long beam tube, employing six separate pairs of stacked beams to provide a relatively high beam flux. In addition to the high signal-to-noise ratio resulting from this design, its use of back-to-back beam pairs provides

a greatly reduced sensitivity of the output frequency

to acceleration. Corresponding improvements have

been made in the associated electronics and in its performance under severe environmental conditions, such as those encountered in many field applications.

Another manufacturer has independently de- veloped a smaller beam tube with a volume of

about 115 cm3 and an accompanying improved

electronics package, which is designed to reduce

the user cost relative to previous versions avail- able. The stability of this standard is also expected

to fall within the upper band plotted in figure 4B.5

[29].The lower band in figure 4B.5 indicates some

documented and projected results for several ver- sions of high-performance cesium beam tubes

developed by private industry. One particular

model, already commercially available, is about

40 cm (16 in) long and employs multiple beams for high beam flux [28]. This tube has a specified

stability performance equivalent to cry (100

107
seconds) = 9x 10 13 or better [30] and has demonstrated a long-term stability of <r y(l0 days) =

1 X 10~ 14 [31]. A different design, high-performance cesium

beam tube has been developed by another manufacturer which may eventually offer even better

performance. Though not yet in commercial pro- duction, a prototype version has achieved measured

stabilities corresponding to cr y(l00 seconds) =

3X10-13 [29]. This tube is about 53 cm (21 in)

long and uses a novel form of hybrid beam optics

featuring one dipole and one hexapole deflecting

magnet. It is interesting to note that the stabilities produced by these commercial high-performance

beam tubes are equal to or better than those characteristic of the most advanced laboratory standards

until very recently.

Some of the newer commercial cesium standards

also reflect significant improvements in their ability

to operate within their stated performance limits under rather severe environmental conditions. One

model is designed to operate within ±1X10~U

over a temperature range from —55 °C. to 4-74 °C.

[28]. The same version also provides a greatly

reduced sensitivity to external magnetic fields and

a much improved stability of its internally-generated

C-field by virtue of better magnetic shielding, more

efficient degaussing techniques, and an improved

C-field structure. More attention has been paid

in recent years to the mechanical design of cesium

beam standards and the newer units are now less sensitive to shock and vibration effects. In some

cases faster warmup of the instrument has been

made possible. These advances, when combined

with the trend towards smaller size, weight, and

electrical power consumption, are likely to stimulate wider use of atomic frequency standards for

field applications in the future. 4B.5. COMMERCIAL RUBIDIUM

STANDARDS

Recent developments in the rubidium standard

marketplace have perhaps been a little less dra- matic than for cesium, but nevertheless very sig- nificant. Figure 4B.6 presents the current state of

the art with respect to the stability performance of

commercial instruments. Models manufactured by

a number of different companies in the United

States, Germany, and Japan provide frequency

stability reasonably consistent with the plotted curve. Development efforts in the rubidium case have concentrated primarily on units which maintain the level of performance indicated in figure

4B.6 over wider ranges of environmental conditions; require smaller size, weight, and electrical power; and cost less. One version has been developed under military contract which has demonstrated state-of-the-art

stability performance in military and airborne

environments [32]. This rubidium standard has

successfully passed all required military specifiAVERAGING TIME (SECONDS)

Fig. 4B.6. Stability performance data for commercial rubidium

standards.

cations for temperature extremes, shock, vibration, and so forth, staying generally within a few

parts in 10 11 even under the most severe conditions.

Another interesting development in the rubidium

standard field has appeared recently in the form of a very compact standard manufactured in Europe,

but also commercially available within the U.S.

[29]. Although its stability specifications of better

than 5 X lO" 11 over 1 second and better than 1 X 10" 10 from month to month are somewhat inferior to those achieved in larger, commercial units, the

device represents a significant technological ad- vance in several other respects. Its packaged size

in one form is only about 10 cm X lO cm X 11 cm

and it weighs only 1.3 kg. It requires only 10

minutes for warmup, 13 W of electrical power at 25 °C. ambient, and will operate within 1 X 10~ 9 over a temperature range from —25 °C. to +65 °C. 4B.6. REFERENCES

[1] Hafele, J. C, and Keating, Richard E., "Around-the-world

atomic clocks: Observed relativistic time gains," Science, 177, No. 4044, pp. 168-170 (July 14. 1972).

[2] Halford, D., Hellwig, H., and Wells, J. S., "Progress and

feasibility for a unified standard for frequency, time and

length," Proc. IEEE (Lett.), 60, No. 5, pp. 623-624 (May 1972) (see chap. 7).

[3] Klemperer, W. K., "Long-baseline radio interferometry

with independent frequency standards," Proc. IEEE, 60,

No. 5, pp. 602-609 (May 1972).

108
[4] MacDoran, P. F., Private communication (June 9, 1972).

[5] NRC cesium beam frequency evaluations:

a. Mungall, A. G., Bailey, R., Daams, H., and Morris, D., "A re-evaluation of the N.R.C. long cesium beam

frequency standard," Metrologia, 4, No. 4, pp. 165-168

(October 1968).

b. Mungall, A. G., Bailey, R., Daams, H., Morris, D., and

Costain, C. C., "A preliminary report on Cs V, the new NRC long-beam primary frequency and time standard,"

Proc. 27th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 12-14, 1973), pp. 317-333 (Electron. Ind. Assn. Washington, DC 20006, 1973).

[6] Becker, G., Fischer, B., Kramer, G., and Mueller, E., "Diskussion der Inneren Unsicherheit des Neuen CasiumStrahl-Zeitnormals der Physikalisch-Technischen Bundesanstalt," (Discussion of the internal uncertainties of the new cesium beam time standard of the PTB), Proc. Colloque Int. de Chronometrie (Paris, France, September

16-20, 1969), Ser. A, Paper A2, 9 pages (Nouvelle Faculte des Sciences 11, Quai St., Paris (5°) France, 1969) (in German).

[7] Glaze, D., "Improvements in atomic cesium beam frequency

standards at the National Bureau of Standards," IEEE

Trans, on Instrum. and Meas., IM-19, No. 3, pp. 156-160

(August 1970) (see also chap. 5B for more recent NBS

results.)

[8] Becker, G., Fischer, B., Kramer, G., and Mueller, E., "Neukonstrucktion eines Casiumstrahl-Zeitnormals an

der Physikalisch-Technischen Bundesanstalt," (New

construction of a cesium time standard at the PTB),

Proc. Colloque Int. de Chronometrie (Paris, France, September 16-20, 1969), Ser. A, Paper Al, 12 pages

(Nouvelle Faculte des Sciences 11, Quai St., Paris (5°) France, 1969) (in German).

[9] Glaze, D., Hellwig, H., Jarvis, S., Jr., Wainwright, A., and

Allan, D., "The new primary cesium beam frequency

standard: NBS-5," Chapter 5B, this volume.

[10] Hellwig, H., Jarvis, S., Jr., Halford, D., and Bell, H. E., "Evaluation and operation of atomic beam tube frequency

standards using time domain velocity selection modulation," Metrologia, 9, No. 107-112 (September 28, 1973).

[11] Daams, H., "Cesium beam servo system using square wave

frequency modulation," Proc. 24th Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command, Ft., Monmouth, NJ, 07703, April 27-29, 1970) pp. 294-300

(Electron. Ind. Assn., Washington, DC, 20006, 1970).

[12] Mungall, A. G., "The second order Doppler shift in cesium beam atomic frequency standards," Metrologia, 7, No. 2, pp. 49-56 (April 1971).

[13] Becker, G., Fischer, B., Kramer, G., and Mueller, E., "The

cesium-beam primary frequency standard CS1 of the Physikalisch-Technische Bundesanstalt," Proc. Fre- quency Standards and Metrology Seminar (Laval University, Quebec, Canada, August 30, 31-September 1, 1971), H. Hellwig (Ed.), pp. 5-16 (Dept. of Elec. Eng., Laval

Univ., Quebec, Canada, June 1972).

[14] Morris, D., "Hydrogen maser wall shift experiments at the National Research Council of Canada," Proc. 25th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 26-28, 1971), pp. 343-347 (NTIS, AD 746211, 1971).

[15] Essen, L., Donaldson, R. W., Bangham, M. J., and Hope,

E. G., "Frequency of the hydrogen maser," Nature, 229,

No. 5280, pp. 110-111 (January 8, 1971).

[16] Hellwig, H., Vessot, R. F. C, Levine, M. W., Zitzewitz,

P. W., Allan, D. W., and Glaze, D. J., "Measurement of the unperturbed hydrogen hyperfine transition frequency," IEEE Trans, on Instrum. and Meas., IM-19, No. 4, pp. 200-209 (November 1970).

[17] Reinhardt, V., "Large storage box hydrogen maser with

flexible bulb," Proc. Frequency Standards and Metrology

Seminar (Laval University, Quebec, Canada, August 30, 31-September 1, 1971), H. Hellwig, (Ed.), pp. 158-163

(Dept. of Elec. Eng., Laval Univ., Quebec, Canada, June 1972).

[18] Debely, P. E., "Hydrogen maser with deformable storage bulb," Proc. 24th Ann. Symp. on Frequency Control

(U.S. Army Electronics Command, Ft. Monmouth,

NJ, 07703, 1970), pp. 259-262 (Electron. Ind. Assn., Washington, DC, 20006, 1970).

[19] Zitzewitz, P. W., "Surface collision frequency shifts in the atomic hydrogen masers," Proc. 24th Ann. Symp. on

Frequency Control (U.S. Army Electronics Command,

Ft. Monmouth, NJ, 07703, pp. 263-269 (Electron. Ind. Assn., Washington, DC, 20006, 1970).

[20] Crampton, S. B., "Prospects for the atomic hydrogen maser

as a primary frequency standard," Proc. Frequency

Standards and Metrology Seminar (Laval University,

Quebec, Canada, August 30, 31-September 1, 1971), H. Hellwig (Ed.), pp. 117-118 (Dept. of Elec. Eng., Laval

Univ., Quebec, Canada, June 1972).

[21] Morris, D., Daams, H., Mungall, A. G., Bailey, R., Miller, L. G., and Thomson, M. M., "Atomic frequency standards and timekeeping at the National Research Council,"

Proc. Frequency Standards and Metrology Seminar

(Laval University, Quebec, Canada, August 30, 31-Sep- tember 1, 1971), H. Hellwig (Ed.), pp. 119-146 (Dept.

of Elec. Eng., Laval Univ., Quebec, Canada, June 1972).

[22] Finnie, C, Sydnor, R., and Sward, A., "Hydrogen maser

frequency standard," Proc. 25th Ann. Symp. on Frequency

Control (U.S. Army Electronics Command, Ft. Monmouth,

NJ, 07703, April 26-28, 1971), pp. 348-351 (NTIS, AD

746211, 1971).

[23] Hellwig, H., and Bell, H. E., "Experimental results with atomic hydrogen storage beam systems," Proc 26th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ, 07703, June 6-8, 1972), pp. 242-247 (Electron. Ind. Assn., Washington, DC,

20006, 1972).

[24] Peters, H., "Hydrogen as an atomic standard," Proc. 26th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ, 07703, June 6-8, 1972), pp. 230-241 (Electron. Ind. Assn., Washington, DC,

20006, 1972).

[25] Hellwig, H., "Areas of promise for the development of

future primary frequency standards," Metrologia, 6, No. 4, pp. 118-126 (October 1970). (See chap. 6). [26] Schiiessler, H. A., "The ion storage tube, a proposal for a new atomic frequency standard," Metrologia, 7, No.

3, pp. 103-107 (July 1971).

[27] Hall, J. L.. and Borde, C, "Measurement of methane hyperfine structure using laser saturated absorption," Phys.

Rev. Lett., 30, No. 22, pp. 1101-1104 (May 28, 1973).

[28] Hyatt, R., Throne, D., Cutler, L. S., Holloway, J. H., and

Mueller, L. F., "Performance of newly developed cesium beam tubes and standards," Proc. 25th Ann. Symp. on Frequency Control (U.S. , Army Electronics Command,

Ft. Monmouth, NJ, 07703, April 26-28, 1971), pp. 313-

324 (NTIS, AD 746211. 1971).

[29] McCoubrey, A. O., and Kern, R. H.. "Precision frequency- sources," Proc. 4th Ann. NASA and DOD Precise Time

and Time Interval (PTTI) Plan. Meet. (NASA. Goddard

Space Flight Center, Greenbelt, MD 20771, November

14-16, 1972), pp. 46-54 (NASA X-814-73-72, Greenbelt, MD 20771,1973).

[30] Hewlett-Packard Company catalog, p. 281 (1973).

[31] Winkler, G. M. R., "Intermediate term frequency measure- ments with the HP computing counter in the USNO clock time system," Proc. 4th Ann. NASA and DOD Precise Time and Time Interval (PTTI) Plan. Meet. (NASA,

Goddard Space Flight Center, Greenbelt, MD 20771. November 14-16, 1972), pp. 152-167 (NASA, X-814-

73-72, Greenbelt, MD 20771, 1973).

[32] Frerking, M. E., and Johnson, D. E., "Rubidium frequency and time standard for military environment." Proc. 26th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ, 07703. June 6-8 1972).

pp. 216-222 (Electron. Ind. Assn.. Washington. DC. 20006.

1972).

109

CHAPTER 5 — PART A

IMPROVEMENTS IN ATOMIC CESIUM BEAM FREQUENCY

STANDARDS AT THE NATIONAL BUREAU OF STANDARDS

David J. Glazet

Contents

Page

5A.1. Introduction 113

5A.2. Modifications to the NBS-III System 113

5A.3. Accuracy Capability of NBS-III (1969) 115

5A.4. Some Immediate Goals 116

5A.5. Conclusions 116

5A.6. References 117

t Time and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302.

Ill
"Science moves, but slowly, slowly, creeping on from point to point." Alfred Tennyson,

Locksley Hall, I. 134 The National Bureau of Standards Frequency Standard, NBS-III, a cesium beam with a 3.66- meter interaction region, has been in operation since 1963. The last published (1966) accuracy capability for NBS-III was 1.1 X 10~ ,2 (lcr). Recently, several new solid-state broadband frequencymultiplier chains have been constructed. Reduction of the random phase noise by more than 20 dB

compared to the previous state of the art has been obtained consistently. In addition, a solid-state servo system has been installed to control the frequency of the 5-MHz slave oscillator. Comparisons were made between NBS-III and one of the commercial cesium standards in the NBS clock ensemble. The relative fractional frequency stability a(N = 2, T=l days, t=1 day) =

1 X 10~ 13 was observed for nine weekly comparisons. The very-long-term frequency stability for this recently improved NBS-III system has not been evaluated fully. Due to the improvements both in electronic systems and evaluative techniques, however, an accuracy of 5 X 10~13 (lo- ) for a single evaluative experiment is reported. Substantial effort is being expended toward improvements of the accuracy of figure of merit

(presently 10) of the NBS cesium standard. The modified system, to be called NBS-5, is expected to be in operation in the latter half of 1970 and to exhibit a figure of merit in excess of 500.

Key words: Accuracy of NBS-III; cesium beam frequency standard; double beam system; error budget, NBS-III; frequency stability, NBS-III; NBS-III precision; NBS-III servo system; NBS frequency

standard; noise effects; quartz crystal reference.

112
5A.1. INTRODUCTION

THE NATIONAL Bureau of Standards Frequency

Standard, NBS-III, a cesium beam with a 3.66- meter interaction region, has been in operation

since September 1963. From that time until October 1965,

NBS-III together with NBS-II, a cesium beam with a

1.64-meter interaction region, comprised the National

Bureau of Standards Frequency Standard (NBSFS). By

December 1965, NBS-II had been converted to an experimental thallium standard, and two Varian Associates H-10 atomic hydrogen masers and one Hewlett-Packard

5060A cesium beam were operating temporarily at the NBS [1]. The subsequent intercomparison of frequencies

among the commerical frequency standards and NBS-III

provided the most accurate measurement of any physical

quantity, namely the frequency of the hyperfine separation

of hydrogen. During these measurements the accuracy

capability consistently obtained from NBS-III was

1.1 X 10~12 (lo-). Improvement of both the accuracy

capability and the precision of the NBSFS is a prime

objective of the NBS. There are several improvements

that have been made since 1965 in NBS-III, the present

NBSFS, shown in Fig. 1. 5A.2. MODIFICATIONS TO THE

NBS-III SYSTEM

During the 1965 intercomparisons mentioned above,

it became evident that phase-difference instability in the NBS-III Ramsey cavity [2] was the major source of uncertainty in the frequency of NBS-III [1], [3]. As ex- pected, replacement of the oil-diffusion pumps with ion pumps in mid-1966 reduced both the phase-shift instability

and the ultimate pressure. The pressure was improved

by a factor of 10 to about 10"8 torr (1.3 X 10"6 N/m2 ), but the phase-difference instability was reduced only by

a factor of 2. The phase-difference instability was not significantly

reduced until a precise procedure was followed whenever

it was necessary to open the vacuum system. This procedure

includes the use of dry highly purified argon gas as the

pressurizing agent, as well as thermal control to prevent water condensation. , When these techniques were used,

Fig. 1. The NBS-III cesium beam frequency standard, August

1966-August 1969.

the discrepancy between the fractional frequency changes

for two reversals of beam direction was 4.0 X 10~ 13

. These two reversals were made, one at the beginning and one at the end of a 9-month period, as part of independent fre- quency calibrations. Also the vacuum system was opened

several times during this period to recharge the cesium

oven. There was no evidence during this period to suggest

any phase-difference instability worse than 4 X 10" 13

. As a result, the magnitude of the fractional frequency

bias correction applied during this period for the phasedifference effect in NBS-III was (38.8 db 2) X 10~ 13

. The

uncertainty of 2 X 10" lj

, listed as item 7) in Table I,

is one-half the discrepancy noted above. It is apparently

attributable to some small amount of chemical reaction on the cavity walls. Although the results for cavity phase-difference stability are improving, it should be stated that the author regards the proper solution of this long-standing problem to be

fourfold.

1) Construct the Ramsey cavity with a low phase

difference such that frequency bias due to this effect is not larger than 1 X 10" 13 [4]. 2) Baffle and getter the beam-coupling holes to the extent that the cesium contamination becomes unimportant.

3) For long interaction-length laboratory standards

such as NBS-III, where the highest possible accuracy is

113
required, construct a double oven and detector system

so that beam-direction reversals through the cavity can

be accomplished in a matter of hours without breaking

the vacuum seals [3]. 4) Construct simple electronic systems to monitor

with ease the long-term stability of the cavity phase

difference, and calibrate these systems initially by means

of the double-beam system in item 3). These improvements

are presently under construction at NBS and will be

installed as modifications to the NBS-III system (see Section IV).

Other improvements have been made, and these are concerned primarily with the NBS-III electronic systems.

The basic configuration of the frequency-lock servo system is shown in Fig. 2. The servo system used to control the frequency of the 5-MHz oscillator is a solid-state unit with an improved phase modulator. The modulator

is a passive device employing varactor phase modulation

of a tuned circuit resonant at 5 MHz. The modulator

operates at a fundamental modulation frequency of 18.75 Hz with a second-harmonic level 85 dB below the

level of the fundamental modulation. This is an improvement of 30 dB compared to the higher second-harmonic

level of the previous modulator and reduces the frequencypulling effects of modulator second-harmonic distortion to insignificant levels. The remainder of the servo system

has numerous test points for measurements to ensure

that errors associated with parameters such as demodulator

asymmetry, demodulator dc offset, and integrator dc offset can be reduced to low levels. For example, the dc offsets in the demodulator and integrator are typically stable enough and low enough so that no errors as large as

1 X 10

-13 accumulate in a two-week period. It is relatively

simple to readjust these parameters for an important

frequency calibration or to monitor them occasionally

during a long run. The stability of this servo is about

ten times better than the system it replaced in mid-1968;

consequently, the reliability and long-term stability of NBS-III have improved accordingly.

Indeed, the relative fractional frequency stability <r(N = 2, T = 7 days, r = 1 day) = 1 X 10~ 13 was observed

for nine weekly comparisons of NBS-III with one of the two commercial cesium standards that are part of the present NBS clock ensemble [5]. Here a

2 is the Allan

variance [6], T is the period of the sampling, and t is the sample time. Each standard, then, is not worse than

1 X 1CT

13

, and if the two standards were assigned equal

weighting, then one would assign to each the value of

<j = 0.7 X 10~ 13 for the one-day samples just described. The frequency stability of the cesium beam standard

is ultimately limited by the shot noise of the particle detection (surface ionization of the cesium atoms is measured with an electrometer). It is important that the performance of the standard is not degraded by other

noise sources, such as a flicker of phase noise process occurring in the frequency-multiplier chains [7] or a

flicker of frequency noise process occurring in the 5-MHz

quartz-crystal oscillator. These processes are described

in detail by Allan [6] and by Cutler and Searle [8]. In

order to meet fully the requirements of improved NBS

cesium beam tube designs, it was decided to lower the

noise levels generated by the frequency-multiplier chains. Several new solid-state 5-60 MHz multipliers were constructed using local radio-frequency negative feedback

in the lower frequency stages to reduce the flicker of phase noise, as suggested and proved by Halford et al, [7]. Improvements in the phase noise level by at least 20 dB

compared to the previous state of the art have been

obtained consistently. One of these frequency-multiplier

chains is presently in use in the 5-60 MHz section of the 9.2-GHz excitation system shown in Fig. 2. For use in future NBS frequency standards, three more of the 5-60

MHz multipliers have just been incorporated in new, all solid-state, 5 MHz-9.2 GHz excitation systems. As ex- pected, the measured phase noise levels of these new

systems are also improved by at least 20 dB compared

to the levels in previous excitation systems. Fig. 3 demonstrates this fact, and the data shown were obtained at

the output frequency of 9.2 GHz.

5 MHz

QUARTZ

CRYSTAL

OSCILLATOR

VARACTOR PHASE

MODULATOR

X 12 X 9 XI7 STEP FREQUENCY FREQUENCY RECOVERY

MULTIPLIER MULTIPLIER DIODE

(TRANSISTORS) t«cuuM Tuees> MULTIPLIER

91800

AMPLIFIER MH

ADJUSTABLE FREQUENCY

Z |SYNTHESIZER

12.6 PHASE MHz DETECTOR

8.75 Hz OSCILLATOR

CORRECTION MONITOR

j I2j6 MHz

1

' F AMPLIFIER XTAL MIXER

CORRECTION VOLTAGE.

SERVO HOT WIRE

PREAMPLIFIER DETECTOR

NBS -m

ATOMIC CESIUM BEAM

NARROW

BANDWIDTH

MAIN SERVO

AMPLIFIER

ADJUSTABLE PHASE

SHIFTER

OPERATIONAL

AMPLIFIER ELECTRONIC INTEGRATOR ERROR

MONITOR

CHOPPER DEMODULATOR

Fig. 2. The NBS-III frequency-lock servo system. The varactor phase modulator and the solid-state frequency multiplier are improved low-noise units.

The quantity £(/) in Fig. 3 is a convenient frequencydomain measure of phase fluctuations, and it is defined

for one device only, that is, for one amplifier or one fre- quency-multiplier chain, etc. It is the ratio of the power

in one phase-noise sideband, referred to the input carrier frequency, on a per-hertz-of-bandwidth basis, to the total signal power, at Fourier frequency / from the carrier. The subscript —1 on <£_, means that the component

114
of £ that varies as is under discussion. In Fig. 3, £ is seen to vary as /

-l in the vicinity of the modulation fre- quency (18.75 Hz), that is, flicker of phase noise is the dominant effect. In order to measure their £ spectrum,

the two chains were driven from a single 5-MHz quartzcrystal oscillator, and the phases of the output signals

to the phase detector were adjusted for maximum sensitivity to phase noise (phase quadrature). The upper

dashed line shows the previous state of the art. Some improvements had already occurred in reduction

of power line related sideband levels, and the new solid- state 5 MHz-9.2 GHz chains are designed to further reduce these effects. These chains are not completely

tested so that valid data on power-line related sideband

levels are not yet available. The flicker of phase and the flicker of frequency noise

levels observed in the best 5-MHz quartz-crystal oscillators are approximately at the level of the shot noise of the

detected beam in the improved cesium beam standards

under construction at NBS, evaluated at the optimum

frequency of modulation of about 1 Hz. Further improvement in the white frequency noise of cesium beam standards

will necessitate improvement in quartz-crystal oscillator frequency stability. A project with the goal of improving

the stability of slave oscillators was established at NBS

in July 1969. 5A.3. ACCURACY CAPABILITY OF

NBS-III (1969)

In Table I are listed those effects that contribute significantly to the inaccuracy of NBS-III. The last item is the

purely random scatter of the measured NBS-III frequency

with running time, for 1-hour averages, in large part

due to the shot noise of the beam. All of the other ten

items are bias uncertainties. The bias uncertainties do

not represent fluctuations with running time, but are instead a measure of the uncertainty of the size of the frequency offset (bias) due to each effect. These offsets tend to remain constant from one measurement interval

to the next. However, these offsets may vary whenever

changes are made in the apparatus. It is the view of the author that the term "accuracy capability" should be

applied to Table I until the long-term behavior of the improved NBS-III system can be evaluated more completely. Accuracy capability is the accuracy attained when

a set of evaluative tests is made, as distinct from the accuracy of the standard when left undisturbed for a

long period of time [9]. Table II lists a typical set of all the frequency bias

corrections applied to NBS-III for each beam direction.

All other biases are estimated to be zero within the uncertainties listed in Table I. Items l)-6) in Table I, though examined more recently,

are identical to the results obtained in 1966 [1], [3] and

will not be discussed in detail here. Of these, items 1), 3), and 5) are actually estimated to be slightly smaller than

1.0 X 10"u

; however, since these effects are examined

rather infrequently, the uncertainty values were rounded

upward to 1.0 X 10" 13

. Item 7) was already discussed in Section II. In order to evaluate item 8), it was necessary to ascertain the power dependence of the frequency of NBS-III for each beam direction through the resonant cavity [3]. At

first it appeared to be impossible to achieve the desired

fractional frequency stability of the reference standard

of 1 or 2 parts in 10

13

, because no suitable atomic reference standards existed at the NBS after 1965. It was suggested

by Halford1 that a high-quality quartz-crystal oscillator be used for the reference.TABLE I Accuracy Capability of NBS-III (1969)

l<r Estimate

Source Parts in 10 13

1) Uncertainty in average C-field magnitude \HC \ < 1.0 2) Use of #c

2 for H*c 0.3

3) Uncertainty due to first- and second-order Doppler shifts < l .o 4) Uncertainty due to inequality of average

C-field magnitudes in cavity and drift regions, \Hc (l)\ *\Hr (L)\ ().:;

.r

)) Uncertainty in T-field polarity-dependent

shifts < 1.0 6) Uncertainty in cavity tuning < 0.15 7) Uncertainty due to cavity phase-difference

instability 2.0 8) Uncertainty in power dependent shifts 2.6 9) Multiplier chain transient, phase-shifts < 2.0 10) Uncertainty due to phasing problems and dc

offsets in servo-system electronics < 2.5

1 1 ) Random uncertainty due to shot noise of beam, for measurement t = 1 hour 1.6 Total l<r estimate of accuracy capability < 5.1 X 10~"

(square root of sum of squares)

Frequency {Hz}

Fig. 3. Normalized spectral density of phase noise power for NBS

frequency-multiplier chains.

TABLE II Typical Fractional Frequency Biases in NBS-III (1969)

Beam Direction 1 Beam Direction 2

Magnetic field + 1087.8 X io--13 + 1087.8 X 10"-13 Cavity phase difference -38.8 X io--13 +38.8 X io--13 Finite radiation field intensity (power

dependence) +7.8 X 10"-13 +7.8 X 10"-11 Second-order Doppler -1.8 X 10"-13 -1.8 X 10"-13

1 D. Halford, private communication, 1968.

115
The quartz-crystal oscillator is an excellent solution

to the problem, as can be seen in Fig. 4, where the methods

of Allan are applied [6]. The quantity r is defined as the

ratio of T to t, where T is the sum of the dead time and

the sample time. A suitable sample time r lies between

the cesium beam servo time constant (~1 second for NBS-III) and point 7, the intersection of the two curves

of Fig. 4. To achieve a high precision, then, the method

of synchronous detection is employed. In other words,

the microwave power incident on the NBS-III cavity is alternately switched between two predetermined levels

1 and 2, and averaging of the frequency difference occurs

for an interval t at each power level. The process continues

until the desired quantity of data is obtained. The fre- quency-difference data are then tabulated in the order

in which they occurred, and algebraic differences between

the first and second, second and third, etc., are computed

and also tabulated. These frequency differences, then,

represent the changing frequency of NBS-III as the microwave power alternates between the two levels 1 and 2. The precision obtained in this manner is limited by the number of independent frequency differences obtained, and it is not degraded by crystal-oscillator

frequency drift or flicker noise level. In this manner the

slopes of the power dependences of the frequency of NBS-III, from the optimum operating power of 1.4 mW

down to 0.4 mW, have been determined with precisions

consistently between 1 and 2 parts in 10

13 for both beam

directions through the cavity. Harrach [3] has shown

that the slopes so obtained from the point of optimum

microwave power (that power for which the detected beam intensity is maximized) decreasing downward

toward zero power are sufficiently linear that the zero- power extrapolation can be based accurately on these

data. The method described by Harrach [3] for extrapolation to zero microwave power was used to estimate

b

Vf

1 1 1 NBS-H vs. Commercia

i H Maser

yN

. 8("2-f|) V

-- 2

r = T 160*30 |n

T " 160

~ M3

B » 1 Hz

Flicker Phase \ Flicker Frequency Two Commercial Quartz Xtal Oscillators^

i i i i

10 10' I0

5 10' Sampling Time t (seconds)

Fig. 4. Relative fractional frequency stability versus sampling

time: NBS-III versus a commercial atomic hydrogen maser, and

two commercial quartz-crystal oscillators versus each other.

the uncertainty quoted in item 8) of Table I. This value

agrees reasonably well with the one obtained in 1965 [1], where hydrogen masers provided the high-stability reference standard. The less expensive quartz-crystal

oscillator is ideal for this application.

Items 9) and 10) are improved significantly with respect

to the situation existing in 1965 [1]. This improvement

is directly attributable to the improved design and per- formance of the solid-state servo and modulator systems,

and the solid-state frequency-multiplier chains as dis- cussed in Section II. 5A.4. SOME IMMEDIATE GOALS

A new solid-state servo system has been designed with

particular attention given to reduction of long-term

transient effects and leakage signals. It is of even more

advanced design than the solid-state servo mentioned

in the earlier sections. Also, new completely solid-state 5 MHz- 9.2 GHz frequency-multiplier chains have just

been constructed, and testing is being conducted now. Components have been completed for a "double-beam

system," that is, a system with an oven and detector

at each end of the beam tube. This arrangement should

ensure that the phase difference of the new Ramsey cavity can be measured easily, and with high accuracy. The

cavity is to be constructed with a very small and very

stable phase difference. These components together with new dipole deflecting magnets are to be assembled into a complete, computer-optimized beam optics system [10] using the NBS-III beam tube. Because of the extensive modifications for improved accuracy and precision, the standard will be redesignated NBS-5. It is expected to exhibit a precision a of measurement for r = 1 second

of better than 2 X 10" 13

. This requires a figure of merit

[11] exceeding 500. This corresponds to an improvement

by more than a factor of 50 over the present NBS-III

system. NBS-5 is expected to be in operation in the latter half of 1970. 5A.5. CONCLUSIONS

It is evident that considerable effort is being expended

by National Standards Laboratories to advance the ac- curacy and precision capabilities of cesium beam frequency

standards [12], [13]. It appears likely that development

will occur soon of laboratory cesium beam frequency

standards with accuracy capabilities of from 1 to 2 parts

in 10

13 (la).ACKNOWLEDGEMENT

The author wishes to express his sincere appreciation to Dr. D. Halford for many helpful discussions and suggestions regarding electronic designs, experiments, and

the preparation of this paper. Others of the NB3 staff whose efforts are similarly appreciated are Dr. J. A. Barnes

for many helpful discussions of the analyses of power

spectra and servo systems; A. E. Wainwright for design,

development, and test of the phase modulator and of the

frequency-multiplier chains; C. S. Snider for assistance

in the operation and maintenance of NBS-III, and for considerable mechanical design on NBS-5; and D. W. Allan

for very valuable assistance in data acquisition and

analysis.

116
5A.6. REFERENCES

[1] R. Vessot, H. Peters, J. Vanier, R. Beehler, D. Halford, R.

Harrach, D. Allan, D. Glaze, C. Snider, J. Barnes, L. Cutler, and L. Bodily, "An intercomparison of hydrogen and cesium

frequency standards," IEEE Trans. Instrumentation and

Measurement, vol. IM-15, pp. 165-176, December 1966.

[2] N. F. Ramsey, "A molecular beam resonance method with

separated oscillating fields," Phys. Rev., vol. 78, pp. 695-699, June 1950.

[3] Robert J. Harrach, "Some accuracy limiting effects in an atomic beam frequency standard," Proc. 20th Ann. Symp. on Frequency

Control (Fort Monmouth, N. J.), pp. 424-435, 1966.

[4] R. F. Lacy, "Phase shift in microwave Ramsey structures,"

Proc. 22nd Ann. Symp. on Frequency Control (Fort Monmouth,

N. J.), pp. 545-558, 1968.

[5] J. A. Barnes, D. H. Andrews, and D. W. Allan, "The NBS-A

time scale—Its generation and dissemination," IEEE Trans.

Instrumentation and Measurement, vol. IM-14, pp. 228-232, December 1965.

[6] D. W. Allan, "Statistics of atomic frequency standards," Proc. IEEE, vol. 54, pp. 221-230, February 1966.

[7] D. Hxlf 3rd, A. E. Wainwright, and J. A. Barnes, "Flicker

noise of phase in RF amplifiers and frequency multipliers: Characterization, cause, and cure," Proc. 22nd Ann. Symp. on

Frequency Control (Fort Monmouth, N. J.), pp. 340-341, 1968.

[8] L. S. Cutler and C. L. Searle, "Some aspects of the theory and

measurement of frequency fluctuations in frequency standards,"

Proc. IEEE, vol. 54, pp. 133-154, February 1966.

[9] R. E. Beehler, R. C. Mockler, and J. M. Richardson, "Cesium

beam atomic time and frequency standards," Metrologia, vol. 1, pp. 114-131, July 1965.

[10] D. J. Glaze (to be published).

[11] R. F. Lacey, A. L. Helgesson, and J. H. Hollowav, "Short-term

stability of passive atomic frequency standards,1

' Proc. IEEE,

vol. 54, pp. 170-176, February 1906.

[12] A. G. Mungall, R. Bailey, H. Daams, and D. Morris, "A

re-evaluation of the N. R. C. long cesium beam frequency

standard," Metrologia, vol. 4, pp. 165-168, October 1968.

[13] G. Becker, B. Fischer, G. Kramer, and E. K. Muller, "Neuentwicklung einer Casiumstrahlapparatur als primares

Zeit- und Frequenznormal an der Physikalisch-Tecnnischen Bundesanstalt," PTB-Mitteilungen, vol. 79, no. 2, pp. 77-80,

April 1969.

Manuscript received February 5, 1970. This work was supported

by the National Bureau of Standards, Boulder, Colo. It is based on

a talk presented at the 16th General Assembly of the International

Scientific Radio Union (URSI), Ottawa, Ont., Canada, August

1969, by Dr. J. A. Barnes, Time and Frequency Division, National Bureau of Standards, Boulder, Colo. The author is with the Atomic Frequency and Time Standards

Section, National Bureau of Standards, Boulder, Colo. 80302.

Reprinted by permission from IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

Vol. IM-19, No. 3, August 1970

Copyright © 1970, by the Institute of Electrical and Electronics Engineers, Inc. PRINTED IN THE U.S.A.

117

CHAPTER 5 -PART B

THE NEW PRIMARY CESIUM BEAM FREQUENCY STANDARD: NBS-5*

David J. Glaze,f Helmut Hellwig,t Stephen Jarvis, Jr.,f

Arthur E. Wainwright,t and David W. Allan

f

Contents

Page 5B.1. Introduction 121

5B.2. The NBS-5 System 121

5B.3. Preliminary Experimental Results (Status April 1973) 122

5B.4. References 124

'Manuscript received May 15, 1973 tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, CO 80302.

119
"Thus times do shift — each thing his turn does hold; New things succeed,

as former things grow old." Robert Herrick The design of NBS~5 is discussed in detail including its relation to previous NBS primary cesium beam frequency standards. Stabilities of 3 X 10~ 14 for one day averaging are reported and tentative data on its accuracy capability are given. Preliminary results give an evaluated accuracy of 2 X 10-13 with indications that this figure may be further improved in the future.

Key words: Cesium beam standard; Doppler effect; frequency accuracy; frequency stability; power

shift; primary frequency standard.

120
5B.1. INTRODUCTION

A primary cesium beam frequency standard

serves to realize the unit of time interval, the second,

in accordance with the international definition as formulated at the XIII General Conference on Weights and Measures in 1967: "The second is the

duration of 9 192 631 770 periods of the radiation

corresponding to the transition between the two

hyperfine levels of the ground state of the cesium133 atom" (see chap. 1). The realization of an output

frequency from a real device involves several steps

of physical and technical processing which may

cause frequency deviation of the output frequency

from the atomic unperturbed transition frequency.

The magnitude of each such bias can be evaluated

with the aid of experiments and of theoretical

considerations. However, these biases are not known to infinite certainty. The magnitude of these

uncertainties depends on the degree of theoretical

understanding as well as on the precision with which

experimental parameters can be measured. This

precision depends on the design and construction

of the cesium beam tube and electronics of the

primary frequency standard as well as on the fre- quency stability of the reference frequency standard

used in the evaluation of the primary standard. The

combined uncertainty of all biases is referred to as the accuracy of the frequency standard.

Since the first atomic clock was realized as an ammonia frequency standard by Harold Lyons at NBS in 1948 [l], 1 several cesium based primary

frequency standards have operated at NBS.

Standards called NBS-I, NBS-II, and NBS-III

served successively as primary frequency standards

during the 1950's and 60's [2, 3]. NBS-III, our

previous operating frequency standard, was

evaluated in 1969 to an accuracy of 5 parts in 10 13 [3] (see chap. 5A).

The experience gained with NBS-III indicated

that the main limitations for accuracy, in addition

to significant electronics problems, were the magnetic field — in particular its homogeneity and

stability — the second-order Doppler effect, and the

cavity phase difference. Therefore the design and

construction of a new primary cesium beam fre- quency standard with the designation NBS-5

was initiated with features incorporated to significantly reduce the above mentioned limitations. 2 The instrument was designed to achieve a frequency

accuracy of 1 part in 1013

. To facilitate accuracy

evaluations, the design also aimed at greatly in- creasing the stability of the device which is basically

given by the available atomic beam intensity and the

1 Figures in brackets indicate the literature references at the end of this Chapter.

2 Another cesium beam frequency standard with the designation NBS-X4 was also constructed in cooperation with the Hewlett Packard Company. This device was not

specifically designed to be used as a primary cesium beam frequency standard, however, new methodology permits such use.

line-Q. The stability for 1 hour sampling time

NBS-III was 2 parts in 1013

. The NBS-.r

, design

aimed at improving this value by at least 1 ordei "I magnitude, thus allowing measurement precisions

approaching 10~ 14 within 1 hour. NBS-S was pul into operation during the latter part of 1972, and

has since undergone several phases of accuracy

evaluation.

5B.2. THE NBS-5 SYSTEM

A photographic view of NBS-5 with all elec- tronics systems is depicted in figure 5B.1. The complete system has a length of about 6 meters overall. The vacuum system is basically a stainless steel tube 25 cm in diameter and is evacuated by three

200 1/s ion pumps which can be closed off with

valves for servicing. In order to minimize thermal

effects, the Ramsey type cavity is located inside

the vacuum system. The total length of the NBS-5

cavity is 3.74 meters. The drift region is carefully

shielded by three magnetic shields. The typical

operating field is about 60 milli-oersted, and a

field homogeneity of better than 1 percent (peak-topeak variation) is achieved along the beam axis. The beam tube permits an atomic beam to traverse the path through the cavity in either direction. Each end of the beam tube is equipped therefore

with both identical magnets and oven-detector

combinations. This capability of beam reversal

allows a measurement of the cavity phase-difference

bias. This bias arises because of a (usually small)

difference in the phase of the microwave signal in the two interaction regions. Indeed, the NBS-5

cavity phase difference was adjusted (by length

trimming of the two halves) to be less than lmrad

before the cavity was installed in the beam tube. The resulting bias changes sign if the beam tra- verses the cavity in the opposite direction. The oven-detector combination is arranged in such a way that it can be adjusted in the deflection

plane of the atomic beam, perpendicular to the beam

axis; in addition, the oven can be aimed independently at different angles. The oven can accept

ampules filled with 3 g to 5 g of cesium which yield a projected lifetime of many months of continuous

operation. The collimator of the oven is an array

of about 500 separate channels producing a beam

with a rectangular cross section of 2 mm X 9 mm.

With an oven temperature of 100 °C the projected

beam intensity at the detector is approximately

108 atoms per second. The detector is a platinum

ribbon. Because of the relatively high beam intensity and the high purity of the platinum ribbon

(total background current is of the order of 0.1 pA), no mass spectrometer and electron multiplier are employed. Instead, a field effect transistor is mounted in close proximity to the detector. The

detector signal is processed in low-noise preamplifiers external to the beam tube. If one end operates

121
Fig. 5B.1. View of NBS-5. All electronics systems are shown.

in the "oven" mode the detector is moved aside;

however, if the end is used in its "detector" mode,

the detector can move in front of the oven and, at the same time, a carbon getter plate baffles the oven

collimator. Lowering the oven temperature to ~ 24 °C also reduces its output.

The microwave signal is obtained from a crystal

oscillator at a basic frequency of 5.00688 MHz,

a subharmonic of the cesium transition frequency.

An associated low noise multiplier chain which

terminates in a step recovery diode produces a

signal at the cesium frequency with a power of up

to several mW. A sinusoidal frequency modulation can be applied with a fundamental frequency of 18.75 Hz. This modulation is generated with second

harmonic suppression of better than 100 dB. The

modulation reappears in the beam current at the

detector, is amplified, phase detected, and proc- essed in two cascaded integrators and used

to servo-control the crystal oscillator. The 5.00688-

MHz crystal oscillator frequency is also synthesized

to a standard 5 MHz frequency. This signal is used

for evaluative and stability measurements, and for time-scale calibrations.

5B.3. PRELIMINARY EXPERIMENTAL RESULTS (STATUS

APRIL 1973)

After a preliminary beam alignment, the (F = 4,

mp = 0)<—>(F — 3, mF = 0) transition was observed

with a peak to valley amplitude of 4 pA. Since the

atomic velocities are determined by the beam optics

and the beam alignment, linewidths of 25 to 45

Hz were measured depending on the alignment.

The signal to noise ratio was also measured, and

from this by Lacey's method [4], the frequency

stability for 1 s sampling times was calculated to be

4 parts in 10 13

. Our best reference sources in stability measurements for very short times were

122
SAMPLE TIME x(s)

Fig. 5B.2. Measured and calculated frequency stability of NBS-5.

crystal oscillators, and for longer times were commercial cesium beam frequency standards. A

plot of the measured square root of the Allan

variance using both of these reference oscillators

is shown in figure 5B.2 together with the calculated

stability of NBS-5. Figure 5B.2 shows that we were

able to obtain measurement precisions in the ac- curacy evaluation of about 3 parts in 1014 for sampling times of 105 s. The calculated, shot noise

limited stability is better than the measured per- formance. This is mostly due to limitations in the

electronics; i.e., due to noise associated with the

beam detector electronics, the servoed quartz

crystal oscillator, etc. In the long term measurements, the available commercial cesium reference was also limiting the measurements precision.

At the time of this writing, for various technical

reasons, we have not proceeded yet with the beam

reversal. However, we have preliminary accuracy

data based on two other methods:

(1) Power shift measurements [5-7]. This method

is based on the fact that the effective mean atom

velocity is a function of the interrogating microwave

power. To use this method it is necessary (a) to know the velocity distribution in the tube (this can be obtained experimentally from pulsed operation

and refined by matching a derived Ramsey spectrum

with the experimentally obtained Ramsey spectrum), (b) to calculate numerically the effective mean velocities at given microwave power settings,

and (c) to measure the change in the output frequency by comparison with a reference standard

at different microwave power settings. This allows

a calculation of the cavity phase difference and the corresponding frequency bias. It must be verified, that the microwave spectrum is of sufficient purity so as not to introduce spectrum related power

shifts.

(2) Pulse method [6, 7]. This method is based on

selecting certain velocities in the beam by pulsing

the microwave power. The velocity selection is based on the time of flight between the two cavity

interrogation regions. This method also allows a measurement of absolute microwave power levels

in the cavity and the determination of the velocity

distribution. With methods 1 and 2 one can obtain the biases

due to the second order Doppler effect and the cavity

phase difference. Our preliminary results are tabulated in table 5B.1. More detail on the biases and

the bias uncertainty can be found in reference [8]. The other biases and bias uncertainties of which we are aware and which we have evaluated in a preliminary way are also fisted. Biases not assigned

a value are nominally zero within the respective

uncertainties shown. From table 5B.1 we can see

that the cavity phase difference is about 0.7 mrad

which leads to a bias (including the second order

Doppler effect) at nominal optimum microwave

power of about 1.5 X 10~ 12

. We have monitored

these values every month during the first three

123
TABLE 5B.1.

Preliminary Accuracy Budget for NBSS

Influencing factors

1. 2d-order Doppler and

phase difference at nominal optimum

power; source: power

shift & pulse method

2. servo system; source: some variation of ser- vo parameters and cal- culations based on measured offsets and

loop gain

3. magnetic field; source: mp 7^ 0 transitions

4. H- —2

" versus H ; source:

rnp # 0 transitions and measurements during

assembly

5. Majorana transitions; source: mF ^ 0 tran- sitions and measure- ments during assembly

6. pulling of neighboring

lines; source: mF ^ 0

transitions

7. cavity pulling; source: worst estimate

8. rf spectrum; source: spectrum recording

9. random uncertainty (la

at 10 h); source: stability measurements

against other cesium

standards

Bias

14.5 x 10'3

1,670.0 x 10

-0.05 x lO" 13

Bias uncertainty

1.6 X 10- 13

1X10-

0.2 X 10"13

0.4 X 10" 13

0.05 X 10" 1

3

0.02 x 10-' 3

0.1 x 10>3

0.4 x 10-' 3

<0.4x 10" 13

months of 1973. We could not find any change in the cavity phaseshift within our measurement

precision. If all the bias uncertainties are statis- tically treated, i.e., we assume that they are independent and uncorrelated, we obtain a total ac- curacy capability of 2 parts in 10~ 13

. It should be

noted however, that all of these reported data ought

to be regarded as tentative, preliminary values,

subject to later verification and/or correction. For

the future we plan to understand fully the beam

optics alignment and the magnetic field properties

of the beam tube. In addition, we expect to compare

the computer-aided beam optics design with actual

performance. We also intend to further investigate

and refine the pulse method as well as the power

shift method, and we will attempt to obtain compatible results with beam reversals. Only after all these tests are completed do we feel that final accuracy figures can be quoted for NBS~5. Further

improvements in accuracy seem likely in view of

new ideas and evaluation methods for NBS_5, and

in view of the beam tube performance to date. In

addition, the availability of an accurate and very

stable reference standard, i.e., NBS_X4, is expected

to facilitate evaluation of NBS_5 and to lead to further improvements in accuracy. ACKNOWLEDGMENTS

The authors wish to express sincere appreciation

for the help of the late J. H. Holloway whose con- tinued interest and support over several years

have contributed very significantly to the success

of this present work.

The authors appreciate the considerable help of

L. S. Cutler and L. F. Mueller of the Hewlett Packard Company. The authors also wish to thank their

colleagues J. A. Barnes, D. Halford, W. D. McCaa,

Jr., H. F. Salazar, and C. S. Snider for their help

throughout many phases of the work on NBS-5.

A special word of commendation should be given

to Ward T. Roberts who constructed almost all of

the NBS-5 beam tube.

Note added in proof: Comparisons between

NBS-5 and NBS-X4 in November 1973 led to a measured frequency stability of ay(T)= 1.3 X

10~12t~ 1/2 (for one device), reaching a measured

value of lXlO-14 in 3.5 hours. Also, successful

beam reversal supports the previously obtained

values for the bias correction and the associated

accuracy claim.

5B.4. REFERENCES

[1] Lyons, H., "Spectral lines as frequency standards," Ann.

N.Y. Acad. Sci., 55, pp. 831-871 (November 1952).

[2] Beehler, R. E., and Glaze, D. J., "The performance and

capability of cesium beam frequency standards at the National Bureau of Standards," IEEE Trans, on Instrum. and Meas.. IM-15, Nos. 1 & 2, pp. 48-55 (March and June 1966).

[3] Glaze, D. J., "Improvements in atomic cesium beam fre- quency standards at the National Bureau of Standards," IEEE Trans, on Instrum. and Meas., IM-19, No. 3, pp. 156-160 (August 1970) (see chap. 5A.)

[4] Lacey, R. F., Helgesson, A. L., and Holloway, J. H., "Short- term stability of passive atomic frequency standards,"

Proc. IEEE (Special Issue on Frequency Stability), 54,

No. 2, pp. 170-176 (February 1966).

[5] Hellwig, H., Barnes, J. A., Glaze, D. J., and Kartaschoff,

P. K., "Frequency shifts due to Ramsey type interrogation

in atomic beam tubes," Nat. Bur. Stand. (U.S.) Tech. Note

612, 25 pages (USGPO, February 1972).

[6] Mungall, A. G., "Cavity phase dependent frequency shifts in cesium beam frequency standards," Metrologia, 8, No. 1, pp. 28-32 (January 1972).

[7] Hellwig. H., Jarvis. S., Jr.. Halford, D.. and Bell, H. E., "Evaluation and operation of atomic beam tube frequency stand- ards using time domain velocity selection modulation,"

Metrologia, 9, No. 3, pp. 107-112 (September 28, 1973).

[81 Glaze, D. J., Hellwig, H., Jarvis, S., Jr., Wainwright, A. E., and Allan, D. W., "Recent progress on the NBS primary fre- quency standard," Proc. 27th Ann. Symp. on Frequency

Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703. June 12-14, 1973), pp. 347-356) (Electron. Ind. Assn., Washington, D.C. 20006, 1973).

124
CHAPTER 6

AREAS OF PROMISE FOR THE DEVELOPMENT OF FUTURE PRIMARY

FREQUENCY STANDARDS

Helmut Hellwigt

Contents

Page 6.1. Introduction 127

6.2. Effects on Frequency: Particle Interrogation 127

6.3. Effects on Frequency: Particle Confinement 129

6.4. Effects on Frequency: Particles and Particle Preparation 130

6.5. Existing Concepts for Quantum Electronic Frequency Standards 131

6.6. Frequency Stability for One Second Averaging 133

6.7. Accuracy Capability 133

6.8. Conclusions 134

6.9. References 135

tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302.

125
"Brief words, when actions wait are well: The prompters hand is on

the bell — Behind the curtain's mystic fold The glowing future lies unrolled."

Francis Bret Harte

This paper discusses possibilities which may lead to the development of future primary frequency

standards of superior accuracy capability. Aspects of cost and field-usage are totally neglected. A

review is given of the various methods and techniques which are currently employed in quantum

electronic frequency standards or which have a potential usefulness. Various effects which influence

the output frequency of a primary standard are associated with these methods. They are discussed in detail, and expectation values for the related uncertainties are given. For selected particles certain methods of interrogation, confinement, and particle preparation can be combined such as to minimize

the net uncertainty due to all applicable effects. Different technical solutions are the result. A review

of existing and proposed devices is given, including quantitative data on the stability and accuracy

capability. Aspects of the most promising devices are discussed, and it is concluded that accuracy

capabilities of 10~14 should be within reach of today's research and development.

Key words: Accuracy (frequency standards); figure of merit; frequency stability; future primary

frequency standard; gas cells; ion storage; masers; particle confinement; particle interrogation; particle preparation; primary frequency; quantum electronic frequency standards; storage beam.

126
6.1. INTRODUCTION

A primary frequency standard is based ultimately on some fundamental property of nature. The actual

realization of an output frequency involves several

steps of physical and technical processing. Each of

these steps may cause a more or less pronounced shift of the output frequency of the standard. The magnitude of each shift must be evaluated theoretically and

experimentally. The resulting corrections are called the biases; however, they are never known exactly

but have associated, with them uncertainties. The

magnitudes of these uncertainties depend on the

degree of theoretical understanding, on experimental

parameters, and on their measurability. The combined

uncertainty of all biases is referred to as the accuracy

capability of the frequency standard.

At present the standard with the highest accuracy

capability is the cesium atomic beam tube. This fact

is reflected in the agreement at the 13th General

Conference on Weights and Measures (1967) to define

the second as the duration of 9192 631 770 cycles of

the unperturbed radiation of the Cs133 hyperfine

transition (F = 4, mF = 0) < > {F = 3,mF = 0). The cesium beam tube, although it still can be improved, is already at a very advanced stage of technical

development. An accuracy capability of the order of

parts in 1013 is now a reality which is achieved in' several laboratories around the world [1—5]. However, a natural demand exists for an even more

accurate definition, and frequency standards of

extreme precision will be needed in various technical

applications. New aspects of scientific, technical, and

metrological importance have evolved because of

recent successes in multiplication of frequencies into

the infrared region of the electromagnetic spectrum

[6—10]. A substitution of conventional length (wavelength) measurements by much more precise and

accurate frequency measurements will soon be possible

and may ultimately lead to a unified (frequency)

standard for frequency, time and length with the speed

of fight being a defined constant. We may look even

further ahead to the possibility that other basic

physical quantities, e.g., the volt via the Josephson

effect, will be based on the same (frequency) standard.

This illustrates the far reaching importance which we

have to attribute to the development of primary

frequency standards.

In the following we will compare and discuss

possibilities in methods and techniques which are at our disposal for pushing the fractional frequency

accuracy capability beyond 10~13

. This will be done

in a way which differs somewhat from the usual

approach of comparing different existing devices [11]. Instead we will compare the methods and techniques

used in quantum electronic frequency standards, and we will try to synthesize from these an optimized

device. As the criterion for excellence in this comparison it appears best to choose accuracy capability

as the prime topic in our discussions. The influences

affecting the frequency of a quantum electronic

frequency standard can be grouped into three classes

:

(1) effects associated with the interrogation of the

atoms or molecules, (2) effects related to the method

of confining the particles, and finally (3) effects associated with the particles themselves and with the

way in which they are treated for an effective inter- rogation by electromagnetic fields. We will discuss these three groups successively in more detail. Since we are aiming for accuracies of

better than the present state-of-the-art (parts in 1013

) we will discard as unimportant only those effects which

lead to fractional uncertainties of less than 10-14

. At

this point it should be emphasized that the following

discussion is based on our present state of knowledge.

There might well be other methods and techniques

which could be used, and there might be additional sources of uncertainty of which we are not yet aware. We also are not going to discuss basic physical and

engineering details of the various techniques and

devices. They may be found in the referenced litera- ture. In particular, Refs. [11—15] will give an intro- duction to the problem area in historic perspective.

6.2. EFFECTS ON FREQUENCY:

PARTICLE INTERROGATION

In a quantum electronic frequency standard we are

127
not only concerned with the actual quantum transition of the particles (clock transition) involved but

also with the production of an output signal. In

general two different tasks are to be accomplished:

(a) the generation of a signal which is to be compared

with the actual "clock" transition, and (b) the generation of a useful standard frequency output. It is obvious that at least one oscillator—in general, more

than one—is necessary for these tasks. These slave

oscillators may be quartz crystals, klystrons, lasers, or any other suitable devices. They must be locked in

frequency or in phase to the "clock" transition. This can be accomplished by four distinctly different methods: The active maser oscillator [16—19], whereby its output frequency is compared to a synthesized

frequency derived from the slave oscillator,; the absorption [20—22] or amplification [16] of an electro- magnetic frequency by the atomic or molecular

transition ; the detection and counting of the number

Table 1 . Effects on frequency; Particle interrogation

Methods Effects

Active : Self-oscillation Noise in: Passive

:

Detector Absorption or amplification Receiver

of radiation Resonance structure

Particle detection Multiplier and synthesizer

Frequency transformation Quantum transition Slave oscillator fluctuations Spectrum asymmetry

Cavity pulling

Interrogating radiation

of particles having undergone a transition caused by

a signal which is derived from the slave oscillator

[1, 23, 24]; and finally the observation of transitions

by their effect on other transitions of different fre- quencies to which the "clock" transition is coupled [25]

(frequency transformation). In the first column of

Table 1 the different interrogation methods are summarized.

The second column lists various effects which give rise to bias uncertainties and which are associated with one or more of the methods of interrogation.

The fractional frequency stability [26] of a quantum electronic frequency standard may con- veniently be written as K 1 fA\

The symbols in (1) have the following meaning : r is the

measurement interval; M is a basic figure of merit1 given by

M = ]/^s Tr , (2)

1 This M differs from traditional figures of merit found in the literature.

where Tt = relaxation time, and ns = flux of signal

particles. The constant K contains the device characteristics. As examples we have for particle detection

[24, 26] (which includes detection of photons with

hv > > hT)

\ -^passive S , (3) and for an active oscillator (with hv < < IcT) [16,26] we

have

^ctiveS -yf^v ]/ T

-- (4) From these equations we see that the flux of signal

atoms and the relaxation time which make up our

basic figure of merit M are not the only important

parameters in determining frequency stability. The

principle which is used in the interrogation of the

particles is also important, and is reflected in the value

of K. For example at hv < < Jc T a device (with the same M for each version) will have a better noise

performance when passive particle detection is used

as compared to using the mode of operation as an

active quantum electronic oscillator [27]. This can be

seen by comparing (3) and (4). Also, additive thermal

noise at any reasonable particle or photon intensity is negligible, and excess noise contributions of particle or photon detectors are typically very low. Thus shot

noise of the incoming particles is usually the only

limitation. In contrast we almost always will encounter

additional noise in an active (maser) oscillator because

of performance limitations in its microwave receiver. Another potential noise source is the frequency

multiplier and synthesis chain connecting the slave

oscillator to the "clock" transition. The current state- of-the-art is such that this noise contribution is negligible compared to the noise due to the slave

oscillator [1, 28]. Noise can also be associated with the

quantum transition itself, i.e., in the form of spon- taneous emission. Such effects will become more

serious at higher (optical) frequencies because the

probability for spontaneous transitions increases as the cube of the transition frequency.

The short-term stability of the slave oscillator is of

equal importance for all methods because its perform- ance determines the stability of the whole standard at short averaging times [26]. The only remedy is the

development of good slave oscillators. Spectral asymmetry of the interrogating signal is of concern for all passive devices [29, 30]. It can be

reduced to unimportance by adequate care in the

electronics. Also the choice of a low frequency transition

might be helpful. In active devices this problem is practically non-existent.

For many devices a resonance structure (cavity)

is necessary to create the required strength and

spatial distribution of the interrogating electro- magnetic field. This leads to the possibility of cavity

pulling which may be written as [16, 29]

Av = O Avc (5)

128
where Avc and Av are the offsets of the cavity and the

output frequencies respectively. For an active oscil- lator the parameter G is approximately the ratio of the

widths of clock transition and cavity resonance [16], for passive methods (sufficiently far from self-oscil- lation) G is approximately the square of this ratio [29]. Thus an active oscillator is inherently more affected by cavity pulling than a passive device. Moreover a

sharp cavity resonance, i.e., a larger G, is a prerequisite

for an active oscillator [16] whereas a broad cavity resonance or—at least in principle—no resonance

structure at all, i.e., G = 0, can be used with passive

methods. Cavity pulling is therefore only of concern to

active oscillators. For laser oscillators we have G 1 which rules out

their use as frequency standards. The stability of the

output frequency would be directly given by the

mechanical stability of the optical resonator. The last item in Table 1 is the effect caused by the

interrogating signal itself. One example is the BlochSiegert frequency shift [30]. The fractional frequency

shift is related to the power of the interrogating signal

and can be expected to be negligible for all techniques

under discussion if excessive power levels are avoided

[30]. Another example is the recoil effect which may

be a serious Hmitation if the photon energy of the

interrogating radiation is large (infrared and optical

frequencies). They are discussed in more detail later in this paper under Conclusions.

We summarize: A passive method is to be pre- ferred over an active oscillator. In addition a passive

method offers more flexibility and freedom for evaluating bias corrections and accuracy limitations, because

a passive technique is not tied to meet an oscillation threshold condition. A low frequency (microwave)

transition ehminates some of the problems ; however,

higher frequencies (infrared) may be used if technical

problems associated with the multiplication process2 can be adequately solved. At high frequencies (optical)

effects associated with photons of higher energy

(recoil) could represent a serious limitation.

6.3. EFFECTS ON FREQUENCY:

PARTICLE CONFINEMENT

A quantum electronic frequency standard is based

ideally on the quantum transition of a particle (atom

or molecule) which is in an unperturbed state and is interrogated for an indefinite period of time.

In principle this may be achieved by confining an

ensemble of particles to that region of space which is

filled with the interrogating radiation and to accomplish this confinement in such a manner as to minimize

the perturbation of the individual particles. In reality

it appears possible to reaUze the ideal of a free particle to a very good approximation; however, it is at the

expense of interrogation time, and vice versa.

Various methods of confinement are at our disposal.

We may use a beam of free particles travelling in vacuum through the region of space where inter- rogation takes place [22, 23]. We may store the

particles in the region of interrogation at low particle

densities by using storage vessels. The storage vessel has to be coated [31, 32] or filled with a buffer gas

[17, 33] in order to reduce the interaction between the

particles and the wall of the storage vessel and among

particles themselves. Or we can do away with physical

walls and use electric or magnetic fields for confinement [34]. Finally, we may just take a gas at a fairly

high pressure and observe absorption [20, 21] of the

interrogating radiation. A summary of these methods

is given in the first column of Table 2. Various effects (listed in the second column of

Table 2) which lead to bias uncertainties are introduced

by the confinement of particles.

Several effects are associated with the line-Q which

is proportional to the product of confinement time and

transition frequency. They include short term stability, cavity pulling, and the performance of the servo

electronics. A high line-Q is desirable but not essential because means can be employed to counter the effects of a low line-Q, e.g., one could render cavity pulling

totally unimportant, regardless of the line-$, by

avoiding a resonance structure (using a passive method). On the other hand a high line-Q can be obtained

with relatively short confinement times by using transitions at high frequencies. For achieving a long duration of confinement, i.e., in excess of one second, storage

methods offer the greatest potential, especially the

coated vessel or the usage of confining fields (ion

storage). Collisions between the particles which lead

to spin exchange and shifts of the energy levels are an

important source of uncertainty in techniques using

comparatively high particle densities. Low density

methods like the free.beam, the storage in a coated

bulb, or the usage of confining fields can be designed

to render this effect unimportant. We also may arrange

the interrogation mode in such a way as not to look at

particles which have experienced a collision, e.g., as in saturated absorption [20]. Wall collisions will intro- duce uncertainties wherever physical walls are used

as a means of confinement. Only the free beam and the

Table 2. Effects on frequency: Particle confinement Methods Effects

Traveling free beam

Storage in: Coated vessel Buffer gas

Electric or magnetic fields Absorption cell

Line-Q

Particle-particle collisions Wall interaction

1st order Doppler

2nd order Doppler

Cavity phase shift

2 We may assume that multiplication, in principle, is possible.

129
confinement by fields are not affected3

. However, we may also use an absorption cell and restrict the region

of interrogation to a small volume within the cell [20],

e.g., by using a laser beam as the interrogating radiation, thus avoiding wall effects. The first order Doppler

effect appears to be mainly a design and engineering

problem and thus of no real consequence for this discussion. We may assume that a suitable approach

in all of the discussed methods will eliminate first order Doppler frequency shifts and line broadening.

This may be done by proper interrogation (e.g., saturated absorption [20]), by storage within dimensions less than one half of a wavelength of the inter- rogating radiation [18], or by a proper mechanical

design as required in the case of a free beam traveling

through a Ramsey cavity [23]. The second order

Doppler shift is of a more fundamental nature. It can

be regarded as the problem to know with adequate

precision the speed or temperature of the particles.

This is difficult in the case of the free beam and is a

severe problem in the case of storage in electric or magnetic fields, whereas the use of physical containers

allows an adequate knowledge ofthe temperature, when

thermal equilibrium of the kinetic energy of the

perticle with the container walls can be established.

Cavity phase shift offsets occur in the case of the free beam traveling through a cavity [1—5]. For all other

methods it is of no concern. We summarize: The choice of a high frequency

transition is to be preferred because this leads to a

reduction of the fractional importance of most effects

;

the Doppler shifts, of course, are excluded. Thus the

(second order) Doppler limitation favors the storage

in containers where thermal equilibrium exists be- tween the kinetic energy of the particles and the walls

of the storage vessel. At low (microwave) frequencies we cannot single out a specific method of confinement

as being inherently superior to others. 6.4. EFFECTS ON FREQUENCY:

PARTICLES AND PARTICLE

PREPARATION

The particles which we choose are either atoms or molecules, and we may use any of the different types

of electric or magnetic dipole transitions. In order to

effect interrogation, the particles are generally pre- pared so that this can be done efficiently. Preparation

usually means the creation of a population difference

of the energy levels which differs from (is larger than)

the thermal distribution.

Only at high frequencies, above one terahertz, does

the preparation of particles lose its importance,

because of the large population differences already

present in thermal equilibrium. This allows efficient absorption of the interrogation signal without pre- paration. Possible methods of preparation are fisted in the first column of Table 3.

3 For the case of a magnetic dipole transition this is true when the particles (ions) are confined by electric fields.

Spatial state selection achieves the change in population difference by ehminating one or more

energy states from a particle beam4 [35]. This method

is based on differences in the electrostatic or magnetic

forces acting in inhomogeneous electric or magnetic

fields on the electric or magnetic dipole moments

which are associated with each energy state. Optical

pumping can be used which causes changes in population difference when the pumping light acts on the

energy levels selectively by proper use of polarization,

filtering [36], etc. Electron collisions can be used to

alter the population of the energy levels from the

thermal equilibrium values. As examples, electron

beams of well defined energy or a gas discharge can be

employed. A change in population can also be accomplished by spin exchange collisions with atoms or molecules which have already been polarized by any

of the other methods [34]. Chemical effects may be

used such as a chemical reaction or a dissociation which

lead to the formation of excited particles.

Again we find various effects associated with the

different methods which give rise to bias uncertainties.

They are listed in the second column of Table 3. The

influence of external electric fields can be made un- important if magnetic dipole transitions such as the

hyperfine transitions in atoms are used [37]. Magnetic

fields can be rendered unimportant when certain

molecular transitions are taken [38]. Shielding will reduce the effects of both. Majorana transitions may

occur if particles travel through regions of varying

static field strength and thus are mainly of some importance for spatial state selection. Frequency uncertainties are introduced by transitions from neighboring states. This effect can be minimized by the

choice of particles with a simple energy level structure and by carefully avoiding the stimulation of neighboring transitions. Two classes of effects, fisted in Table 3 as collisions and coupling of transitions, represent significant sources of frequency bias (and uncertainty) for all methods other than spatial state selection and absorption. Coupling of transitions occurs when the

pumping radiation is present simultaneously with the

interrogating radiation. Colfisional effects will be

encountered when collisions are used as a means of

altering the population difference. The very method

used for particle preparation is the source of a fre- quency bias (and uncertainty), and the more effi- ciently the preparation is made, the more restrictive

is its effect on the performance as a primary frequency

standard. In principle, we have a solution. In analogy

to spatial state selection we may separate spatially the

process of particle preparation from the particle inter- rogation. This can be done, for example, with two

storage vessels connected by a diffusion channel or by

using a traveling beam. An alternate solution is the

4 This method dates back to the famous Stern-Gerlach experiment.

130
separation in time of particle preparation and inter- rogation (pulsed preparation). However, we must

Table 3. Effects on frequency; Particles and particle preparation

Methods Effects

Atoms

Molecules No preparation (absorption)

Spatial state selection Optical pumping

Electron collisions Spin exchange

Chemical reaction

Electric fields Magnetic fields Majorana transitions Neighboring transitions Coupling of transitions

Collisions

realize that both solutions will encounter technical

problems in their practical realization although they

are fundamentally feasible. We summarize: An atom or molecule should be

used which has a simple energy level structure and

properties which reduce the effects of external electric and/or magnetic fields. Obviously, the best choice for a particle preparation method is no preparation at all (simple absorption). However, we must then use

transitions in at least the low terahertz range where the

population difference in thermal equilibrium is suffi- ciently large for efficient interrogation. The optimum

method of particle preparation at low (microwave)

frequencies appears to be the spatial state selection.

6.5. EXISTING CONCEPTS FOR

QUANTUM ELECTRONIC FREQUENCY STANDARDS

We will discuss only those quantum electronic

frequency standards with a current or potential

accuracy capability of better than one part in 1010. Several devices have been developed, and some are even commercially available. They include the fore- runner of all, the ammonia maser [16, 39], the rubi- dium gas cell [40], the cesium beam tube [1 —5. 23],

and the hydrogen maser [18, 19]. Two more devices

have had a preliminary evaluation but are not nearly

as mature as those previously mentioned : the thallium

beam tube [41, 42] and the rubidium maser [17]. Several more concepts are being proposed or are in the early stages of experimentation. They include

saturated absorption of laser radiation (methane [20],

iodine [21], sulfurhexafluoride [43], etc.), simple

absorption of laser radiation by a traveling beam

(iodine [22]), other beam tubes (barium oxide [44]),

ion storage (helium [34], mercury, etc.), and the

storage beam tube (hydrogen [27]).

We will now look into the basic operating principle of each device and discuss briefly the chief

limitation of each by comparing with Tables 1 to 3. It must again be emphasized that any effect imposing an

accuracy limitation of worse than one part in 1014 will

count as a limitation. No attempt will be made at quoting quantitatively these limitations. For those

devices which have been evaluated, the reader is referred to the published data in the referenced

literature. For all other devices and concepts it seems

futile to quote data which cannot adequately be

supported. In order to form his own opinion the reader

should consult the referenced literature. Finally it must be emphasized that the limitations quoted here

SOURCE

H FIELD (Cs)

E FIELD (BaO) DOPPLER SHIFTS

LINE-Q

Fig. 1. Traveling beam tube

should not be regarded as final. They merely reflect the

present state of our knowledge, and future work is likely to change them.

(a) Traveling Beam Tube (Fig. 1). The beam of

particles originates at a suitable source or oven and

travels through a first state selector which focuses only

certain, desired energy states into the cavity region.

Here the particles are interrogated by a microwave

signal. As a result the distribution of particles into the

various energy states is altered when the particles leave

the cavity region. This is analyzed by a second state

selector which focuses particles in selected energy

states on a detector thus generating the error signal for a slave oscillator. Limitations are the spectrum of the

interrogating radiation (Table 1); the phase difference

between the two sections of the Ramsey cavity, the

second order Doppler shift due to the uncertainty in the mean square particle velocity, and the relatively

low line-Q (Table 2) ; and in the case of cesium and

barium oxide the effects of fields (Table 3). (b) Absorption in a Beam (Fig. 2). The beam of

particles originates in a source and travels freely

through a vacuum chamber. A laser which serves as the slave oscillator radiates perpendicularly onto the

particle beam. Changes in the intensity of the laser radiation due to absorption in the beam can be

detected (in-hne position in Fig. 2), or alternately the

intensity of the fluorescence radiated by the traveling

beam may be monitored (displaced position in Fig. 2). Limitations are the spectrum of the laser radiation

and the radiation itself via photon effects (Table 1); and the first and second order Doppler effects (Table 2). (c) Traveling Beam Maser (Fig. 3). The only

example is the ammonia maser. A beam of molecules

leaves the source, is state selected, and enters a cavity

which is tuned to the transition frequency. Because of

the short interaction time between the particles and

131
the microwave field in the cavity a large particle flux

is required to obtain self- oscillation. Also, the delivery

Fig. 2. Absorption in a beam

DOPPLER SHIFTS

STATE SOURCE SELECTOR G

ELECTRIC & MAGNETIC FIELDS

PARTICLE COLLISIONS

CAVITY PULLING

PHASE SHIFTS

NEIGHBORING TRANSITIONS

Fig. 3. Traveling beam maser

SOURCE

CAVITY PULLING

WALL SHIFT

MICROWAVE OUTPUT

CAVITY WITH STORAGE BULB

Fig. 4. Storage beam maser

of the energy from the molecules to the cavity is in general not uniform and not symmetric along the

length of the cavity. This together with the more

complex level structure of ammonia leads to the

following: Cavity pulling (Table 1); first and second

Doppler shifts, particle collisions, and cavity phase

shifts (Table 2) ; and electric fields, magnetic fields, and

the influence of neighboring transitions (Table 3). (d) Storage, Beam Maser (Fig. 4). The only

example is the hydrogen maser. A state selected atomic beam is generated in a fashion similar to the

beam tubes. The atoms are stored in a coated bulb

located within a cavity. The maser will oscillate provided certain conditions are met which relate to

cavity- and line-Q, particle flux, and device geometry.

Limitations are cavity pulling (Table 1); and wall

interaction due to the storage principle (Table 2). (e) Storage Beam Tube (Fig. 5). The hydrogen

storage beam tube is a hybrid between the hydrogen

storage beam maser and the traveling beam tube. The

operation is analogous to beam tubes; however, the

hydrogen storage principle is adopted from the hydrogen maser. The direct flow of atoms from entrance to

exit of the bulb must be prevented. A beam stop might

be used, for example. The only serious hmitation of

this device is the wall shift (Table 2). (f) Optically Pumped Gas Cell (Figs. 6 and 7).

Examples are the rubidium maser (Fig. 6) and the

rubidium gas cell (Fig. 7). Their basic concepts are

SPECTRUM

CAVITY WITH STORAGE BULB

Fig. 5. Storage beam tube

MICROWAVE WALL SHIFT

OUTPUT /

PARTICLE COLLISIONS j /cAVITY PULLINC

LAMP FILTER

CAVITY WITH GAS CELL LIGHT SHIFT

Fig. 6. Optically pumped gas cell maser

SPECTRUM

PARTICLE COLLISIONS,

LAMP FILTER

LIGHT SHIFT LINE-0

Fig. 7. Optically pumped passive gas cell

quite similar. A filtered light beam optically pumps the

rubidium which is stored, together with buffer gases, in a cell within a cavity. The maser will start oscillations under certain conditions. The passive gas cell obtains

the error signal for a slave oscillator from a photocell

which monitors the transmission of fight through the gas cell. Thus a method which was called frequency

transformation in Table 1 is used here, since the

optical transmissivity is a function of the microwave

signal applied to the cavity. Limitations are cavity

pulling (maser only) and the spectrum of the inter- rogating radiation (passive device only) (Table 1); particle collisions, wall interaction, and a relatively low

line-Q (Table 2) ; and the effects caused by the coupling of the clock transition to the optical pump transition which usually are called "light shifts" (Table 3). 132
(g) Saturated Absorption (Fig. 8). A gas cell is used which is irradiated by intense radiation from a

laser which acts as the slave oscillator. Unique advantages of the saturation of an absorption are the

significant reduction of the first order Doppler effect and the automatic exclusion from interrogation of

most of the molecules which have suffered a collision. Known limitations are the spectrum of the laser radiation as well as photon effects of this radiation

itself (Table 1) ; and particle collisions (Table 2). (h) Ion Storage Principle (Fig. 9). Ions are confined by an inhomogeneous rf field, and can be stored

for fairly long time periods. The confining field may be

generated in a quadrupole trap consisting of a hyperbolic doughnutlike ring with hyperbolic caps on top

PHOTON INTERACTION

Fig. 8. Saturated absorption

RF GENERATOR

PARTICLE PREPARATION

Fig. 9. Ion storage principle

and bottom5

. Limitations are imposed by the necessity

to ionize and by the method of particle preparation,

which, so far, is usually spin exchange with an injected

polarized atomic beam. Comments on this aspect were

already made in Section 3. The most severe limitation

is the second order Doppler effect (Table 2).

6.6. FREQUENCY STABILITY FOR

ONE SECOND AVERAGING

In the previous discussion we did not include the

aspects of random uncertainty. These aspects can be

described quantitatively by (1) through (4). In Table 4, an attempt at this is made for the different existing

concepts, whereby we choose the best understood

actual system in each case, e.g., we use the actual

(NBS-III)1 and projected (NBS-5)1 performances of

cesium laboratory standards in the case of the beam

tube concept.

The first column lists nB, the signal particle flux or the number of interrogated particles per second;

the second column gives the interrogation time TT. In the third column the figure of merit M is calculated

from (2). With the transition frequencies, which are

listed in the fourth column, we can calculate from (1),

(3), and (4) the fractional stability for 1 sec averaging

time. It must be emphasized that the values given for n3 and TT and therefore for a are only approximate and

sometimes only "educated guesses." However, they

may serve to give an approximate feeling for the

potential stability performance of each technique. We

also must note that the measured stability usually

will be worse than the calculated stability because of

limitations in the associated electronics, i.e., receiver or detector, slave oscillator, etc. For example the best

actual performance of the hydrogen maser is cr(ls) 8 x IO"13 [45] (5 x 10-13 [46]) and of the methane

saturated absorption is cx(ls) *2x IO-12 [20] (2 x

10-13 [47]).

6.7. ACCURACY CAPABILITY

At the beginning of section 4 we pointed out the

difficulty in quoting quantitative values for the various

error sources which make up the accuracy capability.

Nevertheless it is of interest to quote those accuracy

capabilities which have been determined for actual

systems based on experiments. They are listed in the

Table 4. Data on different concepts for primary frequency standards

Ms TT M v _ K 1 Accuracy capability

(s-

) (s) (s

1/*) (Hz) ffy = m Present Projected

(t = Is) experimental

performance

Traveling beam tube (Cs) 108 io-2 102 9.2 X 109 2 x 10--13 5 X 10-13

[1] 1 X 10~13 Absorption in beam (I2 ) 108 Traveling beam maser (NH3

) 1013 10-6 io-2 5.8 X 10u 3 x 10"-14 better than IO"12 i0~* 3 x 102 2.4 X 1010 5 x 10"-13 io- 11 [48] 10-12 10"u

Storage beam maser (H) 1012 1 106 1.4 X 109 10-" 2 x [49] better than 10-12 Storage beam tube (H) 108 1 104 1.4 X 109 10-h better than 10-12 Optically pumped gas cell (Rb) 10u io-2 105 6.8 X 109 10-H io- 10 [17] 10-io Saturated absorption (CH4 ) 1010 10-5 1 8.8 X 1013 2 x 10"-15 io- 11 [20] better thanlO"12 Ion storage ( 3He+) 105 10 3 x 10s 8.7 X 109 10-M io-9 [34] better than 10-12

5 Several other trap configurations are possible.

133
fifth column of Table 4. There are no experimental

data which would support accuracy capability claims

for the beam absorption and the storage beam techni- ques. The last column in Table 4 depicts the projected

performance which we consider possible from applying

and evaluating the thoughts of Sections 1,2, and 3 of

this paper and from interpreting the experimental data. A comparison between the last two columns of Table 4

gives an approximate idea of the state of knowledge

and development of each concept.

6.8. CONCLUSIONS

The (ammonia) travelling beam maser and the

(rubidium) optically pumped gas cell have been studied

quite extensively and their limitations are well known.

The magnitude of the limitations, stated qualitatively

in paragraphs (c) and (f) of Section 3, is such that we

cannot expect any improvement in the accuracy

capability in the foreseeable future as is indicated in Table 4. Their accuracy capabihty is also, in comparison, so marginal that they are not competitors in the

contest for superior primary frequency standards.

The standard with the best accuracy capability at present is the cesium beam tube. The individual effects contributing to this accuracy capability are also comparatively well understood [1—5]. Therefore it is possible to predict that an accuracy capability of

1 x 10~13 may actually be realized in the foreseeable

future [1]. The projected performances of the remaining concepts, which are listed in Table 4, are quoted

as better than 10-12

. Each of the limiting effects for these concepts, as discussed in the corresponding

paragraphs of Section 4, has the possibility of being

reduced to that level. How far it will be possible to push beyond 10-12 is quite difficult to predict. As a qualitative rule we may

state that the magnitude of an error (bias uncertainty)

will decrease when the corresponding bias correction

is reduced. Also we may gain an advantage when we

choose a concept which involves as few bias correc- tions as possible. Adopting this philosophy we can reexamine those devices listed in Table 4 which hold

promise, and we can try to synthesize an optimum

solution following the thoughts of Sections 1 to 3. It is evident that no single superior concept can be found.

We have to compromise in order to arrive at a practical solution. In Section 2 we pointed out that a passive technique should be preferred over an active oscillator (maser, laser), although it is difficult to give a fair judgment on all parameters involved. In this paper we

are only concerned with "fundamental" hmitations

and it is conceded that technical and design aspects

may well be more important than the fundamental

ones. As an example, it remains to be proven experimentally that the detection of a hydrogen beam in the

hydrogen storage beam device does not create suffi- cient technical problems to render its "fundamental"

superiority over the hydrogen storage maser ineffective.

In the search for an optimum passive technique

the frequency of the transition is an important

parameter. A low frequency is of advantage in the

interrogation of particles; however, effects caused by

particle confinement are fractionally large, and it is necessary to prepare the particles for effective inter- rogation. The most effective method for particle

preparation which also introduces no adverse effects,

if proper care is taken, is spatial state selection of a

particle beam. For particle confinement at low

frequencies we have to rule out simple absorption.

Storage in buffer gases introduces large biases and

with it relatively large errors. A third method, ion

storage, seems to be severely affected by the second

order Doppler effect. A significant reduction of this bias (effective ion temperature) appears difficult and

its knowledge to correspondingly better than 10~13 seems to be a serious problem [50]. Technical diffi- culties associated with the creation, injection, and

preparation of ions may also restrict the usage of ion

storage as a method of confinement. However, it should not be considered experimentally impossible,

especially if heavy ions are used which reduce adverse

heating effects [51]. Two choices are left. The first is the traveling

beam method, i.e., in practice an advanced cesium

beam tube. The use of particles other than cesium will not give a substantial advantage. The prospects can

be fairly well predicted (Table 4). The second choice

is the storage beam tube. So far only atomic hydrogen

can be stored effectively in a vessel with coated walls. The only h'miting effect is the wall interaction (wall

shift). At present the wall shift bias is typically of the

order of 10~n and can be measured to about 10% [49]. Recent experiments show that the wall shift can

actually be made zero at elevated temperatures [52, 53].

We also may assume that bulbs of variable size can be

used to evaluate the wall shift with a higher degree of

accuracy [54], and that considerably larger storage

bulb sizes can be used [55]. If we assume that the wall

shift bias could be reduced by one order of magnitude

and could be measured to 1 % of its value, we would

have an accuracy capabihty of 10-14

. A high frequency transition ehminates most of the

problems associated with particle confinement and

preparation because we can use simple absorption.

Specific problems and technical difficulties may arise in connection with the frequency multiplication and

synthesis into the infrared region. We shall assume

that these problems can be overcome. Confinement in an absorption cell is possible because the fractional

influences of wall and particle collisions are reduced

due to the high frequency. Saturated absorption [20]

will further reduce adverse effects because only

particles with near zero Doppler shift and near zero

colhsional effects are interrogated. Another choice is the use of a traveling beam [22] which absorbs radiation directed perpendicular to the beam. Effects related to the energy of the interrogating photons,

e.g. recoil, can be a hmitation which becomes more

134
pronounced as the transition frequency increases6 [56]

.

Existing methods like the methane saturated absorption will allow a study of these effects and will give an

indication of how well the bias can be determined or avoided. The fractional difference between the

characteristic absorption and emission frequencies

due to recoil is theoretically of the order of 10-11 for methane.

Following these thoughts one may conclude that

such effects are reduced by choosing a transition of

lower frequency, e.g., in the far infrared, while still retaining the advantages of a relatively high transition

frequency. The optimum frequency for such an

approach appears to he in the lower terahertz region.

Here the opportunity for gaining full advantage from

techniques based on simple absorption still exists

(sufficient population and population difference even

at thermal equilibrium, and optical techniques can be

used), but the biases related to the energy of the

interrogating photons are reduced. These effects can

be reduced further and the interrogation time can be

increased by using molecules of larger mass. Also the

absorption in a travehng beam method should be

considered more seriously. Thus accuracy capabilities

of better than 10~13 may be expected.

In summary we may conclude that among other

possibilities the storage beam principle (hydrogen)

holds high promise for a quantum electronic fre- quency standard based on a low (microwave) transi- tion frequency. The other group of techniques which

has a potential of competing with or surpassing the

projected performance of the cesium beam tube is based on simple absorption in transitions of high

frequency, in at least the terahertz region. Both

approaches hold the promise for accuracy capabilities

of 10~14 and are within reach of experimental realization.

Acknowledgements. My paper is based on the work and

thoughts of many during the past years as evidenced by the

list of references which is by no means exhaustive. I gratefully

acknowledge their input to this paper.

I owe special thanks to Donald Halford and John L. Hall who helped shape this paper in many fruitful discussions.

6.9. REFERENCES

1. Glaze, D. J.: Proc. of the XVI General Assembly of URSI,

Ottawa, Canada, August 1969, entitled Progress in Radio

Science, 1966—1969, to be published; also IEEE Trans, on Instrumentation and Measurement IM-19, 156 (1970).

2. KartaschofF, P., Debely, P. E.: Proc. of the Colloque Inter- national de Chronometrie, p. A 3—1 (1969).

3. Becker, G., Fischer, B., Kramer, G., Muller, E. K. : Proc. of the Colloque International de Chronometrie, Paris,

1969, p. A 2—1. 4. PTB-Mitteilungen 2, 77 (1969).

5. Mungall, A. G., Bailey, R., Daams, H., Morris, D. : Metrologia 4, 165 (1968).

6. Hocker, L. 0., Ramachandra Rao, D., Javan, A.: Phys.

Letters 24 A, 690 (1967).

6 The fractional influence for recoil is proportional to v.

7. — Sokoloft', D. R., Daneu, V., Szoke, A., Javan, A.: Appl.

Phys. Letters 12, 401 (1968).

8. Evenson, K. M., Wells, J. S., Mataresse, L. M. : Appl. Phys.

Letters 16, 251 (1970).

9. Elwell, L. B.: Appl. Phys. Letters 16, 159 (1970).

10. Hocker, L. 0., Small, J. G., Javan, A.: Phys. Letters 29 A,

321 (1969). 11. McCoubrey, A. O.: Proc. IEEE 54, 116 (1966). 12. Lyons, H: Ann. N.Y. Acad. Sci. 55, 831 (1952).

13. Barrelland, H., Essen, L.: Sci. Prog. 47, 209 (1959).

14. Mockler, R. : Advances in Electronics and Electron Phys.

15, 1 (1961).

15. Beeh'.er, R. E.: Proc. IEEE 65, 792 (1967).

16. Shimoda, K., Wang, T. C, Townes, C. H.: Phys. Rev. 102, 1308 (1956). 17. Davidovits, P., Novick, R.: Proc. IEEE 54, 155 (1966). 18. Kleppner, K., Berg, H. C, Crampton, S. B., Ramsey, N. F., Vessot, R. F. C, Peters, H. E., Vanier, J.: Phys. Rev. 138, A 972 (1965). 19. Peters, H. E., McGunigal, T. E., Johnson, E. H.: Proc. 23rd Annual Symposium on Frequency Control, Atlantic

City, 1969, p. 297.

20. Barger, R. L., Hall, J. L.: Phys. Rev. Letters 22, 4 (1969).

21. Hanes, G. R., Baird, K. M.: Metrologia 5, 32 (1969).

22. Ezekiel, S., Weiss, R.: Phys. Rev. Letters 20, 91 (1968). 23. Beehler, R. E., Mockler, R. C, Richardson, J. M.: Metrologia 1, 114 ,1965).

24. Lacey, R. F., Helgesson, A. L., Holloway, J. H. : Proc. IEEE 54, 170 (1966).

25. Dehmelt, H. G.: Phys. Rev. 103, 1125 (1956).

26. Cutler, L. S., Searle, C. L.: Proc. IEEE 54, 136 (1966).

27. Hellwig, H: Metrologia 6, 56 (1970).

28. Halford, D., Wainwright, A. E., Barnes, J. A. : Proc. 22nd

Annual Symposium on Frequency Control, Atlantic City,

1968, p. 340.

29. Holloway, J. H., Lacey, R. F.: Proc. of the Colloque

International de Chronometrie, Lausanne, 1964, vol. 1, p. 317.

30. Shirley, J. H: J. Appl. Physics 34, 783 (1963).

31. Ramsey, N. F.: Rev. Sci. Instr. 28, 57 (1957).

32. Kleppner, D., Ramsey, N. F., Fjelstadt, P. : Phys. Rev.

Letters 1, 232 (1958).

33. Dicke, R. H.: Phys. Rev. 89, 472 (1953).

34. Fortson, E. N., Major, F. G., Dehmelt, H. G.: Phys. Rev.

Letters 16, 221 (1966).

35. Ramsey, N. F. : Molecular beams. Oxford: Clarendon 1956.

36. Bender, P. L., Beaty, E. C, Chi, A. R.: Phys. Rev. Letters

1, 311 (1958).

37. Schwartz, C. : Ann. Physics 6, 156 (1959). 38. Barnes, F. S.: IRE Trans, on Instrumentation 1-11, 191

(1962). 39. Shimoda, K: J. Phys. Soc. Japan 16, 1728 (1961). 40. Arditi, M., Carver, T. R.: Proc. IEEE 51, 190 (1963). 41. Bonanomi, J.: IRE Trans, on Instrumentation 1-11, 212

(1962). 42. Beehler, R. E., Glaze, D. J.: IEEE Trans, on Instrumentation and Measurement IM-15, 55 (1966). 43. Rabinowitz, R., Keller, R., La Tourrette, J. T.: Appl.

Phys. Letters 14, 376 (1969). 44. Hellwig, H., McKnight, R., Pannaci, E., Wilson, G.: Proc. 22nd Annual Symposium on Frequency Control, Atlantic

City, 1968, p. 529.

45. Vessot, R., Peters, H., Vanier, J., Beehler, R., Halford, D., Harrach, R., Allan, D., Glaze, D., Snider, C, Barnes, J., Cutler, L., Bodily, L.: IEEE Trans, on Instrumentation

and Measurement IM-15, 165 (1966). 46. Peters, H. E.: Private communication.

47. Hall, J. L. : Private communication.

48. DePrins, J.: IRE Trans, on Instrumentation Ml, 200

(1962). 49. Hellwig, H., Vessot, R. F. C, Levine, M. W., Zitzewitz, P. W., Allan, D. W., Glaze, D. J. : Conference on Precision Electromagnetic Measurements, Boulder, Colorado (1970).

135
IEEE Trans, on Instrumentation and Measurement

IM-19, 200 (1970).

50. Church, D., Dehmelt, H. G.: J. Appl. Phys. 40, 3421 (1969).

51. Dehmelt, H. G.: Advances in Atomic and Molecular

Physics 5, 109 (1969). 52. Zitzewitz, P. W. : Proc. 24th Annual Symposium on Fre- quency Control (1970). To be published.

53. Vessot, R. F. C, Levine, M. W. : Proc. 24th Annual Symposium on Frequency Control (1970). To be published.

54. Debely, P. : Proc. 24th Annual Symposium on Frequency

Control (1970). To be published.

55. Uzgiris, E. E., Ramsey, N. F.: Phys. Rev. A 1, 429 (1970).

56. Kolchenko, A. P., Rautian, S. G., Sokolovskii, R. I.: Zh. Eksp. Teor. Fiz. 55, 1864 (1968) (Engl, transl. in Soviet Phys. JETP 28, 986 (1969).

Contribution of the National Bureau of Standards, not

subject to copyright. Presented at the 24th Annual Symposium on Frequency Control, Atlantic City, N.J., 27—29 April 1970.

Received June 17, 1970

Offprint from "Metrologia"

Journal International de Metrologie scientifique — International Journal of Scientific Metrology

Internationale Zeitschrift fiir wissenschaftliche Metrologie. Vol. 6, No. 4, October 1970, Pages 118—126

136
1

CHAPTER 7

ACCURATE FREQUENCY MEASUREMENTS:

RELEVANCE TO SOME OTHER AREAS OF METROLOGY**

Helmut Hellwigt and Donald Halfordf

Contents

Page 7.1. Introduction 139

7.2. Accurate Frequency Measurements:

Principles and Methods 140

7.2.1. Particle Beams 141

7.2.2. Storage of Particles 141

7.2.3. Saturated Absorption 142

7.3. Survey of Accurate Frequency Measurements 142

7.4. Significance and Impact of Accurate Frequency Measurements 144

7.5. Summary 145

7.6. References 146

7.7. Selected Bibliography: Future Trends in Accurate Frequency/Time Metrology 148

*This chapter contains essentially the text of an original manuscript entitled "Accurate Frequency Measurements: Survey, Significance, and Forecast" which was published in PRECISION MEASUREMENT AND FUNDAMENTAL CONSTANTS, Proceedings of the International Conference held at the National Bureau of Standards, Gaithersburg, Maryland, August 3-7, 1970, Nat. Bur. Stand. (U.S.) Spec. Publ. 343, Edited by Langenberg. D. N.. and Taylor, B. N., pp. 17-25 (USGPO.

August 1971). We have made some modifications and have updated the material to late 1972 mainly through the use of footnotes. •Manuscript received April 1, 1973. • tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302.

137
'Time present and time past Are both perhaps present in time future. And time future contained in time past." Thomas Stearns Eliot

Accurate frequency measurements in the microwave through the infrared regions as well as the imminent realization of accurate frequency measurements in the near infrared and visible regions are surveyed, and their significance on the system of basic standards and fundamental constants is dis- cussed. An exceedingly accurate redetermination of the speed of light, and a single primary unified standard for frequency, time, and length are imminent possibilities. The further possibility of one

primary standard for many (if not all) of the base units exists. Traditional beam techniques, storage methods, and infrared or visible radiation molecular absorptions appear as the most promising can- didates for the primary (frequency) standard.

Key words: Cesium beam; frequency standards; frequency/time metrology; fundamental constants;

International System of Units; length standards; speed of light; unified standard; units of measurements.

138
7.1. INTRODUCTION

The present International System of Units of

Measurement (SI) is built on six base units 1 which

are related— with one exception (mass)— to fundamental properties of nature: time, length, mass,

temperature, electrical current, and luminous

intensity 2 [l]. 3 Of these the unit of time, or more

exactly the unit of time interval, the second, has

been in modern times the most accurately 4 known

and internationally accepted unit. The simple

reason for this is that we are provided by nature

1 In October 1971 the General Conference on Weights and Measures (CGPM) voted

to adopt the mole as a base unit in the SI, thereby increasing the number of base units from six to seven (see footnote 2). The mole is a measure of the quantity of matter [59].

2 Of these, only the first four are represented by independent primary base standards. See footnote 17.

3 Figures in brackets indicate the literature references at the end of this chapter.

4 By accuracy, we mean the degree to which a physical measurement or its measuring

device conforms to a specified definition.

with a unit of time interval: the duration of one day

due to the rotation of the earth. Up to the recent

past the definition of the second was based on the

rotation of the earth and more recently on the

revolution of the earth around the sun [2]. The

accuracy of the second which can be realized by

the definition approaches one part in 10 H for ex- tremely long observation periods (many years)

[2, 3]. For shorter observation periods the accuracy

is correspondingly worse. Figure 7.1 depicts the

development of the accuracy capability of time

interval standards since the advent of atomic clocks. Accuracy capability is here expressed as the one

sigma combined uncertainty of all bias corrections.

The bias corrections are the result of a theoretical

and experimental evaluation of each particular

standard, whose actual performance always deviates

to some degree from the idealized conditions which

are adopted in a definition of a base unit.

1945 1950 1955 1960 1965 1970 1975

1 I I I i ASTRONOMICAL DEFINITIONS OF THE SECOND

1 i ATOMIC DEFINITION

Figure 7.1. Historical development of the accuracy capability of the leading quantum electronic time interval/frequency standards. up to early 1973 (for recent values for time interval see ref. [70, 71]). 139
Figure 7.1 shows that the astronomical definition

held its place exclusively until 1948. In that year

the first ammonia clock was operated by H. Lyons

at the National Bureau of Standards [4]. This clock's

performance did not yet surpass that of the astro- nomical one. However, the advent of the ammonia

clock is important for two reasons: Firstly, the unit

of time interval could be related for the first time

to an (assumed) invariant physical constant, here

to the inversion transition in the ammonia molecule,

instead of being based solely on the movements of

macroscopic celestial bodies which are known to have secular changes (it is possible to correct for some but not all of the secular changes). Secondly,

a frequency standard was used to aid in the defini- tion of time interval; i.e., one used the relationship

77 = for1

, (7.1)

and 6 = 1, with t and v being the period and fre- quency of the radiation which is associated with the

quantum transition. The unit of time interval, the

second, can thus be defined as a certain number of

periods of this radiation. 5 A complete atomic clock system based on a hyperfine transition in cesium was operated and evaluated

in 1955 by Essen at the National Physical Laboratory

[5] and exceeded the performance of previous

standards by one order of magnitude. As indicated

in figure 7.1, further improvements in the cesium

atomic clock at several laboratories around the

world [3], [6-15] pushed its accuracy capability to

its current value of better than 10~ 12 [16-19]. This

performance of cesium clocks led the 13th General

Conference on Weights and Measures in 1967 to accept the following definition: "The second is the

duration of 9 192 631 770 periods of the radiation

corresponding to the transition between the two

hyperfine levels of the ground state of the cesium133 atom." The unit of frequency, the hertz, is then

defined by eq (1) with b = 1 Hz - s.

7.2. ACCURATE FREQUENCY

MEASUREMENTS: PRINCIPLES

AND METHODS

The base standard for time interval, the cesium

atomic beam apparatus, is not only the most accurate frequency source, but also the most accurate

of all base standards by a considerable margin as is illustrated in figure 7.2. This graph depicts the

accuracy capability for all six (see footnote 1) units

of the SI Base Units [1, 20]. The values for time,

length, current, temperature, and luminous intensity

describe the ability of actual instruments to realize the definition of the corresponding base unit. They

5 There could be separate standards for time interval and for frequency. The constant

b in eq (7.1) would then be a fundamental constant in a sense quite similar to the speed

of light, and b would have the dimension Hz ' s.

SI bctu wmJU ofi mMAmmmi

TEMPERA- ELECTRIC LUMINOUS

TIME LENGTH MASS TURE CURRENT INTENSITY

Figure 7.2. Comparison of the current accuracy jn jhe

realizations of the six base units of the International System

of Units (SI) up to early 1973 rounded to orders of magnitude.

(See footnote 1.)

were obtained from theoretical and experimental

evaluations of bias corrections and from national

and international intercomparisons. The only base

unit which is still defined by an artifact is the kilo- gram. Here the accuracy capability is the ability to compare masses with this artifact and to preserve

it unchanged. It must be noted that the precision 6 of relative measurements in any of these base units

may be considerably better than the quoted accuracy

capability of the corresponding base standards. In addition to being the most accurate kind, frequency/

time metrology is the most precise of the many

kinds of metrology (e.g., length, mass, force, pres- sure, resistance, current). Accurate and precise fre- quency measurements can be easily instrumented

and can be highly automated. The versatility of

frequency measurement techniques has led to their

wide usage in metrology in general. Radio broadcasts of accurate frequency and time signals are

available worldwide.

It is obvious from figure 7.2 that measurements

which are based on time interval or frequency

determinations have the potential of exceeding by

far the accuracy of any measurement involving the

five other base units (see footnote 1). Some physical constants can therefore be measured with extreme

accuracy by using time interval and frequency

methods. In particular this is true for the measure- ment of quantum transitions in atoms and molecules. The availability of an exceedingly accurate standard is, however, only one prerequisite for an

accurate measurement. In order to utilize the high

accuracy capability of a time interval/frequency

h By precision, we mean here the reproducibility, within a set, of specified measure- ments taken as a time series.

140
standard, the system which is to be measured has to be brought under such experimental control that

its measurement yields an accuracy which ap- proaches that of the standard. In the limit, the

system under study will have to show properties

which are characteristics of a time interval/ fre- quency standard itself. Therefore, the very systems

which yield the most accurate measurements are simultaneously candidates for new time interval/

frequency standards. We will discuss this aspect

later in this chapter.

A system intended for the measurement of a

transition frequency of an atom or molecule involves

several steps of physical and technical processing

which lead to bias corrections and corresponding

uncertainties. These steps can be classified into three groups: (1) particle preparation, (2) particle

confinement, and (3) particle interrogation [21]. There is no fundamental necessity to prepare the

particles. However, often it is desirable to select only certain energy states or to achieve a desired

population distribution of the energy levels. This can be done by spatial state selection, optical

pumping, etc. Care must be taken to minimize

perturbing effects. A fundamental aim of precise measurements is an observation time as large as possible. Particle

confinement is used to achieve coherent interaction

times between the particles and the interrogating

radiation which are as long as possible without in- troducing undue perturbations or excessive loss of

signal. The confinement technique also is of con- siderable importance in the reduction of the Doppler

effect, which is the most severe limitation in simple

gas cell absorption measurements. Various confinement techniques such as a storage vessel with coated

walls, ion storage, the storage in a cell filled with

buffer gases, or the traveling particle beam are

possible.

The particles have to be interrogated. Usually a resonant structure (e.g., cavity or interferometer) is used to enhance the interaction and to provide a

spatially well-defined interaction region. The inter- rogation process itself may introduce perturbations

such as the Bloch-Siegert effect [22] and photon

recoil [21, 23]. We will now discuss the three methods 7 which

stand out as leading to the most accurate measurements. It is not surprising that all three have in common a significant reduction of the Doppler

effect limitation.

7.2.1. Particle Beams

In a particle beam apparatus, particles emerge

from a source, forming a beam which travels through vacuum as indicated in figure 7.3. A polarizer

(spatial state selector, optical pump, . . .) creates

a certain, more desirable population distribution of

OSCILLATOR G

BEAM L

FREQUENCY COMPARATOR STANDARD

RADIATION

I I SOURCE POLARIZER

IRRADIATION REGION

I I ANALYZER

~

j | DETECTOR

FIGURE 7.3. Accurate frequency measurements: particle beam

method.

the energy levels. The beam then enters the region

of interrogation and is "confined" there for the

duration of the transit time. The interrogation by

radiation of suitable intensity and a suitable

frequency which is compared to the frequency

standard results in a change of the population

distribution and a change of the intensity of the

transmitted or reflected radiation. Two modes of

detection are therefore possible. One is the analysis

of the population distribution by counting the

number of particles in a selected energy state. An analyzer, similar to the polarizer, and a particle

detector are then necessary. An example of this mode of detection is shown in figure 7.3 [24]. The

other mode of detection, which is not shown in figure 7.3, involves the monitoring of the radiation

intensity [25, 26]. Under certain conditions, particularly at sufficiently high beam intensity, the system

converts to a frequency generator (maser, laser

oscillator) [25]. The output frequency is then

detected and measured by comparison with a frequency standard.

In the particle beam the Doppler effect is greatly

reduced by the narrow, unidirectional beam. If care is taken in the design of the resonance structure

so that the beam does not encounter net radiation

power traveling parallel to the beam direction, the

limitations due to the first-order Doppler effect can be virtually eliminated [24]. The second-order

Doppler effect can be measured, or can be cal- culated, if the particle speed is adequately known.

Particle preparation does not introduce frequency

bias if it is spatially separated from the interrogation

region.

7.2.2. Storage of Particles

7 A more detailed discussion of these methods is given in Chapter 6.

In a storage device, particles are stored in a vessel which is located within the resonance

structure as shown in figure 7.4. Particle preparation may be done simultaneously with the interrogation, e.g., by optical pumping and monitoring the

intensity of the transmitted pump radiation as indicated in figure 7.4 [27]. However, this introduces

frequency shifts which are difficult to evaluate [28].

141
RADIATION

PUMP ENERGY DETECTOR SIGNAL

IRRADIATION REGION

CELL

COMPARATOR

DETECTOR

FREQUENCY STANDARD

Figure 7.5. Accurate frequency measurements: saturated absorption method.

Figure 7.4. Accurate frequency measurements: particle storage method.

It is therefore advantageous to separate the preparation and interrogation regions and to use the storage

principle in connection with the polarizing and

analyzing technique of figure 7.3. In other words,

the storage device of figure 7.4 is inserted between

polarizer and analyzer of the system in figure 7.3 thus forming a storage beam device [29, 30]. Again we have the option to adjust the system parameters

(beam intensity, pumping strength, . . .) such that

self-oscillations are possible [28, 31]. The advantage of the storage technique is the

increase in the confinement time leading to a very

sharp line. The first-order Doppler effect also can be virtually eliminated if the movement of the

particles is confined to a region of less than half the

wavelength of the interrogating radiation. This is easy for the case of microwave frequencies but is more difficult at very short wavelengths. However,

buffer gases can sufficiently restrict the particle

movements. Also, buffer gases [28] and coating of

the walls of the storage vessel [31] are used to reduce frequency shifts and relaxation processes

due to wall collisions. The second-order Doppler

shift can be calculated to a high degree of accuracy

from the temperature of the storage vessel since the

kinetic energy of the stored particles is in thermal

equilibrium with the storage vessel.

7.2.3. Saturated Absorption

As shown in figure 7.5, in a saturated absorption

device, the radiation of an oscillator is passed in opposite directions through a cell which is filled with the particles under study. The transmitted

radiation intensity is monitored. Those particles

with a near-zero velocity component parallel to the

radiation propagation vector experience a nonlinear,

enhanced interaction with the radiation field ("Lamb dip") [32, 33]. The system parameters can

be adjusted so that those particles which have a

significant velocity component parallel to the radiation beam are not interrogated. This reduces considerably the first-order Doppler effect and also excludes from the interrogation most of the particles which suffered a collision with other particles. 8 The line width is thus ultimately given by

the transit time of particles across the radiation

beam. The second-order Doppler correction can be

obtained from the gas cell temperature. At higher

frequencies the saturated absorption method may

be limited by photon recoil effects which cause

the emitted frequency v E to be different from the

absorbed frequency vA by the fractional amount

[21,23]

{vA - vE)lv= hv/mc2

, (7.2)

where v is the average of vA and vE , m is the mass of

the particle, h is Planck's constant, and c is the

speed of light.

7.3. SURVEY OF ACCURATE FREQUENCY MEASUREMENTS

For figure 7.6 we have selected the most signifi- cant of the many published accurate frequency

measurements and have plotted the published one

sigma accuracy versus the location of the transition

in the electromagnetic spectrum. The dashed bar

in the case of I 2 indicates that its frequency has not

yet been measured. 9 This is because frequency

synthesis 10 has not yet succeeded in reaching to this frequency. However, advances by several groups,

in particular by K. Evenson of NBS [34] and A. Javan of MIT [35], indicate that success is immi8 Particle collisions lead to changes in particle speed and direction. A strong collision removes the particle from the interrogation process because the collision introduces, with high probability, a significant velocity component parallel to the radiation beam.

9 The first measurement by frequency metrology of the 88 THz frequency of CH 4 was

achieved on 11 November 1971 at NBS [60]. In 1972, the accuracy of the frequency measurement was improved to 6 parts in 10 10 yielding 88.376 181 627 THz [61], As of

late 1972, the 474 THz frequency of I 2 has not yet been measured by frequency metrol- ogy, although the frequency is being determined via length metrology (unpublished work of H. Layer and R. D. Deslatte9). To the best of our knowledge, the highest fre- quency yet synthesized from the frequency of cesium is 177 THz (unpublished work of G. W. Day and H. Hellwig).

10 For a survey of infrared frequency synthesis, see reference [62]. 142
FREQUENCY (Hz]

14 10 15

CH,

CESIUM ACCURACY CAPABILITY

Figure 7.6. A survey of selected accurate frequency measurements throughout the electromagnetic spectrum. The accuracies reflect the state of the art as of early 1973. For I 2 the anticipated value is indicated (see text).

nent. 9 The value indicated for the accuracy of the

anticipated measurement of I 2 is based on the

evaluation of the beat frequency between two lasers which were independently frequency-locked to the

1 2 transition together with absolute wavelength

measurements [33]. Table 7.1 contains information

supplementary to figure 7.6.

The measurements of HCN, H2O, and CO2 were made by frequency multiplication in a metal-metal

point contact diode. The comparatively low accuracy

of these values is due mainly to the fact that the

molecular transition was investigated in a laser

oscillator. This technique introduces large uncertainties because of Doppler effects, pressure

effects, resonator frequency pulling, etc. Application of the saturated absorption method would con- siderably increase the measurement accuracy as is demonstrated by the CH4 and I2 experiments.

The storage of ions is a powerful and very promising spectroscopic tool as is demonstrated by the

3 He + measurement. However, several experimental

parameters are not yet fully understood, and they

need further investigation, especially the kinetic

energy of the stored ions (Doppler effect) [36]. 11 The methods on which the most accurate measure- ments are based were already discussed. They are the saturated absorption (CH4, I2), the storage

vessel (H, D, T), and particle beams (Tl, NH3 , H2 S, Cs). The cesium particle beam tube serves as the primary standard for the base unit of time

interval and frequency. It has been the most

accurate measuring device since 1955 (fig. 7.1). Its present accuracy capability, shown as the

horizontal line across the bottom of figure 7.6, is 2 parts in 1013 [15, 17, 18, 19, 70, 71 (see chap. 5B)].

11 References [63] and [64) give discussions of the ion storage techniques as related to frequency standards.

143
Table 7.1. Survey of accurate frequency measurements

Particle Transition Technique Frequency a Accuracy References

D F, /n/- = f, "1 ^ ^, ^ Storage maser 327 384 352.51 Hz 2 X 10- 10 [37]. H F, m.p = 1, 0 *r> 0, 0 Storage maser 1 420 405 751.768 Hz 1 X'10" 12 [38], [39]. T F, mF = 1, 0 «-» 0, 0 Storage maser 1 516 701 470.809 Hz 5 x 10" 12 [40].

3 He+ r , = 0, 0 <-> 1, 0 Ion storage 8 665 649 905 Hz 6 X 10- 9 [41].

>05T11

1

it m — in ^ n a r , nip — 1, U <-> U, U Particle beam zl 31U 833 V45.9 Hz 1 x 10~ n

L42], [43].

15 MH y, K. — 3, 3 inversion Beam maser 00 7Q0 All 7Q1 TJTM ZZ /oy 4zl (Ol rlZ C \s 1 O— 1

1

V A 41 L44J

.

U32C

11 2 O 1 , *-* 1

,

i-i ii r Q rt i /"» 1 J!l M

1Ifa nAQm iff lIIM lfifl iuo 769 <uz 769 /oz oio 373 Hinz o v in-io Z A 1U U 12P 14M xl L. IN I1U U4U Laser U.ow /olio Irlz 2 X 10-7 r A£L~\ V AH~\ [46], L47].

it i6ri b UUl UzU Laser lfi Tin A73 TTJ 1U. /lo U/3 Iriz 2 X 10~ 7 [47].

12 C1602 P(18). 001 100 Laser 28.359 800 THz 1 X 10~ 6 [34].

12 C

1602 R(12), 001 «-> 020 Laser 32.176 085 THz 6 X 10- 7 [50].

12 CH4 P(7), ?3 band Saturated absorption = 88 THz (1 X 10" 11

) [32].

Is R(127), 11-5 band of electr. trans. B

3 n+ ~x%+

Saturated absorption » 474 THz (2 x 10-"

) [33].

a By definition, vcs = 9 192 631 770 Hz. See text for recent results on CH4.

b The frequencies of several other transitions in water vapor lasers have been measured such as the 2.5-THz (118 (im) line in H20

[48] and the 3.6-THz (84 /^m) line in D2 0 [49].

7.4 SIGNIFICANCE AND IMPACT

OF ACCURATE FREQUENCY

MEASUREMENTS

We can identify four general areas where accurate frequency measurements are significant and where some impact on future scientific and technological

developments is foreseen. These are summarized

in table 7.2. Within the acope of this chapter only

the last area, fundamental constants and basic

standards, is of importance; we will discuss it in

detail and only briefly explain the first three items.

Metrology and applications include radar ranging

especially over long (planetary) distances; planetary

exploration in general; earth and space navigation,

where timekeeping over weeks, months, or even

years without resynchronization is vital; telecommunication aspects including high bit rates and

better usage of the electromagnetic spectrum; and

aircraft collision avoidance systems which can be

based, perhaps with advantage, on time domain

techniques which employ accurate clocks. Accurate frequency measurements throughout

the infrared and visible region will greatly increase our knowledge of the structure of atoms and molecules. Spectroscopic constants such as transition

frequencies, g-factors, Stark coefficients, rotational

distortions, etc., will be accessible to measurements

of unprecedented precision and accuracy. Tests of the general theory of relativity involving

differences of coordinate time and frequency at locations of different gravitational potential will be made with clocks placed in satellites or on other

celestial bodies. An improvement in accuracy of

about one order of magnitude over our present

accuracy capability will permit some tests to be

conducted on the earth's surface.

Table 7.2. Areas of impact

Metrology and Applications to Technology

Spectroscopic Constants

General Theory of Relativity

Fundamental Constants and Basic Standards

The ability to perform accurate frequency

measurements throughout the electromagnetic

spectrum may have a considerable impact on the

system of fundamental constants and basic standards. Figure 7.6 illustrates that frequency measure- ments have already been made in the terahertz

region and that the ability to compare directly the

frequencies of the standard of time interval/frequency (currently 133Cs) and of the standard of

length (currently 86Kr) will soon be a reality. 12 The

relationship between these standards involves the

speed of light c, k=cv~\ (7.3)

where A. is the vacuum wavelength and v is the fre- quency of the radiation. Equation (7.3), as applied

to the direct comparison of length and frequency

(time interval), will lead to a determination of the

speed of light with unprecedented accuracy [34], which will be limited only by the ability to perform

an interferometric length measurement (compare

fig. 7.2). 12

12 This has been partially achieved in 1972. See reference [61].

144
Equation (7.3) is not the only "simple" relation- ship between basic standards involving a fundamental constant. The Josephson phenomenon [51] provides us with a relationship between the electrical potential difference V (relating to the standard

of electrical current) across a superconducting

weak link and the corresponding Josephson oscilla- tion frequency v V= (hl2e)v. (7.4)

Equation (7.4) has already served to determine

Planck's constant h divided by the electronic

charge e with unprecedented accuracy [52, 53]

which led to a refitting of the whole system of

fundamental constants [54]. 13 We can imagine fur- ther simple relationships between basic standards

and the time interval/frequency standard involving

fundamental constants, such as a relationship for the mass m

m=f(v), (7.5)

or for the temperature 14 T

T = g(v). (7.6)

Accurate frequency measurements based on eqs

(7.3) to (7.6) could therefore lead to a more accurate knowledge of the fundamental constants. This

increased accuracy in turn would allow a more

sensitive search for possible spatial and secular

variations of the fundamental constants [55].

It is a consequence of historical development and

experimental expertise that we have a set of base

units and corresponding standards such as the SI; no fundamental physical principle is involved in

this choice. It is already possible to compare spec- troscopic data in the infrared or visible regions using

frequency measurement techniques with a precision

far exceeding that of interferometric (length measurement) techniques.

In view of the success of frequency multiplication

from the microwave region into the infrared region

and its imminent extension into the visible region

it seems to be in order to question, at least philosophically, the need for a separate standard of

length. Length measurements could be related to the base unit for time interval and frequency via eq (7.3). The speed of light would then be a defined constant 15 [56, 57, 58]. The defined value of c would

be chosen to be compatible with its previous best

experimental value, and the most accurate frequency

standard would serve as a Unified Standard for frequency, time, and length. 16

13 It is now possible with the Josephson junction to create an operational substitute

for the traditional bank of saturated cells used to maintain the NBS calibrated sec- ondary working voltage standard ("Legal Volt"). Such an operational system was

formally established in NBS on 1 July 1972 [65].

14 Such a relationship has been used recently for temperature measurements in the

millikelvin range [66, 67). The method is based on the measurement of frequency

fluctuations in a Josephson junction caused by voltage fluctuations which in turn are caused by thermal noise corresponding to the temperature of a resistor shunting the

junction.

15 Compare with footnote 5.

,s These considerations are discussed in more detail in reference [68).

In the limit this philosophy would lead to a base

set of fundamental constants with defined values. The most accurate standard, which is today the

cesium beam frequency standard, would then serve

as The Standard, and all other units of measurement

could be derived using relationships such as eqs

(7.3) to (7.6) with c, /i/(2e), and some yet undetermined function like f(v) and g(v) (see footnote

14) as defined entities. 17 These possibilities add

excitement to the work which is being done on

frequency standards.

7.5. SUMMARY

In the preceding sections, we pointed out that frequency/time metrology is currently the most

precise and accurate kind of metrology, and we

outlined the significance of accurate frequency

measurements and their impact on technology and

physics, and in particular on the system of fundamental constants and basic standards. Possibly

being the Unified Standard or even The Standard in some future system of units of measurement, the

primary frequency standard should get special

attention. At present we see several ways [21] of pushing its accuracy capability beyond the present one sigma performance of 2 X 10~ 13 of the laboratory

cesium beam tube [70, 71]. We discussed the three most promising methods

which allow the most accurate frequency measurements: particle beam, particle storage, and saturated

absorption. We also mentioned that naturally these

very same methods are the most promising ones for the development of future standards of even better accuracy.

In table 7.3, experimental realizations of these

methods are listed together with evaluated accuracy

capabilities and projected performances. Each

projected performance is listed as better than some

quoted value. This value is believed to represent a minimum performance which almost certainly can

be surpassed based on our present experimental

and theoretical knowledge; however, we cannot

predict with sureness if and by how far. In this sense, a technique quoted as "better than 10 -11 " could well surpass one quoted as "better than 10-12." For a more detailed discussion we recommend the

cited literature, and we suggest reference [21] for a

critical comparison and prognostic.

Perhaps a uniquely superior method of accurate frequency measurement will be singled out by

additional experimental and theoretical work, or perhaps these three methods will each improve

significantly so as to remain mutually competitive.

Very likely, in the continuing progress of knowledge and technical abilities, new possibilities will continue to appear.

17 Although there are seven base units in the SI (see footnotel). there are at present

only four independent primary base standards in the SI 169]; water for temperature

(kelvin), prototype kilogram for mass (kilogram), atomic krypton for length (meter), and atomic cesium for time (second). Consequently, to go from four independent

primary base standards to only one (The Standard) would require adoption of a suitable

set of three such definitions, one of which would be the value of the round trip speed

of light c.

145
Table 7.3. Promising candidates for primary frequency standards

Method

Particle beam.

Particle storage.

Saturated absorption.

Device

Cesium beam.

Iodine beam...

Hydrogen Maser

Hydrogen storage beam

3 He + Ion storage (or heavy ions).

f Methane cell, [iodine cell...

.

v{Hz)

Accuracy capability (one sigma)

Present performance Projected

performance

9.2 X 109

5.8 X 10 14

1.4 X 10*

1.4 x 109

8.7 x 109

8.8 X 10 13

4.7 x 10 14

2 X lO" 13 [70, 71]

[26]

1 X lO" 12 [38]

[30] 6 x lO"9 [27]

1 x 10->> [32] 2 x lO" 9 [33]

Better than 10 ~ 13

Better than 10" 12

.

Better than 10 " 12

. Better than 10 12

. Better than 10 " n.

Better than 10 " 12

. Better than 10 _n.

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[37] Larson, D. J., Valberg, P. A., and Ramsey, N. F., "Measure- ments of the hydrogen-deuterium atomic magnetic moment

ratio and of the deuterium hyperfine frequency," Phys.

Rev. Lett., 23, No. 24, pp. 1369-1372 (December 15, 1969).

[38] Crampton, S. B., Kleppner, D., and Ramsey, N. F., "Hyperfine separation of ground state atomic hydrogen," Phys. Rev. Lett. , 1 1 , No. 7, pp. 338-340 (October 1 , 1963).

[39] Hellwig, H. , Vessot, R. F. C.,Levine,M. W. , Zitzewitz, P. W.,

Allan, D. W., and Glaze, D. J., "Measurement of the un- perturbed hydrogen hyperfine transition frequency," IEEE Trans, on Instrum. and Meas., IM-19, No. 4, pp. 200-209 (November 1970).

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N. F., "Hyperfine separation of tritium," Phys. Rev., 158,

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[41] Fortson, E. N., Major, F. G., and Dehmelt, H. G, "Ultra- high resolution of AF = 0, ± 1 (He 3

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ion-storage collision technique," Phys. Rev. Lett., 16,

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147
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7.7 SELECTED BIBLIOGRAPHY:

FUTURE TRENDS IN ACCURATE

FREQUENCY/TIME METROLOGY

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1963: Comm. 1), Radio Measurement Methods and

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electrodynamically contained proton gas," J. Appl.

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[Bll] Cook, A. H., "Quantum metrology-standards of measure- ment based on atomic and quantum phenomena,"

Reports on Progress in Physics, 35, No. 5, pp. 463-528

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Soc. London, A165, No. A921, pp. 199-208 (April 5, 1938). [B14] Essen, L., and Parry, J. V. L., "An atomic standard of frequency and time interval," Nature, 176, No. 4475,

pp. 280-282 (August 13, 1955). [B15] Essen, L., "The units of time and length," Nature (Lett.) 180, No. 4577, pp. 137-138 (July 20, 1957). [B16] Essen, L.. "Electrical standards in terms of frequency and physical constants," Alta Frequenza, 40, No. 8, pp. 329E-332E (August 1971). [B17] Evenson, K. M., Wells, J. S., and Matarrese, L. M., "Absolute frequency measurements of the CO2 cw

laser at 28 THz (10.6 pm)" Appl. Phys. Lett., 16,

No. 6, pp. 251-253 (March 15, 1970). [B18] Evenson, K. M., Wells, J. S., and Matarrese, L. M., "Defining the speed of light: A combination time, frequency, and length standard," Precision Measurement and

Fundamental Constants, Proc. Int. Conf. (NBS, Gaithers- burg, MD 20760, August 3-7, 1970), D. N. Langenberg

and B. N. Taylor, Eds.. Nat. Bur. Stand. (U.S.) Spec.

Publ. 343, pp. 67-69 (USGPO, August 1971). [B19] Evenson, K. M., Day, G. W., Wells, J. S., and Mullen,

L. O., "Extension of absolute frequency measurements

to the cw He-Ne laser at 88 THz (3.39 p)" Appl. Phys.

Lett., 20, No. 3, pp. 133-134 (February 1, 1972). [B20] Evenson, K. M., Wells, J. S., Peterson, F. R., Danielson,

B. L., Day, G. W., Barger, R. L., and Hall, J. L., "Speed

of light from direct frequency and wavelength measure- ments of the methane-stabilized laser," Phys. Rev.

Lett., 29, No. 19, pp. 1346-1349 (November 6, 1972). [B21] Finnegan, T. F., Denenstein, A., and Langenberg, D. N., "AC Josephson-effect determination of e/h: A standard

of electrochemical potential based on macroscopic

quantum phase coherence in superconductors," Phys.

Rev.. B4. No. 5, dp. 1487-1522 (September 1971)

[B22] Fowler, H. A., Witt, T. J., Toots, J., Olsen, P. T., and

Eicke, W., "Referencing of the U.S. national volt against a Josephson frequency-to-voltage source,"

Precision Measurement and Fundamental Constants,

Proc. Int. Conf. (NBS, Gaithersburg, MD 20760, August

3-7, 1970). D. N. Langenberg and B. N. Taylor, Eds., Nat. Bur. Stand. (U.S.) Spec. Publ. 343, pp. 223-225 (USGPO, August 1971). [B23] Gould, G., "Laser frequency standards," Frequency, 1, No. 6, pp. 14-16 (September 1963). [B24] Halford, D., Hellwig, H., and Wells, J. S., "Progress and

feasibility for a unified standard for frequency, time, and

length," Proc. IEEE (Lett.), 60, No. 5, pp. 623-625 (May

1972). [B25] Hall, J. L., and Morey, W. W., "Optical heterodyne measurement of neon laser's millimeter wave difference frequency," Appl. Phys. Lett., 10, No. 5, pp. 152-155 (March 1, 1967). [B26] Hall, J. L., "The laser absolute wavelength standard problem," IEEE J. Quantum Elect., QE-4, No. 10, pp. 638-641 (October 1968). [B27] Hall, J. L., Barger, R. L., Bender, P. L., Boyne, H. S., Faller, J. E., and Ward, J., "Precision long path inter- ferometry and the velocity of light," Electron Technology,

Proc. URSI (Comm. 1) Conf. on Laser Meas., (Warsaw,

Poland, September 24-28, 1968). A. Smolinski and S. Hahn, Eds., 2, No. 2/3, pp. 53-66 (Institute of Electron

Technol., Polish Academy of Sciences, Warsaw, Poland,

1969). [B28] Hanes, G. R., and Baird, K. M., "I 2 controlled He-Ne laser

at 633 nm: preliminary wavelength," Metrologia, 5, No. 1, pp. 32-33 (January 1969). [B29] Hellwig, H., "The hydrogen storage beam tube — a pro148
posal for a new frequency standard," Metrologia, 6, No. 2, pp. 56-60 (April 1970). [B30] Hellwig, H., "Areas of promise for the development of future primary frequency standards," Metrologia, 6,

No. 4, pp. 1 18-126 (October 1970) (see chap. 6). [B31] Hellwig, H., and Halford, D., "Accurate frequency measurements: Survey, significance, and forecast," Precision Measurement and Fundamental Constants, Proc. Int. Conf. (NBS, Gaithersburg, MD 20760, August 3-7, 1970), D. N. Langenberg and B. N. Taylor, Eds., Nat. Bur. Stand. (U.S.) Spec. Publ. 343, pp. 17-25 (USGPO,

August 1971). [B32] Hocker, L. O., Small, J. G., and Javan, A., "Extension of absolute frequency measurements to the 84 p. range,"

Phys. Lett., 29A, No. 6, pp. 321-323 (June 2, 1969). [B33] Josephson, B. D., "Supercurrents through barriers," Adv. Phys., 14, No. 56, pp. 419-451 (October 1965). [B34] Kamper, R. A. , and Zimmerman, J. E. , "Noise thermometry

with the Josephson effect," J. Appl. Phys., 42, No. 1, pp. 132-136 (January 1971). [B35] Kovalevsky, J., "Astronomical time," Metrologia, 1, No. 4, pp. 169-179 (October 1965). [B36] Langenberg, D. N., and Taylor, B. N., (Eds.), Precision Measurement and Fundamental Constants, Proc. Int. Conf. (NBS, Gaithersburg, MD 20760, August 3-7,

1970), Nat. Bur. Stand. (U.S.) Spec. Publ., 343, 543 pp. (USGPO, August 1971). [B37] Markowitz, W., Hall, R. G., Essen, L., and Parry, J. V. L , "Frequency of caesium in terms of ephemeris time,"

Phys. Rev. Lett., 1, No. 3, pp. 105-106 (August 1, 1958). [B38] McDonald, D. G., Risley, A. S., Cupp, J. D., and Evenson,

K. M., "Harmonic mixing of microwave and far-infrared laser radiation using a Josephson junction," Appl.

Phys. Lett., 18, No. 4, pp. 162-164 (February 15, 1971). [B39] McNish, A. G., "The basis of our measuring system,"

Proc. IRE, 47, No. 5, pp. 636-643 (May 1959). [B40] NBS, "Mole adopted as International System Base Unit," Nat. Bur. Stand. (U.S.) Tech. News Bull., 56, No. 2, pp. 42-43 (USGPO, February 1972). [B41] NBS, "NBS to maintain legal volt using 2e/h via the ac Josephson effect," Nat. Bur. Stand. (U.S.) Tech. News

Bull., 56, No. 7, pp. 159-160 (USGPO, July 1972). [B42] Page, C. H., and Vigoureux, P. (Eds.), "The International System of Units," (American translation of "Le Systeme

International dTJnites," 1970 OFFILB, 48 rue GayLussac, F. 75, Paris 5 (Revised Edition 1972).), Nat.

Bur. Stand. (U.S.) Spec. Publ. 330, 45 pp. (USGPO,

April 1972). [B43] Parker, W. H., Langenberg, D. N., Denenstein, A., and

Taylor, B. N., "Determination of e\h using macroscopic

quantum phase coherence in superconductors. I. Experiment," Phys. Rev., 177, No. 2, pp. 639-664

(January 10, 1969). [B44] Petley, B. W., and Morris, K., "A measurement of 2e/h by

the a-c Josephson effect," Metrologia, 6, No. 2, pp. 46-51 (April 1970). [B45] Sanders, J. H, and Wapstra, A. H., (Eds.), Atomic Masses and Fundamental Constants, Proc. 4th Int. Conf. on Atomic Masses and Fundamental Constants (Teddington,

England, September 1971), Part 6, "Velocity of light," pp. 295-336 (Plenum Press, London, England, 1972). [B46] Simkin, G. S., "Establishment of a single time and length

standard," translated from Izmeritel'nava Tekhnika, No.

10, pp. 6-10 (October 1968); Meas. Tech. (USSR), No. 10, pp. 1308-1314 (Consultants Bureau, New York, NY

10011, October 1968). [B47] Sokoloff, D., and Javan, A., "Absolute frequency determination of 9.3 p. CO2 laser transitions," Bull. Am. Phys.

Soc. -Series II, 15, No. 4, p. 505 (April 1970). [B48] Taylor, B. N., Parker, W. H., and Langenberg, D. N., "Determination of e/h using macroscopic quantum phase coherence in superconductors; implications for quantum

electrodynamics and the fundamental physical constants," Rev. Mod. Phys., 41, No. 3, pp. 375-496

(July 1969). [B49] Terrien, J., "Scientific metrology on the international plane and the Bureau International des Poids et Mesures," Metrologia, 1, No. 1, pp. 15-26 (January

1965). [B50] Terrien, J., "News from the International Bureau of Weights and Measures — the 54th meeting of the Comite

International des Poids et Mesures," Metrologia, 1, No. 1, pp. 55-56 (January 1966). [B51] Terrien, J., "Fundamental metrology— present state and

recent progress in some important fields of fundamental

metrology, and functions of consultative committees of the International Committee of Weights and Measures,"

Metrologia, 8, No. 3, pp. 99-108 (July 1972). [B52] Warner, B., and Nather, R. E., "Wavelength independence

of the velocity of light in space," Nature (Lett.), 222,

No. 5189, pp. 157-158 (April 12, 1969). [B53] Wells, J. S., Evenson, K. M., Day, G. W., and Halford, D.. "Role of infrared frequency synthesis in metrology."

Proc. IEEE (Lett.), 60, No. 5, pp. 621-623 (May 1972).

149
I
CHAPTER 8

STATISTICS OF TIME AND FREQUENCY DATA ANALYSIS**

David W. Allan,t John H. Shoaf,f and Donald Halfordt

Contents

Page 8.1. Introduction 153

8.2. Definitions and Fundamentals 153

8.2.1. Aspects of Time 153

8.2.2. Definitions: Stability, Reproducibility, Accuracy 153

8.3. Characterization of Frequency Stability 154

8.4. Requirements for a Measure of Frequency Stability 155

8.5. Concepts of Frequency Stability 156

8.6. The Definition of Measures of Frequency Stability (Second Moment Type) 156

8.6.1. First Definition of the Measure of Frequency Stability— Frequency Domain.. 157

8.6.2. Second Definition of the Measure of Frequency Stability— Time Domain 157

8.6.3. Distributions 158

8.6.4. Treatment of Systematic Variations „. 158

8.7. Translations among Frequency Stability Measures 159

8.7.1. Frequency Domain to Time Domain 159

8.7.2. Time Domain to Frequency Domain 159

8.7.3. Translations among the Time Domain Measures 160

8.8. Examples of Applications of Previously Developed Measures 161

8.8.1. Applications of Stability Measures 161

a. Doppler Radar 161

b. Clock Errors 161

8.9. Measurement Techniques for Frequency Stability 162

8.9.1. Heterodyne Techniques (General) 162

8.9.2. Period Measurement 163

8.9.3. Period Measurement with Heterodyning 163

8.9.4. Frequency Counters 163

8.9.5. Frequency Discriminators 164

8.9.6. Common Hazards 164

8.10. Summary of Frequency Stability Measures 165

8.11. Practical Applications of Frequency Stability Specification and Measurement 165

8.12. Terminology for Specification of Frequency Stability 165

8.13. Comparison of Measurement Techniques 167

8.14. Operational Systems for Measurement of Frequency Stability at NBS (High Fre- quency Region) 168

8.14.1. Frequency Domain Measurements 168

8.14.2. Time Domain Measurements 170

8.14.3. Differential Phase Noise Measurements 171

•Manuscript received May 18, 1973. •Parts of this Chapter have been modified from "Characterization of frequency stability" published in IEEE Trans, on Inslrum. and Meas.. May 1971 (see ref- erence [1]), publication herein is at concurrence of the IEEE. tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302.

151
Page

8.15. Operational Systems for Measurement of Frequency Stability at NBS (Microwave

Region) 171

8.15.1. Basic Considerations of the Microwave (Frequency Stability) Measurement System 173

8.15.2. Description of the Microwave (Frequency Stability) Measurement System... 173

8.15.3. Calibration Procedure 173

8.15.4. Measurement Procedure 173

8.15.5. Additional Techniques for Frequency Stability Measurements at X-Band... 174

8.16. Conclusions/Summary 175

8.17. References 175

Annex 8.A Glossary of Symbols 176

Annex 8.B Translation of Data from Frequency Domain to Time Domain Using the Conversion Chart (table 8.1) 178

Annex 8.C Spectral Densities: Frequency Domain Measures of Stability 178

Annex 8.D A Sample Calculation of Script J£ 180

Annex 8.E A Sample Calculation of Allan Variance, cr'y (t) 181

Annex 8.F Computing Counter Program Using an Efficient Overlapping Estimator for <oi(/V=2, T,T,fh )yi* 182

Annex 8.G Selected Frequency Stability References: Bibliography 182

Annex 8.H Detailed Procedure for Calibrating Microwave (Frequency Stability) Measurement System 187

Annex 8.1 Measurement Procedure for Determining Frequency Stability in the Micro- wave Region 188

Annex 8. J Tables of Bias Functions, Bi and B2 , for Variances Based on Finite Samples of

Processes With Power Law Spectral Densities 190

Table 8.1. Stability Measure Conversion Chart 166

"As a concept for ordering and analyzing real events with variable amounts of information 'time' is much more complex than a simple clock-measure."

Patrick Meredith, Study of Time, p. 84

The fluctuations about the average of a time or frequency signal characterize its quality. The

statistical characteristics of the random fluctuations are needed in any clear statement regarding

the stability of the signal as well as the credibility of the average value. We describe two methods

of characterizing the random fluctuations of a signal, one in the frequency domain and one in the time domain.

In the frequency domain we characterize the fluctuations using the spectral density of the fluc- tuations of the time or of the fractional frequency. We use spectral densities which are one-sided and are on a per hertz basis. In the time domain the Allan variance is employed to characterize the time fluctuations and/or the fractional frequency fluctuations. The need to specify certain aspects

of the measurement is emphasized, i.e., the sample time, the sample repetition rate, the measure- ment system bandwidth, and the number of samples in each variance. The relationships between

these measures of stability are given. Power law spectral densities can describe the commonly occurring kinds of random fluctuations which include white noise and flicker noise time or frequency fluctuations. For these commonly oc- curring noise processes some tables of convenient relationships between the frequency domain and

the time domain measures are also given. In addition, for different, but specific, power law noise processes the dependence of the time domain stability measure on the number of samples or on the dead time of the measurement process is tabulated. The above stability measures have proven very

useful, and examples of application are given, e.g., estimation of the time dispersion of a clock and

specification of the detailed quality of a state-of-the-art frequency standard. Operational systems

for measurement of frequency stability are described in detail sufficient for duplicating techniques and results. Key words: Allan variance; frequency; frequency domain; frequency stability measurements; measure- ment system description; phase noise; sample variance; spectral density; stability definitions; ter- minology standards; time domain clock statistics; time/frequency statistics; variance.

152
8.1. INTRODUCTION

This chapter discusses some reasonable measures

for time and/or frequency deviations. The subject

is treated on both the theoretical and practical level. Section 8.2 presents some definitions and fundamentals to give understanding into what a deviation

is. Sections 8.3 through 8.10 give a theoretical

exposition into measures of frequency stability and

contain major parts of the paper, "Characterization of frequency stability," by J. A. Barnes et al.

[I]. 1 Sections 8.11 through 8.15 show general

applications and examples of stability measures in the laboratory, based on the paper cited above

[1] and from the NBS Technical Note entitled

"Frequency stability specification and measurement: High frequency and microwave signals"

[2]. Standards of terminology and measurement

techniques are recommended to facilitate con- formity in reporting results from various laboratories with a commonality of reference. Some ten annexes are given. They include a glossary of terms,

sample calculations and derivations, a frequency

stability computer program, selected references and

a bibliography applicable to frequency stability,

and a reproduction of bias function tables. This

latter is part of the NBS Technical Note, "Tables

of bias functions, B\ and /?•>, for variances based

on finite samples of processes with power law

spectral densities" [3]. We have attempted to co- ordinate the chapter with sufficient independence

of subject matter but allowing adequate material in a given area to satisfy both the theorist and the

practical engineer.

8.2. DEFINITIONS AND

FUNDAMENTALS

8.2.1. Aspects of Time

Time— as one of the four independent base units

of measurement — has been adopted as a defined

quantity. Currently, the unit of time is defined:

"The second is the duration of 9 192 631 770 periods

of the radiation corresponding to the transition

between the two hyperfine levels of the ground state of the cesium-133 atom," as decreed by the General

Conference on Weights and Measures [4] (see chap.

1, ann. l.A.l). There are three fundamental aspects

of time 2

: the first, covered by the definition above,

is time interval which can be related to frequency—

frequency being the inverse period of an oscillation. The second aspect is that of date or clock reading

which often has been called epoch. We prefer the use of the word date because epoch has alternate meanings that could lead to confusion. Date or

1 figures in brackets indicate literature references at the end of this chapter.

2 See Chapter 1 on "Basic Concepts of Precise Time and Frequency."

clock reading is simply the counting or accumulation—starting from some predetermined origin —

of unit time intervals; e.g., "A special adjustment

to the standard-frequency and rime-signal emissions

should be made at the end of 1971 so that the reading

of the UTC scale will be 1 January 1972, Oh 0m 0s at the instant when the reading of Atomic Time (AT)

indicated by the Bureau International de I'Heure (BIH) wiU be 1 January 1972, Oh 0m 10s" [5] (see

chap. 1, ann. l.B). The third aspect is simultaneity—the practical application of which is clock

synchronization; i.e., two clocks have the same

reading in some frame of reference.

8.2.2. Definitions: Stability, Reproducibility,

Accuracy

Let us define a clock as a frequency standard

coupled with a counter-divider. We next might

question why a clock deviates from the ideal, where

an ideal clock realizes the ultimate of the above

three aspects of time. To further explain, the ideal

clock's unit time interval would agree exactly with

the definition, and at some particular moment the

reading of the clock would agree exactly (would be

synchronous) with some defined date or origin.

Categorically there are two reasons for deviations.

First, the clock may have deterministic biases; e.g., the frequency may drift with time, the calibration

of the unit time interval or the frequency may have

had an error— causing a systematic accumulation

of time error, or the clock's initial reading (date) may

have been set erroneously. This first category may

be called nonrandom. Second, the clock will have

random deviations caused by various kinds of

random noise processes inherent in all clocks; e.g., the shot noise at the detector in an atomic beam

frequency standard causes a random walk in the

time deviations when this standard is integrated in a clock. Often, and meaningfully so, a random

deviation in time or frequency is called a time

fluctuation or a frequency fluctuation, respectively.

We will now define some terms to better describe

nonrandom and random deviations in a time and/or

frequency standard. In this regard we have drawn on

the work of others [6] as well as collaborated with

co-workers [7]; in addition a strong attempt was made to make the definitions consistent with

current methods of characterizing frequency and

time stability.

We consider accuracy as the degree of conformity

of a measured and/or calculated value to some specified figure or definition. For example, the time

accuracy is the degree of conformity of a clock's

date with some defined date; and the time interval

accuracy— which corresponds to the clock rate or frequency accuracy— is the conformity with the

definition for the second as given in Section 8.2.1. Typically, the prime cause of inaccuracy results from nonrandom deviations, but naturally it involves

random fluctuations as well.

153
To determine the accuracy of a device or standard, it is necessary to evaluate every parameter

which may cause a deviation from the definition.

It is necessary to consider both (a) an estimate of

the uncertainty in determining the magnitude of the

deviation (intrinsic reproducibility of that parameter), and (b) the precision (see definition below of

any measurement involved in the evaluation). If the parameters are independent in their effect in causing deviations from the definitions, then the

uncertainties and precisions may be added as the

square root of the sum of the squares to give an

accuracy specification. It clearly should be stated

also whether the accuracy has a one-, two-, or three-sigma (cr= standard deviation) confidence

limit; naturally, the uncertainties and precisions

should be consistent with the estimate of the ac- curacy specification.

By stability we mean the frequency domain

and/or time domain behavior of a process. The

proposed frequency domain measure of frequency

stability is the spectral density of the fractional

frequency fluctuations, Sy (f). The proposed measure of stability in the time domain is the Allan

variance (or its square root) [1, 8]. One commonly

measures the instabilities caused by the random

fluctuations in a device; obviously, though, the

nonrandom deviations can contribute instabilities. Section 8.6 develops and defines stability measures

for frequency and time.

Precision is the performance capability of a measurement process with contributions from both

the measurement equipment and the devices or standards being measured. Precision is often the

best consistently attainable indicator for the meas- urement process. Consider, too, the precision of a frequency standard measurement is limited by the

instability of either the standard or the measurement

equipment, whichever is worse. On the other hand, a time interval measuring instrument may have a precision of 0.1 ns inherent within the processing

electronic counting and measuring devices; in contrast, it may have an accuracy of 1 ns, where

the accuracy now requires also a knowledge of the

actual delays involved in the instrument. The pre- cision of a measurement for a standard with random

uncorrelated fluctuations (usually idealized but an

unrealistic assumption) in output is simply the

standard deviation of the mean of these fluctuations;

typically, a data set taken as a time series has some

correlation. If such is the case, then a measure of

the precision of a measurement could be the time

domain stability (cry (T) (defined in sec. 8.6.2)) at a sampling or averaging time, t, such that the sta- bility no longer improves with increasing t. In such

a specification the r value or values need to be stated

along with the number of samples, the measure- ment system bandwidth, and the dead time between

data samples. The accuracy can never be better

than the precision.

Reproducibility means the degree of agreement

across a set of independent (in space and/or time)

devices of the same design after exclusive evaluation of appropriate parameters in each device.

An independent set of devices may consist of either an ensemble of devices or standards constructed

according to the same procedure, or a single device

having all parameters independently adjusted

through reevaluation. For the single device, the

degree of agreement is often called intrinsic reproducibility. Reproducibility is a relative measure in contrast to accuracy which is an absolute measure. The word accuracy is sometimes erro- neously used in place of reproducibility, and it is clear that a device's accuracy can never be better

than its reproducibility. One acceptable measure

of reproducibility would be the following: given a mean value for each of a set of measurements

across an ensemble or on a device as stated above,

the reproducibility is the standard deviation of this

set of measurements about the mean.

8.3. CHARACTERIZATION OF

FREQUENCY STABILITY

The measurement of frequency and fluctuations

in frequency has received such great attention for so many years that it is surprising that the concept

of frequency stability does not have a universally

accepted definition. At least part of the reason has

been that some uses are most readily described in frequency domain and other uses in the time

domain, as well as in combinations of the two. This situation is further complicated by the fact that only recently have noise models been presented

which both adequately describe performance and

allow a translation between the time and frequency

domains. Indeed, only recently has it been recog- nized that there can be a wide discrepancy between

commonly-used time domain measures themselves.

Following the NASA-IEEE Symposium on ShortTerm Stability in 1964 [9] and the Special Issue on Frequency Stability of the Proc. IEEE of February

1966 [10], it now seems reasonable to propose a

definition of frequency stability. The paper by

Barnes et al. [1] was presented as technical background for an eventual IEEE standard definition. This section attempts to present (as concisely as

practical) adequate, self-consistent definitions of

frequency stability. Since more than one definition

of frequency stability is presented, an important

part of this section (perhaps the most important

part) deals with translations among the suggested

definitions of frequency stability. The applicability

of these definitions to the more common noise

models is demonstrated. Consistent with an

attempt to be concise, the cited references have

been selected for greatest value to the reader

rather than for their exhaustive nature. Annex 8.G

is a more comprehensive reference and biblio- graphic listing covering the subject of frequency

stability.

154
Almost any signal generator is influenced to some

extent by its environment. Thus, observed fre- quency instabilities may be traced, for example, to changes in ambient temperature, supply voltages,

magnetic field, barometric pressure, humidity,

physical vibration, or even output loading to mention the more obvious. While these environmental

influences may be extremely inportant for many

applications, the definition of frequency stability

presented here is independent of these casual

factors. In effect, we cannot hope to present an

exhaustive list of environmental factors and a

prescription for handling each, even though these

environmental factors may be by far the most important in some cases. Given a particular signal

generator in a particular environment, one can

obtain its frequency stability with the measures

presented herein, but one should not then expect

the frequency stability always to be the same in a new environment.

It is natural to expect any definition of stability to involve various statistical considerations such as

stationarity, ergodicity, average, variance, spectral

density, etc. There often exist fundamental difficul- ties in rigorous attempts to bring these concepts

into the laboratory. It is worth considering, specifically, the concept of stationarity since it is at the

root of many statistical discussions.

A random process is mathematically defined as stationary if every translation of the time coordinate

maps the ensemble onto itself. As a necessary

condition, if one looks at the ensemble at one

instant of time, t, the distribution in values within

the ensemble is exactly the same as at any other

instant of time, t' . This is not to imply that the

elements of the ensemble are constant in time, but, as one element changes value with time, other

elements of the ensemble assume the previous

values. Looking at it in another way, by observing

the ensemble at some instant of time, one can deduce no information as to when the particular

instant was chosen. This same sort of invariance of

the joint distribution holds for any set of time h, tz,

. . ., t„ and its translation ti + T, t2 + r, . . ., tn +T.

It is apparent that any ensemble that has both a

finite past and future cannot be stationary, and this neatly excludes the real world and anything of

practical interest. The concept of stationarity does

violence to concepts of causality since we implicitly

feel that current performance (i.e., the applicability of stationary statistics) cannot be logically de- pendent upon future events (i.e., if the process is terminated sometime in the distant future). Also,

the verification of stationarity would involve hypothetical measurements which are not experimentally

feasible, and therefore the concept of stationarity

is not directly relevant to experimentation.

Actually the utility of statistics is in the formation of idealized models which reasonably describe

significant observables of real systems. One may,

for example, consider a hypothetical ensemble of

noises with certain properties (such as stationarity) as a model for a particular real device. If a model

is to be acceptable, it should have at least two

properties: First the model should be tractable; that is, one should be able to easily arrive at esti- mates for the elements of the model; and, second,

the model should be consistent with observables

derived from the real device which it is simulating.

Notice that one does not need to know that the

device was selected from a stationary ensemble, but

only that the observables derived from the device

are consistent with, say, elements of a hypothetically

stationary ensemble. Notice also that the actual

model used may depend upon how clever the experimenter-theorist is in generating models. It is worth

noting, however, that while some texts on statistics give "tests for stationarity," these "tests" are almost

always inadequate. Typically, these "tests" deter- mine only if there is a substantial fraction of the

noise power in Fourier frequencies whose periods

are of the same order as the data length or longer.

While this may be very important, it is not logically

essential to the concept of stationarity. If a nonstationary model actually becomes common, it will almost surely result from usefulness or con- venience, and not because the process is "actually

non-stationary." Indeed, the phrase "actually

non-stationary" appears to have no meaning in an

operational sense. In short, stationarity (or nonstationarity) is a property of models and not a property of data [11]. Fortunately, many statistical models exist which

adequately describe most present-day signal

generators; many of these models are considered

below. It is obvious that one cannot guarantee that

all signal generators are adequately described by

these models, but it is felt that they are adequate

for the description of most signal generators

presently encountered.

8.4. REQUIREMENTS FOR A

MEASURE OF FREQUENCY

STABILITY

To be useful, a measure of frequency stability

must allow one to predict performance of signal

generators used in a wide variety of situations as well as allow one to make meaningful relative comparisons among signal generators. One must be

able to predict performance in devices which may

most easily be described in the time domain, the

frequency domain, or in a combination of the two. This prediction of performance may involve actual

distribution functions, and thus second moment

measures (such as power spectra and variances) are

not totally adequate.

Two common types of equipment used to evaluate

the performance of a frequency source are (analog)

spectrum analyzers (frequency domain) and digital,

electronic counters (time domain). On occasion the

digital counter data are converted to power spectra

155
by computers. One must realize that any piece of

equipment simultaneously has certain aspects

most easily described in the time domain and other

aspects most easily described in the frequency

domain. For example, an electronic counter has

a high frequency limitation, and experimental

spectra are determined with finite time averages. Research has established that ordinary oscil- lators demonstrate noise which appears to be a

superposition of causally generated signals and

random, nondeterministic noises. The random

noises include thermal noise, shot noise, noises of undetermined origin (such as flicker noise), and

integrals of these noises. One might well expect,

that for the more general cases, it would be necessary to use a nonstationary model (not stationary even in the wide sense, i.e., the covariance sense).

Non-stationarity would, however, introduce signifi- cant difficulties in the passage between the fre- quency and time domains. It is interesting to note

that, so far, experimenters have seldom found a non (covariance) stationary model useful in de- scribing actual oscillators. In what follows, an

attempt has been made to separate general state- ments (which hold for any noise or perturbation)

from those which apply only to specific models. It

is important that these distinctions be kept in mind.

8.5. CONCEPTS OF FREQUENCY

STABILITY

To discuss the concept of frequency stability

immediately implies that frequency can change

with time and thus one is not considering Fourier

frequencies (at least at this point). The conventional definition of instantaneous (angular) frequency

is the time rate of change of phase; that is,

of the (pure real) function, g(t), on a per hertz

basis; that is, the total "power" or mean square

value of g(t) is given by

S9 (f)df. (8.3)

Since the spectral density is such an important

concept to what follows, it is worthwhile to present some important references on spectrum estimation.

Many workers have estimated spectra from data

records, but worthy of special note are [12-15].

8.6. THE DEFINITION OF MEASURES OF FREQUENCY STABILITY

(Second Moment Type)

In a general sense, consider a signal generator

whose instantaneous output voltage, V(t), may be

written as 9

V(t)=[V0 + e(t)] sin [2tt^ + <p(t)], (8.4) where Vo and vo are the nominal amplitude and

frequency respectively of the output, and it is assumed that

and

kt)

2ttv0

< 1, (8.5)

(8.6)

for substantially all time, t. Making use of eqs

(8.1) and (8.4) one sees that

277^) = ^"^ = <*>(*), (8.1)

where <$>(t) is the instantaneous phase of the oscillator. By our convention, time dependent frequencies of oscillators are denoted by v(t) (cycle

frequency, hertz), and Fourier frequencies are denoted by a (angular frequency, radians per sec- ond) or / (cycle frequency, hertz) where

0} = 2tt/. (8.2)

In order for eq (8.1) to have meaning, the phase

4>(0 must be a well-defined function. This restric- tion immediately eliminates some "nonsinusoidal"

signals such as a pure, random, uncorrelated

("white") noise. For most real signal generators,

the concept of phase is reasonably amenable to an

operational definition and this restriction is not

serious.

Of great importance to this presentation is the

concept of spectral density, Sg (f). The notation,

Sg(f), represents the one-sided spectral density

<3>(t) = 2iTvot + <p{t), (8.7) and

v(t) = vo +^r <p(t). (8.8)

Equations (8.5) and (8.6) are essential in order that

<p{t) may be defined conveniently and unambiguously (see sec. 8.9). Since eq (8.6) must be valid even to speak of an

instantaneous frequency, there is no real need to distinguish stability measures from instability measures. That is, any fractional frequency stability measure will be far from unity, and the chance of

confusion is slight. It is true that in a very strict sense people usually measure instability and speak

of stability. Because the chances of confusion are

so slight, we choose to continue the custom of

measuring "instability" and speaking of stability

(a number always much less than unity).

Of significant interest to many people is the radio

frequency (RF) spectral density, Sv(f ). This is of direct concern in spectroscopy and radar. However,

this is not a good primary measure of frequency

156
stability for two reasons: First, fluctuations in the

amplitude, e(t), contribute directly to Sv(f); and

second, for many cases when e(t) is insignificant,

the RF spectrum, Sv(f), is not uniquely related to the frequency fluctuations [16].

8.6.1. First Definition of the Measure of

Frequency Stability — Frequency Domain

By definition, let

y(t) _ <p(t)

(8.9)

where <p{t) and v0 are as in eq (8.4). Thus y{t) is the instantaneous fractional frequency deviation

from the nominal frequency vo. A proposed defini- tion of frequency stability is the spectral density

Sy(f) of the instantaneous fractional frequency

fluctuations y(t). The function Sy (f) has the di- mensions of Hz-1

. One can show [17] that if St>(f) is the spectral

density of the phase fluctuations, then

Sy(f)

1 2ttv0

PSAf). (8.10)

Thus, a knowledge of the spectral density of the

phase fluctuations, Se(f), characterizes the spectral

density of the frequency fluctuations, Sy {f) — the

first definition of frequency stability. Of course, Sy (f) cannot be perfectly measured — this is the case for any physical quantity; useful estimates of

Sy (f) are, however, easily obtainable.

8.6.2. Second Definition of the Measure of

Frequency Stability — Time Domain

The second definition is based on the sample

variance of the fractional frequency fluctuations.

This measure of frequency stability uses y>, defined

as follows:

1 ffc+* T L

y(t)dt =

<p(tk + t) — <p(tk ) 2ttvqt

(8.11)

where tk+\ = tk + T; k~ 0, 1, 2, . . .; T is the repeti- tion interval for measurements of duration t; and

to is arbitrary. Conventional frequency counters measure the number of cycles in a period t; that is, they measure v0t(1 + yk ). When t is one second

they count the number vo(l + yk ). The second measure of frequency stability, then, is defined in analogy to the sample variance by the relation

K(yv, r, r)> = 37 2 (y

1 "~h £ n=l \

/T k=l

(8.12)

where (g) denotes the infinite time average of g; that is, the average of the set of all values which g

has over running time, t. This measure of frequency

stability is called the Allan variance of y. It is dimensionless since y is dimensionless.

In many situations it would be wrong to assume

that eq (8.12) converges to a meaningful limit as

/V —> 00. First, one cannot practically let /V approach

infinity, and, second, it is known that some actual

noise processes contain substantial fractions of the

total noise power in the Fourier frequency range

below one cycle per year. It is important to specify

a particular N and T to improve comparability of

data. For the preferred definition we recommend

choosing N=2 and T= r(i.e., no dead time between

measurements). Writing (<r

y (N =2, T = t,t)) as

0-^(7), for this particular Allan variance [8], the

proposed measure of frequency stability in the time

domain may be written as

(yk+i - fk)

2 2

(8.13)

Of course, the experimental estimate of CTy(r)

must be obtained from finite samples of data, and

one can never obtain perfect confidence in the

estimate — the true time average is not realizable

in a real situation. One estimates cry {r) from a

finite number (say, M — 1, M being the number of

samples of %) of values of (Ty (2, t, t) and averages

to obtain an estimate of (Ty (t) as follows:

1

A/-1 2y(T) ~ 2WT) S (ft"-?*)5 (8.13a)

It can be shown that the time average of o~y(2, t, t) is convergent (i.e., as A/—* 00 ) even for noise

processes that do not have convergent (oy{N, r, t)) as A^-^ 00 (see [1] app. I). Therefore, cry(r) has

greater utility as an idealization than does (oy(°°,

t, t)) even though both involve assumptions of

infinite averages. In effect, increasing causes

(rl(N, T, t) to be more sensitive to the low fre- quency components of Sy {f). In practice, one must

distinguish between an experimental estimate of a quantity (say, of ctI(t)) and its idealized value. It is reasonable to believe that extensions to the

concept of statistical ("quality") control [18] may

prove useful here. One should, of course, specify

the actual number, M, of independent data samples

used for an estimate of o-y(r). Confidence on the

estimate has been calculated as a function of M in

ref. [19].

157
In summary, therefore, Sy (f) is the proposed measure of (instantaneous) frequency stability in the (Fourier) frequency domain and cTy(r) is the

proposed measure of frequency stability in the time

domain.

8.6.3. Distributions

This chapter does not attempt to specify a pre- ferred probability distribution measure for fre- quency fluctuations. Whereas (yk+i~fk) could be

specified as the argument of a distribution function, we prefer to wait until further experience has

demonstrated the need for some such specification.

The amplitude probability distribution of the

random noise portions of frequency fluctuations is found usually to be Gaussian. See [19] for two

examples, one for white noise of phase and one for

flicker noise of frequency.

8.6.4. Treatment of Systematic Variations

a. General. The definition of frequency stability

(jy (r) in the time domain is useful for many situations. However, some oscillators exhibit an aging

or almost linear drift of frequency with time. For some applications, this trend may be calculated and

removed [8] before estimating crj (t). In general, a systematic trend is perfectly deter- ministic (i.e., predictable in detail) while the noise

is nondeterministic (i.e., predictable only in a

statistical sense). Consider a function, g(t), which

may be written in the form

g(t) = c(t) + n(t), (8.14)

where c(t) is some deterministic function of time

and n(t), the noise, is a nondeterministic function

of time. We will define c{t) to be the systematic

trend to the function g(t). A problem of significance

here is the determination of when and in what

sense c(t) is measurable.

b. Specific Case — Linear Drift. As an example,

if we consider a typical quartz crystal oscillator whose fractional frequency deviation is y(t), we may let

g(t) = jt y(t). (8.15)

Let c{t) be the drift rate of the oscillator (e.g., 10" 10 per day) and n(t) is related to the frequency

"noise" of the oscillator by a time derivative. One

sees that the time average of g(t) becomes

if"

1 J t0 g{t)dt = c l + n(t)dt, (8.16)

where c(t) =cj is assumed to be the constant drift rate of the oscillator. In order for C\ to be an ob- servable, it is natural to expect the average of the

noise term to vanish, that is, converge to zero.

It is instructive to assume [8, 20] that in addition

to a linear drift the oscillator is perturbed by a

flicker noise frequency modulation (FM), i.e.,

h-if-i, o </•*=/,,

/>/*,

s.,(/) =

{ 0

~~

where is a constant (see sec. 8.7.1(b)) and thus,

W)-{0i f> , (8.18)

for the oscillator we are considering. With these

assumptions, it is seen that

1 rto+T Urn- n(t)dt = K(Q)=0, (8.19)

and that

Lir

T-im jvariance

j; n(t)dt^=0, (8.20)

where k(/) is the Fourier transform of n(t). Since

S„(0) = 0, k(0) must also vanish both in probability

and in mean square. Thus, not only does n(t)

average to zero, but arbitrarily good confidence in the result may be obtained by longer averages. Having shown that one can reliably estimate the

drift rate, c%, of this (common) oscillator, it is in- structive to attempt to fit a straight line to the

frequency aging. That is, let

and, thus,

g(t) = y(t), (8.21)

g(t) =c0 +c1 (t-t0 ) + n'(t), (8.22)

where Co is the frequency intercept at t — to and C\

is the drift rate previously determined. A problem

arises here because

and

Sn>(f)=Sy(f), (8.23)

njvariance j »'(«)<&.Lim J =°°, (8.24)

Tfor the noise model we have assumed. This follows

from the fact that the (infinite N) variance of a

flicker noise process is infinite [17, 8, 20]. Thus, Co cannot be measured with any realistic precision — at least, in an absolute sense. We may interpret these results as follows: After

experimenting with the oscillator for a period of

time one can fit an empirical equation to y{t) of the form

y(t) = c0 + tc1 + n'(t). (8.25)

158
where n ' (t) is nondeterministic. At some later time

it is possible to reevaluate the coefficients c» and

Ci. According to what has been said, the drift rate

C\ should be reproducible to within the confidence

estimates of the experiment regardless of when it is reevaluated. For c0 , however, this is not true. In

fact, the more one attempts to evaluate Co, the larger are the fluctuations in the result. Depending on the spectral density of the noise

term, it may be possible to predict future measure- ments of Co and to place realistic confidence limits on the prediction [21]. For the case considered

here, however, these confidence limits increase

when the prediction interval is increased. Thus, in a

certain sense, Co is "measurable" but it is not in

statistical control (to use the language of the quality

control engineer [18]).

8.7. TRANSLATIONS AMONG FREQUENCY STABILITY MEASURES

8.7.1. Frequency Domain to Time Domain

a. General. It is of value to define r—T/r; that is, r is the ratio of the time interval between successive measurements to the duration of the averaging

period. Cutler has shown that ([1] app. I)

(<rl(N, T,r)) = -^yy |°° dfSy {f)

[sin2 (-"•/>)] (tt/t) 2 sin2 (7rr/7VT)

N2 sin2 (irr/T)

(8.26)

Equation (8.26) in principle allows one to calculate the time domain stability (cr'UN, T, t)) from

the frequency domain stability Sy (f).

b. Specific model. A model which has been found

useful [17-22] consists of a set of five independent

noise processes, zn {t) , n — — 2, — 1, 0, 1,2, such that

y{t) =z-2 (t) +2-1 (0 +z0 (t) + Zl (t)+z2 (t), (8.27)

and the spectral density of zn is given by

s*n (/) =

{£ f>fh , n=-2,-l, 0, 1, 2,

(8.28)

where the h n are constants. Thus,S y (/) becomes

Syif) = h-rf-2 + h-tf-* + hQ + hyf+ h?f\ (8.29)

for 0 =s /=S fh and Syif) is assumed to be negligible

beyond this range. In effect, each zn contributes to both Syif) and (o-'y iN, T, t)) independently of the

other zn . The contributions of the z„ to (oy iN, T,

t) ) are tabulated in Appendix II of reference [1] (see

also table 8.1 in sec. 8.12).

Any electronic device has a finite bandwidth and

this certainly applies to frequency measuring equipment also. For fractional frequency fluctuations,

yit), whose spectral density varies as

Sf/ 1/")-/0

, a^-1, (8.30)

for the higher Fourier components, one sees (from

ref. [1], app. I) that ((T

y iN, T, t)) may depend on

the exact shape of the frequency cutoff. This is true because a substantial fraction of the noise

"power" may be in these higher Fourier components. As a simplifying assumption, this chapter assumes a sharp cutoff in noise "power" at the fre- quency fh for the noise models. It is apparent from

the tables in reference [1] (app. II) that the time

domain measure of frequency stability may de- pend on fh in a very important way, and, in some

practical cases, the actual shape of the frequency

cutoff may be very important [17]. On the other

hand, there are many practical measurements

where the value of //( has little or no effect. Good

practice, however, dictates that the system noise

bandwidth,//,, should be specified with any results. In actual practice, the model of eqs (8.27), (8.28), and (8.29) seems to fit almost all real frequency

sources. Typically, only two or three of the

/i-coefficients are actually significant for a real de- vice and the others can be neglected. Because of

its applicability, this model is used in much of what

follows. Since the z» are assumed to be independent

noises, it is normally sufficient to compute the

effects for a general z„ and recognize that the superposition can be accomplished by simple additions

for their contributions to Syif) or (ay iN, T, t)).

8.7.2. Time Domain to Frequency Domain

a. General. For general (cr^N, T, t)) no simple

prescription is available for translation into the fre- quency domain. For this reason, one might perfer

S,/if) as a general measure of frequency stability.

This is especially true for theoretical work.

b. Specific model. Equations (8.27), (8.28), and

(8.29) form a realistic model which fits the random,

nondeterministic noises found on most signal generators. Obviously, if this is a good model, then the

tables in reference [1] (app. II) or table 8.1 may be

used in reverse to translate into the frequency

domain.

Allan [8] and Vessot [22] showed that if

10, />/,,

(8.31)

where a is a constant, then

<a2 (/V, T, t)> ~ |tK 2TTTfh » 1, (8.32)

159
a's) can also be treated by this technique, e.g., eq (8.29). One may define two "bias functions,"

Bi and Bz by the relations [3]:

and

RiN wig T> T))

B2 (r, ft) <<r*(2, T, t)>

<<r*(2, t,t)>

Figure 8. 1 . Mapping of exponents fx. — a (see eq 8.37).

(8.33)

(8.34)

T

for /V and r = - held constant, and the constant /J- T

is related to a by the mapping shown 3 in figure 8.1.

If eqs (8.31) and (8.32) hold over a reasonable range

for a signal generator, then eq (8.31) can be substi- tuted into eq (8.26) and evaluated to determine the constant h a from measurements of ((T~(N, 7\ t)).

It should be noted that the model of eqs (8.31) and

(8.32) may be easily extended to a superposition of

similar noises as in eq (8.29).

8.7.3. Translations Among the Time Domain

Measures

a. General. Since (<r*(N, T, t)) is a function of

N, T, and t (for some types of noise fu is also important), it is very desirable to be able to translate among different sets of N, T, and t (ft, held constant); this is, however, not possible in general.

b. Specific model. It is useful to restrict consideration to a case described by eqs (8.31) and (8.32). Superpositions of independent noises with different power-law types of spectral densities (i.e., different

3 It should be noted that in Allan [8] the exponent, a, corresponds to the spectrum

of phase fluctuations while variances are taken over average frequency fluctuations. In the present paper, a is identical to the exponent a + 2 in reference [8].

Figure 8.2. The bias function, Bi(N, r=l,/i).

Figure 8.3. The bias function, B2 (r, /a).

160
where r — T\t and /x is related to a by the mapping

of figure 8.1. In words, B\ is the ratio of the average

variance for /V samples to the average variance for 2 samples (everything else held constant); while B>

is the ratio of the average variance with dead time

between measurements 1) to that of no dead

time {r—1, N=2, and r held constant). These

functions are tabulated in reference [3], and re- produced in Annex 8.J. Figures 8.2 and 8.3 show a computer plot of Bi(N, r= 1, /jl) and B2 (r, /x). Suppose one has an experimental estimate of (cr*(Ni, Ti, Ti)) and its spectral type is known —

that is, eqs (8.31) and (8.32) form a good model and

fji is known. Suppose also that one wishes to know

the variance at some other set of measurement

parameters, N2 , T2 , t2. An unbiased estimate of

(cr*(N2 , T2 , t2 )) may be calculated by the equation:

K(/v2 ,r2 ,T2 )> = ^-

T2 B i{N2 ,r2 ,ix)B 2 (r2 ,fJL)] B 1 (N1 ,n, (i)B 2 (r i ,fJL)\

(trttNuTuTi)). (8.35)

where r x = 7\/ti and r2 = T2 /t2 .

c. General-Bias Functions. While it is true that the concept of the bias functions, B\ and B2 , could

be extended to other processes besides those with

the power-law types of spectral densities, this generalization has not been done. Indeed, spectra of

the form given in eq (8.31) (or superpositions of

such spectra as in eq (8.29)) seem to be the most

common types of non-deterministic noises encount- ered in signal generators and associated equipment.

For other types of fluctuations (such as causally

generated perturbations), translations must be

handled on an individual basis.

8.8. EXAMPLES OF APPLICATIONS

OF PREVIOUSLY DEVELOPED

MEASURES

8.8.1. Applications of Stability Measures

Obviously, if one of the stability measures is exactly the important parameter in the use of a

signal generator, the stability measure's application

is trivial. Some nontrivial applications arise when

one is interested in a different parameter, such as

in the use of an oscillator in Doppler radar measure- ments or in clocks.

a. Doppler Radar

(1) General. From its transmitted signal, a Doppler radar receives from a moving target a fre- quency-shifted return signal in the presence of

other large signals. These large signals can include

clutter (ground return) and transmitter leakage into the receiver (spillover). Instabilities of radar signals

result in noise energy on the clutter return, on spill- over, and on local oscillators in the equipment. The

limitations of subclutter visibility (SCV) rejections

due to the radar signals themselves are related to the RF spectral density, S\(f). The quantity

typically referred to is the carrier-to-noise ratio and

can be mathematically approximated by the quantity

Sv(f)

Svif'W

(This quantity is actually the noise-to-carrier ratio,

but using the reciprocal is more convenient in what

follows, and there is little chance for confusion.)

The effects of coherence of target return and other

radar parameters are amply considered in the litera- ture [23-26].

(2) Special Case. Because FM effects generally

predominate over AM effects, this carrier-to-noise

ratio is approximately given by [16]

Sv(f)

s: Svif'W

|mi/-*»d, (8 36)

for many signal sources provided |/ — vo | is sufficiently greater than zero. Thus, if /— v<> is a frequency separation from the carrier, the carrier- to-noise ratio at that point is approximately

! Ml/ fo Sy{\f-V0 \)

(8.37)

b. Clock Errors

(1) General. A clock is a device which counts the

cycles of a periodic phenomenon. Thus, the reading

error x(t) of a clock run from the signal given by

eq (8.4) is

x{t) =

<p(t)

(8.38)

and the dimensions of x(t) are seconds. If this clock

is a secondary standard, one could have a past

history of x(t), the time error relative to the standard clock. It often occurs that one is interested in predicting the clock error x(t) for some future

date, say to + T, where to is the present date. Obviously, this is a problem in pure prediction and can be handled by conventional methods [13].

161
(2) Special Case. Although one could handle the

prediction of clock errors by the rigorous methods

of prediction theory, it is more common to use

simpler prediction methods [20, 21]. In particular, one often predicts a clock error for the future by

adding a correction to the present error; this cor- rection is derived from the current rate of gain (or loss) of time. That is, the predicted error x{to + r)

is related to the past history of x(t) by the equation

X(h + T) =x(t0 ) +T x{t0 ) —x(t0 — T)

(8.39)

As a specific example, let T— r, then the meansquare error of prediction becomes

([x(to + T)-x(to + r)Y) = ([x(to+T)

-2x(to)+x(to-T)] 2 ), (8.40)

which, with the aid of eq (8.13), can be written in the form

([x(to + T)-x(to + T)¥)=2T2 (Tl(T). (8.41)

8.9. MEASUREMENT TECHNIQUES

FOR FREQUENCY STABILITY

8.9.1. Heterodyne Techniques (General)

It is possible for oscillators to be very stable and

values of cry(r) can be as small as 10~14 in some

state of the art equipment. Thus, one often needs

measuring techniques capable of resolving very

small fluctuations in y(t). One of the most common

techniques is a heterodyne or beat frequency tech- nique. In this method, the signal from the oscillator

to be tested is mixed with a reference signal of

almost the same frequency as the test oscillator; one is left then with a lower average frequency for analysis without reducing the frequency (or phase)

fluctuations themselves. Following Vessot et al. [27], consider an ideal reference oscillator whose output

signal is Vr (t) — Vor Sin 2TTV0t, (8.42)

and a second oscillator whose output voltage V{t)

is given by eq (8.4): V{t) = [V0 + e{t)] sin [27TVot +

V? (f ) ] . Let these two signals be mixed in a product

detector; that is, the output of the product detector

v(t) is equal to the product yV(t) X Vr (t), where

y is a constant (see fig. 8.4). Let v(t) , in turn, be processed by a sharp, lowpass filter with cutoff frequency f'h such that

0 </»</'„ < ^o. (8.43)

LOOP FILTER

REFERENCE OSCILLATOR

(VCO)

V (t)

PRODUCT DETECTOR

LOW PASS FILTER

OSC I LLATOR V(t)

Figure 8.4. Example of heterodyne scheme.

One may write

yV(t) Vr (t)=yV0r (Vo + e)

[sin2*7rjv] [sin(277iV + <£)]

(VorVo) (, , e

[cos <p — COS (4lTVot + <p) ]

.

(8.44)

Assume that cos[<p(t)] has essentially no power in Fourier frequencies / in the region / 2s f'h

. The

effect of the low-pass filter then is to remove the

second term on the extreme right of eq (8.44); that is,

v(t ) = y—(l+y

) cos <p(t). (8.45) 0/

This separation of terms by the filter is correct

only if < < 1 for all t (see eq (8.6)). 2"7ruo The following two cases are of interest:

(a) Case I The relative phase of the oscillators is adjusted

so that \(p(t) | < < 1 (in-phase condition) during

the period of measurement. Under these conditions

v'{t) ~y- V0r V0 +^ V0re(t), (8.46)

since cos <p{t) ~ 1. That is to say one detects the

amplitude noise e(?) of the signal. . (b) Case II The relative phase of the oscillators is adjusted

to be in approximate quadrature; that is

<p'(t) = <f(t) +-> (8.47)

where \<p'(t) \ < < 1. Under these conditions,

cos<f(t) = sin<£>'(0 = <p'(t), (8.48)

162
and

v'(t)=^V0r V0<p'(t) +

J- Vnr<p'(t)e(t). (8.49)

If it is true that 6(0 v0 < < 1 for all t (see eq (8.5)), then eq (8.49) becomes

v'(t) ~~VorVo<p'(t); (8.50)

that is, v'(t) is proportional to the phase fluctuations. Thus, in order to observe <p' (t) by this method,

eqs (8.5) and (8.6) must be valid. For different average phase values, mixtures of amplitude and

phase noise are observed.

To maintain the two signals in quadrature for long observational periods, one can use a voltage

controlled oscillator (VCO) for a reference and feed

back the phase error voltage (as defined in eq

(8.50)) to control the frequency of the VCO [28]. In

this condition of the phase-locked oscillator, the

voltage v' (0 is the analog of the phase fluctuations

for Fourier frequencies above the loop cutoff frequency of the locked loop. For Fourier fre- quencies below the loop cutoff frequency, v (t)

is the analog of frequency fluctuations. In practice, one should measure the complete servo loop response.

8.9.2. Period Measurement

V0 < < 1

Assume one has an oscillator whose voltage output may be represented by eq (8.4). If

for all t and the total phase

®(t)=2Trvot-{-<p(t),

is a monotonic function of time (that is, <p(t)

(8.7)

1). then the time t between successive positive-going zero crossings of V(t) is related to the average fre- quency during the interval, t; specifically,

1 = v0 (l + yn ) (8.51)

If one lets t be the time between a positive going

zero crossing of V(t) and the Mth successive positive going zero crossing, then

M = vq{\ +y„) (8.52)

If the variations At of the period are small compared to the average period To, Cutler and Searle

[17J have shown that one may make a reasonable

approximation to (<r*(/V, T, t0 )) using period

measurements.

8.9.3. Period Measurement with

Heterodyning

Suppose that <p(t) is a monotonic function of time. The output of the filter of Section 8.9.1, eq

(8.45) becomes

v (t) ~y—— cos <p(t), (8.53)

if e(0< < 1. Then one may measure the period t

of two successive positive zero crossings of v'{t).

Thus

~ = vo | fn |

,

T

and for the Mth positive crossover M— = vo\yn \-

(8.54)

(8.55)

The magnitude bars appear because cos <p(t) is an even function of <p(t). It is impossible to deter- mine by this method alone whether (p is increasing

or decreasing with time. Since y„ may be very small

(~ 10" 11 or 10~12 for very good oscillators), r may

be quite long and thus measurable with a good

relative precision. If the phase, <p(t), is not monotonic, the true yn may be near zero but one could

still have many zeros of cos tp(t) and thus eqs (8.54)

and (8.55) would not be valid.

8.9.4. Frequency Counters

Assume the phase (either or <p) is a monotonic

function of time. If one counts the number M of

positive going zero crossings in a period of time t, M

then the average frequency of the signal is —. If we

t assume that the signal is V(t) (as defined in eq

(8.4)), then

M— = 1*0(1 + 301). (8.56)

If we assume that the signal is v (0 (as defined in eq (8.50)), then

M

T

^0 1 y„ I (8.57)

Again, one measures only positive frequencies.

163
8.9.5. Frequency Discriminators

A frequency discriminator is a device which

converts frequency fluctuations into analog voltage

fluctuations by means of a dispersive element. For

example, by slightly detuning a resonant circuit from the signal V(t) the frequency fluctuations — <p{t) are converted to amplitude fluctuations of

the output signal. Provided the input amplitude

e(t)

fluctuations r/ are insignificant, the output ampliv n tude fluctuations can be a good measure of the fre- quency fluctuations. Obviously, more sophisticated

frequency discriminators exist (e.g., the cesium

beam). From the analog voltage one may use analog

spectrum analyzers to determine Sy (f), the fre- quency stability. By converting to digital data, other

analyses are possible on a computer.

8.9.6. Common Hazards

a. Errors caused by signal processing equipment.

The intent of most frequency stability measurements

is to evaluate the source and not the* measuring

equipment. Thus, one must know the performance

of the measuring system. Of obvious importance

are such aspects of the measuring equipment as noise level, dynamic range, resolution (dead time),

and frequency range.

It has been pointed out that the noise bandwidth

fh is very essential for the mathematical conver- gence of certain expressions. Insofar as one wants

to measure the signal source, one must know that the measuring system is not limiting the frequency

response. At the very least, one must recognize

that the frequency limit of the measuring system

may be a very important, implicit parameter for either cr'y(t) or Sy (f). Indeed, one must account

for any deviations of the measuring system from

ideality such as a "non-flat" frequency response of

the spectrum analyzer itself. Almost any electronic circuit which processes a

signal will, to some extent, convert amplitude

fluctuations at the input terminals into phase

fluctuations at the output. Thus, AM noise at the

input will cause a time-varying phase (or FM noise)

at the output. This can impose important constraints on limiters and automatic gain control (AGC)

circuits when good frequency stability is needed.

Similarly, this imposes constraints on equipment

used for frequency stability measurements.

b. Analog spectrum analyzers (Frequency

Domain). Typical analog spectrum analyzers are very similar in design to radio receivers of the super- heterodyne type, and thus certain design features

are quite similar. For example, image rejection

(related to predetection bandwidth) is very

important. Similarly, the actual shape of the

analyzer's frequency window is important since

this affects spectral resolution. As with receivers,

dynamic range can be critical for the analysis of

weak signals in the presence of substantial power

in relatively narrow bandwidths (e.g., 60 Hz).

The slewing rate of the analyzer must be consist- ent with the analyzer's frequency window and the

post-detection bandwidth. If one has a frequency

window of 1 hertz, one cannot reliably estimate the

intensity of a bright fine unless the slewing rate is much slower than 1 hertz/second. Additional postdetection filtering will further reduce the maximum

usable slewing rate.

c. Spectral density estimation from time domain

data. It is beyond the scope of this paper to present a comprehensive list of hazards for spectral density

estimation; one should consult the literature [12-15].

There are a few points, however, which are worthy of special notice:

(1) Data aliasing (similar to predetection bandwidth problems);

(2) spectral resolution; and

(3) confidence of the estimate.

d. Variances of frequency fluctuations, 0^(7-).

It is not uncommon to have discrete frequency

modulation of a source such as that associated with

the power supply frequencies. The existence of

discrete frequencies in S y (f) can cause o~

2u (t) to be

a very rapidly changing function of t. An interesting

situation results when r is an exact multiple of the

period of the modulation frequency (e.g., one makes

t = 1 second, and there exists 60-Hz frequency

modulation on the signal). In this situation, cr

y (t — Is) can be very small relative to values with

slightly different values of t. One also must be con- cerned with the convergence properties of o"*(t)

since not all noise processes will have finite limits

to the estimates of ct'u (t) (see ref. [1], app. I). One

must be as critically aware of any "dead time" in the measurement process as of the system bandwidth.

e. Signal source and loading. In measuring fre- quency stability one should specify the exact location in the circuit from which the signal is obtained

and the nature of the load used. It is obvious that the

transfer characteristics of the device being specified

will depend on the load and that the measured fre- quency stability might be affected. If the load itself

is not constant during the measurements, one

expects large effects on frequency stability.

f. Confidence of the estimate. As with any meas- urement in science, one wants to know the confi- dence to assign to numerical results. Thus, when one measures S y(f) of cr'^r), it is important to know the

accuracies of these estimates.

(1) The Allan variance [8]. It is apparent that a

single sample variance, e.g., cr

y (2, r, t), does not

164
have good confidence, but by averaging many samples, one can improve greatly the accuracy of the esti- mate. A detailed discussion of the confidence of the

estimate for finite data lengths is given in reference

[19]. It has been shown that the infinite average of a

set of samples of <x^(/V, T, t) converges for all power

law spectral densities as given in eq (8.31) where a >—3 [1]. It is worth noting that if we were inter- ested in a2y (N=°°, T, t), then convergence only occurs for a > —1 [1-3]. Since most real signal generators possess low frequency divergent noises in the range —1 5s a > —3, (cr2y (N, T, r) ) is more useful

than the classical variance, &1y {N=^, T, t).

Although the sample variances, cr'2J2, t, t), will not be normally distributed, the variance of the average

of M independent (nonoverlapping) samples of

o~^(2, t, t) (i.e., the variance estimate of this particular Allan variance) will decrease as 1/M provided

the conditions on low frequency divergence are met. For sufficiently large M, the distribution of the

M-sample-averages of crj(2, r, t) will tend toward

normal (central limit theorem). It is, thus, possible to estimate confidence intervals based on the normal

distribution [19]. As always, one may be interested in t- values

approaching the limits of available data. Clearly,

when one is interested in r-values of the order of a

year, one is severly limited in the size of M the number of samples of cr^(2, t, t). Unfortunately, there seems to be no substitute for many samples and one

extends r at the expense of confidence in the results. "Truth in packaging" dictates that the sample size M be stated with the results.

(2) Spectral density. As before, one is referred

to the literature for discussions of spectrum esti- mation [12-15]. It is worth pointing out, however,

that for S y (f) there are basically two different types

of averaging which can be employed: sample aver- aging of independent estimates of S y (f) and fre- quency averaging where the resolution bandwidth is made much greater than the reciprocal data length.

8.10. SUMMARY OF FREQUENCY

STABILITY MEASURES

A good measure of frequency stability is the

spectral density, S y {f), of fractional frequency

fluctuations, y(t). An alternative is the expected

variance of /V sample averages of y{t) each taken

over a duration t. With the beginning of successive

sample periods spaced every T units of time, the

variance is denoted by cr

y (N, T, r). The preferred

time domain stability measure, is the expected

value of many measurements of cry {N, T, r), with

N — 2 and T = t, defined as ct§(t). For all real experiments one has a finite bandwidth. In general,

the time domain measure of frequency stability,

o-|(t), is dependent on the noise bandwidth of the

system. Thus, there are four important parameters

to the time domain measure of frequency stability:

/V, the number of sample averages (N — 2 for preferred measure);

T, the repetition time for successive sample

averages (T = t for preferred measure);

t, the duration of each sample average; and

fh, the system noise bandwidth.

Translations among the various stability measures

for common noise types are possible, but there are

significant reasons for choosing N — 2 and T = t

for the preferred measure of frequency stability in the time domain. This measure, the Allan

variance for N — 2 and T — t, has been referenced

by [19, 22, 29-31] among others. Although Sy (f)

appears to be a function of the single variable /,

actual experimental estimation procedures for the

spectral density involve a great many parameters.

Indeed, its experimental estimation can be as in- volved as the estimation of cr

2 (t) .

8.11. PRACTICAL APPLICATIONS

OF FREQUENCY STABILITY

SPECIFICATION AND MEASUREMENT

Up to this point we have considered principally

the statistical theory of time and frequency data

analysis showing general applications of stability measures. We would now like to show practical

laboratory examples to establish standards of

terminology and measurement techniques for frequency stability. Emphasis is placed on details of

useful working systems (apparatus) that could be

duplicated by others in the field of frequency

stability measurements. Uniformity of data presentation is stressed to facilitate interpretation of

stability specifications and to enable one to communicate and compare experimental results on a common base. This part of the chapter is based

primarily on the theory given in Sections 8.1-8.10

and the paper by Barnes et al. [1]. We review the

terminology for specification of frequency stability

and describe the performance of frequency stability

measurement systems capable of precise measure- ments on state-of-the-art sources in both the High

Frequency (HF) and Microwave (X-band) regions.

8.12. TERMINOLOGY FOR SPECIFICATION OF FREQUENCY

STABILITY

The term frequency stability encompasses the

concepts of random noise, intended and incidental

modulation, and any other fluctuations of the output

frequency of a device. (In a very loose sense frequency stability can be considered as the degree

to which a signal source (e.g., oscillator) produces

165
the same frequency throughout a specified period

of time.) In this chapter we are mainly (but not

totally) concerned with random fluctuations corre- sponding to Fourier frequencies in the 10° to 10 6 hertz range. The measurement of frequency stability can be accomplished in both the frequency domain

(e.g., spectrum analysis) and the time domain (e.g., gated frequency counter). Previously, in Section 8.6, we described two independent definitions, each

related to different but useful measurement

methods.

The first definition offrequency stability (frequency

domain) is the one-sided spectral density of the

fractional frequency fluctuations, S y (f), where

y=8v/vo (see ann. 8.A for glossary which defines

symbols). The fractional frequency fluctuation

spectral density S u (f) is not to be confused with

the radio frequency power spectral density

Svrfp(v), or Ssv (v), which is not a good primary measure of frequency stability because of fluctua- tions in amplitude and for other reasons (see sec. 8.6

and ref. [32]). Phase noise spectral density plots

(i.e., S !><!>( f) versus /) are a common alternative

method of data presentation. The spectral density

of phase fluctuations is related to S y (f) by

Ss*(/) = UimSu (f). (8.58)

The second definition of frequency stability {time

domain) uses the type of sample variance called the

Allan variance [8] of y:

I 1 N I 1 N \

2\

h = 1 k = I (8.59)

Note: Equation (8.59) is identical to eq (8.12) except

that the measurement system bandwidth, fn, has

been explicitly inserted in the parenthesis on the

left. The particular Allan variance with N = 2 and

T — t is found to be especially useful in practice.

Table 8.1. Stability measure conversion chart* (frequency domain-time domain ).

S (0 s one-sided spectral density of y (dimensions are y^/f), 0 £ f £ f^, f^ = B, Zv f^ T » lj S (f a f

General Definition: <a^ (N. T, T, fj,)) = ^ (y n~ 17 ^

2 Z /

l \+\'V Special Case: o* (T) = (

o" (N = 2, T = T, T, f, )> =

y y h

dx _ _ 6f

:rr = y = —

Useful Relationships:

(2TT) 2 = 39.48

In 2 = 0 69 3 2 In 2 = 1 3 86

In 10 = 2 303

Time Domain

(Allan variances. • • •)

Frequency Domain

(Power law spectral densities!

0- (T) y

[N = 2, r = 1]

<CT (N, T = T. T, f, )> y h

[r = 1]

<CT (N, T, T, £, )> y n

S (f) = h A

Z (S (f) =-2 y 2 N + 1

N(2rr)

2 tyrI 0 otherwise

S (f) = h f S (f) = L_

(2*) f

' T

2

(27T) 2 2 + 31n(2lrfh

T) - In 2

1 Nt 2

(2it) h N

2

- J

1 N(N - 1) £ (N - n) • In

WHITE y (Random Walk x)

S (f) = h S (f) =

1

1

• 1 h. • T r(N+ 1) T . for Nr s 1 0 6

1 N(N - 1) J] (N - n) -2(nr) ln(nr)

(2ir) £" (nr + l) 2 ln(nr + 1) + (nr - l) 2 In |nr - 1

|

RANDOM WALK y

h

2 / h

-2

S (£) =-~^ (S..(f) =

(2ff) T [r(N H) - 1], r a 1

''Adapted from J. A. Barnes et al. , "Characterization of Frequency Stability. NBS Technical Note 394 (October 1970); also published in IEEE Trans, on

Instrumentation and Measurement IM-20 . No. 2, pp. 105- 120 (May 1971).

John H. Shoaf, 273. 04

National Bureau of Standards February 1973

166
This dimensionless measure of stability is denoted

by:

, , N /(fk+i — fk)\

o2,(r) s <<r *(^v=2,r=T,T,/*)>=^

f).

(8.60)

By way of review, the bar over the y indicates that y

has been averaged over a time interval t; the angular

brackets indicate an average of the quantity over

time. In the time domain we are concerned with a measure of the square root of each side of eq (8.59) over different time intervals. Plots of cr v (r) versus t ("sigma versus tau") on a log-log scale are com- monly used for data presentation. A convenient

chart which enables one to translate from frequency

domain measures to time domain measures (and

often conversely) is given in table 8.1. An example of

this translation is shown in Annex 8.B. An additional frequency domain measure of

phase fluctuations (noise, instability, modulation)

used in the Time and Frequency Division (T&FD) at NBS is caUed Script ^(f). Script if (/) is defined

as the ratio of the power in one phase modulation

sideband (referred to the input carrier frequency, on a spectral density basis) to the total signal power,

at Fourier frequency / from the signal's average

frequency vo, for a single specified signal or device

(see ann. 8.C); i.e.,:

Power density (one phase modulation sideband)

Power (total signal)

(8.61)

For small 8(/>, S^{f)=2Sf(f). (8.62)

A practical system for the measurement of or

Sbd>if) is described later in Section 8.14.1. In all known signal sources the output frequency

is affected by noises of various types. The random

noises [1] include white thermal and shot noises,

flicker noise, and integrals of these noises. The

noises can be characterized by their frequency

dependence as shown in table 8.2. It is the examination of these noise spectra with which we are con- cerned in the analysis of the frequency stability.

Frequency drift is defined as a systematic (nonrandom, typically-linear) increase or decrease of frequency with time. This is characterized as "aging

rate" in crystal oscillators and is expressed in fractional parts per period of time. This section on

frequency stability does not include a discussion of the so-called "linear drift."

TABLE 8.2. Frequency dependence of various noise I ,/;<•>,

Noise type

Frequency dependence

Spectral

jLp.it liciisiiy —

phase

fluctuations 1

Spectral

density —

frequency

fluctuations 2

White phase noise J j Flicker phase noise /-' P

White frecjuency noise (random

walk of phase) f

-2 r

Flicker frequency noise f-. /-

1 i.e., Ss«(/).

2 i.e.,S 6 „(/)=/2S 6(t (/) = ^S„(/).

8.13. COMPARISON OF MEASUREMENT TECHNIQUES

In this discussion, the primary concern is the

measurement of frequency fluctuations, i.e., instability or stability and not the accuracy of a frequency. It is sometimes convenient to refer to the instability as fractional frequency deviation.

The measurement of frequency fluctuations can be accomplished by one or more of several methods.

In each method it is essential to use a precise

reference which is stable in time. In the case of

measuring accurate frequency sources an equally

excellent reference source is needed.

A straight forward method is by direct counting

of frequency (cycles) by means of counters. Here,

successive values of frequency are read out directly

and can be recorded. (The reference signal controls

the counter gate.) Statistical analysis of the results are usually made. When measuring the lower

frequencies, high resolution is not possible by this method unless frequency multiplication is used.

There are at least two disadvantages of frequency

multipliers: a pair of specialized multiplier chains

may be needed for each different carrier frequency

range and noise from the multiplier itself may be

introduced.

Another method involves mixing the two fre- quencies and recording the beat or difference

frequency. When the reference and signal fre- quencies are close in value, this requires determination of the fluctuations in very long beat periods.

A quantitative measure of short-term frequency

stability is not practical in this case. However,

when a large offset frequency is introduced, the

method is feasible for assessing stability when

a readout device, such as a period counter, is used

for observing fluctuations.

A somewhat similar method uses a phase sensitive detector for determining phase fluctuations between

two signals which are approximately in phase quadrature (and hence must be at the same frequency).

167
Short-term (or long-term) phase fluctuations may be

recorded. In order to facilitate statistical analysis

it is advantageous to use an analog-to-digital converter and a printout type counter. This method is related to the NBS system (time domain) which is described in detail in Section 8.14.2. An interesting and rapid method for comparison

of frequencies and also applicable to stability meas- urement (time domain) is the commercially available

frequency error expander. Since frequency multiplication is used, the same disadvantages are present

as in the first method in which multipliers are employed. The error expander synthesizes one of the

signals to a convenient offset frequency which is then mixed and multiplied in stages to obtain higher

and higher resolution. Eventually, however, the

region is reached where the noise becomes excessive

and frequency comparison is no longer possible.

Note that none of the above-mentioned conventional methods of measuring frequency stability

utilize frequency domain techniques. As indicated

previously, we prefer that the measurements in- volve both frequency and time domain techniques

for a comprehensive and sufficient indication of

frequency stability. This is recommended even

though it is possible to compute time domain per- formance from frequency domain results and often

conversely [1]. Table 8.1 shows translation from one domain to the other. At least one manufacturer has

made it convenient to determine frequency stability

in the time domain automatically through computer

programming [33, 34]. Others in the frequency and

time community outside NBS have reported on ex- cellent systems for both frequency and time domain

measurements of frequency stability [17, 35-37]. In principle, some of these resemble the systems

used at NBS; the techniques described by Van

Duzer [35] and Meyer [36] are excellent examples.

Fortunately, frequency domain and time domain

methods for measuring frequency stability require

similar apparatus with the following exceptions:

frequency domain measurements require a fre- quency window (spectrum analyzer) following the

detector; for time domain measurements a time

window (gated counter) must follow the detector. We next describe specific operating procedures at NBS utilizing the aforementioned techniques.

8.14. OPERATIONAL SYSTEMS

FOR MEASUREMENT OF FREQUENCY STABILITY AT NBS

(HIGH FREQUENCY REGION)

Until recently, most conventional systems for measurement of frequency stability primarily have

utilized time domain techniques; however, a complete measure of frequency stability requires use

of both frequency and time domain techniques.

The introduction of good double-balanced mixers

permitted measurement of frequency stability by

improved techniques [35-38] . The double-balanced

mixer, considered as a phase sensitive detector,

provides meaningful frequency stability measure- ments of high-quality signal sources in both the

frequency domain and the time domain. The results are quantitative and may be obtained from a measurement system which is reasonable in cost. The frequency stability measurement systems de- scribed below have been used at NBS since 1967

for measurements in the HF region. The functional

block diagrams in figures 8.5, 8.11, and 8.13 are referred to in the detailed descriptions of the

particular systems. The carrier frequency range

103 Hz to 10 9 Hz, and higher, is easily covered

with these techniques.

8.14.1. Frequency Domain Measurements

Figure 8.5 illustrates our measurement system

typically used for frequency domain measurements;

it should be noted also that time domain data can be

obtained simultaneously, although that is not often

done. (For time domain measurements it is often more convenient to use a slightly modified measure- ment setup described in Section 8.14.2.) In the

frequency domain setup of figure 8.5, the oscillator signal under test (A), is fed into one side of a lownoise double-balanced mixer (D) which utilizes Schottky barrier diodes. The other side of the mixer

is the reference oscillator signal (B), attenuated

about 10 dB by pad (C) shown in figure 8.5. The

mixer acts as a phase sensitive detector; when the

two signals are identical in frequency and in phasequadrature, the output is approximately zero volts dc. When this output is returned to the reference

VERY LOOSE PHASE LOCK

LOOP . VOLTAGE VARIES

AS PHASE IN SHORT TERM _ JI)

Trc filter!

I IMS! I (G)VOLT

I0X U?I 0„F I L~ I

TIME 00MAIN

(OPTIONAL)

FREQUENCY DOMAIN

A) OSCILLATOR UNDER TEST

6 J REFERENCE OSCILLATOR OF HIGH SPECTRAL PURITY (VARACTOR TUNING)

C) ADJUSTABLE ATTENUATOR (TYPICALLY 1 0d B

)

0) OOUBLE-BALANCEO MIXER (SCHOTTKY BARRIER DIODES)

E) NBS LOW-NOISE dc AMPLIFIER (SEE FIG. 8.7)

F) OPERATIONAL AMPLIFIER (SEE FIG. 8.6)

(G) BATTERY BIAS BOX (SEE FIG. 8.9)

H) SPECTRUM ANALYZER (LOW FREQUENCY, HIGH RESOLUTION)

( 1 1 A0JUSTA8LE RC FILTER

FIGURE 8.5. Typical frequency domain measurement of fre- quency stability (phase sensitive mode).

168
oscillator via the varactor tuning, phase lock is achieved. The phase lock loop contains proper

termination at the output of the mixer followed by

operational amplifiers (E, F) with adjustable gain.

The time constant of the loop may be adjusted as needed by varying the amplifier gain within the

loop and to a lesser extent, by use of the r\C filter 4

(I) indicated in the diagram of figure 8.5. Finally, a battery bias box (G) is included at the varactor

input to insure operation in a suitably linear portion

of the varactor's frequency versus voltage curve. A very loose phase lock loop is indicated inasmuch

as the voltage varies as phase (in short term), and

in this frequency domain measurement we are observing the small phase variations directly. The

phrase —very loose phase lock loop — means that the

bandwidth of the servo response is small compared

to the lowest frequency, /, at which we wish to measure (i.e., the response time is very slow). For

convenience in adjusting the gain and the advantage

of a self-contained battery supply voltage we use

operational amplifiers (stepped gain-commercial) as arranged in the circuit shown in figure 8.6. Special

NBS low-noise dc amplifiers used in certain pre- cision measurements are shown in figure 8.7. At

NBS we have arranged the adjustable RC or CR

filters in a small chassis according to the diagram

of figure 8.8; we utilize low-noise components, and

rotary switches provide various combinations of R

and C. The battery bias box (shown in fig. 8.9) is arranged with a vernier, thus facilitating fine fre- quency adjustments via the varactor frequency ad- justment in one oscillator. A commercial wave

analyzer provides the noise plot information rele- vant to stability (frequency domain). The phase

noise sideband levels are read out in rms volts on

the analyzer, set to certain chosen values of fre- quency, /. For typical high quality signal sources,

this corresponds to measuring only those phase

noise sidebands which are separated from the

carrier by the various /intervals chosen. Script ^if)

OVERLOAD INDICATOR^ nT)V 327 LAMP

5k(i

2 EA -5 IN270

| ZERO AC

2.43kii °

1 k!(

INPUTl L^J s-K

2 EACH

D MERCURY

CELLS IN PARALLEL

IOi.F ^24V

1 50

HPS

6521

1 50pF

4 EA 6V BATTERIES

IN SERIES

X

MERCURY

BATTER' H|l|#|lh

10.8V

OUTPUT

FROM: A. E. WAINWRIGHT

NOTEBOOK AUG. 1967, p. Ill

Figure 8.7. Low noise amplifier.

BCi° OCR 111111111

* This filter can cause instabilities if its time constant, RC, is too large.

SI: FILTER MODE SWITCH (ROTAS*. 3 WAFER)

S2: RESISTOR SWITCH (ROTARY, SHORT I NG TYPE)

S3: CAPACITOR SWITCH { ROTARY , PROGRESSIVE SHORTING)

Figure 8.8 Adjustable RC filter.

I.OuF 1 kit —I I 1.4V MERCURY CELLS

Hr-T-ir

JT2V | 2.8V I

FRONT

REAR

1 .4V HERCUR v CELL.I

f RON REAR •-6H

Figure 8.6. Stepped-gain operational amplifier. Figure 8.9. Battery bias box.

169
FREQUENCY DOMAIN MEASUREMENT

SCRIPT ^(f) IS A FREQUENCY DOMAIN MEASURE OF PHASE FLUCTUATIONS (NOISE, INSTABILITY, MODULATION}. SCRIPT^(f)

IS DEFINEO AS THE RATIO OF THE POWER

IN ONE PHASE NOISE SIDEBAND, REFERRED

TO THE INPUT CARRIER FREQUENCY, ON A PER HERTZ OF BANDWIDTH SPECTRAL DENSITY

BASIS, TO THE TOTAL SIGNAL POWER, AT FOURIER FREQUENCY f FROM THE CARRIER,

PER ONE DEVICE . 2^(f) FOR SMALL 6*

FLICKER PHASE (f~ 1 )~

FIGURE 8. 10. Script if) versus frequency/.

may be calculated with the assumption that both

oscillator sources contribute equally; however, if one source were the major contributor, then the

noise of that source would be no worse than 3 dB

greater than the value of ^(f) so calculated. A

typical plot of script ^(f) versus frequency is shown in figure 8.10; a sample calculation is given

in Annex 8.D.

(A) TEST

OSC ILLATOR

(0) MIXER

(C)

50S! —r

' J_0.001uf i

(0)

(N)

VERV TIGHT PHASE LOCK LOOP. VOLTAGE VARIES AS FREQUENCY

REFERENCE OSCILLATOR

(G) VOLT

BOX

RT

TIME DOMAIN

SPECTRUM ANALYZER

FREQUENCY

L'lj MA 1 N (OPT IONAL

)

ITEMS (A) THROUGH (I) SIMILAR TO FIGURE 8.5.

(J) OPERATIONAL AMPLIFIER

K) STRIP CHART RECORDER FOR QUALITATIVE OBSERVATION

(L) VOLTAGE-TO-FREQUENCY CONVERTER

(M) FREQUENCY COUNTER WITH LOW OEAO TIME

(N) DIGITAL RECORDER WITH FAST RECORDING SPEED (INHIBIT TIME COMPATIBLE WITH COUNTER DEAD TIME)

(0) COMPUTER (OPTIONAL METHOD OF DATA ANALYSIS)

8.14.2. Time Domain Measurements Figure 8.11. Typical time domain measurement of frequency

stability (frequency sensitive mode).

Figure 8.11 shows a measurement system typically used at NBS for stability measurements in the

time domain. Note that the principle of operation is similar to that used in the frequency domain meas- urement wherein the reference oscillator is locked

to the test oscillator. However, for the time domain

measurement we use a very tight phase lock loop

and the correction voltage at the oscillator varies

as frequency. The phrase —very tight phase lock

loop — means that the bandwith of the servo re- sponse is relatively large (i.e., the response time

is much smaller than the smallest time interval, t, at which we wish to measure). This is a very con- venient system for observing frequency fluctuations

in longer term. However, with the time constant

appropriately adjusted and the means for taking

sufficiently short samples, the system is readily

used for both short and long term measurements in the time domain. For qualitative observations any

suitable oscilloscope or strip chart recorder may be

used. For quantitative measurements the system at NBS utilizes a voltage-to-frequency converter, a frequency counter, and a printer capable of re- cording rapid samples of data with very short dead

time. The data are analyzed typically by computer

via a program designed to compute the appropriate

Allan variance [1, 8]. In our computer program log

(cr2 (/V, 7\ t,/;,) ) 1/2 versus log t (ct versus t) along

with the associated confidence in sigma are auto- matically plotted on microfilm. For small batches of

data a desk calculator could be used, and the computer analysis would not be necessary. An example

of a specific Allan variance computation is shown

in Annex 8.E. Figure 8.12 gives a typical plot of

cr versus t. The dashed lines indicate the slopes

which are characteristic of the types of noise

indicated.

The convenience of obtaining time domain data

has been greatly enhanced by utilizing recently

developed counters [33, 34] which are programmable

to automatically compute cr versus t. A block dia- gram (fig. 8.13) shows a measurement system for determining frequency stability by using a computTIME DOMAIN MEASUREMENTS

WHITE PHASE OR FLICKER PHASE NOISE

WHITE FREQUENCY NOISE

FLICKER FREQUENCY NOISE

o o o °

0.01 0.1 . 1.0 10 100 1000

SAMPLE TIME INTERVAL, t(SECONDS)

Figure 8.12. Sigma o>(t) versus tau, t.

170
INPUT | si 52 S3 S4 S5 S6 S7 58 UUUUULJLJU 16° 32° 64° 90°

FIGURE 8.13. Frequency stability measurements

puting counter. using a coming counter programmed to estimate (cr'1 (N—2,

T, t, fh)) l ' 2

. A typical program for such use is given

in Annex 8.F. Certain limitations of deadtime are inherent in the use of this time domain method.

However, in general (except for very short t), fre- quency stability in the time domain may be measured

quickly and accurately using a computing counter.

8.14.3. Differential Phase Noise

Measurements

An additional useful system, illustrated in figure

8.14, measures differential phase noise of various

discrete components which are frequently found in stability measurement systems. In this system only one frequency source is used. Its output is split so

that part of the signal passes through the component to be tested. The signal is adjusted via a phase shifter (fig. 8.15), so that it is in phase quadrature with the other part of the original signal and

is downconverted in the Schottky barrier diode

mixer as described for previous systems. The switchable 50fl load in figure 8.15 is not essential but is included for convenience. A low-pass filter is in- cluded before the signal is amplified in special lownoise, low-level dc amplifiers and observed on the

spectrum analyzer. Script ^(f) values are calculated at various frequency values,/, and plotted. A

sample calculation is shown in Annex 8.D.

FREQUENCY DOMAIN

ITEMS ( B

) THROUGH (0) SAME AS FIGURES 8.5 AND 8. II (P) ANY DEVICE OR COMPONENT UPON WHICH NOISE MEASUREMENT S ARE DESIRED

(AMPLIFIERS, FILTERS. CAPACITORS, CABLES, PADS , ETC.)

(0) NBS ADJUSTABLE PHASE SHIFTER, 5MHz (SEE FIGURE 8.15)

Figure 8.14. Differential phase noise measurement.

3>

RG174/U CABLE WAS USED FOR EACH SEGMENT OF PHASE SHIFT CALCULATED AT -10 cm PER DEGREE AT 5 MHz.

FIGURE 8.15. Adjustable phase shifter (5-MHz delay line).

The measurement system noise level (e.g., see

fig. 8.10) is easily evaluated. Using the differential phase noise measurement system shown in figure

8.14, one can use a short length of coaxial cable

(which is itself not a source of significant noise) as the "device under test." The small amount of noise

observed on the spectrum analyzer represents the system noise, mainly due to the mixer (O) or the

first amplifier (E) in figure 8.14. The calculation of

the system noise is the procedure illustrated in Annex 8.D.

8.15. OPERATIONAL SYSTEMS

FOR MEASUREMENT OF FREQUENCY STABILITY AT NBS

(MICROWAVE REGION)

The systems we have described up to this point

have been used extensively for determining fre- quency stability of 1 to 100-MHz frequency sources. However, we anticipate that these measurement

systems would provide useful data for frequency

sources up to 2 GHz, using the identical system

illustrated in figures 8.5 and 8.11, with some modifications for the higher frequencies. Section 8.15 describes measurement procedures for microwave

frequency sources at X-band (5—12.4 GHz). For the

frequency band 2 to 5 GHz we expect that either the

HF or microwave (wave guide components) systems

may be used; the wave guide system would be more

expensive, and the HF method would require more

sophisticated circuitry for good phase lock. Thorough investigation of stability measurement

techniques in the X-band region (5-12.4 GHz), re- vealed that it generally was desirable to use a method different from that previously described for HF measurements. The recommended measure- ment system for the microwave band follows; other techniques of stability measurements in X- band will be discussed to a lesser extent. The

recommended system 5 is a single-oscillator system

as shown in the photograph of figure 8.16 and in the block diagram of figure 8.17. These measure- ment systems are based on earlier work by Ashley

et al. [38] and Ondria [39].

s The recommended system is discussed here as a frequency domain measurement. However, time domain measurements can also be made.

171
FIGURE 8.16. Single oscillator frequency stability measurement system. (Pictorial).

(A) (B) (0

ISOLATOR VARIABLE

ATTENUATOR

DIRECTIONAL

COUPLER

X-BAND

SOURCE

(D)

ISOLATOR

(I)

CIRCULATOR

(E)

VARIABLE ATTENUATOR

(F) (G)

PHASE

ISOLATOR SHIFTER

(K)

(REFERENCE CHANNEL)

(SIGNAL CHANNEL)

(J) (L)

ISOLATOR VARIABLE ATTENUATOR

DIRECTIONAL

COUPLER

(N) (0)

(P)

CRYSTAL

DETECTOR

ISOLATOR

DC VOLTMETER

(H)

BALANCED MIXER

(Q)

SPECTRUM ANALYZER

Figure 8.17. Single oscillator frequency stability measurement system. (Block diagram).

172
8.15.1. Basic Considerations of the Microwave

(Frequency Stability) Measurement System

The single-oscillator frequency stability measure- ment system is basically a frequency modulation

(FM) demodulator. That is, it can retrieve from the

modulated carrier the signal with which the carrier was originally frequency modulated.

An important consideration when making these

measurements is maintenance of the quadrature

condition — a 90° average phase difference between

the reference channel and the signal channel as seen at the mixer. Unfortunately, there is a fairly

high probability that, during the course of a measurement, the average phase difference will fluctuate

a few degrees about the desired 90° setting. Therefore, it is recommended that an occasional check

of the quadrature condition be made. (In a twooscillator system of measurement, discussed later,

the quadrature condition — in long term — is established and maintained by phase-locking one source

to the other. A similar procedure could be used

here, but we consider it to be unnecessary in practice.) In practice, there is a low frequency limit to the

usefulness of this method for the measurement of

FM noise. We have seen limiting values of / ranging

from as high as 500 Hz to as low as 2.5 Hz. The

single-oscillator system and the two-oscillator system

each have an upper frequency limit; i.e., a value of

/ above which frequency stability measurements

cannot meaningfully be made. For the single- oscillator system, as described here, this upper

limit is / ~ Wc , where Wc is the 3-dB resonance

linewidth of the loaded discriminator cavity. In the

NBS single-oscillator system, measurements were made at values of /as high as 100 kHz.

8. 15. 2. Description of the Microwave

(Frequency Stability) Measurement System

Operation of the single-oscillator measuring

system may readily be followed by referring to the

pictorial view in figure 8.16 and the block diagram,

given in figure 8.17. The X-band source under test

is connected at the left-hand side of the system. The

signal passes through an isolator (A) and variable attenuator (B) before it is split via a 3-dB directional

coupler (C). (It should be noted that isolators (A),

(D), (G), (K), and (O) are used at several points

throughout the system as a means of preventing

any serious reflections which might otherwise exist.)

The signal from output 1 of the coupler enters the

reference channel (upper arm), passing through a phase shifter (F) via a variable attenuator (E) and

eventually through a 90° twist into the balanced

mixer (H). Output 2 from the coupler enters the

signal channel (lower arm), passing through a three- port circulator (I) connected to a discriminator

cavity (M) at one port. A variable attenuator (J) reduces the circulator output in the signal channel

before it reaches the balanced mixer (H). The out- put of the mixer goes to either of two spectrum

analyzers (Q). A 10-dB directional coupler (L) is utilized in the signal channel to facilitate detection

of resonance tuning of the cavity. This is observed

via a detector (N) with a dc voltmeter readout (P). The only component in the system, not readily

available as a commercial stock item, is the dis- criminator cavity (M). It is a TEon right circular

one-port cavity. A movable end wall provides the coarse tuning. The fine tuner is a small diameter

rod which can be moved coaxially in the cavity.

The diameter of the rod should be such that the

cavity frequency changes no more than 1.5 MHz

for 0.05 inch (~ 1 millimeter) change in depth of

insertion. At any desired frequency the coupling

of the cavity should be such that the absorption is very nearly complete. For further discussion of

cavity coupling see reference [38]. The cavity Q

must be both high enough for good sensitivity and

sufficiently low for the required bandwidth. The

cavity used in the NBS frequency stability measure- ment system has an unloaded Q of approximately

20,000.

8.15.3. Calibration Procedure

Initial calibration of the measurement system is necessary for assignment of an absolute scale to the stability measurements. To facilitate calibration, a sinusoidally-modulated X-band source is used to drive the system. The frequency-modulated

signal is observed on an RF power spectral density

analyzer (not shown in figs. 8.16 and 8.17) and the

modulation level is adjusted to a value sufficient to completely suppress the X-band carrier. For

sinusoidal modulation, the first carrier null cor- responds to a modulation index of 2.4. Modulation

at 5 kHz was convenient because of the particular

dispersion and bandwidth settings which were

available on the particular spectrum analyzer used

to display the carrier suppression. The detailed

procedure for obtaining the calibration factor is given in Annex 8.H.

8.15.4. Measurement Procedure

The procedure for obtaining data for the spectral

density plot is quite similar to the calibration pro- cedure except that the X-band carrier is not subjected to intentional modulation. Detailed steps for X-band frequency stability measurements are given

in Annex 8.1. Included are techniques for calculating

values of S^if). Results of such calculations for an X-band Gunn diode oscillator signal source is given in figure 8.18.

173
_l I I 1 I I III —1 I I I 1 1

1

100

f (Hz)

Figure 8.18. Frequency domain plot of phase noise of X-band Gunn diode oscillator signal source (single oscillator method).

CORRECTION VOLTAGE

"-BAND 9.5 GH2 SOURCE

(BU<500 kHz)

Figure 8.19. Frequency stability measurement system

(phase-lock servo loop).

FIGURE 8.20. Frequency stability measurement system

(offset-frequency phase-lock servo loop).

8.15.5. Additional Techniques for Frequency

Stability Measurements at X-Band

It has been found convenient and desirable, under

certain circumstances, to use other techniques for measuring frequency stability at X-band. Where

two X-band sources are available, phase- or frequency-locking techniques similar to those used

at HF can be used. (See figs. 8.19-8.21). Good wideband double-balanced mixers with coaxial con- nectors are available [40] which permit many of the

measurements to be performed without use of

waveguide components.

The measurement setup, shown in the block dia- gram of figure 8.13, also can be used at microwave

frequencies; this system utilizes a computing

counter for time domain measurements. Extensive

X-BAND

SOURCE

X-BAND MIXER

310

MHz

X-BAND | 9-190 GHz SOURCE I

XTAL

0SC.

E

200 MHz

110 MHz

100

MHz

SYNTHESIZER

10MHz

CORRECTION

VOLTAGE

^Mf^- SPECTRUM ANALYZER

XTAL

0SC.

Figure 8.21. Frequency stability measurement system

(large frequency-offset phase-lock servo loop).

174
measurements of frequency stability have been

made on stabilized X-band sources [40]. Time

domain data obtained via the computing counter have been compared with frequency domain data

obtained via several methods. The example shown

in Annex 8.D, the frequency domain data of figure

8.18, are translated into time domain data; these

data are plotted in figure 8.22. In the same figure we have plotted time domain data taken directly

via a computing counter using the system shown in figure 8.13.

10 7 P

1—I

i l 1 1 ii| 1—n miii| 1—i i i i n i| 1

i |

1—i 1 1 i m

O DATA OBTAINED FROM METHOD IN FIGURE 8.13 - CALCULATED FROM FREQUENCE DOMAIN DATA

(SEE FIG . 8.18 AND ANNEX 8.B)

10"'°l 1 1 I I I III! 1—I I I I nil 1 I I I Mill I

I i 0.001 0.01 0.1 1 10

T (SECONDS)

Figure 8.22. Time domain plot of X-band Gunn diode oscillator signal source.

8.16. CONCLUSIONS/SUMMARY

Concise definitions for specifying frequency

stability have been given for measurements in the

frequency domain and time domain. The first part

of this chapter gives an in-depth characterization

of frequency stability to enable understanding of the basic concepts. This is followed by a description

of operational systems for measurement of fre- quency stability in detail sufficient for duplication

of the required instrumentation. Uniform methods

of reporting data and techniques of measurement

both are recommended as advantageous and desir- able for better interpretation of frequency stability

specifications. The methods are applicable for both

HF and microwave frequency sources.

8.17. REFERENCES

[1] Barnes, J. A., Chi, A. R.. Cutler, L. S., Healey, D. J.. Leeson,

D. B., McGunigal, T. E., Mullen, J. A., Jr., Smith, W.L.,

Sydnor, R., Vessot, R. F. C, and Winkler, G. M. R., "Characterization of frequency stability," IEEE Trans, on Instrum. and Meas., IM-20, No. 2, pp. 105-120 (May

1971).

[2] Shoaf, J. H.. Halford, D.. and Risley, A.. "Frequency stability specification and measurement: high frequency and micro- wave signals," Nat. Bur. Stand. (U.S.) Tech. Note 632, 70 pages (USGPO. January 1973).

[3] Barnes, J. A., "Tables of bias functions, Bi and fi 2 , for variances based on finite samples of processes with power

law spectral densities," Nat. Bur. Stand. (U.S.) Tech. Note 375, 37 pages (USGPO. January 1969).

[4] CGPM, Com/Jtes Rendus des Seances d<- In Trrizu-me Conference General des Poids el Mesures, (Proceedings of the Sessions of the 13th General Conference of Weights and

Measures) (Paris, France, October 1968), p. 103 (GauthierVillars, Paris, France, 1968) (in French — see chap. 1 —

ann. l.A.l).

[5] CCIR, "Detailed instructions by Study Group 7 for the implementation of Recommendation 460 concerning the improved coordinated universal time (UTC) system, valid from 1 January 1972," in XUth Plenary Assembly CCIR

(New Delhi, India, 1970), III, p. 258 a-d (ITU, Geneva,

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Metrologia, 1, No. 3, pp. 114-131 (July 1965).

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J. A., and Beehler, R. E., NBS/CCIR Study Group 7

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[8] Allan, D. W.. "Statistics of atomic frequency standards,"

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[9] Chi, A. R. (Chairman). IEEE-NASA Symp. on Short-Term Frequency Stability (Goddard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964) NASA SP-80,

317 pages (USGPO, 1965).

[10] Chi, A. R., (Guest Ed.)Spea'a/ Issue on Frequency Stability, Proc. IEEE, 54, No. 2, pp. 101-280 (February 1966).

[11] Jaynes, E. T.. "Information theory and statistical mechanics," Phys. Rev., 108, Sec. 15, pp. 171-190 (October

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[12] Bingham, C, Godfrey, M. D., and Tukey, J. W.. "Modern

techniques of power spectrum estimation," IEEE Trans. Audio AU-15, No. 2, pp. 56-66 (June 1967).

[13] Blackman, R. B., Linear data smoothing and prediction in theory and practice, 182 pages (Addison-Wesley Publishing Co., Reading, MA 01867, 1965).

[14] Blackman, R. B.. and Tukey, J. W., The measurement of power spectra, 190 pages (Dover Publishing Co., New

York, NY 10014, 1958).

[15] Brigham, E. O.. and Morrow, R. E., "The fast Fourier transform," IEEE Spectrum, 4, No. 12, pp. 63-70 (December 1967).

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status," Proc. IEEE-NASA Symp. on Short-term Frequency

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[18] Shewart, N. A., Economic control of quality of manufactured product, p. 146 (Van Nostrand-Reinhold Co., New York, NY 10001, 1931).

[19] Lesage, P.. and Audoin, C, "Characterization of frequency

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No. 2, pp. 157-161 (June 1973).

[20] Barnes, J. A., "Atomic timekeeping and the statistics of precision signal generators," Proc. IEEE, 54, No. 2. pp. 207-220 (February 1966).

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J., Cutler, L.. and Bodily, L.. "An intercomparison of hydrogen and cesium frequency standards." IEEE Trans, on Instrum. and Meas., IM-15, No. 4, pp. 165-176 (December 1966).

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[23] Leeson, D. B., and Johnson, G. F., "Short-term stability for a Doppler radar: requirements, measurements, and

techniques," Proc. IEEE, 54, No. 2, pp. 244-248 (Feb- ruary 1966).

[24] Saunders, W. K., in Radar Handbook, Skolnik, M. I. (Ed.), "CW and FM radar," Chap. 16, pp. 16-1-16-38 (McGraw-Hill Book Co., New York, NY 10036, 1970).

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1966).

[26] Leeson, D. B., "A simple model of feedback oscillator noise spectrum," Proc. IEEE, 54, No. 2, pp. 329-330 (Feb- ruary 1966).

[27] Vessot, R. F. C, Mueller, L., and Vanier, J., "The specification of oscillator characteristics from measurements made in the frequency domain," Proc. IEEE, 54, No. 2, pp. 199-207 (February 1966).

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& Sons, New York, NY 10016, 1966).

[29] Menoud, C, Racine, J., and Kartaschoff, P., "Atomic

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(Hewlett-Packard, Palo Alto, CA 94304, October 1968).

[32] Halford, D., Shoaf, J. H., and Risley, A. S., "Spectral

density analysis: frequency domain specification and measurement of signal stability," Proc. 27th Ann. Symp.

on Frequency Control (U.S. Army Electronics Command,

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(Electron. Ind. Assn., Washington, DC 20006, 1973).

[33] Hewlett-Packard staff, "Precision frequency measurements," Application Note 116, 12 pages (Hewlett-Packard, Palo Alto, CA 94304, July 1969).

[34] Hewlett-Packard staff, Computer Counter Applications

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difference of two frequency standards;" No. 27 — "Fractional frequency deviation measurements on ultrastable sources;" and No. 29 — "Frequency stability measure- ments of crystals in the presence of significant frequency

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[35] Van Duzer, V., "Short-term stability measurements,"

Proc. of IEEE-NASA Symp. on the Definition and Measurement of Short-Term Frequency Stability (Goddard

Space Flight Center, Greenbelt, MD 20771, November

23-24, 1964), NASA SP-80, pp. 269-272 (USGPO, 1965).

[36] Meyer, D. G., "A test set for measurement of phase noise on

high quality signal sources," IEEE Trans, on lustrum, and

Meas., IM-19, No. 4, pp. 215-227 (November 1970).

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MTT-16, No. 9, pp. 753-760 (September 1968).

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fli(/V,r,/x):

C0

ANNEX 8.A

GLOSSARY OF SYMBOLS

<4ptp Peak-to-peak voltage of a beat

frequency at output of mixer.

B High frequency cutoff fu

(bandwidth).

Ba Analysis bandwidth (frequency

window) of the spectrum

analyzer.

Bias functions for variances

based on finite samples of a process with a power-law

spectral density (see ref.

[3]). A real constant defined in reference [1]. Real constants. A real, deterministic function

of time.

Expected value of the squared

second difference of x(t)

with lag time t. (see ref. [1]). Fourier frequency of fluctuations. High-frequency cutoff of an

idealized infinitely sharp cutoff, low-pass filter (see

symbol B)

.

Low-frequency cutoff of an

idealized infinitely sharp

cutoff, high-pass filter. A real function of time.

Positive real coefficient

Co, C\ c(t)

DUt)

f - W27T

fh

fi

g{t)

ha

i, j , k, m, n K

M

off"

in a power series expansion

of the spectral density of the

function y(t)

.

Integers, often a dummy in- dex of summation.

Calibration factor used in the

single oscillator stability

measurement system for microwave frequencies, K

( A^Orms/^rmsFrequency domain measure of

phase fluctuation sidebands;

Script JZ'(f) is defined as the ratio of

Power density (one phase

modulation sideband)

Power (total signal)

For small 8$, Sh(b (f) = 2J?(f).

Total number of data values

available (usually M > N).

176
N

n(t)

^total Ry(r) rSUf)

Ss*(/) Sv iv) V RFP SB (f)

Sy(f) ttou

V(t)

Also, positive integer giving

the number of cycles aver- aged.

Positive integer giving the

number of data values used

in obtaininga sample vari- ance.

A nondeterministic function of

time.

Total power of signal.

Autocovariance function of

y(t) (seeref. [1]). Parameter related to dead time

(T-r);r=TJr.

Spectral density of frequency

fluctuations.

Spectral density of voltage

fluctuations.

Spectral density of phase

fluctuations:

SUf) p

Sy(f) P

Spectral density of the (square

root of the) radio frequency

power.

One-sided (power) spectral

density ona per hertz basis

of the pure real function

g(t). The dimensions of

S(i(f) are the dimensions of g2 (t)lf.

A definition for the measure

of frequency stability. Onesided (power) spectral density of y(t) on a per hertz

basis. The dimensions of Sv (/) are Hz-1 (spectral

density of fractional fre- quency fluctuations).

Time interval between the

beginnings of two successive

measurements.

Time variable. An arbitrary fixed instant of

time.

The time coordinate of the

beginning of the A;th meas- urement of average fre- quency. By definition tit+i = tk + T,Jc = 0,l,2. . .. Dummy variable of integration; u — 7t/t. Instantaneous output voltage

of signal generator; see eq

(8.4).

V0 v~ rms

v(t)

v'(t) wc

x(t)

x{t) Xy

y(t)

fk

(y).v

Zn{t) { ) ayA8

8v

80

Nominal peak amplitude of

signal generator output; see eq (8.4). Peak amplitude of reference

signal; see eq (8.42). Instantaneous voltage of refer- ence signal; see eq (8.42). Root-mean-square voltage of

the output of an FM demodulator due to intentional

modulation.

Root-mean-square (noise) volt- age at output of mixer as measured by a spectrum

analyzer.

Voltage output of ideal product detector. Low-pass filtered output of product detector. The — 3 dB resonance line- width of the loaded dis- criminator cavity.

Real function of time related

to the phase of the signal

V(t) by the eqx(f) = [<p(t)]l

(2ttv0 ).

A predicted value for x{t).

Time interval fluctuations; —= V, hence x = Sr. dtFractional frequency fluctua- _8v

tions,

y =

Po Average of y over

a specified

time interval, T. Fractional frequency offset of

V{t) from the nominal fre- quency; see eq (8.9). Average fractional frequency

offset during the Arth meas- urement interval; see eq

(8.11). The sample average of

N

successive values of fk\ see reference [1]. Nondeterministic (noise) function with (power) spectral

density; see eq (8.28). Infinite time average operator.

Exponent of / fora power-law

spectral density.

Positive real constant. Difference operator.

Fluctuation operator.

Frequency fluctuations. Phase fluctuations and is equivalent to 4>{t)-

177
8fc (r-l) The Kronecker 8 function de- fined by

8V,v

e(t)

f(0

*(/)

<rl(N, T,T,fh )

(<7*(N, T, T,fu))

**(7\ t)

8fc (.r-l) -

1, if r= 1 otherwise.

Voltage fluctuations.

Amplitude fluctuations of sig- nal; see eq (8.4). Exponent of r; see eq (8.32).

Signal frequency (carrier fre- quency) variable. Instantaneous frequency of V(t). Defined by

v(t)

2tt dt

Nominal (constant) frequency of

V(t).

The Fourier transform of n{t).

Square root of a variance.

Sample variance of /V averages of y(t) , each of duration t, and

repeated every T units of time

measured in a post-detection

noise bandwidth of fh\ see eq (8.59). Average value of the sample var- iance <T

2y (N, T, T,fh ); (Allan

variance).

Specific Allan variance where

N=2, T = t; see eq (8.60); Allan variances.

Sampling time interval; see eq

(8.11). Post-detection averaging time of

the spectrum analyzer. Instantaneous phase of V{t).

Defined by <t>(0 = 2Trv0t + <p(t). Instantaneous phase fluctua- tions about the ideal phase

27TiV; see eq (8.4) and is equivalent to 8(f>. Mean-square time error for Doppler radar; see reference

[1]. Signal angular frequency (car- rier angular frequency),

H = 2irv. Fourier angular frequency of

fluctuations, (o = 2irf.

ANNEX 8.B

TRANSLATION OF DATA FROM

FREQUENCY DOMAIN TO TIME

DOMAIN USING THE CONVERSION CHART (table 8.1)

Referring to the frequency domain plot in figure

8.18 it is determined that Ss4>(f) indicates /~3 behavior over the total range plotted. Therefore Sg„(/)

is proportional to/" 1 (i.e., flicker frequency noise).

At/= 1000 Hz, S6v (f) is equal to -0.3 dB relative

to 1 Hz (see table 8.2). The carrier frequency, v0 , is 9.5 GHz.

Sy(f)

Ssv (f)_ (10-°- 03 Hz)

(9.5 x 109 Hz) 2 1.04 x 10-20Hz-!

(8.B.1)

Sy(f) = Y

(8.B.2)

(see conversion chart-table 8.1).

h-i = Sy (f) X/=(1.04xlO-20Hz- 1 ) x (103 Hz) = 10.4x 10- 18

. (8.B.3)

o2 (r) = h-i- 2 In 2= 10.4 X 10" 18

x 1.39= 14.5 x 10" 18

. (8.B.4)

o>(t) = 3.8 X lO"9. (8.B.5)

For flicker frequency noise there is no t dependence. A dashed fine at this calculated value is plotted on the same graph as data taken directly

in the time domain (fig. 8.22). ANNEX 8.C

SPECTRAL DENSITIES: FREQUENCY DOMAIN MEASURES

OF STABILITY

Stability in the frequency domain is commonly

specified in terms of spectral densities. We have

used the concept of spectral density extensively

in this chapter. The spectral density concept is simple and very useful, but care must be exercised

in its use. There are at least four different, but

related, types of spectral densities which are used in this chapter. In this Annex, we state and explain some of the simple, often-needed relations among

these often-used types of spectral densities.

178
8.C. 1 . Some Types of Spectral Densities

Four types of spectral densities which are most

relevant to frequency and phase fluctuations are

Sy(f) Spectral density of fractional frequency

fluctuations, y (noise, instability, modulation). The dimensionality is per hertz. The range of / is from zero to infinity.

Ssv(f) Spectral density of frequency fluctuations

8v (noise, instability, modulation). The

dimensionality is hertz squared per hertz. The range of / is from zero to infinity.

Sdd>(f) Spectral density of phase fluctuations

8(f) (noise, instability, modulation). The

dimensionality is radians squared per hertz. The range of / is from zero to infinity.

<£f(f) Script <SC(f) is a frequency domain

measure of phase fluctuation sidebands

(noise, instability, modulation). Script

^?(f) is defined as the ratio of the power

in one phase modulation sideband, referred

to the input carrier frequency, on a spectral

density basis, to the total signal power, at Fourier frequency / from the signal's

average frequency v0 , for a single specified

signal or device. The dimensionality is per

hertz. The range of / is from minus v0 to plus infinity.

Each of these spectral densities is one-sided and

is on a per hertz of bandwidth density basis. This means that the total mean-square fluctuation (the

total variance) of frequency, for example, is given

mathematically by

f

S6v (f) df,

and, as another example, since Script ^if) is a normalized density, that

-t /

is equal to unity.

Two-sided spectral densities are defined such that the range of integration is from minus infinity to plus infinity. For specification of noise as treated

in this chapter, our one-sided spectral density is twice as large as the corresponding two-sided

spectral density. That is, j[S

Two-Sided] df= 2

f

+ X

[S

Two-Sided]

(Jf

= [

+ °° [S0ne- Sided

] df. (8.C.1)

Two-sided spectral densities are useful mainly in pure mathematical analysis involving Fourier

transformations. We recommend and use one- sided spectral densities for experimental work.

We use the definition

8u

(8.C.2)

and it follows that

Sy (f) =SSv (f)=(-)*Sliv (f). (8.C.3)

To relate frequency, angular frequency, and phase we use

2tt|>(0] = fl(t)

</<£>( Q

dt

' (8.C.4)

This may be regarded as a definition of instantaneous frequency v(t). From eq (8.C. 4), a direct

result of transform theory is

2 2

Script y{f) can be related in a simple way to

Sf,<j>(f), but only for the condition that the phase

fluctuations occurring at rates /and faster are small

compared to one radian. Otherwise Bessel function

algebra must be used to relate Script to

Sf,<t,(f). Fortunately, the "small angle condition"

is often met in random noise problems. Specifically we find

1 2 rad2

provided that

J,

SH{f')df <1 rad 2

.

(8.C.6)

(8.C.7)

For the types of signals under discussion and for

|/| < Vo, we use as a good approximation

Jf{-f)~J?(f). (8.C.8)

Script Jz?(f) is the normalized version of the

phase modulation (PM) portion of S^/rfp^),

with its frequency parameter / referenced to the

signal's average frequency vo as the origin such

that / equals v — v0 . In the absence of amplitude

modulation (AM), all of the radio frequency power

(RFP) in the sidebands is associated with phase

modulation. In high quality signal sources, it is often found that the AM is negligible compared

to the PM.

179
8.C.2. Some Mathematics of Phase Sideband

Power as Related to Phase Fluctuations

A simple derivation of eq (8.C.6) is possible. We

combine the derivation with an example which

illustrates the operation of a double-balanced

mixer as a phase detector. Consider two sinusoidal

5-MHz signals (having negligible amplitude modulation) feeding the two input ports of a doublebalanced mixer. When the two signals are slightly out of zero beat, a slow sinusoidal beat with a period

of several seconds at the output of the mixer is measured to have a peak-to-peak swing of Aptp . Without changing their amplitudes, the two

signals are retuned to be at zero beat and in phase

quadrature (that is, it/2 out of phase with each

other), and the output of the mixer is a small

fluctuating voltage centered on zero volts. Pro- vided this fluctuating voltage is small compared to

d.ptp/2, the phase quadrature condition is being

closely maintained, and the "small angle condition"

is being met. Further details on this measurement

procedure are given in Section 8.14.1 and figure

8.5.Phase fluctuations 8(f) between the two signals

of phases 4>2 and 4>i , respectively, where

80 = 8(02 -<M (8.C.9)

will give rise to voltage fluctuations 8V at the out- put of the mixer

8V iptp

8<j>, (8.C.10)

where we have used radian measure for phase

angles, and we have used

sin 8(f) ~ 8(f), (8.C.11)

for small 8(f) (8(f) < I rad). We solve eq (8.C.10)

for 8(f), square both sides, and take a time average

((8V) 2

) W)2

> ~ 4 ,l J ' <8- C- 12) (Aptp) 2

If we interpret the mean-square fluctuations of

8(f) and of 8V, respectively, in eq (8.C.12) in a spectral density fashion, we may write

S*(/>~

2fi^' (8C.13)

where we have used

(/U) 2 = 8(/f rms ) 2, (8.C.14)

For the types of signals under consideration, by

definition the two phase noise sidebands (lower side- band and upper sideband, at — / and + / from v0 , respectively) of a signal are coherent with each

other. As already expressed in eq (8.C.8), they are

of equal intensity also. The operation of the mixer,

when it is driven at quadrature, is such that the

amplitudes of the two phase sidebands add linearly

in the output of the mixer, resulting in four times

as much power in the output as would be present

if only one of the phase sidebands were allowed to contribute to the output of the mixer. Hence for

| f\ < vo we obtain

(A \2 ^ p

^iV1 ' V^rms/ 1 total

and, using the definition of Script Jf{f),

(8.C.15)

which is valid for the sinusoidal beat signal.

-W) -

[Sv%

( "° + /)] PM ~

I

S»{ |/| )

,

'total ^

(8.C.16)

provided the phase quadrature condition is approximately valid. Recall that we assumed the signals

have negligible amplitude modulation. The phase

quadrature condition will be met for a time interval

at least r long, provided

| .SniDdf « lrad2

, (8.C.17)

J(2ttt)

and hence eq (8.C.16) is useful for values offat least as low as (2irr)~ l

. Equations (8.C.16) and (8.C.17)

correspond to eq (8.C.6) and (8.C.7), respectively.

ANNEX 8.D

A SAMPLE CALCULATION OF

script se

For convenience of computation and plotting it often is advantageous to set the beat frequency

voltage (before locking) to volts (0.316 V) peakto-peak at the mixer output. Then (after lock) with

the output of the phase detector expressed in rms

nanovolts per root hertz, direct plotting is facili- tated for Script in decibels versus frequency

in hertz. In this case 1000, 100, and 10 nanovolts

per root hertz correspond to — 110, — 130, and — 150

dB respectively. A sample calculation demonstrating

this convenience is shown below. Equation (8.D.3)

given for Script ^f(f) is valid for the case where

two equally noisy signals are driving the mixer.

180
Given:

^= 0,316 v(i.e.,^=v\' (8.D.1)

v=\00 nV Hz 11 - @f=20 Hz, (8.D.2)

from a pair of equally noisy signals.

(8.D.3)

'100 nV Hz- 1/2\

2 / 10

0.316 V

, Hz- 1= Hz 1 10" 1

10-13 Hz" 1 = -130 dB,

TABLE 8.E.I. Sample data tabulation

Data values

(?)

892 809

823

798

671 644

883

903 677

First differences (fk+i— fk)

-83

14 -25

-127 -27

239

20 -226

First differences squared — 9k)'1

6889

196 625

16129 729

57121 400

51076 £ (yk +l -fk) 2 = 133165

Based on these data:

or using logarithms:

... , 133165 _„_„

°"|/( T )=^77^=8322 - 81 ' ( 8-E.2) z (»)

=^(20 Hz)= 20 login — (8.D.4)

\AptpJ

(10- 7 V • Hz_1/2

) 20 logic =20(-7 + 0.5)

(lO-"2 V)

-130 dB.

If the phase noise follows flicker law, at /— 1 Hz it is 20 times worse (or 13 dB greater); that is

-S?(lHz)=-130 dB+13 dB = -117 dB. (8.D.5)

ANNEX 8.E

A SAMPLE CALCULATION OF

ALLAN VARIANCE, <tHt)

o2 (t) -<o-2 (/V=2, T=r,r)) (yk+i fx) 2 -— £ (yk+ i-yk )\ (8.E.1) 2(M

in the example below

Number of data values available, M= 9

Number of differences averaged, M—1 — 8

Sampling time interval t= Is

[ct2 (t)] , / 2 = V8322.81 = 91.23, N=2, T = t= 1 s. (8.E.3)

In this example, the data values may be understood

to be expressed in parts in 1012

; the data may have

been taken as the counted number of periods, in the time interval t, of the beat frequency between the

oscillator under test and a reference oscillator,

divided by the nominal carrier frequency vo, and

multiplied by the factor 1012

. Using the same data as in the above example it is possible to calculate the Allan variance for r = 2 s by averaging pairs of adjacent data values and using

these averaged values as new data values to pro- ceed with the calculation as before. Allan variance

values may be obtained for t = 3 s by averaging

three adjacent data values in a similar manner,

etc., for larger values of t. Ideally the calculation is done via a computer and

a large number, M, of data values should be used.

(Typically M= 256 data values are used in the NBS

computer program.) The statistical confidence of

the calculated Allan variance improves normally as the square root of the number, M, of data values

used [19]. For M=256, the confidence of the Allan

variance is expected to be approximately ±

^/^g

X 100 percent ~ ± 7 percent of its value. The use of

M > > 1 is logically similar to the use of B„ t„ > > 1 in spectrum analysis measurements, where B„ is the analysis bandwidth (frequency window) of the spectrum analyzer, and T„ is the post-detection

averaging time of the spectrum analyzer.

181
ANNEX 8.F ANNEX 8.G

COMPUTING COUNTER PROGRAM

USING AN EFFICIENT OVERLAPPING ESTIMATOR FOR

<<7

y

2 (iv=2,r,T,/,» 1/ 2

(1) MANUAL

(2) Enter carrier or basic frequency

(3) c^x

[skip to (33) if pro- gram is already in]

(4) LEARN

(5) CLEAR x

(6)

(7) OMODULE or PLUG-IN

(8) a^*x

(9) x*Ter program

(10) MODULE or PLUG-IN

(11) <C~*x

(19) REPEAT

(20) X FER PROGRAM

(21) Nxy

(22) Nx7

(23) + (add)

(24) a^x

(25) bly*

(26) axy

(27) - (divide)

(28) 1 (29) Vx

(30) cxy

(31) (divide)

(32) PAUSE

(33) RUN

(12) axy

(13) - (subtract)

(14) xy

(15) X (multiply)

(16) bxy

(17) + (add)

(18) b^x

(34) START

Program will automatically repeat unless right

hand PAUSE switch is in HALT position. PAUSE

DISPLAY switch must

be on. t= SaTnple time (computing counter "measurement

time").

T — t — 0.003 seconds (compute + cycle time)

/V = 2

fh = Measurement system bandwidth

Number set on repeat loop corresponds to the

number of estimates of the variance. For good

confidence levels 100 or more estimates usually

are required.

SELECTED FREQUENCY STABILITY REFERENCES: BIBLIOGRAPHY6

8.G.I. Selected References (Proceedings, Special Issues, etc.) Applicable to Measurement and Specification of Fre- quency Stability. 8.G.2. Bibliography of Time and Frequency Stability References.

ANNEX 8.G.1

Selected References (Proceedings, Special

Issues, etc.) Applicable to Measurement

and Specification of Frequency Stability

[Rl] 7 IEEE Trans, on Instrum, and Meas. (Principle proceedings

of the International Conference on Precision Electro- magnetic Measurements (CPEM), held every two years) (November or December of even-numbered years). [R2] Proc. IEEE, Special Issue on Frequency Stability (IEEENASA Symp.) 54, No. 2 (February 1966). [R3] IEEE-NASA, Proc. of the IEEE-NASA Symp. on the Defini- tion and measurement of Short-Term Frequency Stability

(Goddard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964) NASA-SP-80, 317 pages (USGPO

1965). [R4] Barnes, J. A., Chi, A. R., Cutler, L. S., Healey, D. J., Leeson,

D. B., McGunigal, T. E., Mullen, J. A., Jr., Smith, W. L., Sydnor, R., Vessot, R. F. C, and Winkler, G M. R., "Characterization of Frequency Stability," Nat. Bur. Stand. (U.S.) Tech. Note 394, 50 pages (USGPO, October

1970); also published in IEEE Trans, on Instrum, and

Meas., IM-20, No. 2, pp. 105-120 (May 1971). This is the most definitive discussion to date of the characterization and measurement of frequency stability. It was prepared

by the Subcommittee on Frequency Stability of the Insti- tute of Electrical and Electronic Engineers.

[R5] IEEE Trans, on Microwave Theory and Techniques, Special

Issue on Noise, MTT-16, No. 9 (September 1968). [R6] Proc. IEEE, Special Issue on Time and Frequency, 60, No. 5, (May 1972).

182

6 Annotated when additional information is pertinent.

7 R denotes reference listing.
[R7] U.S. Army Electronics Command, Proc. Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703). These symposia are held usually at Atlantic City during the spring of each year. The Proceedings contain a wide variety of frequency/time papers,

including general interest, progress reports, and well- documented state-of-the-art accounts. Information about

the Proceedings for the last years is given on page 178, together with the source of availability.

tant reprints of NBS papers written during I960 to 1970

(February) on various time and frequency subjects includ- ing statistics of frequency and time measurements.

[R9] Blair, B. E., "Time and frequency: A bibliography of NBS

literature published July 1955-December 1970." Nat.

Bur. Stand. (U.S.), Spec. Publ. 350, 52 pages (U.S. GPO,

June 1971). This publication is a rather complete bibliog- raphy (for the time period noted) on many aspects of time and frequency as studied by NBS.

Symposium

Number Date

Proceedings Accession No. Pages Availability

10*

1112

1314

1516

1718

1920

2122

2324

2526

27

May 15-17, 1956.

May 7-9, 1957 May 6-8, 1958 May 12-14, 1959 May 31-June 2, 1960. May 31-June 2, 1961.

April 25-27, 1962 May 27-29, 1963 May 4-6, 1964

April 20-22, 1965

April 19-21, 1966

April 24-26, 1967

April 22-24, 1968 May 6-8, 1969

April 27-30, 1970

April 26-28, 1971. June 6-8, 1972.... June 12-14, 1973.

AD 298322

AD 298323 AD 298324 AD 298325 AD 246500 AD 265455 AD 285086 AD 423381 AD 450341 AD 471229 AD 800523 AD 659792 AD 844911 AD 746209

AD 746211

585

634

666

723 443

335 455

618

597

673 679

579 620

313

361

351 322 446

National Technical Information Service, Sills Build

ing, 5285 Port Royal Road, Springfield, VA 22151 NTIS

NTIS

NTIS

NTIS

NTIS , NTIS

NTIS

NTIS

NTIS

NTIS

NTIS

NTIS

NTIS , Electronics Industries Assn., 2001 Eye Street, NW

Washington, DC 20006. NTIS

Electronics Industries Assn

Electronics Industries Assn

* First published proceedings.

[R8] Blair, B. E., and Morgan, A. H. (Eds.), Precision Measure- ment and Calibration-Selected NBS Papers on Frequency

and Time, Nat. Bur. Stand. (U.S.) Spec. Publ. 300, V, 555 pages (USGPO, June 1972). This volume contains impor-

[R10] Shoaf, J. H., Halford, D., and Risley, A., "Frequency stability specification and measurement: high frequency and microwave signals," Nat. Bur. Stand. {U.S.) Tech. Note

632, 70 pages (USGPO, January 1973).

183
ANNEX 8.G.2

Bibliography of Time and Frequency Stability References

[Bl] s Allan, D. W., "Statistics of atomic frequency standards,"

Proc. IEEE, 54, No. 2, pp. 221-230 (February 1966). A thorough understanding of this paper is important for everyone who wishes to measure and quote performance

of frequency standards" in the time domain, e.g., <J versus t plots. The data analysis must take into account

the number of samples taken and how they are used.

[B2] Allan, D. W., Blair, B. E., Davis, D. D., and Machlan,

H. E., "Precision and accuracy of remote synchronization via portable clocks, Loran C, and network tele- vision broadcasts," Proc. 25th Ann. Symp. on Frequency

Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 26-28, 1971) pp. 195-208 (NTIS, AD 746211, 1971); also published in Metrologia,

8, No. 2, pp. 64-72 (April 1972). [B3] Allan, D. W., Gray, J. E., and Machlan, H. E., "The

National Bureau of Standards atomic time scales: generation, dissemination, stability, and accuracy," IEEE Trans, on Instrum. and Meas., IM-21, No. 4, pp. 388-391 (November 1972). (See Chap. 9). [B4] Allan, D. W., Machlan, H. E., and Marshall, J., "Time

transfer using nearly simultaneous reception times of a common transmission," Proc. 26th Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 6-8, 1972) pp. 309-316

(Electron, Ind. Assn., Washington, DC 20006, 1972). [B5] Anderson, A. E., and Brower, H. P., "A tunable phase

detector for short-term frequency measurement,"

Proc. IEEE-NASA Symp. on the Definition and Measure- ment of Short-Term Frequency Stability (Goddard

Space Flight Center, Greenbelt, MD 20771, November

23-24, 1964), NASA SP-80, pp. 295-302 (USGPO, 1965). [B6J Ashley, J. K., and Searles, C. B., "Microwave oscillator noise reduction by a transmission stabilizing cavity," IEEE Trans, on Microwave Theory and Techniques.

MTT-16, No. 9, pp. 743-748 (September 1968). [B7] Ashley, J. R., Searles, C. B., and Palka, F. M., "The meas- urement of oscillator noise at microwave frequencies," IEEE Trans, on Microwave Theory and Techniques,

MTT-16, No. 9, pp. 753-760 (September 1968). [B8] Atkinson, W., and Fey, L., "Statistical aspects of clock

errors," Unpublished report (January 1960). [B9] Atkinson, W. R., Fey, L., and Newman, J., "Spectrum

analysis of extremely low frequency variations of quartz

oscillators," Proc. IEEE (Corresp.). 51, No. 2, p. 379

(February 1963). [B10] Baghdady, E. J., Lincoln, R. D., and Nelin, B. D., "Short- term frequency stability: theory, measurement, and

status," Proc. IEEE-NASA Symp. on the Definition and

Measurement of Short-Term Frequency Stability (God- dard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964), NASA SP-80, pp. 65-87 (USGPO, 1965); also Proc. IEEE, 53, No. 7, pp. 704-

722 (July 1965); and Proc. IEEE (Corresp.), 53, No. 12, pp. 2110-2111 (December 1965). Among many other

topics, the possible problem of AM noise is discussed.

[Bll] Bagnall, J. J., Jr., "The effect of noise on an oscillator controlled by a primary reference," NEREM 1959

Record, pp. 84-85 (March 1961). [B12] Barber, R. E., "Short-term frequency stability of precision

oscillators and frequency generators," Bell Sys. Tech. J., 50, No. 3, pp. 881-915 (March 1971).

B denotes bibliographic listing.

[B13] Barnes, J. A., "Studies of frequency stability," Unpublished report (August 1969). [B14] Barnes, J. A., "Frequency measurement errors of passive resonators caused by frequency-modulated exciting

signals," IEEE Trans, on Instrum. and Meas., IM-19,

No. 3, pp. 147-152 (August 1970). [B15] Barnes, J. A., "Atomic timekeeping and the statistics of precision signal generators," Proc. IEEE, 54, No. 2, pp. 207-220 (February 1966). [B16] Barnes, J. A.. "Tables of bias functions, Bi and Bz, for variances based on finite samples of processes with power law spectral densities," Nat. Bur. Stand. (U.S.) Tech. Note 375, 37 pages (USGPO, January 1969). [B17] Barnes, J. A., and Allan, D. W.. "A statistical model of

flicker noise," Proc. IEEE, 54, No. 2, pp. 176-178

(February 1966). [B18] Barnes, J. A., and Allan, D. W., "Effects of long-term stability on the definition and measurement of short-term

stability," Proc. IEEE-NASA Symp. on the Definition and Measurement of Short-Term Frequency Stability, (Goddard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964), NASA SP-80, pp. 119-123 (USGPO, 1965). [B19] Barnes, J. A. et al. (see ref. [R4] ). [B20J Barnes, J. A., and Heim, L. E., "A high-resolution ammonia maser spectrum analyzer," IRE Trans, on Instrum., 1-10, No. 1, pp. 4-8 (June 1961). [B21] Barnes, J. A., and Mockler, R. C, "The power spectrum and its importance in precise frequency measure- ments," IRE Trans, on Instrum., 1-9, No. 2, pp. 149-

155 (September 1960). [B22] Baugh, R. A., "Frequency modulation analysis with the Hadamard variance," Proc. 25th Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 26-28, 1971), pp. 222-225

(NTIS, AD 746221,1971).

[B23] Baugh, R. A., "Low noise frequency multiplication," Proc. 26th Ann. Symp. on Frequency Control (U.S. Army

Electronics Command, Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 50-54 (Electron. Ind. Assn., Washington, DC 20006, 1972). [B24] Becker, G., "Mathematische Filterung von Mebwerten; Anwendungen im Bereich von Zeit und Frequenz"

(Mathematical filtering of measuring values; applications in the scope of time and frequency), PTB Mitt., 79. No. 4, pp. 247-252 (August 1969). [B25] Bendat, J. S., Principles and Applications of Random

Noise Theory, 431 pages (John Wiley and Sons, New

York, NY 10016, 1958). [B26] Bennett, W. R.. Electrical Noise, 280 pages (McGraw-Hill

Book Co., New York, NY 10036, 1960). [B27] Bennett, W. R.. "Methods of solving noise problems,"

Proc. IRE, 44, No. 5, pp. 609-638 (eq 223 ff.) (May

1956). [B28] Berstein, I., and Gorelik, G., "Frequency modulation noise

in oscillators." Proc. IRE (Corresp.), 45, No. 1. p. 94

(January 1957). [B29] Bingham, C, Godfrey, M. D.. and Tukey, J. W., "Modern

techniques of power spectrum estimation," IEEE Trans. Audio, AU-15, No. 2, pp. 56-66 (June 1967). [B30] Blackman, R. B., and Tukey, J. W., The Measurement of Power Spectra, 190 pages (Dover Publishing Co., New

York, NY 10014, 1958). [B31] Brandenberger, H., Hadorn, F., Halford, D., and Shoaf,

J. H., "High quality quartz crystal oscillators: frequency

domain and time domain stability," Proc. 25th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 26-28, 1971), pp. 226-230 (NTIS, AD 746211, 1971). An example

of 11970 "state-of-the-art" measurements.

[B32] Brigham, E. O., and Morrow, R. E., "The fast Fourier transform," IEEE Spectrum; 4, No. 12, pp. 63-70 (December 1967).

184
[B33] Buck, J. R., and Healey, D. J., Ill, "Calibration of short- term frequency stability measuring apparatus," Proc. IEEE (Lett.), 54, No. 2, p. 305 (February 1966). [B34] Buck, J. R., and Healey, D. J., Ill, "Short term frequency

stability measurement of the crystal controlled x-band

source," Proc. IEEE-NASA Symp. on the Definition and

Measurement of Short Term Frequency Stability,"

(Goddard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964), NASA SP-80, pp. 201-209 (USGPO, 1965).

[B35] Buck, J. R., Healey, D. J., Ill, and Meiseles, M., "Measure- ment of phase stability of quartz crystal oscillators for airborne radar applications," IEEE Intern. Conv. Rec,

pt. 8, pp. 34-42 (March 1964). [B36] Campbell, G. A., and Foster, R. M., Fourier Integrals for

Practical Applications, 177 pages (D. Van Nostrand

Reinhold Co., New York, NY 10001, 1948). [B37] Campbell, R. A., "Stability measurement techniques in the frequency domain," Proc. IEEE-NASA Symp. on

the Definition and Measurement of Short-Term Fre- quency Stability (Goddard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964), NASA SP-80,

pp. 231-235 (USGPO, 1965). [B38] Chenette, E. R., "Low noise transistor amplifiers," Solid

State Design, 5_, pp. 27-30 (February 1964).. [B39] Chramiec, J., "Noise properties of a superregenerative

parametric amplifier," Proc. IEEE, 54, No. 4, p. 704

(April 1966). [B40] Crow, E. L., "The statistical construction of a single standard from several available standards," IEEE

Trans, on Instrum. and Meas., IM-13, No. 4, pp. 180-

185 (December 1964). [B41] Cutler, L. S., "Some aspects of the theory and measure- ment of frequency fluctuations in frequency standards "

Proc. IEEE-NASA Symp. on the Definition and Measure- ment of Short-Term Frequency Stability (Goddard

Space Flight Center, Greenbelt, MD 20771, November

23-24, 1964), NASA SP-80, pp. 89-100 (USGPO, 1965). [B42] Cutler, L. S., "Present status in short-term frequency

stability," Frequency, 5, No. 5, pp. 13-15 (SeptemberOctober 1967). This is a well-written, concise progress

report with indications for future effort. Caution: His examples I and II were not in fact state-of-the-art, while example IV shows some typographical errors. [B43] Cutler, L. S., and Searle, C. L., "Some aspects of the theory and measurement of frequency fluctuations in frequency standards," Proc. IEEE, 54, No. 2, pp. 136-

154 (February 1966). This is a useful treatment of some

theory, mathematics, and measurement techniques —

with physical insight into the noise processes of practical concern.

[B44] Davenport, W. B., and Root, W. L., An Introduction to the Theory of Random Signals and Noise, "Spectral

Analysis" Chap. 6, pp. 87-111 (McGraw-Hill Book Co., New York, NY 10036, 1958). [B45] DePrins, J., and Cornelissen, G., "Analyse spectrale discrete" (Discrete spectral analysis) (EUROCON '71, IEEE Region 8 Convention, Lausanne, Switzerland, October 1971), Bull, de VAcademie Royale de Belgique

(Classe des Sciences) 57, Series 5°, pp. 1243-1266

(Palais des Academies, Bruxelles, Belgium, December

1971). [B46] DePrins, J., Descornet, G., Gorski, M., and Tamine, J., "Frequency-domain interpretation of oscillator phase

stability," IEEE Trans, on Instrum. and Meas., IM-18,

No. 4, pp. 251-261 (December 1969). [B47] Driscoll, M. M., "Two-stage self-limiting series mode type

quartz crystal oscillator exhibiting improved short- term frequency stability," Proc. 26th Ann. Symp. on

Frequency Control (U.S. Army Electronics Command,

Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 43-49

(Electron. Ind. Assn., Washington, DC 20006, 1972).

I B48| Dvornikov, E. V., Mavrin, E. A., and Morkovin. N. V., "A

high-stability transistorized crystal oscillator," Pribory

i Tekhn. Eksperim. (USSR), No. 4 (July-August 1963). For English translation see Instr. Exper. Tech., No. 4, pp. 672-674 (Instr. Soc. Amer., Pittsburgh, PA 15222, February 1964). [B49] Edson, W. A., "Noise in oscillators," Proc. IRE, 48,

No. 8, pp. 1454-1466 (August 1969). Note: This paper

is an old "classic." [B50] Edson, W. A., "Progress and problems in short term

stability," Proc. 19th Ann. Symp. on Frequency Control

(U.S. Army Electronics Command, Ft. Monmouth, NJ

07703, April 20-25, 1965), pp. 43-48 (NTIS, AD 471229,

1965). [B51] Esposito, R., and Mullen, J. A., "Noise in oscillators with general tank circuits," IRE Intern. Conf. Rec, pt. 4, pp. 202-208 (March 1961). [B52] Finnie, C, Sydnor, R., and Sward, A., "Hydrogen maser

frequency standard," Proc. 25th Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command,

Ft. Monmouth", NJ 07703, April 26-28, 1971), pp. 348-

351 (NTIS, AD 746211, 1971). [B53] Fey, L., Atkinson, W. R., and Newman, J., "Obscurities of

oscillator noise," Proc. IEEE (Corresp.), 52, No. 1, pp. 104-105 (January 1964). [B54] Gerber, E. A., and Sykes, R. A., "State of the art — quartz

crystal units and oscillators," Proc. IEEE, 54, No. 2, pp. 103-116 (February 1966) (see chaps 2A and 2B). [B55] Gerber, E. A., and Sykes, R. A., "Quartz frequency stand- ards," Proc. IEEE, 55, No. 6, pp. 783-791 (June 1967). [B56] Glaze, D. J.; "Improvements in atomic beam frequency

standards at the National Bureau of Standards," IEEE

Trans, on Instrum, and Meas., IM-19, No. 3, pp. 156-

160 (August 1970) (see chap. 5A). [B57] Golay, M. J. E., "Monochromaticity and noise in a regenerative electrical oscillator," Proc. IRE, 48, No. 8, pp. 1473-1477 (August 1960). [B58] Grauling, C. H., Jr., and Healey, D. J., Ill, "Instrumentation for measurement of the short-term frequency stability of microwave sources," Proc. IEEE, 54, No. 2, pp. 249-257 (February 1966). [B59] Gray, R. M., and Tausworthe, R. C "Frequency-counted measurements and phase locking to noisy oscillators," IEEE Trans, on Comm. Tech., COM-19, No. 1, pp. 21-

30 (February 1971). [B60] Grivet, P., and Blaquiere, A., "Nonlinear effects of noise

in electronic clocks," Proc. IEEE, 51, No. 11, pp. 1606-

1614 (November 1963). [B61] Groslambert, J., Olivier, M., and Uebersfeld, J., "Automatic plotting systems for frequency stability curves and discrete spectral density of frequency standards," IEEE Trans, on Instrum, and Meas., IM-21, No. 4, pp. 405-408 (November 1972). [B62] Hadad, J. D., "Basic relation between the frequency stability specification and the application," Proc. IEEE- NASA Symp. on the Definition and Measurement of

Short-Term Frequency Stability (Goddard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964), NASA SP-80, pp. 11-18 (USGPO, 1965). [B63] Hafner, E., "The effects of noise on crystal oscillators," Proc. IEEE, 54, No. 2, pp. 179-198 (February 1966). [B64] Halford, D, "A general mechanical model for |f| a spectral density random noise with special reference to flicker noise l/|f|," Proc. IEEE, 56, No. 3, pp. 251-258 (March

1968). [B65] Halford, D.. Wainwright, A. E.. and Barnes, J. A., "Flicker

noise of phase in rf amplifiers and frequency multipliers: characterization, cause, and cure," (Summary),

Proc. 22nd Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703,

April 22-44, 1968), pp. 340-341 (NTIS, AD 844911.

1968).

185
[B66] Halford, D., Shoaf, J. H., and Risley, A. S., "Spectral

density analysis: frequency domain specification and measurement of signal stability," Proc. 27th Ann. Symp.

on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 12-14, 1973), pp. 421-431 (Electron. Ind. Assn., Washington, DC

20006, 1973). |B67J Healey, D. J., Ill, "Flicker of frequency and phase and

white frequency and phase fluctuations in frequency

sources," Proc. 26th Ann. Symp. on Frequency Control

(U.S. Army Electronics Command, Ft. Monmouth, NJ

07703, June 6-8, 1972) pp. 43-49 (Electron. Ind. Assn., Washington, DC 20006, 1972). [B68] Hellwig, H., "Frequency standards and clocks: a tutorial introduction," Nat. Bur. Stand. (U.S.) Tech. Note 616, 69 pages (USGPO, April 1972). [B69] Hewlett-Packard. Staff, Frequency and Time Standards,

Application Note 52, 91 pages (Hewlett-Packard, Palo

Alto, CA 94304, 1965). [B70] Hewlett-Packard Staff, Precision Frequency Measurements, Applications Note 116, 12 pages (Hewlett- Packard, Palo Alto, CA 94304, 1969). [B71] Hewlett-Packard Staff, Computing Counter Applications

Library, Nos. 7, 22, 27, 29 (Hewlett-Packard, Palo Alto, CA 94304, 1970). [B72] Holman, R. H., and Paciorek, L. J.. "Short-term stability measurement techniques and results," Proc. IEEE- NASA Symp. on the Definition and Measurement of Short-Term Frequency Stability (Goddard Space Flight Center, Greenbelt, MD 20771, November 23-24, 1964), NASA SP-80, pp. 237-252 (USGPO, 1965). [B73] Johnson, S. L., Smith, B. H., and Calder, D. A., "Noise spectrum characteristics of low-noise microwave tubes and solid-state devices," Proc. IEEE, 54, No. 2, pp. 258-265 (February 1966). [B74] Kartaschoff, P., "Shot-effect influence on the frequency of an oscillator locked to an atomic beam resonator,"

Proc. IEEE-NASA Symp. on the Definition and Measure- ment ofShort-Term Frequency Stability (Goddard Space

Flight Center, Greenbelt, MD 20771, November 23-24,

1964), NASA SP-80, pp. 303-308 (USGPO, 1965). [B75] Kartaschoff, P., and Barnes, J. A., "Standard time and

frequency generation," Proc. IEEE, 60, No. 5, pp. 493-501 (May 1972). [B76] Lacey, R. F., Helgesson, A. L., and Holloway, J. H., "Short-term stability of passive atomic frequency

standards," Proc. IEEE, 54, No. 2, pp. 170-176

(February 1966). [B77] Larson, R. W., "Power spectrum of oscillator and fre- quency multiplier phase jitter," Proc. IEEE (Lett.), 54,

No. 5, pp. 796-799 (May 1966). [B78] Leeson, D. B., "A simple model of feedback oscillator noise spectrum," Proc. IEEE (Lett.), 54, No. 2, pp. 329-330 (February 1966). [B79] Leeson, D. B., and Johnson, G. F., "Short-term stability for a Doppler radar: requirements, measurements, and

techniques," Proc. IEEE, 54, No. 2, pp. 244-248

(February 1966). [B80] Lerner, R. M., "The effect of noise on the frequency

stability of a linear oscillator," Proc. Natl. Electr. Conf. (Chicago, IL, October 22-24, 1951), 7, pp. 275-286

(February 1952). [B81] Lesage, P., and Audoin, C, "Characterization of fre- quency stability: Uncertainty due to the finite number of measurements," IEEE Trans, on lustrum, and Meas., IM-22, No. 2, pp. 157-161 (June 1973). [B82] Malakhov, A. N., "Spectral-correlational analysis of

signals with non-integrable spectra," Izvestiya VUZ.

Radiofizika, 9, No. 3, pp. 595-607 (1966) (English

translation) Soviet Radiophysics, 9, No. 3, pp. 360-366

(Consultants Bureau, New York, NY 10011, MayJune 1966).

[B83] Malakhov, A. N., "Fluctuations in a quartz oscillator," Izvestiya VUZ. Radiofizika, 9, No. 3, pp. 622-624 (1966) (English translation) Soviet Radiophysics, 9, No. 3, pp. 376-377 (Consultants Bureau, New York, NY 1001L May-June 1966). [B84] Malakhov, A. N., "Shape and width of the spectral line of

oscillations in the presence of nonstationary frequency

fluctuations," Izvestiya VUZ. Radiofizika, 9,|No. 3, pp. 625-627 (1966) (English translation) Soviet Radiophysics, 9, No. 3, pp. 378-379 (Consultants Bureau, New York, NY 10011, May-June 1966). [B85] Malakhov, A. N., and Solin, N. N., "Fluctuations in a quartz oscillator," Izvestiya VUZ. Radiofizika, 12, No.

4, pp. 529-537 (April 1969) (English translation) Radiophysics and Quantum Electronics, 12, No. 4, pp. 419-

425 (Consultants Bureau, New York, NY 10011, April 1969). [B86] Mailing, L., "Phase-stable oscillators for space communications, including the relationship between the phase

noise, the spectrum, the short-term stability, and the Q of the oscillator," Proc. IRE, 50, No. 7, pp. 1656-

1664 (July 1962). [B87] Mandelbrot, B., "Some noises with 1/f spectrum, a bridge between direct current and white noise," IEEE Trans, on Inform. Theory, IT-13, No. 2, pp. 289-298 (April

1967). [B88] McDade, J. C, "Measurement of additive phase noise contributed by the step-recovery diode in a frequency

multiplier," Proc. IEEE (Lett.), 54, No. 2, pp. 292-294

(February 1966). [B89] Meyer, D. G., "A test set for measurement of phase noise on high quality signal sources " IEEE Trans, on lustrum, and Meas., IM-19, No. 4, pp. 215-227 (November

1970). [B90] Morgan, A. H., and Barnes, J. A., "Short-time stability of a quartz-crystal oscillator as measured with an ammonia maser," Proc. IRE (Corresp.), 47, No. 10,

p. 1972 (October 1959). [B91] Mullen, J. A., "Background noise in nonlinear oscillators," Proc. IRE, 48, No. 8, pp. 1467-1473 (August 1960). [B92] Mullen, J. A., "Background noise in oscillators with rf pushing," J. Electron, and Control, 10, pp. 127-138

(February 1961). [B93] Okoshi, T., Hashiguchi, S., and Kotani, M., "A new

method of measuring microwave oscillator noises (longline method)," Electron, and Commun. in Japan, 53-B,

No. 8, pp. 80-85 (August 1970). [B94] Ondria, J. G., "A microwave system for measurements of AM and FM noise spectra," IEEE Trans, on Microwave

Theory and Techniques, MTT-16, No. 9, pp. 767-781 (September 1968). [B95] Paradysz, R. E., and Smith, W. L.. "Measurement of FM

noise spectra of low-noise VHF crystal controlled oscil- lators," IEEE Trans, on lustrum, and Meas., IM-15,

No. 4, pp. 202-211 (December 1966). [B96] Peterson, M. E., "The design and performance of an ultra low-noise digital frequency synthesizer for use in VLF

receivers," Proc. 26th Ann. Symp. on Frequency Control, (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 55-70 (Electron. Ind. Assn., Washington, DC 20006, 1972). [B97] Prabhu, V., "Noise performance of abrupt-junction var- actor frequency multipliers," Proc. IEEE (Lett.), 54,

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York University, New York, NY 10003, July 1-September 30, 1961). [B99] Reeve, G. R., "Signal detection systems," unpublished

report (Sponsored by Army/Navy/Air Force, JTCGMETCAL/CCG on Cont. 69-25b, October 1967).

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[B100] Rihaczek, A. W., "Signal energy distribution in time and

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V. J., "Computer-aided calculation of frequency,"

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Flight Center, Greenbelt, MD 20771, November 23-24,

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(April 1969) (English translation) Radiophysics and

Quantum Electronics, 12, No. 4, pp. 426-429 (Consultants Bureau, New York, NY 10011, April 1969). ANNEX 8.H

DETAILED PROCEDURE FOR CALIBRATING MICROWAVE (FREQUENCY-STABILITY) MEASUREMENT SYSTEM

The reader is referred to figure 8.17 in following

the step-wise calibration procedure below. Note that a sinusoidally-modulated X-band frequency source

is used to drive the system to facilitate the calibration. (For a general overview of the method see sec.

8.15.3.)

(a) With the discriminator cavity (M) far off resonance, set the level of the X-band signal (as

determined with a dc voltmeter (P) at the detector

(N)) to a convenient value and record the value. The

first variable attenuator (B) should be used for this adjustment. Any convenient level may be chosen

provided an equal amount of power also will be

available from the signal source which is to be

evaluated.

(b) Attenuate the intentional modulation so that no sidebands are visible on the power spectral

density analyzer (see sec. 8.15.3).

(c) Adjust the cavity to resonance. The dc volt- meter at the detector is used to determine reso- nance. Place the dc voltmeter at the output of the

mixer (H) and adjust the phase shifter (F) in the

reference channel until the dc output at the mixer

is zero (phase quadrature). Remove the dc voltmeter

and connect the output of the mixer to a spectrum

analyzer (Q) tuned to the modulation frequency, 5 kHz. Replace the intentional modulation so that the

187
carrier is, again, fully suppressed. Record the rms

voltage reading ( Vrms ) of the spectrum analyzer.

(d) It is now possible to calculate the calibration

factor K.

K

(Af),

(8H.1)

where (Av)^ is the rms frequency deviation of the

carrier due to intentional frequency modulation.

This deviation is calculated using the equation

(Av) ms = 0.707 (Av) peak (8H.2)

where (At, ) peak is the product of the modulation

index with the frequency of sinusoidal modulation,

i.e., 2.405 X 5 kHz = 12.025 kHz. Therefore the cali- bration factor in our case is

K

0.707(12.025 kHz) 8.51kHz

(8H.3)

ANNEX 8.1

MEASUREMENT PROCEDURE FOR

DETERMINING FREQUENCY STABILITY IN THE MICROWAVE

REGION

The ensuing detailed steps are given to aid one

in determining frequency stability of microwave

sources. Referral to figure 8.17 will help in following

the sequence of the test procedure. The procedure

includes instruction and example on the calculation

and presentation of Ss<t>(f)-

(a) Be sure the intentional modulation has been

completely removed from the X-band source. With

the cavity far off resonance, set the level at the

detector to the same value obtained during calibration. Use the variable attenuator (B) for this adjust- ment. The other variable attenuators (E) and (J) are

set to zero.

(b) Adjust the cavity frequency to that frequency

of the X-band source. Adjust the phase shifter (F) so that the dc output at the mixer (H) is zero. Attach

the spectrum analyzer to the output of the mixer

and record rms voltage readings (V'Tms ) for various

frequency settings of the spectrum analyzer. A low

noise amplifier may be necessary to obtain useful

readings at large Fourier frequencies. A second

reading (V'rms) should be taken at each value off

with the signal strongly attenuated in the signal

channel. This is to record the residual additive

background noise not attributable to actual phase

noise on the carrier. This attenuation is accomplished by inserting all (> 20 dB) of the attenuation

in the variable attenuator (J). (c) In order to calculate values of Ss<t>(f) for plotting at various Fourier frequencies, it is con- venient to make a tabulation of results. An example

of some typical results is given in table 8.1.1. The

following relations are used:

^rms= V(rrms ) 2 -(rr

'ms ) 2

- (8.1.1)

(8.1.2)

(°>rms)

2

Sv rms — Vrms x K

S8v (f) =

B

(8.1.3)

where B is the bandwidth at which the readings were made on the spectrum analyzer, and

S 6*(/) =

SsAf)

f

2 (8.1.4)

Values of Ssj, (/) which were calculated this way

(table 8.1.1) are plotted in figure 8.18.

188
TABLE 8.1.1. Tabulation ofS^ff) at various Fourier frequencies

/(Hz)

f

(Hz2

)

B

(Hz)

^rms &*V)Sarins (Hz)(Sl^rms) 2

(Hz2

)

StAf)

(Hz)

St*(f)

(dB) a

5X103 2.5 x 10 7

(74 dB) b 100 660 6.38 40.7 0.41 (-3.9 dB) e -77.9

2.5 X 103 6.2 x 10" (68 dB)

100 780 7.54 56.9 0.57 (-2.4 dB)

-70.4

1 x 103 1.0 x 106

(60 dB)

100 1000 9.67 93.5 0.94 (-0.3 dB)

-60.3

640 4.1 x 105

(56 dB)

10 1200 11.6 135.0 1.4(1.5 dB)

-54.5

320 1.0 x 105

(50 dB)

10 460 4.45 19.8 2.0

(3.0 dB)

-47.0

210 4.4 X 104

(46 dB)

10 580 5.61 31.5 3.2

(5.1 dB)

-40.9

150 2.2 x 104

(44 dB)

10 680 6.58 43.3 4.3

(6.3 dB)

-37.7

90 8.1 x 103

(39 dB)

1 230 2.22 4.93 4.9

(6.9 dB)

-32.1

40 1.6 x 103

(32 dB)

1 300 2.90 8.41 8.4

(9.3 dB)

-22.7

20 400

(26 dB)

1 450 4.35 18.9 19.0(12.8 dB)

-13.2

10 100

(20 dB)

1 700 6.77 45.8 46.0

(16.6 dB)

-3.4

a Ss<t,(/) is tabulated in decibels relative to 1 radian2 Hz" 1

b dB relative to 1 Hz2

c dB relative to 1 Hz2 Hz-'

Calibration factor K= —

— = 9.67 x 103 Hz/V.

189
ANNEX 8.J

TABLES OF BIAS FUNCTIONS, B,

AND B 2 , FOR VARIANCES BASED

ON FINITE SAMPLES OF PROCESSES WITH POWER LAW

SPECTRAL DENSITIES9

8.J.I. Description of the Bias Functions, B\ and B >

Following Allan [8] consider a random process

y(t) with continuous sample functions. We assume

that y{t) has a spectral density, S </(/), which obeys

the law

Sy (f) = h\f\ a ,fi<\f\<fn , (8.J.1)

where h is a constant, the limit frequencies fi and

fu satisfy the relations

and any intervals of time, At, of any significance

satisfy the relations

1 . 1 Jh Jl

In short, y(t) has a power law spectral density over

the entire range of significance.

Consider a measurement process which deter- mines an average value of y{t) over the interval

t to t + r. That is,

-I ( t+T y{t')dt'. (8.J.2)

One, now, may determine an estimated variance

from a group of N such measurements spaced every

T units of time; that is,

<tHN, T,t)

1 JL NX r -J {f(t+n T)

%y(t+ kT)\* (8.J.3)

fc= i N '

Allan [8] has shown that under these conditions,

(o-2 (N, T, t)> « tk yy and T/t constant,

'From Barnes, J. A., Nat. Bur. Stand. (U.S.) Tech. Note 375 (January 1968) [3); references are identical to those given in the main body of Chapter 8.

where fi is related 10 to a according to the mapping

shown in figure 8.1 (see ref. [8] and [26]). The

relation between fi and oc may be given as

{- 2 if a 3* 1 — oc — 1 if — 3 < a

not defined othen

1 otherwise.

This mapping involves a simple extension of

Allan's work [8] to the range 0 < /x < 2. This extension was also mentioned in [20]. Allan [8] considered in some detail the case where T—t. This is the case of exactly adjacent

sample averages — no "dead time" between measurements. Allan defined a function, x(^' as follows

<Q- 2 (/V, T, T)>

<o-f,(2,r, T)>

(8.J.4)

where it is again assumed that

(o-'-N, t, t)> « N constant.

Allan shows [8] that experimental evaluations of

X(/V, fi) may be used to infer fx and hence the

spectral type by use of the mapping of figure 8.1. Since many experiments actually have dead

time present, it is of value to make two different extensions of this function, x(^' A1 )- First, define

Bi (N, r, fi) by the relations

B (N r ri- <"UN> T*r))

(8.J.5)

where r = T/t and

(a2y (N, T, t)> « t^, and r constant.

The second function, Bz{r, fi) , is defined according

to the relation

B2 (r, (j,) =

<o2,(2, T, t))

(o-2,(2,t, t)>

(8.J.6)

where r=T/r. In words, B\ is the ratio of the

expected variance for iV samples to the expected

variance for 2 samples (everything else fixed);

while Z?2 is the ratio of the expected variance with

10 It should be noted that in reference [8] the exponent, a, corresponds to the spec- trum of phase fluctuations while variances are taken over average frequency

fluctuations. In the present paper, or is equal to the exponent, a, in [8] plus two. Thus,

in this paper, all considerations are confined to one variable, y{t) (analogous to fre- quency in [8]) and the spectral density of y, Sy (f). This paper does not consider the spectrum of the integral of y{t). 190
dead time to that of no dead time (with N—2 and

t held constant). The B's, then, reflect bias relative

to N=2 rather than /V=°°. It is apparent that Bt (N, r=hfi) = X (N,fi).

For the conditions given above and with reference

to Allan [8], one may write expressions for both

B\ and B2 , as follows:

#i(/V,r,/x)

i+2 NN(N-l) I 2\nr\» +2 - \nr+ 1 k+2 ~ \nr-l \n

1 + 2|rk +2 — Ir+lW* 2 — \r — lkH

in particular for r — 1

,

N(l-N»)

2{N-1) (1-2**)'

(8.J.7)

(8.J.8)

and

B2 (r,fi)

1+

l

2|rh + 2 -|r+lk+2 - |r-lk+2

2(1-2")

(8.J.9)

except that by definition, B2 (l, ll) — 1. The magnitude bars are essential on the r — 1 term when

r < 1, and, indeed, proper. Since Allan was

involved with r 2= 1 the magnitude bars were dropped

in reference [8]. For ^=0, eqs (8.J.7), (8.J.8), and (8.J.9) are in- determinate of form 0/0 and must be evaluated by

L'Hospital's rule. Special attention must also be

given when expressions of the form 0° arise. One may obtain the following results:

B,(2,r,/x) - 1

N

5,(^,1,1)=-

B^N, r,-l) = lifr3* 1 Bi(N, r,-2) = lifr^ 1 or 0

B2 (0,n) = 0

B2 (l,/i)=l. fi 2 (r,2) = r

2

fl2 (r,l)=|(3r-l)ifr^ 1 R(r n

_frif0^r^l

f0ifr=0

B»(r,-2) = 1 if r= 1

I 2/3 otherwise

Values of the functions Bx (N, r, ll ) and B2 ( r . ll ) are tabulated on the following pages for values of

N, r, ll as shown below:

ll = - 2.0 to 2.0 in steps of 0.2; N = 4, 8, 16, 32, 64, 128, 256, 512, 1024,

«

; r = 0.001, 0.003, 0.01, 0.03, 0.1, 0.2, 0.4, 0.8, 1, 1.01, 1.1, 2, 4, 8, 16, 32, 64, 128, 256, 512,

1024, 2048, ».

Figure 8.3 is a graphical representation of B2 (r, ll) forO =s r < 2 and- 2 =£ ll < 2.

8.J. 1.1. Examples of the Use of the Bias

Function

The spectral type, that is, the value of ll, may be

inferred by varying t, the sample time [8, 26]. Another convenient way, however, of determining

the value of ll is by using Bi(N, r, /i.) as follows: calculate an estimate of (cr 2 (/V, T, t)) and of

(cr 2 (2, T, r) ) and hence Bi (N, r, ll) ; then by use of

the tables the value of ll may be inferred.

Suppose one has an experimental value of

(o- 2 (/Vi, Ti, Ti)) and its spectral type is known —

that is, ll is known. Suppose also that one wishes to know the variance at some other set of measure- ment parameters, N2 , T2 , t2 . An unbiased estimate of

(tTy(N2 , T2 , t2 )) may be calculated by the equation:

(o-2 (/v2 ,r2 ,r2 ))

r2 B r (N2 ,r2 ,LL)B2 (r2 ,LL) y

rj lB l (Nu rl ,LL)B2 (r l ,LL) }

<<r«(JVi,ri,n)),

(8.J.10)

where r\ = T\\T\ and r2 = T2 /t2. Obviously one might be interested in iV2 = x. In this case if ll S5 0, the expected value of

(Ty (°°, T2 , t2 ) is also infinite. This is true because,

for ll ^ 0. Also, it

Limfi,(yV2 ,r2,Ai) =

should be noted that, for ll = 2,

(o-y^/V, T, t) ) is a function of /; for any N 3= 2, T, t, even though B X (N, r, 2) and B2 (r, 2) as determined

from eqs (8.J.7), (8.J.8), and (8. J.9) are finite and well

behaved [20]. In this region, ll ~ 2, the low fre- quency behavior is critically important.

8.J.2. ACKNOWLEDGEMENTS

Acknowledgement is given to Mrs. Bernice Bender

who capably assisted in writing the computer pro- grams and evaluated the functions.

191
Table 8.J.I. Functions ofB, and B2 The tables are typeset from a computer printout. Each entry for the value of the functions. Bi and B2 consists of a decimal number

followed by an integer which is the exponent of 10. Ten raised to this power should multiply the decimal number. Thus the table entry "2.752 + 003" could be written 2.752X 103 or, simply 2752. Similarly. "9.869 -001" = 9.869 X 10' = 0.9869. Note for the specific case where /la = —2: As can be seen from figure 8.1, the value of a is ambiguous for this case (a 5= + l). The

values tabulated for £i =—2 are for a = +2 (white noise phase modulation). Slight variations occur (of a few percent) in#i(/V, r, fi= —2) and B2 (r, ft——2) if a=+l , and if 2-rrrfh is not very large compared to 1. If very precise variance information is desired in such a case as a=+l (flicker noise phase modulation), it is recommended that one use the fundamental equations given in table 8.1.

BAN. r, fj. ) for r = 0.001 N

4 8 16 32 64 128 256 512 1024 00

2.00 3 333 + 000 1 200 + 001 4.533 + 001 1 760 + 002 6 933 + 002 2 752 + 003 l 097 + 004 4 378 + 004 1 749 + 005 00 1.80 3 333 + 000 1 200 + 001 4 533 + 001 1 760 + 002 6 931 + 002 2 749 + 003 1 099 4- 004 4 326 + 004 1 690 + 005 00 1.60 3 333 + 000 1 200 + 001 4.533 + 001 1 759 + 002 6 926 + 002 2 743 + 003 1.087 + 004 4 265 + 004 1 628 + 005 00 1.40 3 333 + 000 1 200 + 001 4.532 + 001 1 758 + 002 6 916 + 002 2 734 + 003 1.078 + 004 4 187 + 004 1 560 + 005 oo 1.20 3 333 + 000 1 200 + 001 4.529 + 001 1 756 + 002 6 894 + 002 2 716 + 003 1.064 + 004 4 081+004 1 484 + 005 00 1.00 3 332 + 000 1 199 + 001 4.520 + 001 1 749 + 002 6 847 + 002 2 682 + 003 1.041 + 004 3 931+004 1 392 + 005 00 0.80 3 328 + 000 1 195 + 001 4.497 + 001 1 733 + 002 6 743 + 002 2 617 + 003 1.001 + 004 3 708 + 004 1 276 + 005 00 0.60 3 317 + 000 1 186 + 001 4.435 + 001 1 695 + 002 6 519 + 002 2 491 + 003 9.344 + 003 3 373 + 004 1 124 + 005 oo 0.40 3 284 + 000 1 161 + 001 4.280 + 001 1 608 + 002 6 058 + 002 2 259 + 003 8.233 + 003 2 877 + 004 9 247 + 004 00 0.20 3 200 + 000 1 101+001 3.943 + 001 1 435 + 002 5 220 + 002 1 875 + 003 6.563 + 003 2 200 + 004 6 786 + 004 00 -0.00 3 027 + 000 9 877 + 000 3.354 + 001 1 157 + 002 3 985 + 002 1 355 + 003 4.491 + 003 1 429 + 004 4 201 + 004 00 -0.20 2 761 + 001 8 268 + 000 2.585 + 001 8 231 + 001 2 624 + 002 8 281 + 002 2.558 + 003 7 622 + 003 2 120 + 004 3 066 + 005 -0.40 2 450 + 000 6 549 + 000 1.837 + 001 5 269 + 001 1 520 + 002 4 365 + 002 1.235 + 003 3 399 + 003 8 860 + 003 6 507 + 004 -0.60 2 150 + 000 5 053 + 000 1.250 + 001 3 172 + 001 8 138 + 001 2 089 + 002 5.325 + 002 1 335 + 003 3 224 + 003 1 592 + 004 -0.80 1 888 + 000 3 881 + 000 8.397 + 000 1 868 + 001 4 211 + 001 9 545 + 001 2.162 + 002 4 865 + 002 1 076 + 003 3 983 + 003 -1.00 1 667 + 000 3 000 + 000 5.667 + 000 1 100 + 001 2 167 + 001 4 300 + 001 8.567 + 001 1 710 + 002 3 417 + 002 1 000 + 003 -1.20 1 482 + 000 2 344 + 000 3.868 + 000 6 547 + 000 1 124 + 001 1 945 + 001 3.386 + 001 5 936 + 001 1 057 + 002 2 512 + 002 -1.40 1 327 + 000 1 854 + 000 2.680 + 000 3 959 + 000 5 921 + 000 8 924 + 000 1.353 + 001 2 068 + 001 3 236 + 001 6 310 + 001 -1.60 1 198 + 000 1 487 + 000 1.890 + 000 2 442 + 000 3 185 + 000 4 179 + 000 5.511 + 000 7 317 + 000 9 946 + 000 1 585 + 001 -1.80 1 091 + 000 1 210 + 000 1.360 + 000 1 541+000 1 757 + 000 2 010 + 000 2.306 + 000 2 656 + 000 3 106 + 000 3 981 + 000 -2.00 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000

Bi(N, r, fi) for r= 0.003

N

M 4 8 16 32 64 128 256 512 1024 OO 2 oo 3 333 + 000 1 200 + 001 4 533 + 001 1 760 + 002 6.933 + 002 2.752 + 003 1 097 + 004 4.378+004 1.749 + 005 OO

1 HO 3 333 + 000 1 200 + 001 4 532 + 001 1 759 + 002 6.917 + 002 2.732 + 003 1 072 + 004 1.112 + 004 1.514 + 005 OO

1 60 3 333 + 000 1 200 + 001 4 530 + 001 1 756 + 002 6.892 + 002 2.706 + 003 1 046 + 004 3.854 + 004 1 311 + 005 00

1 40 3 333 + 000 1 199 + 001 4 526 + 001 1 752 + 002 6.853 + 002 2.671 + 003 1 015 + 004 3.596 + 004 1 132 + 005 oo

1 20 3 332 + 000 1 198 + 001 4 516 + 001 1 744 + 002 6.788 + 002 2.620 + 003 9 774 + 003 3.330 + 004 9 717 + 004 00

1 00 3 329 + 000 1 195 + 001 4 494 + 001 1 728 + 002 6.674 + 002 2.543 + 003 9 290 + 003 3.043 + 004 8 254 + 004 oo 0 80 3 321 + 000 1 189 + 001 4 446 + 001 1 696 + 002 6.473 + 002 2.425 + 003 8 645 + 003 2.721 + 004 6 875 + 004

0 60 3 302 + 000 1 173 + 001 3 342 + 001 1 634 + 002 6.124 + 002 2.242 + 003 7 765 + 003 2.346 + 004 5 536 + 004 oo 0 40 3 256 + 000 1 138 + 001 4 132 + 001 1 519 + 002 5.544 + 002 1.967 + 003 6 584 + 003 1.907 + 004 4 210 + 004 oo 0 20 3 157 + 000 1 069 + 001 3 753 + 001 1 330 + 002 4.667 + 002 1.589 + 003 5 103 + 003 1.414 + 004 2 927 + 004 00 -0 00 2 981 + 000 9 558 + 000 3 177 + 001 1 066 + 002 3.541 + 002 1.143 + 003 3 490 + 003 9.224 + 003 1 794 + 004 00 -0 20 2 729 + 000 8 054 + 000 2 474 + 001 7 694 + 001 2.377 + 002 7.169 + 002 2 061 + 003 5.175 + 003 9 470 + 003 4.488 + 004 -0 40 2 435 + 000 6 454 + 000 1 790 + 001 5 052 + 001 1.425 + 002 3.955 + 002 1 058 + 003 2.511 + 003 4 330 + 003 1.142 + 004 -0 60 2 145 + 000 ."> 024 + 000 1 236 + 001 3 112 + 001 7.881 + 001 1.982 + 002 4 870 + 002 1.085 + 003 1 765 + 003 3.434 + 003 -0 80 1 887 + 000 3 876 + 000 8 372 + 000 1 857 + 001 4.167 + 001 9.363 + 001 2 085 + 002 4.326 + 002 6 638 + 002 1.066 + 003 -1 oil 1 667 + 000 3 000 + 000 5 667 + 000 1 100 + 001 2.167 + 001 4.300 + 001 8 567 + 001 1.637 + 002 2 368 + 002 3.333 + 002 -1 20 1 482 + 000 2 344 + 000 3 870 + 000 6 556 + 000 1.128 + 001 1.960 + 001 3 451 + 001 6.001+001 8 168 + 001 1.043 + 002 -1 40 1 328 + 000 1 854 + 000 2 681 + 000 3 964 + 000 5.941 + 000 9.001 + 000 1 386 + 001 2.159 + 001 2 756 + 001 3.264 + 001 -1 60 1 199 + 000 1 487 + 000 1 890 + 000 2 443 + 000 3.191 + 000 4.205 + 000 5 623 + 000 7.711 + 000 9 174 + 000 1.021 + 001 -1 80 1 091 + 000 1 210 + 000 1 360 + 000 1 542 + 000 1.759 + 000 2.016 + 000 2 331 + 000 2.759 + 000 3 031 + 000 3.196 + 000 -2 00 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000

192
Bi(N, r, fi) forr = 0.010

JV

IX 4 8 16 32 64 128 256 512 1024 00

2.00 3 333 + 000 1 200 + 001 4.533 + 001 1 760 + 002 6.933 + 002 2.752 + 003 1.097 + 004 4.378 + 004 1.749 + 005 oc 1.80 3 333 + 000 1 199 + 001 4.526 + 001 1 750 + 002 6.819 + 002 2.623 + 003 9.737 + 003 3.493 + 004 1.231+005 00 1.60 3 332 + 000 1 198 + 001 4.514 + 001 1 738 + 002 6.688 + 002 2.493 + 003 8.637 + 003 2.793 + 004 8.697 + 004 00 1.40 3 330 + 000 1 196 + 001 4.494 + 001 1 720 + 002 6.530 + 002 2.359 + 003 7.640 + 003 2.234 + 004 6. 169 + 004 00 1.20 3 327 + 000 1 192 + 001 4.461 + 001 1 693 + 002 6.330 + 002 2.215 + 003 6.717 + 003 1.782 + 004 4.383 + 004 00 1.00 3 319 + 000 1 185 + 001 4.403 + 001 1 653 + 002 6.066 + 002 2.055 + 003 5.842 + 003 1.412 + 004 3.109 + 004 00 0.80 5

QflO _1_ HAH i

i 1 7A _1_ (\f\ 1 4.303 + 001 1X 5.708 + 002 1.869 + 003 4.991+003 1.104 + 004 2.189 + 004 00 0.60 3 268 + 000 1 143 + 001 4.133 + 001 1 495 + 002 5.221+002 1.649 + 003 4.142 + 003 8.419 + 003 1.514 + 004 00 0.40 3 203 + 000 1 095 + 001 3.857 + 001 1 354 + 002 4.572 + 002 1.390 + 003 3.287 + 003 6.172 + 003 1.014 + 004 00 0.20 3 089 + 000 1 018 + 001 3.448 + 001 1 162 + 002 3.763 + 002 1.097 + 003 2.446 + 003 4.263 + 003 6.453 + 003 00 -0.00 2 912 + 000 9 076 + 000 2.909 + 001 9 282 + 001 2.857 + 002 7.951 + 002 1.672 + 003 2.719 + 003 3.826 + 003 00 -0.20 2 677 + 000 7 714 + 000 2.296 + 001 6 836 + 001 1.976 + 002 5.220 + 002 1.036 + 003 1.580 + 003 2.084 + 003 5.581 + 003 -0.40 2 407 + 000 6 279 + 000 1.703 + 001 4 655 + 001 1.247 + 002 3.106 + 002 5.814 + 002 8.357 + 002 1.043 + 003 1.715 + 003 -0.60 2 134 + 000 4 959 + 000 1.205 + 001 2 977 + 001 7.296 + 001 1.697 + 002 2.995 + 002 4.076 + 002 4.851 + 002 6.423 + 002 -0.80 1 884 + 000 3 860 + 000 8.303 + 000 1 828 + 001 4.041+001 8.691+001 1.443 + 002 1.868 + 002 2.137 + 002 2.519 + 002 -1.00 1 667 + 000 3 000 + 000 5.667 + 000 1 100 + 001 2.167 + 001 4.255 + 001 6.628 + 001 8.190 + 001 9.064 + 001 1.000 + 002 -1.20 1 482 + 000 2 346 + 000 3.880 + 000 6 598 + 000 1.145 + 001 2.026 + 001 2.947 + 001 3.486 + 001 3.754 + 001 3.980 + 001 -1.40 1 328 + 000 1 856 + 000 2.688 + 000 3 991+000 6.054 + 000 9.500 + 000 1.282 + 001 1.456 + 001 1.532 + 001 1.585 + 001 -1.60 1 199 + 000 1 487 + 000 1.893 + 000 2 455 + 000 3.239 + 000 4.440 + 000 5.505 + 000 6.002 + 000 6.198 + 000 6.309 + 000 -1.80 1 091 + 000 1 210 + 000 1.360 + 000 1 545 + 000 1.772 + 000 2.089 + 000 2.349 + 000 2.456 + 000 2.494 + 000 2.512 + 000 -2.00 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000

fi,(/V, r, fi) for r= 0.030 N

4 8 16 32 64 128 256 512 1024 00

2.00 3.333 + 000 1 200 + 001 4 533 + 001 1.760 + 002 6.933 + 002 2.752 + 003 1.097 + 004 4.378 + 004 1.749 + 005 00 1.80 3.331 + 000 1 196 + 001 4 487 + 001 1.706 + 002 6.374 + 002 2.304 + 003 8.142 + 003 2.849 + 004 9.936 + 004 00 1.60 3.327 + 000 1 191 + 001 4 431+001 1.650 + 002 5.851+002 1.930 + 003 6.068 + 003 1.866 + 004 5.684 + 004 00 1.40 3.320 + 000 1 184 + 001 4 360 + 001 1.588 + 002 5.352 + 002 1.615 + 003 4.535 + 003 1.228 + 004 3.276 + 004 00 1.20 3.309 + 000 1 172 + 001 4 267 + 001 1.518 + 002 4.867 + 002 1.348 + 003 3.392 + 003 8.128 + 003 1.903 + 004 00 1.00 3.290 + 000 1 155 + 001 4 141 + 001 1.437 + 002 4.382 + 002 1.117 + 003 2.533 + 003 5.395 + 003 1.114 + 004

0.80 3.257 + 000 1 128 + 001 3 966 + 001 1.339 + 002 3.887 + 002 9.152 + 002 1.879 + 003 3.580 + 003 6.554 + 003 00 0.60 3.203 + 000 1 087 + 001 3 728 + 001 1.220 + 002 3.372 + 002 7.357 + 002 1.376 + 003 2.364 + 003 3.868 + 003 00 0.40 3.118 + 000 1 027 + 001 3 412 + 001 1.077 + 002 2.835 + 002 5.750 + 002 9.868 + 002 1.541 + 003 2.277 + 003 00 0.20 2.992 + 000 9 460 + 000 3 013 + 001 9.127 + 001 2.286 + 002 4.324 + 002 6.856 + 002 9.834 + 002 1.328 + 003 00 -0.00 2.819 + 000 8 430 + 000 2 546 + 001 7.348 + 001 1.748 + 002 3.096 + 002 4.568 + 002 6.082 + 002 7.611 + 002 00 -0.20 2.604 + 000 7 242 + 000 2 047 + 001 5.581+001 1.259 + 002 2.094 + 002 2.897 + 002 3.619 + 002 4.256 + 002 8.571 + 002 -0.40 2.362 + 000 6 005 + 000 1 566 + 001 3.993 + 001 8.524 + 001 1.335 + 002 1.744 + 002 2.066 + 002 2.314 + 002 3.099 + 002 -0.60 2.114 + 000 4 838 + 000 1 147 + 001 2.706 + 001 5.441 + 001 8.049 + 001 9.997 + 001 1.134 + 002 1.225 + 002 1.403 + 002 -0.80 1.878 + 000 3 825 + 000 8 141 + 000 1.753 + 001 3.304 + 001 4.626 + 001 5.499 + 001 6.029 + 001 6.341 + 001 6.770 + 001 -1.00 1.667 + 000 3 000 + 000 5 667 + 000 1.100 + 001 1.928 + 001 2.560 + 001 2.929 + 001 3.127 + 001 3.229 + 001 3.333 + 001 -1.20 1.484 + 000 2 355 + 000 3 918 + 000 6.768 + 000 1.093 + 001 1.378 + 001 1.525 + 001 1.595 + 001 1.626 + 001 1.651+001 -1.40 1.329 + 000 1 863 + 000 2 719 + 000 4.133 + 000 6.080 + 000 7.268 + 000 7.815 + 000 8.044 + 000 8.135 + 000 8.191 + 000 -1.60 1.199 + 000 1 491 + 000 1 910 + 000 2.532 + 000 3.341 + 000 3.782 + 000 3.963 + 000 4.030 + 000 4.053 + 000 4.064 + 000 -1.80 1.091+000 1 211 + 000 1 366 + 000 1.573 + 000 1.827 + 000 1.950 + 000 1.995 + 000 2.010 + 000 2.015 + 000 2.016 + 000 -2.00 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000

193
fii (/V, r, n) foYr= 0.100 N

M 4 8 16 32 64 128 256 512 1024 00

2.00 3.333 + OOU 1.2UU + UU1 4 533 + 001 1. /6U + UOz 933 + 002 O ICO 1 AAO z.752 + 003 1.U97 + 004 4.o7o + UU4 1.749 + 005 00

i on l.oU q q i c _i_ Ann 1 1 7/1 _l_ AA1 1 . 1 / 4- + UU

1

4 252 + 001 l.Dl / + UUZ 5 330 + 002 1.O0O + U03 a /IA7 _i_ nno 0.40/ + UU3 O OCA _i_ mi 1 1 Z.ZOU + UU4 /.B3U + 0U4 GO

l AA 1 .OU 3 003 _i_ nnn 1 1 /1 7 _i_ AA1 1. 14/ i UU1 3 982 + 001 i 3no _i_ n/io 1 . oUy -r UUz 4 113 + 002 1 OA 3 i flf\9 1.Z03 + UU3 3 CM 3 _1_ flflQ O.o4o + UUo 1 1 AA _l_ (WflA 1 . lOO -r UU4 o.ooo + UU4

1 Afi d.zOd -r UUU 1 HO i_ AA1 l.llo-r UU1 3 721 + 001 1 . loU -r UUz 3 183 + 002 o.Ooo T UUZ Z.3U4 + UUo A 1 AQ _l_ AAQ O. lUO T" UUO 1.013 + UU4 2

1 OA 1 .ZU o.zoU T UUU 1 ACM _l_ AA

1

1 . Uo4 T UU 1 3 463 + 001 V. < Zo -f- UU1 2 470 + 002 o.y'to t uuz l.oy* -r UUo 3 OQO _i_ AAO a.ZoZ i UUo / .4bo + UU3

iI.UUnn o. lo4 + UUU 1 fiA C. _U AA 1 1.U40 -r UU1 3 204 + 001 c 3,17/ -t_ T nmUU1 1 918 + 002 1 1^ -r UUZ q _i_ nno o.OZo T UUz 1 7QC i AAQ 1 . / OO T UUO 3 i;nn _i_ nn3 o.DUU -r UUo

AU.oUQA 3 i 03 _i_ nnn o. izo -r UUU O QQQ _l_ AAA y.voy t uuu 2 938 + 001 / . 1 lo T UU1 1 487 + 002 Z.oOz + UUz c oao _l nno o.zoy + UUz O A AA _J_ AAO y.40o t UUz i A7Q _i_ nno 1.0(O + UU3

0.60 3.043 + 000 9.445 + 000 2 663 + 001 6.014 + 001 1 149 + 002 1.999 + 002 3.295 + 002 5.265 + 002 8.254 + 002 GO 0.40 2.940 + 000 8.804 + 000 2 376 + 001 5.015 + 001 8 816 + 001 1.397 + 002 2.084 + 002 2.993 + 002 4.194 + 002 00 0.20 2.810 + 000 8.065 + 000 2 080 + 001 4.111 + 001 6 690 + 001 9.750 + 001 1.331 + 002 1.741 + 002 2.214 + 002 00 -0.00 2.653 + 000 7.236 + 000 1 779 + 001 3.300 + 001 5 003 + 001 6.771 + 001 8.566 + 001 1.037 + 002 1.219 + 002 00 -0.20 2.472 + 000 6.344 + 000 1 481+001 2.585 + 001 3 673 + 001 4.664 + 001 5.542 + 001 6.314 + 001 6.989 + 001 1.156 + 002 -0.40 2.273 + 000 5.430 + 000 1 199 + 001 1.971 + 001 2 642 + 001 3.177 + 001 3.592 + 001 3.910 + 001 4.153 + 001 4.922 + 001 -0.60 2.065 + 000 4.540 + 000 9 423 + 000 1.461 + 001 1 859 + 001 2.137 + 001 2.326 + 001 2.452 + 001 2.537 + 001 2.702 + 001 -0.80 1.860 + 000 3.720 + 000 7 204 + 000 1.055 + 001 1 281+001 1.419 + 001 1.502 + 001 1.550 + 001 1.577 + 001 1.616 + 001 -1.00 1.667 + 000 3.000 +000 5 375 + 000 7.429 + 000 8 653 + 000 9.312 + 000 9.652 + 000 9.825 + 000 9.912 + 000 1.000 + 001 -1.20 1.491+000 2.396 + 000 3 931 + 000 5.125 + 000 5 751+000 6.046 + 000 6.177 + 000 6.235 + 000 6.260 + 000 6.278 + 000 -1.40 1.337 + 000 1.907 + 000 2 832 + 000 3.477 + 000 3 772 + 000 3.892 + 000 3.938 + 000 3.954 + 000 3.960 + 000 3.962 + 000 -1.60 1.205 + 000 1.522 + 000 2 021+000 2.329 + 000 2 449 + 000 2.490 + 000 2.502 + 000 2.505 + 000 2.505 + 000 2.504 + 000 -1.80 1-.093 + 000 1.226 + 000 1 438 + 000 1.546 + 000 1 579 + 000 1.586 + 000 1.586 + 000 1.585 + 000 1.584 + 000 1.583 + 000 -2.00 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000

i B,(/V, r, fj.) for r= 0.200 N

4 8 16 32 64 128 256 512 1024 00

2 (10 3.333 + 000 1.200 + 001 4.533 + 001 1 760 + 002 6.933 + 002 2.752 + 003 1.097 + 004 4 378 + 004 1.749 + 005 00

1 HO 3.279 + 000 1.131+001 3.925 + 001 1 358 + 002 4.700 + 002 1.629 + 003 5.657 + 003 1 967 + 004 6.843 + 004

1 60 3.222 + 000 1.065 + 001 3.404 + 001 1 053 + 002 3.209 + 002 9.729 + 002 2.946 + 003 8 923 + 003 2.703 + 004 00

1 40 3.162 + 000 1.002 + 001 2.955 + 001 8 204 + 001 2.208 + 002 5.868 + 002 1.552 + 003 4 096 + 003 1.081 + 004

1 20 3.096 + 000 9.409 + 000 2.567 + 001 6 420 + 001 1.533 + 002 3.581+002 8.286 + 002 1 909 + 003 4.391 + 003 00

1 00 3.024 + 000 8.811 + 000 2.229 + 001 5 044 + 001 1.074 + 002 2.215 + 002 4.501+002 9 072 + 002 1.821 + 003 00 0 80 2.942 + 000 8.219 + 000 1.933 + 001 3 977 + 001 7.593 + 001 1.392 + 002 2.496 + 002 4 420 + 002 7.771 + 002 00 0 60 2.849 + 000 7.624 + 000 1.671+001 3 143 + 001 5.424 + 001 8.907 + 001 1.420 + 002 2 225 + 002 3.445 + 002 00 0 40 2.743 + 000 7.023 + 000 1.438 + 001 2 488 + 001 3.912 + 001 5.811+001 8.330 + 001 1 166 + 002 1.607 + 002 00 0 20 2.622 + 000 6.414 + 000 1.229 + 001 1 969 + 001 2.847 + 001 3.870 + 001 5.054 + 001 6 421 + 001 7.994 + 001 -0 00 2.487 + 000 5.796 + 000 1.042 + 001 1 555 + 001 2.088 + 001 2.631 + 001 3.180 + 001 3 733 + 001 4.288 + 001 00 -0 20 2.337 + 000 5.175 + 000 8.751+000 1 224 + 001 1.542 + 001 1.825 + 001 2.075 + 001 2 295 + 001 2.487 + 001 3.793 + 001 -0 40 2.176 + 000 4.558 + 000 7.262 + 000 9 581+000 1.143 + 001 1.287 + 001 1.399 + 001 1 484 + 001 1.550 + 001 1.757 + 001 -0 00 2.008 + 000 3.958 + 000 5.949 + 000 7 450 + 000 8.497 + 000 9.211+000 9.692 + 000 1 001 + 001 1.023 + 001 1.066 + 001 -0 HO 1.836 + 000 3.387 + 000 4.808 + 000 5 746 + 000 6.318 + 000 6.658 + 000 6.857 + 000 6 974 + 000 7.042 + 000 7.136 + 000 -1 00 1.667 + 000 2.857 + 000 3.833 + 000 4 395 + 000 4.692 + 000 4.845 + 000 4.922 + 000 4 961+000 4.980 + 000 5.000 + 000 -1 20 1.505 + 000 2.379 + 000 3.016 + 000 3 333 + 000 3.476 + 000 3.539 + 000 3.565 + 000 3 575 + 000 3.579 + 000 3.582 + 000 -1 40 1.355 +000 1.960 + 000 2.346 + 000 2 507 + 000 2.568 + 000 2.588 + 000 2.594 + 000 2 595 + 000 2.595 + 000 2.593 + 000 -1 60 1.221 + 000 1.601+000 1.805 + 000 1 873 + 000 1.890 + 000 1.892 + 000 1.890 + 000 1 889 + 000 1.888 + 000 1.886 + 000 -1 HO 1.102 + 000 1.300 + 000 1.378 + 000 1 390 + 000 1.387 + 000 1.382 + 000 1.378 + 000 1 376 + 000 1.375 + 000 1.374 + 000 -2 00 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000

194
BAN, r, n) for r= 0.400 N

M 4 8 16 32 64 128 256 512 1024 00

2.00 3 333 + 000 1 200 + 001 4 533 + 001 1.760 + 002 6.933 + 002 2 752 + 003 1.097 + 004 4.378 + 004 1.749 + 005 00 1.80 3 186 + 000 1 052 + 001 3 540 + 001 1.207 + 002 4.152 + 002 1 436 + 003 4.984 + 003 ii 739 -1- ftftk 6.026 + 004 00 1.60 3 047 + 000 9 247 + 000 2 780 + 001 8.345 + 001 2.511 + 002 7 574 + 002 2.289 + 003 e.o Q9Q -1- 00'-1 2.099 + 004 00 1.40 2 915 + 000 8 151+000 2 197 + 001 5.825 + 001 1.536 + 002 4 046 + 002 1.066 + 003 o RIO 4- 003 7.412 + 003 00 1.20 2 790 + 000 7 205 + 000 1 748 + 001 4.110 + 001 9.529 + 001 2 196 + 002 5.051 + 002 1 161 + 003 2.666 + 003 00 1.00 2 670 + 000 6 384 + 000 1 401 + 001 2.936 + 001 6.011 + 001 1 216 + 002 2.447 + 002 4 909 + 002 9.832 + 002 00 0.80 2 5554-000 5 670 + 000 I 131 +001 2.126 + 001 3.868 + 001 6 908 + 001 1.221 + 002 2 144 + 002 3.752 + 002 00 0.60 2 443 + 000 5 046 + 000 9 201 + 000 1.563 + 001 2.546 + 001 4 045 + 001 6.323 + 001 9 780 + 001 1.503 + 002 00

ft Aft 2 334 + 000 4 499 + 000 7 544 + 000 1 1 f\l -4- ftfll 1 791 _1_ 001 2 457 + 001 0.4*00 3 d.33 -i- ftfii r 4 725 + 001 f\u.too 433 -1- — ftfll UU1

0.20 2 227 + 000 4 017 + 000 6 232 + 000 8.870 + 000 1.196 + 001 1 556 + 001 1.973 + 001 2 454 + 001 3.009+001 00 -0.00 2 121 + 000 3 589 + 000 5 187 + 000 6.856 + 000 8.572 + 000 1 032 + 001 1.209 + 001 1 387 + 001 1.566 + 001 00 -0.20 2 015 + 000 3 207 + 000 4 346 + 000 5.389 + 000 6.330 + 000 7 169 + 000 7.913 + 000 8 569 + 000 9.144 + 000 1.306 + 001 -0.40 1 909 + 000 2 864 + 000 3 664 + 000 4.305 + 000 4.811 + 000 5 208 + 000 5.516 + 000 5 753 + 000 5.936 + 000 6.518 + 000 -0.60 1 802 + 000 2 555 + 000 3 105 + 000 3.489 + 000 3.755 + 000 3 937 + 000 4.060 + 000 4 144 + 000 4.200 + 000 4.313 + 000 -0.80 1 694 + 000 2 274 + 000 2 642 + 000 2.864 + 000 2.997 + 000 3 077 + 000 3.123 + 000 3 151 + 000 3.167 + 000 3.191+000 -1.00 1 583 + 000 2 018 + 000 2 254 + 000 2.376 + 000 2.438 + 000 2 469 + 000 2.484 + 000 2 492 + 000 2.4% + 000 2.500 + 000 -1.20 1 471 + 000 1 782 + 000 1 926 + 000 1.987 + 000 2.011 + 000 2 021 + 000 2.024 + 000 2 025 + 000 2.026 + 000 2.025 + 000 -1.40 1 356 + 000 1 565 + 000 1 644 + 000 1.670 + 000 1.677 + 000 1 678 + 000 1.677 + 000 1 676 + 000 1.675 + 000 1.674 + 000 -1.60 1 240 + 000 1 363 + 000 1 401 + 000 1.408 + 000 1.408 + 000 1 406 + 000 1.404 + 000 1 403 + 000 1.402 + 000 1.402 + 000 -1.80 1 121 + 000 1 175 + 000 1 188 + 000 1.188 + 000 1.186 + 000 1 184 + 000 1.183 + 000 1 182 + 000 1.182 + 000 1.182 + 000 -2.00 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000

BAN, r, ft) for r= 0.800 N

4 8 16 32 64 128 256 512 1024 00

2.00 3 333 + 000 1 200 + 001 4.533 + 001 1 760 + 002 6.933 + 002 2.752 + 003 1.097 + 004 4.378 + 004 1.749 + 005 00 1.80 3 032 + 000 9 694 + 000 3.213 + 001 1 089 + 002 3.739 + 002 1.292 + 003 4.483 + 003 1.558 + 004 5.421 + 004

1.60 2 765 + 000 7 876 + 000 2.297 + 001 6 806 + 001 2.038 + 002 6.135 + 002 1.853 + 003 5.608 + 003 1.698 + 004 00 1.40 2 529 + 000 6 441 + 000 1.658 + 001 4 305 + 001 1.125 + 002 2.953 + 002 7.770 + 002 2.047 + 003 5.398 + 003 00 1.20 2 319 + 000 5 306'+ 000 1.210 + 001 2 762 + 001 6.317 + 001 1.447 + 002 3.319 + 002 7.617 + 002 1.749 + 003 00 1.00 2 134 + 000 4 405 + 000 8.950 + 000 1 804 + 001 3.622 + 001 7.259 + 001 1.453 + 002 2.908 + 002 5.817 + 002 00 0.80 1 969 + 000 3 688 + 000 6.718 + 000 1 203 + 001 2.132 + 001 3.753 + 001 6.579 + 001 1.150 + 002 2.008 + 002 00 0.60 1 823 + 000 3 117 + 000 5.128 + 000 8 225 + 000 1.296 + 001 2.018 + 001 3.116 + 001 4.782 + 001 7.310 + 001 00 0.40 1 693 + 000 2 660 + 000 3.986 + 000 5 783 + 000 8.193 + 000 1.140 + 001 1.567 + 001 2.130 + 001 2.876 + 001 00 0.20 1 578 + 000 2 293 + 000 3.160 + 000 4 196 + 000 5.416 + 000 6.840 + 000 8.492 + 000 1.040 + 001 1.260 + 001 -0.00 1 477 + 000 1 998 + 000 2.558 + 000 3 149 + 000 3.761 + 000 4.389 + 000 5.027 + 000 5.671+000 6.318 + 000 00 -0.20 1 387 + 000 1 760 + 000 2.115 + 000 2 446 + 000 2.749 + 000 3.023 + 000 3.267 + 000 3.483 + 000 3.673 + 000 4.968 + 000 -0.40 1 308 + 000 1 .568 + 000 1.786 + 000 1 966 + 000 2.112 + 000 2.229 + 000 2.321 + 000 2.392 + 000 2.447 + 000 2.624 + 000 -0.60 1 238 + 000 1 413 + 000 1.541 + 000 1 634 + 000 1.700 + 000 1.748 + 000 1.780 + 000 1.803 + 000 1.818 + 000 1.850 + 000 -0.80 1 177 + 000 1 287 + 000 1.357 + 000 1 400 + 000 1.427 + 000 1.444 + 000 1.454 + 000 1.461 + 000 1.464 + 000 1.470 + 000 -1.00 1 125 + 000 1 187 + 000 1.219 + 000 1 234 + 000 1.242 + 000 1.246 + 000 1.248 + 000 1.249 + 000 1.250 + 000 1.250 + 000 -1.20 1 081 + 000 1 109 + 000 1.117 + 000 1 118 + 000 1.117 + 000 1.116 + 000 1.115 + 000 1.114 + 000 1.114 + 000 1.113 + 000 -1.40 1 045 + 000 1 050 + 000 1.045 + 000 1 039 + 000 1.035 + 000 1.032 + 000 1.030 + 000 1.029 + 000 1.028 + 000 1.028 + 000 -1.60 1 017 + 000 1 010 + 000 1.000 + 000 9 922 - 001 9.872 - 001 9.843 - 001 9.827 - 001 9.819-001 9.814-001 9.809-001 -1.80 1 001 + 000 9 914-001 9.826 - 001 9 768 - 001 9.734 - 001 9.715-001 9.704-001 9.699 -001 9.697-001 9.694-001 -2.00 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000

195
Bi(N, r, fi) for r=1.00 N

4 8 16 32 64 128 256 512 1024 CO

2 00 a mo 4- nnn 1 200 + 001 4 533 + 001 1 760 4- 009 /; QQQ _1_ 009 9 7^9 -1-001 Z. 1 OZ ^ UUJ l nQ7 4- nod 4 378 + 004 1 749 + 005

1 80 o qqo _i_ nnn 9 490 + 000 3 138 + 001 i1 . t\f>i UOO 4- nn9 UUZ 0 AAA _]_ 009 1 9An -I- fW15 1 .ZOU ^ UUo J. 379 4- nm 519 + 004 5 286 + 004

1 60 oZ.OOo aoq _i_ nnn uuu 7 555 + 000 2 191 + 001 f.O.^/V 4.70 _i_ nmUUl 1 QQQ ftftO 1 .yoo ~r UUZ C. QQQ _1_ HA9 D. Oao + UUz 1 7A9 _1_ AAQ 1 . / OZ + UUo 5 331 +003 1 615 + 004

1 40 9z . A9ft <*ZO -i- T nnn uuu 6 059 + 000 1 546 + 001 o.yyy

o qqq i nmUU1 1 0/1yl _U 009 9 7QQ _i_ HA9 Z. 1 OO "T UUz 7 9n9 _i_ nn9 / -ZUZ -r UUz 1 897 + 003 5 003 + 003

1 20 Z.9 i1?0oft -i- nnn uuu 4 900 + 000 1 104 + 001 9 caa -j- nni Z . OUO UUl e; 71 7 _i_ 001 D. f 1 < ~r UUl i QnQ _l nn9 1 . OUo T UUz 9 QQQ 4_ QQ9 z.yyy + uuz 6 881 +002 1 580 + 003

1 (id 9Z.UUU nnn 4- nnn uuu 4 000 + 000 8 000 + 000 i1 .DUU 6nn-unni UUl 0. 900 -L 00

1

D.ZUU t UUl O.^-UU "T UUl i1 -ZoU 9ftn 4-T nn9 uuz 2 560 + 002 5 120 + 002

0 HO 11 . Q97 OZ i _i_ — nnn uuu 3 299 + 000 5 894 + 000 1.U4D -r UUl 1I .o^rl fiA 1 4-i 001 UUl o.zou

o 9Qn _i_ + nmUUl o^ . ac.9 ooz 4-— nmUU 1 9 872 + 001 1 722 + 002

0 60 1.677 + 000 2 750 + 000 4 424 + 000 7.006 + 000 1.096 + 001 1.698 + 001 2.614 + 001 4 005 + 001 6 114 + 001 CO 0 40 1.546 + 000 2 320 + 000 3 391+000 4.846 + 000 6.801+000 9.407 + 000 1.287 + 001 1 744 + 001 2 350 + 001 0 20 1.432 + 000 1 982 + 000 2 658 + 000 3.471 + 000 4.432 + 000 5.555 + 000 6.858 + 000 8 363 + 000 1 010 + 001 CO 0 00 1.333 + 000 1 714 + 000 2 133 + 000 2.581+000 3.048 + 000 3.528 + 000 4.016 + 000 4 509 + 000 5 005 + 000 CO -0 20 1.247 + 000 1 502 + 000 1 754 + 000 1.994 + 000 2.216 + 000 2.418 + 000 2.599 + 000 2 759 + 000 2 900 + 000 3.863 + 000 -0 40 1,172 + 000 1 333 + 000 1 476 + 000 1.599 + 000 1.700 + 000 1.782 + 000 1.847 + 000 1 898 + 000 1 938 + 000 2.065 + 000 -0 60 1.107 + 000 1 197 + 000 1 271+000 1.327 + 000 1.370 + 000 1.401+000 1.422 + 000 1 438 + 000 1 448 + 000 1.470 + 000 -0 HO 1.050 + 000 1 088 + 000 1 117 + 000 1.137 + 000 1.150 + 000 1.160 + 000 1.165 + 000 1 169 + 000 1 171+000 1.175 + 000 -1 00 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1 20 9.569-001 9 284-001 9 105 - 001 8.997-001 8.933 - 001 8.897 - 001 8.877-001 8 866 - 001 8 860-001 8.854-001 -1 40 9.193-001 8 700-001 8 410-001 8.245-001 8.154 - 001 8.105-001 8.079-001 8 065-001 8 058 - 001 8.051-001 -1 60 8.866 - 001 8 221-001 7 864-001 7.672-001 7.570-001 7.517-001 7.490-001 7 476-001 7 468-001 7.461-001 -1 HO 8.581-001 7 827-001 7 431-001 7.226-001 7.122-001 7.068 -001 7.042-001 7 028 - 001 7 021-001 7.014-001 -2 00 8.333 - 001 7 500-001 7 083 - 001 6.875-001 6.771-001 6.719-001 6.693-001 6 680-001 6 673 - 001 6.667-001

£,(/V, r, n) for r=1.01 N

4 8 16 32 64 128 256 512 1024 00

2 00 3.333 + 000 1.200 + 001 4.533 + 001 1.760 + 002 6.933 + 002 2 752 + 003 1 097 + 004 4 378 + 004 1 749 + 005 00

1 80 2.986 + 000 9.482 + 000 3.135 + 001 1.062 + 002 3.643 + 002 1 259 + 003 4 367 + 003 1 518 + 004 5 280 + 004 00

1 60 2.685 + 000 7.542 + 000 2.187 + 001 6.466 + 001 1.934 + 002 5 822 + 002 1 758 + 003 5 321 + 003 1 611 + 004 00

1 40 2.422 + 000 6.045 + 000 1.542 + 001 3.988 + 001 1.041 + 002 2 730 + 002 7 180 + 002 1 892 + 003 4 988 + 003 00

1 20 2.194 + 000 4.885 + 000 1.100 + 001 2.497 + 001 5.695 + 001 1 303 + 002 2 987 + 002 6 854 + 002 1 573 + 003 00

1 00 1.995 + 000 3.985 + 000 7.966 + 000 1.593 + 001 3.185 + 001 6 369 + 001 1 274 + 002 2 547 + 002 5 095 + 002 00 0 80 1.822 + 000 3.285 + 000 5.864 + 000 1.039 + 001 1.830 + 001 3 212 + 001 5 619 + 001 9 814 + 001 1 712 + 002 00 0 60 1.672 + 000 2.738 + 000 4.400 + 000 6.963 + 000 1.089 + 001 1 687 + 001 2 597 + 001 3 978 + 001 6 073 + 001 00 0 40 1.541 + 000 2.309 + 000, 3.371 + 000 4.814 + 000 6.754 + 000 9 340 + 000 1 277 + 001 1 731 + 001 2 332 + 001 X

• 0 20 1.428 + 000 1.972 + 000 2.642 + 000 3.447 + 000 4.400 + 000 5 512 + 000 6 804 + 000 8 296 + 000 1 002 + 001 00 -0 00 1.329 + 000 1.706 + 000 2.120 + 000 2.563 + 000 3.025 + 000 3 500 + 000 3 984 + 000 4 472 + 000 4 963 + 000 00 -0 20 1.243 + 000 1.495 + 000 1.743 + 000 1.980 + 000 2.200 + 000 2 400 + 000 2 579 + 000 2 737 + 000 2 877 + 000 3.829 + 000 -0 40 1.168 + 000 1.327 + 000 1.468 + 000 1.589 + 000 1.689 + 000 1 770 + 000 1 835 + 000 1 885 + 000 1 924 + 000 2.050 + 000 -0 60 1.104 + 000 1.193 + 000 1.265 + 000 1.321 + 000 1.362 + 000 1 393 + 000 1 414 + 000 1 429 + 000 1 440 + 000 1.461+000 -0 80 1.048 + 000 1.085 + 000 1.113 + 000 1.133 + 000 1.147 + 000 1 155 + 000 1 161 + 000 1 165 + 000 1 167 + 000 1.170 + 000 -1 00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1 20 9.599 - 001 9.331-001 9.160 - 001 9.056-001 8.995-001 8 960-001 8 940-001 8 929-001 8 924 - 001 8.917-001 -1 40 9.286-001 8.840-001 8.573-001 8.419-001 8.333 - 001 8 287 -001 8 262 - 001 8 249 - 001 8 242-001 8.235-001 -1 60 9.098 - 001 8.566-001 8.264-001 8.098-001 8.009 - 001 7 963-001 7 938-001 7 926 - 001 7 920-001 7.913-001 -1 80 9.156 - 001 8.682 - 001 8.425 - 001 8.288-001 8.217-001 8 181-001 8 162 - 001 8 153 - 001 8 148-001 8.143-001 -2 (H) 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000

196
I BAN, r, ix) for r= 1.10 N

4 8 16 32 64 128 256 512 1024 00

2.00 3.333 + 000 1 200 + 001 4.533 + 001 1.760 + 002 6 933 + 002 2 752 + 003 1 097 + 004 4.378 + 004 1 749 + 005 CO 1.80 2.972 + 000 9 418 + 000 3.111+001 1.053 + 002 3 614 + 002 1 249 + 003 4 333 + 003 1.506 + 004 5 238 + 004 CO 1.60 2.660 + 000 7 443 + 000 2.154 + 001 6.366 + 001 1 904 + 002 5 730 + 002 1 731 + 003 5.237 + 003 1 586 + 004 00 1.40 2.391 + 000 5 929 + 000 1.508 + 001 3.897 + 001 1 016 + 002 2 666 + 002 7 011 + 002 1.847 + 003 4 870 + 003 00 1.20 2.158 + 000 4 766 + 000 1.069 + 001 2.422 + 001 5 521+001 1 263 + 002 2 894 + 002 6.640 + 002 1 524 + 003 CO 1.00 1.957 + 000 3 870 + 000 7.696 + 000 1.535 + 001 3 065 + 001 6 126 + 001 1 225 + 002 2.449 + 002 4 898 + 002 CO 0.80 1.783 + 000 3 177 + 000 5.637 + 000 9.954 + 000 1 750 + 001 3 068 + 001 5 365 + 001 9.366 + 001 1 634 + 002 CO 0.60 1.633 + 000 2 640 + 000 4.213 + 000 6.639 + 000 1 035 + 001 1 602 + 001 2 463 + 001 3.771 + 001 5 754 + 001 00 0.40 1.504 + 000 2 223 + 000 3.219 + 000 4.575 + 000 6 398 + 000 8 828 + 000 1 205 + 001 1.632 + 001 2 197 + 001 00 0.20 1.393 + 000 1 898 + 000 2.521 + 000 3.272 + 000 4 160 + 000 5 199 + 000 6 404 + 000 7.797 + 000 9 402 + 000 CO -0.00 1.298 + 000 1 643 + 000 2.026 + 000 2.435 + 000 2 863 + 000 3 304 + 000 3 752 + 000 4.205 + 000 4 661 + 000 -0.20 1.217 + 000 1 444 + 000 1.671 + 000 1.889 + 000 2 091 + 000 2 275 + 000 2 440 + 000 2.586 + 000 2 714 + 000 3.593 + 000 -0.40 1.147 + 000 1 288 + 000 1.416 + 000 1.526 + 000 1 617 + 000 1 692 + 000 1 751+000 1.797 + 000 1 832 + 000 1.948 + 000 -0.60 1.088 + 000 1 166 + 000 1.230 + 000 1.281+000 1 319 + 000 1 346 + 000 1 366 + 000 1.379 + 000 1 389 + 000 1.408 + 000 -0.80 1.040 + 000 1 072 + 000 1.096 + 000 1.114 + 000 1 126 + 000 1 134 + 000 1 139 + 000 1.142 + 000 1 144 + 000 1.147 + 000 -1.00 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 -1.20 9.696 - 001 9 482 - 001 9.341-001 9.254-001 9 201-001 9 171-001 9 154-001 9.145-001 9 140-001 9.134-001 -1.40 9.493 - 001 9 157-001 8.948 - 001 8.825-001 8 755-001 8 717-001 8 696-001 8.685-001 8 680 - 001 8.674-001 -1.60 9.415-001 9 048-001 8.831-001 8.709-001 8 642-001 8 607 -.001 8 588-001 8.578-001 8 574-001 8.569-001 -1.80 9.527-001 9 243-001 9.082-001 8.994-001 8 948 - 001 8 924-001 8 911-001 8.905-001 8 902-001 8.898 - 001 -2.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000

BAN, r, ix) for r=2.00 N

4 8 16 32 64 128 256 512 1024 00

2.00 3.333 + 000 1 200 + 001 4.533 + 001 1 760 + 002 6.933 + 002 2 752 + 003 1.097 + 004 4 378 + 004 1 749 + 005 00 1.80 2.908 + 000 9 132 + 000 3.006 + 001 1 017 + 002 3.487 + 002 1 205 + 003 4.179 + 003 1 453 + 004 5 053 + 004

1.60 2.552 + 000 7 012 + 000 2.014 + 001 5 935 + 001 1.773 + 002 5 334 + 002 1.611+003 4 874 + 003 1 476 + 004 00 1.40 2.255 + 000 5 439 + 000 1.366 + 001 3 512 + 001 9.142 + 001 2 395 + 002 6.299 + 002 1 659 + 003 4 374 + 003 00 1.20 2.007 + 000 4 271 + 000 9.409 + 000 2 114 + 001 4.800 + 001 1 096 + 002 2.510 + 002 5 756 + 002 1 321+003 00 1.00 1.800 + 000 3 400 + 000 6.600 + 000 1 300 + 001 2.580 + 001 5 140 + 001 1.026 + 002 2 050 + 002 4 098 + 002 00 0.80 1.628 + 000 2 750 + 000 4.733 + 000 8 215 + 000 1.431+001 2 494 + 001 4.347 + 001 7 576 + 001 1 320 + 002 00 0.60 1.486 + 000 2 264 + 000 3.485 + 000 5 371 + 000 8.262 + 000 1 267 + 001 1.937 + 001 2 955 + 001 4 498 + 001 00 0.40 1.369 + 000 1 901 + 000 2.644 + 000 3 659 + 000 5.025 + 000 6 847 + 000 9.267 + 000 1 247 + 001 1 670 + 001 00 0.20 1.273 + 000 1 629 + 000 2.075 + 000 2 615 + 000 3.256 + 000 4 005 + 000 4.876 + 000 5 882 + 000 7 042 + 000 00 -0.00 1.195 + 000 1 427 + 000 1.688 + 000 1 971+000 2.267 + 000 2 573 + 000 2.884 + 000 3 198 + 000 3 515 + 000 -0.20 1.133 + 000 1 277 + 000 1.425 + 000 1 568 + 000 1.702 + 000 1 824 + 000 1.934 + 000 2 031 + 000 2 117 + 000 2 704 + 000 -0.40 1.084 + 000 1 168 + 000 1.246 + 000 1 315 + 000 1.373 + 000 1 420 + 000 1.457 + 000 1 487 + 000 1 509 + 000 1 583 + 000 -0.60 1.046 + 000 1 090 + 000 1.126 + 000 1 156 + 000 1.178 + 000 1 195 + 000 1.207 + 000 1 215 + 000 1 221 + 000 1 233 + 000 -0.80 1.019 + 000 1 035 + 000 1.048 + 000 1 058 + 000 1.064 + 000 1 069 + 000 1.072 + 000 1 074 + 000 1 075 + 000 1 077 + 000 -1.00 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 -1.20 9.886 - 001 9 799-001 9.738-001 9 699-001 9.675-001 9 661-001 9.653-001 9 648 -001 9 646 - 001 9 643-001

-1.40 9.837-001 9 719-001 9.641-001 9 593-001 9.565 - 001 9 550-001 9.541-001 9 537 -001 9 534-001 9 532 - 001 -1.60 9.845-001 9 737-001 9.669 - 001 9 630 - 001 9.607-001 9 595-001 9.589 - 001 9 586-001 9 584 - 001 9 582-001

-1.80 9.901-001 9 836 - 001 9.796-001 9 774-001 9.761-001 9 755-001 9.752-001 9 750-001 9 749 - 001 9 748 - 001 -2.00 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000

197
BAN, r, fi) for r = 4.00

V

4 8 16 32 64 128 256 512 1024 CO

z.uu o nn i in _i_ nnn ll.ZW onn -i- T nmUUl a. c33 _i_ nni 4.0OO i UUl 11. 7An /OUT_L. nno uuz aO.yoo o33 _i_ nno I uuz 0 7^o _i_ nni Z. ioZ-r UUo 1 no7 _L ( im i.uy / + uu4 4

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A OO 1 f\f\A 4Zy + UU4 A 070 4_ nni *.y /z "t uui1 AO 1 .ou o cn^ _i_ nnn Z.0U4 T UUU £ Qio i nnn O.ol V T UUU l ncio _i_ nni i .yoz + uui 0.c 7/i /4oc _i_ t nmUUl 1 7 1 c _i_ nno 1 . / lo t UUZ c 1 An _i_ nno 0. lOU T UUZ 1 crcti j nni l.ooo -r UUo A<t 71/14- nni tLl^r UUo 1 A OQ 4_ f\f\A l.QZo T UU4

1.40 o l n/i _i_ nnn Z. iy4 + UUU c o l n _i_ nnn D.ZlV ~r UUU i1 . oUo ini _i_ -r nmUU 1 o.o4U q Qin 4_ nm ~r UUl q0.000 /.ua 4_+ nmUUl 0 07c _i_ nno Z.Z to + UUZ c oqi _i nno o.yol + UUZ 11 0 1 0 — UUO a i ca 4_ nni 4. 104 -r UUo

1 on l.ZU i oict a. nnn 1 .Voo t UUU 4,U4o a f\Ac. _i_

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il .uu nn i1 . 707 / Z / _i_ T nnn uuu O.i iloZoo j_T nnn uuu f\ noi -i- nnn O.U71 T UUU 1i.iyj lm^nm + uui 0 icic -i- nni Z.ODD X UUl <i ^fto 4- nni ^.OoZ X UUl o 11^ 4- nni y.000 t uui 1 865 + 002 0.1 79A t zo 4-X nno uuz

0.80 i ccc _i_ nnn l.ooo + UUU o Cdo i nnn Z.o4o + UUU /i ini _i_ nnn 4.oUo + UUU 7 ice jl nnn /.OOO + UUU i1 .Z070to +1 nmUUl 0 01 n _i_ nm Z.Z19 + UUl 0.00U 1 oAfi _l+ nmUUl 6 718 + 001 1 1 70 4_ nno 1. 1 /U + UUZ

0.60 1.415 + 000 2.082 + 000 3.129 + 000 4.748 + 000 7.229 + 000 1.101 + 001 1.676 + 001 2 550 + 001 3.875 + 001 CO 0.40 1.303 + 000 1.742 + 000 2.356 + 000 3.196 + 000 4.326 + 000 5.834 + 000 7.837 + 000 1 049 + 001 1.399 + 001 00 0.20 1.214 + 000 1.495 + 000 1.848 + 000 2.275 + 000 2.783 + 000 3.377 + 000 4.067 + 000 4 865 + 000 5.784 + 000 00 -0.00 1.144 + 000 1.318 + 000 1.514 + 000 1.726 + 000 1.949 + 000 2.179 + 000 2.414 + 000 2 651+000 2.890 + 000 CO -0.20 1.092 + 000 1.194 + 000 1.298 + 000 1.399 + 000 1.494 + 000 1.580 + 000 1.658 + 000 1 727 + 000 1.788 + 000 2,204 + 000 -0.40 1.054 + 000 1.109 + 000 1.160 + 000 1.205 + 000 1.243 + 000 1.274 + 000 1.299 + 000 1 318 + 000 1.333 + 000 1.382 + 000 — 0.60 1.027 + 000 1.053 + 000 1.075 + 000 1.093 + 000 1.107 + 000 1.117 + 000 1.124 + 000 1 129 + 000 1.132 + 000 1.140 + 000 -0.80 1.010 + 000 1.019 + 000 1.026 + 000 1.031+000 1.035 + 000 1.037 + 000 1.039 + 000 1 040 + 000 1.041+000 1.042 + 000 -1.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000+000 1 000 + 000 1.000 + 000 1.000 + 000 -1.20 9.953-001 9.916-001 9.890-001 9.873-001 9.862-001 9.856 - 001 9.853 - 001 9 851-001 9.850-001 9.849 - 001 -1.40 9.941-001 9.898 - 001 9.869 - 001 9.851-001 9.840 - 001 9.834 - 001 9.831-001 9 829-001 9.829-001 9.828-001 -1.60 9.952 - 001 9.918-001 9.896 - 001 9.884 - 001 9.876 - 001 9.873-001 9.870 - 001 9 869 - 001 9.869-001 9.868-001 -1.80 9.974 - 001 9.957-001 9.946 - 001 9.940-001 9.936 - 001 9.935 - 001 9.934 - 001 9 933-001 9.933-001 9.933-001 -2.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000

B, (A\ r, fj.) for r=8.00 N

4 8 16 32 64 128 256 512 1024 00

2.00 3.333 + 000 1.200 + 001 4.533 + 001 1.760 + 002 6.933 + 002 2.752 + 003 1.097 + 004 4 378 + 004 1.749 + 005 00 1.80 2.870 + 000 8.963 + 000 2.945 + 001 9.951 + 001 3.413 + 002 1.179 + 003 4.090 + 003 1 421 + 004 4.945 + 004 00 1.60 2.486 + 000 6.751 + 000 1.930 + 001 5.678 + 001 1.695 + 002 5.099 + 002 1.540 + 003 4 658 + 003 1.411+004 00 1.40 2.170 + 000 5.135 + 000 1.279 + 001 3.276 + 001 8.515 + 001 2.230 + 002 5.862 + 002 1 544 + 003 4.071+003 00 1.20 1.910 + 000 3.953 + 000 8.590 + 000 1.917 + 001 4.341 + 001 9.898 + 001 2.265 + 002 5 195 + 002 1.192 + 003 00 1.00 1.696 + 000 3.087 + 000 5.870 + 000 1.143 + 001 2.257 + 001 4.483 + 001 8.935 + 001 1 784 + 002 3.565 + 002 00 0.80 1.521 + 000 2.453 + 000 4.101 + 000 6.996 + 000 1.206 + 001 2.090 + 001 3.630 + 001 6 315 + 001 1.099 + 002 00 0.60 1.380 + 000 1.991+000 2.950 + 000 4.433 + 000 6.706 + 000 1.017 + 001 1.544 + 001 2 345 + 001 3.559 + 001

0.40 1.268 + 000 1.657 + 000 2.202 + 000 2.946 + 000 3.949 + 000 5.286 + 000 7.062 + 000 9 414 + 000 1.252 + 001 00 0.20 1.181+000 1.420 + 000 1.720 + 000 2.083 + 000 2.514 + 000 3.019 + 000 3.606 + 000 4 284 + 000 5.066 + 000 00 -0.00 1.116 + 000 1.255 + 000 1.413 + 000 1.584 + 000 1.763 + 000 1.969 + 000 2.137 + 000 2 328 + 000 2.520 + 000 00 -0.20 1.069 + 000 1.145 + 000 1.223 + 000 1.299 + 000 1.371 + 000 1.436 + 000 1.494 + 000 1 546 + 000 1.592 + 000 1.905 + 000 -0.40 1.037 + 000 1.075 + 000 1.110 + 000 1.142 + 000 1.168 + 000 1.189 + 000 1.207 + 000 1 220 + 000 1.231+000 1.264 + 000 -0.60 1.017 + 000 1.033 + 000 1.047 + 000 1.058 + 000 1.067 + 000 1.073 + 000 1.078 + 000 1 081+000 1.083 + 000 1.088 + 000 -0.80 1.006 + 000 1.011+000 1.014 + 000 1.017 + 000 1.020 + 000 1.021+000 1.022 + 000 I 022 + 000 1.023 + 000 1.023 + 000 -1.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 -1.20 9.980 - 001 9.963-001 9.952-001 9.945 - 001 9.940-001 9.938 - 001 9.936-001 9.935 - 001 9.935 - 001 9.934-001 -1.40 9.978 - 001 9.961-001 9.950-001 9.944 - 001 9.940-001 9.937-001 9.936 - 001 9 936 - 001 9.935 - 001 9.935 - 001 -1.60 9.984 - 001 9.973-001 9.966 - 001 9.962 - 001 9.960 - 001 9.958-001 9.958 - 001 9 957-001 9.957-001 9.957 - 001 -1.80 9.993 - 001 9.988-001 9.985 - 001 9.983-001 9.982-001 9.981-001 9.981-001 9 981-001 9.981-001 9.981-001 -2.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000

198
B,(N, r, /x) for r = 16.00

N

4 8 16 32 6.A 04 128 256 512 1024 00

Z.UU o nn QO

5Q7 i AftA ooo ~r UUU 11 OAA _1_ AA1 ZUU -r UU1 A

He coo i AA1 OOO "T UU1 i / OU *T UUZ f\O.VoO -1- ~p ftftO uuz oz 7CO _1_ AAO / oz -r UUo li AQ7 _1_ AA/I uy t -r uu<t

A

Ht 17Q _1_ AA^ o / o -r UU4 ii 1A O _1_ AAC. /4v -r UUo

1 .oU 2

i AAA OOO T UUU 8 949 + 000 2

Cl/IA _1_ AA1 V4U T UU1 9 934 + 001 o AClfx -4- ftftO O.^UO i uuz 111 77 _1_ AAO 1

/

1 T UUo A noo i AAQ Uoa 7 UUo 11 A 1 O _1_ AA/1 *1Vt UU4 A no/: i AA/I yoo -r UU4

1 .OU 2

A QA _1_ AAA 4oU -r UUU 6 727 + 000 1 VZOT UU

1

5 654 + 001 1 f»ftft -i- ftft9 1 .OOO i UUZ rO A77 _l_ AAO \)( 1 -r UUZ 1 Mjt CQQ 1 AAO UUo AHe AQO _1_ AAQ OoV -r UUo 1

/I AC _1_ AA/1 4UO -r UU4

1 /1ft 1 .4U 2

It! i AAA 161 + UUU 5 104 + 000 1 07A l AA1 Z /U + UUl 3 251 + 001 Q A C,ft _l_ Hftl 0.<+DU i UU1 2

Oil i AAO zlo + UUz 5 Q17 i AAO ol / + UUz 1

C 0 O _i_ AAO ooz + UUo 4

AOA _1_ AAO Uo9 + UUo cc

1 Oft 1 OAO l AAA o9o + UUU 3 914 + 000 8

/lOl l AAA 491 + UUU 1 894 + 001 'r.t.Oo i UU1 91CA _L AA1 /6V + U01 2 OOi i AAO zo6 + UUz 51 07 _1_ AAO Iz / + UUz 11 77 _1_ AAO 1 / / + UUo

1 ATI l.UU 1 681 + 000 3 043 + 000 5 766 + 000 1 121+001 9 011-1- ftftl Z.Z1 1 T UU1 4 389 + 001 8 747 + 001 1 746 + 002 3 489 + 002 CO

ft Qft U.oU 1 504 + 000 2 404 + 000 3 997 + 000 6 794 + 000 1 1 f%Q -I- ftft 1 i . ioy i uui 2 023 + 001 3 512 + 001 6 106 + 001 1 062 + 002 CO 0.60 1 360 + 000 1 939 + 000 2 848 + 000 4 254 + 000 6.409 + 000 9 696 + 000 1 469 + 001 2 228 + 001 3 379 + 001 CO 0.40 1 247 + 000 1 606 + 000 2 108 + 000 2 794 + 000 3.717 + 000 4 950 + 000 6 587 + 000 8 754 + 000 1 162 + 001 CO 0.20 1 160 + 000 1 372 + 000 1 637 + 000 1 958 + 000 2.340 + 000 2 787 + 000 3 307 + 000 3 907 + 000 4 599 + 000 CO -0.00 1 097 + 000 1 214 + 000 1 346 + 000 1 489 + 000 1.639 + 000 1 794 + 000 1 952 + 000 2 112 + 000 2 273 + 000 CO -0.20 1 054 + 000 1 113 + 000 1 174 + 000 1 233 + 000 1.289 + 000 1 339 + 000 1 385 + 000 1 425 + 000 1 461 + 000 1.705 + 000 -0.40 1 026 + 000 1 053 + 000 1 078 + 000 1 101 + 000 1.119 + 000 1 135 + 000 1 147 + 000 1 157 + 000 1 164 + 000 1.188 + 000 -0.60 1 011 + 000 1 021 + 000 1 030 + 000 1 037 + 000 1.043 + 000 1 047 + 000 1 050 + 000 1 052 + 000 1 053 + 000 1.056 + 000 -0.80 1 003 + 000 1 006 + 000 1 008 + 000 1 010 + 000 1.011+000 1 012 + 000 1 012 + 000 1 013 + 000 1 013 + 000 1.013 + 000 -1.00 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1.20 9 991-001 9.984 - 001 9 979-001 9.976-001 9.974 - 001 9 973-001 9 972 - 001 9 972-001 9 972-001 9.971 - 001 -1.40 9 992 - 001 9.985 r 001 9 981-001 9.979-001 9.977-001 9 976-001 9 976 - 001 9 976-001 9 975 - 001 9.975 - 001 -1.60 9 995 - 001 9.991-001 9 989-001 9.987-001 9.987-001 9 986-001 9 986 - 001 9 986 - 001 9 986-001 9.986- 001 -1.80 9 998-001 9.997-001 9 996-001 9.995-001 9.995 - 001 9 995 - 001 9 995 - 001 9 995 - 001 9 995 - 001 9.995- 001 -2.00 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000

B,(/V, r, /*) for r = 32.00

/V

4 8 16 32 64 128 256 512 1024 CO

2.00 3 333 + 000 1.200 + 001 4 533 + 001 1.760 + 002 6 933 + 002 2.752 + 003 1.097 + 004 4.378 + 004 1 749 + 005

1.80 2 865 + 000 8.945 + 000 2 938 + 001 9.928 + 001 3 405 + 002 1.176 + 003 4.081 + 003 1.418 + 004 4 934 + 004 CO 1.60 2 478 + 000 6.719 + 000 1 920 + 001 5.646 + 001 1 685 + 002 5.070 + 002 1.531 + 003 4.632 + 003 1 403 + 004 CO 1.40 2 158 + 000 5.091 + 000 1 266 + 001 3.242 + 001 H 425 + 001 2.206 + 002 5.799 + 002 1.527 + 003 4 027 + 003 CO 1.20 1 893 + 000 3.898 + 000 8 448 + 000 1.883 + 001 4 261 + 001 9.714 + 001 2.223 + 002 5.097 + 002 1 170 + 003 CO 1.00 1 674 + 000 3.021+000 5 716 + 000 1.111 + 001 2 188 + 001 4.344 + 001 8.656 + 001 1.728 + 002 3 453 + 002

0.80 1 494 + 000 2.378 + 000 3 940 + 000 6.685 + 000 1 149 + 001 1.986 + 001 3.447 + 001 5.992 + 001 1 042 + 002

0.60 1 348 + 000 1.908 + 000 2 787 + 000 4.147 + 000 6 231 + 000 9.408 + 000 1.424 + 001 2.158 + 001 3 270 + 001 CO 0.40 1 233 + 000 1.572 + 000 2 046 + 000 2.693 + 000 3 565 + 000 4.729 + 000 6.275 + 000 8.320 + 000 1 102 + 001 CO 0.20 1 146 + 000 1.338 + 000 1 579 + 000 1.871+000 2 218 + 000 2.625 + 000 3.097 + 000 3.643 + 000 4 272 + 000 CO -0.00 1 083 + 000 1.184 + 000 1 297 + 000 1.420 + 000 1 550 + 000 1.683 + 000 1.819 + 000 1.957 + 000 2 095 + 000 CO -0.20 1 043 + 000 1.090 + 000 1 139 + 000 1.186 + 000 1 230 + 000 1.271 + 000 1.307 + 000 1.339 + 000 1 368 + 000 1.563 + 000 -0.40 1 019 + 000 1.039 + 000 1 057 + 000 1.073 + 000 1 087 + 000 1.098 + 000 1.107 + 000 1.114 + 000 1 119 + 000 1.136 + 000 -0.60 1 007 + 000 1.014 + 000 1 019 + 000 1.024 + 000 1 028 + 000 1.030 + 000 1.032 + 000 1.033 + 000 1 034 + 000 1.036 + 000 -0.80 1 002 + 000 1.003 + 000 1 005 + 000 1.006 + 000 1 006 + 000 1.007 + 000 1.007 + 000 1.007 + 000 1 007 + 000 1.008 + 000 -1.00 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 -1.20 9.996 - 001 9.993 - 001 9.991-001 9.990-001 9 989 - 001 9.988-001 9.988 - 001 9.988 - 001 9 988 - 001 9.988 - 001 -1.40 9.997 - 001 9.994-001 9.993 - 001 9.992-001 9 991-001 9.991-001 9.991-001 9.991-001 9 991-001 9.991-001 -1.60 9.998-001 9.997-001 9.996-001 9.996 - 001 9 996 - 001 9.995 - 001 9.995 - 001 9.995 - 001 9 995 - 001 9.995 - 001 -1.80 9.999-001 9.999-001 9.999 - 001 9.999-001 9 999 - 001 9.998-001 9.998 - 001 9.998 - 001 9 998 - 001 9.998 - 001 -2.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000

199
Bl (N, r, fi) for r = 64.00

V

M 4 8 16 32 64 128 256 512 1024

2.00 3 333 + 000 I onn + 001 4 Q33 j- 001 \ 760 + 00? 6

93a _i_ 009 2

7QO -L 003 1.097 + 004 4 378 4- 004. 1.749 + 005

1.80 2 865 + 000 8 943 + 000 2 938 + 001 9 927 + 001 3 404 + 002 1

l if. i 003 4.080 + 003 I 4.1 R 4- 004 4 933 -)_ 004

1.60 2 477 + 000 716 + 000 I 919 + 001 5 644 + 001 \ 685 + 002 5 067 + 00? 1.530 + 003 4 630 4- 003 1.402 + 004

1.40 2 156 + 000 5 087 + 000 I 265 + 001 3 238 + 001 8 415 + 001 2 ?04 + 00? 5.793 + 002 I 5?6 4- 003 4.022 + 003 00 1.20 1 890 + 000 3 89] + 000 8 429 + 000 I 879 + 001 4 251 + 001 9 690 + 001 2.218 + 002 5 08S + 00? 1.167 + 003

1.00 1 670 + 000 3 010 + 000 5 691 + 000 1 105 + 001 2 177 + 001 4 322 + 001 8.611 + 001 1 719 + 002 3.435 + 002

0.80 1 489 + 000 2 363 + 000 3 909 + 000 6 624 + 000 1 137 + 001 1 966 + 001 3.411 + 001 5 929 + 001 1.031 + 002 00 0.60 1 341 + 000 1 889 + 000 2 749 + 000 4 080 + 000 6 119 + 000 9 229 + 000 1.396 + 001 2 114 + 001 3.203 + 001 00 0.40 1 224 + 000 1 548 + 000 2 003 + 000 2 624 + 000 3 461 + 000 4 578 + 000 6.060 + 000 8 023 + 000 1.062 + 001 00 0.20 1 135 + 000 1 313 + 000 1 536 + 000 1 808 + 000 2 129 + 000 2 506 + 000 2.944 + 000 3 450 + 000 4.033 + 000 00 -0.00 1 073 + 000 1 161 + 000 1 261 + 000 1 369 + 000 1 482 + 000 1 600 + 000 1.719 + 000 1 840 + 000 1.961 + 000 00 -0.20 1 035 + 000 1 073 + 000 1 112 + 000 1 151 + 000 1 187 + 000 1 220 + 000 1.249 + 000 1 275 + 000 1.298 + 000 1.456 + 000 -0.40 1 014 + 000 1 028 + 000 1 042 + 000 1 054 + 000 1 064 + 000 1 072 + 000 1.078 + 000 1 083 + 000 1.087 + 000 1.100 + 000 -0.60 1 005 + 000 1 009 + 000 1 013 + 000 1 016 + 000 1 018 + 000 1 020 + 000 1.021 + 000 1 022 + 000 1.022 + 000 1.024 + 000 -0.80 1 001 + 000 1 002 + 000 1 003 + 000 1 003 + 000 1 004 + 000 1 004 + 000 1.004 + 000 1 004 + 000 1.004 + 000 1.004 + 000 -1.00 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000+000 1 000 + 000 1.000 + 000 1.000 + 000 -1.20 9 998 - 001 9 997-001 9 996-001 9 995-001 9 995-001 9 995-001 9.995 - 001 9 995-001 9.995-001 9.995-001 -1.40 9 999-001 9 998-001 9 997-001 9 997-001 9 997-001 9 997-001 9.997-001 9 996-001 9.996-001 9.996-001 -1.60 9 999-001 9 999-001 9 999 - 001 9 999-001 9 999 - 001 9 999-001 9.998-001 9 998-001 9.998-001 9.998-001 -1.80 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 -2.00 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000

fl,(/V, r, /i.) for r= 128.00

V

4 8 16 32 64 128 256 512 1024 00

2.00 3 333 + 000 1 200 + 001 4.533 + 001 1 760 + 002 6.933 + 002 2 752 + 003 1.097 + 004 4.378 + 004 1 749 + 005 00 1.80 2 865 + 000 8 943 + 000 2.938 + 001 9 926 + 001 3.404 + 002 1 176 + 003 4.080 + 003 1.418 + 004 4 932 + 004 00 1.60 2 477 + 000 6 715 + 000 1.919 + 001 5 643 + 001 1.684 + 002 5 067 + 002 1.530 + 003 4.629 + 003 1 402 + 004 00 1.40 2 156 + 000 5 085 + 000 1.265 + 001 3 237 + 001 8.411 + 001 2 203 + 002 5.790 + 002 1.525 + 003 4 021 + 003 00 1.20 1 889 + 000 3 887 + 000 8.421 + 000 1 877 + 001 4.246 + 001 9 680 + 001 2.215 + 002 5.079 + 002 1 166 + 003 00 1.00 1 668 + 000 3 005 + 000 5.679 + 000 1 103 + 001 2.172 + 001 4 311 + 001 8.589 + 001 1.714 + 002 3 426 + 002 00 0.80 1 486 + 000 2 354 + 000 3.891 + 000 6 589 + 000 1.131 + 001 1 955 + 001 3.391 + 001 5.893 + 001 1 025 + 002 00 0.60 1 336 + 000 1 877 + 000 2.725 + 000 4 037 + 000 6.048 + 000 9 115 + 000 1.378 + 001 2.086 + 001 3 160 + 001 00 0.40 1 217 + 000 i 532 + 000 1.973 + 000 2 576 + 000 3.388 + 000 4 471 + 000 5.909 + 000 7.813 + 000 1 033 + 001 00 0.20 1 127 + 000 1 294 + 000 1.504 + 000 1 759 + 000 2.062 + 000 2 416 + 000 2.827 + 000 3.303 + 000 3 851 + 000 00 -0.00 1 065 + 000 1 144 + 000 1.232 + 000 1 329 + 000 1.430 + 000 1 534 + 000 1.640 + 000 1.748 + 000 1 856 + 000 00 -0.20 1 029 + 000 1 060 + 000 1.092 + 000 1 124 + 000 1.153 + 000 1 181 + 000 1.205 + 000 1.226 + 000 1 245 + 000 1.375 + 000 -0.40 1 010 + 000 1 021 + 000 1.031 + 000 1 040 + 000 1.047 + 000 1 053 + 000 1.058 + 000 1.062 + 000 1 065 + 000 1.074 + 000 -0.60 1 003 + 000 1 006 + 000 1.008 + 000 1 010 + 000 1.012 + 000 1 013 + 000 1.014 + 000 1.014 + 000 1 015 + 000 1.015 + 000 -0.80 1 001 + 000 1 001 + 000 1.002 + 000 1 002 + 000 1.002 + 000 1 002 + 000 1.002 + 000 1.002 + 000 1 002 + 000 1.002 + 000 -1.00 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 -1.20 9 999-001 9 999 - 001 9.998-001 9 998-001 9.998-001 9 998-001 9.998-001 9.998-001 9 998-001 9.998-001 -1.40 1 000 + 000 9 999-001 9.999-001 9 999-001 9.999 - 001 9 999-001 9.999-001 9.999-001 9 999-001 9.999-001 -1.60 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 9.999-001 9.999-001 9 999 - 001 9.999-001 -1.80 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 -2.00 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000

200
Bt(N, r, n) for r= 256.00 N

4 8 16 32 64 128 256 512 1024 00

2.00 3.333 + 000 1.200 + 001 4.533 + 001 1.760 + 002 6.933 + 002 2.752 + 003 1.097 + 004 4.378 + 004 1.749 + 005 00 1.80 2.865 + 000 8.943 + 000 2.938 + 001 9.926 + 001 3.404 + 002 1.176 + 003 4.080 + 003 1.418 + 004 4.932 + 004 00 1.60 2.477 + 000 6.715 + 000 1.919 + 001 5.642 + 001 1.684 + 002 5.066 + 002 1.530 + 003 4.629 + 003 1.402 + 004 00 1.40 2 156 + 000 5 084 + 000 1.264 + 001 3.236 + 001 8.410 + 001 2.202 + 002 5 789 + 002 1 525 + 003 4.020 + 003 OS 1.20 1 889 + 000 3 886 + 000 8.418 + 000 1.876 + 001 4.244 + 001 9.675 + 001 2 214 + 002 5 077 + 002 1.165 + 003 00 1.00 1 668 + 000 3 003 + 000 5.673 + 000 1.101 + 001 2.169 + 001 4.305 + 001 8 578 + 001 1 712 + 002 3.421+002 00 0.80 1 484 + 000 2 350 + 000 3.881 + 000 6.570 + 000 1.127 + 001 1.948 + 001 3 380 + 001 5 873 + 001 1.022 + 002 00 0.60 1 333 + 000 1 869 + 000 2.709 + 000 4.010 + 000 6.003 + 000 9.042 + 000 1 366 + 001 2 068 + 001 3.132 + 001 00 0 40 1 212 + 000 1 520 + 000 l1.7JZ ot;o -lT nnn UUU L . 1 i UUU q qqc _i_ nnn 4, ,j7't I UUU 5 800 + 000 7 662 + 000 i ni 9 -i- nni 1 .Ulz UUl

0.20 1 121+000 1 280 + 000 1.479 + 000 1.722 + 000 2.009 + 000 2.346 + 000 2 737 + 000 3 189 + 000 3.710 + 000 00 -0.00 1 059 + 000 1 130 + 000 1.210 + 000 1.296 + 000 1.388 + 000 1.482 + 000 1 577 + 000 1 674 + 000 1.772 + 000 00 -0.20 1 024 + 000 1 050 + 000 1.077 + 000 1.103 + 000 1.127 + 000 1.150 + 000 1 170 + 000 1 188 + 000 1.204 + 000 1.311+000 -0.40 1 008 + 000 1 016 + 000 1.023 + 000 1.029 + 000 1.035 + 000 1.039 + 000 1 043 + 000 1 046 + 000 1.048 + 000 1.055 + 000 -0.60 1 002 + 000 1 004 + 000 1.005 + 000 1.007 + 000 1.008 + 000 1.008 + 000 1 009 + 000 1 009 + 000 1.010 + 000 1.010 + 000 -0.80 1 000 + 000 1 001 + 000 1.001+000 1.001 + 000 1.001 + 000 1.001 + 000 1 001 + 000 1 001+000 1.001 + 000 1.001+000 -1.00 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 -1.20 1 000 + 000 9 999-001 9.999-001 9.999-001 9.999-001 9.999-001 9 999 - 001 9 999-001 9.999-001 9.999 - 001 -1.40 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 9 999-001 9.999-001 9.999-001 -1.60 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 -1.80 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 -2.00 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1.000 + 000

Bx(N, r, ix) for r= 512.00

N

4 8 16 32 64 128 256 512 1024 00

2.00 3 333 + 000 1.200 + 001 4.533 + 001 1 760 + 002 6.933 + 002 2.752 + 003 1 097 + 004 4.378 + 004 1.749 + 005 00 1.80 2 865 + 000 8.943 + 000 2.938 + 001 9 926 + 001 3.404 + 002 1.176 + 003 4 080 + 003 1.418 + 004 4.932 + 004 00 1.60 2 477 + 000 6.714 + 000 1.919 + 001 5 642 + 001 1.684 + 002 5.066 + 002 1 530 + 003 4.628 + 003 1.402 + 004 00 1.40 2 156 + 000 5.084 + 000 1.264 + 001 3 236 + 001 8.410 + 001 2.202 + 002 5 789 + 002 1.525 + 003 4.020 + 003 00 1.20 1 889 + 000 3.885 + 000 8.416 + 000 1 876 + 001 4.243 + 001 9.673 + 001 2 214 + 002 5.076 + 002 1.165 + 003 GO 1.00 1 667 + 000 3.001 + 000 5.670 + 000 1 101 + 001 2.168 + 001 4.303 + 001 8 572 + 001 1.711 + 002 3.419 + 002 00 0.80 1 483 + 000 2.347 + 000 3.875 + 000 6 558 + 000 1.125 + 001 1.945 + 001 3 373 + 001 5.862 + 001 1.020 + 002 00 0.60 1 331+000 1.864 + 000 2.699 + 000 3 992 + 000 5.973 + 000 8.994 + 000 1 359 + 001 2.056 + 001 3.114 + 001 00 0.40 1 209 + 000 1.512 + 000 1.936 + 000 2 516 + 000 3.296 + 000 4.338 + 000 5 721 + 000 7.553 + 000 9.973 + 000 00 0.20 1 116 + 000 1.268 + 000 1.460 + 000 1 692 + 000 1.967 + 000 2.290 + 000 2 665 + 000 3.098 + 000 3.598 + 000 -0.00 1 054 + 000 1.118 + 000 1.191 + 000 1 270 + 000 1.353 + 000 1.438 + 000 1 526 + 000 1.614 + 000 1.703 + 000 00 -0.20 1 020 + 000 1.042 + 000 1.064 + 000 1 086 + 000 1.107 + 000 1.125 + 000 1 142 + 000 1.157 + 000 1.170 + 000 1.261 + 000 -0.40 1 006 + 000 1.012 + 000 1.017 + 000 1 022 + 000 1.026 + 000 1.030 + 000 1 032 + 000 1.034 + 000 1.036 + 000 1.041 + 000 -0.60 1 001 + 000 1.003 + 000 1.004 + 000 1 004 + 000 1.005 + 000 1.006 + 000 1 006 + 000 1.006 + 000 1.006 + 000 1.007 + 000 -0.80 1 000 + 000 1.000 + 000 1.001 + 000 1 001+000 1.001 + 000 1.001+000 1 001 + 000 1.001 + 000 1.001+000 1.001+000 -1.00 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.20 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.40 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.60 1 000 + 000 1.000 + 000 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.80 1 .000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -2.00 1 .000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000

201
Bi {N, r, ix) for r= 1024.00

N

4 8 16 32 64 128 256 512 1024 00

2 [)[) 3 333 + 000 1.200 + 001 4 533 + 001 1 760 + 002 6.933 + 002 2 752 + 003 1 097 + 004 4 378 + 004 1 749 + 005 00

1 80 2 865 + 000 8.943 + 000 2 938 + 001 9 926 + 001 3.404 + 002 1 176 + 003 4 080 + 003 1 418 + 004 4 932 + 004 00

1 60 2 477 + 000 6.714 + 000 1 919 + 001 5 642 + 001 1.684 + 002 5 066 + 002 1 530 + 003 4 628 + 003 1 402 + 004 00

1 40 2 156 + 000 5.084 + 000 1 264 + 001 3 236 + 001 8.409 + 001 2 202 + 002 5 789 + 002 1 525 + 003 4 020 + 003 GO

1 20 1 889 + 000 3.885 + 000 8 416 + 000 1 876 + 001 4.243 + 001 9 672 + 001 2 213 + 002 5 075 + 002 1 165 + 003 00

1 00 1 667 + 000 3.001 + 000 5 668 + 000 1 100 + 001 2.167 + 001 4 301 + 001 8 569 + 001 1 711 + 002 3 418 + 002 CO 0 80 1 482 + 000 2.345 + 000 3 872 + 000 6 552 + 000 1.124 + 001 1 942 + 001 3 369 + 001 5 855 + 001 1 018 + 002 CO 0 60 1 330 + 000 1.860 + 000 2 693 + 000 3 980 + 000 5.953 + 000 8 963 + 000 1 354 + 001 2 049 + 001 3 102 + 001 CO 0 40 1 206 + 000 1.505 + 000 1 924 + 000 2 497 + 000 3.268 + 000 4 297 + 000 5 663 + 000 7 472 + 000 9 862 + 000 00 0 20 1 112 + 000 1.259 + 000 1 444 + 000 1 668 + 000 1.934 + 000 2 245 + 000 2 607 + 000 3 025 + 000 3 507 + 000 00 -0 00 1 049 + 000 1.108 + 000 1 175 + 000 1 248 + 000 1.324 + 000 1 402 + 000 1 483 + 000 1 564 + 000 1 645 + 000 00 -0 20 1 017 + 000 1.035 + 000 1 054 + 000 1 073 + 000 1.090 + 000 1 106 + 000 1 120 + 000 1 132 + 000 1 144 + 000 1.220 + 000 -0 40 1 004 + 000 1.009 + 000 1 013 + 000 1 017 + 000 1.020 + 000 1 022 + 000 1 024 + 000 1 026 + 000 1 027 + 000 1.031 + 000 -0 60 1 001 + 000 1.002 + 000 1 002 + 000 1 003 + 000 1.003 + 000 1 004 + 000 1 004 + 000 1 004 + 000 1 004 + 000 1.004 + 000 -0 80 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1 (in 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1 20 1 Q00 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1 40 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1 60 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1 80 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -2 00 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000

B,(N, r, n) for r= 2048.00 N

M 4 8 16 32 64 128 256 512 1024 00

2.00 3 333 + 000 1 200 + 001 4.533 + 001 1 760 + 002 6 933 + 002 2 752 + 003 1 097 + 004 4 378 + 004 1 749 + 005 00 1.80 2 865 + 000 8 943 + 000 2.938 + 001 9 926 + 001 3 404 + 002 1 176 + 003 4 080 + 003 1 418 + 004 4 932 + 004 CO 1.60 2 477 + 000 6 714 + 000 1.919 + 001 5 642 + 001 1 684 + 002 5 066 + 002 1 530 + 003 4 628 + 003 1 402 + 004 00 1.40 2 156 + 000 5 084 + 000 1.264 + 001 3 236 + 001 8 409 + 001 2 202 + 002 :> 789 + 002 1 525 + 003 4 020 + 003 CO 1.20 1 889 + 000 3 885 + 000 8.415 + 000 1 875 + 001 4 243 + 001 9 672 + 001 2 213 + 002 5 075 + 002 1 165 + 003 00 1.00 1 667 + 000 3 000 + 000 5.667 + 000 1 100 + 001 2 167 + 001 4 301 + 001 8 568 + 001 1 710 + 002 3 417 + 002 00 0.80 1 482 + 000 2 345 + 000 3.870 + 000 6 548 + 000 1 123 + 001 1 941 + 001 3 367 + 001 5 851 + 001 1 018 + 002 00 0.60 1 329 + 000 1 858 + 000 2.688 + 000 3 972 + 000 5 941 + 000 8 942 + 000 1 351 + 001 2 044 + 001 3 095 + 001 00 0.40 1 204 + 000 1 501 + 000 1.916 + 000 2 483 + 000 3 247 + 000 4 266 + 000 5 620 + 000 7 412 + 000 9 780 + 000 00 0.20 1 108 + 000 1 251 + 000 1.431 + 000 1 648 + 000 1 906 + 000 2 209 + 000 2 560 + 000 2 966 + 000 3 434 + 000 CO -0.00 ] 045 + 000 1 100 + 000 1.162 + 000 1 229 + 000 1 299 + 000 1 372 + 000 1 446 + 000 1 521 + 000 1 596 + 000 CO -0.20 1 014 + 000 1 030 + 000 1.046 + 000 1 061 + 000 1 076 + 000 1 089 + 000 1 101 + 000 1 112 + 000 1 122 + 000 1.186 + 000 -0.40 1 003 + 000 1 007 + 000 1.010 + 000 1 012 + 000 1 015 + 000 1 017 + 000 1 018 + 000 1 019 + 000 1 020 + 000 1.023 + 000 -0.60 1 001 + 000 1 001 + 000 1.002 + 000 1 002 + 000 1 002 + 000 1 002 + 000 1 003 + 000 1 003 + 000 1 003 + 000 1.003 + 000 -0.80 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1.00 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000+000 1.000 + 000 -1.20 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1.40 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1.60 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -1.80 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000 -2.00 1 000 + 000 1 000 + 000 1.000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1 000 + 000 1.000 + 000

202
B,(/V, r, ft) forr=»

N

4 8 16 32 64 128 256 512 1024 00

2.00 3.333 + 000 1.200 + 001 4.533 + 001 1.760 + 002 6.933 + 002 2.752 + 003 1.097 + 004 4.378 + 004 1.749 + 005 00 1.80 2.865 + 000 8.943 + 000 2.938 + 001 9.926 + 001 3.404 + 002 1.176 + 003 4.080 + 003 1.418 + 004 4.932 + 004 00 1.60 2.477 + 000 6.714 + 000 1.919 + 001 5.642 + 001 1.684 + 002 5.066 + 002 1.530 + 003 4.628 + 003 1.402 + 004 00 1.40 2.156 + 000 5.084 + 000 1.264 + 001 3.236 + 001 8.409 + 001 2.202 + 002 5.789 + 002 1.525 + 003 4.020 + 003 00 1.20 1.889 + 000 3.885 + 000 8.415 + 000 1.875 + 001 4.243 + 001 9.672 + 001 2.213 + 002 5.075 + 002 1.165 + 003 00 1.00 1.667 + 000 3.000 + 000 5.667 + 000 1.100 + 001 2.167 + 001 4.300 + 001 8.567 + 001 1.710 + 002 3.417 + 002 00 0.80 1.482 + 000 2.343 + 000 3.867 + 000 6.543 + 000 1.123 + 001 1.940 + 001 3.364 + 001 5.846 + 001 1.017 + 002 00 0.60 1.327 + 000 1.854 + 000 2.680 + 000 3.958 + 000 5.916 + 000 8.903 + 000 1.344 + 001 2.034 + 001 3.080 + 001 00 0.40 1.198 + 000 1.487 + 000 1.890 + 000 2.441+000 3.184 + 000 4.174 + 000 5.489 + 000 7.231 + 000 9.533 + 000 00 0.20 1.091 + 000 1.210 + 000 1.360 + 000 1.541 + 000 1.757 + 000 2.009 + 000 2.303 + 000 2.642 + 000 3.033 + 000 00 -0.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -0.20 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -0.40 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -0.60 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -0.80 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.20 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.40 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.60 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.80 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -2.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000

B2 (r, ft)

r

M 0.001 0.003 0.010 0.030 0.100 0.200 0.400 0.800

2.00 1.000- 006 9.000 -006 1.000 -004 9.000- 004 1.000- 002 4.000 -002 1.600 -001 6.400 -001

1.80 1.072- 006 9.645 -006 1.072 -004 9.642 - 004 1.070- 002 4.263 -002 1.686 -001 6.525 -001

1.60 1.152- 006 1.037 -005 1.152 -004 1.036- 003 1.147- 002 4.547 -002 1.776 -001 6.652 -001

1.40 1.245- 006 1.120 -005 1.244 -004 1.118 — 003 1.233- 002 4.860 -002 1.871 -001 6.781 -001

1.20 1.356- 006 1.221 -005 1.355 -004 1.216- 003 1.333- 002 5.207 -002 1.972 -001 6.910 -001

1.00 1.500- 006 1.349 -005 1.495 -004 1.337- 003 1.450- 002 5.600 -002 2.080 -001 7.040 -001

0.80 1.698- 006 1.524 -005 1.683 -004 1.493- 003 1.593- 002 6.052 -002 2.196 -001 7.170 -001

0.60 2.001- 006 1.788 -005 1.955 -004 1.708- 003 1.773- 002 6.583 -002 2.321 -001 7.299 -001

0.40 2.530- 006 2.228 -005 2.381 -004 2.020- 003 2.006- 002 7.219 -002 2.457 -001 7.426 -001

0.20 3.594- 006 3.048 -005 3.100 -004 2.494- 003 2.316- 002 7.996 -002 2.607 -001 7.549 -001

-0.00 6.065- 006 4.745 -005 4.404 -004 3.250- 003 2.742- 002 8.962 -002 2.773 -001 7.667 -001

-0.20 1.260- 005 8.606 -005 6.921 -004 4.507 - 003 3.340- 002 1.018 -001 2.959 -001 7.775 -001

-0.40 3.174- 005 1.809 -004 1.204 -003 6.664- 003 4.195- 002 1.175 -001 3.168 -001 7.869 -001

-0.60 9.231- 005 4.280 -004 2.288 -003 1.047- 002 5.438- 002 1.379 -001 3.407 -001 7.944 -001

-0.80 2.949- 004 1.101 -003 4.662 -003 1.735- 002 7.271 — 002 1.646 -001 3.682 -001 7.992 -001

-1.00 1.000- 003 3.000 -003 1.000 -002 3.000- 002 1.000- 001 2.000 -001 4.000 -001 8.000 -001

-1.20 3.525- 003 8.489 -003 2.225 -002 5.362- 002 1.410- 001 2.472 -001 4.371 -001 7.954 -001

-1.40 1.276- 002 2.467 -002 5.081 -002 9.828- 002 2.032- 001 3.104 -001 4.808 -001 7.832 -001

-1.60 4.708- 002 7.306 -002 1.183 -001 1.836- 001 2.979- 001 3.956 -001 5.324 -001 7.606 -001

-1.80 1.762- 001 2.195 -001 2.793 -001 3.479- 001 4.431- 001 5.107 -001 5.936 -001 7.236 -001

-2.00 6.667- 001 6.667 -001 6.667 -001 6.667- 001 6.667- 001 6.667 -001 6.667 -001 6.667 -001

203
B2 (r, At)

M 1.00 1.01 1.10 2.00 4.00 8.00 16.00 32.00

2.00 1 AArt i AAA 1.000 + 000 1 020 + 000 i ni a i aaa 1.210 + 000 4.000 + 000 1.600 + 001 6.400 + 001 2.560 + 002 1.024 + 003

1.80 i aaa i aaa 1.000 + 000 1 019 + 000 i i no 1 AAA 1.198 + 000 3.642 + 000 1.289 + 001 4.513 + 001 1.574 + 002 5.485 + 002

1.60 1.000 + 000 1 018 + 000 1.186 + 000 3.316 + 000 1.039 + 001 3.188 + 001 9.706 + 001 2.947 + 002

1.40 1.000 + 000 1 017 + 000 1.174 + 000 3.018 + 000 8.389 + 000 2.259 + 001 6.008 + 001 1.590 + 002

1.20 1.000 + 000 1 016 + 000 i i £. o i aaa 1.162 + 000 2.747 + 000 6.784 + 000 1.607 + 001 3.741 +001 8.644 + 001

1.00 1.000 + 000 1 015 + 000 1.150 + 000 2.500 + 000 5.500 + 000 1. 150 -t- 001 2.350 + 001 4.750 + 001

0.80 i aaa i aaa 1.000 + 000 1 014 + 000 1.138 + 000 n mr i AAA 2.275 + 000 4.475 + 000 8.297 + 000 1.495 + 001 2.653 + 001

0.60 1.000 + 000 1 013 + 000 1.126 + 000 2.071 + 000 3.658 + 000 £. AC 1 I AAA 6.051 +000 9.673 + 000 1.516 + 001 0.40 1.000 + 000 1 012 + 000 1.114 + 000 1.886 + 000 3.007 + 000 4.473 + 000 6.404 + 000 8.951 + 000

0.20 1.000 + 000 1 011 + 000 1.102 + 000 1.718 + 000 2.489 + 000 3.364 + 000 4.365 + 000 5.514 + 000 -0.00 1.000 + 000 1 010 + 000 1.089 + 000 1.566 + 000 2.078 + 000 2.581 + 000 3.082 + 000 3.582 + 000 -0.20 1.000 + 000 1 009 + 000 1.075 + 000 1.429 + 000 1.752 + 000 2.027 + 000 2.265 + 000 2.472 + 000 -0.40 1.000 + 000 1 007 + 000 1.060 + 000 1.304 + 000 1.494 + 000 1.633 + 000 1.738 + 000 1.817 + 000 -0.60 1.000 + 000 1 006 + 000 1.043 + 000 1.192 + 000 1.290 + 000 1.351 + 000 1.392 + 000 1.418 + 000 -0.80 1.000 + 000 1 004 + 000 1.024 + 000 1.091 + 000 1.128 + 000 1.148 + 000 1.159 + 000 1.166 + 000 -1.00 1.000 + 000 1 000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.20 1.000 + 000 9 929-001 9.693-001 9.181-001 8.990-001 8.912-001 8.879-001 8.865 - 001 -1.40 1.000 + 000 9 776 - 001 9.281-001 8.446 - 001 8.192-001 8.103 - 001 8.071-001 8.058-001 -1.60 1.000 + 000 9 429 - 001 8.708-001 7.787-001 7.561-001 7.494-001 7.472-001 7.465-001 -1.80 1.000 + 000 8 614-001 7.883-001 7.196-001 7.062-001 7.028-001 7.018-001 7.015-001 -2.00 1.000 + 000 6 667-001 6.667-001 6.667-001 6.667-001 6.667-001 6.667-001 6.667 - 001

B2 (r, ft)

64.00 128.00 256.00 512.00 1024.00 2048.00

2.00 4.096 + 003 1.638 + 004 6.554 + 004 2.621+005 1.049 + 006 4.194 + 006 CO 1.80 1.910 + 003 6.653 + 003 2.317 + 004 8.067 + 004 2.809 + 005 9.783 + 005 00 1.60 8.937 + 002 2.710 + 003 8.215 + 003 2.490 + 004 7.550 + 004 2.288 + 005 00 1.40 4.201 + 002 1.109 + 003 2.928 + 003 7.727 + 003 2.039 + 004 5.381 + 004 GO 1.20 1.991+002 4.579 + 002 1.052 + 003 2.418 + 003 5.555 + 003 1.277 + 004 00 1.00 9.550 + 001 1.915 + 002 3.835 + 002 7.675 + 002 1.536 + 003 3.071+003 00 0.80 4.669 + 001 8.179 + 001 1.429 + 002 2.493 + 002 4.346 + 002 7.570 + 002 00 0.60 2.348 + 001 3.609 + 001 5.521 + 001 8.418 + 001 1.281 + 002 1.946 + 002 00 0.40 1.231 + 001 1.674 + 001 2.260 + 001 3.031 + 001 4.050 + 001 5.395 + 001 CO 0.20 6.834 + 000 8.351 + 000 1.009 + 001 1.209 + 001 1.439 + 001 1.704 + 001 00 -0.00 4.082 + 000 4.582 + 000 5.082 + 000 5.582 + 000 6.082 + 000 6.582 + 000 00 -0.20 2.652 + 000 2.809 + 000 2.945 + 000 3.064 + 000 3.167 + 000 3.258 + 000 3.863 + 000 -0.40 1.877 + 000 1.923 + 000 1.957 + 000 1.983 + 000 2.003 + 000 2.018 + 000 2.065 + 000 -0.60 1.436 + 000 1.447 + 000 1.455 + 000 1.460 + 000 1.463 + 000 1.465 + 000 1.470 + 000 -0.80 1.170 + 000 1.172 + 000 1.173 + 000 1.174 + 000 1.174 + 000 1.174 + 000 1.175 + 000 -1.00 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 1.000 + 000 -1.20 8.859-001 8.856-001 8.855 - 001 8.854-001 8.854-001 8.854-001 8.854-001 -1.40 8.053 - 001 8.052 - 001 8.051-001 8.851-001 8.051-001 8.051-001 8.051-001 -1.60 7.462 - 001 7.462-001 7.461-001 7.461-001 7.461-001 7.461-001 7.461-001 -1.80 7.015-001 7.014-001 7.014-001 7.014-001 7.014-001 7.014-001 7.014-001 -2.00 6.667-001 6.667-001 6.667-001 6.667-001 6.667-001 6.667-001 6.667-001

204
CHAPTER 9

THE NATIONAL BUREAU OF STANDARDS ATOMIC TIME SCALE:

GENERATION, STABILITY, ACCURACY

AND ACCESSIBILITY**

David W. Allan,t James E. Gray,t and Howard E. Machlanf

Contents Page

9.1. Introduction 207

9.2. Basic Time and Frequency Considerations 208

9.3. Clock Modeling 208

9.3.1. Deterministic Properties 208

9.3.2. Random Perturbation of a Clock's Time 209

9.3.3. Clock Noise Characterization and Data Simulation 212

9.4. The AT (NBS) Time Scale System 214

9.4.1. The NBS Primary Frequency Standard and Measurement System 214

9.4.2. The Clock Ensemble and Time Difference System 215

9.4.3. Atomic Time Scale Algorithms 215

9.5. The UTC (NBS) Coordinated Scale 220

9.6. UTC (NBS) Accessibility 221

9.7. The International Atomic Time Scale (TAI) 223

9.8. Conclusions 223

9.9. References! 224

Annex 9. A. Optimum Filters for Various Noise Processes (Eq (9.19)) 225

Annex 9. B. Time Dispersion with Recursive Filter Applied to Flicker Noise FM 226

Annex 9. C. Mini-Computer Program for First Order Time Scale Algorithm 227

Annex 9. D. Selected Bibliography on Time Scales and Their Formation 230

• This chapter was presented in part as a paper at the Precision Electromagnetic Measurements Conference (CPEM), Boulder. CO, June 1972. A small part of the chapter includes material from "The National Bureau of Standards atomic time scales: generation, dissemination, stability and accuracy," published in IEEE

Trans, on lustrum, and Meas., November 1972 (see ref. B6). Material is republished at concurrence of the IEEE. tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, CO 80302.

205
"Go wond'rous creature, mount where science guides. Go, measure earth, weigh air and state the tides; Instruct the planets in what orbs to run, Correct old time, and regulate the sun,"

Pope's Essay on Man

The atomic time scale at the National Bureau of Standards, AT(NBS), depends upon an ensemble

of continuously operating cesium clocks calibrated occasionally by an NBS primary frequency standard. The data of frequency calibrations and interclock comparisons are statistically processed to provide

near-optimum time stability and frequency accuracy. The noise spectrum of each clock is represented

by_ a simple mathematical model, with parameters determined by the behavior of that clock. These

noise parameters are used in a nearly optimum procedure for periodically recalibrating the frequency

of each clock and for combining the clock readings to produce AT(NBS). The long-term fractional frequency stability of AT(NBS) is estimated to be a few parts in 1013

, and the accuracy is inferred to be

1 part in 1012. A small coordinate rate is added to the rate of AT(NBS) to generate UTC(NBS): this small addition

is for the purpose of maintaining synchronization within a few microseconds of other international timing centers. Today, UTC(NBS) is operationally available over a large part of the world via; WWV,

WWVH, WWVB, and telephone; some time transfer systems, e.g., Loran-C and the TV line-10 sys- tem; and experimental systems such as the ATS-3 satellite. We indicate the precision and accuracy

of these dissemination systems. The clocks composing AT(NBS) provide part of the input into the International Atomic Time

scale (TAI). The TAI scale is described and new proposals for improvement of this time scale are discussed. Many of the concepts and algorithms developed in this chapter may be directly applicable

to the construction of a TAI scale in conformity to the SI unit of time.

Key words: AT(NBS); atomic clock; atomic time scale; clock ensemble; primary frequency standard; SI second; TAI; time/frequency dissemination; time scale; time scale algorithms; UTC(NBS).

206
9.1. INTRODUCTION

Although the atomic definition of the Systeme

International (SI) Second has been accepted inter- nationally, several differing techniques have been

advanced for the construction and maintenance

of atomic time scales. These varied techniques

capitalize to different degrees on such factors as accuracy, stability, modeling and simulation of

atomic clocks, availability and cost and, to a large

extent, where developed within particular circumstances of given laboratories. Such techniques

include a time scale averaged over a multiplicity of selected commercial cesium beam clocks

[l], 1 continuous use of a long-beam, primary cesium

standard (laboratory) for generation of a time scale more nearly in conformity with SI [2], maintenance

of a time scale generated by an ensemble of statis- tically weighted cesium atomic clocks which are

periodically compared to an evaluable primary

frequency standard (laboratory) [3, 4], and establishment of a statistically weighted atomic time

scale based on some 7 International atomic time

scales (International Atomic Time — TAI) [5].

The independent atomic time scale at the National

Bureau of Standards, AT(NBS), depends upon

an ensemble of continuously operating cesium

clocks calibrated occasionally by an NBS primary

frequency standard from which the AT(NBS)

scale derives its accuracy. The stability of the en- semble between calibrations is of fundamental

importance.

The instabilities of each clock in the ensemble

may be bicategorized: First, there are deterministic

processes that should be considered for each clock;

e.g., frequency and time offsets, changes in these

offsets, and frequency drift. Changes or drifts in frequency may be estimated by referring to the

definition of time across the ensemble and/or

with reference to a primary standard. Second, there

are random fluctuations (nondeterministic). The

noise spectrum of these random fluctuations for each clock is deduced by comparing each clock

with all the others. A simple mathematical model

reasonably represents this noise spectrum with

parameters determined by the random behavior

of each clock. These noise parameters provide near optimum filtering of each clock's noise and

give a best estimate (in the sense of minimum

squared error of prediction) of the apparent time

and frequency of each clock with respect to the

clock ensemble. Knowledge of the noise spectrum

for each clock allows an estimate of the noise of the

ensemble; the long-term random fluctuation of the

fractional frequency of AT(NBS) are estimated to be a few parts in 1014

, whereas, the instability due

to deterministic process are estimated to be less than about 2 X 10- 13 /year.

1 Figures in brackets indicate the literature references at the end of this chapter.

The inaccuracy of a primary frequency standard

may also be bicategorized. In an evaluation of the

parameters which affect the frequency of the primary standard, there are two factors associated

with each parameter; i.e., a bias (possibly zero)

and a random uncertainty in our knowledge of its effect. If the time scale has excellent stability, one can average the random portion (in an appropriate weighted sense) of all the frequency cali- brations with a primary frequency standard.

The AT(NBS) scale in overview is an ensemble

of eight commercial cesium beam clocks maintained independently. The clocks are statistically

weighted (i.e., filtered) to generate a time scale,

AT(NBS), with nearly optimum stability. This

scale is used as a memory for frequency in utilizing

all of the frequency calibrations with respect

to an NBS primary frequency standard. These

calibrations are then used after appropriate weighting and filtering to determine the proper

2 rate and the accuracy of the AT(NBS) scale. This scale,

along with the atomic time scales of six other

laboratories, is used to generate the International

Atomic Time Scale, TAI, at the Bureau Inter- national de l'Heure (BIH)[5].

In conjunction with the AT(NBS) proper time

scale, we also generate the coordinate time scale,

UTC(NBS). This latter scale is both synchronized

(coordinated) to within a few microseconds of the

UTC(BIH) scale and mutually coordinated with the

UTC(USNO) scale. This coordination is accomplished by small discrete rate changes (of the order

of 10- 13

) in UTC(NBS) and in. UTC(USNO). One

second time jumps are made as announced by the

BIH for keeping these scales within 0.7s of the UT1

scale [6] (see chap. 1). The UTC(NBS) scale is used as the reference

for time and frequency broadcasts of the National

Bureau of Standards. The time of this scale and

frequencies derived therefrom are currently made

available via sundry methods: e.g., the two radio

transmitters at Ft. Collins, Colo., WWV and

WWVB [7, 8]; the radio transmitters at Kekaha,

Kauai, Hawaii, WWVH; portable clocks [9];

both the television color subcarrier and line-10 time transfer systems [10, 11]; telephone (303)

499-7111; and the experimental ATS-3 satellite [12], which broadcasts time and frequency infor- mation with a format similar to that of WWV and

WWVH. The future holds many possibilities of

providing time and frequency information including an active TV line-21 system, a relay satellite system,

and a time code on the Omega transmissions.

The chapter discusses basic ideas inherent

in consideration of an atomic time scale including

terminology, statistical clock modeling, and realiza- tion of a near optimum atomic time scale. The dis- cussion includes topics such as deterministic

1 Proper is used here in the relativistic sense. 207
properties, random perturbations of a clock's time,

and atomic time scale algorithms. There is a detailed description of the NBS atomic time scales

including their derivation and stability. Also, there is a brief discussion of the TAI and its stability;

the ensemble analysis has relevance to the composite International Atomic Time (TAI) scale. The chapter includes a description of the UTC(NBS)

time scale, its accessibility, and a comparison of

accuracy, coverage, cost, etc. for different methods

of access. The annexes at the end of the chapter

give detailed derivations and an example of a computer program of a time scale algorithm.

9.2. BASIC TIME AND FREQUENCY

CONSIDERATIONS

At this point we will review some basic time and

frequency ideas described in other chapters of

this monograph. Time — as a fundamental parameter in physics — almost always appears as an independent variable in any of the physical laws

involving time. In contrast; it is our intent to derive time, i.e., we will express time as a dependent

variable. Explicitly, time will be a function of how

a particular clock ensemble and frequency standard

are utilized. (A clock is a frequency standard coupled

to a divider or counter.) This functional dependence

may clearly be formalized by introducing some

fundamental concepts of time.

First is the concept of time interval. Currently,

the SI unit of time, the second, "is the duration of

9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine

levels of the ground state of the cesium-133 atom"

as defined by the General Conference of Weights

and Measures [13]. Since the frequency of the

radiation corresponding to the above transition,

v, has also been defined as 9 192 631 770 Hz, we

retain the convenient relationship that Vi=1/ti,

and we see simply how a frequency standard is also a time interval standard. The second concept

is that of date, clock reading, or clock time which

often has been called epoch.3 Date is simply the

counting or accumulation — starting from some

predetermined origin — of unit time intervals. Explicitly, the date, t, is a counting of the periods

of the above defined cesium transition; i.e.,

t = Nm + to, (9.1)

where to denotes some defined and/or agreed upon

date of an event when the counting started, N] is the number of periods that have occurred since to, and Ti is the ideal period given by the defined

cesium resonance. The ideal proper time of a clock

is, therefore, given by t in eq (9.1).

3 See discussion of date and epoch in Chapter 1.

A third concept is simultaneity: Two events are simultaneous if equivalent signals, propagating in a given media arrive coincidentally at a common

point in space which is geometrically an equal dis- tance from the source of each event. In practice a much broader definition is often used for clock

synchronization; i.e., two clocks have the same

reading in a specific reference frame.

In any discussion of an atomic time scale it is essential that there be understanding as to the basic

terms of reference and terminology. Such terms

include accuracy, stability, precision, and reproducibility. The reader is referred to Chapter 8 for comprehensive definitions of these expressions.

9.3. CLOCK MODELING

In this section we will assume that we have a perfect clock reference denoted by t. In theory when we assume certain clock models and simulate data

based on those models the above assumption is totally valid. In practice we make an effort to ap- proach its total validity.

As it is often much easier to deal with residuals, we will refer to a clock's time difference from the

ideal (or its estimation of the ideal in practice).

This section describes deterministic properties,

random perturbations of a clock's time, and clock

noise characterization and data simulation.

9.3.1. Deterministic Properties

Deterministic properties indicate frequency off- set or time drift, frequency or time jumps and other

kinds of clock aging. We consider various aspects

of such factors below:

a. Accuracy and precision ofsynchronization. The

apparent time of the ith clock is:

t i = Ni T i +Ti(t0 )+to, (9.2)

where Ti(to) denotes the difference from ideal time

of its reading at to, Ni is the number of its periods

that have transpired since to and t, is the period of

the ith clock (the number of seconds per cycle). The

accuracy of its reading at a particular time t is given

by the actual value of Ti(t) — ti — t (how well it is synchronized); whereas, the time precision is given

by the uncertainties in how well the value of Ti(t)

is known. If the rate of the ith clock is correct

(Ti = T/) , then the accuracy and precision at any

time t are limited only by the accuracy and precision

at the origin, Ti(to) —essentially unrealizable in practice.

b. Accuracy and precision of clock rate or fre- quency. If the frequency of the ith clock is not

correct (tj ^t/) but is constant then the reading

of the clock will diverge from the ideal reference.

The residual time difference Ti(t) — ti~ t will be

208
given by:

Ti (t)=NiTi-NITI +Ti(t0 ), (9.3)

which may be rewritten as Ti (t) = R i x[t-t0 ] + Ti (t 0 ). (9.4)

Ri denotes the relative rate offset of the ith clock;

e.g., a particular clock may differ in frequency such

that it runs fast + 8.64 nanoseconds per day (86400s).

This relative rate offset is equivalent to the fractional frequency which we will denote by y% (in this case yi=10-13

), where

V,

Vl

(9.5)

The accuracy of the fractional frequency of the

tth clock is given by an estimate of y;; whereas, the

precision of its fractional frequency is given by the

uncertainties in how well the value of y% is known.

c. Frequency drift of a clock. Essentially, all quartz crystal oscillators and rubidium gas cell frequency standards exhibit nonzero linear fre- quency drift [14]. Recently there has been documentation of the same phenomena in some commercial cesium beam frequency standards [2], and we

will give additional documentation later in this chapter. Obviously, in this case the rate does not remain constant and we must modify eq (9.4) to give the following model:

Ti(t)=Wi* [t-t0 ]

2 + Ri(t0 ) x [t-t0 ] + Ti(t0 ),

(9.6)

where Di is the fractional frequency drift per unit time and is here assumed constant. Note, the rate

is now specified at a particular date.

d. Other deterministic perturbations. Occasionally—due to some perturbation either external or

internal — a clock will manifest a different drift rate, a step change in its rate, or a step in its time.

Mechanisms and/or methods to detect these kinds

of perturbations should therefore be employed in order to affect a uniform time scale. In Section 9.4.3 we will discuss some possible methods of detection.

9.3.2. Random Perturbation of a Clock's Time

After the deterministic processes are properly

assessed and accounted for in a clock, there will

still remain a time deviation from this deterministic

model, e.g., see eq (9.6). These deviations or fluctu- ations will be classified as random. Later, a causal

relationship may be found which will account for some part of these deviations, but until such time,

it is useful to use statistical techniques to categorize

these random processes. This section describes the

random (nondeterministic) fluctuations in a time

scale; it gives statistical tools for modeling fre- quency stability and time dispersion.

a. Statistical Modelsfor Frequency Stability. As a general model of clock behavior, let x(t) denote

these random deviations, and we will add this term

to (9.6) to give:

Ti(t)=WiX [t-to] 2 + Ri(t0 ) X [t-tu]

+ Ti (tl) )+xi (t). (9.7)

Dr. James A. Barnes has conducted some tests on

the distribution o{x(t) for cesium and quartz clocks,

and in those cases it was found to be normal. If we can assume normality, and know the spectral

density or the auto-correlation function iorx(t), we

would then have a complete statistical description

of this process. Most high performance clocks can

be well modeled statistically with a power law

spectral density; i.e. S„(f)=ha \f\°, (9.8)

where /is the Fourier frequency, ha is the amplitude

of the spectral density for a particular power law a, andSy(f) denotes the one-sided spectral density of the fractional frequency fluctuations y, and y is normally distributed [15, 16]. It should be noted

that equation (9.5) for yi is a fractional frequency

offset, where y denotes flucations. The two designations differ only by a delta function at zero Fourier

frequency, which is uninteresting and has caused

little or no confusion in the past.

Typically, clock data (time or phase points) are taken in the time-domain; and time-domain stability measures involving auto-correlation functions are

useful. In particular, we have employed the Allan

variance [15, 16]

:

{o$(N, ^T,/0)=(^[iyfj) -^(irO-))

2 lV

(9.9)

where y(j) is the 7th data point in a sequence of

fractional frequency data samples each of which

is averaged over a nominal time r and at a sampling

rate 1/T; fh is the high frequency cutoff (the meas- urement system's effective bandwidth), and the

angle brackets denote infinite time average. Two

convenient relations may quickly be shown by set- ting yV= 2 and T— t in eq (9.9), and we then have,

<o-*(2, r, t,/*)>=o-S(t) / [yO'+D-yQ')] 2

(9.10)

209
or

°1(T)=^ [Wx (t)-Ux (2t)], (9.11)

where

UAT) = ([x(t)-x(t + T)Y-). (9.12)

Note, that fh is not explicitly indicated as a variable

in eqs (9.10)-(9.12), because typically it is held constant for a given experiment; none-the-less, its value

should be stated. Though the data may have been

taken with T # t, it is often possible to convert eq

(9.9) for any TV, T, and t to that given by eq (9.10)

(see ref. [17], also chap. 8). This particular auto- correlation function Ux (t) is useful in dealing with some of the low frequency divergent power law spectral densities; viz., flicker noise frequency modulation [18]. Using the appropriate Fourier transform

relationships one can write the following:

2h f f>> °1 (t) =7^1 dffa~2 sin4 ( WT/>' (9-13)

(7TT) 2 Jo

where the spectral density is given by eq (9.8) and

oc is greater than —3 [16]. Equation (9.10) is a very

simple time-domain calculation (the infinite time

average is normally well approximated with a few

hundred data points in a sequence). Equation (9.13)

gives a convenient relationship between these fre- quency-domain and time-domain measures of stability. For further details see Chapter 8 or reference

[16].b. Statistical Models for Time Dispersion. Typically the greatest contribution to the time dispersion

in a clock comes from the first two terms on the right

of eq (9.7); i.e., frequency drift and frequency offset.

If, however, these can be measured to first order and

accounted for, then the last term x(t) becomes the

primary contribution to the time dispersion. In

practice, of course, the first three terms of eq (9.7) are observed only in the presence of the noise, x(t).

If the spectral character of the noise is known, then

in principle one could design an optimum filter in some sense to best examine the signal for frequency

drift, frequency offset, and time residual through

the noise. In contrast, improper use of the time data

from a clock may result in much larger errors than

from optimal usage of the statistical data. In such

sense, this is a fairly classical problem in signal

detection in the presence of noise.

We will illustrate the above using the simple case

of white noise frequency modulation [S y (f) = ho].

h

For this case eq (9.12) takes the form Ux (t) = —t,

and therefore:

<tJ(t) = ~ (9.14)

It is easily shown that for this kind of noise the optimum estimate of a clock's rate (i.e., the signal) over

a calibration interval tc is obtained by simply using

the time of the clock at the beginning and end of the

interval; i.e.,

R^t-^y

TM-TM-^, (9.15)

where the " " over the Ri indicates an estimate.

The mean-square time error realized by using this equation is given by

<£?(f)> = < [ft(t + T) -Tt (t + T)Y) , (9.16)

where 7j(f + T) denotes the time residual calculated

from the rate given by eq (9.15), linear prediction rather than the exact rate. Equation (9.16), after substitutions and time averages are taken, becomes

<ef(T)>=~ [Tc(Tc + T)UXi (T)+T(Tc + T)UXi(Tc ) 'c

-TctUx .(tc + t)]. (9.17)

After substituting the above value of Ux {t) for white

noise frequency modulation (FM), eq (9.17) becomes

<ef(T)>=[<r»

1 (Tc)] [tc +t]t. (9.18)

Let us examine three cases for eq (9.18); viz.,

<6?(t)> =TcO-2.(tc )t, t<<tc . (9.18a)

<e?(T» = 20-|.(Tc)f2, T=TC . (9.18b)

(€?(t)> = o2 .(t c )t2

, t>>tc . (9.18c)

Note two things: first, the squared error is twice as

large if the calibration interval is only equal tor, the

prediction interval, (eq (9.18b)) as compared to having a very long calibration interval relative to the size of t (eq (9.18a)); second, the squared error disperses

as t

2 if the calibration interval is much shorter than

t (eq (9.18c)), which points out that the dispersion

is not due to the noise after the calibration, but

rather to the noise during the calibration causing an

210
TABLE 9.1. Frequency-Domain and Time-Domain Characteristics of Various Power Laws

Power Laws

Characterization

Sy(f) Ux(t)

White Noise PM

Flicker Noise PM

Random Walk PM

or White Noise FM

Flicker Noise FM

Random Walk FM

h 2f>

hj

ho

h-if~'

3A2//1

(2tt) 2t

2

-4hr_9' 2 + 3 ln(277/Ar)-ln (2)]

ho27

2A_, In (2)

(2tt) 2

, 6

h - 2T

2hifh

(2tt) 2

[9/2 + 3 In (277/„T)-ln(2)]

ho

2A-, In (2)t-° +1 nm „—

^-1 2-2-

12

~ Constant

~ Constant + In (t)

~ T

~ T

2

~ T

3

PM = Phase Modulation; FM = Frequency Modulation; for White Noise PM and Flicker Noise PM we assume rft, > 1.

error in determining the clock's rate, Riyt—^J,

over too short a calibration interval. Data can be

and often are misused in this manner— yielding

a much greater time dispersion than would be

necessary.

It is useful to tabulate some of the common kinds

of power law noise processes which perturb the

outputs of the high performance clocks currently

available. In table 9.1 these power laws are listed along with their frequency-domain and time-domain

characterization. The equation for Ux (t) and the

basic behavior for the mean square time dispersion

after optimal data usage are also listed in table 9.1.

It should be clearly noted that the time dispersion

is dependent upon how the data are utilized, and

in some cases it is highly dependent, as illustrated above for white noise FM, where for too short a

calibration interval the mean square time dispersion goes as t

2 rather than as t. White noise PM and Flicker noise PM are typically the predominant noise processes for values

of t less than 1 second; e.g., in quartz crystal

oscillators and hydrogen maser frequency standards.

For longer than one second, the predominant noise

processes are usually white noise FM, flicker noise

FM, and in some cases random walk FM. One or more of these last three noise processes are applicable in many frequency standards; e.g., cesium

beam, hydrogen maser, rubidium gas cell, quartz

crystal oscillator, and probably any oscillator

stabilized by a passive frequency resonance as in the methane stabilized helium-neon laser. Figure 9.1, showing some time-domain stability

characteristics of various frequency standards

measured at NBS, illustrates most of the above

kinds of noise processes. As a stability plot is analyzed, it is useful to note and it may be shown

[15, 16, 19] that if: o2 (t) ~ then

— 2, for a — a — 1 , for —3 > a

1 and \Tfh \ >1;

1. (9.19)

10'

i6'°

10

10 -

10'

SOME EXPERIMENTAL FREQUENCY STABILITY _ Sj/ / Fractional Frequency \ y ~ v \ Stability oer Device /

.fib CO,

r°„ 'v et/

. CH

VV H Maser

10' I 10 10 10 10 10 10 10 Sample Time, r (seconds)

Figure 9.1. Fractional frequency stability of several types of

oscillators as a function of sample time.

211
Annex 9.A considers an optimum filter (optimum in the sense of giving a minimum squared error of

time prediction (e^C?"))) in detail for each of the

above kinds of noise processes. If a process can be

reduced to that of white noise through linear trans- formation, then the simple mean of the transformation gives the optimum predictor for this white noise

process. By taking the inverse transform, one can

generate the optimum filtered output for minimum

squared error time prediction for the process itself

[20].At this point we will illustrate a very simple re- cursive relationship which yields near optimum time

prediction for some important practical instances.

Consider specifically the noise process for a = — 1; this is a noise type commonly observed in long term

in high performance clocks. In this case cr^ (r) is independent of t. (We will not treat the case where

a— 1 as it has much less relevance for timekeeping;

however, the same principles apply to both flicker noise FM and flicker noise PM).

Consider a sequence of measurements of the

fractional frequency on the ith clock, yi(j), where

thej denotes the particular member of the sequence

as in eq (9.9). An exponential weighting of the past

measurements to yield a near optimum estimate for the current frequency of an a = — 1 noise process is given approximately by the following recursion re- lationship [21];

1 ytU) = briU) + myi (j-l)]. (9.20)

The time constant of the exponential weighting

filter is given by to. The general expression for the

squared error of prediction is given by:

m

k= l

2k

m~ \to +

+ uJ(k-l)r)]-Ux (kT)^

+

mr~ \m +

m

l) \m + V

{I [^(/-*--1)t) + £/x ((/-*+1)t)]

UAV -*))}. (9.21)

For a given noise process and a given prediction

interval t, there exists a value of to which will give a minimum squared error for eq (9.21).

Substituting the equation for Ux (t) for flicker noise FM (a = — 1) from table 9.1 into eq (9.21) and

choosing the optimum value of to (to = 0.6 for a = — 1) yields the result that the root-mean- squared error given by eq (9.21) is only a factor of

1.13 times larger than that for an optimum prediction routine. The residual time calculation is based

on the operationally very simple recursion relation- ship for the rate given in eq (9.20).

9.3.3. Clock Noise Characterization and Data

Simulation

Once the deterministic and random properties

of a clock have been estimated, then it is possible

to simulate a clock's behavior. The simulation of

the deterministic part is, of course, very straightforward using, step, ramp, and quadratic functions.

The random portion, characterized by power law

spectral densities (Sy (f)—haf

a

), may be simulated using Gaussian white noise generators and

the white noise to flicker noise filters, including

integrals of the same [22]. The deterministic part

of a clock's behavior is usually well modeled by

eq (9.6). Quite commonly we find that the random

part, x (t) , is well modeled by the following equation

(see fig. 9.1):

Sy(f) = h0 +h.1 f-i,

or in the time-domain:

(9.22)

°-!(T) = lTT-1 + /i- 1 21n(2), (9.23)

where

y(t) =

dx{t)

dt

(9.23a)

Assuming the statistical model of eqs (9.22) and

(9.23), we will calculate the mean-squared time

error for an interval t for the two useful time

calculation techniques discussed above, viz., linear

prediction and exponential prediction. First, consider the calibration interval tc with the residual

rate of a clock being calculated using eq (9.15). Then using the appropriate equation for Ux (t)

from table 9.1 and substituting these into eq (9.17)

gives:

<<= 2 (t)> = ^(tc + t)-t

+ ^[^(?+ 1)

2 ln(?

+ 1)-(?+ 1 ).n(?)].

(9.24)

212
For a given set of noise levels h0 and hi and for a

particular prediction interval t, there is a value of

tc that will give a minimum for eq (9.24). Let us examine the following special cases:

(eHrD-jT + i, (l + ln^r2

, t<tc .

(9.21a)

(e2 (T)) = h0T + 4h- 1 In (2)-r 2

,

< e 2( T))

^T2 + /l _

T=TC .

(9.24b)

T ^> Tc .

(9.24c)

Note in eq (9.24a) that as the calibration interval

grows even longer, the error deteriorates only very

slowly for the flicker noise FM contribution (second

term on right), and the error approaches a minimum

(optimum) for the white noise FM contribution (first term on right). Note, in eq (9.24c) that the mean

squared time error goes as t

2 for both terms, and

which one predominates depends not only on the

intensity of each kind of noise (h0 and A-i), but

also on the calibration interval (tc ). In figure 9.2 we have plotted the root-mean- square time error given by eq (9.24) for two atomic

clocks with different levels of noise. The time fluc- tuations are assumed to follow the model in eqs

(9.22) or (9.23), and the values for the noise intensity were chosen to nominally cover most of the commercial cesium beam clocks presently being used

in the field. This illustration assumes that the

deterministic terms in eq (9.7) are accounted for, and the time dispersion is due primarily to x(t) at the noise intensities indicated.

Second, for exponential prediction, consider the

mean-square time error in calculating time based on

eq (9.20) and assuming the same statistical model;

viz., that given in eqs (9.22) or (9.23). Again taking

the appropriate value of Ux {r) from table 9.1 and

substituting into eq (9.21) gives:

<e2 (r)> =

hp(m+ 1)

2m+l

+

m2 (2m+ 1)

m

m+1 k

2 \n(k). (9.25)

It is again worth noting that the value of m (the

exponential frequency-weighting time constant)

which gives a minimum for eq (9.25) will depend

upon the level of white noise FM (h0 ) and flicker noise FM (h-i). For convenience we have tabu200

150

100

.

K

V 2

Cs « 3.4X10"" 3.0X10"

Cs B 8.4 x 10 " 0.6x10"" 2000

10' 10

1 10' 10

s 106 10'

CALIBRATION SAMPLE TIME,t

c (s)

Figure 9.2. Root-mean-square time error of two cesium clocks

as a function of calibration sample time.

lated in table 9B.1 (ann. 9.B) some useful values of

the infinite sum in the second term on the right of eq (9.25). Note, as m becomes large, the first term

on the right of eq (9.25) approaches the optimum.

Assuming that — = m in eq (9.24), it can be shown

T

that eq (9.25) always gives at least a slightly smaller

value for the error than does eq (9.24). For m<^l,

both terms on the right of eq (9.25) become significantly less than in eq (9.24); and specifically,

comparison of the terms due to white noise FM

show that eq (9.24) gives a squared error which is l/(2m) larger than in eq (9.25). A comparison of the squared error due to the

flicker noise FM terms (second term on right) in eqs (9.24) and (9.25) is shown in figure 9.3.

~i—i—i—i i 1 1

1

1

1—i—i i i 1 1

1

1 i i i i i 1 1

1

^ RATIO OF CALIBRATION INTERVAL TO PREDICTION INTERVAL

_i i i i i i 1 1

1

Linear Prediction

-Recursive or Eiponential

Prediction

_i i _i i i i i 1 1

1

1.0 10 m= TIME CONSTANT FOR REC0RSIVE PREDICTION

100

FIGURE 9.3. Comparison of mean-square time error of linear and

exponential predictors for flicker noise FM. 213
Note, the minimums occur at m=l for the term

from eq (9.24) and for m = 0.6 for the term from

eq (9.25). Although there may be any number of time pre- diction algorithms their efficiency and accuracy

may be determined by applying certain tests;

e.g., by processing simulated data; comparing with

optimum prediction for the models assumed;

and making sure that the algorithm is not highly

model dependent. (In other words, the kinds of

noise and the levels of noise don't have to be crit- ically determined.) The two prediction algorithms

whose frequencies are given by eqs (9.15) (linear)

and (9.20) (exponential) pass these tests as long

as m is approximately equal to or larger than its optimum value. They are both very easy to implement; eq (9.20) is easier to employ and is more

nearly optimum. We have developed a first order

time scale algorithm based in part on eq (9.20).

9.4. THE AT(NBS) TIME SCALE

SYSTEM

Figure 9.4 is a functional diagram of the NBS

Atomic Time Scale system (AT(NBS)). The theory

of operation is as follows: Block A represents a device which will accurately produce the SI

second or a known fraction thereof. Block B

denotes a precise measurement of the frequency

{vi) or rate (/?*) and hence of the period (jj) of each

of n clocks. Block C represents a set of n independent clocks with fail-safe power supplies, where n

is large enough to do individual clock characterization and to provide sufficient redundancy to guarantee that clocks will always be running.

Each clock serves as an independent memory

of vo or to; and together they evaluate each other. Block D denotes a precise and accurate measure- ment of the time differences between the clocks

and indicates the mechanism for this evaluation.

The time differences and the rate information

are optimally used in a time scale algorithm to produce a time as shown in block E. This time is as near synchronous as possible with ideal time

as discussed earlier. The time derived from the

primary frequency standard, had it been running

continuously at its correct (evaluated) rate, is also an approach to ideal time, but in practice there

are two reasons that make this difficult to achieve.

We will discuss these reasons and the functions

indicated by each block in figure 9.4 in detail.

9.4.1. The NBS Primary Frequency Standard

and Measurement System

Historically, the primary frequency standard

at NBS has been a very elaborate laboratory

cesium beam device which cannot reasonably be

operated continuously. Tn fact the decision for nonAT(NBS) TIME SCALE SYSTEM

NBS PRIMARY

FREQUENCY STANDARD

PERIODIC RATE

B CALIBRATION

v. FROM CLOCK i i = 1, n

C

n CLOCK

ENSEMBLE

CLOCK i i = 1, n i * j CLOCK j

TIME DIFFERENCE

Tj [t] —Tj

(t)

TIME SCALE

I ALGORITHM

AT(NBS)

Figure 9.4. Block diagram of the AT(NBS) time scale system.

continuous operation was made so that we could

properly evaluate all known parameters which

may affect the accuracy realizing vo. The last full evaluation and calibration of the NBS-III primary

frequency standard (May 1969 [23]) indicated an

accuracy of 5 X 10" 13 (lcr). Two new state-of-theart primary standards have been constructed at NBS, viz., NBS-X4 and NBS-5. A preliminary

214
evaluation of NBS-5 has been made in late 1972

and early 1973, and the estimated frequency of

NBS-III via the AT(NBS) clock ensemble is within

1 part in 10 13 (lcr confidence of 1 part in 1012

) with

respect to the best estimate of frequency given by

NBS-5.

NBS-X4 is still to be evaluated, and the final evaluation on NBS-5 is proceeding at the time of

this writing. When the primary frequency standard

is operating, a 5-MHz signal, v'0 , is synthesized from

this standard and compared with a 5-MHz source from each of the clocks in the ensemble. The prime

on vo in this text denotes a known frequency offset between the synthezised signal and the best

estimate of a 5-MHz signal based on the primary

cesium beam standard. The comparison is per- formed in a low noise double-balanced Schottky

barrier diode mixer. The mixer provides the dif- ference (beat) frequency (Af;= v% — v'o) between

the primary standard and the ith clock. The equation for the precision of such a measurement system

is given by:

. , 8t& Aj^

<Ty(r) = , (9.26) T V

where 8t& is the precision with which the beat period

(t&= 1/Ay) is known, and t is the time interval over which the beat signal is sampled; i.e., sample time.

The AT(NBS) rate measurement system is called

a chronograph; the chronograph data, occurence

times of the zero crossings of the beat frequency

(Av) on an arbitrary scale, are measured to a precision of 10/z.s. In a typical situation we may have

a value of rb of 100s, which gives cth (t) — 2 X 10_14/t (T^ 100s).

A chronograph system has the theoretical potential of an extremely precise time interval device:

e.g., in the above example one could measure time

(phase) fluctuations between two clocks to a pre- cision of 20 femtoseconds (20 X 10~15 s) since, from

eq (9.25), we may derive:

ensemble. Six of these units are located at the NBS/

Boulder, CO laboratories in an environmental

chamber which is controlled in temperature to better than 0.1 degree C at a nominal ambient

temperature of about 23 degrees C. Each of these

six units is also electrically isolated and shock

mounted with an independent fail-safe power supply. The whole system is backed up with an emer- gency generator power source. Each of these six standards drives two frequency dividers — one from

5 MHz to 1 pulse per second (pps) and the other

from 100 kHz to 1 pps. The latter divider is a re- dundant backup. The 5-MHz dividers are classically called "window" dividers and have pulses which

are stable to subnanosecond with 6 ns rise times.

The other two atomic frequency standards are at the WWV radio station near Ft. Collins, CO in a shielded and temperature controlled room. They are

similarly followed by dividers from 5 MHz to 1 pps

and the occurrence times of these clocks are communicated to Boulder, CO via the TV line-10 time

transfer system [7, 9].

Time differences are measured to an accuracy

of 2 ns and a precision of 0.5 ns with a commercial

time interval counter. The time differences between

one specific clock and all the others are measured

automatically at the same time each day; an on-line

computer is available for processing and diagnosing

the data. In practice the 1 pps signal from clock i starts the counter and at a time t later the 1 pps

signal from clockj stops the counter; this gives:

Ti(t) -Tj(t + r) = Ti (0—Tj (t ) +ry }{t) . (9.28)

The third term on the right of eq (9.28), Tff(t),

denotes r times the average fractional frequency

offset of the y'th clock over the interval from t to

t + T. This term is usually negligible since t< 1 s and y

T (t) < 10 -11

. However, caution should be

used if one has a clock with a large fractional

frequency offset, since this third term usually is ignored in practice.

8(Af)=—, (9.27) V

where 8(At) denotes the uncertainty of the change

in the time (phase) difference measurement.

In practice dc drifts and component delay varia- tions will prohibit achieving the precision given by

eq \? 37). Some tests have been conducted on the

chronograph which have indicated that its contribution to the instabilities of a measurement are usually

negligible — consistent with eq (9.26).

9.4.2. The Clock Ensemble and Time

Difference System

There are currently eight commercial cesium

beam frequency standards in the AT(NBS) clock

9.4.3. Atomic Time Scale Algorithms

In theory one could perform a complete characterization of both the random and the deterministic

properties of each member of a set of clocks in a given ensemble. After such a characterization,

favorable processors could be applied to the data

to yield a theoretically optimum time scale. The

obvious problem with this approach is that optimum

time cannot be known during any part of the characterization interval until after all the data have been

processed which may require weeks, months or

years. Another problem is — even though eqs (9.7) and (9.8) are believed to be good models for high per215
formance clock data— occassionally a change may

occur in one of the coefficients, i.e., Ri(to),

Ti (to ) , h0i , or h-i t , (e.g., the cesium getters saturate

in the clock causing ho to increase). The changes

may occur discretely or gradually. Methods of detection should, therefore, be incorporated to sense such changes. One has the additional theoretical

complication that a gradual change in Ti(to),

starting at some date t, cannot be separated from

a discrete change in Rj(to), at that same date; a similar situation exists for Ri(to) and D, re- spectively. In practice, however, it is immaterial

as to which assignment is made, and one is prone

to choose the most convenient.

In light of the above we take the following ap- proach for the AT(NBS) scale. With a very small

sacrifice in accuracy of dating we maintain an online clock which constantly predicts the date that would be given by the clock ensemble (first order

processed), and which is updated after each

periodic (~ once per day) ensemble processing.

This first order time scale algorithm has dynamic

sensing qualities; i.e., after the data are processed

through a near optimum filtering routine, the algorithm senses and compensates for any changes in Ri(to), Ti(to), and in the noise intensity. After a

sufficient amount of data has been collected (over

months or years), a second order time scale algorithm is applied to the data to give a best estimate

of dating from the ensemble and primary frequency

standard, and to update the coefficients for the

first order algorithm. We will discuss the first order algorithm in some detail, but only some

aspects of the second order algorithm as it is still being developed and tested.

a. Clock Characterization. In order to best

estimate the deterministic coefficients (signal) for eq (9.7), we first estimate the noise characteristics so that suitable data filtering can be employed

to yield near optimum signal to noise. The noise

characteristics of the ith clock can be estimated

by comparing it with a clock whose noise is less that its own noise over the stability region of interest

(the values of t). An example of this is shown in figure 9.5, where an NBS clock is compared with a Hydrogen Maser. It is highly desirable to use the

"best" clock in the ensemble, and hence a dif- ferent technique needs to be employed to estimate

its stability. If the three clocks i, j, and k are independent, then we may use the following as an estimate of the ith clock's stability:

o? (r) =\ [(o-?-(t) -o-yr)) + (o^t) " (cr%U) -o-yr))], (9.29)

where (t?j(t), etc., are the measured stabilities between i andj, etc., and the (t) are the measure- ment noise contributions respectively. If the

Fractional Freqency Stability (clock 2 vs. NP3)

2 10

CO

Sid13I0 3

'72h_, Log(2) =-2.5X10"-

I L

.Vy

h

° = 6x io"

I04 I05 Sample Time T(seconas)

I0 6

Figure 9.5. Hydrogen Maser (NP3), cesium beam (clock 2) comparison, showing the fractional frequency stability as a function of sample time.

measurement noise, ct2 (t), is the same for each

measurement pair, then eq (9.29) may be approximated by:

°?-(T)=i[o-5(7+<(T)

o-A(t)-o-„2 (t)]. (9.29a)

Of course, ct 2 (t) needs to be measured as a separate experiment or calculated from known

pertinent parameters.

Given n clocks in an ensemble there will be

(n — 1) !/(2!(ra — 3)!) different, but not all independent,

estimates of df{r). By taking an appropriate

weighted combination — recognizing that some

estimates will have much better confidences than

others — we get a best estimate along with the

confidence of the estimate for the stability of each

clock in the ensemble.

During the winter of 1969 and 1970 we had the

advantage of using the National Aeronautics and

Space Administration's (NASA) NP3 hydrogen

maser, for study of the above method of clock stability estimation [24]. Figures 9.6 and 9.7 are

(Ty (t) versus t plots of NBS clocks 1 and 3, which

show the estimated stabilities. After the stabilities of each clock were estimated, an approximation

of the ensemble stability can be made by taking the

appropriate weighted combination of the stability

plots for each clock. These weighting factors are discussed below. Figure 9.8 shows such a stability

plot for the NBS clock ensemble. By taking the

stability estimate for the clock ensemble and

combining it with the stability estimate for the

NP3 hydrogen maser, we compared the estimated

stability of the combination with that which was

actually measured. Figure 9.9 shows the excellent

agreement of this comparison.

b. Calculation of Ensemble Time. Assume

that an optimal rate, Ri(to) , calibration has occurred

for each clock using the clock ensemble and/or

216
Sample (Days)

FIGURE 9.6. Fractional frequency stability of clock 1 estimated by comparison with all other clocks in the AT(NBS) clock ensemble.

Sample (Days)

Figure 9.8. Fractional frequency stability of weighted 6 clock ensemble as determined from individual clock-estimates.

5 10 Sample Time r (Days)50

Figure 9.7. Fractional frequency stability of clock 3 estimated by comparison with all other clocks in the AT(NBS) clock ensemble.

10

12

-Oo

o5o

c

<L>

CD

O

co

o

o

-13 10

-14 10

i I r TTT| 1

o Experimental

x Calculated

« 9 o

x

J i 5 10 Sample Time r (Days)

50

Figure 9.9. Hydrogen Maser (NP3) AT(NBS) clock ensemble

(6 clocks) comparison showing experimental and calculated values of fractional frequency stability as a function of sample

time. 217
the primary frequency standard, and assume

further that the residual time difference between

each clock and that time given by the ensemble

at an agreed upon date to is known, 7f(to). We

have had insufficient data to determine the Di

coefficients which require, ideally, fairly frequent

and precise calibrations with an accurate primary

standard whose intrinsic reproducibility is suf- ficiently good so that undue noise is not added to the stability of the clock ensemble. We know the

Di coefficients are usually small, but their quadratic

time dispersion rate is probably not insignificant.

We will assume that they are negligible for the

first order algorithm, and give proper accounting

for them in the second order algorithm. For the

first order algorithm, we may then optimally predict

the following residual time for clock i:

r,(f0 + T) =Ri(t0)

• T+ Ti(to), (9.30)

neglecting second order terms. Now we may combine the measured time dif- ference data,

70-(*o + t) - Ti (to + t) - Tj (t0 + t) ,

with eq (9.30) for all the clocks to give:

Tj (to +T)=f/ Wi (T) [7i(*0 + T)-7V(«0 + T)],

(9.31)

where the Wi are appropriate weighting factors depending upon the quality of each clock. In order

to have a minimum squared error of the weighted

ensemble from ideal time, it may be shown that:

Wi (t)

<€?(T)>

(9.32)

where (el(r)) is the estimated squared error of

the ensemble and is given by

<«S(t)> = (9.33)

From eq (9.33) one can see that all clocks contribute positively to the stability of the ensemble;

i.e., a poor clock does not degrade the stability.

Further, the stability of the clock ensemble is better

than that of the most stable clock in the ensemble.

For reasons given in the previous section we

currently use an exponential prediction routine in our first order algorithm. Therefore, we may

calculate the mean-squared clock error using eq

(9.25) — having estimated the noise characteristics

using eq (9.29). We may also experimentally estimate the time dispersion of a clock if we have

several time measurements with respect to the en- semble over equally spaced intervals. A bias is introduced when measuring a clock's time against

the time of the ensemble of which it is a member

since it would not, then, be statistically independent.

An estimate of the unbiased error of the 7th clock

accumulated over the interval t is given by:

I ej(r) I = I Tj(to + r) - Tj(to + r) \ + ^yii ,

(9.34)

where the 0.8 arises from the assumption of a normal

distribution of errors. The average square of eq

(9.34) then gives an experimental estimate of eq

(9.25). We have tested both methods of clock error estimation and obtained reasonable agreement be- tween them.

Equation (9.31) gives the time of the 7th clock

with respect to ideal time, estimated by a procedure

which minimizes the squared error; hence a working

clock can be made to read "correctly" by adjusting

its tick to be Tj(to +r) later than that of the 7th

clock. Once the residual time of each clock has been

calculated, we have in effect a new origin and in general we may replace to by t in eqs (9.30) and

(9.31). Generalizing these latter two equations for any time t, one has the advantage of both sensing

and accounting for the previously mentioned dynamic changes in a clock's characterization.

All that is required to confidently sense rate changes or time jumps in a clock is a stable ref- erence. Since the primary frequency standard is not continuously available, we simply use the clock

ensemble, which in principle is better than the

best clock in the ensemble, as our stable reference

between calibrations. Equation (9.20) is used as a near optimal update for the rate Ri(t) of each

clock. Figure 9.10 shows the rates (converted to fractional frequency, yt(t)) for some of the clocks

composing the AT(NBS) scale ensemble. These

rates were determined with respect to the en- semble, not the primary standard. The ordinate was arbitrarily and conveniently chosen for each

clock. Annex C gives a computer program written

for a mini-computer, covering some aspects of our

first order time scale algorithm which generated the

rates shown in figure 9.10. Whereas the weighting factors which give a minimum mean squared time error are given by eq

(9.32) , the time constant m,r (m as in eq (9.20)), coupled with Wi determine the weighting factors which give the near optimum frequency stability for the clock ensemble. A classic illustration of the

above weightings is a quartz crystal clock as compared to a commercial cesium beam clock (see

fig. 9.1). If the interval t between time interval

measurements were short (a few seconds) then a

218
_, 0-"L ' 5

1 u_

Feb I Ian 1 Ian 1 May 15 1970 1971 1972 TIME

Figure 9.10. Relative fractional frequencies of five selected cesium clocks in the AT(NBS) scale as a function of time with

the AT(NBS) scale used as the reference (note the arbitrary

origin).

larger weight would be given to the quartz crystal

clock (per eq (9.32)) than to the commercial cesium

clock — yielding a very stable time scale in short- term. However, in long-term the superior frequency

stability of the atomic clock shows an optimum value

of m much larger than for the quartz crystal clock

and yields a very stable time scale, as the composite rate would be determined by the commerical

cesium beam clock. For the above particular exponential time prediction algorithm, we have conducted tests to see how

variations in the value of t (the interval between

time difference measurements) affects the overall

stability characteristics of the ensemble. A small

effect was observed; e.g., increasing t by about a

factor of 10 improved the long-term stability by a few percent. This is a direct indication that this particular algorithm is only near optimum. For

practical applications, however, where clocks can

only be characterized to confidences of a few per- cent, the ease of implementation of this exponential

prediction routine has proved to be efficient and

adequate for our first order time scale algorithm.

The value of r can be chosen pretty much for the

convenience of data acquisition and analysis without

any significant degradation of the time scale

stability.

We currently measure the time differences

between the clocks each day; such measurements

are done automatically in our time scale automation

system. Figure 9.11 is a plot of the accumulated time

errors summed from the errors determined after each day's measurement for the more important

clocks in the NBS clock ensemble. Currently for t = 1 day the experimental ensemble error given by

eq (9.33) is about 5 ns. If we may assume that the

ensemble stability plot shown in figure 9.8 is repre- sentative for longer values of t, then we can use eq (9.25) to estimate the time dispersion of the clock

ensemble for the 2 years and 3 months period shown

for some of the individual clocks in figure 9.11. Assuming hit for the clock ensemble is about 8 days, we derive a time dispersion for the clock ensemble

of about 4/>is, which appears conservative in comparison with the time dispersion of the individual

clocks. Note, that this is the time dispersion due to the random error predominantly, and does not ac- count for non-random dispersion such as may be

caused by steps and drifts in frequency.

c. Rate Accuracy of AT(NBS) Scale. Ultimately

the accuracy of the rate of an atomic time scale must

depend upon the accuracy of one or more evaluable

primary frequency (rate) standards. In our case

a primary reference was NBS — III in the past, and

is now NBS — 5 and NBS — X4. The primary function

of a clock ensemble as regards rate accuracy is to serve as a memory of past calibrations. The better

the clock ensemble stability the more nearly perfect

the memory of the proper rate given by a primary

standard from which the clock ensemble derives its accuracy.

In any given evaluation of a primary rate standard

there are associated inaccuracies. Each of these

inaccuracies arises from the uncertainty in knowing

how much a particular parameter biases the fre- quency of the primary standard. It is convenient to categorize these bias uncertainties: first are those

uncertainties cr ruc(/), which will be random and

uncorrelated in their inaccuracy contribution from

one evaluation to the next; second are those which

are otherwise, <r&(Z); these are typically constant for a given device. The overall accuracy may then be

written for the /th evaluation:

0"(/)= [0- ruc

2 (/) + 0-i(/)]l/2. (935)

If we had a time scale with perfect memory the

first inaccuracy contribution would average as the

square root of the number of calibrations. In such a

CLOCK CLOCK

1 4

"*

Feb 1 ianl Ian! May' 15

1970 1971 1972 TIME

Figure 9.11. Long-term accumulated time errors of 6 selected cesium clocks in the AT(NBS) time scale.

219
case we could have a time scale with an accuracy of

rate better than that from a single evaluation of the

primary standard, given a sufficient number of

calibrations. In practice, of course, there is some

frequency dispersion in the time scale memory as well as the possibility of -some deterministic drifts,

Dj # 0 (see fig. 9.10). Assuming that the deterministic aspects such as Z), can be properly accounted

for in the second order time scale algorithm and

assuming that each calibration is optimally weighted, we may then write the following for the squared

accuracy of the calibrated clock ensemble, cr% (/), after the /th calibration:

accuracy and stability are preserved for the atomic

time scale. Incorporating this philosophy we in- creased the rate of AT(NBS) by 0.5 parts in 1013 —

a

frequency step which is the order of the time scales

frequency instability— at 0000 hours AT, 1 May

1973. The frequency of these steps will be kept

small enough so that they are essentially masked

by the long-term dispersion of the clock ensemble.

At this writing the accuracy rate of AT(NBS) using

eq (9.36) is 5.2 parts in 1013

, crb(l) is estimated at about 5 parts in 1013

, and the best estimate of the

rate of AT(NBS) is too low by 4.6 parts in 1013 with

respect to NBS-5.

1 l" 1 +

(<r% (2,7\T,/„)>+o-f(/-l)-o-|(/-l)_

(9.36)

where {(Ty

e (2,T,T,fh)) is the clock ensemble fre- quency stability (see eq (9.9); ( T is the time from the

beginning of one calibration to the next, and t is the calibration sample time). We have also implicitly

assumed that the same primary standard is employed and that &\ (I) remains the same or improves

with experience. If either or both of these assumptions are not true, one can improve on eq (9.36)

through techniques to be published in the future. From eq (9.36), we see that with an adequately

stable clock ensemble, the accuracy of the clock

ensemble approaches that of cr&(/). In the case of

AT(NBS) the last calibration was May 1969, and

cr|(Z— 1) was 5 X 10~ 13 [23]. Our first preliminary

calibration of AT(NBS) with NBS-5 occurred over

the period 13—22 January 1973 with preparatory

measurements being made during November and

December of 1972. This calibration measured

AT(NBS) too high in rate by 6.9 parts in 1013

. The

use of eq (9.36) and weighting of the two above

mentioned calibrations inversely proportional to their accuracies indicated that we should decrease

the rate of AT(NBS) by 4.5 parts in 1013

; this change was made at 0000 hours AT on 1 February 1973. Between 27 January 1973 and 6 April 1973 we per- formed four more preliminary calibrations, and

again the application of eq (9.36) for each of these

indicated that we should increase the rate of AT-

(NBS) by 5.1 parts in 1013

. These experimental results give direct evidence

for the second reason we believe it is not best to use

a primary frequency standard as a clock; i.e., the

biases which need to be taken into account in order

to obtain an accurate frequency estimate are not always constant from one calibration to the next. Hence, if the clock ensemble is more stable than

the changes in these biases, an appropriate filter may be applied to the calibration values so that both

9.5. THE UTC(NBS) COORDINATED

SCALE

The atomic time scale AT(NBS) is an independent

and proper4 time scale. The readings of any two

such scales will have a comparative dispersion for two fundamental reasons: first, from deterministic

differences; and second, from the random noise

inherent in any time scale system. The first reason

for dispersion may be caused by differences in accounting for the biases affecting the primary

frequency standards of each scale; these differences

should fall within the ascertained accuracy limits. Or it may be caused by the difference in gravitational

potential at which the two scales are running

(—gH/c2

; H is the differential height). The second

reason for dispersion may be caused by fundamental

noise processes in the clocks and/or by noise in- serted by the measurement system or while the

data are being processed in a particular time scale

algorithm; i.e., different algorithms will have

different amounts of dispersion.

Because of the above mentioned dispersion, if two

different time scales are to be kept synchronized, it becomes necessary to insert a rate and a time cor- rection in one or the other or in both time scales. Starting on 1 October 1968 a mutual coordination

agreement was made with the United States Naval

Observatory (USNO) to keep the UTC(USNO) and

UTC(NBS) scales synchronized to within about

5 fxs by making equal and opposite coordinated rate corrections [25]. More recently the philosophy that NBS has

adopted is to generate a nonindependent coordinated time scale UTC(NBS) which is kept synchro- nous with the internationally adopted time scale

maintained at the Bureau International de l'Heure

(BIH) — denoted UTC [6]. This is accomplished as indicated in figure 9.12 with slight rate and leap

second additions to AT(NBS). The constant C was

chosen so that at 00 h 00 min 00 s UTC on 1 January

1972 the UTC(NBS) scale was synchronous to within about 3 ^is of UTC. Because of similar direc4 Proper is here used in the relativistic sense.

220
Independent

No

Vo

Nc

= ^ + t„ + C

A T (NBS)

Coordinated

Rate Correction

tc = Mxls +^ + t 0 + C

vc

-- V0 (1+8

Leap Second

Adjustments

UTC (NBS)

Six other Atomic Time Scales

T A 1

) 7

Leap Second

Adjustments

I+Mxls , r

U r c

Comparison via Loran

Cs. portable clocks

For measurements and dissemination

Figure 9. 12. Block diagram showing the derivation of UTC(NBS)

from AT(NBS) and its coordinated relationship to UTC(TAI).

tions taken by the USNO to keep their UTC(USNO)

scale synchronized to UTC after 1 January 1972 the

above agreement to keep nominal synchronization

will continue to be maintained to within a few

microseconds.

The insertion of leap second adjustments is determined by the BIH following CCIR regulations

[25]. The insertion usually occurs on 30 June

and/or 31 December for the purpose of keeping

the time difference | UTC — UT1 | nominally less than 0.7s. M was set to minus 10 on 1 January 1972^

minus 11 on 30 June 1972, minus 12 on 31 December

1972. and minus 13 on 31 December 1973

The equation relating AT(NBS) and UTC(NBS) as

of 1 May 1973 is given by:

AT(NBS)— UTC(NBS)= 12.045153000s - (129.6 ns/day) • (MJD - 41803 days), (9.37)

where MJD is the Modified Julian Day number.

Equation (9.37) does not account for second order

terms; i.e., atomic days are not used. (Recent in- vestigations indicate that we need to define an Atomic Julian Day count or its modified equivalent

for consistency so that eq (9.37) can be made exact.)

It is anticipated that the S NBs coordinate rate corrections will be made on 1 January of each year in order to keep the time difference |UTC — UTC-

(NBS) | as small as practicable while also maintaining close coordination with UTC(USNO).

9.6. UTC(NBS) ACCESSIBILITY

The determination of a date on the AT(NBS)

scale or on the coordinated UTC(NBS) scale requires some method of accessibility. Figure 9.13 gives a

fractional frequency stability, cr y

(T) versus t plot for the main methods of communicating the time

and/or frequency of these two scales. The stability

data for figure 9.13 were taken from references

[9, 26—29] or were measured and computed by the

authors. Typically, the UTC(NBS) scale is the one

disseminated and eq (9.37) or its updated version,

which is published in reference [30], is required to compute AT(NBS). For comparison purposes the

estimated stability of AT(NBS), which will be

essentially the same as the stability for UTC(NBS),

and the calculated and measured stability of NBSX4 and of NBS-5 respectively are also plotted in figure 9.13. It is anticipated that the stability of

NBS-5 will improve from further advancements in both its electronic servo system and its beam optics.

The date on the UTC(NBS) scale is communicated

from NBS/Boulder, CO to the NBS radio stations

(WWV, WWVB, and WWVL) near Ft. Collins, CO

via the TV line-10 time transfer system [7, 9, 11]. Notice the excess noise (day to day) on the accumulated time error plot for clock 8 in figure 9.11. This

is one of the three cesium clocks at WWV which is used in the AT(NBS) clock ensemble. This excess

noise is in the TV line-10 time transfer system and

amounts to (<j%(2, T= 1 d, r = Hfh,fh)) 1/2 = 30 ns. Time and/or frequency are communicated to WWVH

at Kekaha, Kauai, Hawaii via WWVB transmissions

and portable clocks.

NOMINAL FRACTIONAL FREQUENCY STABILITY

OF POSSIBLE FREQUENCY CALIBRATION METHODS

10' 10'

SAMPLE TIME , t [s]

Figure 9.13. Fractional frequency stability as a function of sample time for several UTC(NBS) dissemination techniques.

221
Note that the signals from Loran-C, 60-Hz power

line, as well as TV line-10 need to be used in the

time transfer mode; i.e., the date of arrival of the

signal on the UTC(NBS) scale must be differenced

with the date of arrival of the signal ascertained with

the user's clock in order to determine if a change

has occurred in the user's clock time since the last measurement. In the case of the latter two the path

delay has to be calibrated for time transfer (not

frequency transfer), e.g., with a portable clock. The following relationship allows the conversion

from the fractional frequency stability to the time

stability for most of the methods shown in figure

9.13 (see ref. [18]):

<<t»(2,7\tx,A)>i/» =

V4-2^+ 2 o-„(t), (9.38)

where 2 < \x < 0, T—t, tx «^ 7

1

, and it will be

remembered that cr y

(t) ~ t

m/2 . Applying eq (9.38) to the long-term stability data for Loran-C and TV

line-10 as an example yields ~ 2.5 ns t

1/3 s _1/3 over

the range 1 day < t < 100 days.

Table 9.2 has been compiled to show characteristics of methods of obtaining data on the UTC-

(NBS) scale. There are additional factors that need

to be considered from the users point of view such

as reliability, greater skill required, and number of users that can be served (see chap. 10, sec. 10.6 or

ref. [26]). In addition to the techniques listed in table 9.2, personnel at NBS/Boulder, CO also monitor other radio stations (NAA, GBR, NLK), and

these may be used in the time transfer mode to communicate UTC(NBS) date as the readings are published monthly [30]. The users' cost effectiveness for the precision and

accuracy achieved by the techniques of TV line-10

and the ATS-3 satellite, respectively, is very good.

Insertion of an active time code on a line in the

blanking interval of the TV transmissions has been

experimentally tested [31, 32] and the method has

the potential of being extremely cost effective for the excellent precisions (< 1 /xs) achievable; in addition, it shows accuracy of maintaining the date once the path has been calibrated. The ATS-3 date

transfer method was experimental and terminated

Table 9.2. UTC(NBS) Accessibility

Method of access Ti mes avai la ble

Nominal

accuracy for date transfer

Additional equipment

cost to user WWV and WWVH

WWVB

WWVL

ATS-3 Satellite

Telephone (303) 499-7111..

Portable Cs. Clock

Portable Rb. Clock

Loran-C (ground wave)

Line-10 Television

60-Hz Power Line

Omega Navigation System.

hemisphere

North America

global

hemisphere

North America

global

1

globall

east of Rocky Mtns. (N.. Am.), through Europe.

requires common re- ception of east USA

network programs.

USA and some adjacent

areas. (Verified be- tween CO and CA.)

global

continuously

continuously

experimental

experimental 1700 to 1715 UTC 2300 to 2345 UTC daily (ter- minated late 1973).

continuously

per user's desire

per user's desire

1500 UTC each work

day.

~ 1330 local time

(Boulder) each work day.

proposed

< 1 ms

~ 50 jits

envelope ~ 500 /as

10 to 50 /as

< 0.03 s

~ 0.1 /as

~ 1 /as

< 3 /AS

need to calibrate path; precision - 1 ns t

1 ' 2 t>33 ms

need to calibrate path: precision

$lms To 17 ms < T < 105

S.

~$200 to $2,000.

~ $400 to $4,000.

~ $4,000.

~ $150.

price of phone calls.

- $19,000.

- $12,000.

~ $5,000 to $10,000.

- $100 to $500.

~ $10 to $100.

proposed. < 10/AS. $16,000.

222
late 1973; however, the tests have proven successful

[12]. There are plans for an NBS experiment which

would provide time from UTC-(NBS) continuously,

using a Department of Commerce satellite. The direct signal from the 60-Hz power line is not very stable; cr y {r) = 5 X 10~ 5 for 17 ms < t < 105

s). However, the stability of the differential delay

between two points has much greater stability. The

60-Hz power line stability data shown in figure 9.13

represent the differential path delay between Santa

Clara, CA and Boulder, CO. A similar study was

performed for the path between Ft. Collins, CO and

Boulder, CO, and the stability was about 5 times

better. This very inexpensive time transfer system

has significant potential for users needing syn- chronization to about 1 ms [33]. An exotic time and frequency dissemination

system of the future with a potential of nanosecond

precision and accuracy of date transfer may employ

a belt of geostationary satellites around the globe.

Each satellite may have an rf communications

transponder and a triggerable infrared pulsed laser radiating the earth. Using trilateration with a grid

of synchronous ground station clocks the position

of the satellite could be determined to a few centi- meters, and thence communicated, along with the

dates of occurrence of the laser's pulses, to the

appropriate receiving equipment. The infrared seems desirable because of available bandwidth,

accurately calculable path delay, less problems

with cloud cover than with the visible, and some

comparative cost considerations.

9.7. THE INTERNATIONAL ATOMIC

TIME SCALE (TAI)

The TAI scale is constructed at the BIH using the

input via Loran—C and TV time transfer techniques

of several cesium standards located in many of the

time and frequency laboratories throughout the

world — including the standards used to generate

AT(NBS) (see fig. 9.12). There is reason to believe

that the TAI is stable to about 1 X 10~ 13 for cr y (t ~ 1 year) and is probably the most stable reference

time scale available [3], hence its use as a reference

may provide reasonable comparisons among the

primary frequency standards of these laboratories.

The fractional frequency of TAI with respect to four of the evaluable primary frequency standards

in the world are as follows: for PTB (Germany),

CS1 [+ 12 ± 4 (lo-)] X 10- 13

, March-July 1970 [34]; for NRC, Cs III [+ 8 ± 15 (2a)] X 10- 13

, July 2-

November 9, 1970 [2, 35]; fo NBS, NBS-III [+10

±5 (Io-)]X10- 13

, 5 May 1969 [23], and NBS-5

[12 ±5 (Io-)]X10-13

, 5 January-April 1973 [36].

5 These values account for - 1.8 parts in 1013 gravitational red shift due to the

elevation of Boulder, Colorado.

AT(NBS) was in rate agreement to within 1 X 10~ 13 of the NBS primary frequency standard NBS-III

in May 1969. Since that date NBS-III has been

disassembled; parts were used in the construction

of NBS-5. The rate of TAI with respect to AT(NBS)

as of January 1, 1973 was about -HllXlO -13 via Loran—C [37]. If TAI were perfect the preceding

would imply a decrease in the rate of AT(NBS) of about ~ 2 X 10~ 13 in approximately 4 years. Such a rate drift singularly considered would

cause a time dispersion of about 25 /as over this same period. However, if in eq (9.7) ^at(nbs) is assumed zero and /?at(nbs) is —75 ns/day as was

estimated in 1969 by Dr. Guinot (The Director of the

BIH), then the calculated value using eq (9.7) differs only by about 5 fxs from that measured over

the same 4 years. (Note: AT(NBS) is not totally

independent of TAI.)

In the past the primary consideration for the TAI

has been uniformity, with accuracy of secondary

importance. With the adoption of TAI scale by the

14th General Conference of Weights and Measures

(CGPM) in 1971 [38], conforming to the definition of

the SI second, there is added emphasis upon

accuracy. A recent study by the BIH has shown that the TAI scale has a 50 percent probability of an annual frequency drift of about |0.5 X 10 _13

| [5]. "Except through the participation of NRC the scale

unit of TAI is not anchored to the Systeme Inter- national d'Unites (SI) second and may diverge

indefinitely from it. Recalibration is necessary."

[5] There is a general awareness of this problem, and

recommendations have been made by Dr. Guinot

and others for reasonable corrective procedures

(see sec. 1.5 of chap. 1) [39, 5]. Principally, the BIH

is seeking individual clock data in place of a constructed time scale of an individual laboratory;

this obviates some errors from individual clock

and/or time scale equipment failures, as well as differences in method of calculating the individual

laboratory time, TA(i), used in the construction of

TAI. Dr. Guinot also recommends frequent comparison of the TAI second with that generated by

evaluable primary frequency standards. After

initial calibration, it will probably be necessary to make a frequency adjustment to the TAI scale and

thereafter apply an intentional frequency drift (~ ± 1.0 X 10" 13/year) so that TAI agrees with

evaluations of the SI second [5]. It is hoped that many of the concepts and algorithms developed in this chapter may be of help to the BIH staff in their

important task of constructing a TAI scale in con- formance with the SI unit of time.

9.8. CONCLUSIONS

The rate of the AT(NBS) (proper) scale serves as

a memory of the rate of the NBS primary frequency

standard. The stability of the statistically weighted

eight clock ensemble making up AT(NBS) deter- 223
mines the quality of the memory. The random frac- tional frequency fluctuations have been estimated

and are reasonably modeled by:

<r% (t) - (5 x 10-12

) 2 r

1 +(3 x 101-^)2, (9.39)

where 1 s r ~ 10 7 s. Some relative frequency

drift has been observed between the members of

the commercial cesium beam frequency standards

composing the clock ensemble, and an estimate of

the possible drift of the ensemble indicates that it should be | De \ < 2 X 10~ 13 per year. The accuracy

(lcr) of the rate of AT(NBS) is currently estimated

to be 5.2 x lO" 13. The method employed for generating the AT-

(NBS) scale is based on a particular clock model.

This model assumes that a linear frequency drift, a frequency offset, a time offset, and random noise can all perturb the time of a clock. A convenient

recursive filter has been employed to process the

data in a near optimum way, and to properly filter the perturbations introduced by all but the fre-* quency drift; this drift can be measured over a sustained period with a primary frequency standard

and can then be properly taken into account. The UTC(NBS) scale differs in rate from the

independent AT(NBS) scale by coordinated rate corrections; such corrections keep UTC(NBS) in nominal synchronization (to within a few /jls) with

UTC (the international Coordinated Universal

Time scale maintained at the BIH). The clocks

composing the AT(NBS) scale provide some of the

input data for the time scale algorithm which

generates TAI (UTC is kept within about 0.7 s of

the UT1 scale by making leap second adjustments

of UTC with respect to TAI ). Time and frequency are accessible from the

UTC(NBS) scale via sundry dissemination and time

communication methods; e.g., HF and LF radio

(WWV, WWVH, WWVB, WWVL), telephone,

portable clocks, Loran-C, line-10 TV and network

TV color subcarrier frequency. These differ in accuracy of date transfer from ~ 50 ms to a few

nanoseconds, and in the precision of a frequency

calibration from parts in 107 to a few parts in 1014

. Nominally, the quality of precision is commensurate

with equipment cost; i.e., higher precision requires

increased equipment cost to the user. (TV and some

satellite methods give the minimum cost per pre- cision and accuracy achievable.)

The fractional frequencies of the TAI have been

determined with respect to four of the world's

evaluable primary frequency standards. TAI is probably the most stable time scale in the world

with a stability of about 1 X 10~13 for crjj ~ 1 year)

[3]; it has been reported that this scale shows

frequency drifting of some |0.5 X 10~ 13

| per year [5]. The BIH is proposing several solutions for improving

this free running scale and making it more nearly

in agreement with the SI unit of time. Some of the

techniques discussed in the chapter could aid

conceivably in the evaluation and construction of

the TAI. Possible means for comparing time scales

include portable clocks [9], aircraft flyover [40],

satellite/television techniques [41], and Loran-C [9]. AT(NBS) was in rate agreement to within 1 X 10~13 of NBS-III in May 1969. The rate of TAI with re- spect to AT(NBS) as of January 1973 was about

11X10-13 via Loran-C. If TAI were perfect this implies a decrease in the rate of AT(NBS) of ~ 2 X 10~13 over approximately 4 years; this is well

within the uncertainties internally assigned to the

AT(NBS) system. The accuracy goal for NBS-5 is

1 X 10~13

. Attainment of this goal obviously will allow

a significant improvement in the accuracy of the

AT(NBS) rate. A preliminary calibration with

NBS-5 of AT(NBS) was made during January-April

1973; the rate measured for AT(NBS) was within

1 X 10" 13 of NBS-5's rate. As of March 1973,

TAI appeared to be too high in rate by 12 X 10~ 13 ± 5 X lO-13 (the current accuracy estimate for AT(NBS) and NBS-5) with respect to NBS-5 and

via a filtered estimate using Loran-C data as a time transfer mechanism.

9.9. REFERENCES

[1] Winkler, G. M. R., Hall, R. G., and Percival, D. B., "The

U.S. Naval Observatory clock time reference and the performance of a sample of atomic clocks," Metrologda,

6, No. 4, pp. 126-134 (October 1970).

[2] Mungall, A. G., "Atomic time scales," Metrolofria, 7, No.

4, pp. 146-153 (October 1971).

[3] Allan, D. W., "Statistical modeling and filtering for optimum

atomic time scale generation," Proc. Frequency Standards and Metrology Seminar (Quebec, Canada, August 30, 31-September 1, 1971) H. Hellwig (Ed.), pp. 388-410

(Dept. Elec. Eng., Laval Univ., Quebec, Canada, June

1972).

[4] Yoshimura, K., "The generation of an accurate and uniform

time scale with calibrations and prediction," Nat. Bur. Stand. {U.S.) Tech. Note 626, 64 pages (USGPO, November 1972).

[5] Guinot, B. and (iranveaud, M., "Atomic time scales," IEEE Trans, on Instrum. and Meas., IM-21, No. 4, pp. 396-400 (November 1972).

[6] CCIR, "Detailed instructions by Study Group 7 for the implementation of Recommendation 460 concerning the improved coordinated universal time (UTC) system, valid from 1 January 1972," in XHth Plenary Assembly CCIR

(New Delhi, India, 1970). Ill, pp. 258a-d (ITU: Geneva,

Swtizerland, 1970) (see chap. 1-ann. 1.B.2).

[7] Milton, J. B., "Standard time and frequency: its generation,

control, and dissemination from the National Bureau of Standards Time and Frequency Division," Nat. Bur. Stand. (U.S.) Tech. Note 379, 27 pages. (USGPO, August

1969) (see future updates).

[8] Viezbicke, P. P. (Ed.), "NBS frequency and time broadcast services, radio stations WWV, WWVH, WWVB,

WWVL," Nat. Bur. Stand. (U.S.) Misc. Pub. 236, 19 pages (USGPO, May 1973). Note: A new edition is published annually.

[9] Allan, D. W., Blair, B. E., Davis, D. D. and Machlan, H. E.. "Precision and accuracy of remote synchronization via network television broadcasts, Loran— C and portable clocks," Metrologia, 8, No. 2, pp. 64-72 (April 1972).

[10] Davis, D. D., "Frequency standard hides in every color set," Electronics, 44, No. 10, pp. 96-98 (May 10, 1971).

[11] Davis, D. D., Blair, B. E., and Barnaba, J. F., "Long term

continental U.S. timing system via television network. IEEE Spectrum, 8, No. 8, pp. 41-52 (August 1971). 224
[121 Hanson, D. W.. Hamilton, W. F., and Gatterer, L. E., "The

NBS frequency and time satellite experiment using

ATS-3, Proc. 3rd Ann. Precise Time and Time Interval (PTTI) Strategic Planning Meeting (Washington, DC

20390, November 16-18, 1971), pp. 155-165 (USNO,

Washington, DC 20390, January 1972). (NTIS, AD 758739)

[131 CGPM, Comptes Rendus des Seances de la Triezieme Conference Generale des Poids el Mesures (Proceedings of the Sessions of the 13th General Conference of Weights and Measures) (Paris, France, October 1968), p. 103

(Gauthier-Villars, Paris, France 1968) (in French — see

chap. 1-ann. I.A.I.). [14) Hellwig, H., "Frequency standards and clocks: a tutorial introduction," Nat. Bur. Stand. (U.S.) Tech. Note 616, 69 pages (USGPO, April 1972).

[15] Allan, D. W., "Statistics of atomic frequency standards,"

Proc. IEEE, 54, No. 2, pp. 221-230 (February 1966).

[16] Barnes, J. A., Chi, A. R., Cutler, L. S., Healey, D. J., Leeson,

D. B., McGunigal, T. E., Mullen, J. A., Jr., Smith, W. L., Snydor, R., Vessot, R. F. C, and Winkler, G. M. R., "Characterization of frequency stability," IEEE Trans, on Instrum. and Meas., IM-20, No. 2, pp. 105-120 (May 1971) (see chap. 8). [17] Barnes, J. A., "Tables of bias functions, #i and B2 , for variances based on finite samples of processes with power

law spectral densities," Nat. Bur. Stand. (U.S.) Tech. Note 375, 37 pages (USGPO, January 1969) (see chap. 8). [18] Barnes, J. A., "Atomic timekeeping and the statistics of precision signal generators," Proc. IEEE, 54, No. 2, pp. 207-220 (February 1966).

[19] Vessot, R. F. C, Mueller, L. F., and Vanier, J., "The

specification of oscillator characteristics from measure- ments made in the frequency domain," Proc. IEEE, 54,

No. 2, pp. 199-207 (February 1966).

[20] Barnes, J. A. and Allan, D. W., "A statistical model of flicker noise," Proc. IEEE, 54, No. 2, pp. 176-178 (February

1966).

[21] Becker, G., "Mathematische Filterung von Messwerten; Anwendurgen im Bereich von Zeit und Frequenz" (Mathematical filtering of measuring values; applications in the area of time and frequency), PTB-MITT, 79, No. 4, pp. 247-252 (August 1969) (in German).

[22] Barnes, J. A., and Jarvis, S. J., Jr., "Efficient numerical and

analog modeling of flicker noise processes," Nat. Bur.

Stand. (U.S.) Tech. Note 604, 22 pages (USGPO, June

1971).

[23] Glaze, D. J., "Improvements in atomic cesium beam fre- quency standards," IEEE Trans, on Instrum. and Meas., IM-19, No. 3, pp. 156-160 (August 1970) (see chap. 5A).

[24] Risley , A. S. , Allan, D. W. , Gray, J. E. , Shoaf, J. H. , Machlan

,

H. E., Glaze, D. J., Peters, H. E., Johnson, E. H., Vessot,

R. F. C, and Levine, M. W., "Long term frequency

stability of a NASA prototype hydrogen maser" (Summary), CPEM Digest (1970 Conf. on Precision Electro- magnetic Meas., Boulder, CO 80302, June 2-5, 1970), pp. 74-75 (IEEE, New York, NY 10017, 1970).

[25] Allan, D. W. and Gray, J. E., "Comments on the October

1970 Metrologia Paper 'The U.S. Naval Observatory

clock time reference and the performance of a sample

of atomic clocks'," Metrologia, 7, No. 2, pp. 79-82 (April

1971).

[26] Jespersen, J. E., Blair, B. E., and Gatterer, L. E., "Characterization and concepts of time-frequency dissemination,"

Proc. IEEE, 60, No. 5, pp. 502-521 (May 1972) (see chap. 10). [27] Watt, A. D., Plush, R. W., Brown, W. W., and Morgan, A. H., "Worldwide VLF standard frequency and time signal broadcasting," J. Research Nat. Bur. Stand. (U.S.) (Radio

Propagation), 65D, No. 6, pp. 617-627 (November/

December 1961).

[28] Morgan, A. H., "Distribution of standard frequency and

time," Proc. IEEE, 55, No. 6, pp. 827-836 (June 1967).

[29] Winkler, G. M. R., "Path delay, its variations, and some

implications for the field use of precise frequency stand- ards," Proc. IEEE, 60, No. 5, pp. 522-529 (May 1972).

[30] Viezbicke, P. P. (Ed.), "NBS time and frequency services

bulletin" (Published monthly by the Frequency-Time

Broadcast Services Section, NBS, Boulder, CO 80302).

[31] Davis, D. D., Jespersen, J. L., and Kamas, G., "The use of

television signals for time and frequency dissemination,"

Proc. IEEE (Lett.), 58, No. 6, pp. 931-933 (June 1970).

[32] Howe, D. A., "Nationwide precise time and frequency

distribution utilizing an active code within network

television broadcasts," IEEE Trans, on Instrum. and

Meas., IM-21, No. 3, pp. 263-276 (August 1972).

[33] Allan, D. W., Machlan, H. E., and Marshall, J., "Time

transfer using nearly simultaneous reception times from

a common transmitter," Proc. 26th Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 309-316

(Electron. Ind. Assn., Washington, DC 20006, 1972).

[34] Becker, G., Fischer, B., Kramer, G., and Muller, E. K., "Wissenschaftliche Abhandlungen der Physikalisch- Technischen Bundesanstalt" (Scientific Trans, of the PTB), 22, pt. 1, pp. 41-42 (1970) (in German).

[35] Mungall, A. G., "The second order Doppler shift in cesium beam atomic frequency standards, Metrologia, 7, No. 2, pp. 49-56 (April 1971).

[36] Allan, D. W., Glaze, D. J., Machlan, H. E., Wainwright,

A. E., Hellwig, H., Barnes, J. A., and Gray, J. E., "Per- formance, modeling, and simulation of some cesium beam

clocks," Proc. 27th Ann. Symp. on Frequency Control

(U.S. Army Electronics Command, Ft. Monmouth, NJ

07703, June 12-14, 1973), pp.334-346 (Electron. Ind. Assn., Washington, DC 20006, 1973).

[371 Computed from the Bureau International de l'Heure, Cir. D. Bull. (BIH, Paris, France, 1972).

[38] CGPM, Comptes Rendus des Seances de la Quatorzieme

Conference Generale des Poids et Mesures (Proceedings

of the Sessions of the 14th General Conference of Weights and Measures) (Paris, France, October 4-8, 1971), pp. 49-52; 77-78 (BIPM, Sevres, France, 1972) (in French

see chap. 1-ann. LA.3). [39] Smith. H. M., "International time and frequency coordination," Proc. IEEE, 60, No. 5, pp. 479-487 (May 1971).

[40] Besson, J., "Comparison of national time standards by

simple overflight," IEEE Trans, on Instrum. and Meas., IM-19, No. 4, pp. 227-232 (November 1970).

[41] Palii, G. N. and Fedorov, Y. F., "Method of relating time

scales with the aid of a satellite link and terrestrial tele- vision networks" (translated from Izmeritel'naya Tekhnika, No. 3, pp. 23-26, March 1972), Meas. Tech. (USSR),

15, No. 3, pp. 380-384 (Consultants Bureau, New York,

NY 10017, March 1972).

ANNEX 9.A.

OPTIMUM FILTERS FOR VARIOUS

NOISE PROCESSES (Eq (9.19))

This Annex considers in detail optimum filters for noise processes in eq (9.19) as follows:

— a — 1, for — 3 < a < 1.

(Optimum, as used here, gives a minimum squared

error of time prediction (^fpt (t)).)

The cases for a = 2, 0, — 2 are straightforward.

For a = 2, white noise PM, the time fluctuations are already a white noise process; hence, the simple mean of the residual time fluctuations is the optimum predictor, and the standard deviation of the

225
mean is an estimate of (e 2 (r)). In timekeeping

practice this predictor has not been very useful

since white noise PM usually predominates in high

performance clocks for times only much shorter

than 1 second.

For a = 0— white noise FM or random walk of

phase (time)— the random walk time fluctuations

may be reduced easily to a white noise process by

taking the first finite difference for discrete data

(Ax(y')) or the time derivative (

-j— ) for the con- tinuous case. The simple mean of either of these over the data set is the optimum predictor. This is equivalent to predicting the time from the residual

rate given in eq (9.15), i.e., using the residual

times at the beginning and end of the data set. The

mean-square time dispersion is given by eq (9.18)

where tc is the time interval over the data set. Obviously tc should be kept much larger than t, the prediction interval, for optimum data usage

where white noise FM is the predominate random

perturbation. This noise process predominates in many frequency standards and in most cesium beam

frequency standards for values of t at least in the

range 1 s < t < 10 5 s — see figure 9.1. Hence, this noise process is fundamental in atomic timekeeping.

For a = — 2 — random walk FM reduces to a white noise process by taking the second finite difference for equally spaced discrete data (A?x(j))

or the second time derivative ( — f°r tne con- tinuous case. For the discrete case the optimum

time prediction at t + T for the random fluctuations

would then be given by:

x(t+r) = l&x+2x(t)-x(t-r), (9.A.1)

where A

2* is the average over the data set. The

mean-square time error is given by:

<<e2 (t)> = 2t2o2 (t), (9.A.2)

which is also equal to ((A2x) 2

).

For a= 1 and a = — \ —flicker noise PM and its integral flicker noise FM—the optimum prediction

problem is more sophisticated. Recently some work

has been done showing how flicker noise can be

efficiently generated from white noise [21]; Barnes

and Jarvis have pointed out that such a filter could

be used in reverse to transform flicker noise into white noise. Once the appropriate averaging and

inverse transformations were taken, one would

have, in principle, an optimum flicker filter over an

arbitrary number of decades of t. We are studying

this technique at the present time; however, in the

past we have investigated some very simple recur- sion relationships which yield near optimum time

prediction (see sec. 9.3.2, eq (9.20)).

ANNEX 9.B.

TIME DISPERSION WITH RECURSIVE FILTER APPLIED TO

FLICKER NOISE FM

The second term on the right of eq (9.25) gives

the mean-squared time error after an interval r when a recursive filter, as in eq (9.20), is applied to a flicker noise FM process of intensity h-i. Such a

filter is approximately equal to an exponential

filter having a time constant mr. Since from table

9.1 we have the following

oy

2 (r)=2/i-1 ln (2), (9.B.1)

the mean-squared time error due to h-i in eq (9.25)

may be rewritten as:

<e

2 (r)> = oy2 (T)F(m) • r\ (9.B.2)

where

F(m) =

21n (2)m2 (2m+l)|1 (^Tl)'

C kHnL

(9.B.3)

Table 9.B.1 is a list of some pertinent values for F(m). The time dispersion due to flicker noise FM

over an interval t may be easily calculated (the

square root of eq (9.B.2))by use of table 9.B.1 once we know the stability cry (T), and the value of m.

Table 9.B.I. Correspondence of Values m and F(m) in eq (9.B.3 )

F{m)= 1 y (—rrf

2 ln k (9- B- 3) 2 In (2)m2 (2m + l) *f \m + l/

m F(m) m F(m)

0 2.00 10 2.60

0.1 1.93 20 2.99

0.2 1.89 30 3.23

0.3 1.86 40 3.42

0.4 1.85 50 3.56

0.5 1.85 60 3.69

0.6 1.84 70 3.79

0.7 1.85 80 3.88

0.8 1.85 90 3.96

0.9 1.86 100 4.03

1.0 1.87 200 4.51

2 1.97 300 4.80

3 2.08 400 5.00 4 2.18 500 5.16

5 2.27 600 5.29 6 2.35 700 5.40

7 2.42 800 5.49 8 2.48 900 5.59

9 2.54 1000 5.65

226
ANNEX 9.C.

MINI-COMPUTER PROGRAM FOR

FIRST ORDER TIME SCALE

ALGORITHM

This program is written in a Fortran dialect compatible with a mini-computer which has a 4k twelvebit word memory. The computation has been simplified with Fortran variables redefined, in an effort to work within the capabilities of the mini-computer.

The program of computation is explained by the Fortran listing with its comment statements. In these statements the computed time scale is often

called the "paper clock."

Input required by the computer program:

DAY2 If initial values are to be supplied,

DAY2 is 9, otherwise it is the date on which the clock readings were taken,

i.e., the modified Julian day number.

FN(I) is the number of measurement intervals

to be used as a time constant when computing a new rate for clock I.

R(I) is the rate of clock I with respect to that of the paper clock in nanoseconds

per day.

D(I) is the time of clock I with respect to the

paper clock in nanoseconds; D(I) =

clock I— paper clock.

SIG(I) is (ef(T = ld)) 1 / 2 for clock I in nanoseconds.

SUME(I) is the total time error (nanoseconds) ac- cumulated by clock I, with respect to the paper clock, since sum error was

last set equal to zero.

DAY 1 is the date on which the last set of readings were taken.

T is the hour at which the readings were

taken. In this program, T is not used in the computation, the readings being

taken at the same time each day.

D31 is the time interval, in nanoseconds, be- tween the 1 pps of clock 3 and that of

clock 1, etc. for all the other clock dif- ferences entered into the program.

D3S is the time interval, in nanoseconds, be- tween the 1 pps of clock 3 and that of clock S. Clock S is the on-line clock

which approximates UTC(NBS) — often

called the working standard.

Interpretation of the computer printout:

(1) Modified Julian day: The date.

(2) Clock number: The clocks of the ensemble are numbered 1 through 8.

(3) Error: The error in nanoseconds, accumulated

by clock I during the measurement interval, with

respect to the paper clock.

(4) Frequency: The frequency of clock I with re- spect to that of the paper clock, in parts in 10 14

, averaged over the measurement interval.

(5) Sigma of the set: Corresponds to (e|(T=ld)) 1/2 in eq (9.25).

(6) Time of the working standard: The time of clock

S with respect to the paper clock in nanoseconds.

The remaining output is data that is to be put back

into the computer for computation on the next day. In case of clock reset, the following are unchanged: sum error, rate, and sigma. The "Error" printout

has the same significance as usual, and the rate is unadjusted.

Fortran listing follows:

227
C; TIME SCALE PROGRAM (15 MARCH 71). A MINUS (-) INDICATES THAT

C; THE CLOCK IS EITHER LOW IN FREQUENCY OR LATE IN TIME.

1; FORMAT ( I ,E,E,E,E,/ ) 21 FORMAT ( "CLOCK " * I

, "RESET"

,

/ > 3; FORMAT (// , "SMPL AVG RATE TIME SIGMA

At FORMAT < E

)

51 FORMAT < I , E , E , / ) 6; FORMAT(/ , "MODIFIED JULIAN DAY ",E,/>

7; FORMAT <///// ) 8; FORMAT ( "T I ME OF WORKING STANDARD IS ",E,/>

91 FORMAT </, "SIGMA OF SET ",E,/>

DIMENSION R(8>, D(8>, SI GC8 ) * ER<8>, DP(8>, IRJT<8>, SUME<8),FN(8

Hi FORMAT (/ * "CLOCK ERROR ' FREQ X 10 TO 14",/)

Nl = 1 N8 = 8

10; ACCEPT 4, DAY2

IF (DAY2-9. ) 30,30*40

30; DO 39 I=N1,N8

ACCEPT 4»-FNCI>« RCI>, D(I),SIG(I>, SUME(I)

391 CONTINUE

ACCEPT A» DAY 1 GO TO 10

40; ACCEPT A, T,D31 , D32 , D3 4 , D35 , D84, D8 6, D3 7, D3S

T=DAY2-DAY

1

DO 49 I=N1,N8

DP < I ) = R( I )*T + D ( I )

I R JT ( I )=0

49J CONTINUE

N = 0

50; ER( 1 >=DPC 1 >-D3S+D31

ERC2>=DP(2)+D32-D3S

ER(3)=DP(3)-D3S

A=D34-D3S

ER<4)=DP(4)+A

ER(5)=DP(5)+D35-D3S

ER< 6>=DP< 6>+A-D84+D8 6

ER( 7)=DP( 7)-D3S+D37

ER(8)=DP(8)+A-D84

ANRM=0.

DS=0.

DO 69 I=N1,N8

IF (IRJT(I)-N) 68,68*69

228
68; DS=DS+ER( I >/SI GC I > **2

ANRM=ANRM+1 . /SIGC I )**2

69 1 CONTINUE

DS=DS/ ANRM

DAY 1 =0.

DO 79 I=N1*N8

ER( I )=DS-ER( I ) DAY1 =DAY1 + ER( I )*ER< I ) 791 CONTINUE

M = 0

DO 89 I=N1*N8

A-ER( I )*ER( I >-.2*DAYl -4.E4

IF (A) 86*87*87

861 A= ( ER ( I )/?)*( ERC I )/T) - 9.*SIG<I>**2

IF (A) 88* 85* 85

871 IRJT(I)=9

GO TO 84

881 IRJT(I)=0

GO TO 89

851 IRJT(I)=N8

841 M = M + 1 891 CONTINUE

IF (M-N) 60*90,60

601 N=M

GO TO 50

901 TYPE 6* DAY2

TYPE 11 ANRM=SQTF< 1 ./ANRM ) DO 98 I =N 1 *N8

DAY 1 =DP C I ) + ERC I )

I F ( IRJTC I ) ) 10*91*96

911 SUME ( I ) = SUME ( I ) +ER ( I ) A=(DAY1 -D(I ) >/<T*.864>

R < I ) = ( R < I > * FN < I > + • 8 64 *A ) / ( FN ( I ) + 1 • ) ERNM = SQTF(ER( I )*ER( I ) ) / T + . 8 *ANRM* *2/ S I G< I ) C= < 31 . *SI G( I )**2+ERNM**2)/32.

SIGd ) = SQTF(C)

GO TO 9 7 961 TYPE 2* I 971 DCI)=DAY1

TYPE 5* I * ER ( I ) * A

981 CONTINUE

TYPE 9* ANRM

TYPE 8* DS

TYPE 3

DO 119 I=N1*N8

TYPE 1* FN(I>* R(I>* DCI>* SIGCD* SUME(I)

1191 CONTINUE

TYPE 7 DAY 1 =DAY2

GO TO 10

END

229
ANNEX 9.D.

SELECTED BIBLIOGRAPHY ON

TIME SCALES AND THEIR

FORMATION

[Bl] Allan, D. W., "Statistics of atomic frequency standards,"

Proc. IEEE, 54, No. 2, pp. 221-230 (February 1966). [B2] Allan, D. W., "Statistical modeling and filtering for opti- mum atomic time scale generation," Proc. Frequency

Standards and Metrology Seminar (Laval University,

Quebec, Canada, August 30, 31, September 1, 1971), H. Hellwig (Ed.), pp. 388-410 (Dept. Elec. Eng., Laval

Univ., Quebec, Canada, June 1972). [B3] Allan, D. W., Fey, R. L., Machlan, H. E., and Barnes, J. A., "An ultra-precise time synchronization system designed

by computer simulation," Frequency, 6, No. 1, pp. 11-14

(January 1968). [B4] Allan, D. W., Gray, J. E., and Machlan, H. E., "The NBS

atomic time scale system: AT(NBS), SAT(NBS), and UTC(NBS)," (summary) Proc. 24th Ann. Symp. on Fre- quency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 27-29, 1970), p. 361 (Electron.

Ind. Assn., Washington, DC 20006, 1970). [B5] Allan, D. W., and Gray, J. E., "Comments on the October

1970 Metrologia Paper The U.S. Naval Observatory

clock time reference and the performance of a sample of atomic clocks," Metrologia, 7, No. 2, pp. 79-82 (April

1971). [B6] Allan, D. W., Gray, J. E., and Machlan, H. W., "The National Bureau of Standards atomic time scales: generation, dissemination, stability, and accuracy,"

(Proc. of the 1972 Conf. on Precision Electromagnetic Meas. (CPEM), Boulder, CO 80302, June 26-29, 1972); IEEE Trans, on Instrum. and Meas., IM-21, No. 4, pp. 388-391 (November 1972). [B7] Barnes, J. A., "The development of an international atomic

time scale," Proc. IEEE, 55, No. 5, pp. 822-826 (June

1967). [B8] Barnes, J. A., and Allan, D. W., "An approach to the pre- diction of coordinated universal time," Frequency, 5,

No. 6, pp. 15-20 (November-December 1967). [B9] Barnes, J. A., Andrews, D. H., and Allan, D. W., "The

NBS_A time scale — its generation and dissemination," IEEE Trans, on Instrum. and Meas., IM-14, No. 4, pp. 228-232 (December 1965). [B10] Barnes, J. A., Chi, A. R., Cutler, L. S., Healey, D. J., Leeson, D. B., McGunigal, T. E., Mullen, J. A., Jr., Smith, W. L., Sydnor, R. L., Vessot, R. F. C, and

Winkler, G. M. R., "Characterization of frequency

stability," IEEE Trans, on Instrum. and Meas., IM-20,

No. 2, pp. 105-120 (May 1971) (see chap. 8). [Bll] Barnes, J. A., and Fey, R. L., "Synchronization of two

remote atomic time scales," Proc. IEEE (Corresp.), 51,

No. 11, p. 1665 (November 1963). [B12] Barnes, J. A., and Jarvis, S., Jr., "Efficient numerical and

analog modeling of flicker noise processes," Nat. Bur. Stand. (U.S.) Tech. Note 604, 22 pages (USGPO, June

1971). [B13] Becker, G. , "Von der Astronomischen zur Atomphysikalischen Definition der Sekunde," (From the astronomical

to the atomic definition of the second), PTB-Mitt., 76,

No. 4, pp. 315-323 and No. 5, pp. 415-419 (August and

Octover 1966) (in German).

[B14] Becker, G., "Mathematische Filterung von Messwerten; Anwendurgen im Bereich von Zeit und Frequenz,"

(Mathematical filtering of measuring values; applications

in the area of time and frequency), PTB-Mitt, 79, No. 4, pp. 247-252 (August 1969) (in German).

[B15] Becker, G, "Uber die Begriffe Phase, Phasenzeit und

Phasenwinkel bei Zeitabhangigen Vorgungen," (About

the terms phase, phase time, and phase angle in time

dependent processes), PTB-Mitt., 81, No. 5, pp. 348-

352 (October 1971) (in German).

[B16] Becker, G., "Was ist eine Zeitskala?," (What is a time

scale?), PTB-Mitt., 81, No. 6, pp. 405-411 (December

1971) (in German).

[B17] Besson, J., "Comparison of national time standards by

simple overflight," IEEE Trans, on Instrum. and Meas., IM-19, No. 4, pp. 227-232 (November 1970). [B18] BIPM (International Bureau of Weights and Measures),

"Changement de la definition de la seconde," (Change

of the definition of the second), Comptes Rendus des Seances de la Triezieme Conference Generate des Poids

et Mesures, (Proc. Meet, of 13th General Conf. of Weights and Measures, October 10-16, 1967; October 15, 1968,

Paris, France), pp. 58-60; Unit of time (second) resolution, p. 103 (Gauthier-Villars & Cie, Paris, France, 1969)

(in French — see chap. 1-ann. l.A.l). [B19] Bodily, L. N., and Hyatt, R. C, "'Flying clock' comparisons extended to east Europe, Africa, and Australia," Hewlett- Packard J., 19, No. 4, pp. 12-20 (HP Co., Palo Alto, CA 94304, December 1967). [B20] Bonanomi, J., Kartaschoff, P., Newman, J., Barnes, J. A., and Atkinson, W. R., "A comparison of the TA, and the NBS-A atomic time scales," Proc. IEEE (Corresp ). 52,

No. 4, p. 439 (April 1964). [B21] CCDS, "Recommendations du comite consultatif pour la definition de la seconde . . .," (Recommendations of the Consultative Committee for the definition of the second . . .), Comite consultatifpour la Definition de la Seconde (CIPM, 5

e Session, Paris, France, June 18-19,

1970), pp. S21-S23 (CIPM, Sevres, France, 1971) (in French — see chap. 1-ann. 1.A.2). [B22] CCIR, "Comparisons of time scales by various methods,"

CCIR Study Group 7, Doc. 7/8-E, Rep. 363-, Xllth Plenary Assembly CCIR (New Delhi, India, 1970), III, pp. 249a-b (ITU: Geneva, Switzerland, 1970). [B23] CGPM, Comptes Rendus des Seances de la Quatorzieme

Conference Generate des Poids et Mesures (Proc. of the Sessions of the 14th General Conference of Weights and

Measures) (Paris, France, October 4-8, 1971), pp. 49-52; 77-78 (BIPM, Sevres, France, 1972) (in French -see

chap. 1-ann. 1.A.3). [B24] CIPM (International Committee of Weights and Measures),

Comite Consultatif pour la Definition de la Seconde

(Consultative Committee for the Definition of the Second), 3

e Session~1963, 72 pages; 4

e Session_1967, 29 pages (Gauthier-Villars & Cie, Paris, France, 1964; 1968) (in French).

[B25] Essen, L., "Time scales," Metrologia, 4, No. 4, pp. 161—

165 (October 1968). [B26] Essen, L., "A revolution in time-keeping," Proc. ofConf. on

Freq. Generation and Control for Radio Syst. (C. E. Tate, Chairman, London, England, May 22-24, 1967), Inst. Elec. Eng. (London) Conf. Publ. No. 31, pp. 11-15

(Savoy Place, London, England, 1967). [B27] Fey, R. L., Barnes, J. A., and Allan, D. W., "An analysis of low information rate time control unit," Proc. 20th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 19-21, 1966), pp. 620-635 (NTIS, AD 800 523, 1966). [B28] Ganter, W. A., "Modeling of atomic clock performance and

detection of abnormal clock behavior," Nat. Bur. Stand.

(U.S.) Tech. Note 636, 30 pages (USGPO, March 1973). [B29] Guinot, B., "Characteristics of a scale of time," Alta. Fre- quenza, 40, No. 8, pp. 320E-322E (August 1971) (in English). [B30] Guinot, B., Feissel, M., and Granveaud, M., Bureau Inter- national de I'Heure Annual Report for 1970 (BIH, Paris, France, 1971). [B31] Guinot, B., "Sixieme rapport due comite consultatif pour de la definition de la seconde au comite international des

poids et mesures," (Minutes of the 6th Session Consulta230
tive Committee for the Definition of the Second) (CIPM,

6

e Session, Paris, France, July 6-7, 1972) (CIPM, Sevres, France, 1972) (in French — see chap. 1-ann. I.C.I.). [B32] Guinot, B., and Granveaud, M., "Atomic time scales," IEEE Trans, on Instrum. and Meas., IM-21, No. 4, pp. 396-400 (November 1972). [B40]

[B33] Hudson, G. E., "Some characteristics of commonly used

time scales," Proc. IEEE, 55, No. 6, pp. 815-921 (June [B41]

1967). [B34] Kartaschoff, P., and Brandenberger, H., "A digital servo

for frequency and time scale conversion," Proc. 20th [B42] Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 19-21, 1966),

pp. 577-586 (NTIS , AD 800 523, 1966). [B43]

[B35] Kovalevsky, J., "Astronomical time," Metrologia, 1, No. 4, pp. 169-180 (October 1965). [B36] Leschiutta, S., "The IEN time scale as an application of [B44] some ideas on timekeeping," Proc. Frequency Standards and Metrology Seminar (Laval University, Quebec,

Canada, August 30, 31-September 1, 1971), H. Hellwig [B45]

(Ed.), pp. 411-430 (Dept. Elec. Eng., Laval Univ., Quebec, Canada, June 1972). [B37] Markowitz, W., "The atomic time scale," IRE Trans, on

Instrum., 1-11, Nos. 3 and 4, pp. 239-242 (December

1962). [B46]

[B38] Milton, J. B., "Standard time and frequency: its generation,

control and dissemination from the National Bureau of Standards Time and Frequency Division," Nat. Bur. Stand. (U.S.) Tech. Note 379, 27 pages (USGPO, August [B47]

1969) (see future updates). [B39] Morris, D., Daams, H., Mungall, A. G., Bailey, R., Miller, L. G., and Thompson, M. M., "Atomic frequency standards and timekeeping at the National Research Council,"

Proc. Frequency Standards and Metrology Seminar

(Laval University, Quebec, Canada, August 30, 31- September 1, 1971), H. Hellwig (Ed.) pp. 119-146 (Dept.

Elec. Eng., Laval Univ., Quebec, Canada, June 1972). Mungall, A. G., "Atomic time scales," Metrologia, 7, No. 4, pp. 146-153 (October 1971). Mungall, A. G., Daams, H., and Bailey, R., "Note on atomic timekeeping at the National Research Council," Metrologia, 5, No. 3, pp. 73-76 (July 1969). NBS, "Nation gets unified time system" Nat. Bur. Stand.

(U.S.) Tech. News Bull., 53, No. 2, p. 34 (USGPO,

February 1969). Newman, J., Fey, R. L., and Atkinson, W. R., "A comparison of two independent atomic time scales," Proc. IEEE(Corresp.), 51, No. 3, pp. 498-499 (March 1963). Putkovich, K., "Automated timekeeping," IEEE Trans, on Instrum. and Meas., IM-21, No. 4, pp. 401-405 (November 1972). Winkler, G. M. R., "Explanation and requirements for universal time," Proc. PTTI (Precise Time and Time

Interval Strategic Planning Meeting), (USNO, Washington, DC 20390, December 10-11, 1970), 1, pp. 152-

155 (NTIS, AD 881 014-L, 1970). Winkler, G. M. R., Hall, R. G., and Percival, D. B., "The

U.S. Naval Observatory clock time reference and the performance of a sample of atomic clocks," Metrologia,

6, No. 4, pp. 126-134 (October 1970). Yoshimura, K., "The generation of an accurate and

uniform time scale with calibrations and predictions," Nat. Bur. Stand. {U.S.) Tech. Note 626, 64 pages (USGPO,

November 1972).

231

CHAPTER 10

TIME AND FREQUENCY DISSEMINATION: AN OVERVIEW OF PRINCIPLES

AND TECHNIQUES**

Byron E. Blairt

Contents

Page 10.1. Introduction 235

10.2. Dissemination Concepts 235

10.2.1. Basic Considerations Inherent in Transfer of Time and Frequency 235

10.2.2. Frequency from Time Measurements 237

10.2.3. Elements that Characterize the Dissemination System 237

10.2.4. Basic Techniques Common to a Clock Synchronization System 238

10.3. Radio Dissemination of Time and Frequency 239

10.3.1. Radio Propagation Factors 240

10.3.2. Radio Dissemination Techniques 240

a. Standard Frequency and Time Broadcasts 240

b. Very Low Frequency (VLF) Time and Frequency Systems 241

c. Low Frequency (LF) Time and Frequency Dissemination 245

d. High Frequency (HF) Time and Frequency Dissemination 247

e. Radio Navigation Systems for TFD 251

(1) Omega navigation system for TFD 251

(2) Loran-C navigation system for TFD 253

(3) Loran-A navigation system for TFD 257

f. Television TFD Techniques 259

g. TFD via Earth Satellites 269

h. Microwave Time and Frequency Transfer (SHF) 281

i. Commercial Radio TFD Techniques 282

j. TFD from VHF Signals Reflected from Meteor Trails 283

10.3.3. Advanced T/F Systems Using Radio Techniques 284

a. Very Long Baseline Interferometry (VLBI) Time Synchronization 284

b. Moon Bounce Time Synchronization (MBTS) 286

c. Aircraft Collision Avoidance System (ACAS) 288

10.4. Dissemination of Time and Frequency via Portable Clock 290

10.4.1. On-Site Visits 292

10.4.2. Aircraft Flyover 293

10.5. TFD via Other Means 294

10.5.1. Time Transfer via Optical Pulsar Signals 294

10.5.2. TFD in Telephone Line and Coax Cable Transmission 296

10.5.3. Power Line (60-Hz) Signals as a Time Transfer Technique 298

10.6. T/F User and System Evaluation 299

10.6.1. Classification of T/F Users 299

10.6.2. Evaluation of T/F Systems 300

ivianuacnpi received /\pm i, ... - rrr M 1Q70 f •Parts of this chapter have been modified from "Characterization and concepts of time-frequency dissemination published in Froc. Ittt, May (see rei- erence [16]). Publication herein is at concurrence of the IEEE. tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, CO 80302.

233
Page 10.7. Conclusions 302

10.8. References 303

Annex 10. A. Characteristics of Radio Frequency Bands 4 through 10 310a

Annex 10.B. Characteristics of Standard Frequency and Time Signals in Allocated Bands... 311

Annex 10.C. Characteristics of Stabilized Frequency and Time-Signal Emissions Outside

Allocated Frequency Assignments 312

Annex 10.D. Characteristics of Frequency Stabilized Navigation Systems Useful for Time/

Frequency Comparisons 313

"In any observation process there must be a signal coming from the observed system to the recording apparatus, and since the propagation

of any signal requires a finite time interval, this gives the possibility of defining the arrival of the signal to be 'later' than the time of emission."

L. Rosenfeld, Study of Time, p. 479

This chapter reviews basic concepts and common elements that characterize time and frequency

dissemination. The means by which time and frequency can be disseminated fall into four main

categories: radio broadcasts, on-site comparisons, events in nature, and hardline wire systems.

Interrelated elements include active and passive transfer methods and supplementary techniques

available from systems with differing primary objectives (piggyback operations). Three categories of time and frequency users are classified according to accuracy needs, and means of providing these needs are shown. Various characteristics of time and frequency dissemination systems are charted and evaluated in terms of such factors as accuracy, ambiguity, geographical coverage, reliability, cost

of user equipment, etc. Appraisal of these factors reveals many interrelationships and limitations to be

functions of nature, economics, need, and availability. Annexes give descriptions of radio frequency

propagation in various bands as well as characteristics of stabilized radio broadcasts useful for time and

frequency dissemination. The most accurate means of time and frequency dissemination today is through portable clocks, such as on-site visits and/or aircraft flyover; accuracy needs of the majority of time and frequency

users can be met in a variety of ways; and existing or planned navigation and communication systems

show excellent potential for time-frequency dissemination at little or no additional cost. We conclude

that (1) no one system will satisfy all user needs, (2) any general purpose timing system should cost the user in proportion to his accuracy requirements, and (3) existing or proposed electronic systems

with a time-frequency dissemination capability should be utilized to the fullest extent to realize frequency/spectrum conservation. Key words: AC power lines; Aircraft Collision Avoidance System (ACAS); aircraft flyover; characteristics

of stabilized broadcasts; commercial radio; HF radio; LF radio; line-10 TV; Loran-A; Loran-C;

meteor trails; microwave systems; moonbounce; navigation systems; Omega; portable clocks; pulsars; radio propagation; satellite; standard frequency broadcast; telephone; television; TIMATION; time- frequency accuracy; time-frequency dissemination; time-frequency evaluation; time-frequency user needs; timekeeping; TRANSIT; very long base interferometry (VLBI); VLF radio.

234
10.1. INTRODUCTION

In recent years, advances in technologies of

communication, transportation/navigation, timekeeping, and space tracking have placed stringent

requirements on time and frequency information.

In general, one might consider that optimum comparison of frequency standards or time scales to be

through side by side measurements in a laboratory.

Many needs of time and frequency, however, are

at great distances from a standard time and fre- quency center. In this chapter we consider what means are available to bridge the distance gap

between a standard-time and frequency source and

a remotely located user. The concept of our presentation is graphically shown in figure 10.1, with a standard time and frequency source at the center

of a circle and segments of larger concentric circles portraying various independent means of trans- ferring this standard to a diverse group of users. The majority of dissemination methods employ some type of radio transmission, either in dedicated

time and frequency emissions or established sys- tems such as navigation and television. The most

accurate means of time and frequency dissemination today is through portable clocks, such as on

site visits and aircraft flyover. Looking into the

future, one foresees that satellite systems and micro- wave communication networks will play a large

part in providing time and frequency information

to many users. This chapter reviews some of the basic characteristics and limitations shared by most time and

frequency dissemination (TFD) systems. Some

systems, such as radio stations CHU and WWV,

were built specifically for TFD while others, such

as the Loran-C navigation system, can be adapted

for TFD; in a few cases it even is possible to use a natural event such as a pulsar for time transfer. A user of a TFD system is generally trying to establish one or more of the following: time of day or

date; frequency or time interval; and synchronism.

The degree to which he can achieve these objectives

will depend upon a number of elements which

characterize the system, e.g., accuracy, ambiguity,

repeatability, coverage, cost, etc. These various

factors are interrelated; they are limited by nature,

as well as the users' resources and skill. Such

characteristics form a common base which permit

evaluation of both new and old systems in similar

terms of reference. Classification of timing needs

into low, medium, and high-accuracy users gives one an overview of the general time and frequency

community. From the discussion it is apparent that no one system will satisfy all user needs; that any

general purpose timing system should cost the user

proportionately to his accuracy requirement; and

that actual or proposed electronic systems, having a potential for dissemination of time and frequency at additional modest cost, should be employed to stem

a proliferation of limited-scope, special purpose

timing systems. The dissemination techniques are

adaptable to a great variety of user needs and these

should be properly weighed in any evaluation, consideration, or application of specific methods.

The intent of this chapter is to give a broad over- view of various ways of disseminating time and

frequency. Because of the scope and breadth of

such an objective, one cannot give complete details for a given system; however, we have attempted to include adequate references for further study of

specific dissemination techniques. Excellent publications exist which describe general aspects of time and frequency [1, 2, 3,4].' (Our approach does

not consider detailed system-receiving techniques;

these will be detailed in later NBS publications.)

Section 10.2 of the chapter defines and describes

basic concepts inherent in time and frequency

dissemination. This is followed by a section dis- cussing aspects and techniques of radio dissemination of time and frequency. The final sections of the

chapter discuss portable clock techniques, dis- semination by other than radio means, and classi- fication of users and evaluation of the various

dissemination techniques. Annexes briefly describe

radio propagation in various bands and give

characteristics of stabilized broadcasts useful for TFD.

10.2. DISSEMINATION CONCEPTS

This section touches on basic considerations

inherent in the transfer of time and frequency

information; discusses elements that characterize

the dissemination system; and describes utilization of a transfer standard. The section sets a foundation

for comparative insight into the various techniques

of time and frequency dissemination. It is taken for granted that the desirability of transferring time

and/ or frequency from a prime standard to a user

as depicted in figure 10.1 is paramount. Frequency/

time standards are not discussed in detail in this chapter; for such information the reader is referred

to Chapters 2, 3, 4, 5, 6, and 9. We base our discussion on the following clock concepts. A clock is the

fundamental component of timekeeping; it consists

of a frequency standard, a means for counting and

keeping track of oscillations, and a readout device

for displaying the count. Often an interpolation

device is added for use between counts. In essence,

a clock is a device which accumulates the cycles of an oscillator (frequency standard) and presents the

result in some convenient form.

10.2.1. Basic Considerations Inherent in

Transfer of Time and Frequency

There are several basic concepts implicit in the

transfer of time and frequency information, including

date, frequency or time interval, and time/frequency

(T/F) synchronization. By date we mean time of day

1 Figures in brackets refer to the references at end of this chapter.

235
236
such as 1965, July 12th, 12h, 24m, 43.010 ... s. In

other words the time of an event reckoned from some concensual origin. Time interval refers to duration — the difference in time between two dates. Note that a time interval of lh can be shown by a clock that is not on time, although running at the

correct rate. Also, time interval and frequency are

closely related concepts; the frequency of some

phenomenon can be determined by the number of occurrences within a measured time interval. Synchronized clocks read the same time at a given

point in time, although not necessarily on the basis

of an absolute time scale. A coherent communications system is a good example of showing a requirement for synchronization. High rate messages, per- haps of 10 /xs duration, are transmitted, to an

addressee who must be synchronized in time with

the sender to obtain the message. For further dis- cussions of these basic concepts the reader is re- ferred to Chapter 1. Time is a basic dimension that, apart from

physical aspects, influences everyone. History has

shown man attempting to keep time by various

crude and sundry instruments such as water

buckets, candles, sundials, and pendulum clocks [5]. In today's world, time indicators vary from wrist- watches, chronometers, wall clocks, and radio

signals to crystal oscillator and atomic clocks. Each

of these timing devices shows varying degrees of

accuracy and precision; a wristwatch meets a casual

need, whereas exact time may require an atomic

clock. For any particular event to occur, within some accuracy framework, it is important that all devices maintaining time indicate the same time of

day; but since all time pieces are less than perfect,

they gradually "drift" and must be continually set to a standard. The time standard has evolved through

the years as pointed out by Humphrey Smith [6], and

today the second is defined in terms of the resonance

of cesium (see chap. 1). However, the cesium standard is much more stable than a time standard based

on the earth movement, i.e., the lengths of atomic

seconds are nearly identical. On the other hand,

atomic time is essentially independent of that time

required by navigators, geodesists, astronomers, and

others requiring time based on earth rotation. Thus,

a time scale called UTl (universal time corrected

for polar motion of earth) is also necessary; UTl is referenced to the 0 meridian at Greenwich.

Many people today depend upon the electric wall

clock whose rate is fixed by the power company's

generator. In the United States the power utilities synchronize their generators to the National Bureau

of Standards' low frequency broadcast, WWVB [7]. Thus, the U.S. clocks generally run at the same rate. The U.S. citizenry normally set such clocks through

time announcements, either by radio or telephone.

Radio time signals can be used either to perform

a clock function or to set clocks. When one uses a

radio wave instead of a clock, however, new considerations evolve. One is the delay time of approximately 3/as per km (propagation delay) it takes the

radio wave to propagate and arrive at the reception

point. Thus, a user 1000 km from a transmitter

receives the time signal 3 ms later than the on-time

transmitted signal. If time is needed to better than

3 ms, correction must be made for the travel delay.

An additional allowance must be made for the signal

to pass through the antenna/receiver (receiver

delay). Other problems related to radio wave propagation will be discussed later on. In most cases the standard time and frequency

emissions such as CHU, JJY, WWV, and WWVH

are more than adequate for everyday needs. The

launching of earth satellites during the late 1950's,

however, required snychronization of worldwide

tracking networks to better than 1 ms. In addition,

the appearance of portable atomic frequency

standards initiated planning of new navigational

and communication systems requiring microsecond

timing.

Today, many systems exist which are able to disseminate standard frequencies and time signals

with sufficient convenience and accuracy for most

users in metrology. These same systems may be

used someday to disseminate other standard units

of measurement, including those for electromagnetic

force (volt), length (meter), and attenuation (decibel),

among others. These dissemination systems,

together with the inherently high precision of fre- quency standards and of frequency/time metrology,

may help to establish a unified standard for measure- ment [8]. The progress and feasibility for a unified

standard is discussed also in Chapter 7.

10.2.2. Frequency from Time Measurements

Dimensionally, frequency is the reciprocal of

time interval. Frequency implies periodic motion

or oscillation such as cycles per second (Hz). Its unit can be given as the period of one cycle, i.e., V6o Hz ~ 17 ms. It is no surprise, then, that a fre- quency dissemination service can be useful for timekeeping and that frequency information can

be obtained from a time broadcast. Any "time

dissemination" service can be used as a frequency

reference. If the time difference between a user's clock and the reference clock increases between

measurements, the user knows that the oscillator

in his clock is running at a different rate than that

of the reference clock, and he can compute his frequency offsets.

10.2.3. Elements that Characterize the Dissemination System

A number of common elements characterize most

time/frequency dissemination systems. Among the

most important are: accuracy, ambiguity, repeatability, coverage, availability of time signal, reliability, ease of use, cost to the user, and the number

of users served. There does not now appear to be

any single system which incorporates all desired

characteristics. The relative importance of these

237
characteristics will vary from one user to the next,

and the kind of compromise solution for one user may not be satisfactory to another. We will intro- duce these common elements through detailed

examination of a possible radio signal.

Consider a very simple system consisting of an unmodulated 10-kHz signal as shown in figure 10.2.

RECEIVED

SIGNAL

00001 T

•—PERIOD —

;i00uS-»10kHz)

//

/

,—REPEATABILITY (DAV-TO DAY -VAR I AT I ON

)

PROPAGATION /

DELAY, t 4 / a AMBIGUOUS CYCLES (ZERO CROSSINGS) yA\ a a / 1

50us

TIME

FIGURE 10.2. Single tone time dissemination. A positive going zero-crossing of this signal, leaving

the transmitter at 0000 UT, will reach the receiver

at a later time equivalent to the propagation delay.

The user must know this delay because the accu- racy of his knowledge of time can be no better than

the degree to which this delay is known. (By accu- racy we mean the degree of conformity to some

specified value or definition.) Since all cycles of

the signal are identical, the signal is ambiguous

and the user must somehow decide which cycle is the "on time" cvcle. This means, in the case of our hypothetical 10-kHz signal, that the user must

know the time to ± 50/ns (half the period of the signal). Further, the user may desire to use this system,

say once a day, for an extended period of time to check his clock or frequency standard. However,

it may be that the delay will vary from one day to the next, and if the user is unaware of this variation, his accuracy will be limited by the lack of

repeatability of the signal arrival time.

Many users, geophysicists and seismologists for example, are interested in making time coordinated measurements over large geographic areas. They would like all measurements to be referenced

to one time system to eliminate corrections for dif- ferent time systems used at scattered and/or

remote locations. This is a very important practical

consideration when measurements are undertaken

in the field. In addition, a one reference system,

such as a single time broadcast, increases confi- dence that all measurements can be related to each other in some known way. Thus, the coverage

of a system is an important concept. Another

important characteristic of a timing system is the

percent of time available. The man on the street who has to keep an appointment needs to know

the time perhaps to a minute or so. Although he

requires only coarse time information, he wants it on demand so he carries a wrist watch that gives

the time to him 24 hours a day. On the other hand,

a user who needs time to a few microseconds

employs a very good clock which only needs an

occasional update, perhaps only once or twice a

day. An additional characteristic of time/frequency

dissemination is reliability, i.e., the likelihood

that a time signal will be available when scheduled. Propagation fadeout can sometimes prevent

reception of HF signals. The characteristics dis- cussed so far are for the most part related to the

design of the signal and to the propagation characteristics of the medium. However, there are some

important economic and human considerations.

Economic and human factors in a TFD system

include (1) the cost of establishing and maintaining

the service; (2) the number of users to be served

by the system; (3) the cost of equipment investment

to meet a given need; (4) the operator skill re- quired for operation; and (5) data analysis required

for timekeeping.

These factors are interrelated such that various

combinations can determine accuracy levels,

number of users served, and ultimate costs to both

TFD sender as well as receiver. It appears to be an

important corollary that the cost to the user for a

particular time service should be proportional to the level of need. It is also true that as the accuracy

needs become more stringent the number of potential users decrease.

10.2.4. Basic Techniques Common to a Clock

Synchronization System

Identification, synchronization, and delay cali- bration are three operations that are common to

all time dissemination schemes. In a standard time

emission an event such as the transition from the zero to the one state in a binary system, or the

beginning of a tone or a particular zero-crossing of

a continuous tone in an analog system, is chosen to represent the time mark. This event must be identified unambiguously at the time reference trans- mitting station, and synchronized with the reference

clock. The equipment delay is calibrated and the

transmitted time adjusted accordingly. In order to recover the time from the received signal, a user must unambiguously identify the time mark in the

signal format and synchronize his clock to it after accounting for the delay both in propagation and

the receiving equipment. Thus identification,

synchronization, and calibration operations must

be performed at both the master and the user time

stations. In the case of a standard time broadcast

service these operations are being performed

simultaneously by many users, while they are being

performed only once at the reference station.

238
The dissemination "system" should be construed

to include the equipment of all users as well as that of the reference station. The costs of the standard

time broadcast service "system" are allocated such

that the investment in user equipment at a single user station is vastly less than the investment in equipment at the reference station. Thus a standard time broadcast service is designed along the

lines of a public utility, where a great many cus- tomers require the availability of similar services

at all times. It is convenient, but not necessary in principle, for time or frequency information to be

transferred from the reference station to the user

station by a radio emission originating at the

reference station. Let us now consider the concepts of a time-transfer system as shown in figure 10.3. Assume that the reference station A and the user station B both

have receivers tuned to monitor some electromagnetic event that is going to occur at a remote location TS. The coordinates of locations A, B, and TS

are not known but are fixed. Both points A and B

have monitoring devices that will record the time

displayed by their clocks at the reception of the

electromagnetic disturbance associated with the

event. Finally, assume that clocks A and B are on

time with each other. At t A seconds after the event

occurs, the time TA displayed by clock A will be

recorded, where tA is the propagation delay from

TS to point A. (This clock reading will depend on

both the propagation delay and when the event

occurred.) The time TB , displayed in clock B, will be recorded tB seconds after the event occurs. Since the time at which the event occurred is not known, and since the distances of points A and B

from the source TS are not known, t A and t B are

not predictable. But if the time readings TA and

TB are compared (i.e., subtracted), one can learn

the difference in Tdl in the propagation delay time

along the two fixed paths. If a second event is monitored at some later time the new readings, T'A and TB , recorded at A and B will obviously be

different from the first set. But the time difference rdl will be the same as before (provided that the

clocks are still synchronized).

DIFFERENTIAL TIME BETWEEN

STATIONS A AND B,x. =t D -t. d. B A

Figure 10.3. Time transfer system.

A change in this difference, Tdl , could only be ex- plained by a loss of coordination or change in path

delay between clocks A and B. If clock B is ad- justed by an amount equal to the change in rdl then

it will once again be synchronized with clock A,

since we had assumed initially that clocks A and

B were synchronized. If no further loss of synchronization occurs, rdl computed for yet another event

will be identical to its initial value. Thus the time

difference between a reference clock and a user's clock can be determined by comparing each in turn

to an independent "tick" available to both, and then

differencing the comparisons. It resembles comparisons with a portable standard known to be operating

at the correct rate but not necessarily on time.

The time is "transferred" by a standard which is not, itself, on time; hence the term "time-transfer"

technique.

The example used was chosen to emphasize the

following aspects of the transfer standard technique:

(1) The coordinates of the reference station, the user station, and the source of the transfer

standard need not be known although they

must not change.

(2) The "event" monitored contains no time in- formation, and the time of its occurrence need not be known; it must only be unambiguously identifiable.

(3) If the "transfer standard" is a radio broadcast, as it normally is, the transmitting station

plays no active part in the process and need

not even be aware that it is being so used.

The requirement that the event must be un- ambiguously identifiable implies that the time

separation between "events" must be greater than

the uncertainty associated with the knowledge of

both the user's clock time, and the propagation

delays. If other means are employed to maintain

gross clock coordination and the "transfer" tech- nique is being used to keep track of short-term

drifts, then the time separation of events need only

be greater than the peak-to-peak drifts involved.

Synchronization pulses from commercial television

transmitters serve nicely for this purpose; Loran-C

is also commonly used.

If a user wishes to initiate this technique to transfer time to a location having a clock not known to be on time, he may begin making comparisons and

bring in a portable clock to "calibrate" the link at his convenience. He can then reconstruct the time

history of his clock prior to the portable clock visit as well as maintain an "on time" clock.

10.3. RADIO DISSEMINATION OF

TIME AND FREQUENCY

This chapter attempts to delineate distinguishing

features of both present and future means of dis239
seminating time and frequency information to a

distant user. Radio waves are essential to most

dissemination techniques. Although different radio

frequency bands show characteristic and relevant

traits, and a multitude of techniques have emerged

in these bands within the last 40 years, the words

of NBS scientists in 1932 still hold true; "radio waves of which the frequency is carefully controlled

and accurately known furnish a standard of fre- quency which is simultaneously available every- where that the waves can be received." [9]. In 1932

the transmitted accuracy of WWV, based on the

primary frequency standard was about 1 X 10~6

; this accuracy could readily be obtained from received

signals. Today the accuracy of the transmitted

signal has been improved some five or six orders of

magnitude, but the accuracy of the received signal

has lagged considerably behind.

10.3.1. Radio Propagation Factors

Radio has offered attractive means of transferring

standard time and frequency signals since the early

1900's [10]. As opposed to the physical transfer of

time via portable clocks, the transfer of information

by radio entails propagation of electromagnetic

radiation through some transmission medium from

a transmitter to a distant receiver. Let's consider

a typical standard frequency and time emission. In such broadcasts the signals are directly re- lated to some master clock and are transmitted

with little or no degradation in accuracy. In a vacuum, and noise free background, one should

be able to receive such signals at a given point

essentially as transmitted, except for a constant path delay with the wave propagating near the speed

of light (i.e., 299,773 km/s). The propagation media,

including the earth, atmosphere, and ionosphere,

as well as physical and electrical characteristics

of transmitters and receivers, influence the stability

and accuracy of received radio signals, dependent

upon the frequency of transmission and length of

signal path. Variation and anomalies in propagation

delays are affected in varying degrees by extraneous

radiations in the propagation media, solar disturb- ances, diurnal effects and weather conditions,

among others.

It is possible to classify radio dissemination

systems in a number of different ways; one could

divide those carrier frequencies low enough to be

reflected by the ionosphere (below 30 MHz) from

those sufficiently high to penetrate the ionosphere

(above 30 MHz). The former may be observed at great distances from the transmitter but suffer from

ionospheric propagation anomalies that limit accuracy; the latter are restricted to line-of-sight applications but show little or no signal deterioration

caused by propagation anomalies. The most accurate systems tend to be those which use the higher,

line-of-sight, frequencies, while broadcasts of the

lower carrier frequencies show the greatest number

of users.

A complete evaluation of propagation characteristics of the various bands used for time and

frequency dissemination is beyond the scope of

this chapter. (Frequency bands 4 through 10 are used and include VLF through SHF (3 kHz to 30

GHz)).2 A summary description of propagation

factors and general experience in these bands is given in the table of Annex A. Descriptions and

mathematical models of the propagation medium

useful for designing and understanding time/

frequency dissemination systems are given by

Wait, Budden, Crombie and others [11, 12], Johler

[13], Davies [14], and Thompson et al. [15], among

others. Various noise processes, such as additive

and multiplicative, and considerations in signal

design for TFD systems have been discussed by

Jespersen et al. [16]. Basic understanding of radio

propagation in the various frequency bands should

permit one to optimize a choice for either dissemination or reception of time/frequency information.

10.3.2. Radio Dissemination Techniques

Referring to figure 10.1, one sees the variety of

radio means for disseminating time and frequency

information. This section gives pertinent characteristics of the various techniques, including ad- vantages and limitations, and refers the reader to in-depth studies of various aspects. These tech- niques include dedicated systems as well as those

outside the allocated bands; included are VLF,

LF, and HF broadcasts; navigation systems; and

methods using television, satellites, and microwave

signals. Passing mention is made of techniques of

limited potential such as meteor burst and commercial radio broadcasts. In this cursory survey

lack of space prevents comprehensive analyses of

various systems; some of the newer and more promising techniques are described at some length.

a. Standard Frequency and Time Broadcasts

The World Administrative Radio Council (WARC)

has allocated certain frequencies in five bands for standard frequency and time signal emission as shown in table 10.1. For such dedicated standard

frequency transmissions the CCIR recommends

that carrier frequencies be maintained so that the

average daily fractional frequency deviations from

the internationally designated standard for measure- ment of time interval should not exceed ±1 X 10~ 10

. Annex B gives characteristics of standard fre- quency and time signals that are assigned to allo- cated bands, as reported by the CCIR. Annex C

gives characteristics of stabilized frequency and

time signals that are broadcast outside the allo- cated frequencies which can, however, provide

2 By international agreement, frequency band "N" is the frequency range between

0.3 X 10N Hz and 3.0 X 10N Hz. Thus, band 6 lies between 300 kHz and 3 MHz. See Annex 10. A,

240
Table 10.1. International standard time and frequency radio assignments

Band No. Designation Frequency Range

4 VLF (Very Low

Frequency).

20.0 kHz±50 Hz.

6 MF (Medium Fre- quency).

2.5 MHz±5 kHz.

7 HF (High Frequency) <

5.0 MHz±5 kHz.

10.0 MHz±5 kHz.

15.0 MHz ±10 kHz.

20.0 MHz ±10 kHz.

25.0 MHz ±10 kHz.

9 UHF (Ultra High

Frequency).

400.1 MHz ±25 kHz

(satellite).

10 SHF (Super High

Frequency).

4.202 GHz±2 MHz

(satellite- space to

earth). 6.427 GHz±2 MHz

(satellite-earth to

, space).

useful time and frequency information. Information

contained in Annexes B and C includes transmitter

coordinates, frequency, radiated power, and ac- curacy of transmitted signals. The map in figure 10.4 shows the location of many radio stations used

for TFD.

b. Very Low Frequency (VLF) Time and Frequency

Systems

TFD systems in the VLF band nominally operate

at frequencies from 10 to 30 kHz. The 10-13 kHz

band is used by the Omega Navigation system and

is described later in Section 10.3.2.e.(l). In this section we describe briefly the development and

uses of VLF apart from the Omega system. VLF and

the related LF transmissions are not new; they were used in the early 1900's for long range communications between colonial empires, by various

navies, and for general transoceanic services [17,

18]. Even at that time VLF transmissions showed

165' EAST 180' WEST 165° LONGITUDE135' 120' 105' 90° 45* 30' 15-WEST 0° EAST 15' 30* 45'

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0

- LF STATIONS (

- HF STATIONS (

- VHF STATIONS )

DESIGNATE STATIONS

IN T/F ALLOCATED

BANDS d

Ld 10 Q |

t I

h- S < I

105' 120' 135" 150' 165" EAST 180° WEST 165' 150' 135° 120' 105' 90' 75' 45' 30' 15" WEST O'EAST 15' 30' 45*

Figure 10.4. Worldwide location of broadcasting stations useful for TFD. (annexes 10.B and 10.C give additional information to keyed broadcast stations.) 241
good reliability with relatively low signal attenuation over large distances [19]. Many of these trans- missions were replaced later by the lower-cost

high frequency (HF) broadcasts which employed

much smaller antennas, at increased efficiency over VLF antennas. Many different VLF antenna configurations have been built, e.g., long cables have

been strung several km across volcano craters and

valleys or from towers several hundred meters in height [18]. The present NAA antenna at Cutler,

Maine (radiated power 1 Megawatt) is a top hat

system supported by 26 masts ~ 300 m in height,

covering an area ~ 2.2 km2

; its radial ground

system consists of ~ 3.3 X 106 m of buried copper

wire.

During World War II and shortly thereafter,

attention was directed again to the low frequency

band for navigation and communication. From such

interest evolved the "Radux" navigation system

[20, 21], where the low frequency carriers showed

the excellent stability required for navigation

systems. From the mid_ 1950's onward, there have

been great strides in worldwide frequency and time

comparisons via low frequency broadcasts. Methods

used by Pierce, Mitchell, and Essen [22]; Pierce

[23]; and Crombie et al. [24], among others showed

improvement in frequency comparisons of two to three orders of magnitude better than those of HF

techniques. It is particularly noteworthy that the more stable atomic frequency standards were re- placing the crystal oscillator control of many of

the VLF transmissions about this same time; thus

in 1960, Pierce, Winkler and Corke showed that transatlantic phase comparisons of a 16-kHz carrier

frequency could be made to about 2 /is in a 24h

period using atomic cesium standards [25]. Attention thus was directed towards VLF standard

frequency broadcasts [23, 26, 27], and the VLF

method has proven advantageous for comparing

atomic frequency standards at global distances

[28-32]. Today most VLF transmissions used for TFD are controlled by atomic frequency standards

referenced to a coordinated international time base

(UTC — see chap. 1). This has resulted in a reason- ably economic and reliable means of disseminating

frequency to several parts in 10 11 or better in a 24h

period.

The characteristics of various VLF broadcasts

(outside the Omega band) useful for TFD are given

in Annex 10.C. The propagation of VLF signals is described in Annex 10.A. Of particular significance are the diurnal phase shifts which are somewhat

frequency dependent but quite distance related. Typically, these predictable shifts range from ~ 20

to 80 fxs for distances of 2000 to 10,000 km at frequences of ~ 14 to 20 kHz [33, 34]. Within the last decade a variety of VLF tech- niques have been developed for time and frequency

comparison. These methods have confirmed the

excellent stability shown in the 1950's and even

today there is evidence that the limiting precision

of VLF measurements has not been reached [35,

36]. We will briefly review several VLF time and

frequency techniques.

(1) VLF Single Frequency Comparison. A com- mon and economical VLF method utilizes single

frequency phase comparison, such as shown in figure 10.5 [37]. In such an electromechanical

system the servo-driven phase shifter continuously

phase locks a synthesized signal from the local standard to the received VLF signal. A linear

potentiometer output, connected to a constant

direct voltage, generates a voltage signal and

permits an analog recording of the phase shifter position. In other words, the recording shows the

amount of phase shift the local synthesized signal

experiences to agree with the phase of the received

signal. A very narrow bandwidth (~ 0.01 to 0.001

Hz) is required for extraction of the coherent VLF

signal level from characteristic higher noise levels > 20 to 40 dB. (Electronic-servo VLF comparators

with internal calibrator-signal generators are now

available; these units are more stable than the elec- tromechanical type and provide improved control

for clock synchronization.)

Measurements are made on the phase records

generally at 24h intervals and at times when the

propagation path is sunlit and phase fluctuations are minimal. The duration of such a quiet period

varies with the seasons, reception path, and the

path direction. (The standard deviation of phase

fluctuations in NBA signals received and compared at NBS, Boulder— 4300 km — were several

tenths of a txs for a series of 20 min measurements

taken over a 7h period [38].) The single VLF

comparison technique does not permit initial clock

Figure 10.5. Typical VLF single-frequency comparator.

242
synchronization; it does, however, give day to day

comparisons of a local clock to microseconds [2, 39-41]. Corrections to many VLF broadcasts can be

made after the fact from periodic publications of

various laboratories such as NBS [42], the USNO

[43], and the Research Institute of the Swedish

National Defense [44].

(2) Multiple-Frequency VLF Techniques. Another

VLF approach is the so-called multiple-frequency

technique which uses two or more coherently

related, closely spaced signals which are trans- mitted sequentially [45, 46]. The method is based

on similar principles as the Radux-Omega Navigation system [21]. It is the hope that this method

might permit initial synchronization of clocks at remote sites and/or resynchronization of interrupted

clocks. There is a distinction between such syn- chronization; i.e., initial synchronization, via a radio signal, requires accurate knowledge of the

propagation delay. Initial synchronization along

with direct measure of the propagation delay,

however, can be performed by transportation of a portable clock to the site. On the other hand,

clocks can be resynchronized through the multiple

frequency technique by adjusting for the known

propagation delay. There is evidence that theoretical

predictions of propagation delay compare favor- ably with experimental results [47]. The multiple carrier VLF method extracts timing information in the difference frequencies,

allowing individual cycle identification of one of the

carrier frequencies. The method has been used

with WWVL and is applicable to the Omega fre- quencies [48, 49]. The technique demands extreme

stability in the signals as transmitted, the trans- mission medium, and the receiving/comparison

equipment. In a typical synchronization, coarse time would be set initially via HF radio trans- missions to several ms to resolve the difference

frequency ambiguity (<V2 of the difference fre- quency period; i.e. ~ 2.5 ms for the dual Omega

frequencies of 12.5 and 12.7 kHz). In using Omega

frequencies of 12.5 and 12.7 kHz, it is necessary

that the residual phase error (differential propagation delay corresponding to one cycle offset = ±1.26 fxs) be less than 0.6 /as for resolving cycle

ambiguity at 12.5 kHz [49]. That is, each cycle of

12.5 kHz (individual cycle period of 80 fxs) shows

a differential phase offset of 1.26 fjis at an appropriate comparison point of the 12.7 kHz signal.

The number of error cycles within the difference

frequency interval depends upon the so called

magnification factor, f2 l'ft~j i, or 63.5 in the example of the 12.5 and 12.7-kHz signals [f\ and /2 respectively). Thus, the product of the magnification factor and the ft period gives the period of the difference

frequency. A lower magnification factor places

lesser demands on the measurement sensitivity.

The multiple carrier VLF method includes a

local calibration signal for simulating the frequency

of the received signal to relate the local time scale

to that of the transmitter. Agreement between the

received and calibrated VLF phases is made

systematically and the local clock phase-shifter

adjusted until all simulated signal phases are

identical to the actual received signal phases for a single setting of the phase shifter. This phase

relationship remains essentially unchanged (except

for clock interruption and phase loss), and the

VLF receiver can be turned off and on without

affecting the calibration. A basic paradox in using 2 VLF signals for clock

synchronization is that an increase in the spacing

of the frequencies improves the cycle resolution

problem but places more stringent requirements on

the coarse timing. Reception of three or more VLF

signals, such as provided by Omega, gives a combination of both narrow and wide separation of fre- quency pairs, thus insuring cycle identification of

the prime carrier; the stability, after synchronization, should be equivalent to that of the single fre- quency system. Several laboratories have used the

multifrequency VLF techniques in combination with

other systems for resynchronization timing [40, 48].

(3) VLF Time Transfer Techniques. A time trans- fer VLF technique has been demonstrated by

Becker [31]. This method also uses a simulated carrier calibration which obtains a daily time difference

between the local time scale and the received signal.

The USNO simultaneously each day makes identical

measurements. The daily differences of these A^'s gives a time difference of the time scales of the PTB

and USNO via given VLF transmissions. These

measurements, confirmed by Loran-C data, aver- aged over an 18 month period (NSS to PTB path ~ 6000 km) show an uncertainty of ~1X10~ 13

. Becker also asserts that filtering and averaging tech- niques used at the PTB for analysis of VLF data

could be employed profitably by the BIH in formation of the International Time Scale (TAI).

(4) VLF Pulse Methods. Several VLF transmitters periodically broadcast time signals (see ann.

10.C). Time pulses transmitted at VLF show a slow

rise time (15 ms at NBA— 18 kHz in 1960) because of

the high Q of the antennas and a resultant large time

delay. Stone determined time from the NBA trans- mitted pulses at Summit, Canal Zone to a receiver at NRL in Washington, DC to a precision of —500 ^ts

[50]. While such time determinations might be

resolved to higher precision, limiting factors include

the difficulty in fixing the start of the pulse and the

uncertainty of the transmitter, propagation, and

receiver delays.

(5) Statistical Smoothing of VLF Data. Allan and

Barnes [51] and Guetrot et al. [52] have shown means for statistically reducing phase fluctuations on long term data. Guetrot applied optimum smoothing techniques to differential VLF data of NSS (21.4

kHz) and WWVL (20.0 kHz) over reciprocal paths in a study with the USNO. The results were compared

243
with portable clock measurements and showed day

to day deviations of 70 ns over this 2400 km path.

(6) Time Comparison via Frequency Shift Keying

(FSK) of VLF Carriers. Frequency Shift Keying

(FSK) of VLF stabilized communication transmissions has been proposed for TFD [53]. This method

shifts two carrier frequencies either plus or minus

50 Hz with bit lengths of 20 ms and a transition

time between shifts of 2 ms. At such rates, phase

coincidence of the two carrier frequencies occurs at a point within each transition time. The 20 ms time

markers will occur nearly continuously and permit

coarse timing to such a level. The transition points are "on time" within ±1 /as of the station clocks. FSK transmissions are planned in 1973, and it is believed that the mid-point transition times can be

resolved at a receiving site to ± 10 /u,s since the VLF

signal periods range from ~ 30 to 60 /xs a particular

cycle can be identified and time extracted from the

cycle zero crossing to ~ l£is. It is proposed also to transmit time-code pulses once an hour, possibly

the last five minutes before the hour. Stone et al. [53] give results of two techniques for resolving FSK

signals at a receiving station to about ± 10/ns; e.g., through frequency discriminator techniques and/or

those of a synchronous detector as used in many

VLF tracking receivers. A signal averager is used

for optimum resolution. The method shows promise

for precise timing although receiving equipment is somewhat complex and costly.

(7) Summary Statement of VLF Use in TFD. The

stability and reliability of VLF standard frequency

transmissions during the last decade is attested to by their use for international comparisons of atomic

frequency standards as previously mentioned; for control of HF standard frequency emissions [54]; for navigation [55]; for propagation studies [56-58];

and for adjustment of rubidium frequency standards

which control the frequency of color TV broadcasts

[59]. The Sperry report on methods for synchronizing

remote clocks states in its conclusions: "Do not over- look the possibilities of obtaining both accuracy and

low cost in the combination of a clock stabilized by

reference to VLF signals and set once by a master

clock" [2]. Advantages of VLF systems for TFD

• VLF phase comparisons can be made to several

/as continuously at continental distances from

a transmitter up to ~ 10,000 km and with low

signal attenuation and stable propagation.

This is an improvement of several orders of

magnitude over HF techniques.

• Generally continuous transmission (24h per

day) and many stations located at widely

separated points.

• Single frequency comparisons can be made

with relatively low-cost receiving equipment.

• Most VLF transmitters today are stabilized

with atomic frequency standards, which, in part, accounts for VLF signal stability.

• Many VLF transmissions are monitored by

national laboratories which publish corrections

and permit reference to their time scales

(after the fact).

• Although VLF signals are subject to diurnal

phase variations, such changes are both

predictable and repeatable.

• Once a propagation path is calibrated, multiple

frequency VLF techniques can permit ^synchronization of clocks at a remote site.

Limitations of VLF Systems Used for TFD

• Atmospheric noise at VLF is quite high and

coherent signals often must be detected well

below the noise. Noise from lightning strokes

is a maximum at these frequencies, and the low

attenuation rates of atmospheric noise at VLF

allows worldwide propagation of such static.

• VLF propagation is subject to many phase

anomalies such as diurnal variations, cycle

slips, strong attenuation over ice fields, solar disturbances (Sudden Ionospheric Disturbances-SID's), long versus short path inter- ference, nuclear blast effects, seasonal changes,

and nighttime irregularities. In many cases, however, these are easily recognizable and can be accounted for. Some reduction in phase

anomalies can be realized through composite wave analysis suggested by Pierce [60].

• For best results, phase measurements should

be made when the transmitter-receiver path is sunlit. Some paths at high latitude can show

limited sunlit conditions, however.

• Maximum success in VLF measurements

requires atomic frequency standards at both

the transmitter and receiver; good temperature control of equipment; back up battery

supply for AC power; periodic phase and amplitude calibration for detection of phase drifts or jumps in the local equipment; and periodic

checks of antenna connections, circuit board

and chassis contacts [58].

• VLF transmissions received at distances of

1000 km or less from a transmitter are difficult to interpret because of the interference

between ground and sky waves. There are also sensitive path distances at which modal inter- ference critically destruct a received VLF

signal, particularly during sunset and sunrise.

• VLF techniques alone are not now capable

for initial clock setting at a remote site. Generally, propagation delay is determined and

initial clock setting is performed by a portable

clock visit.

• VLF signals experience dispersion (different

phase velocities) and this can result in prohibitive variation in received signals for cycle

identification in the multiple frequency

technique.

• VLF techniques, although simple in concept

and design, require experienced personnel to

244
properly interpret and analyze the signals as transmitted, propagated and received at a remote site.

c. Low Frequency (LF) Time and

Frequency Dissemination

LF signals are transmitted in the band between

30 and 300 kHz. Today, at least 10 LF broadcasts

(shown in annexes 10.B. and C.) are frequency

stabilized in the accuracy range of ±0.1 to 10 parts

in 10 10 and are useful for TFD. As the development of LF transmissions paralleled the VLF

broadcasts, no attempt will be made to trace its history. Also, the Loran-C navigation system

(100 kHz) is described separately in Section

10.3.2.e.(2). Although the LF band also has long been known

for its stability and reliable propagation to long dis- tances, it was not until the late 1940's that Pierce

showed the value of LF transmissions for navigation [201. In 1950 the British commenced standard

frequency broadcasts at 60-kHz (MSF) at daily

short intervals of time [61]. In 1956 NBS also com- menced low power 60-kHz broadcasts (KK2SEI later changed to WWVB) [62]. From limited broadcasts of these two stations, Pierce was able to predict daily measurement accuracies of 1 or 2

parts in 10 11 for LF comparisons [63]. He was

limited to a large extent by the variable crystal

oscillator control of most transmissions at that time. As Pierce's predictions proved true, especially with the advent of atomic frequency control

of transmitters, many frequency stabilized LF

transmitters were constructed and are used for time/frequency dissemination today.

At this point we will discuss certain low frequency

and time measurements in terms of the National

Bureau of Standards WWVB broadcasts at 60

kHz. The NBS low-power LF station was moved

to Ft. Collins, CO in mid-1963; today its radiated

power is ~ 13 kw [64], and it generally can be

received as a stable frequency source anywhere

in the continental USA. Three types of LF time

and frequency comparisons are considered:

(1) Single-Frequency Phase Tracking at LF. This

method is quite similar to the VLF procedure [65].

LF signals usually propagate with greater attenuation than VLF, although perhaps at improved stability at distances up to —2500 km. Ground wave LF

signals provide a very stable reference at distances

up to about 500 km. A typical WWVB phase record

for the Ft. Collins, CO to Greenbelt, MD path

(—2400 km) is shown in figure 10.6. This 50 /xs full scale record shows (a) the excellent phase stability

during the sunlit portion of the path; (b) the repeatable diurnal phase shift at both sunset and sunrise

when the effective ionosphere rises and lowers;

(c) a typical cycle slip or fadeout at sunrise (Greenbelt); and (d) the somewhat irregular phase pattern

when the path is in darkness. It is of particular note

that WWVB transmitted with a radiated power of

about 2 W at this time with frequency control via a rubidium atomic frequency standard. As previously

pointed out, WWVB was used together with WWVL

to remotely control the frequency of WWV in Maryland prior to its move to Ft. Collins, CO, to several

parts in 1011 over a 21-month period [54]. The construction of a simple and economical receiver (cost — $100) has been described for local WWVB comparisons [66].

(2) WWVB Time Code. Although the WWVB

antenna shows a relatively high Q, its transmission

characteristics are such as to support time code

modulation. Since 1965 WWVB has broadcast time

information continuously via a 10-dB level-shift carrier code. This binary coded decimal (BCD) code is synchronized with the 60-kHz carrier which, in turn,

is referenced to the UTC(NBS) time scale [64]. Fig- ure 10.7 shows the format of the WWVB pulse-width

code which is repetitive and updated at one minute

intervals. Basically, the code consists of one second

markers, generated by reduction of the carrier

power by 10! dB at the start of each corresponding

second; power is restored 200 ms later for an uncoded marker or binary 0; 500 ms later for a binary 1, and 800 ms later for either a 10-s position

marker or minute reference marker. Thus, the lead- ing edge of each negative going pulse is on time;

each minute frame contains coded information within

12 groups which includes complete UTC(NBS) timeof-year data in minutes, hours and day-of-year, the

estimated difference of UT1 minus UTC (called

DUT1), and the positive or negative relationship of

the UT1 scale with respect to the UTC scale. The

SUNSET-GREENBELT. MD

SUNSET-BOULDER. COLO

SUNRISE GREENBELT, MD

SUNRISE-BOULDER. COLO TIME. UT

SUNSET-BOULDER. COLO

SUNSETGREENBELT. MD

SUNRISE BOULDER. COLO

SUNRISE GREENBELT, MD n

8 8 8 l!

50 /j sec

WWVB IN TERMS OF WWV j CONTROLLING OSCILLATOR" 'JUNE 3.4 & 5. 1963 711

H4

SLOPE +1 ^sec/24 HRS (1800 1800 UT| WWVB IS 1*10"

" pis. ABOVE WWV.

FIGURE 10.6. Typical LF phase record (WWVB transmission from NBS, Boulder, CO and received at Greenbelt, MD).

245
TIME FRAME 1 MINUTE

INDEX COUNT 1 SECOND)

10 20 POINTJU, 40 50

(0)

I 60

I 1 I I I I 1 I I I I I I I I I I I I I I I I I I I I I I I I I ! I I I I I I I I I I I I I I I -ON TIME

(6PPM POSITION I .D

.

MARKERS , P0 TO P 5 , FOLLOWED BY 0.2 s INTERVALS.

)

P

l

WEIGHTED CODE DIGIT ! (CARRIER RESTORED IN 0.5s BINARY ONE . ) v

i

UNWEIGHTED CODE DIGIT (CARRIER RESTORED IN -0.2S-BINARY ZERO. )

MINUTE FRAME REFERNCE

MARKER

Odd tD J-^(M — . OO CD*"-r "'o^ — O O OOOO (D J- CM — QCQQ CO o OOOO Q => Q

RELATIONSHIP —UT, SET CORRECTION

0.8s MARKER PULSE

0.5s BINARY CODE "ONE"

I— 0.2s BINARY CODE "ZERO"

EXAMPLE OF TIME

(SUMMING BINARY

AT POINT A CODE ONES) DAYS 258 HOURS 18 MINUTES 42 SECONDS 35-0.7

258 da 18

h 42min 34.3 S

Figure 10.7. Format of WWVB one-minute time code.

individual pulses yields seconds information; the

minute reference marker begins at zero seconds.

Complete details of the WWVB time code are given

in reference [64]. Equipment is available for automatically decoding

the WWVB time code, and it has been stated that the time information is available to 50 /is over a wide

geographical area with the provision that propagation delay corrections are made from station WWVB

[68]. The WWVB standard frequency and time code

broadcasts are used to maintain synchronization

of interconnected power grids in the continental U.S.

[7]. Improved system control, using these low fre- quency broadcasts, has been proposed to attain fre- quency and time agreements between North

American power areas of ±0.001 Hz at 60 Hz and

better than 50 ms respectively [69]. The code is used

also for time reference of seismic recordings [70,

71]; and the WWVB 60-kHz signal is used as a standard for the telephone company [72J.

(3) LF Pulse Decay Time Measurements. Andrews,

Chaslain, and DePrins reported on time pulses

emitted by HBG (75 kHz) and WWVB (60 kHz) at distances ~ 80 to 1000 km and obtained time to an

accuracy of ±40 /is or better from measurements of

the arrival time of an LF pulse [67]. Basically, they

selected a point on the decay curve of the pulse

(essentially transmitted as a square wave) and,

through photographic integration, determined that

the minimum overall error occurs when the amplitude point selected for measurement on the decay

envelope is between 75 and 90 percent. The timing

error is directly related to the amplitude point

chosen and depends also on (a) changes in pulse

shape caused by variations in the transmitting antenna; (b) variations in propagation conditions

and; (c) amplitude measurement errors of the

received pulse envelope. During the measurements

it is important that the phase between the received

signal and the local reference remain unchanged

during the integration time. In Brussels, Belgium the

method has been used for time synchronization with ~ 40 /is accuracy and for frequency measurements

with an error less than 7 parts in 10 12 over periods of

a year [67]. The advantages and limitations of LF trans- missions for TFD are quite similar to those shown

for VLF. Some additional characteristics might

include the following:

Advantages of LF Signals for TFD

• Stable results are obtained within groundwave

distance of an LF transmitter because ground- wave and skywave signal interference is not present at such ranges.

• Time pulse modulation, which is possible at LF, permits time synchronization to ~ 100 /is or better, provided the propagation delay is known.

246
• The WWVB time code has proven of value in timing of seismic events, and coordinating

North American power grids.

• Single LF phase comparisons can be made

at accuracies of parts in 10 11 per day with

reasonably simple and economical receiving

equipment.

Limitations of LF systems for TFD

• Automated decoding of LF time codes requires

relatively expensive equipment.

• Because of attenuation factors LF signals are generally less useful than VLF at large dis- tances from a transmitter ( > 2500 km).

• Ionospheric anomalies degrade reception of

WWVB in some geographic areas of the United

States.

• LF propagation is subject to ionospheric

variations; phase changes occur from diurnal

effects, solar disturbances, and modal inter- ference. (This latter factor can cause "cycle

slippage" at critical propagation distances.)

• As for VLF comparisons, extreme care is required of LF receiving equipment for optimum results. Proper interpretation of data

requires experienced personnel.

• It is not now possible to initially set remote

clocks to high accuracy via LF radio techniques

alone.

d. High Frequency (HF) Time and

Frequency Dissemination

Today there are some 20 countries broadcasting

stabilized HF standard time and frequency signals

[73, 74]. Characteristics of many of the international stations, broadcasting in the frequency band

between 3 and 30 MHz, are listed in Annex 10.B

and 10.C. The ease of usage and worldwide reception capability of HF signals for TFD attests to their acceptance and value. In the U.S. the Navy

first broadcast spot-time signals about 1904 [10]; in 1923 the NBS station WWV, commenced standard frequency broadcasts from the Washington,

D.C. area. These transmissions were improved

and later included standard time signals; in 1948

coverage of such T&F information was extended to the Pacific area with the WWVH emissions from

Hawaii. The accuracy of the WWV signals as transmitted and received initially was about a part in 105

. Improvements in equipment and frequency

control raised this to parts in 107 during the 1950's. Further progress, principally through use of atomic

frequency standards as reference oscillators,

improved the transmitted accuracy several orders

of magnitude to today's value of a few parts in 1012

[64]. Unfortunately, ionospheric propagation of

HF signals via skywaves generally restricts the

accuracy of received standard frequencies to a few parts in 107 and received time signals to ~ 1

ms. (Long term refinements can improve these

accuracies as described later). Accuracy of signals received beyond groundwave

range of an HF transmitter (~ 160 km) has not improved since World War II. This is shown

graphically in figure 10.8 where the frequency

accuracy of WWV transmissions is plotted for a 50-year period since 1923. Most of the restrictive ionospheric effects at HF are described in Annex

10.A. These uncontrollable ionospheric factors

dictate the accuracy levels of HF time and fre- quency dissemination via skywaves and would

preclude frequency accuracy improvements in the

NBS high frequency transmitting equipment. At

the receiving end, systems using diversity tech- niques for automatically and continuously locking on the optimum signal of several WWV or WWVH

frequencies may provide some improvement in accuracy of received signals [75]. Also other

diversity techniques such as separation of antennas

in space, frequency separation and antenna polarization might be beneficial [76].

T

YEAR

Figure 10.8. Accuracy of WWV transmissions from 1923 to 1973. Shaded area shows WWV as received via sky-wave path.

Many excellent HF broadcasts exist for TFD such

as CHU, JJY, and MSF; various HF emission for- mats for TFD are illustrated in reference [73]. At this point we will describe briefly the WWV/WWVH for- mats to show the composition of a typical HF standard time and frequency transmission.

Station WWV now broadcasts from Ft. Collins,

CO at the international allocated frequencies of 2.5,

5.0, 10.0, 15.0, 20.0, and 25.0 MHz [64, 77, 78]; sta- tion WWVH transmits from Kauai, Hawaii on the same frequencies with the exclusion of 25.0 MHz.

247
The WWV transmitter building is shown in fig- ure 10.9. The hourly broadcast formats of both

WWV and WWVH are shown in figure 10.10; the

broadcast signals include standard time and fre- quencies and various voice announcements. Complete details of these broadcasts are given in reference [64]. Both HF emissions are directly controlled by Cs beam frequency standards with periodic reference to the NBS atomic frequency and

time standards [79]; corrections are published

monthly [42]. Besides the standard carrier frequencies, an important part of the WWV and WWVH emissions

includes audio tones and time ticks as shown in figure 10.10. The 1 -second UTC markers are trans- mitted continuously by WWV and WWVH, except

for omission of the 29th and 59th marker each minute. With the exception of the beginning tone at each

minute (800 ms) all 1-second markers are of 5-ms

duration; these WWV and WWVH pulses consist of 5 cycles of 1000 Hz and 6 cycles of 1200 Hz respectively as shown in figure 10.11; this figure shows also the spectra of the WWV and WWVH pulses. Each

pulse is preceded by a 10-ms period of silence and

followed by 25 ms of silence; time voice announce- ments are given also at 1-minute intervals. All time

announcements are Greenwich Mean Time and the

actual reference time scale is the Universal Coordinated Time Scale UTC(NBS) (see chap. 1 for time zone changes from Greenwich).

WWV and WWVH also continuously emit a 100-Hz time code. This is an IRIG-H type of code

with a 1-minute time frame; it uses the BCD system,

includes 60 markers per second, and the leading

edge of each pulse coincides with a positive zero-axis

of the 100-Hz modulating frequency. The code contains similar information to the WWVB time code

and 10-ms resolution should be obtainable. For

details of the WWV/VH time code see reference

[64].There are various means of using the HF standard

frequency and time emissions; they include the

248
WWV BROADCAST FORMAT

VIA TELEPHONE 13031 499-7111

(NOT A TOLL-FREE NUMBER)

I HOUR MARK -NBS RtSfflVEO

STATION 10 ' 3*0 ATM MESSAGES ^

STORM INFORMATION

• BEGINNING OF EACH HOUR IS IDENTIFIED BY

O B SECOND LONG. 1500 Hi TONE • BEGINNING OF EACH MINUTE IS IDENTIFIED BY

0 9 SECOND LONG 1000 Hj TONE • THE 29th & S9th SECOND PULSE OF EACH MINUTE IS OMITTED

(a)

WWVH BROADCAST FORMAT VIA TELEPHONE (SOB) 336-4363 (NOT A TOLL-FREE NUMFJERI

STORM INFORMATION

(b)

THE 29ih & 59th SECONO PULSE OF EACH MINUTE IS OMIT T £0

Figure 10. 10. Hourly broadcast format of WWV (a) and WWVH (b).

1.0

I

0.5 5

-0.3

v|

\

\ \mVH / j

i

l

1

i 1

i

i

t

i kf

/ \

i\

V

i y

\ r

» \i /

500 1000 FREOUENCY, CPS1 300 2000

WWV AND WWVH SECONDS PULSES

THE SPECTRA ARE COMPOSED OF DISCRETE FREQUENCY COMPONENTS

AT INTERVALS OF 1.0 CPS. THE COMPONENTS AT THE SPECTRAL MAXIMA HAVE AMPLITUDES OF 0.005 VOLT FOR A PULSE AMPLITUDE OF 1.0 VOLT. THE WWV PULSE CONSISTS OF FIVE CYCLES OF

1000 CPS. THE WWVH PULSE CONSISTS OF SIX CYCLES OF 1200 CPS.

TONE — 0.010

SEC.

0.005 0.025

SEC. SEC. TONE

WWV

WWVH

Figure 10.11. Characteristics of time-pulse emission from NBS radio stations WWV and WWVH.

249
zero-beat method of comparing frequencies (employing either multiplication or division to obtain a suit- able frequency), time comparisons for either time or frequency information, and decoders for the IRIG-H

time code [1, 4, 80, 81]. Although the previously

stated accuracies for HF comparisons generally

hold, Watt et al., have shown that improvements in precision can be obtained through averaging [27]. Their results are plotted in figure 10.12; frequency

measurements are less precise than those by time

pulse. They used a running 10-day average tech- nique to obtain precisions of several parts in 1010 for a 30-day period. Angelotti and Leschiutta studied

the MSF 10-MHz signals (path length 1040 km from

Rugby, England to Torino, Italy) and for 3500 independent daily measurements over a 10-year period

obtained a yearly mean average time difference of

200 fxs between received signals and local clocks. Winkler also reports that WWV can be received at the USNO (15 MHz at the same time each day) to about 200 us [83].

100 IK 10K 100K 1M 10M OBSERVING PERIOD (T) , SEC

I i l I 1 I I 0.01 0.1 1 10 30 100 DAYS

LINE A-— 100s SAMPLES; FREQUENCY COMPARISONS AT 1 SAMPLE/DAY (NOON)

LINE B-~24-HR AVERAGE EACH DAY OF TIME PULSES COMPARED

AT 10 A.M. LOCAL TIME

Figure 10.12. WWV/WWVH frequency comparison precision

(10 MHz).

Optimum HF radio measurements can be

obtained by following the below named procedures:

(a) Make measurements at the same time each

day when the radio path is in full daylight or darkness;

(b) record no measurements when an ionospheric

disturbance is in progress;

(c) use the highest reception frequency which

gives consistent results;

(d) avoid radio paths that pass over or near

either auroral zone;

(e) use a good quality communications or special

timing receiver with directional antenna

oriented to provide shortest propagation path.

As with all radio systems, the determination of

propagation delay limits the usefulness of HF

signals for timing. An approximation for propagation delay for one hop skywaves, reflected from the

E and F layers of the ionosphere, can be deter- mined from a graph developed by Morgan and

shown in figure 10.13 [84]. (E-layer exists during

daytime only.) This graph shows an error of about

400 /as for a variation of 200 km in ionospheric

height at a 3000 km single hop distance. HF methods

are critical, especially at distances where transitions

between dominant modes may occur; also in the

determination of the existence of one-hop, two- hop, etc., conditions. With consideration of error sources, one can probably estimate HF propagation

delay to about 1 ms. Barghausen et al., have

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

GREAT CIRCLE DISTANCE (PER HOP ) km(lxl0 3

)

Figure 10.13. HF propagation delay versus distance for several ionospheric heights of reflection. 250
developed methods and techniques for predicting

long-term performance of HF telecommunication

systems [85]. Their computer programs can yield

much useful information on given frequencies and

propagation paths as described in Annex 10.A.

Advantages of High Frequency TFD

• Receiving equipment and antennas are simple

and economical for time accuracies of ~ 1 ms.

• The widespread location of HF time and

frequency transmitters, broadcasting UTC

signals, enables reception of at least one of

these transmissions almost anywhere in the

world; they also serve an unlimited number of users simultaneously.

• HF transmitters and antennas are smaller,

simpler, and of less cost than the low fre- quency broadcasting stations.

• Long-term averaging of HF data can remove some propagation anomalies, approaching

precisions of parts in 10 10 over 30-day periods.

• Groundwave signals (~ 160 km from trans- mitter) can be received with about the same

accuracy as transmitted.

• Sufficient bandwidth is available at these

frequencies to enable time pulse modulation.

Limitations of High Frequency TFD

• Received HF skywave signals suffer erratic excursions in time delay from ionospheric

irregularities; this both degrades time and

frequency comparisons and causes unreliability of reception.

• Propagation delays of HF skywaves are diffi- cult to determine to better than 1 ms because

of ionospheric variability from sunspot activity,

time of day, seasons, distance, Doppler shifts,

etc.

• The transmission modes (number of hops

propagated) are difficult to predict for HF

radio paths exceeding ~ 3500 km.

• Atomic frequency control of HF broadcasts

give instantaneous frequency stabilities in the

transmitted signal some four orders of magnitude greater than that realized at a receiver via

skywave propagation; it appears that no equipment improvement can overcome this limitation of nature.

e. Radio Navigation Systems for TFD

Radio navigation systems have much in common

with standard time and frequency radio emissions

[86]. Both depend upon the constancy of the speed

of light for their concept of operation and both

employ some type of periodic format. Because of some nearly identical requirements in timing, communication, and navigation, various radio transmissions of precisely controlled frequency can serve

multiple roles.

As one example of how standard time transmissions can be used for navigation consider the idea of range-range or rho-rho navigation. Refer to fig- ure 10.14; assume that a time signal transmitted

from Ti is received at a ship located at A. If the coor- dinates of the transmitter are known, and the ship

has an on-time clock, one could readily determine

the propagation delay, ta, of the received signal. This

value would enable one to compute the distance,

di (since td'C = di, where c= velocity of light). It is thus determined that the ship is somewhere on a

circle of radius dx

. If one receives another time sig- nal from T2 , whose coordinates are also known, such

information would also place the ship on another

circle of radius d2 , either at point A or B, the inter- section points of the two circles. Such a position

ambiguity could be resolved by other navigation means or by measuring a time signal from a third

transmitter of known coordinates.

FIGURE 10.14. Concept of range-range navigation.

A corollary to this example is the use of navigation systems for time and frequency dissemination;

it would be necessary that the signal format generator be frequency stabilized and that some recog- nizable character within the format be synchronized

with the time tick. The accuracy of ranging and timing capability of some systems are graphed in figure 10.15. Characteristics of some navigation systems useful

for TFD are given in Annex 10.D. The following subsections give details of the radio navigation systems;

Omega, Loran-C and Loran-A.

(1 ) Omega Navigation Syttem for TFD This system was originally conceived as a VLF

radio navigation system for ships, submerged submarines, and aircraft [87, 88]. It is expected that both

civilian and military craft of many nations eventually

251
TIME ACCURACY

Figure 10.15. Relationships between ranging (navigation) and timing (clock) accuracy.

will navigate by Omega. For the past decade the sys- tem has been operating experimentally, using only

four of the proposed eight transmitters broadcasting

at low power and showing potential in both navigation and timekeeping [89, 90]. On October 1, 1968

the U.S. Defense Department approved an eightstation, 10-kW, Omega system with an operational

target date in early 1970. (Now scheduled for the

mid-1970's.) System implementation will involve

capital expenditures of about $100 million. Four

cesium beam clocks will be installed at each of the

eight transmitting stations. The eight-station system

will provide reliable and near-global coverage. Fig- ure 10.16 gives the proposed worldwide location of

the eight-station network. (The Omega station at La

Moure, North Dakota (USA) is now operational at

full power.)

In the Omega system, each transmitter broadcasts

several time-shared carrier frequencies between 10

and 14 kHz. The primary navigation frequency is 10.2 kHz. The basic Omega pattern consists of an

eight-element 10-second format, within which the

fundamental signals are of about 1 -second duration

[59] (see fig. 10.17 as an example of one proposed

format). At a receiver, phase differences between

10.2-kHz signals from pairs of transmitters define

hyperbolic lines of position. Since the observed

phase differences of one frequency as received from

two transmitters show multiple ambiguities (repeat

at intervals of one-half wave length — about 29 km at 10.2 kHz) submultiple frequencies are employed in stages to permit observer location or so-called lane

identification (equivalent to cycle identification in the timekeeping sense). Stated accuracies are about

1 km in the daytime and double that at night, and

the VLF Omega frequencies can be received adequately at ranges up to about 13,000 km. After an

initial fix (and barring unforeseen instrumental or transmitter difficulties), a ship's receiver system will automatically keep track of lane position while the

ship is underway. Although the Omega signals are

sensitive to propagation vagaries such as diurnal

variations, solar activity, and polar cap attenuation

[91], compensating factors such as the provision of

multiple frequencies can overcome many of these

degrading influences.

Conversely, in terms of TFD, frequency comparisons via Omega signals can be made now to a few

parts in 1011 per day with commercially available

equipment; extraction of timing information is similar to VLF techniques previously described. Daily

phase values of currently-operating Omega trans- missions are published weekly in terms of'UTC

(USNO) [43]. In this way corrections can be made

after the fact. With the new Omega system, it is anticipated that one can continuously maintain

phase to 3 (as or less per day and/or make frequency

comparisons to several parts in 10 12 at global dis- tances [59]. Lead-edge envelope timing measure- ments can be made with a precision of about 100 /jls

Figure 10.16. Proposed worldwide location of eight-station navigation Omega (VLF) network [59]. 252
SEGMENT DURATION

(SECONDS)

OMEGA UNIQUE FREQUENCIES

STATION DESIGNATION F 2

A 1 2 . 1 OkHz 1 2 .35kHz

B 1 2 .00 1 2.25

C 1 1 .80 11.55

D 13.10 12.85

E 12.30 12.05

F 12.90 13.15

G 13 .00 12.75

H 1 2 .80 13 .05

g E f G w

0.9 1 .0 1 .1 1 . 2 1 .

1

0.9 1 .2 1 .0 *— 0.2s

10 SECONDS -

12.35kHz [~ToT^~| flTT] [717333] | Fl [ [77777] \^JfJ] | F

, / F

? | ["^7^71

[

12.25 [77?^ pioT] pf3X~| | 11.333

I r^T^ [fT/fT]I Fl /F

2 | f^TT] |

.55 [fTfTI rVFTI 1 13.6 j [TiTTsT] fTT^ | f^f, | [77777] |

12.85 [yr-| [T7f7| [-7777] I 10.2

I r~T3T6~] [TU33]I Fj LpT^TjJ

12.05 [TTfTI I Fl /F

2 | I Fl /F2 I I F^F, || 10.2 | |l3. 6| [ll.333| | F, ]|

'3-15

I FjI I F] /F2 | I Fl /F? I I Fl /F

2 || Fl /F

2 I I 10-2| | 13.6 | |H.333||

l2 - 75 |n-333|| Fl I I Fl /F

2 I I F l/F? I I Fl /F? I iF^F^l | 10.2 | | 13.6 ||

13.05

I 13.6 I |ll.333|I F,| | F1 / F? |

| F

1 / F? |

| F

\ / 7} \ F

, /F, | | 1 0 2 ||

Figure 10.17. Proposed Omega eight-element 10-second format [92].

[59]. Since the phases of all the transmitted frequencies are closely synchronized, there is opportunity

to employ the multiple VLF carrier technique such

as NBS used with the WWVL broadcasts [46]. This

method should resolve the basic timing ambiguities

inherent in VLF techniques and permit identifica- tion of a specific cycle, thus allowing resynchronization of remote clocks. An experimental Omega

precise timing receiver has been developed recently

and is now being evaluated [92]. The Omega format

also offers an excellent opportunity for disseminating time information such as day/hours/minutes in a

low-bit-rate time code using two unique frequencies

assigned to each station [93]. Such timing would not be required in the navigation function; it does, however, illustrate the significant potential of operational systems providing alternate functions to diverse user groups at negligible cost and

inconvenience.

Civilian direction of the operational Omega sys- tem will be under the Department of Transportation

(DOT) with control of non-U.S. stations provided by

the foreign country furnishing the transmitter site. Such an arrangement, subject to international agree- ment, should insure some degree of permanency

and reliability to both civilian and military users.

Advantages of the Omega system for TFD

• Transmitted frequencies of each station are based on concensus of four commercial cesium

beam standards, and assure both reliability

and stability of the Omega transmitted signals.

• The eight-station network will be synchronized

to about 1 fxs and can provide VLF signals

from 3 to 5 separate stations to global receiving

sites.

• Day to day phase maintenance of several /as appears feasible with corresponding frequency

measurements to several parts in 10 n. • System offers a strong potential for disseminating a time code at small additional costs.

• Nearly continuous operation of 24h/day.

• Some propagation factors are predictable,

and time is traceable to UTC(USNO) through

U.S. Naval Observatory monitoring and

reporting.

• Omega system has potential for providing

simultaneous timing and navigation information

without interference to either.

Limitations of Omega TFD include the following:

• Repeated measurements at various frequencies

or an external time source may be required to

initially set the date or periodically verify coarse time.

• Modal or long-path/short-path interference can

adversely affect reception, especially at critical ranges.

• Stable phase periods are generally restricted

to certain times of the day, and the VLF signals are subject to degradation in accuracy from

propagation factors, such as SID's, diurnal

effects, SPA's, etc. (see VLF limitations

sec. 10.3.2.b.)

• The Q of the transmitter antenna limits the

accuracy to which pulse transmission can be

accomplished at VLF.

(2 ) Loran-C Navigation System for TFD Loran-C (LOng RAnge Navigation) is a navigation system which evolved from World War II

253
technology to provide precise position for ships,

submarines, and aircraft. In the early 1960's NBS

explored the timing potential of this navigation

system and found encouraging results [94, 95]. Since then many studies have verified its use- fulness for timekeeping [96-98].

Loran-C uses an LF 100-kHz carrier frequency

(20 kHz bandwidth) and pulse transmission to form hyperbolic lines of position. The U.S. Coast

Guard now operates and manages the system with

close synchronization to the U.S. Naval Observatory time scale [UTC(USNO)]. The basic Loran-C

unit is a chain, consisting of a master station and

two or more slave stations located within ground- wave range of the master transmitter. There are now eight worldwide chains in operation, which,

together with slave stations, comprise a total of

about 34 stations. These stations are listed in table

10.2. Note that four chains, with details given in

Annex 10.D, are time synchronized and phase

controlled within ± 15 fis of UTC(USNO). The other

four chains employ Cs standards for frequency

control but are not maintained within the limits of ± 15 /as of UTC. Synchronization of stations

within a chain is held usually within ±0.2 /us. The

coverage of the multicontinental Loran-C system

is shown in figure 10.18. Loran-C uses a pulse-coded format with rates assigned to (a) separate and identify chains and its members, (b) eliminate stray interference that is coherent, and (c) provide the optimum SNR for given geographic chain coverage. Pulse transmissions enable users to separate multipath (skywave)

signals from the earlier arriving and more stable groundwave signals. Within a chain, a master station

transmits exactly spaced groups of nine pulses and

slave stations eight pulses, within the Group Repetition Period (GRP) assigned to the particular chains.

Table 10.2. Characteristics of Loran-C stations

Chain Rate Stations Emission Delay

(MS) Power(kW)

U.S. East Coast SS7 M r i- Mr 1,000 w Jupiter, FL 13,695.48 400 X Cape Race, NF z,ouu Y Nantucket Is., MA 52,541.27 400 z Dana, 1IN 68,560.68 400

Mediterranean SL1 M 300 X Lampedusa, Italy *19 7^7 19 400 Y Targabarun, Turkey 32,273.28 300 Z Estartit, Spain 50,999.68 300

Norwegian Sea SL3 M 400 W Sylt, Germany 30,065.69 400 X Bo, Norway 15,048.16 300 Y Sandur, Iceland 48,944.47 1,500 Z Jan Mayen, Norway 63.216.20 300

North Atlantic SL7 M Angissoq, Greenland 500 W Sandur, Iceland 15,068.10 1,500 X Ejde, Faroe Is 27,803.80 400 z Cape Race, NF 48,212.80 2,500

North Pacific SH7 M St. Paul, Pribiloffls 400 X Attu, AK 14,875.30 400 Y Port Clarence, AK 31,069.07 1,800 Z Sitkinak, AK 45,284.39 400

Central Pacific SI M 400 X Upolo Pt., HI 15,972.44 400 Y 34,253.02 400

Northwest Pacific SS3 M 3,000 W Marcus Island 15,283.94 3,000 X Hokkaido, Japan 36,684.70 400 Y Gesashi, Okinawa 59,463.34 400 Z Yap, Caroline Islands 80,746.78 3,000

Southeast Asia SH3 M 400 X Lampang, Thailand 13,182.87 400 Y Con Son, South Vietnam 29,522.12 400 Z Tan My, South Vietnam 43,807.30 400

*Approximate value, station operation scheduled to begin fall, 1972. 254
LOKAN-C COVKKACK DIACKAM

C !0 C f

INDIAN OCfAH

Prepared by

U.S. Naval Oceanographic Office—1972

65' 75" 90" 105* L20' 165" 150' 135" 120" 15" 30*

Figure 10.18. Coverage of Loran- C navigation system.

BEGINNING OF GROUP REPETITION INTERVAL (GR1

)

- 79,900ps(RATE SL-1

)

SECONDARY NIMH -—__ REPETITION INTERVAL

SEC0N0ARY mi

r

A A A A

—1^1000 ps SPACING

FOR ALL SECONDARY

_____ STATIONS A A^°°^A

HILL

MASTER PULSE GROUP

PEAK REACHED MO ps AFTER DEFINED START POINT

START

LORAN

50 1 00 150 200 MICROSECONDS

OF C PULSE [103]

Figure 10.19. Loran- C pulse group format.

The Loran-C pulse group format is shown in fig- ure 10.19. This figure also shows a typical pulse with

a rise time near 30 fj,s (following first 3 cycles) for reaching about 60 percent of peak value; a feature

permitted by the relatively wide bandwidth of

±20 kHz.

For timing it is important to know the time of coincidence (TOC) of Loran-C signals relative to a uni- versal time second on the UTC scale. Since these

signals are transmitted by each station once during

the GRP, only a particular pulse coincides with the

UTC second, followed by periodic coincidence.

Times of coincidence vary for the different rates; for example a repetition period of 59,600 /jls gives a coincident interval of 149 whole seconds, whereas a

rate of 49,600 jits repeats every 30 s. The basic rates and specific times of coincidence for Loran-C sig- nals are shown in table 10.3. Generally, a Loran-C

pulse coincides with a UTC second at least once

after each 10,000 repetition periods [98]. The USNO

devised a null ephemeris table which provides specific coincidences for the master Loran chains in operation. Coincidence measurements using slave

255
Table 10.3. a. Loran-C basic and specific rates 1

Specific Basic—* S SH SL ss

0 50.000 60,000 80,000 100.000

1 49,900 59,900 79,900 99,900

2 49,800 59,800 79,800 99,800

3 49,700 59,700 79,700 99,700 4 49^600 59^600 79^600 99^600

5 49,500 59,500 79,500 99,500 6 49,400 59,400 79,400 99,400

7 49,300 59,300 79.300 99,300

'Pulse group repetition interval — /xs.

Table 10.3. b. Period of time between UTS'2 and Loran rate coincidences (seconds)

Specific Basic—* S SH SL SS

0 1 3 2 1

1 499 599 799 999

2 249 299 399 499

3 497 597 797 997 4 31 149 199 249

5 99 119 159 199 6 247 297 397 497

7 493 593 793 993

2 UTS =Universal Time Second or UTC second.

stations must account for corresponding emission

delays. The initial date (epoch) for all Loran-C master stations has been set arbitrarily at 00ft 00m00s

, 1 January 1958. The USNO publishes the periodic

coincidence from this origin in null ephemeris tables

for each calendar year in the Series 9 of the Time

Service Announcements [99]. The accuracy of timekeeping via Loran-C

depends upon (a) the propagation delay and its vari- ation between the transmitter and receiving antenna,

(b) the delay through receiving equipment, and (c) operator skill in cycle selection. (The daily relative phase values are published by the USNO [43] and

corrections can be made later.) In addition, syn- chronizations should be made at TOC seconds and

time of the local clock must be known to better than

one-half of the period of the appropriate chain repetition rate to eliminate GRP ambiguity (~ 25 to 50 ms).

The propagation delays depend upon such factors as all sea-water paths, mixed land and sea-water

paths, groundwave or skywave propagation, and ir- regular terrain effects. Propagation delays can be

computed using methods devised by Johler [100],

Johler and Berry [101], and Wieder [102], with fair success. Potts and Wieder [103] point out that a single

portable clock visit to a user site can calibrate propagation delay for skywave propagation and reduce

the error to within an order of magnitude of that observed in groundwaves. If signals are embedded

in noise, special procedures are required to enhance

the Loran-C pulses. Stetina and Zufall give useful

details for obtaining time synchronization of remote

clocks from Loran-C signals [98]. Their report presents a description of Loran-C techniques for clock

synchronization of the Manned Space Flight Net- work (MSFN) and illustrates use of the USNO Time

of Coincidence (TOC) charts. Pakos [97] has assessed the various errors in- volved in Loran-C timing and has devised some

qualitative error budgets for different categories of

synchronization; e.g., synchronizing to the same

Loran-C station, two stations within a chain,

stations in different chains, or "real" time or

"after the fact" synchronization. Based on such

estimates he obtains an rms error of about 0.35 /xs for two users within groundwave distance of the same station, wishing to synchronize with each

other but not with the UTC time scale. Typically,

much larger errors occur when synchronizing to stations in different chains. Shapiro [104] reports

microsecond timing capability for Loran-C signals

received at groundwave ranges of 1500 km landward

and at twice this range over water. (The groundwave

range is limited or effected by transmitter power,

ground conductivity, noise, interference and signal

averaging time.)

Users outside the normal groundwave range of

the LF Loran-C signals can obtain useful timing

information from skywave propagation but at reduced accuracy. Stone [105] has reported skywave

synchronization accuracies at night of ±50 lis over mixed land and sea paths of 8000-km length. (This

experiment was a visual technique requiring syn- chronous detection.) Doherty [106] has shown

carrier phase stabilities of ± 1 and ±4 /lis for daytime

and nighttime, respectively, at ranges to 3200 km

for single hop skywaves. Mazur recently reported

time synchronization to better than 25 fxs using

nighttime skyway reception of Loran-C at distances

of ~ 15,400 km [107]. He points out that such

results are demanding of both receiver performance

and operator technique.

Advantages of Loran-C for TFD

• A fully operational system with firm implementation plans for equal status chains (i.e., UTC synchronization) will provide coverage

to a large percentage of the world.

• Redundant cesium frequency standards are used for frequency and time control with

monitoring and referencing to USNO(UTC)

in most cases; phase corrections for six chains are published weekly by the USNO.

• Groundwave stability of Loran-C signals

show microsecond precision capability with

accuracies limited to about a /xs because of

propagation effects. Skywave capabilities, de- pending upon hops, can give ±10-50-/ns

synchronization accuracy. TOC for time

coordinated chains are published in advance

by USNO.

• Depending upon user requirements, equipment costs are reasonable but increase as timing needs become more stringent.

• The accuracy and stability of the Loran-C

256
system enable comparison of frequency

standards and time scales of many nations and

provide a highly rated input to the International

Atomic Time (TAI) scale at the BIH in France.

• As with the Omega system, timing and navi- gational functions can coexist in one system

with minimum interference, thus conserving

electromagnetic spectrum.

Limitations of Loran-C for TFD

• The timing accuracies are limited to how well

both propagation and equipment delays can be

determined. Mixed ground and land paths,

coupled with terrain effects, can limit accuracy.

• The local clock time must be known to better

than half the chain repetition period to elimi- nate GRP ambiguity.

• Cycle selection is difficult and requires high

operator skill.

• Coverage is not global and many areas in the

southern Hemisphere are unable to receive

Loran-C signals.

(3 ) Loran-A Navigation System for TFD Loran-A is an MF radio navigation system, devel- oped during World War II, to operate in the fre- quency range of 1.750 to 1.950 MHz [108, 109]. In this frequency range, coverage is limited to a typical sta- tion service area of radius 1800 km (groundwave

range over land is reduced considerably); however,

installations are worldwide (essentially in the north- ern Hemisphere) and are located at or near coastal

areas. Some 60 pairs of Loran-A stations border the

Atlantic and Pacific Oceans. Figure 10.20 gives a projected coverage map for the wide spread

Loran-A stations. The U.S. Coast Guard maintains

operation of the system, and it is used extensively

for navigational purposes. Within certain restric- tions, Loran-A is capable of microsecond relative timing or synchronization within moderate coverage

areas of particular stations [2]. Loran-A stations operate in pairs using pulse

transmissions on three frequency channels as

follows:

Channel 1 1.950 MHz

Channel 2 1.850 MHz

Channel 3 1.900 MHz

Specific pulse repetition rates (PRR) are assigned a given Loran-A pair and each station transmits one

pulse per Loran-A sequence [2]. The three basic

repetition rate are 20, 25, and 33 V3-pulses per sec- ond coded as S, L, and H respectively. Repetition

periods for given PRR's are coded zero through

seven; each integer represents 100 microseconds to be subtracted from the basic repetition period of — 40,000 fjis. Thus a Loran-A pair is designated by

frequency channel, pulse repetition rate, and specific repetition period; e.g., 1S4 denotes a pair operating on the Channel 1 frequency (1.950 MHz), a PRR of 20 pulses per second and a specific repeti- tion period of 39,500 lis. Pulses from two transmitters of a Loran-A pair are radiated with a fixed delay to ensure identification of the master and slave

signals within the coverage areas. Baselines of Loran-A pairs range from about 300 to 1200 km and

specific repetition rates are chosen to minimize

interference from other pairs. Sometimes a third sta- tion is provided to form a Loran-triad. This station can operate on both specific repetition rates and

perform mixed functions. The Loran-A pulse envelope has a cosine square shape; the pulse envelope

rise time at the 50 percent amplitude point is about

20 lis and the width at this point is about 40 fxs. A

typical Loran-A pulse is shown in figure 10.21. Limited clock synchronization via Loran-A is feasible. Since each pair transmits independently,

synchronization can be accomplished only within

the coverage area of a particular pair. There is no UTC time base for Loran-A stations; each pair

has its independent time base. Reception of these

sky signals is limited by propagation effects [110]. Propagation of these MF signals over land paths

is extremely limited. The groundwave signal

strength of a 100-kW transmitter at 2 MHz received over an ~ 200-km land path is about equivalent to that received over a 1200-km seawater path. On the

other hand, the propagation of skywave signals is about equivalent for water and land paths. Skywave

signals, via one-hop E-nighttime transmissions,

are usable to about 2500 km, but with reduced

accuracy. The ambient noise level experienced at MF also effects the usable range of Loran-A. A

typical signal level of 5 /x.V/m is required during

the day in the middle latitudes to provide a maximum range of about 1200 km.

Advantages of Loran-A for TFD

• The system provides a means for synchronization to several /as within coverage range of

pairs of stations (in the sense of a transfer

standard) within groundwave proximity to the

transmitters. Synchronization to 5 lis is claimed

for nighttime skywaves received in an area

of over 3000-km radius about the transmitter

[2].

• Ultimate system precision, through application

of corrections for propagation effects, is pre- dicted at 0.1 (jls over seawater [110].

• Receiving equipment and antenna requirements are minimal, however, commercial

Loran-A receiving systems are not available

solely for purposes of T/F comparison.

• System employs many worldwide stations in northern hemisphere with signals available to many coastal areas.

• All Loran-A transmitters are accurately located

to within about 30 m (equivalent to less than

0.1 /is error).

257
CT!

p

li

258
Figure 10.21. Typical Loran- A pulse envelope.

Disadvantages of Loran-A for TFD

• Pairs of stations in the Loran-A network are

not linked together in time and repetition

rates; they have no relation to the UTC time

scale and are essentially 60 independent

broadcasting systems.

• The area over which Loran-A time measure- ments could be made is limited to that in which

signals from either of a pair of Loran-A

transmitters can be received.

• Frequency generators are crystal oscillators which show aging effects relative to time; phase

corrections are not published.

• Reception of Loran-A signals is limited to relatively short ranges and is subject to fluctu- ations inherent in MF propagation.

• The altitude of a receiving site above the

surface is a factor that must be corrected for

in precise time measurement; i.e. in an aircraft.

• Range of transmission coverage is affected by

ambient noise level and is related to location on the earth, season, and day or night trans- mission.

• Land masses in the course of signal path

adversely affect propagation.

f. Television TFD Techniques

Time and frequency comparisons via television

signals have become a valuable and useful tech- nique in many countries during the past 5 or 6

years [111-120]. Tolman et al., first demonstrated

the utility of synchronizing remotely located clocks

with television pulses transmitted over many

microwave links; VHF television signals from one

transmitter also provided clock synchronization

to the same accuracy within the local TV broadcast

service area [111]. A primary concern in long-term

TV comparisons is the constancy of the propagation

path delay between a multiplicity of microwave

relays. Many studies have substantiated that such

path stability is in the range of 0.1 to 1.0 /as [112,

113, 116, 119]. For "on time" synchronization it is necessary to know the propagation path delay

between the transmitter and receiver. This can be

calibrated by a portable clock visit. Tolman et al.

,

[111] reported that measured path delays agreed

well with calculated values based on geographical

distances and assumption of speed of light propagation. Leschiutta recently compared geographical

delay computations for the Rome to Turin path in Italy (~ 745 km) with both round trip TV measure- ments and Loran-C data [120]. Geographical delay was determined by an ellipsoid computer program

using established coordinates for transmitters,

microwave relay stations, and receiving points. The

calculated differential path delay agreed with the

Loran-C data to less than 1 /las and with the round

trip TV values to about 6 /as. Uncertainties in coordinates account for variation in these data. Such computed delays could prove useful to TV

clock comparisons, dependent upon the accuracy

required.

At this point we will consider the mechanism of

various TV techniques for TFD. The following four

categories have been investigated and will be dis- cussed in terms of experience in the U.S.:

(1) Time dissemination. TV transmissions can be

utilized without auxiliary coding as a "transfer

standard" (passive) for clock coordination

[111, 112, 117].

(2) Time and frequency dissemination. Sync

pulse trains can be stabilized in frequency,

then aligned in some fashion with a time

scale [121].

(3) Frequency dissemination. Frequencies con- tained in the TV transmission can be stabil- ized, providing accurate frequency information directly, or they can be used in a "transfer

standard" application [116, 122].

(4) Time and frequency dissemination. Time

and frequency information can be injected

into unused portions of the TV format for dissemination (active) [116, 119, 123, 124].

(l.a) Sync Pulse "Transfer Standard" Clock

Coordination. The method was first demonstrated

in 1965 when synchronization via TV microwave

links was accomplished between Prague, Czechoslovakia and Potsdam, Germany [111]. The method

has since gained wide acceptance. In 1968, NBS

began using TV sync pulses from a common trans- mitter to synchronize the time broadcasts from

Fort Collins, Colorado, to the UTC(NBS) Time

Scale at NBS, Boulder [79]. The accuracy of such

measurements is better than 1 /as with an rms

day-to-day deviation of about 30 ns. (Lb) NBS Line-10 "Transfer Standard" Time Dissemination. Following the work of Tolman and

others, NBS developed the TV line-10 system as a

passive means of comparing geographically-separated precision clocks [116, 125]. Figure 10.22 gives

259
•DEPENDING ON NETWORK

Figure 10.22. Overview showing routing of TV signals for time/frequency comparisons.

an overview of the system which permits periodic

comparison of clocks throughout the U.S. via com- monly received network broadcasts at a specified

time. The broadcasts used by NBS originate from

the New York City studios of three commercial TV

networks (ABC, CBS, and NBC). 3 These originating

networks stabilize their transmissions with independent atomic frequency standards (rubidium gas

cells). The New York signals, broadcast without

auxiliary time coding, traverse varied and long paths

using relays at microwave frequencies. This relay

system is a chain of broadband radio links encom3 The results of this report are not to be used for advertising or promotional purposes,

or to indicate endoresement or disapproval of the product(s) and/or services of any commercial institutions by the National Bureau of Standards.

passing the continental United States at line-of-sight

distances of 40 to 60 km between repeaters. The

routing of such networks in NBS experiments is shown in figure 10.23. The microwave relay sytem

carrying over 95 percent of intercity television pro- grams is known as the TD-2 system [126]. At a terminating station, such as an affiliate local trans- mitter, the microwave signal from the applicable

repeater station is converted to a video signal and

retransmitted by VHF or UHF (commercial TV) to a

local service area. Reception points for typical

line-10 experiments included the USNO at Washington, DC and NBS at Boulder, CO.

This version of TV timing uses the pulse identifying line-10 of the odd field in the 525-line system M

(FCC standard for the U. S. and one of some 12

worldwide system [127]), as a passive transfer

pulse. This pulse occurs during the blanking retrace

interval between successive fields as shown in fig- ure 10.24. The line-10 pulse, as the transfer standard

element, is easy to identify with simple logic cir- cuits. Figure 10.25 shows a typical equipment configuration for line-10 clock synchronization at a receiver site. Clock comparison occurs through

differential measurements of TV line-10 data. Basic

data are taken simultaneously from a common TV

broadcast at given receiving sites; the differences

between clock-counter output readings remain

essentially unchanged within a few microseconds

from day to day except for infrequent reroutes of

microwave signals and/or instability or relative frequency offsets among the reference clocks [125].

260
Line 22. field 1 (odd)

262'/! Lines

per field

2nd field (even) [272]

[10] even

i 4 4

[262] Lines - \ 4 I 4 I. 4 4 I 4 4 4 * 4 * 4 I A^^-3H 3H —H H H r—

TimeIH = 63.55- -us

- Vertical retrace (650 ps

-Vertical blanking of picture tube (—1400 ps)

Start of

field 2 scan

Blanking or black level

[525] [1] [2] / — Lines -

Video signal

4 4 4 4 4 4

[10]odd [14] [22]odd

4 4 H4 4 4 4 4 4 4 4 1 Mi

jULT/mji^rLnri"LiJiJjj^Lr:..Ji jljljljlji

2nd field (even)

Equalizing - pulses —Serrated — vertical —

sync pulses

Equalizing — pulses —

Horiz Sync Pulses

Start of

field 1 scan

1st field (odd)

Time identification for

line -10 system- Trailing edge

Figure 10.24. Pulses in vertical blanking interval of TV format.

VHF VIDEO ABOUT 5000

LOCAL TV TRANSMITTER

LOCAL ATOMIC

Figure 10.25. Typical equipment configuration for line-10 clock synchronization at a receiving site.

Likewise, other clocks in the U.S. can be related

to the UTC(USNO) and UTC(NBS) scales through a

similar reception and data processing technique.

Comparisons can be made with daily line-10 meas- urements made at the USNO and NBS and published periodically [42, 43]. If the system is to be

used to accurately set the clock's date, the delay of

the propagation paths involved must be known; e.g., calibrated with a portable clock. Since the period of one TV frame is 33.3 . . .ms, it is also necessary to resolve this ambiguity at the receiving site to ~ 16 ms.

Typical TV signals in the U.S. may be routed over

paths two to four thousand kilometers in length. The

occasional network reroutes mentioned previously

will produce an effective change in the propagation

path delay. If the rerouting is not common to all clock comparison links it will adversely affect the

results; consequently, it is highly advantageous to use all three networks to enable identification of any

such changes in one link. A detailed analysis was made of TV line-10 data

for the period June 1969 to December 1970 [128]. Figure 10.26 gives a plot of fractional frequency

stability Acry (r) 4 versus the sample time t in days

for the microwave paths between Washington, DC

and Boulder, CO for each of the three networks;

the instabilities of the reference time scales are assumed negligible. The time fluctuations were

analyzed directly, and it was determined that the

TV noise was reasonably modeled with an a = 1 process, i.e., flicker noise phase modulation for this path [129, 130]. The dashed line in figure 10.26

corresponds to a noise process with a 2^ 1. The

fractional frequency between AT(USNO)5 and

4 The symbols used in Chapter 10 are defined in the glossary in Annex 8. A of Chapter

8.

s The designation AT(USNO) parallels our designation AT(NBS); it follows the New Delhi CCIR Recommendation 458 of Study Group 7 for Standard Frequency and Time Signals. USNO (Mean) or A.l (Mean) in reference [131] is identical to AT(USNO)

as used herein.

261
X

>)/ AT

TV

| NETWORK

\\

AT(USNO)" r

AT(NbS)// AT(NBS) X NBC

| A CBS o ABC I o .52 ABC + .1 NBC

+ .38 CBS

FLICKER NOISE PHASE MODULATION

J I

1/2 YR&.

1 &± I

SAMPLE TIME <T> IN DAYS

FIGURE 10.26. Fractional frequency stability <r y (t) versus sample time of AT(USNO)-AT(NBS) time scales compared

by three-network TV line-10 technique.

AT(NBS) [131, 132] calculated over the period of

analysis was:

(4.48 x 10 13 via ABC

^AT(USNO)-^AT(NBS) _ ] 4 4? V vj a (10.1)

fat<nbs) U.56 x 10-13 via NBC

The precision of these measurements is ±3 X 10~ 14 as indicated by the stability shown at t=224 days.

The three essentially independent networks

enables one to optimally combine the data by

weighting each network set inversely proportional

to its variance. The squares in figure 10.26 represent

the combined network stability using such an optimum weighting procedure. Figure 10.27 gives a

plot of relative time differences (average rate re- moved) of the AT(NBS)-AT(USNO) time scales for the 1969-71 test period in terms of three-network

TV line-10 (weighted), Loran-C, and cesium

portable clocks. Good agreement is shown with

portable clock measurements, and the maximum

spread is well within ±2 /as. The results of the

TV line-10 study indicated that this three-network

TV system (properly filtered) could be used in major

portions of the United States to maintain clock

synchronization within an RMS precision of about:

To-y(r) = 5ns t

1/3s

_1/3 (10.2)

where t ranges from 86400 s to about 2 X 10 7 s

(1 to 224 days). Equation (10.2) is based on the

assumption that the clocks were synchronized

previously [128].

(2) Real Time Synchronization from Stabilized

TV Sync Pulses. The USNO recently proposed a modification of the TV line-10 passive time synchronization technique [121]; in this method the TV color

subcarrier frequency (3.57 . . . MHz) is stablized

with a cesium atomic standard [122] and phase

shifted so that sync pulses in the vertical interval

coincide with 1-pps signals referenced to the USNO

master clock (MC). The method can be used to set remotely located clocks in a TV local service area

within several nanoseconds of an absolute time

scale. In a particular experiment the USNO stabi- lized the color subcarrier frequency of a local TV

station in the Washington, DC area and maintained

coincidence between the line-10 pulse marker (odd

field) with a one-second pulse of the USNO-MC.

Coincidence occurs at exactly 1001 seconds (16 min

41 s) intervals because of the unique TV frame repetition rate (33.366, 667 ms per frame — see refero -1

-2-

8(aT(USN0) - AT(NBS)) - DAY COUNT X 3H.56ns/DAY

LORAN-C

3 NETWORK TV

Cs PORTABLE CLOCK A

0%

o ^\

DO o3

J I I I L

0Left, e*® e»

J L J I I L J L J I L J I A M J JA SO ND'JF

1969 MAMJJASOND'JFM

1970 1971

FIGURE 10.27. Relative time differences of the AT(NBS)-AT(USNO) time scales compared by

the Loran-C, three-network TV line-10, and cesium portable clock techniques (plus arbitrary

constants).

262
ence [125]). Such a relationship permits calculation

of time of coincidence (TOC) dates or times, months

in advance, referenced to some arbitrary initial TOC. The USNO has set an initial coincidence as 0000 UT January 1, 1958 and computed 3 time of coincidence Ephemeris Reference Tables similar to those used in Loran-C (see sec. 10.3. 2. e(2)). An

example of TOC table use for "on time" clock comparison is shown in table 10.4. The USNO line-10 TV measurements at a receiving site are identical to those discussed previously

in the NBS line-10 section. In the USNO experiment [121] the cesium oscillator controlling the local TV transmitter was not maintained in synchronism

with the USNO Master Clock; however, over a 2-month period only a small drift of about 1 /as was

recorded between the two frequency standards.

Absolute frequency stabilization of a TV trans- mission, together with TOC charts, offers an eco- nomical and accurate synchronization technique for referencing clocks in local TV service areas at any

convenient time and completely independent of contact with the time referencing laboratory.

Certain advantages and limitations of passive tele- vision time synchronization techniques are outlined

in table 10.5. (3) Stabilization of TV Color Subcarrier. In the U.S. the major TV networks provide a means for precise frequency measurements in their color

broadcasts. In such broadcasts a color subcarrier

of 63/88 of 5 MHz (3.57 . . . MHz) is derived from

a rubidium oscillator/synthesizer (stable to ~ 1 part in 1012 per day) at the originating station in New York City and transmitted on each horizontal

sync pulse, together with the picture information.

It is used as a reference to phase-lock the crystal

oscillator in the home color TV receiver for demodulating the chrominance sidebands and maintaining

color shades. Frequency stability measurements of the color subcarriers of the three major networks

(originating in New York City) have been made

at NBS, Boulder, Colorado [122]. The received subcarrier is compared in frequency to the NBS standard, and the networks are advised of their frequency

offset so that they can adjust their oscillators. The

rubidium oscillator frequencies are measured

Table 10.4. Example of using USNO Time of Coincidence (TOC) Ephemeris Reference Tables for frequency stability-TV, line-10 [121]

(a) Assume a clock synchronization was desired at about 1930 UT on September 19, 1971 in a local TV service area. Measurements

between the local clock and the received line-10 signals gave the following printout:

h min s

19 30 02 19 987.67/u 19 30 01 18 987.67

19 30 00 17 987.67

19 29 59 16 987.67

19 29 58 15 987.67

(b) TOC table values:

Table 1 First TOC

each Day

Table 2

All TOC's

per Day

TOC -Sept. 1971 Near 1930 UT

(Addition Tables 1 and 2)

Table 3

Interpolation

of Seconds Between TOC's

9/19/71 00 12 26 near

1930 UT

h min s

19 11 09

19 27 50

19 44 31

19 23 35

19 40 16

19 56 57 6 25

6

m

25 s — 17 966.67 us

(c) .-. The TV line-10 odd pulse following the 19 h30 m 00 s UT 1-pps will be transmitted at 19 h 30 m0.017966.67 s

(d) Calculation of clock differences:

Local clock difference with received TV line-10 pulse

(19 h 30 m00s - September 19, 1971) 17 987.67/xs Propagation time — 18.00

17 969.67, TOC chart time of transmission — 17 966.67

Clock difference

Thus UTC(local clock)- UTC(TVref )=3.00/xs (1930 UT September 19, 1971).

263

3. 00/us.
Table 10.5. Advantages and limitations of passive television techniques for TFD

Television Technique Advantages Limitations

(1. a) Transfer standard (dif- ferential) using a TV sync

pulse received in a TV

transmitter local service

area.

1. Precise clock comparisons can be made to better than 100 ns.

2. Comparisons can be made at any time during

transmission without modification or influence on network programming.

3. Method is independent of microwave network

routing.

4. Comparison equipment at a receiving station

is relatively inexpensive.

5. Measurement methods are simple.

6. Simultaneous clock measurements can be made

at an unlimited number of stations within a local service area.

1. Clock readings must be taken simultaneously

by timing centers requiring synchronization.

2. Data must be exchanged between participating

stations after the fact of measurement.

3. Technique gives only comparative clock dif- ferences. Calibrated path delays between

stations is required for absolute time comparison.

4. Coverage is limited to line of sight VHF or UHF

signals which may be subject to multipath inter- ference within a local TV service area.

(1. b) Transfer standard (dif- ferential) using received TV line-10 throughout continental U.S.

1. Precise clock comparisons can be made to about several microseconds nearly anywhere

throughout continental U.S.

2. Three television networks with atomic clock

references (Rb) provide redundancy and

enable cross synchronization; system has no

effect on network programming.

3. The required instrumentation is simple, easy

to use, and reasonably inexpensive. (The line-10 pulse code generator costs less than $200.)

4. One-a-day measurements are adequate for precise frequency standards.

5. Users can compare TV line-10 measurements

with published NBS and USNO values and

relate time scales if propagation path is calibrated.

6. Modular frame intervals can permit advance

predicted TV delays.

1. Microwave paths can be interrupted or networks

rerouted without notice.

2. Clock readings must be made simultaneously

by all stations requiring synchronization.

3. Measurements require simultaneous viewing of

"live" broadcasts originating from New York

City studios for near-continental coverage; present network distribution system uses a delay

tie-in with West Coast transmission lines which

limits coverage of West Coast area; also there is limited availability of simultaneous viewing of nationwide network programs.

4. System will not work with tape delays.

5. NBS and USNO measurements are not made on weekends and reference data at these times are

unavailable.

6. Line-10 TV system ambiguity is ~33 ms.

7. Propagation anomalies may limit system's use- fulness in some areas of the continental U.S.

(2) Real time transfer from

time-scale-related trans- missions (line-10 in local TV service area).

1. System can set or synchronize clocks within

the local TV service area to a few nanoseconds

of a reference clock.

2. The stabilized modular frame intervals permit

prediction of TOC between 1 pps of an atomic

time scale and emitted line-10 odd pulses, months in advance. This allows construction

of TOC charts and independent clock synchronizations.

3. System will operate with existing line-10 TV

receivers.

4. Operation is without interference or effect on

regular programming.

5. Measurement methods are simple.

1. Requires installation of atomic cesium clock and

phase shifting synthesizer at local TV transmitter.

2. Absolute clock calibrations require knowledge

of delay between the transmitter atomic standard and local standard at TV receiving site. 3. Clock time must be known to half the system

ambiguity or ~ 16 ms.

4. Same as item 4 for technique (1. a) previously

given.

regularly at Boulder in terms of the rate of AT(NBS),

and the average weekly data are published for the

benefit of users throughout the country [42]; representative data are given in table 10.6. Note the agree- ment in offset frequency among the three networks

during the week of January 22-26, 1973. Such

agreement was intentional to permit interchange

and split screen synchronization of the three net- work TV cameras during President Nixon's in- auguration; the AT(NBS) scale was used as a common reference for such adjustment. (TV color

subcarrier frequencies are still offset from nominal

by about -300 parts in 1010.) NBS designed instrumentation both to synthesize

the output of a 1- or 5-MHz local frequency standard

to 3.57 . . . MHz and to compare phases of the

local synthesized signals to the received subcarrier

frequency [122]. Figure 10.28 gives a block diagram

of such a calibration system. Frequency stability

measurements of the color subcarriers received

at Boulder indicated resolution of the phase differ- ence between the subcarrier and local 3.57 . . . —

264
Table 10.6. U.S. television network atomic standard fre- quencies in terms of AT(NBS)

Dates of Measurement Period 1973

Average Fractional Frequency

Offset (parts in 10'°) NBC CBS ABC

2 Jan.- 5 Jan. -302.85 -295.87 -305.18

8 Jan.-12 Jan. -301.27 -295.85 -305.25

15 Jan.-18 Jan. -301.21 -295.89 -299.23

22 Jan.-26 Jan. -299.27 -299.04 -299.37

28 Jan.- 2 Feb. -299.26 -295.84 -299.36

From NBS Time and Frequency Services Bulletin, February

1973. See reference [42].

bt 10"10

4 lO" 12

/ Cs p,c. a

\ LOPAN-C O

y

a FRACTIONAL FREQUENCY FOR I TV-LINE 10 Q

( TV-COLOR

\ SUBCARRIER

1 DAY

o

1 I10NTH

SAMPLE TIME (T) IN SECONDS

VHF COLOR SIGNAL

FROM LOCAL TV TRANSMITTERORIGINATING FROM

NYC STUDIOS.

LINEAR | 1 PHASE / COMPARATOR I LI

CHART RE COROER 14

FIGURE 10.28. Equipment configuration for TV color subcarrier frequency comparisons.

MHz signal to less than 10 ns; this corresponds to a frequency resolution of about one part in 1011 in ~ 17 minutes. A plot of relative fractional fre- quency stability versus sample time is given for the

following data in figure 10.29: CBS TV color subcarrier; weighted three-network TV line-10; cesium

portable clock and Loran-C [128]. An estimate

of the time dispersion of the color subcarrier data

plotted in figure 10.29 is as follows:

TO- y (T) = 0.3ns t^s-1 ' 3 (10.3)

with t in the range 125 =S t =£ 384 s. The measured

frequency stability of the color subcarrier gave a

T(jy {r) of 1 nanosecond in the range 1 lis ^ t ^ 1 s. Figure 10.29 permits comparison of relative stabili- ties (precision) of the several techniques; e.g., at t= 200 s the values of cr y (T) for Loran-C, TV

color subcarrier, and cesium portable clock are

1 X 10-10

, 1 X 10" u , and 4 X 10~12 respectively

[128].

Figure 10.29. Relative fractional frequency stability, (tv (t) versus sample time for CBS TV color subcarrier; Loran-C;

three-network TV line-10; and cesium portable clock.

Some advantages and limitations of the TV color

subcarrier technique (3) of comparing frequency

standards are as follows:

Advantages

• Provides resolution of frequency differences to about one part in 10 n in less than 30 minutes;

excellent short term stability is shown.

• TV color subcarrier comparisons can be made

to the NBS(UTC) time scale through periodically published data [42].

• Comparison equipment is relatively inexpensive

and simple to use (parts cost for the 5.0 to 3.57 . . . —MHz synthesizer and linear phase

comparator is about $100).

• The several independent networks allow both

flexibility and redundancy of measurement.

Limitations

• Requires TV color transmission referenced to atomic frequency standard (originating network

in New York City).

• Microwave relay links can fail or be rerouted

causing disruption of signal.

• West coast tie-in to "live" programming from

New York City is limited and the networks give

minimal coverage to West coast areas of the U.S.

• Taped programs with local low grade oscillator control is unsatisfactory for color subcarrier

comparisons.

• Propagation anomalies can limit usefulness of

TV color subcarrier comparisons in some areas

of the U.S.

(4) Injection of Time and Frequency Information

into TV Format (Active). Techniques for transmitting

time and frequency information within the broadcast TV format have been developed at NBS. Initial

265
tests were made at Denver, CO, using lines 15 to 17 [116]. In January 1971, Koide and Vignone tested

the technique on a 45-km path in California and

found the synchronization accuracy better than

100 ns [133]. The favorable results experienced in the early tests led to refined experiments across the

continental U.S. from New York City to Boulder,

CO and to Los Angeles, CA [123, 124]. This active

line technique, called the "NBS TV Time System,"

used line one of the vertical blanking interval for transmission of time and frequency information.

Such a proposed time and frequency dissemination

system is undergoing evaluation. A section of the

system, useful for local area distribution, is shown

schematically in figure 10.30. The time and fre- quency information is injected into line one as shown

in the wave form diagram of figure 10.31. The user station is equipped with a TV receiver, a decoder, an alphanumeric character generator, and

optional auxiliary equipment for automatically

measuring the time difference between the received

time signal and the user's clock. Several modes of

operation are available to the user (see fig. 10.30).

(a) Coarse time (hours, minutes, and seconds) can be displayed on demand on the user's TV screen

in alphanumeric characters.

(b) The time difference between the received time

and the user's clock time can be displayed on the

TV screen with nanosecond resolution.

(c) The received 1-MHz sine wave can be used for direct frequency comparison.

Digital time dissemination: A reference time

standard and a time code generator are installed at the point of program origin (network or local studio).

Both the code and its complement are sent for redundancy. The code, injected in the second half of

line-1, carries hour-minute-second (HMS) information derived from the reference time standard

(see fig. 10.31). The system does not measure propagation delay time; this delay is treated as clock error, which is insignificant for coarse timing. The user must make a calibration of the path delay between

the clock at the code injection point and the clock

at the receiver if accurate time is desired.

At the user's clock station a decoder is required.

Optional comparison instrumentation is available

if desired. The active line system provides an HMS

readout on a modified commercial TV receiver,

which includes a built-in digital clock regulated by

the time code. In the event no code is received, the

digital clock reverts to internal control.

Figure 10.30. Active-line TV Time system at local television station.

266
1-MHz frequency dissemination: The active line system also provides a precise frequency standard.

A stable 1-MHz carrier is transmitted during the

interval between the first and second equalizing

pulses of lines 1 and 262 V2 (see fig. 10.31). At the

decoder, a phase-locked oscillator recovers this signal using an approach similar to the detection

of the color subcarrier in a color TV receiver.

Results at NBS indicate that such a received

standard frequency permits calibration of a local standard to 1 part in 10 11 in less than V2 h.

VERTICAL BLANK I NG

100 IRE

FIGURE 10.31. Method of injecting time-frequency information on active line in vertical blanking interval.

The reported active line-1 experiment compared a cesium reference 1-MHz signal at NBS Boulder to a TV line-1 received 1-MHz signal generated by a cesium standard at the ABC New York City studio

[123, 124]; typical phase variations of about ± 10 ns were shown in one hour as indicated by a comparison record given in figure 10.32. The short term

stability of a 1-MHz quartz oscillator, phase locked

to the received 1-MHz TV signal originating at New

York City, was determined; measurements indi- cated that this active line-1 data were only slightly less stable than the color subcarrier data except for measurement times < ~ 20 ms [124]. This is note- worthy, in that the line-1 system is sampled at about 1/100 the rate as that for the color subcarrier.

Figure 10.33 is a block diagram which shows the

capability of phase-locking a local crystal oscillator

to a received 1-MHz signal from an active TV line. This TV system shows a long term (several days)

stability of a few parts in 10 12

. (It should be noted

that the Department of Commerce petitioned the

FCC in December 1972 for the use of line 21 in the

vertical interval for time and frequency dissemination similar to the line-1 active system.)

Capabilities and limitations of the active line TV

dissemination of time and frequency are listed in table 10.7.

Table 10.7. Capabilities and limitations of active line TV timeIfrequency dissemination (category 4)

Television Technique Capability Limitations

Time and frequency

coding of active line in Blanking Interval.

1. System permits calibration and phase-locking

of remote oscillator to about 1 part in 10"

within V2 h.

2. System can transfer real time to submicro- second accuracy in a local service area; pro- vides hrs., min., and seconds in continuous

digital update.

3. It is estimated that 70% of the U.S. population could be reached by installing synchronized

coders at network centers in New York City and distributing the active code over existing

microwave links.

4. Transmission of data has no effect on network programming and system transmission is cost

free to user.

5. As the UTC scales of both NBS and USNO

are mutually coordinated to — ±5 /xs of each

other, users of TV active line system would have

effective access to both scales.

6. User cost is proportional to required precision.

7. System is unambiguous to 24 h for date information, and reliability to 10 fis. 8. Three or four major networks would provide

redundancy and permit cross checking.

9. System supports other uses such as captioning

for the hearing impaired.

1. Requires installation of cesium standard and

encoders at TV transmitters. (A time and fre- quency decoder, capable of nanosecond resolution, would cost about $1000.)

2. Clock decoder must be installed at clock comparison receiving station.

3. Microwave paths can be interrupted or networks

rerouted without notice.

4. Equipment requires modification to allow time code compatibility with local time in case of taped shows.

5. The viewing time of nationwide network pro- grams is limited; the active line must be "live"

for measurements referred to the network cesium beam standard.

6. Real time comparisons require knowledge of propagation and equipment delay time between

the transmitter atomic standard and the fre- quency standard at the receiver.

267
MINUTE CODE

MINUTE COUE

VECTOR VOLT

1MHz FROM RECEIVER PLL

L.

LINE-l DECODE*

ji 12-3-71 RELATIVE PHASE ABC VS NBS,

S lOcm/hr Hx: WINUY, OVERCAST

TYPICAL ONE DAY PHASE RECORD MAUL AT iJOUUJLR. COLO. STTE

10.32 U) (b)

Figure 10.32. (a) Typical equipment configuration for phase versus time measurements (TV); (b) phase record comparing 1-MHz

signal from cesium standard at Boulder, CO with 1-MHz signal derived from line-1 active code generated from cesium standard

at New York City studio. 268
1 MHz OUTPUI

Figure 10.33. Phase locked crystal oscillator via TV line-1 (1-MHz reference signal).

g. TFD via Earth Satellites The appearance of Sputnik satellites in 1957

signalled a new potential in terrestrial-space radio

techniques. Since then, artificial earth satellites have been proposed and used for a variety of pur- poses including telecommunications, navigation,

geodesy, traffic control, and safety [134-138]. It

is significant that many of these applications require

time/frequency techniques, yielding an ancillary

capability for TFD. Satellites are more advantageous

than many conventional TFD techniques in terms of

global coverage, accuracy of time transfer and

propagation degradation. This occurs through the

unique height position of a satellite relative to earth,

allowing satellite visibility to intercontinental areas using line of sight radio frequency propagation.

During the past decade many TFD experiments have

been made via satellite; the results have been very

encouraging. In the future, satellites may broadcast

time and frequency signals on an operational basis; such transmissions, however, will no doubt be

supplementary in function, as the cost of construction, launch, and maintenance would seem to prohibit a dedicated satellite solely for purposes of

TFD. It is beyond the scope of this study to examine

in detail the many satellite transfers of time and

frequency. In turn we will (1) discuss some basic

concepts of satellites as related to TFD, (2) give

comparative results of TFD via satellite over the

last 10 years, (3) briefly describe several U.S. Navy navigation satellite systems useful for TFD,

(4) show the NBS approach to distributing time and

frequency signals via satellite, and (5) outline

both advantages and limitations of satellite systems

for TFD.

(7) Some Basic Satellite Concepts. The major

problem confronting the user of TFD techniques

by earth-bound radio signals is the difficulty of

predicting the radio delay path which results from

the complexities and reflections in the ionosphericatmospheric propagation. Artificial satellites,

however, are used both as relays and signal sources

with onboard clocks and, in combination with

VHF (and higher) radio signals, can overcome the

radio delay uncertainty problem to a large extent

[139]. Propagation delays of satellite signals can be

calculated to high accuracy («£ 10 ^ts); the re- fractive index for most satellite-to-earth radio paths

is near the free space value since the ionosphere

and troposphere constitute a small fraction of the

total path; and multipath effects are negligible for

all but the highest accuracy users who might receive

the signals at low elevation angles. On the other

hand, satellite systems are expensive, launched for primary missions other than TFD, and the satellite

is never exactly fixed in position relative to a user antenna. Consequently, there is a multiplicity of

choices and tradeoffs to be made in designing a

satellite system for a given situation.

Table 10.8. Classification of satellites by altitude

Altitude Altitude Range — km

Classification (Above earth's Satellite Period

surface) Low 900- 2,700 ~ 100 to 150 min. Medium 13,000-20,000 7 to 12 h High 22,000-45,000 13 to 35 h (Synchronous) 36,000 24 h

Consider the matter of orbit. Should it be circular or elliptical? At what altitude above earth? Easton

classifies satellites by altitude as shown in table 10.8

[140]. Very definite characteristics are implicit in these 3 classifications. Figure 10.34 shows one of these; namely, the farther out the satellite is the

greater the earth coverage until near maximum cov- erage is reached at synchronous altitude. On the

other hand, the signal strength decreases with alti- tude increase; also, if the satellite is equipped to maintain a precise orbit and fixed orientation to earth as well as possess the capability of transponding signals, additional integral components are

required. Or, look at the factor of earth coverage —

one synchronous equatorial satellite is constantly in view (24 h) to about l/z of the earth's surface (3 satellites could provide near global coverage); a decrease

in satellite altitude is characterized by a shortened

period with nearly global coverage (in view for short

periods of time at one station), and the Doppler

effect, sometimes used in navigation, becomes more

pronounced. Operation of a satellite with an

on-board clock complicates clock maintenance and

necessitates periodic adjustments, although no con- tinuous RF transmission is required from the

ground. Use of a satellite relay or transponder per- mits the clock to be maintained on the ground and

allows use of a general purpose communication

satellite on a time-shared basis. In a one-way satellite system the users receive signals from the satellite in a listen or receive-only mode. A two-way

satellite system usually involves bilateral communications between separated reference and receiver

269
SYNCHRONOUS

Figure 10.34. Relative earth coverage by satellites at various

altitudes.

Figure 10.35. One-way satellite timing mode.

clocks on the ground through relay via the satellite transponder. In either one or two-way transponder

mode the satellite must be visible to both the ground

transmitter and all receiving stations at an angle of

at least 5° above the horizon of each. An on-board

clock mode provides timing information directly

from a satellite in a one-way mode. The following

discussions describe the 3 major means of satellite TFD:

One-way mode. The users operate in a listen or receive-only method. As shown in figure 10.35 the

transmitted terrestrial standard source is relayed by

the satellite transponder to the earth receiver. The

accuracy of time transfer in this mode is dependent

upon the knowledge of the absolute propagation

delay between the ground transmitter— satellite transponder— and ground receiver.

With VHF transponders (ATS 1 and 3) the avail- able bandwidth is ~ 100 kHz which limits use of pulses at fast risetime. An alternative means for resolving time differences in the one-way mode

employs the so-called side-tone ranging technique.

(This technique also can be used in the two-way

mode.) There are variations even in this technique; one method uses a 10-kHz tone, phase locked to a time standard with its zero crossing coincident with

the clock's 1 pps [141]. Bursts of the 10-kHz tone are transmitted at different repetition rates to resolve

ambiguities. The receiving station detects the satel- lite-transponded signal and decodes with sampling

rates equivalent to the transmitted tone-burst rate in terms of the receiver clock. A typical decode by this technique is shown in figure 10.36, where burst repetition rates of 1, 10, 100, and 1000 times per second,

as well as the continuous frequency of 10 Hz, were

transmitted and received to determine the total rela- tive time difference between two remote clocks. The

beginning of each tone burst marks the time delay

increment for each different pulse rate except that

the continuous 10-Hz signal is read when the tone

crosses the zero axis. The lowest tone used reduces

the ambiguity of the timing information, while the

highest tone provides the limit of resolution. The

delay thus determined includes the clock differ- ences, equipment delays, and propagation path

delays.

CONTINUOUS 10ns

RELATIVE SCOPE SCALE

FIGURE 10.36. Example of arrival time via side-tone ranging of

satellite signals [150].

If the path delays can be separated out, the other

factors are resolvable to high accuracy. Path delays

may be determined from orbital elements which

sometimes are relayed by satellite. (Orbital elements

describe the satellite's orbit and its position in that

orbit at a given date; they include six constants of

motion which in one form include period, eccentricity and inclination [142].) The orbital elements

270
are obtained from observations over a period of time

and are issued periodically by agencies responsible

for operation of a given satellite. A major difficulty in timing via the one-way mode satellite system is the variability in delay caused by the satellite motion.

A Root-Sum-Square (RSS) error analysis for the

one-way mode is reported as 0.9 /as when factors of

equipment and VHF propagation delays, position

uncertainties of the satellite and receiving stations,

and clock instabilities are taken into account [2]; another analysis, without a clock instability factor,

gives an RSS error of 0.35 /as [3],

-1 SEC /

MASTER

CLOCK TICKS

1 «•— 1 SEC

- SLAVE

1

1 —1- ^CLOCK TICKS

1

1 —

M

fit

Figure 10.37. Typical two-way satellite time diagram.

Two-way mode. The users operate in both a listen (passive) and transmit (active) mode, although the

satellite still relays the signals as in the one-way

case. However, an exchange of information between

the two ground sites permits a measure of the path

delay, thus obviating the need for knowing the location of either the satellite or earth stations. A simplified timing diagram for a two-way satellite system is shown in figure 10.37. Specific techniques vary but

the following is given as an example. Assuming

that the master and slave clocks are synchronized

to one second, one can adjust the transmitted time

signals to arrive "on time" at the slave site via a voice communication link. The total delay in the

transmitted time signal is designated A in figure

10.37. A is related to the time difference between

the master and slave clocks, 8t, and the one-way

path delay between ground transmitter— satellite —

slave ground station, Td, as follows (using 1 pulse

per second time ticks):

A = 8t+ (1-Td ). (10.4)

Following synchronization of the slave clock with

the master clock, the slave station transmits uncorrected clock signals directly back to the master

station where they arrive via the satellite relay at a time B later. B has the following relationship

B=8t+Td . (10.5)

Since one can measure both A and B at the master

station, the difference between the two ground

clocks, 8t, can be determined by combining eqs

(10.4) and (10.5) with the propagation delay, Td -

dropping out. Thus,

8t= (A + B-DI2. (10.6)

In this case 0 8t Ta \ in most cases 8t will be less than Td which is ~ 0.25 s in the synchronous satellite case. (Different formulas hold for other clockdifference, propagation-delay relationships.)

Jespersen et al., used the above technique with

alternate pulse rates of 1 and 100 pps to synchronize

widely separated clocks to about 4 /as with a syn- chronous-satellite transponding VHF signals [143]. Degrading factors such as satellite movement

during satellite signal exchange, nonreciprocity

of path, carrier frequency dispersion, and variation

in equipment delays can adversely affect the

accuracy of the two-way mode. If one neglects clock

instability, two reported error budgets give RSS

values of —0.2 /as [2] and —0.14 /as [3], of which

equipment delays are principal contributors.

On-board clock mode. This satellite technique can employ either a crystal or atomic clock within

the satellite which transmits timing information

directly to a terrestrial receiver. (It is conceivable

that aircraft also could receive such timing infor- mation for use in collision avoidance or air traffic control.) The degree of accuracy realized in this timing mode is directly related to the certainty

with which the propagation delay between the

satellite and ground station is known, as in the one- way mode. This technique offers an excellent means

of clock time transfer whereby two stations receive

the same satellite transmission and difference

their results over a period of time (time transfer

technique). Although the position of a clock-carrying

satellite in geostationary orbit could be fairly well

established, time data from such synchronous

satellites would be subject to relativistic gravita- tional shifts of ~ 50 /As/day and second order

Doppler shifts of about 4.4 /As/day [144]; these constant terms, however, are compensable and

should not limit the accuracy. On the other hand, TFD via low altitude orbiting

satellites is complicated by the Doppler effect of

the moving transmitter which can cause shifts as large as 25 X 10~6 in the received frequency at a ground station (minimum Doppler shift occurs at closest approach to an earth receiver). Thus, timing

resolution requires accurate tracking information.

An error budget for the satellite on-board clock

has been given as 0.25 /as RSS [3] and 0.7 /as RSS

[2]. The variations of these estimates result from

differences in the assumptions for carrier-frequency

propagation errors and uncertainties in both satellite position and equipment delays. In summary, the one-way mode can satisfy a

multiplicity of users at widely separated points with some sacrifice in accuracy principally because of

path delay uncertainties caused by satellite position

error. The two-way mode can service only a small

271
number of users, but, with elimination of the path

delay problem and the addition of a communication

link, it appears this method could realize submicrosecond capability. On-board clock techniques have

similar advantages and limitations of the one-way

mode.

(2) Some results ofTF comparisons via satellites. The first time experiments via artificial satellites were conducted in August 1962, using the communication satellite Telstar [145]. These experiments re- lated time at the USNO in Washington, DC to that at the Royal Greenwich Observatory (RGO) in England

to about 1 jus (with about ±20 /as assigned to an LF

ground link error). The two-way mode was employed

using 5-/us pulses at a 10-pps rate and microwave

carrier frequencies. Since that time many experiments have been made via the one-way mode and

the low orbiting on-board clock technique. Laidet

reports a relative accuracy of 20 fis between the

TRANSIT satellite on-board clock and Centre National d'Etudes Spatiales (CNES) network clocks

[146]. Table 10.9 shows results of various time and

frequency experiments via satellites during the past

ten years, including applicable satellite characteristics. These results indicate the excellent

potential for TFD via satellites between widely

separated global points in the microsecond accuracy

range.

TABLE 10.9. Selected Time/Frequency Comparisons via Satellites (1962-1973)

Dale Satellite Orbit Carrier frequency Mode of measurement

Purpose

of test Stated accuracy Reference

August 1962 TELSTAR Elliptical Apogee ~ 4800 km

Perigee - 800 km

(SHF) 6.4/4.1 GHz Two-way relay Clock comparison — RCO

(England)and USNO

(Washington. DC) via Andover, ME

— 1 Ms [145]

February 1965 RELAY II Elliptical Apogee ~ 4800 km

Perigee ~ 1400 km

(SHF) 1.7/4.1 CHz Two-way relay Clock comparison — RRL

(Japan) and USNO via Mojave, CA

~ 0.1 ms [147, 148]

June-July 1967 ATS-1 Equatorial near synchronous (VHF) 149.2/135.6 MHz

Two-way relay Two-way time sync experiment 4±2 ms [143]

November- December 1967 ATS-1 Equatorial near synchronous (VHF) 149.2/135.6 MHzOne-way relay Worldwide time sync experiment

10 to 60 |ts* [149]

January 1968- April 1972 CEOS- II Elliptical near polar Apogee 1480 km

Perigee 1110 km

(VHF) 136.3 MHz One-way from

on-board

clock

Time sync of some 8 worldwide tracking

stations

25 /xs [150, 151]

March- October 1969 TRANSIT Low altitude (-1100

km) circular/ polar (UHF/VHF) 400.0/ 150.0 MHz

One-way from

on-board

clock

Synchronization of 6 French satellite control networks20 ms [146]

February 1970 DSCS Near synchronous

drifting — 25°/day (SHF) Two-way relay Experimental program to determine feasibility of replacing military portable clock trips

0.1 ms

(o-~0.2ms)

[152]

June-July 1970 ATS-3 Equatorial near synchronous (SHF)(C-Band)6.2;

6.3/4.1 CHz

Two-way relay Time sync experiments at C-band carrier fre- quencies0.05 /lis [153]

February- August 1971 fTACSAT

^LES-6

Equatorial near synchronous

Equatorial near synchronous

(UHF/VHF) 303.4/ 249.6 MHz

(UHF/VHF) 302.7/ 249.1 MHz

One-way relay

One-way relay

Evaluation of one-way mode for clock sync at stations in North and

South America

150 Mst

25 ms t

[154, 155]

Late 1971 TIMATION II Low altitude (~ 925 km) circular 70°

inclination

(UHF) 400 MHz One-way from

on-board

clock

Satellite time sync experiment ~ 1 MS ~ 4 ms

[156]

August 1971-1973 ATS-3 Equatorial near synchronous (VHF) 149.2/135.6 MHz

One-way relay- wide area broadcast

Experimental Time/Fre- quency Dissemination ~ 50 ms [157]

Dependent upon age of orbital elements,

t Within 2 weeks of orbital element date,

t Within 12 h of orbital element date. 4-day old orbital data. 6-day old orbital data.

272
Table 10.10. Characteristics of the Operational TRANSIT Satellites

Scientific Name Designation Launch Date

Period

(min) Perigee

(km)

Apogee

(km)

Inclination (deg)Eccentricity Right Ascension of Ascending Mode (deg)

1970 67A 30190 27 Aug 1970 106.98 949.7 1218.2 90.04 0.018 238.2 1968 12A 30180 2 Mar 1968 106.93 1024.7 1138.4 89.99 0.0076 279.0 1967 92A 30140 25 Sept 1967 106.75 1036.0 1110.6 89.23 0.0050 88.1 1967 48A 30130 18 May 1967 106.96 1066.8 1099.0 89.63 0.0022 12.4 1967 34A 30120 14 Apr 1967 106.48 1046.9 1074.3 90.20 0.0018 348.8

(3) Timing via U.S. Navy navigation satellites.

(a) Navy Navigation Satellite System (NNSS)—

TRANSIT. The NNSS is primarily a means for determining accurate navigation fixes through Doppler measurements of accurate radio signals trans- mitted from low-altitude moving satellities (velocity 7 m/ms) [142, 158, 159]. A secondary function,

of interest to TFD, is the continuous transmission

of timing marks at 2-minute intervals. These marks

are referenced to the UTC time scale and are periodically updated through a ground support network.

The TRANSIT system became operational in 1964;

it presently consists of 5 satellites with on-board

clocks and in nearly-circular polar orbit as shown in figure 10.38. The satellites were spaced initially so

that their planes of orbit would be —45° apart at the equator. Each are visible from all points on earth

several times a day due to their orbital motion

around the rotating earth. Characteristics of the 5

orbiting satellites are given in table 10.10. A fairly elaborate correction network exists for the TRANSIT system. It consists of 4 tracking sta- tions in Hawaii, California, Minnesota, and Maine,

NAVIGATIONAL SATELLITE SYSTEM

ADDED IN AUGUST 1 970

Figure 10.38. TRANSIT satellites showing 4 polar orbits. (Consecutive orbits do not repeat around rotating earth.)

a computing center, a time reference fink to the

USNO, and two ground to satellite communication

sites or injection stations [160]. A pictorial diagram

of the TRANSIT system is given in figure 10.39. The satellites are monitored continuously with infor- mation flow to the computing center; orbit predictions for the 16-hr intervals are determined and

transmitted to the TRANSIT satellites, together

with timing resets, from the injection stations. This

information is rebroadcast from the satellites as explained below.

The heart of the on-board clocks consists of high

quality 5-MHz crystal oscillators, requiring a fre- quency stability of at least a part in 109 for an observation period of ~ 15 minutes. An example of the

TRANSIT crystal oscillator stability is shown in figure 10.40 where the effects of launch are shown

as well as the stability recovery 12 to 16 hours after launch. About 2 weeks later the stability per day is better than a part in 10 10

. Current in-orbit oscil- lators exhibit stabilities of several parts in 10 n per

day over intervals of 100 days [160]. The TRANSIT satellite continuously transmits

crystal stabilized signals at two phase modulated

(PM) frequencies- ~ 150 and - 400 MHz. (Two

frequencies are used to minimize the refraction

error which is inversely proportional to the square

of the carrier frequency.) The radiated power is ~ 0.1 watt, providing useful signals up to distances

of about 3500 km [160]. Navigation information is given in 2-min segments which begin and end at the

instant of each even minute. A digital encoded time

marker is broadcast with time uniquely marked

at the instant of the even minute by the appear- ance of a 400-Hz switching tone. A typical TRANSIT

timing signal is shown in figure 10.41. Laidet used

such TRANSIT signals in synchronizing worldwide

French tracking stations to 20 /xs [146]. In the timing application of TRANSIT signals one must know the orbit of the satellite and the location

of receiving site. For a stationary receiving position one can fix the satellite's position from the trans- mitted orbital parameters, calculate the range and

thus determine the signal propagation delay. Presently, the satellite time is set to UTC in 10-fxs steps; thus, 10 /xs is the upper bound of clock set- ting accuracy although averaging can reduce these

time step effects [146]. The equipment for the complete navigation capability for NNSS, including

273
TIME-T, TIME-T TIME-TTRANSIT

SATELLITE ORBIT

REFRACTION

CORRECTED

DOPPLER DATA

DOPPLER SIGNAL ORBITAL PARAMETERS

TIME

I TRACKING STATION (MINN.) II COMPUTING CENTER (PT. MAGU, CALIF.) Ill INJECTION STATION

RECEIVES, RECORDS & DIGITALIZES DOPPLER

SIGNALS

CALCULATES FUTURE ORBITAL PARAMETERS

RECEIVES UPDATED TIME DATA

ERASES SATELLITE MEMORY TRANSMITS NEW ORBITAL PARAMETERS & TIME CORRECTION

FIGURE 10.39. TRANSIT satellite system operation.

SATELLITE 30190 (197067A)

16 -

1x10 s

8 _ T

4 -

fjl 1 II I I I I 220 240 260 280 300 320

DAY OF YEAR 1970

Figure 10.40. Typical TRANSIT on-board oscillator stability curve.

digital computer and data processor is quite expensive, however, a simple non-directional whip antenna can be used at a ground station with a commercially available "satellite time recovery receiver,"

TRANSMITTED

T = 4 . 91 5 ms

RECEIVED

Figure 10.41. TRANSIT timing signal (transmitted every 2 min. [146]).

costing about $2500 [160J. Future plans for TRANSIT

type satellites include crystal oscillator drift correction, coarse time resolution to 200 ns, date adjustment precision ~ 1 ns, and pseudo random noise

(PRN) time-code modulation [160, 161].

274
Table 10.11. Characteristics of TIMATION Satellites

Name Launch Date Period

(min)

/\iiiiuue (km)Carrier FrequencyOscillator

Stability Status

TTM ATTON ii UiSI Mav 1 TACIT 1967 A. S\J 1 ~ 103 Circular

70° inclination 925 400 MHz 3 X 10~" Inactive

TIMATION II 30 Sept 1969 103.4 Circular

70° inclination 925 [150 MHz

[400 MHz

1 X 10-" Active

TIMATION III FY 1974 -480 Circular

125° inclination

13,875 f 335 MHz

11580 MHz

~ 2x 10-,a Scheduled Launch

(6) Navy TIMATION satellites for TFD. TIMATION is a proposed navigation system using a multiplicity of medium-altitude, circular-orbiting satellites with on-board clocks. Two experimental satellites have been launched to date in a low-altitude orbit; a third launch to medium altitude is planned for the near future [140, 163]. Characteristics of TIMATION satellites are given in table 10.11. Easton has described a TIMATION timing tech- nique for determining the travel times between a moving satellite and a receiving station through

phase comparisons of a received radio signal [140]. His technique includes (1) transformation of the

satellite position to that of a celestial navigation concept; (2) use of a Marcq St.-Hilaire type of precomputed intercept chart for plotting arrival times and

determining a fix; (3) transmissions of low frequency

modulations on a UHF carrier, sequenced in order

similar to side-tone ranging; (4) comparison of the

received signals at a remote site where a duplicate

sequence of time-ordered frequencies is generated,

thereby determining an arrival time measurement

consisting of both propagation delay and satellite- receiver clock differences, and (5) plotting the arrival times on the Marcq St.-Hilaire intercept chart to determine the clock differences as well as the range

and/or path delay to the satellite. TIMATION satellite positions, both prediction and post-diction, were

obtained from Doppler measurements by the

TRANET tracking network and processed to give

a computed time delay between the satellite and

selected receiving stations. In 1968, TIMATION satellites were used in an

experiment to compare widely separated clocks in Alaska; Colorado; Washington, DC; and Florida.

The results of these time-transfer measurements

are given in figure 10.42; the overall RMS error shown over a period of 10 to 15 days is stated to be

0.55 /xs [140]. Experiments in late 1971, using TIMATION II passes in a southeasterly direction over the

central USA and the Atlantic Ocean, gave differ- ences between computed and measured delays of ~ 1 fis for 4-day old orbit ephemeris data; 6-day old

data gave results 3 to 4 fxs in error [156]. In 1972 time

transfer measurements between clocks at the Royal

Greenwich Observatory (RGO) and the USNO were made via TIMATION II at nearly concurrent times.

0

-2

-4

0 h

-2

NRL- ALASKA

rms 0.44/iS

SLOPE 0.03/is/DAY

NRL- COLO,

rms - Q67/tS

NRL - TEXAS

rms - 0.66/iS SLOPE - 0.055/is/DAY

NRL- FLORIDA

rms -0.37jiS

SLOPE - 0.07/is/DAY

J I L 1

I I I I I 20 25 0 5 10 15 20 25 0 5 DAYS

10 15 20 25

Figure 10.42. Time transfer results via Timation II satellite

[140].

The results were comparable to Loran-C and por- table clock measurements within 1.5 /as and indi- cated a time-transfer capability of 0.5 fxs accuracy

[162]. TIMATION III, scheduled for launch in Fiscal

1974, is a considerably improved version of TIMATION II [163]. It will be visible over intercontinental

ranges for observation periods of ~2 hr; provide

limited use of pseudo-noise modulation signals at 1.580 GHz, and possess a memory which can store

orbital information. Considerable attention is given

275
the TIMATION crystal oscillators to compensate

for temperature changes and radiation effects as

well as lower the crystal aging rate. A TIMATION

satellite receiver has been developed and built; its cost estimate is $20,000, although quantity demand

should reduce this considerably.

(c) Defense Satellite Communication System

(DSCS)for TFD. The DSCS uses some 21 equatorial

drifting satellites (Phase-1 type drifting ~ 25°/day

at >32,000-km altitude [135, 152, 164]) for communication, and the system provides a precise time

mechanism for comparison of clocks at inter-continental military installations. The DSCS method is being used to successfully compare distant clocks

to less than 1 /as, replacing many expensive portable

clock trips.

With certain communications equipment the time

transfer requires no signal insertion or disturbance

of normal operation; the regular pseudo-random

code stream is transmitted, received, and matched

to give a measure of clock difference if the propagation delay is accounted for. Both two-way and one- way modes have been used to determine clock dif- ferences in the time transfer method (subtraction of

clock data). DSCS timing tests between Brandywine,

MD and the SATCOM facility at Helemano, HI

gave about 0.1 -/jls clock difference and a standard

deviation of 0.16-/ns for a series of 34 clock measure- ments in 1970 [152]. DSCS time transfer systems

have been developed for terminals not equipped

with regular communication modems (mini-modems)

[165]. Clock comparisons have been made between

short earth distances to about 0.2 /lis using the MiniModem equipment [152]. The DSCS operationally

transfers USNO time, via a microwave link to the

Brandywine, Maryland terminal, to points in Europe, USA, and the Pacific area to ~ 0.1 lis as shown in figure 10.43 [166].

FIGURE 10.43. TFD via Defense Satellite Communication

System (DSCS).

(4) NBS satellite TFD experiments. The high

accuracy and wide bandwidth at microwave carrier

frequencies of complex military satellite transmissions is at the expense of costly equipment which

is beyond the range of many users. Such high cost

of equipment prompted NBS to take a somewhat

different approach to still realize the potential of accurate time and frequency dissemination via

artificial earth satellites. An experimental satellite timing program has been in progress at NBS since

mid 1967 and is part of a continuing research effort to develop systems beneficial to a large number of

users. NBS has worked only with geostationary

satellites, and initially conducted two-way experiments using the NASA-Application Technology

Satellites (ATS) containing VHF transponders at about 150 MHz. With inexpensive receivers and

transmitters, accuracies of about 4 /us were reported

for these studies [143]. Basic ionospheric effects did not appear to limit the results. One-way satellite experiments, using the ATS transponder at VHF,

gave clock comparison accuracies of 10 and 60 /as for respective orbit positions a) at the time of

measurement, and b) for a one week advanced

prediction [149]. Recently, NBS has performed additional one-way

transmission tests with communications satellites such as LES-6 (Lincoln Experimental Satellite)

and TACSAT (Tactical Communications Satellite)

[154, 155] as well as the Application Satellite ATS-3 [157]. These satellites operated in the VHF

and UHF bands in the frequency range of 150 to 304 MHz. At these frequencies and with the power

of transmission involved, one is able to use small,

inexpensive antennas with a SNR more than adequate for the measurements. A pictorial view of the

master station and five receiving stations used in typical one-way clock synchronizations is shown in figure 10.44. The results of such measurements have

been given in table 10.9.

MASTER CLOCK AND TRANSMITTER

LINCOLN LABORATORIES

Figure 10.44. Experimental TACSAT and LES-6 satellite network 276
As noted earlier, the satellite positions used in the

NBS experiments have been based on orbital infor- mation supplied by the agencies controlling the

satellites. NBS investigated an alternative approach

which could prove adequate for many users. Tri- lateration techniques were used to locate a satellite through relay range measurements by three widely

separated stations during simultaneous transmission of timing signals. Concurrent with the trilatera- tion measurements was the synchronization of

clocks at other remote sites; the same timing signal was used for simultaneous ranging and clock syn- chronization. The accuracy of the range determination depends upon the accuracy of the clock syn- chronization at the remote sites as well as the range

measurement resolution. (A rather low range resolution of 3000 meters was obtained for these experiments.) From the determined satellite position,

propagation delays to earth points can be computed;

using this approach, it was possible to synchronize

clocks other than tracking site clocks to about 40/u,s over intercontinental distances using TACTAC and

LES-6 at two different times [155]. It is estimated

that the technique could provide accuracies near

1 to 10/x.s if one used precisely synchronized clocks

and improved the range resolution; i.e., less uncertainty in the equipment delays.

A similar technique has been reported by Russian

scientists; they used an ISZ type MOLNIYA-1

satellite (in an inclined elliptic orbit at low to high

altitude [136, 167]) together with the "orbit" tele- vision system to synchronize remotely-located time

scales [115]. The satellite coordinates were deter- mined at the moment of time synchronization from

three widely separated points; i.e., Moscow and

Vladivostok in Russia and a reception point of the

"orbit" television signals in France. The experimental results, after establishing earth coordinates

and measuring delays, showed synchronization of

time scales to about IOais over earth distances of

8000 km. The technique is of value for synchronizing remote sites which are inaccessible to direct TV

reception [115]. At this point we will describe some concepts and

techniques which have evolved from recent experimental work at NBS with the ATS-3 satellite. A

promising experiment, ending in late 1973, consisted

of two 15-min broadcasts (5 days a week) with a WWV/WWVH type format from ATS-3 [157]. The

broadcasts were "on time" with reference to UTC

and originated at the NBS Laboratories at Boulder,

CO. The signals were transmitted (uplink) to the

ATS-3 satellite via a 149.245 MHz carrier; they were transponded (downlink) at a carrier frequency

of 135.624 MHz to a wide earth coverage area in- cluding North and South America, large parts of the

Atlantic and Pacific Ocean and parts of Western

Europe and Africa.

The 1971-73 experiments show a potential for various accuracy levels of service; three have been

demonstrated and will be described briefly. First,

a coarse time check is possible through simply

listening to the time ticks or voice announcements

broadcast from the satellite. These signals are accurate to about 0.25 second — the signals left Boulder on time but were delayed in traveling to the

satellite at ~ 36,000 km altitude and back to earth. (The transponder delay is insignificant at this level.) The second level of accuracy is attained by

measuring the difference between the arrival time

of the received "ticks" and those generated by a

local clock. From oscilloscope measurements one

can achieve 10-ms resolution between the received

signal and his clock by visually averaging the posi- tion of a positive-going zero crossing of the first cycle of the tick. However, as in all one-way satellite measurements, allowance must be made for propagation delay. To overcome this problem NBS pre- pared path delay contours on ATS-3 coverage

maps, based on orbital elements issued by NASA, as shown in figure 10.45. From such contours one can

read the propagation delay from the Boulder trans- mitter to the satellite and from the satellite to an

earth receiving point. Satellite movement obsoletes

these contours; updated contours were published

monthly, together with receiving antenna pointing

charts which gave elevation and azimuth angles to the satellite anywhere within the coverage area

[42]. Application of such chart corrections to the

oscilloscope readings provides timing to a few

milliseconds.

The third level of service provides timing to better

than 50 /as. This technique is predicated upon the

accuracy of NASA's orbital elements which permit

predicted propagation delays from Boulder to any

point in the satellite's view to within 10 to 20 tis. Voice broadcast gave the satellite's longitude, lat- itude and a radius correction. To take advantage

of this capability for the benefit of the user, NBS

designed a special purpose delay computer in the

form of a circular slide rule [168]. Figure 10.46 shows

a picture of the prototype delay computer. To use

this computer one enters the satellite position infor- mation together with the latitude/longitude coor- dinates of the receiving point and determines the

propagation delay to within 10 to 20 tts. The differences between theoretical delay meas- urements and slide rule calculations at NBS Boulder

from the transmitter— satellite — receiver are shown

in figure 10.47. The slide rule calculated delays

agree with the theoretical computer delays to several

microseconds over a relatively large range of latitude

and longitude. The results of these ATS-3 experiments are reported in detail by Hanson and Hamilton

[157]. Figure 10.48 gives both a block diagram and

photo of the receiving equipment that could be used

in the ATS-3 timing experiments. The receiving

equipment can be simple and inexpensive; for op- timum results it included a 10-dB gain Yagi antenna,

low-noise transistorized preamplifier and a modified FM receiver which costs ~ $150.

The experimental ATS-3 satellite broadcasts

have proven that concepts of simplicity, various

277
Figure 10.45. ATS-3 satellite coverage map with propagation delay contours (1700-1715 GMT,

March 1973).
SUB SATELLITE POINT

(SSP) = 0.518°N, 68.601°W

10 AV . 7 0° LAT. rms

AV . -

AV . 50° rms

AV .

20'

AV

AV

AV .

AV,

1 0 20 30 40 50 60 70 RELATIVE LONGITUDE

1 .67ys

6 AOys

.12gs

4.19ms

2 .99us 5.69ms

1 .49ys

5.77ms

.69ms

4 .80ms

2 .40ms

6.48ms

3 .54ms

5 .96ps

. 58ms

4 .86ms

Figure 10.47. Theoretical propagation delay minus slide-rule calculated delay (systematic errors removed).

TIME INTERVAL COUNTER

OSCILLOSCOPE

PREAMPLIFIER

EXT.

FM TRIG. RECEIVER

VIDEO VERTICAL

OUTPUT INPUT

1 *

i pps cr*" REFERENCE

DELAYED

1 PPS DELAYED OUTPUT

(SLEWABLE DIVIDER)

(SWEEP CALIBRATION ONLY

)

| DELAYED

1 1 kHz

FREQUENCY STANDARD

AND CLOCK

Figure 10.48. Block diagram and photo of equipment for ATS-3 satellite experiments.

279
levels of accuracy, and reliability are achievable

with low-cost receiving equipment and are commensurate with the degree of the measurement

complexity. NBS may provide 24-h experimental

timing at some future time through a Department of

Commerce satellite. Many of the concepts and

techniques developed in these experimental pro- grams would be applicable to an eventual TFD

service via satellite. (5) Advantages and limitations of satellites for

TFD. The advantages and limitations are given in

Table 10.12. Advantages and Limitations of Satellites for TFD

Satellite Type rv\l A H vV dll Q ti tI aa cr** c fit s Limitations

Low-altitude orbiting satellite with on-board clock.

1. Worldwide (periodic) coverage is possible even

with one satellite (polar orbit).

2. Timing synchronization is available to an un- limited number of passive users within sight of the satellite at any one time.

3. Users do not require transmitters as in a two- way mode.

4. Short line-of-sight range between the satellite and the user gives a favorable SNR at high

elevation angles.

5. Clock differences can be determined between

receiving stations in a short time period with auxiliary communication.

6. This technique is capable of synchronizing world wide clocks to one primary time

standard.

1. The satellite dynamic motion causes variation

in the signal propagation delay and requires

correction for Doppler effects. Compensation

for propagation delay is a major factor for use

of these satellites in TFD; knowledge of orbit position is essential.

2. The availability of timing signals is limited to ~ 10 to 15 min per pass several times a day.

3. Accurate time comparison requires continual accounting for equipment delays.

4. The on-board clock has limited life and cannot be repaired or modified.

5. Clocks in orbit require monitoring and periodic

adjustment.

6. Operational military systems require expensive and complex receiving components which are impractical for many users.

7. Satellite power can fail and/or the satellites can be destroyed.

8. The system requires many satellites for redun- dant and frequent passes.

Radio-relay type satellites in synchronous orbit.1. There is continuous availability of timing

signals to a large area of the earth ( 1/3 of the globe).

2. Two-way modes using simultaneous radio transmissions over reciprocal paths need no

correction for propagation delays.

3. The system offers an attractive means for re- broadcast of standard frequency radio

signals to simultaneous receivers at high accuracy and low cost, using VHF-UHF

transponders.

4. The master clock is accessible at a ground

station and can be continuously referenced

to UTC(NBS).

5. Wide band microwave transponders are availa- ble which permit fast rise pulses and clock

synchronization at a receiver to less than

1 /us. This is at the expense of costly equip- ment, however.

6. The ionosphere-atmosphere portion of the

radio path is small in relation to the total path and causes minor degradation in the

line-of-sight VHF and higher frequencies.

7. System can replace expensive portable clock

trips.

1. Near world-wide coverage requires at least three

equatorial synchronous satellites.

2. Even synchronous satellites show some movement, and accurate orbital elements are required at the time of measurement for microsecond time synchronization.

3. The much longer radio path than that of the

low-altitude satellites requires higher trans- mission power and/or the use of high gain

directional antennas.

4. Synchronous satellites can be moved, thus changing the earth coverage area, or they may

be destroyed.

5. Synchronous satellites are considerably more

expensive to launch than low-altitude satellites. 6. Accurate time comparison requires knowledge

of equipment delays.

table 10.12 for the two categories of the lowaltitude orbiting clock and the synchronous radiorelay. In this evaluation one assumes that these

satellites are not launched or justified solely for TFD. (Synchronous satellites with on-board clocks

have been proposed but are not considered in this evaluation.) The net conclusion is that satellites offer an excellent potential of meeting the timing

needs of many classes of users at various accuracy

levels.

280
h. Microwave Time and Frequency Transfer (SHF)

The usefulness of this band for TFD has been

demonstrated by the TD-2 microwave system in the

USA and various systems abroad in long distance

routing of television signals; such techniques were

discussed earlier in Section 10.3.2. f. Two specific

examples of microwave TFD are now described.

Phillips et al., have demonstrated that time and

frequency can be transferred two-way at a frequency

of ~ 7 GHz between the Naval Research Laboratory

(NRL) and the USNO (line-of-sight path of 11.75 km

in the Washington, DC area) [169]. In the NRL/

USNO microwave experiment, NRL transmitted a 1-MHz signal, derived from a hydrogen maser, to the

USNO as shown in figure 10.49. This signal was compared to the USNO master clock; also, the

USNO transmitted time and frequency information

simultaneously to NRL by the algebraic addition

of a 1-MHz signal and 1-pulse per second, both in terms of the USNO master clock. Such a technique

enables continuous comparison of both phase (fre- quency) and date (time) at NRL. Phase resolution was found to be better than 10 ns and date transfer

ssO.l /x.s. A second microwave link between the

LSNO and the Waldorf Satellite Research Communication Station (path length of 32.2 km) also provided phase resolution to better than 10 ns. Such

a link to nearby Brandywine, MD will be used in connection with the DSCS network for disseminating T/F information to continental terminals [170]

(see sec. 10.3.2. g).

The NRL/USNO link has been operating for more than 3 years and shows no diurnal dependence

with little effect from seasonal or temperature

changes. Wet snow accumulating on the antenna

did adversely affect the results. The effects of highdensity air traffic crossing the transmission path at a local airport were minimal and of small conse- quence. The propagation delay is determined by a portable atomic clock. The carrier frequency stability was not critical, and the narrow beam width

minimized multipath error. The first information

received was by direct path so that the pulse lead- ing edge was used for timing when multipath reflec- tion occurred.

The Jet Propulsion Laboratory (JPL) is also pur- suing microwave TFD to link 3 remotely located

precision timing systems to a master timing source

over distances up to ~ 16 km at the Goldstone Deep

Space Communications Complex (GDSC) [171]. They transmit a 1-pps of 50 ^s duration at baseband

frequencies generally above 2.5 MHz. The rise time

of the return pulses is ~ 0.4 /xs between 10 and 90

percent of the initial slope as compared to half that time for the input pulse. Over a period of time some

microwave system drift was noted, up to ±200 ns. These changes were cyclic and believed to be

related to weather anomalies such as relative humidity, temperature changes, and dust storms. In

a typical 10-day period the total cyclic excursion

did not exceed ~±20 ns. This microwave system

presently links two stations in the Goldstone complex to a relative synchronization accuracy of better

than 1 /xs.

NAVAL RESEARCH LABORATORY

NRL

11 .7 5 km PATH TOTAL TIME DELAY 40.6ms

PHASE ACCURACY lOus

NAVAL OBSERVATORY

TRANS. FREQ. POWER TRANSMISSION

7.137 GHz

1 WATT DERIVED 1MHz SIGNAL FROM HYDROGEN MASER

TRANS . FREQ. POWER TRANSMISSION

7 .415 GHz

1 WATT

1MHz SIGNAL AND

1 pps FROM MASTER CLOCK

Figure 10.49. NRL/USNO microwave links.

281
Advantages of Microwave TFD

• The system provides extremely accurate transfer of frequency and time information, i.e., phase resolution to ~ 10 ns and time to 0.1 fxs.

• System is reliable generally showing small

effects from diurnal changes, propagation

anomalies, weather, or temperature.

• Once established, the measurement system is simple and straight-forward.

• Simultaneous time and frequency measure- ments are possible between remote sites of

limited range (~ 40 km) with good reliability.

• System requires very low power of radiation

(~ 1 watt).

• Multipath causes small interference and carrier frequency stability is not critical (precise

modulation).

Limitations of Microwave Time and Frequency

Transfer

• Initial cost of microwave equipment is high.

• The system is limited to line-of-sight distances

of maximum range ~ 40 km.

• Accumulation of snow or ice on the dish anten- nas can seriously affect the microwave

transmission.

• Only a very limited number of users can be

served with a microwave T&F system because

of geometric limitations of the transmission

beams.

i. Commercial Radio TFD Techniques

The idea of providing standard frequency signals

from commercial radio broadcasts is not new,

having been employed in the United States in the

middle 1920's [172]. In 1927 there were 13 so- called standard frequency stations broadcasting

in the range of 17 to 1000 kHz and referenced to standards at the National Bureau of Standards at Washington, DC. The number of stations was

limited to those which could be received regularly

and reliably at NBS; the results of these measure- ments were published monthly. Additional "constant frequency stations" were designated when

broadcast frequencies were maintained close to licensed values. Of course the accuracies of these

signals were many orders of magnitude less than now obtainable; they do, nevertheless, foreshow a

potential means of standard frequency dissemination possible today.

About 36 years ago a commercial station in Nashville, TN stabilized their broadcast carrier at 650 kHz to an accuracy of ~ 1 part in 106

. They used

a multiple temperature-controlled oscillator which was periodically checked with WWV at Beltsville,

MD [173]. Within the last several years a CCIR

member encouranged this clear channel station to improve the precision control of their broadcasts.

They have demonstrated that, today, a commercial

broadcast station can transmit precise time and

frequency information traceable to NBS and at relatively low cost [174]. The carrier frequency is phase locked to the WWVB received signals at 60

kHz through division, multiplication, and long-term

integration, and the resultant frequency stability

is ^ 1 X 10~9

. In addition, a 1-kHz time pulse signal

of 400 ms duration is broadcast every 15 minutes.

This time is referenced to WWV, with allowance

made for propagation delay, and is considered

accurate within the range of 1 to 10 ms [175]. A lowcost receiver frequency-marker-generator ($100) has

been designed and built; this unit will receive the

650-kHz signal, to which a 10-MHz crystal oscil- lator is locked, and produce marker pulses from

10 MHz down to audio frequencies. Initial tests have shown satisfactory results from Nashville to both Evansville, IN (~ 225 km) and to Boston, MA

(~ 1500 km). Generally, the signal is stable during

daytime, but multipath adversely affects it at night.

The received accuracy of the broadcast carrier

within groundwave distance should be equivalent

to that as transmitted in the local Nashville area; received accuracies at skywave distances will be

degraded in a similar manner as MF transmissions.

Advantages of Commercial Broadcast TFD

• Simple, cheap and readily available receivers can be used to obtain time and frequency infor- mation to relatively high accuracy within ground wave distance of a commercial broadcast station. The commercial station thus serves as a secondary standard which is directly traceable

to NBS standards of time and frequency.

• The commercial broadcast station can perform

an additional service to the public at small

additional cost to itself through NBS lowfrequency broadcast reference.

• The service would be of special value to a great

number of users who do not require the full accuracy capability of the NBS standard time

and frequency broadcasts.

• A network of frequency-stabilized commercial

broadcast stations located throughout the larger

populated areas of the U.S. could provide

secondary time and frequency references to a

large percentage of the population.

Limitations of TFD via Commercial Broadcast

Stations

• The high accuracy signals generally are limited

to ground wave range around the transmitting antenna.

• Special techniques are required for high accu- racy comparisons through skywave reception of commercial broadcasts.

282
j. TFD from VHF Signals Reflected from Meteor Trails Both in the United States and Russia, investigators have reported that meteor burst links will support precise time synchronization and frequency

comparisons between remote sites via reflection of

VHF signals [176-178]. Sporadic meteors, entering

the upper atmosphere about 120 to 80 km above the

earth's surface, evaporate and form a thin ionized

trail, ~ 15 to 50 km long with a typical lifetime of

fractions of a second (100% > 150 ms and 2% ~ 1.5 s [179]); durations up to a minute, however, have been

observed [180]. Meteor scatter forward reflection

provides optimum support at the lower portions of

the VHF band and the maximum great circle range,

limited by the earth's curvature, is ~ 2100 km.

Sporadic bursts occur randomly with some 40 to 150

usable meteor trails available per hour. Latorre

indicates the minimum time between bursts as one second with only about 5 percent of the intervals

between bursts exceeding 100 s [179]. The number

of bursts predominate in July with a minimum in February. There are orientation restrictions in transmission and reception of the VHF signals, and

directional antennas generally are used. Reflections

are specular (angle of incidence equals the angle of

reflection at the grazing point of the meteor trail), and the time and frequency measurements depend

upon mutual reciprocity of the reflected VHF signals.

Sanders et al., report an equivalent rate in change

of the propagation path delay as 0.137 (xs/s for operation at 46.55 MHz [177]. Such a change, even for a

1 ms time interval between alternate reflections from

a common meteor trail, represents ~ 0.1 ns and

would be insignificant in precise timing.

Most of the time synchronization studies via

Meteor Burst in the U.S. were made between

Seattle, WA and Bozeman, MT during the 1960's

[176, 177, 181]. The great circle path distance was

880 km and a 46.55-MHz carrier frequency was

used at a peak power of ~ 1 kW. In one mode of

operation both stations transmitted 50 to 100 pps, derived from local clocks which were coarse syn- chronized to several ms through WWV broadcasts.

At the occurrence of a usable meteor trail, each site simultaneously receives pulses transmitted from

the opposite station since they traveled the nearly

reciprocal path and experienced the same propagation delay. The time relationship of the received

pulses to the local clock pulses provides a measure

of the time difference, 8, between the clocks at the

two remote sites. Consider the simplified timing

diagram in figure 10.50. Transmitter No. 1 transmits

a square wave pulse with positive-going leading edge

at t = 0; at the time t = 8, transmitter 2 also trans- mits a pulse. While a meteor trail is reflecting, sta- tion 1 receives a pulse at time To + 8 and station 2

at a time To — 8 as measured at stations 1 and 2 respectively (where T0 is the propagation delay

between a transmitter, meteor and receiver). As

different meteors with varying paths are used, To

will vary but 8 will remain essentially unchanged

RECEIVER

NO. 2

n

TRANSMITTER

NO. 2

r

RECEIVER

NO. 1

TRANSMITTER

NO. 1

= CLOCK DIFFERENCE

= ONE WAY PROPAGATION TIME

FROM TRANSMITTER VIA METEOR

TO RECEIVER

FIGURE 10.50. Simplified meteor-burst timing pulses.

for precise atomic clocks. The difference between

the readings at the two stations cancels the propagation delays and yields twice the clock error; the sign

of the difference shows the sense of one clock error

in terms of the reference clock. A comprehensive

analysis must include allowance for transmitter

equipment and receiver delays as well as the degree

of reciprocity in the propagation delays. It is felt that these delays can be determined ultimately to several hundred nanoseconds [182]; use of identical

equipment at each end of the path would minimize

the delay determination. The meteor burst method is unique in that the actual propagation delay is measured and can be known.

Different modes of operation have been tried,

including both manual and automatic systems.

Sanders et al., from timing measurements over a 30- day period, determined the frequency offset bvjvo

between two remote frequency standards; these

data agreed with VLF/LF phase measurements to several parts in 1010 [177]. March et al., has shown

the inherent phase stability of the meteor-trail, reflected VHF signals and reports that time syn- chronization via this method has fis capability [181]. In 1971 it was reported that the Khar'kov State

Scientific Research Institute of Metrology (Kh

GNIM) compared time scales with the State Standard Scale of the All-Union Scientific Research

Institute of Physicotechnical and Radiotechnical

Measurements (VNIIFTRI) via meteoric reflection of radio waves [178]. Their method is similar to that previously described except that they employ duplex

transmission and retransmission of different pulse

trains between two remote sites. This permits an independent readout of the clock difference. 8. at each station. The method also minimizes equipment

delay errors provided that identical equipment is

283
used at each station. The system uses a 72.0-MHz

carrier frequency with a pulse power of 30 kW and

a directional antenna; pulses are of 4 /as duration

and grouped into code pulses — 4 for interrogation

and 7 for reception. The marker repetition rate is 10 ms. Measurements were made at 0100 to 0400

(Moscow time) to eliminate interference from AM

and FM broadcasting stations, usually off the air at this time. A series of 12 timing measurements for one day over a 4-hour period showed deviations less than 0.8 fxs and standard deviations of 0.2 to 0.3 /us.

Advantages of VHF Reflection from Meteor Trails

for TFD

• The phase stability of the VHF propagation

enables comparison of time scales to high

accuracy (< 1 ^ts) and frequency to parts in 10 11

at remote sites up to several thousand km apart.

This distance probably could be extended

through intermediate repeator stations.

• The technique is based on the natural event of

meteor bursts and from this standpoint is independent of man-made devices or systems.

• The system would be useful for time and fre- quency comparisons at remote sites such as the far north and/or inaccessible islands where

other techniques are unsuitable or unavailable.

• The technique does not appear to be limited by

the propagation, and lack of delay reciprocity seems to be minimal.

• Portable equipment could be used as accurate knowledge of path distance is not required.

Limitations of the Meteor Burst System for TFD

• The accuracy of the system is equipmentlimited by bandwidth, S/N, and the ability to measure actual component delays.

• The number of potential users is severely

restricted because of the directional nature of the propagation.

• The meteor bursts are sporadic, unpredictable

as to time of occurrence, and of variable short

life. (Some of these limitations can be over- come by statistical techniques and coherent

detection.)

• Reception and pulse recognition is hampered by

multipath effects, such as Sporadic E, aurora, multiple meteor trails , or changing trail patterns.

These effects will vary with such factors as season, time of day, location on the earth,

operating frequency, and the orientation of the

meteor trail (reflections are specular).

• The meteor burst channel is noncontinuous,

and it is indeterminate when time and fre- quency comparisons can be made.

• Curvature of the earth's surface limits the maximum great circle distance between sites to ~ 2100 km.

• Additive noise can adversely affect the leading

edges of the received pulses causing uncertainty in the pulse position measurements.

• The necessary equipment is somewhat complex with relatively high initial cost.

10.3.3. Advanced T/F Systems Using Radio

Techniques

Varied types of advanced systems with primary

or related time synchronization capability, have

been operated and/or proposed within the last several years. Several of these such as very long

base interferometry (VLBI), the "moon bounce"

(lunar radar) synchronization method, and aircraft

collision avoidance systems (ACAS) are considered

briefly to acquaint the reader with their capabilities

and characteristics.

a. Very Long Baseline Interferometry (VLBI) Time

Synchronization

Within the last several years, a new technique of

radio interferometry has evolved whereby a point source of radio radiation can be received and co- ordinated at independent antennas, separated by

thousands of kilometers, through precise timing

available with atomic frequency standards [183-

186]. Initially, long baseline interferometry was

used for precise angular measurements of extraterrestrial radio sources. The increased sensitivity

of VLBI, resulting from long, widely-separated baselines with independent coherent time references at each end, gives impetus to various scientific experiments and proposals; included are studies of global

geodesy, radio astronomy, tidal oscillations, continental drift, polar motion, earth rotation, relativity

measurements, and global time and frequency

synchronization [187-190].

Let's look initially at the basic concepts of VLBI.

Figure 10.51 gives the geometry of VLBI in simplified form. Two antennas, Nos. 1 and 2, are separated on earth by a distance D, and this baseline forms an

angle, 6, within a line to the source of electromagnetic radiation. With extraterrestrial radio sources,

the wave front is considered plane to the earth

surface and traveling with the speed of fight in a vacuum (disregarding at the moment atmospheric

RADIO STAR SOURCE

TY OF LIGHT

RECEIVER RECORDER

ATOMIC CLOCK 1

RECEIVER

RECORDER

ATOMIC CLOCK 2

Figure 10.51. Geometry of VLBI receiving sites. 284
effects, etc.). At points A and B, the signals are

identical; however, the phase of the received signals

at antennas 1 and 2 will differ by the delay time,

Afv . (Atv is a key factor in nearly all VLBI proposals

and experiments, and its determination results from many measurements of various point sources

at different observatories with a complicated statis- tical structure, involving many parameters.) Shapiro

and Knight [188] point out, however, that the various

geophysical effects proposed for study all have

characteristic time variations in the observed A£v , and extraction of the estimated relevant geophysical

quantities is feasible. At a given antenna, the received signals are con- verted to video frequencies, tape recorded on magnetic tape, and time referenced to local atomic

clocks. The recordings from two widely separated

and independent receivers are then brought to- gether and cross correlated through computer

reduction and manipulation; maximum cross cor- relation occurs when the recordings are offset in time by Afv for the various frequencies of radiation

(essentially microwave band), based on synchronous

time sources at both antenna sites. Corrections are made for the earth's orbital motion and Doppler

shifts from the earth rotation. In one series of

measurements in January 1969, reported by Shapiro

and Knight [188], an 845-km path separated the

MIT 120 ft. (-37 m) diameter Haystack dish

antenna in Tyngsboro, MA, and the National Radio

Astronomy Observatory (NRAO) 140 ft (~43 m)

diameter dish antenna in Green Bank, WV. The

measurements were at L-band (1.6 GHz) of 24 hours

duration, and included observations of sources 3C

273, 3C 279, 3C 345, and 3C 454.3. The experiment

included 30 different measurements of Afv from

these four distant objects to determine some 12

parameters. The error in determining each Afv was

estimated as 1 ns, and the standard error in de- termining the baseline, d, as about 1.5 meter (5 ns). This is tempered with the statement that the "true

error may be somewhat greater." Hydrogen masers

were used at both receiving sites. The worldwide

net of radio astronomy stations that have participated in VLBI experiments are shown in figure

10.52. More recently, VLBI experiments were per- formed at a baseline length of 8035 km between

NRAO, Green Bank, WV and the Crimea Astro- physical Observatory on the Crimea peninsula,

USSR [191]. With such promising results, it is not surprising

that suggestions are made to use the VLBI tech- nique in reverse to synchronize remotely located

clocks; i.e., to provide precise time transfer via a common source [186, 188, 190]. Such a technique

requires knowledge of the geometric delay, Afv

. Thus, recordings of signals from a point source, received at two widely separated fixed points and

referenced to precise frequency standards, could

be time shifted to obtain maximum correlation. The

Figure 10.52. Worldwide net of radio astronomy stations participating in VLBI experiments.

difference between this time offset and Afv is essentially the clock difference. VLBI time synchronizations are limited by the precision in the Afv determinations; Rogers and Moran state that "without first using the interferometer as a survey instrument, the

geometric delay can only be computed reliably to within 20 nanoseconds" [190]. Uncertainties in A^

occur from errors in estimating positions of both the source and receiving antenna as well as variable

propagation delay of signals through the atmosphere

[192]. It is predicted that intercontinental syn- chronizations of precise clocks can be made via

VLBI techniques within the range of 1 to 50 ns

[186, 190, 192]. Recently, frequency differences

between two hydrogen frequency standards were

determined as several parts in 10 14 through VLBI

measurements over a 16-km baseline; (10-min to 4 h measuring period [193]). Lunar and/or satellite beacons as well as moon based antenna have been

proposed for increased sensitivity of VLBI [188].

Advantages of VLBI Clock Synchronization

• Clock synchronizations to nanoseconds or better at widely separated intercontinental

distances appear possible.

• Although the present VLBI systems are fixed- base, portable installations with transportable

antennas 3-5 meters in diameter, could be

situated globally for time synchronization

purposes [194].

• At the 50-ns region the results are relatively

independent of ionospheric and atmospheric

effects [190]. Ionospheric effects can be re- duced through the use of frequencies above ~ 5 GHz [195].

285
• The actual sync measurements require short

integration times (in order of minutes), although

the data reduction, correlation and processing

may take days. Rogers and Moran [190], however, suggest that suitable HF links could be

tied into a computer to obtain nearly real-time

synchronization.

• Radio astronomy sites are geographically well

known and already the installations include

much of the equipment required for VLBI.

• Radio astronomy sites could provide primary

time synchronization referenced to a national

or international time scale.

• Clocks can be compared independent of physical transfer, and the synchronization possibilities could be extended to aircraft or ships

at sea through appropriate communication links

and computer facilities.

• Apart from clock synchronization, VLBI

methods offer promise of precisely determining

many geodetic and radio astronomical factors

as well as relativity effects.

Limitations of VLBI Time Synchronization

• The system is elaborate, cumbersome and

requires expensive instrumentation, such as high-speed, digital tape recorders, low-noise

microwave receivers, and auxiliary equipment.

In addition, the data must be reduced and cross

correlated by computer analysis. Equipment

costs, apart from computer time but including

atomic clocks and dividers at an observatory

with a large dish antenna is estimated at about

$145,000.

• The method is limited to the extent to which

the geometric delay, A£v can be determined.

This determination is based upon systematic

errors in source positions, receiving site locations, baseline length, and sidereal time.

• VLBI is subject also to errors from atmospheric

delay caused by variation in water vapor content, ionospheric and plasma phase delays,

signal to noise ratio of the receiving system,

instability of atomic frequency standards during

measurement (timekeeping for maintaining

minimum "clock offset errors" between inter- ferometer sites may require 8h clock stability

of 0.1 ns; many measurements now are inte- grated over 3-min periods), and changes in antenna orientation. Minimum atmospheric

errors occur when the zenith angle is small at both terminals; however, separations at inter- continental distances at various latitudes give

different elevation angles at the receiving

antennas, and high accuracy measurements

at such locations would require atmospheric

correction.

• The system cannot determine time through

single frequency recording of a given radio

source, but requires wide band measurements

to resolve the Afv factor through sampling

many widely-separated narrow band frequency

channels [196].

• Clock synchronization via VLBI is now at the

experimental and proposal stage. While the

technique shows great promise, much work yet

remains in making measurements at many

sites, encompassing diverse global baselines

at different latitudes, from various extraterrestrial sources to adequately define the geo- metric delay, Afv , and to simplify the reduction and correlation processes of the data

analysis.

• Clock synchronizations would be delayed after the fact.

b. Moon Bounce Time Synchronization (MBTS)

This technique, also called a lunar radar time

synchronization system, was devised and designed

by the Jet Propulsion Lab, Pasadena, CA [197-199].

The system is in operational use for deep space

tracking and synchronizes clocks within 20/xs or better at 5 worldwide tracking stations with a master

clock at Goldstone, California, through reflections of radar signals off the moon.

Basically, the MBTS method uses biphase modulated, X-band radar (8.4501 GHz) signals which are

transit- time and Doppler shift corrected, bounced

from the moon, and received on time at tracking

stations. A primary concept of the system stresses simplicity of the receiving antenna and the receiver

operation at the tracking site; the moon must be

simultaneously visible to both the transmitter and

receiver for at least 10 minutes daily. This latter point coupled with the necessity of computer cor- rections for transit time and Doppler shifts at a given station, dictates that only one station can be

synchronized at a given time period.

A simplified diagram of the MBTS system is shown in figure 10.53. Briefly, the essentials of

operation are as follows:

(1) The X-band transmitted signal is pseudonoise (PN) modulated; it is both frequencycompensated for Doppler shifts at the receiver

and time-advanced by 2-3 seconds for propagation time delay determined by a computer.

(2) The PN code is transmitted at one minute

intervals and scans ±30 (is in l-/xs steps.

(3) The transmitted signal is directed at and re- flected from the moon at an effective subradar point and received and compared at the

remote station with a PN code generated by

the local clock and identical to the trans- mitted code.

(4) The offset between the received and locally

generated code is determined by cross cor- relation between the two as shown on a strip

286
TRANSMITTER CHARACTERISTICS

FREQUENCY : 8.4501 GHz iDOPPLER OFFSET

POWER : 100 kw (AS OF 1971) ANTENNA: 30 FT (9m) PAROBOLA

ANTENNA GAIN: 56 dB ANTENNA BEAM WIDTH: 0.27° ANTENNA CONTROL : ±0.015° OSCILLATOR CONTROL:

Cs & Rb FREQUENCY STD

TRANSMITTER LOCATION GOLDSTONE, CALIF.

X-BAND TRANSMITTER

RECEIVER CHARACTERISTICS

FREQUENCY: 8.4501 GHz (FIXED TUNED)

S/N RATIO: 9.4 dB ANTENNA: 4 FT (1 .2m) PARABOLA

ANTENNA GAIN: 38 dB ANTENNA BEAM WIDTH : 2.1° RECEIVER GAIN: 142.5 dB RECEIVER BANDWIDTH: 10 Hz OSCILLATOR CONTROL: Rb FREQUENCY STD

RE C E I VER OUTPUT RECORDER

PROGRAMED OSCILLATOR

RECEIVER

CLOCK

RECEIVER LOCATIONS

SPAIN AFRICA AUSTRALIA (2) CALIFORNIA (USA)

LUNAR EPHEMER I

S

MASTER

CLOCK

RECEIVED CODE CORRELATED LOCAL CODE JU L_n_nj LTTJTJ LP UNCORRELATED LOCAL CODE

Figure 10.53. Simplified diagram of MBTS (Lunar Radio) system.

chart recorder at the receiver. Thus, maximum correlation occurs when the two codes

are in coincidence; typically, this point occurs

within the 60-second scan of 1 /x.s/second

(± 30 fis overall) and gives the time differ- ences between the master and receiver,

provided the propagation delays, Doppler

shifts, etc., are correct. If the receiver clock

has an error in excess of ± 30 fis or if there is a clock failure, one can resynchronize to 10 ms through radio standard-time transmissions

such as WWV. The Goldstone control facility can change the transmission code rate scan

to 10 or 90/x.s/s thus giving a search range

flexibility of up to 5400 /is. This technique

permits setting a clock within 10 ms of true time and synchronizing to the original accuracy

of ~ 20 us by scanning through 3 trans- mission periods.

Some interesting work reported by Higa and Ward

[200] gives evidence of lunar topography causing

fluctuations in the MBTS method. Librations of the moon cause the subradar reflection point to move

from hills to valleys within the lunar period of 28

days; this front cap can be considered as a complex

surface about 180 km in diameter which moves from

day to day. Higa and Ward, through meticulous

calculation, determined the varying altitudes of the

equivalent frontal cap for a three-month period in 1970 and converted these distances to equivalent

propagation delay times. At the same time, MBTS

measurements were made between the Goldstone

transmitter and a receiver at the USNO. Figure

@ 10 us REMOVED FROM THESE POINTS A RADAR MEASUREMENT — CALCULATED

8 -

-8 -

1 5 10 1 5 20 2 5 1 5 10 1 5 20 2 5 1 5 10 1 5 20 25 MAY JUNE JULY

1970

Figure 10.54. MBTS (Lunar Radar) results at Goldstone, CA

(Courtesy Jet Propulsion Laboratory).

10.54 gives the results, and a very high correlation

exists between the two sets of measurements. It

is concluded that the MBTS accuracy can be improved from about ±20/is to ±5/i.s through corrections for lunar topography. Much work has been

reported by JPL in the prototype work, implementation, and operational use of the MBTS method

[201-203]. Higa lists advantages and limitations of

the MBTS [198], some of which appear below:

Advantages of MBTS for TFD

• MBTS can provide ±20/ts accuracy as proven

by portable clock measurements. With further

improvement and lunar topography corrections the technique shows an accuracy potential of ±5/Lts; as such it could provide worldwide time synchronization to widely separated

clocks.

287
• Varying ionospheric or earth atmosphere

propagation effects have minimal influence on

this TFD system.

• Receiving sites maintain atomic frequency

standards and time scales which can provide

fxs timing related to NBS or USNO time to about ±10/is and can serve as time reference

stations for portable clock calibrations.

• The moon is likely to hold its orbit indefinitely,

its position can be determined and predicted

with precision, and it passively reflects radio

signals in contrast to the limited and inherent

electronics of artificial satellite transponders.

• Accurate /as measurements require a relatively

short time period (about 10 min).

• The receiver operation is simple and requires

a minimum of man-power and maintenance.

The complicated computer programming for continuously updating the ephemeris and

Doppler delays is performed at the transmitter,

and these functions are independent of the

receiving site.

• The system is capable of resetting clocks on

time provided rough synchronization to about

10 ms can be obtained by other means such as HF radio time broadcasts.

Limitations of MBTS for TFD

• Receiver systems are expensive (about $50,000

per unit); however, Baumgartner [197] states a simplified receiver could be built for about

$15,000.

• The moon must be in common view of both the

transmitter and receiver sites for T/F measurements. The time period of common views for worldwide sites can vary from ~ 10 min to several hours per day; there are variations also

at monthly intervals as well as every 19 years.

• Propagation delays must be known between the

transmitter and a receiver site (ephemeris

data) well in advance of measurements.

• Coordination with JPL and both the USNO

and NBS would be required for time synchronizing a remote site via moon-bounce to UTC(USNO) and/or UTC(NBS).

• The system is subject to various systematic

errors, such as ephemeris discrepancies

(present accuracy can predict moon's center

of gravity to 150 m which could cause a time

error of about 1/u-s), variation in reflection

points on moon (roughness), errors in station

location, unknown equipment delays, code

jitter and noise sources. The variance of

all these errors is felt to fall well within ±10/is

limits [204], however.

• Fixed station reception at known geographic

sites is required for time synchronization; as such, system is unsuitable for synchronizing

clocks at nonstationary or portable sit s.

• Only one receiving station can be synchronized at a given time period.

c. Aircraft Collision Avoidance System (ACAS)

Disastrous collisions between flying aircraft over the past decades, coupled with ever-increasing

aircraft congestion, have aroused much public concern and shown the need for better air traffic control. Culminating many years of research and

development, the ATA (Air Transport Association —

composed of airlines, manufacturers, and govern- ment representatives) has proposed a time and

frequency collision avoidance system (TF-CAS)

[205, 206]. In its present concept, the TF-CAS

is complex, expensive and specialized. Because the

system has varied and imminent potential for time

and frequency dissemination for the non-aircraft user, it is included with a brief description. For

in-depth detail, the reader is referred to publications

in the open literature [207-211].

Basically, the proposed ATA CAS is cooperative

(all aircraft are equipped and carry precision oscillators); will perform in aircraft densities > 1000

in number within 250 miles (—400 km) or line-of- sight; and will protect aircraft operating at speeds

as high as Mach 3, up to altitudes of 80,000 ft. (24 km). The system is T/F referenced and predicated on each participating aircraft maintaining time

synchronization < 1 /is [212, 213]. Prime synchronization is initiated by master ground stations; it can be maintained by ground stations and/or

other aircraft through a hierarchy classification up

to ~ 40 units, which, dependent upon their time

degradation, can give or receive time information.

The ATA proposal provides for a time-ordered

format of 2000 message slots, each of 1500-/1 s duration, repeated every 3 seconds. Each aircraft or ground station is assigned particular message

slots (for transmission of their CAS data) which

are switched sequentially at 5-MHz increments at L-band assigned frequencies in the range of 1.592-

1.622 GHz. A simplified CAS fine time synchronization is diagrammed in figure 10.55. TF-CAS,

relying on both precise time and frequency syn- chronization, automatically provides one way Doppler ranging, closing rate determination, and altitude difference measurements between aircraft. The

basic criterion for determining collision potential

is the "tau" (t„) parameter, the ratio of reported

range to closing rate or time to nearest approach or

collision projected under existing conditions. Its value is the key to no action, or positive instruction

to either climb or descend with a warning period of

60 s or less. As presently conceived, Ta is only as good as the time synchronization of the on-board

clocks, considered as a common time reference

between aircraft (0.1 /as insures ranging accuracy

of about 100 ft. or 30.5 m). The system can use

288
AIRCRAFT TRANSMITS IN APPROPRIATE SYNC CHANNEL AIRCRAFT RECEIVES

CODED SYNC SIGNAL

GROUND STATION REFERENCE TIME

9 P PROPAGATION DELAY

Figure 10.55. Simplified CAS fine time synchronization.

crystal clocks in aircraft (stability of 1 X 108 or

better), provided sufficient repetitive resynchronizations are made at least every 3-min to insure

overall synchronization to ~ 2/u.s [214]. An atomic

clock has recently been developed for airborne CAS

which can extend resynchronization time to more

than 28 hours [215]. Such clocks would be ex- tremely valuable and almost necessary for long, oversea flights.

A commercial TF-CAS incorporating many of

the ATA recommended features has been developed

and shown successful operation since 1965 for some 17,000 flights, centered around one ground

station [214]. As presently proposed, time syn- chronization is zoned around ground stations with

other aircraft in the vicinity supplying backup

synchronization. As a plane leaves a given zone, supposedly no time degradation would occur at re- synchronization with a new ground station. It has been reported that a network of some 60 ground

stations is planned by the FAA to adequately

cover the continental U.S. [210]. Eventual worldwide networks are implied in the long range plans.

A major problem will be the synchronization of such

ground stations to within 0.1 /lis of each other, and

considerable study is now occurring in this area

[216]. A typical ground station timing system has

been suggested by Perkinson and Watson [214]

and is shown in figure 10.56. Besides the collison avoidance, traffic control,

and navigation/communication aspects of T/F-CAS,

Perkinson and Watson also point out its potential for TFD [214]. Three particular areas are mentioned:

(1) walk-in service; (2) passive reception; and (3) active participation. Ground stations, considered as reservoirs of precise standards referenced to national

standards, could provide T/F synchronization of

portable standards on a walk-in basis. The passive

reception of CAS radio signals within line-of-sight of a ground station would provide a submicrosecond

CESIUM 8EAM FREQUENCY

STANDARD

TIME/ FREQUENCY MONITOR

CAS TRANSMITTER

RECEIVER

1 600 - 1 61 S MHz

STATION CLOCK

UTC

MONITOR BUFFER

AND COMPARATOR

SIGNAL DECODING

RESYN SUPPLY LOGIC

FLY8Y SYNC DECODER

AUTOMATIC/SEMI-AUTOMATIC STATION CONTROL Figure 10.56. ACAS ground timing station.

time source, with calibration of the RF propagation

time between the ground station and the user. A

receiver and decode equipment for such use is esti- mated as costing ~ $200. The third mode of operation

might satisfy needs of automatic vehicular monitoring (AVM) [217], marine position fixing [218],

and others requiring position of moving vehicles

within range of a T/F-CAS ground station or overflying aircraft. In this case modified equipment,

estimated to cost ~ $1000, can actively participate

in the TF-CAS and obtain fix position through

trilateration and difference in arrival time calculations. A further consideration of TF-CAS is the

precise clock intrinsic to each aircraft equipment. This provides an excellent potential for air- craft flyover T/F synchronization similar to that dis- cussed in Section 10.4.2. If the system becomes

operational in 8 to 10 years with both flying aircraft and ground stations synchronized worldwide to 0.1

/as, it will have tremendous impact on time and

frequency technology.

Advantages of TF-CAS Time and Frequency Synchronization {partlyfrom [214])

• Synchronizations to less than 1 /lis appear

feasible over large areas of the earth, either

through line-of-sight jLtwave signals from ground

stations or flying aircraft. Fail safe operation

is assured and the coherent signals are trans- mitted at low power with little or no interfer- ence.

• Portable equipment can be synchronized due

to the worldwide coverage of the synchronization network.

• At line-of-sight distances, propagation effects are minimal, requiring little or no correction.

• Receiving and comparison instrumentation

should be relatively inexpensive, although there

must be provision for decoding time ordered

slots for time synchronization.

289 t
• TF-CAS provides a network for coordination

and maintenance of a worldwide primary time

scale such as the TAI.

• The time period required for synchronization

is only of the order of minutes at the most,

and initial clock setting appears possible.

• In some modes no physical transport of clocks

is required.

• System could provide multilateral functions

with T/F aspects such as surveillance, navigation, vehicular location, etc.

Limitations of TF-CAS Time Synchronization

• The system in its present form is expensive

and requires complex instrumentation tech- niques (the best aircraft system is estimated

to cost about $50,000 [207], although cheaper,

less versatile systems would be available).

• The system will not be operational for at least 8 to 10 years.

• The TF-CAS will require exquisite synchronization techniques with backup facilities for maintaining and controlling worldwide timing

to about O.l^ts.

• Reception is limited essentially to line-of-sight

distance from a transmitter (aircraft or ground

station).

• Possibility exists for multipath interference

causing degradation of time synchronization.

• Some time variation may occur as a synchronizee changes references from one master

station to another.

10.4. DISSEMINATION OF TIME

AND FREQUENCY VIA PORTABLE CLOCK

The general method of transporting and inter- comparing frequency standards is not new. W. G. Cady, in 1923, made international comparisons of

frequency standards by carrying portable piezo resonators to seven laboratories in Italy, France,

England, and the United States [219]. He showed

agreement between primary standards to about 1 part in 103

. From 1925 to 1927, the U.S. National

Bureau of Standards made similar tests using quartz

crystal oscillators and determined average agree- ment between frequency standards of five national

laboratories in 1927 as about 3 parts in 105

. This

informative comparison and the relation of ac- curate frequency to reduction of interference in the new field of radio are ably described by Dellinger

in 1928 [220]. At about this same time, Marrison de- scribed the first quartz crystal clock [221], a precise

timekeeping device which integrated or summed

up recurrent cycles of accurate frequency generated

by the crystal oscillator. He indicated the rate of

these crystal clocks to be stable to a few parts

in 107 or approximately 10 ms per day. During the

interim between the 1930's and the present day,

many refinements and improvements were incorporated into quartz crystal standards. A bibliography

of pertinent references is beyond the scope of this paper; much of the work has been reviewed in the

literature [222-226] (see also chap. 2). A fundamental problem in quartz oscillators, still existing

today, is crystal aging with time. Aging can be compensated to some extent, however, by drift correction [227]. In the late 1950's, commercial cesium beam

standards were developed in which a quartz

crystal oscillator was controlled, through electronic servo systems, to the atomic resonance of cesium.

This provided the impetus for side by side comparison of atomic frequency standards of different

construction. In 1958, two U.S. commercial atomic

frequency standards were transported to the

National Physical Laboratory in England and

compared with the NPL laboratory atomic standard

[228]. Agreement of several parts in 1010 was shown with a measurement precision of several

parts in 10n . In 1958, Morgan proposed synchronizing widely separated clocks by transporting a master

clock to correct remotely-located slave clocks

[84]. During 1959, Reder and Winkler organized

a worldwide synchronization of atomic clocks by

air-transporting commercial atomic standards to slave sites in the continental U.S., Hawaii, Australia,

and South America [229]. Synchronization at the

various stations was maintained between clock

visits via phase tracking of VLF signals. These

test results indicated global time synchronization

via flying atomic clocks then to be about 5 /xs [230]. The experiments also revealed areas for improvement such as reduction in the size and weight

of the frequency standards, a decrease in power

consumption, inclusion of standby battery supplies,

modification of electronic divider circuitry, and a lessened sensitivity to rotational movements.

In 1962, a portable crystal clock was used to compare time scales between WWV at Greenbelt,

Maryland, and NBS, Boulder, Colorado, with an

overall time closure of 5 /as [231]. Dependent upon

the timing requirements, cost limitation, and accessibility, the crystal clock can be very useful

in time and frequency synchronization.

In 1964, a new portable cesium beam clock was

developed which was considerably improved in size and weight characteristics; it also showed accuracy

and stability approaching a laboratory standard,

required low power with a standby battery supply,

included a quartz crystal oscillator which of itself aged at a rate less than 5 /i-s/day, and was coupled

to an electronic clock which integrated the cesium

resonance frequency to give a true atomic time

output and display [232]. A series of "flying clock"

measurements, using these standards, were made

290
from 1964 to 1967 [233-235]. Standard time and fre- quency were correlated and compared at some 50

laboratories, observatories, standard frequency

broadcast stations, etc., in 18 countries in Europe,

Asia, Africa, and North America through this portable clock carrying technique. The 1967 experiment

continued over a period of 41 days and the clocks were transported over a distance range of some

100,000 km. The time closure between the reference

standard and the two portable clocks was several

/as, corresponding to frequency differences of parts

in 1013 between the portable atomic standards.

The time correlations on the 41-day trip were be- lieved to be accurate to about 0.1 /as. Time scale

comparisons, made 16 months apart on two of these

experiments, between NBS and seven worldwide

laboratories are given in table 10.13. An average

time change of about 50 /as in 16 months indicates an agreement of time scales to about 2 parts

in 10 12. Also, in 1967, Swiss portable atomic clocks

(cesium) were flown to various time centers in the U.S., Canada, and the Far East for time comparisons. At the conclusion of these tests, one of the

clocks showed a time closure of 26.7 /as over a 255-day period when compared with the laboratory

standard at the Cantonal Observatory [236].

Smaller and lighter weight cesium beam standards

are being developed [215]; also, small portable

rubidium clocks are available, however, little has

been written about their use.

Table 10.13. Differences between 7 International Time Scales and the NBS UA Time Scale for two comparisons made 16 months apart via portable clocks (from ref. [235]

)

Laboratory

1966 1967 Change

(LIS Date Time

Diff.

/JLS Date Time

Diff.

/AS

Radio Research 18 May 1,474 16 Oct. 1,400 -75

Laboratory

(Japan) National Research 19 May 200,489 18 Sept. 200,557 + 68

Council (Canada)

USN Observatory 18 May 79 11 Sept. 165 + 86 (USA)

Neuchatel (TUA) 22 May 2,405 23 Sept. 2,468 + 63 Observatory

(Switzerland) Dominion Ob- 20 May 1 17 Sept. 54 + 53

servatory (Canada)

Physikalisch- 3 June *433 26 Sept. 489 + 56 Technische

Bundesanstalt (Germany)

Royal Greenwich 3 June 59 4 Oct. 154 + 95 Observatory

(England)

1 1966 time difference value corrected for known time scale frequency

offset existing from 3 June to 30 December 1966.

291
10.4.1. On-site Visits

There have always been and presumably will be

applications for time synchronization that exceed

the capabilities of dedicated time dissemination

services for coverage or accuracy. Portable clocks can be employed to meet requirements which are hard to satisfy by other techniques. Basically, a portable clock consists of a stable oscillator whose

output is integrated or counted by a clock mechanism

to indicate time. Typical outputs include standard

frequencies such as 5 MHz, 1 MHz, and 100 kHz

and time ticks such as 1 pps. The portable clock

method consists of establishing the time of the

portable unit (which may be a quartz crystal or atomic clock) in terms of the reference time scale

prior to a clock synchronization trip. Usually, the

clock is flown to a general area where the measure- ments are to be made, with intermediate transportation by auto. A typical scene in the transportation

of a portable cesium beam clock is shown in figure

10.57. Self-contained batteries can maintain power

for periods of hours. Time synchronization consists

of bringing designated time pulses into coincidence

or to fixed delay relationships. Frequency comparison can be made through phase intercomparison

for a given time interval. At the conclusion of a

trip the portable clock is again compared with the

original time scale reference, and the time closure

difference is distributed backwards as the deviation within which the portable clock measurements

fall.

Figure 10.57. Example of portable clock carrying in Oslo, Norway during a 1966 clock synchronization experiment (photo courtesy of Hewlett-Packard).

The success of portable atomic clocks to bridge

distance gaps between a master standard and user

led the U.S. Naval Observatory (USNO) to establish

in 1968 a master clock location and six worldwide

time reference stations around the world [237].

(These station locations are shown in ann. ll.E.l of

chap. 11.) Reference atomic clocks at each of the

time stations are available for precise time measure- ments which can be referred to the USNO

master clock in Washington, D.C. Periodic portable

clock measurements between the USNO master

clock and the reference station clock show typical

time closures of ~ 1 fis [238]. As the USNO and

NBS UTC time scales are mutually coordinated

within ~ 5 /as of each other [239] clock synchronizations at the USNO time reference stations can

also be related to the NBS time scale within this tolerance (or even better post facto). The effective- ness of portable clock carrying has been demonstrated by the periodic synchronization of some 21

worldwide laboratories or remote sites as reported

by the USNO over the last several years [43]. General methods of maintaining synchronization

at remote stations between portable clock checks

include VLF phase tracking, navigation system comparison, satellite comparisons, and TV measure- ments as discussed in detail in Section 10.3.2. In consideration of the portable clock method of time

and frequency dissemination, we list below both

advantages and limitations of the method:

Advantages:

• Provides a means of microsecond time syn- chronization of remote clocks without a dependent link to a master clock with attendant delays

and propagation errors as in radio methods.

• A minimum of manpower is required, and the

synchronization can be simply and quickly

performed with the usual equipment found in a standards laboratory.

• The portable clocks are relatively lightweight,

rugged, and have a power operation versatility

from either internal standby batteries or ac/dc

current; such flexibility maintains accuracy,

stability, and reliability over long periods of

time.

• The portable clocks are easily transported by

commercial airlines and automobiles.

• Newer portable cesium beam standards are

relatively insensitive to shock and vibration,

smaller in size, and lighter in weight.

Limitations:

• The most accurate portable clocks are ex- pensive, and the method requires physical

transportation of the clocks, which of itself can be a monetary concern. The accuracy obtainable is directly related to the cost of the

clock.

• The clocks are usually hand-carried and,

although experience has indicated high

reliability, there is possibility of clocks stopping

or changing rate en route due to power outages,

excessive vibration, or environmental changes

of temperature, humidity, or air pressure.

• It is difficult or impossible to make portable

clock side-by-side measurements at some loca292
tions such as inaccessible islands, mountain

stations, beacons, ships, etc. (The aircraft flyover technique may be used in some of these

instances, however, see following sec. 10.4.2.)

Auxiliary equipment is required to maintain

synchronization between clock settings. In summary the best clock for a particular

application is not necessarily the most expensive

or accurate clock available. Specific need, environmental conditions, budgets, and other considerations may all interface to dictate the optimum choice

and/or compromise for a given portable clock

measurement. The cost of portable clock comparisons may decrease in the near future with the availability of a new and smaller cesium beam portable

clock [215].

10.4.2. Aircraft Flyover

Another method of time synchronization is a refinement of the portable clock technique. In

aircraft flyover, planes carry an atomic clock and

transmit a coherent time signal to synchronize a time scale at a receiving site. The method dispenses

with cross-country and local transportation, reduces

the time required to synchronize many remote

locations, and affords the opportunity to synchronize

inaccessible sites such as mountain or island sta- tions, ships, other aircraft, etc. Some aspects of

this method were considered in connection with

early aircraft collision avoidance studies. The

method was first reported by Markowitz [240] and was recently refined by Besson [241]. The basic

technique of aircraft flyover synchronization is illustrated in figure 10.58. The S-band transmissions

(2.2 to 2.3 GHz) are amplitude modulated at a peak

power of about 50 W. The pass band is 10 MHz. The

time scale is coded and sent at a 10-Hz rate permitting 10 time scale measurements per second. The

receiving site uses a counter with 10-/is resolution

and a readout which prints the deviations between

the radio-received time scale and the local time

scale 5 to 10 times per second.

Aircraft flyover determines the clock difference

between the ground station time, Hg, and aircraft time, Ha, which is shown to be

Hg -Ha =(Hg-Ha .)-(ttr +tp ), (10.7)

where H.r = received aircraft time at ground station; — HA — (ttr — tp ); ttr = time delay of transmitter-receiver

equipment (nearly constant); TP = time delay for aircraft signal to reach

receiver, dependent upon aircraft location relative to receiver.

0ATOMIC FREQUENCY

STANDARD CLOCK

AIRBORNE EQUIPMENT

o o

TRANSMITTER X I 2. 2-2. 3GHz

SON

H A = AIRCRAFT TIME

HG = GROUND TIME

H A

. = RECEIVED AIRCRAFT TIME T„ = SIGNAL PROPAGATION TIME

Figure 10.58. Aircraft flyover method of T/F comparisons.

293
The evaluation of ttr and tp should resolve the

time scale deviations, {Hg — Ha)- Two methods

have been proposed.

Method 1. This is a one-way system in which the

aircraft passes over the site to be synchronized at low altitude (100-300m) at a flight speed of about

50 m/s and transmits timing pulses. The observed

time scale difference, Hq — Ha', approaches a minimum as the aircraft reaches the point directly over the receiver and then increases as flyover

continues. The minimum reading corresponds to the

vertical distance between the aircraft and receiver

and is the true altitude recorded by the aircraft instruments. This critical distance point should not exceed 10° from perpendicularity. Besson indicates

that with a transmission rate of 10 sync pulses per

second and a 3-percent altitude error, the propagation time standard deviation, Atp

, is 30 ns or less. The instrumentation delay standard deviation,

Attr , is reported as 10ns or less [241]. Method 2. This technique is a two-way system

involving simultaneous transmission by both the user and the aircraft so the propagation time delay, tp , drops out of the equation for clock time differ- ence. The aircraft does not have to fly directly over

the receiver at a fixed altitude. Limitations in the

two-way system include the degree of accuracy to which the time scale deviations between the air- craft and ground station clocks can be measured

in the short time available and the difficulty of

measuring the equipment delays at both time

sources.

In September 1970 the French group (Office

National d'Etudes et de Recherches) cooperated

with several globally located time centers and made

an international comparison of atomic clock scales

through aircraft overflight. The experiment plan

included both one- and two-way type of comparisons with three or four overflights of each time

center. A nonstop one-way flight was expected to take about 18 hours. The experiment, named

Synchran (North Atlantic Synchronization), was

performed during the period September 9-15,

1970. Corrections included propagation delays,

instrument factors, clock drifts, and relativity

effects. The results show that aircraft flyover

has many attractive features in rapidly intercomparing time scales at remote points with standard

deviations typically 30 to 40 ns [242].

Advantages of aircraft flyover time dissemination

include:

* Rapid precise synchronization of many inter- continental clocks without physically trans- ferring clocks; provides a means of quickly

evaluating the TAI.

• Enables clock synchronization at remote sites inaccessible to physical clock-carrying.

• The over-all short duration of worldwide comparisons lessons the possibility of clock fail- ures and enhances the probability of successful

clock comparisons.

• Insignificant propagation degradation with

line-of-sight microwave frequencies.

Disadvantages include:

• Method is expensive; it requires the use of air- craft and auxiliary equipment such as trans- mitters, receivers, etc.

• Clock synchronization at a given site requires

auxiliary techniques to maintain accurate time

between clock comparisons.

10.5. TFD VIA OTHER MEANS

The following TFD methods are unique in that conventional radio waves are not involved in carry- ing the timing information. The methods include

optical pulsar signals, telephone/coax cable trans- mission, and ac power lines. The techniques are characterized by some of the most complex as well

as simplest noted in this dissemination overview.

10.5.1. Time Transfer via Optical Pulsar

Signals

The precise periodicity of pulsar radiations can

provide a means of time transfer to remote points on

earth. Pulsars are believed to be rapidly rotating

neutron stars which periodically emit a narrow beam, like a lighthouse, each time the beam inter- cepts an observer [243, 244]. Neutron stars consist

of tightly packed neutrons with a mass approximately that of the sun but a radius of less than 30

km [245]. First discovered in 1967 [246], there are now about 60 such identified bodies [247]. A striking

characteristic of today's known pulsars is the vari- ability of their periods; these range from 33 ms to about 4 s with the average about 1 s [245]. After

months of study it was found that the periods of

pulsars are increasing; i.e., the apparent pulsations

are slowing down and those rotating the fastest at the greatest rate. The slow-down rates vary from

about 40 to 0.3 ms per day [243]. Initially, all pulsar

received-signals were from radio sources; in 1968

and later it was discovered that the Crab Nebula

Pulsar (NP 0532) exhibits similar pulsations and

structure at radio, optical, and X-ray frequencies

[248-251]. (As of 1972 the Crab Nebula pulsar is the

only such body known to be radiating optical

wavelengths.)

The Crab Nebula was found to contain the fastest rotating pulsar — namely the NP 0532 — which flashed

about 30 times a second. This body is ~ 6600 light years distant and believed to be the remnant of a supernova explosion observed by Chinese astrono- mers in 1054 AD [243]. NP 0532 shows a mean pulse

294
period of 33.105 ms (November 1969-April 1970)

[252] with a slow down of ~ 36.5 ns per day (~ 4

parts in 104 per year in terms of the mean period)

[243]; its emitted optical signal consists of both a major and minor pulse separated by ~ 14 ms. In terms of power emitted, the optical flux is roughly

102 greater than the radio flux; the X-ray flux ex- ceeds the optical by ~ 102 [243]. The absolute times of arrival of optical pulsar

signals has been determined to an accuracy of

several /ms (UTC) by Papaliolios et al. [250], who also suggest that time-of-arrival measurements of pulsar

signals would enable clock synchronizations to several ^ts at any two observatories with at least 24-in (61-cm) telescopes observing the Crab Pulsar.

Recently, Allan has shown this possibility of trans- ferring time in the fJis range between two widely

separated points on earth via near-synchronous

reception of the NP 0532 pulsar optical signals

[253]. He analyzed pulsar reception data from the

Lawrence Radiation Laboratory (LRL), Berkeley,

California, and Harvard University, Cambridge,

Massachusetts, which were compared previously

[254]. The basic data were obtained at one end of

the link by a method similar to that diagrammed in figure 10.59. Several thousand pulsar optical emissions, received by a phototube at the focus of a tele- scope, are amplified, enhanced, and averaged by a

signal averager to improve the SNR. The signal

averager scans the phototube signals at the simulated pulsar rate via a synthesizer referenced to a precise reference clock. The output of the signal

averager gives the time interval between the pulsar

30.2 Hz OPTICAL PULSAR SIGNALS /S N

FROM NP 0532 r

TELESCOPE

PORTABLE CLOCK

OR L0RAN-C

COMPARISON

REFERENCE

CLOCK

COOLED PH0T0MULT I PL I ER

PULSE ENHANCEMENT

SYNTHESIZER

SYNC 30.2 Hz

SIGNAL AVERAGER

arrival time and the local clock. To evaluate the

pulsar time transfer system, differences were taken

in pulsar arrival times at Harvard and LRL for two

periods in 1970 (adjustments in the raw-data were

required to provide a commonality in the reduced

data). The data difference took the form:

TH (t) —TL {t') = AT(t), (10.8)

where t and t' represent the local clock times at Harvard and LRL, respectively, on nights of mutual

observations. Both the Harvard and LRL local clocks were referenced to the same time scale via

the Loran-C East Coast system and an atomic

clock at Santa Clara, California, respectively.

The stability of the differential data was deter- mined as follows:

&T(t + Ts )-bT(t) _8v

Ts V

(10.9)

where rs is the time interval between nights of

mutual observation of the pulsar signals. A data

plot of such differential fractional frequency deviations between the Harvard and LRL clocks versus sample time is shown in figure 10.60. The dashed

line approximates a fit for the data and indicates an rms time error of ~ 13/u.s; the slope of the line,

inversely proportional to the sample time, provides

evidence that uncertainties of the pulsar reception

times are influenced by white noise statistics.

©

X

EARLY 1970

LATE 1970 EARLY 4 LATE

1970 COMBINED

PULSE ARRIVAL TIME WITH RESPECT TO REFERENCE CLOCK

Figure 10.59. Method of time transfer via optical pulsar pulses.

SAMPLE TIME IN DAYS

Figure 10.60. Differential fractional frequency deviations between Harvard and LRL clocks vs. sample time via optical pulsar signal NP 0532.

295
There are indications that nonuniformity of deter- mining the arrival times at the observatory sites, as well as equipment differences, adversely affected

the data analysis.

Advantages of Pulsar Optical Time Transfer TFD:

• The pulsar time transfer technique offers both

accuracy and precision in the fxs region on a

global basis. (A resolution to ~ 2/xs is believed

possible at a 2-h sampling time using a 24-in (61-cm) diameter telescope [253].

• The propagation effects for pulsar optical emissions are minimal; the earth's atmosphere

increases the delay by ~ 10 ns, and the spinning

earth delay is < 8 ns if the earth position can be

known to < 5 ms (1500 km).

• Pulsar photons are natural events which can

provide a free source for time transfer without

interference to or dependence on man-made

systems.

Limitations of the Pulsar Optical Time Transfer

Technique:

• Measurements can be made only at night;

measurements are not possible during the latter part of May, all of June, and early July because

at these times the source is within a few degrees

of the sun.

• The signal strength of pulsar emissions at the

earth is low, and relatively expensive equipment

is required for detection and comparison

(~ $20,000 without telescope and atomic clock).

• Comparisons are restricted to fixed locations

housing telescopes and required instrumentation.

• The data anlysis for time synchronization re- quires computer techniques as well as communications between comparing sites or observatories. Measurements should be made

simultaneously or nearly so for optimum results.

• Cloud cover severely affects the effectiveness

of pulsar time transfer.

• Pulsar period show jumps because of quakes or sudden disturbances [250], and this could cause errors in extrapolated sampling rates for the signal averager.

10.5.2. TFD in Telephone Line and Coax

Cable Transmission

Telephone lines and/ or coax cables often are used

for time and frequency distribution between closely

spaced points (~ 1 to 30 km). This section briefly

reviews the properties and characteristics of such

hardwire systems for TFD.

a. Telephone Line Distribution. In 1965 the Naval

Research Laboratory (NRL) in Washington, D.C.,

used underground balanced land lines (broadband —

100 to 15,000 Hz) to carry a 10-kHz signal, derived

from a hydrogen maser, for comparison with atomic

frequency standards at the USNO [255]. This

dedicated line was 16 km in length one-way and

passed through no switching centers. Narrow band

amplifiers were used at each end of the line to improve the SNR and isolate the output. The 10- kHz signal was stable in frequency to better than

1 part in 1012 as transmitted. The same signal,

returned from the USNO, was compared with the

NRL transmitted signal to determine the effect of

the telephone line on the transmission. The phase

differences were found to be < l/u,s, and averages

over a 24-hour period gave frequency errors to < 1- part in 1012

. Notice that these telephone lines were

underground and thus at fairly constant temperature.

In 1966 Koide also described the use of multipair

telephone lines for TFD [256]. He transmitted a 1- kHz standard frequency over leased multipair tele- phone lines, extending 37 km one-way. (Some tests were run two-way for a total path distance of 74

km.) This line, from Downey to Anaheim, California, was routed about halfway underground and the

remainder by pole suspension in air; the voice grade

line was without loading coils or repeater amplifiers. Each multiplier telephone cable consisted of

four pairs (three different wire sizes) with each line showing a SNR > 50 dB at 1 kHz; at the terminals

the crosstalk between adjacent lines was atten- uated =S 40 dB. It was found that daily temperature

changes caused diurnal phase shifts in the trans- mitted 1-kHz signal similar to diurnal ionospheric

effects in VLF/LF propagation. From relationships

of the 1-kHz phase change vs. temperature change,

and changes in temperature versus dc resistance of

the telephone line, it was possible to determine the

resistance change versus the 1-kHz phase change.

Illustrative simultaneous plots of dc resistance and

phase change over the two-way, 74-km telephone

path are shown in figure 10.61. These plots show

that the dc phone line resistance correlates directly

with the phase changes, and there is significant

phase delay during the nighttime transmission.

29 NOVEMBER 1964 30 NOVEMBER 1964

40

100

1 r i i i \ - PHASE

i i i i i j 0100 0600 1200 1800 2400 0600

LOCAL TIME

Figure 10.61. Diurnal changes in resistance of phone line and

transmitted 1-kHz phase, caused by temperature change.

296
Figure 10.61 indicates an increase in dc resistance

of ~ 285 O caused a phase retardation of 30/as over a 6-hour period. Over a 4-month period the dc

resistance-phase sensitivity averaged somewhat

less; i.e., 8.3 fi per /as over this telephone path.

With such information it was possible to design an Automatic Phase Corrector (APC). This device,

placed at the transmitting end of the line, sensed the

dc resistance change in the telephone line and,

through a Wheatstone bridge and servo potentiometers, maintained a null in the bridge; the servo simultaneously drove a phase shifter which cor- rected the transmittal signal an amount proportional to the resistance change. A round trip evaluation showed a corrected phase variation < 0.5 /as for a 12-hour period in which the actual phase in an

adjacent line varied from — 24 to + 18 /as. This cor- rection is equivalent to a frequency offset of ~ IX

10~n. On short underground telephone lines (2-3

km in length) Koide has used various carrier fre- quencies from 1 kHz to 1 MHz; the higher fre- quencies showed stability and noise degradation

coupled with much greater attenuation [257]. Typically, 22 gauge wire shows ~ 5-dB attenuation

per 1.61 km at 10 kHz [258]. In comparing frequency standards at the Mt. Stromlo Observatory in Australia, Grimsley and

Miller report the transmission of a 10-kHz standard

signal over a 12-km landline ([—10.5 km underground and 1.5 km in air) [259]. During a 40-hour

period with a temperature variation of — 1° to + 16.5° C, no diurnal effect was noticeable in the

received signal; a phase comparison between a rubidium standard and a crystal oscillator at nearly

equal frequency indicated no frequency errors >1X10"U resulting from the telephone trans- mission.

The WWV standard time and frequency broadcasts are now available via telephone by dialing

(303) 499-7111 (Boulder, Colorado). The telephone

signals are the live broadcasts as transmitted by

WWV. Propagation and equipment delays limit the

accuracy of these telephone signals to ~ 30 ms or better as received anywhere in the continental

USA [64]. A service call is automatically limited to 3 minutes.

b. Coax Cable Distribution. Information on the use and stability of coax cable is limited; we will review several examples in the literature. In 1945-

46, phase comparisons were made in England be- tween spaced aerial systems via coax cable from

London to Birmingham, a one-way distance of 163

km [260]. The primary signal frequency was 1 kHz,

and the standard deviation of the phase change over

the entire loop (326 km) for periods of several weeks

was 7° or ~ 20 /as. There were unspecified long and

short period variations, and it is unknown whether

the cable was underground. Tolman et al. [Ill]

used a coax cable link ~ 340 km long in connection

with microwave TV time comparisons in 1965 and

determined agreement to 2 /as irrespective of the

transmission medium used.

Koide mentions the use of coax cable in the distri- bution of standard 100 and 1000-kHz signals for slaving electronic counters (external time base

signal) and timing clocks within a manufacturing/

engineering laboratory [257]. He used coax lengths up

to ~ 180 m for distribution within buildings and employed coax impedance transformers. Frequency

checks over such lines, using an Rb atomic standard, indicate that the coax cable contribute errors ^

parts in 1010 [258]. At the Jet Propulsion Laboratory (JPL) in Cali- fornia, coax cable is used to distribute precise 1 pulse per second (pps) signals over short distances

between distribution amplifiers and microwave

transmitters at the Goldstone tracking facility [261]. About 100 /as in duration, and with a risetime near 200 ns, such pulses were degraded little by the coax

distribution; a combination coax-microwave system

(base bands 3= 2.5 MHz) transfers such pulses with an uncertainty of ±3 /as. In a typical installation the coax cables were run underground via constant- temperature cable tunnels, avoiding diurnal de- grading effects. Leschiutta recently reported impressive test results for transmission of phase data over coax

lines between Rome and Turin, Italy— a distance of ~ 740 km [120]. Phase changes from diurnal

temperature variations were avoided since the cable

and associated amplifiers were underground at a depth > 1 meter. A stabilizer carrier frequency of 300 kHz was transmitted from Rome; received at Turin it was continuously compared with a synthesized 300-kHz signal from a local frequency standard.

Such a system is calibrated every third month and

within the last several years has drifted < 100 ns. The received signal shows white phase noise for time intervals 10 ms to 10 s; for t=1s, a fractional

frequency stability of ~3X10~9 was shown. The

transmitted data were subject to random jumps of

30 and 50 ns, probably caused by line connections

or amplifier changes. Such jumps are inconsequential on the stability measurements for long term. Comparisons of transmitted time and frequency

data over the coax line and a nearly identical TV

path (microwave fink using eight relay stations)

yielded a difference usually < 3 /as over measure- ment periods of 100 days. Part of this difference is attributed to propagation delay variations in the

radio links.

Advantages of Hardwire Distribution Systems for

TFD

•• Dedicated telephone lines offer a relatively inex- pensive means for distributing standard fre- quencies (1 to 10 kHz) between points ~ 30 km

apart at accuracies ^ 1 X 10~10. (Monthly

lease charges approximate $2 to $3 per airline mile for a two pair-four line circuit.)

• Underground telephone fines require little maintenance and show minor temperaturecaused phase variations in transmitted signals.

297
• Precise time pulses can be transmitted over coax cable for relatively short distances with

little degradation with care, provided pulse

shaping techniques are used. Underground

coax cable shows excellent stability for trans- mission of standard frequencies (~ 300 kHz)

over relatively long distances (~ 750 km).

• Reliability and percent-of-time available factors are excellent for hardwire systems.

• WWV telephone signals can provide time to ~ 30 ms anywhere in continental U.S.

Limitations of Hardwire Distribution TFD Systems

• Aerially mounted hardwire systems degrade

the transmitted precision signal because of

temperature-related variations of the line dc

resistance. Precise TFD via hardwire requires

undergrounding of all transmission cable.

• Auxiliary equipment such as automatic phase

correctors (APC), amplifiers, and filters are required for transmission and recovery of

signals over long telephone lines in the open air.

• The signal attenuation per kilometer increases

with frequency and is a practical limitation to the use of frequencies higher than 100 kHz in many cases. The fines are distance-limited for a given frequency because of signal attenuation.

• Coax cables may be impracticable for T/F dis- tribution for distances much greater than

several hundred meters because of the high

cost of either initial purchase or monthly lease.

• As opposed to radio coverage, hardwire systems

are inflexible to the extent that coverage is limited to those users connected into the

system.

• For T&F distribution, telephone fines must be

dedicated to this sole transmission; they

should be balanced, unloaded, without re- peaters, and bypass switching centers. The

telephone TFD cannot tolerate unknown and

variable delays from these latter factors.

• It is impractical to transmit timing pulses with

high precision over telephone fines because of

band pass limitations.

• Underground hardwire systems require a constant ambient temperature environment for highest precision.

10.5.3. Power Line (60-Hz) Signals as a Time

Transfer Technique

Large a-c power utilities in the continental U.S.

are divided into a network of interconnected sys- tems serving major portions of the country [262]. The American Electric Power (AEP) Company at Canton, Ohio, synchronizes and manually controls

the electric time of these grids with a tolerance of

±2 seconds; offsets of the 60-Hz frequency in steps

of ±0.02 Hz compensate for time errors [7]. The

time and frequency reference for most of these net- works is the NBS 60-kHz broadcast from Ft. Collins,

Colorado. (Cohn proposes automatic and continuous

time error control through use of NBS standard

frequency broadcasts in all power areas [263].)

Time coordination enables efficient transfer of power from one area to another (load diversity)

without inadvertent interchange time accumulation.

The U.S. coast-to-coast interconnected power

grid is essentially a phase coherent system. Allan

et al. have shown its potential as a time transfer

system [264]. We will describe several of their

examples. Initially, they studied the fractional fre- quency stability of the 60-Hz power signal at the

NBS Laboratories, Boulder, Colorado. In using

(Ty{r) (square root of an Allan variance [129. 130]),

it was determined that the data exhibited flicker noise frequency modulation (see chap. 8) over a t range of 17 ms to 105 s and at a '(a- 2y (N, T, r,/ft )) 1/2 range of ~ 5 X 10-5

. Similar results were obtained

for measurements on different dates. Another study compared the 60-Hz power line phase in California and Colorado relative to atomic

clocks at the Hewlett-Packard (HP) Laboratory,

Santa Clara, California, and at the NBS, Boulder,

Colorado. Part of these data are plotted in figure

10.62, and strong phase correlation exists for the

TIME FLUCTUATIONS OF 60 H2 (P0UER LINE) CLOCKS COMPARED WITH ATOMIC CLOCKS AT NBj/BOULOER, COLORADO AND HP/ SANTA CLARA, CALIFORNIA

Figure 10.62. Comparison of 60-Hz (power line) clocks and

local atomic clocks at Boulder, CO and Santa Clara, CA.

two distant sites in different interconnected sys- tems [264]. A study of the differential delay, td,

between Santa Clara and Boulder (determined by

differencing the first zero-crossing measurements

of the 60-Hz signal following a given second tick at each site) gave a fractional frequency stability of

1 part in 108 for r— 1 day. Similar data for longer

periods of time suggest that two remote clocks,

located at distant points within different grid net- works, could be kept within 1 ms, provided the

particular path was calibrated.

Day-to-day synchronization requires that no cycle

slips occur between measurement points. Tests were run, using dividers which generated precise

1 pps from the 60-Hz signal, and no cycle slippage

occurred between three sites (Santa Clara, CA;

Boulder, CO; and Ft. Collins, CO) over an interval

of several days with continuous power. A plot of the

fractional frequency stability versus averaging time

298
10"

~l 1—I—I I I I I "1 1—I—I I I 1

1

6- N

10"

10 10

\ WHITE NOISE PHASE MODULATION \ ^ OR FLICKER NOISE PHASE MODULATION

O

VQ 520 ms

N = 2

r ^ T/T = 1

1 WEE K I

i i i i i i i

°oW 0

o ^

o

1 monthJ c^o

I I I 'Nil'

1 10 10 SAMPLE TIME x (DAYS)

Figure 10.63. Fractional frequency stability vs. averaging time for 60-Hz power frequency between Santa Clara, CA

and Boulder, CO.

of the Santa Clara-Boulder path is shown for 60-Hz

power line data in figure 10.63. The 60-Hz stability

data for the shorter WWV-Ft. Collins to Boulder

path shows an improvement by a factor of 6 over the

longer Santa Clara-Boulder path. Although the

stability degrades with distance, stability of clock

measurements of several ms may be possible across interconnected power systems throughout the continental U.S.

Advantages of a-c Power (60-Hz)for TFD

• Equivalent precision to WWV received sky- wave signals is possible from 60-Hz power fine signals via the differential mode. (The WWV

time signals are much more accurate than 60- Hz power line signals.)

• The 60-Hz time transfer system utilizes exceptionally cheap receivers (e.g., ~ $20 for a low

pass filter and transformer).

• The a-c power is continuously available to wide

areas throughout the continental U.S.; the

power grids of the U.S. are interconnected

and synchronized to form a phase coherent

system.

• The ambiguity of 16.67 ms could probably be

resolved nearly everywhere in the USA via

the WWV audio telephone signal, (303)

499-7111.

Limitations of the 60-Hz Power System for TFD

• The stability of the 60-Hz power system de- grades with distance.

• Local area power outages or phase shifts occur, which can cause errors in the clock comparisons.

• The ambiguity of the 60-Hz power system is 16.67 ms.

• The system does not provide precise or accurate timing for the sophisticated user.

10.6. T/F USER AND SYSTEM

EVALUATION

Having described the varied means of TFD, we

would now subjectively classify real and potential

T/F users as well as evaluate the various T/F

dissemination systems and techniques. Three

classes of users in terms of accuracy requirements

are discussed below; the evaluation of systems pro- vides direct comparison in some ten pertinent

categories.

10.6.1. Classification of T/F Users

It is convenient to classify users of time into three categories: low accuracy (coarser than 1 ms);

intermediate (1 ms to about 50 /jls); and high ac- curacy (more stringent than 50 fxs). Figure 10.64

illustrates the time accuracy requirements of some

users below the time scale line and the normal

capabilities of representative time dissemination

techniques and services above the reference line. The accuracy obtainable by a given technique varies

considerably with the location and skill of the user. The low accuracy group contains the largest

number of users; their needs are generally met by

telephone time-of-day service, telephone access to WWV, commercial radio time announcements, and

standard time emissions (WWV, CHU, JJY, etc.). The intermediate group is fast growing. Organizations engaged in satellite geodesy, seismic monitoring, and satellite tracking require time in the

intermediate accuracy range. The basic characteristics of reliability, geographical coverage,

availability of signals, accuracy propagation pre- dictions, and equipment costs relevant to needed

accuracy have been explored largely in response

to this group's needs.

High accuracy is required by coherent detection

communication systems, long baseline inter- ferometry facilities, and organizations engaged in precision ranging. Submicrosecond accuracy is generally sought by laboratories with clocks capable

of maintaining time at that level. The proposed T/F

aircraft collision avoidance system, for instance,

requires widespread dissemination of time with

submicrosecond accuracy [214]. Reliability, per- centage of time available, coordination among facilities and systems, and worldwide coverage are of paramount importance to system designers in the

high accuracy group. Although the number of time

users who have present requirements for submicrosecond accuracy is relatively small, these are not

negligible and can be met with sophisticated but

expensive techniques.

299
COMMERCIAL TELEPHONE

( BASED ON WWV6)

DISSEMINATION «y

TECHNIQUES

TIME SCALE

REQUIREMENTS

HF RADIO (CHU.JJY.WWV)

LF ( HBG , WWVB

)

LORAN-C

(SKY WAVE

)

OMEGA

TV - L I NE - 1

0

SATELLITE (PASSIVE)

(2 HAY ) VLF -PHASE

TV-LINE-I

(ACTIVE) MICROWAVE

HF RADIO

pps

TIME SCALE

60 Hz POWER GRID

SATELLITE

(TRANSIT) PULSARS A

LORAN-C

(GNO WAVE) MOONUOUNCE

AIRCRAFT

FLYOVER SATELLITE

(DCSC) PORTABLE

CLOCKS

AVERAGE

CITIZEN

RAOIO AMATEURS

SMALL BOAT NAVIGATION

TIME BASE ASTRONOMY AIRLINES

RADIO STATIONS

t

RAILROADS

LOW ACCURACY

SOME TRACKING

RANGES

t

INDUSTRY

WORLD MAPPING PROPAGATION

STUDIES SURVEILLANCE

SATELLITE

GEODESY

SEISMIC MONITORING

CAR LOCATION

SPACE TRACKING

RELATIVITY EXPERIMENTS

AIRCRAFT TRAFFIC CONTROL

SOME MILITARY

SYSTEMS

TIME/FREQ

STANDARDS

LABS

COHERENT DETECTION

SYSTEMS

NAVIGATION STANDAROS LABORATORIES

HIGH ACCURACY

Figure 10.64. Time-accuracy requirements and capabilities of some time dissemination techniques and services.

10.6.2. Evaluation of T/F Systems

Figure 10.65 compares some TFD techniques.

Such an evaluation is subjective, and some classifi- cations are borderline. It is an attempt though, to show a realistic picture of present or proposed dis- semination systems in terms of their capabilities

and potentials. Accuracy figures are documented

by applicable references. The ratings of good, fair, and poor are both arbitrary and broad. In the context of this presentation they are given for pur- poses of comparison and evaluation. Further

explanatory comments concerning the scope and

intent of the various characteristics identified in figure 10.65 follow:

(1) Accuracy of date transfer. Refers to that ac- curacy (degree of conformity with some specified

value) to which time of day can be established at a given location. The numbers given are believed to be realistic for most users; it must be recognized

that these numbers must be adjusted for either

extremely favorable or unfavorable conditions,

locations, etc. The ratings of good, fair, and poor

are referenced to the needs of high, medium, and

low accuracy users as shown in figure 10.64.

(2) Accuracy offrequency synchronization. Refers

to that accuracy to which frequency standards can be synchronized within some frame of ieference.

As with date transfer the three basic ratings are in terms of the classes of accuracy users shown in figure 10.64.

(3) Ambiguity. Applies to that interval of time

which a given system or technique can provide

with certainty. In some cases two values are shown,

one is the basic period of a given carrier frequency,

sequence, or audible tone; the other, by means of

time code provides date information for periods

up to a year. For instance, the period of a TV frame,

33 ms, is the ambiguity of the TV line-10 technique.

The line-1 TV system, using the coded data dis- plays, has 24-hour ambiguity.

(4) Coverage. Refers to the geographical region

in which the dissemination technique can be used

to obtain the stated accuracy. In many cases special

considerations such as ground wave versus sky

wave, propagation over land or water, availability

of TV line networks, etc., may affect the coverage

of a specific signal.

(5) Percent of time available. Describes the operating time of a service, i.e., continuous (good), a certain portion of a day (usually specified fair), or only occasionally, irregularly or by special ar- rangement (poor). Interruptions caused by propagation conditions such as sudden ionospheric

disturbances, VLF diurnal phase shifts, or HF

ionospheric disturbances are not considered.

300
DISSEMINATION TECHNIQUES

VLF RADIO

COMMUNICATION/SFB

GBR. NBA. WWVL 0 i«ro" ENVELOPE500 us ^^PHASE

-50 us

GLOBAL

NAVIGATION OMEGASYSTEM

0/P <M0~" <10us"

PROPOStO ;°,?>Phase mm ^-lOOus

GLOBAL TIME CODE 59.93.26S

LF RADIO

STANDARD FREQ BROADCAST IWWVB) 0 WO""

(PHASE 24h|

(J|

ENVELOPE ~50us1 YR USA IWWV8I

LIMITED

Mfinf RAT F USA IWWVBI

EUROPE OTHERS

65.67

NAVIGATION SYSTEM

LORAN C

0 WO""

GND

-luslGNOI

50us|SKY| 50ms>^PHASE

10us

SPECIAL AREAS — SPECIAL AREAS

35.103

HF/MF

RADIO

STANDARD FREQ. BROADCASTS IWWVI 1000 us

1 DAY^^

^^05 min HEMISPHERE DEPENDS ON

CONDITIONS

81.266

NAVIGATION SYSTEM

LORAN-A

0 B»1ff"

1!]

2 5 us NOT UTCLIMITED AREAS

OEPENOS ON

CONDITIONS mm SPECIAL AREAS

TELEVISION (VHF/SHF

RADIO)

PASSIVE -LINE- 10 0

(24li) ~lus

1 DAY^^

^^~33ms

NETWORK

COVERAGE

"LIVE" PROGRAMS

USA FOR EXAMPLE

111.125,128

ACTIVE-LINE 1 (NBS TV TIME SYSTEMI E 1-10"" (<30 mini < 100ns * 1 DAY ^^~33ms

NETWORK

COVERAGE USA FOR EXAMPLE 124

SATELLITES

(UUp/iiup/QHF (vnr/unr/onr

RADIO)

STATIONARY SATELLITES (TRANSPONDER)

ONE WAY E/0

i«id'° (24hl 10-50 usDEPENOS ON FORMAT HEMISPHERE STATIONARY

1

149.154,157

STATIONARY SATELLITES (TRANSPONDERI TWO WAY

E/0 wo"

(24h) ~IOOns OEPENOS ON FORMAT HEMISPHERE 1 J mm

ON BOARD CLOCK (ACTIVE! ONE WAY - LOW ALTITUDE

0 ~wo'°

|24fi| 0 5-50US

DEPENDS ON FORMAT WORLD

10 15 mm

PER PASS

2 4 PER DAY

CLOCK NEEDS ADJUSTMENT 5

140.146.160

SHF RADIO

MICROWAVE E/0 -wo"'

1

(PER WEEK)

< 100ns PHASE COMPARISON

LOCAL LINKS 169

VLSI P 5«10" ~lns OEPENOS ON FORMAT HEMISPHERE AS NtEDED 186.192

PORTABLE CLOCKS

PHYSICAL TRANSFER 0 III? 100ns* 1 DAY

LIMITED BY TRANSPORTATION AS NEEDED NONE :

235.238

AIRCRAFT FLYOVER 2-WAY

E wo" < 100ns DEPENDS ON FORMAT

LIMITED 8Y TRANSPORTATION

AS NEEDEO 240.241

PULSARS OPTICAL SIGNAL-»NP 0532 P Kid'

0 ~10us ~33ms HEMISPHERE NIGHTTIME

MINIMAL MINIMAL

CONTINENTAL USA

253

AC POWER LINE POWER NETWORK SYSTEM P Wff' 16 7ms

CONTINENTAL USA

264

NOTES: (1) Status of technique indicated as follows: O-Operational; P-Proposed; E/O-Experimental operational. (2) Estimates of day-to day measurements within 2000 km(1250 mi) of Loran-A stations. These emissions not coordinated with UTC and manually operated crystal clocks drift. (3) From day-to-day phase measurements

e.g., 1 fJS per day phase change approximates 1 pt. in 10^ ' in frequency difference. (4) Left-hand designation gives the shortest time interval that cannot be resolved; Right- hand number gives basic ambiguity. , by ground wave 1600 km; by sky wave thousands of kilometers depending upon conditions. , with proposed time code. •, closure

after 1 day. * within local service area of TV transmitter and path delay known.

FIGURE 10.65. Evaluation of selected time/frequency dissemination techniques.

(6) Reliability. Estimates the degree of con- fidence in the operation of a system; considers

such factors as propagation conditions, system

components in satellite environment, rerouting of

TV network programs, etc.

(7) Receiver cost for stated accuracy. Refers

to the relative cost of an appropriate receiver

and antenna system for obtaining the stated

accuracy of a given technique. Equipment such

as oscilloscopes, digital counters, etc., is not in- cluded. A poor rating implies a cost greater than

several thousand dollars; fair refers to a cost in the

$1,000 to $2,000 range; and good indicates a cost

less than $1,000.

(8) Cost per calibration. Considers factors such

as the cost of required instrumentation to make

the calibration and the probable frequency of

calibration.

(9) Number of users that can be served. Refers

to the probable number of users for a given dis- semination technique assuming regular availability of the service, and considering the equipment costs involved. For example, the TV technique is con- sidered to have more potential users than the

WWVB broadcasts, even though both cover the

continental U.S. Relevant factors also include the

low cost of TV receivers and random propagation

disturbances associated with WWVB reception.

301
(10) Operation skill required for stated accuracy. Describes the degree of difficulty in making a time/

frequency measurement to the stated accuracy.

A good rating is shown if the time information can be obtained simply from an oscilloscope display

or a counter reading. A fair category indicates

that the user must process the data to obtain the

required information, make multiple measurements

or select particular cycles of a radio signal, and/or use specialized receiving techniques. A poor rating

indicates that complex procedures and special

skills are required for a given technique. The use

of the Omega system for determining time, for example, requires envelope recognition followed by

cycle identification. The following connotations are used in figure 10.65

in connection with the satellite techniques: A trans- ponder satellite relays time signals from a ground

reference station to users in either a one-way or two-way mode. In this evaluation active describes

a satellite with an onboard clock. A stationary

satellite is earth-synchronous or geostationary

while an orbiting satellite is one with a period of

revolution other than 24 hours.

It must be emphasized that the ratings are rela- tive and arbitrary. Indeed, a system with a poor

rating may be the best choice for many users. A

severe limitation on the usefulness of figure 10.65

is that it reflects judgments of all parameters of a given system assuming that a user desires the

highest accuracy normally available from the sys- tem. In the case of Loran-C, for example, use of a sky wave is excluded, with the result that coverage

is rated poor. A system designer will probably be forced to make compromises in choosing a dissemination

service. He may have to trade receiver cost for

reliability, or accept a low percent of time available

for high accuracy and good coverage. Note that most

techniques that rate "good" in accuracy are shown

as fair or poor in other important categories. No

one technique shows all favorable ratings, but HF

broadcasts, stationary satellite relays (passive), and

the proposed NBS TV Time System stand out with

only one poor rating each. At present there is no implemented time dissemination system that permits comparison of a user's clock to a primary

standard anywhere in the world at will and to an accuracy level that fully exploits the capability of

atomic standards. Satellites appear to be capable

of meeting such a challenge but worldwide satellite time dissemination service has not yet been

implemented.

10.7. CONCLUSIONS

We have attempted to present a snapshot of

proposed, experimental and operational systems

for bridging the dissemination gap between a frequency standard and a remote user. Many options

are available to a time frequency user; choices must

be based on evaluations of overall objectives, economies, advantages, and limitations for a particular

situation. The picture is one of contrasts and varia- tions in techniques, user requirements and ac- curacies, coupled with a multiplicity of inherent

characteristics. In detail we see the time and

frequency technology touching many diverse and

increasingly important areas of human life; e.g. public safety, national defense, electric power

utilities, integrated computing networks, broadcasting/television activities, transportation including aircraft-collision avoidance, telecommunication

systems, etc. Basic science is influenced also in terms of a unified standard, international time

scales, time/frequency calibrations, and time

bases for monitoring natural events of nature. In summary, many time and frequency needs are now being met at various accuracy levels and in a variety of ways; on the other hand, some needs are

unfulfilled because of accuracy requirements,

economic factors, location of receivers, etc. We

would emphasize the capability of present day

communication and navigation systems (which of

themselves require high timing accuracy) for providing time and frequency dissemination at small

additional cost and ultimately at great savings to the

frequency spectrum. Operationally, it is apparent

that the capability for keeping accurate time has

outstripped the capabilities for widespread and

economic dissemination for the last several decades.

Nevertheless, proposed and experimental systems

show great promise. If one integrates and optimizes

the TFD possibilities in today's picture and projects

these elements into the future, an achievable chal- lenge is seen; one can foresee the dissemination

gap effectively eliminated with user equivalence of

on-site standards-comparison at high accuracy,

nearly global coverage and with reasonable-cost

equipment.

ACKNOWLEDGEMENTS

As an overview chapter, this presentation relies extensively upon published material as referenced; we are indebted, thus, to the research efforts of

many individuals. We wish to thank R. Beehler, J. Barnes, J. Stanley, W. Hanson, A. Risley, and W.

Hamilton of the National Bureau of Standards,

Boulder, Colorado; and W. Klemperer and D. Hil- liard of the National Oceanic and Atmospheric Administration, Boulder, Colorado, for their contributions in reviewing and discussing portions of this paper. In addition, we thank G. Hufford, Anita Longley, G. Haydon, G. Gierhart, and B. Wieder of the

Office of Telecommunications staff (ITS) at Boulder

for detailed review and comments on Annex 10.A. The help of Sharon Erickson is greatly appreciated

in the typing and preparation of this Chapter.

302
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[236] Philibert, V., "The cesium-beam atomic clock," Electron. World, 83, No. 6, pp. 40-41,67 (June 1970). [237] USNO, "U.S. Naval Observatory time reference stations," Time Service Announcement, Series 14, No. 1, 2 pages (USNO Washington, DC 20390, April 17, 1968)

(see chap. 11 — ann. ll.E.l). [238] Hall, R. G., Private communication (January 1972). [239] NBS, "Nation gets unified time system," Nat. Bur. Stand.

(U.S.) Tech. News Bull., 53, No. 2, p. 34 (USGPO,

February 1969).

308
[240] Markowitz, W., "Air/ ground synchronization," LISNO

Report (August 1966). [241] Besson, J., "Comparison of national time standards by simple overflight," IEEE Trans, on Instrum. and

Meas., IM-19, No. 4, pp. 227-232 (November 1970). [242] CCIR, "International comparison of atomic time scales," CCIR Study Group 7 Doc. 7/8-E, Rep. 363-1, 4 pages

(ITU, Geneva, Switzerland, December 1970). [243] Tilson, S., "Pulsars may be neutron stars," IEEE Spec- trum,7,No. 2, pp. 42-55 (February 1970). [244] Pacini, F., and Rees, M. J., "Rotation in high energy

astrophysics," Scientific American, 228, No. 2, pp

98-105 (February 1973). [245] Smith, S. G., "The pulsars," Telecommunications J., 37, No. 11, pp. 750-752 (November 1970). [246] Hewish, A., Bell, S. J., Pilkington, J. D. H., Scott, P. F., and Collins, R. A., "Observations of a rapidly pulsating

radio source," Nature, 217, No. 5130, pp. 709-713

(February 24, 1968). [247] Manchester, R. N., "Pulsars: Observations and current

investigation," 1971 IEEE International Conv. Digest, No. 71C8-IEEE, pp. 154-155 (March 1971). [248] Staelin, D. H., and Reifenstein, E.C., III, "Pulsating

radio sources near the Crab Nebula,"Science, 162, No.

3861, pp. 1481-1482 (December 27, 1968). [249] Cocke, W. J., Disney, M. J., and Taylor, D. J.. "Discover,

of optical signals from Pulsar NP 0532," Nature, 221, No. 5180, pp. 525-527 (February 9, 1969). [250] Papaliolios, C, Carleton, N. P. and Horowitz, P., "Absolute time-of-arrival measurements of optical pulses from the Crab pulsar," Nature, 228, No. 5270, pp. 445-450 (October 31, 1970).

[251] Fritz, G., Henry, R. C, Meekins, J. F., Chubb, T. A., and

Friedman, H., "X-ray pulsar in the Crab Nebula,"

Science, 164, No. 3880, pp. 709-712 (May 9, 1969). [252] Duthie, J. G., and Murdin, P.. "Accurate timing of light flashes from the pulsar in the Crab Nebula during the 1969-1970 season," Astrophys. J., 163, No. 1, pp. 1-10 (January 1,1971). [253] Allan, D. W.. "Time transfer using near-synchronous

reception of optical pulsar signals," Proc. IEEE (Lett.), 60, No. 5, pp. 625-627 (May 1972).

[254] Horowitz, P., Papaliolios, C, Carleton, N. P., Nelson, J., Middleditch, J.. Hills, R., Cudaback, D., Wampler, J., Boyton, P. E., Groth, E. J. Partridge, R. B., Wilkinson,

D. T., Duthie, J. G., and Murdin, P., "Optical time-ofarrival measurements from the Crab pulsar: comparison

of results from four observatories," Astrophys. J., 166, pp. L91-L93 (June 15, 1971). [255] Hastings, H. F., "Transmission to Naval Observatory

of reference derived from hydrogen masers at NRL. NRL Progress Rep., pp. 46-47 (March 1965). [256] Koide, F. K. , "Standard frequency transmission over telephone line," Instrum. and Control Syst., 39, No. 4, pp. 123-128 (April 1966). [257] Koide, F. K., ' Aerospace frequency and time distribution system," Meas. and Data, 1, No. 3, pp. 98-108 (May/ June 1967). [258] Koide, F. K., Private communication (Autonetics, Cali- fornia, January 1973). [259] Grimsley, S. W., and Miller, M. J., "Phase comparison of frequency standards," Proc. IREE (Australia), 29, No.

1, pp. 14-17 (January 1968).

[260] Redgeman, P. G., and Watson, D. W., "Very-long-wave

phase differences between spaced aerial systems,"

Proc. Inst. Elec. Eng. (London), 94, No. 6. Pt. Ill A.

pp. 1016-1022 (1947). [261] Curtwright, J. B.. "Intra-DSCC microsecond timing

using a communication microwave link," JPL Space

Programs Summary 37-59, II, pp. 154-157 (JPL,

Calif. Inst, of Technol., Pasadena, CA 91103, September

20, 1969). [262] Cohn, N., Control of generation and power flow on inter- connected systems, 132 pages (John Wiley and Sons, Inc., New York. NY 10016, 1966).

[263] Cohn, N., "Techniques for improving the control ol bulk power transfers on interconnected systems," IEEE Trans, on Power Applicat. Syst., I'AS-90, .No. 6, pp. 2409-2419 (November/December 1971 1. [264] Allan, D. W., Machlan, H. E.. and Marshall, J., "Time

transfer using nearly simultaneous reception times ol a common transmission," Proc. 26th Ann. Symp.

Frequency Control (U.S. Army Electronics Command,

Ft. Monmouth, NJ 07703, June 6-8, 1972), pp. 309-

316 (Electron. Ind. Assn., Washington, DC 20006.

1972). [265] Palmer, W., "The Omega navigation system as a source

of frequency and time," Proc. 24th Ann. Symp. on Frequency Control (U.S. Army Electronics Command,

Ft. Monmouth, NJ 07703, April 27-29, 1970). pp. 345-360 (Electron. Ind. Assn., Washington, DC 20006,

1970). [266] Dejager, C, and Jappel, A., (Eds.), "Commission 31: Time (I'Heure), Report of Meetings 19, 21, 24 and 26, August 1970," Trans. IAU, XIV-B, page 196 (D. Reidel Publishing Co., Holland, 1971). [267] Kaiser, A. B., "An explanation of VLF diurnal phase

change observations," Radio Science, 4, No 1, pp

17-21 (January 1969). [268] Budden, K. G., Radio Waves in the Ionosphere, 542 pages (Cambridge University Press, London, England,

1961). [269] Johler, J. R., "Loran-C, D phase corrections over irregular, inhomogeneous terrain-simplified computer methods,"

ESSA Tech. Report ERL 116-ITS 83, 55 pages (USGPO.

April 1969); also see ref. [13]. [270] Berry, L. A., "Wave hop theory of long distance propagation of low frequency radio waves," Radio Science

(J. Research) NBSIUSNC, URSI, 68D, No. 12, pp. 1275-1284 (December 1964). [271] Belrose, J. S., "The lower ionosphere — a review," Proc. Conf. on MF, LF, and VLF Radio Propagation (London,

England, November 8-10, 1967), Inst. Elec. Eng. (Lon- don) Conf. Publ. No. 36, pp. 331-339 (1967). [272] Kobayashi, S., Nakajima, M., and Sato, T., "Accuracy

of the domestic time synchronization by the reception

of JJY signals at long distances," Radio Res. Lab.

Rev., 14, No. 72, pp. 373-377 (May 1968) (in Japanese).

[273] Haydon, G. W., Lucas, D. L., and Hanson, R. L., "Technical considerations in the selection of optimum fre- quencies for high frequency skywave communication

services," unpublished report (1962). [274] Bullington, K., "Radio propagation at frequencies above

30 megacycles," Proc. IRE, 35, No. 10, pp. 1122- 1136 (October 1947). [275] Lawrence, R. S., Little, C. G., and Chivers, H. J. A.. "A survey of ionospheric effects upon earth-space

radio propagation," Proc. IEEE, 52, No. 1, pp. 4-

27 (January 1964). [276] Aarons, J., Whitney, H. E.. and Allen, R. S., "Global morphology of ionospheric scintillations," Proc. IEEE,

59, No. 2, pp. 159-172 (February 1971). [277] Reed. H. R., and Russell, C. M., Ultra High Frequency

Propagation, 562 pages (Boston Tech. Publ., Cambridge, MA 02139, 1964). [278] Bean, B. R., and Dutton, E. J.. Radio Meteorology, Nat. Bur. Stand. (U.S. ) Monogr. 92, 435 pages (USGPO,

1966). [279] Dougherty, H. T.. "A survey of microwave fading mechanisms, remedies, and applications," ESSA Tech. Rep. ERL 69-WPL4, 82 pages (USGPO, April 1968). [280| Thompson, W. I., Ill, "Atmospheric transmission handbook: A survey of electromagnetic wave transmission in the earth's atmosphere over the frequency (wavelength) range 3 kHz (100 km)-3000 THz (0.1 micron m)." Dept

Trans. Tech. Rep. DOT-TSC-NASA-71-b. 296 pages (NTIS. N71-20121. February 1971).

[281] Guinot. B.. Feissel. M., and Graveaud. M.. Bureau Inter- national de I'Heure Annual Report — 1971 (BIH. Paris. France, 1972).

309

tOUGH 10

Frequency Band

Frequency Ranges General Description of Frequency Band Transmission

VLF

(Very Low

Frequency)

Band 4

LF

(Low

Frequency)

Band 5

3-30 kHz

Ome^a

(10.2 to 13.6 kHz Communications

(16 to ~26 kHz) Time/Frequency

(20 kHz)

30-300 kHz Time /Frequency

(40 to ~100 kHz) Loran-C (100 kH;

Stabilized Carrie Broadcast Station

{~90 to 200 kHz)

mainly Europear

stations

the bounds of the ionospheric D layer and earth and are thus guided around the curvature of the w attenuation and excellent stability. Diurnal changes are very abrupt when transmitter and relongitude; the amount of the diurnal change varies with the distance of the path travel and car- phase shift is predictable to several microseconds [ 34, 267], VLF propagation haB been extena, 12a, 268] and models have been developed for predicting phase delay and signal strength at er power. It has been found both experimentally and theoretically that the phase variation with regular in the 10-20 kHz region as the distance from the transmitter increases. The high Q of

I pulse rise which limits envelope timing to about 1 ms. VLF signals are broadcast from worldut 1 kW to 1 MW power. Stable VLF signal reception, during daylight hours with totally sunlit

; comparisons accurate to one or two ^is [ 30, 31, 46], (Swanson and Kugel [59] describe both

gation is similar to that of VLF signals. The higher frequency broadcasts are most stable with- transmitter (about 500 km), LF signals generally show greater attenuation with distance than

dth permits pulsed signals at 100 kHz. This allows separation of the stable ground wave pulse

se up to 1500 km and overseas ranges to more than 2000 km. LF signals are broadcast from

apan with transmitter radiated powers of 5 to 400 kW, Stable CW LF signal reception during

nlit path can give phase comparisons to several /is for paths greater than 5000 km [ 54], LF

*e good to about 40-50/2S [67] while LF ground wave signals provide precisions of nanoseconds LF propagation characteristics have been described by Johler, Berry, and Belrose [ 269-271] . e the Loran-C navigation system and its use for time dissemination. )

MF

(Medium

Frequency)

Band 6

300 kHz-3 MHz

Commercial

Station Broadcast

(535-1605 kHz) Lor anA

(1. 85-1. 95 MHz)

ithin ground wave distance (less than 150 km in the day, perhaps half of that at night). It will

t bandwidth for time pulses, especially at the high end. Coarse time signals are accurate to accuracies of ±30/is are expected from JJY broadcasts at reception distances of 1000 km using mercial broadcast station in Tennessee, U.S.A. (650 kHz) is phase stabilized to severalus/day

173], providing a local relay standard frequency service. Standard frequency and time broad-

;d powers ranging from less than 1 kW to about 5 kW.

HF

(High Frequency)

Band 7

3. 0-30 MHz

Worldwide

Short W avc Broadcasts

! band. The ionosphere absorbs little energy, resulting in worldwide reception. Movement of Doppler shifts and fluctuations in amplitude and phase, degrading accuracy to pts in 10^. For

s limited to the ground wave at distances less than 1 6 0 km during the day, perhaps half that at ;he approximate upper limit for usual sky wave propagation. Sufficient bandwidth is available on in this frequency band. Many studies of HF band have been made [ 14, 273], Computer jjro- able frequencies (MUF), optimum frequencies (FOT), and critical frequency with given circuit different locations, directions of propagation, time of day, season, sunspot activity, etc. Lgnals received at the USNO, Washington, DC (2400 km land path) showed day-to-day variations

i duplicated at the same time every day on the same frequency. Receiving equipment and anten-

, Standard frequency and time are transmitted at radiated powers that range from 0. 5 - 20 kW,

VHF

(Very High

Frequency)

Band 8

30-300 MHz ly limited to line-of-sight and near line-of-sight (usually <150 km); however, ionospheric scat- >ospheric scatter (<1000 km) systems exist. Signals penetrate the ionosphere with low loss of es). Satellite transmitter power is relatively low (40-100W), and can transfer signals tonearly transmissions show potential for precise time broadcasts in a local service area[ 116,121,133],

/e been described by Bullington; Lawrence, et al. ; Aarons, et al. [ 274-276], For low power

a and receiving equipment is fairly low. Directional antennas, capable of respondingto varied sponse to VHF satellite signals.

UHF

(Ultrahigh Frequency)

Band 9

300 MHz-3. 0 GHz s are found in this band. These are high powered, point-to-point communication links from 100 wise, signals are limited to line-of-sight (usually less than 100 km). Such signals are very

ion and fading may be present. Propagation characteristics are described by Reed and Russell; any of the environmental satellites and most of the broadcast satellites are expected to operate

lie and can be used in ways similar to TV at VHF. Relatively low power of transmission is re2 of satellite signals with excellent stability. Directional antennas are advisable; both antenna

o increase, especially at the higher frequencies.

SHF

(Super High

Frequency)

Band 10

3. 0-30 GHz : or centimeter wave band. Signals are limited to line-of-sight, and the microwave relay sysrt (40-60 km) hops or links. The long haul lines of the common carriers usually use such sysrange stabilities of several us [ 125, 128] . Microwave links are also used to relay time signals

least terminal. A 32 km link at the USNO uses signals in the 7GHz region (radiated power 7 W)

than 10 ns and a time setting capability better than 100 ns [ 169]. Antennas are usually highly quipment tund to be both expensive and complex. At the higher end, where molecular ahsorptheless "windows" which enable stable signals to be transmitted between earth and space with

.gation characteristics are described by Dougherty and Thompson [ 279, 280]

.

310a

ANNEX 10.A. CHARACTERISTICS OF RADIO FREQUENCY BANDS 4 THROUGH 10

310a
I
ANNEX 10.B. CHARACTERISTICS OF STANDARD FREQUENCY AND

TIME SIGNALS IN ALLOCATED BANDS* J >

HAP

NO. STATION TRANS UTTER CARRIER 1

2

) TIME ' ll lifll c jJUHHLo 1 2) PERIOD OF OPERATION

SEE FIGURE

10.4

CALL SIGN APPROXIMATE

LOCAT I ON LONGITUDELAT I TUDE ANTENNA

TYPE

RADIATED °

CARRIER *

POWER m

kW ?

simultaneousItransmissions STANDARD FREQUENCIES

MHz

MODULATION ACCURACY

PTS IN 10

10 TIME PULSES

pps

DURATION

M1N

TIME ADJUSTMENT

OAYS

PER WEEK

HOURS

PER

DAY

1 ATA

New Del hi , INDIA +28*34 ' N -77 *1 9

' E HORIZONTAL

DIPOLE 2 10 1 ; 1 000 ±200 YES CONTINUOUS VLF STEERING PORTABLE CLOCK 5

2 FFH Paris, FRANCE +48*32 ' N -02*27 * E RADIATING

MAST 5 ] 2.5 1 ; 1 000 ±2 YES 30/h UTC S(H-F) e.s

3 I AM ITALY

+4 1 "52 ' N

- 1 2*27 ' E

V ERT I CAL

X/4 1 1 5 1 ; 1 000 ±0.5 YES 10/15 UTC 6 2

4 IB F Torino, +45*02 |N VERTICAL

5 1 ; 1 000 ±0.5 YES CONTINUOUS UTC 7 2.75

5 JG2AR Tokyo,

JAPAN

I i', 4 2

' N -139*31 ' E OMNI- DIRECTIONAL 3 1 0.02 ! ±1 CONTINUOUS NON-OFFSET

CARRIER

5(M-F) 2 (0530- 0730 UT

Tokyo,

JAPAN

+ 35°42 'N -139*31 'E

VERTICAL A/2 DIPOLES;

{A/2 DIPOLE,

TOP -LOADED

FOR

2.5 MHz)

2 2.515

1 0 ; 1 5

1 ;600;

1 000; 1500 ±0 .

5

YES CON T I NUOUS

24

(9 MI

K

PER h)

7 LOL Buenos Aires, ARGENTINA

-34*37 'S +58*21 'W

HORIZONTAL

3-WIRE FOLDED D I POLE

2 3 5 ; 1 0 ; 1 5

1 ;440; 1000 ±0.2 YES CONTINUOUS UTC 7 5

8 Rugby

,

KINGDOM

+ 52*22 'N

+ 01 "11 "W

HORIZONTAL

QUADRANT

DIPOLES; (VERTICAL MONOPOLE

.

2.5 MHz

)

0.5 3 2.5;5;T0 1 ;1000 ±1 YES 7 24

9 OHA Praha

,

CZECHOSLOVAK

S.R.

+ 50*07 ' N -14*35 'E

T 1 1 2.5 1 ; 1000 ±10 15/30 UTC /

7 24

10 RWM/RES Moskva

,

U.S. S.R.

+ 55*45 'N -37*1 8

1 E 20 1 5 ; 1 0 ; 1

5

1 ;1000 ±50 YES 10/2 h UTC

(UT1 -UTC

TO 10 ms)

7 19

1 1 WUV

(3)

Fort Collins, COLORADO

U.S.A.

+40*41 1 N + 105*02 'H

VERTICAL

A/2 DIPOLES

2.5-10

(VARIES WITH CARRIER FREQ)

6

2 . 5 ; 5 ; 1 0 15;20;25

1 ;100;44U; 500;600;

1 000 ;1 500 ±0.1 YES CONTINUOUS UTC 7 24

WWVH

(3)

' Kama*.

H AWA I I U.S.A.

+ 21°59'N +159°46'W

PHASED VERTICAL

A/2 DIPOLE ARRAYS

(VERTICAL

A/2 FOR

2.5 MHz)

2.5-10

{ V AR I ES WITH CARRIER FREQ)5

2 . 5 ; 5 ; 1 0 15;20

1 ;1 00;440;

500 ; 600

;

1 200;1 500 ±0 .

1

YES 7 24

13' WWVL

(4)

Fort Collins, COLORADO

U.S.A.

+40*41 'N

+ 1 05*03 'W

TOPLOADED VERTICAL

1 .8 1 0.02 NIL ±0.1 NIL NIL NON-OFFSET

CARRIER 7 24

1 4 ZLFS Lower Hutt,

NEW ZEALAND

-41*14 'S

-1 74*55 'E 0.3 1 2.5 NIL ±1 NIL NIL 1 3

1 5 ZUO

01 ifantsfontein. REPUBLIC OF SOUTH AFRICA

-25*58 'S -28*14 'E VERTICAL

MONOPOLE 1 1 ,1000 ±0.5 YES CONTINUOUS UTC 7 24

16 ZUO Johannesburg , REPUBLIC OF SOUTH AFRICA

-26*1 1 'S -28*04 ' E HORIZONTAL

DIPOLE 0.25 1 10 1 ; 1 000 ±0.5 YES CONTINUOUS UTC 7

NOTES: (1) PRINCIPAL INFORMATION EXTRACTED FROM CCIR PROC. Xllth PLENARY ASSEMBLY (NEW DELHI, INDIA, 1970).

VOL. Ill [73] AND THE BIH ANNUAL REPORT FOR 1971 [281], WE REFER THE READER TO THESE DOCUMENTS FOR ADDITIONAL NOTES ON VARIATIONS OF SOME BROADCASTS, AS WELL AS TRANSMISSION FORMATS.

(2) UTC TIME ADJUSTMENT AND ZERO OFFSET OF CARRIER FREQUENCIES (ATOMIC FREQUENCY) COMMENCED JANUARY 1, 1972. STEP ADJUSTMENTS OF 1 s (LEAP SECONDS) WILL BE MADE AT DESIGNATED TIMES TO PREVENT UT1 DIFFERING

FROM UTC BY MORE THAN ±0.7s. A SPECIAL CODE IS DISSEMINATED WITH TIKE SIGNALS TO GIVE DIFFERENCE UT1 - UTC TO 100 ms. THE USSR BROADCASTS ALSO WILL GIVE DIFFERENCE TO 10 ms . TIME SIGNALS OF ALL STANDARD FREQUENCY BROADCASTS ARE TO BE MAINTAINED WITHIN +1 ms. OF UTC.

(3) AN IRIG-H (MODIFIED) BCD TIMING CODE IS TRANSMITTED CONTINUOUSLY. THIS CODE IS PRODUCED AT A 1 pps RATE

AND CARRIED ON A 100 Hz SUBCARR I ER , AT A COMPLETE TIME FRAME OF 1 min. THE CODE GIVES UTC IN s, min, h AND DAY OF YEAR AND CONTAINS 60/min CLOCKING RATE', 6/min POSITION IDENTIFICATION MARKERS, AND A 1/min REFERENCE MARKER. THE 100 Hz IS SYNCHRONOUS WITH THE CODE PULSES, PROVIDING 10 ms RESOLUTION.

(4) WWVL CAN BE USED FOR SYNCHRONIZATION; IT IS AN EXPERIMENTAL BROADCAST ONLY AND IS ON AN INTERMITTENT TRANSMISSION SCHEDULE.

311
ANNEX 10.C. CHARACTERISTICS OF STABILIZED FREQUENCY AND

TIME-SIGNAL EMISSIONS OUTSIDE ALLOCATED FREQUENCY

ASSIGNMENTS*1 *

MAP

NO

.

STATION TRANSMITTER CARRIER . TIME SIGNALS PERIOD OF OPERATION

SEE FIGURE

10.4

CALL

SIGH APPROXIMATE

LOCATION LONGITUDE

LATITUDE ANTENNA

TYPE

RADIATED

CARRIER

POWER

kW »

OF

SIMULTANEOUS

BROADCASTS STABILIZED

FREQUENCIES

kHz

MODULATION ACCURACY

PTS IN 10

10 TIME

PULSES

pps

DURATION

M IN

TIME SIGNAL ADJUSTMENT

DAYS

PER WEEK

HOURS

PER

DAY

A FRANCE -02*12 '£ DIRECTIONAL 500 1 163.84 NIL ±0.5 NIL NIL ZERO OFFSET CARRIER 7 24

B CHU Ottawa

,

CANADA

+45° 1 8

'

N

+75-45 'W

FOLDED DIPOLES J RHOMBIC

3 3330:7335;

14670 1 ; 1000 YES CONTINUOUS

FR/ENG VOICE ANNOUNCEMENT

UTC 7 24

C GERMANY

+4 9 "34 ' N -09 e ll ' E OMNI- DIRECTIONAL

70 > 15) NIL ±0.3 NIL NIL ZERO OFFSET CARRIER 7 24

D DCF77

Ma i nf 1 i ngen

,

F.R. of GERMANY

+50°01 '

N

-09°00'£ OMNI- DIRECTIONAL 12 77 .5 1 ,440 ±0.2 YES CONTINUOUS ZERO OFFSET CARRIER 7 24

E Droitwich,

UNITED KINGDOM

+ 52°15 'N +02°09'W T 400 < 200 NIL ±0.2 NIL NIL ZERO OFFSET CARRIER 7 22

F GBR

Rugby, UNITED KINGDOM

+52*22 ' N +01°11 'W OMNI- DIRECTIONAL 60(EST.) 1 5 .95 16.00 • ±0.2

Al TYPE PER DAY

UTC 7

22 (OFF

1 300-

1430 UT

DAI LY

G MBG Prang ins. SWITZERLAND 46°24 ' N -06*15'E

OMNI- DIRECTIONAL 20 75 1 ±0.2 CARRIER INTERRUPTION CONTINUOUS UTC 7 24

JJF-2 JG2AS Chi ha C JAPAN

+ 35°38'N

-140*04 'E OMNI- DIRECTIONAL 10 1 40 NIL ±0.5 NIL NIL UTC 7 24

I MSF Rugby , + 01-11 'W DIRECTIONAL 50 60 ±0.2 CARRIER INTERRUPTION CONTINUOUS UTC 7 24

J NAA

(4) Cutler, MAINE +44°39 'N OMNI- DIRECTIONAL

1000

1 17.8 NIL ±0.5 NIL NIL UTC 7

K NBA

(4) Salboa, Pana- ma, Canal Zone

U . S . A.

+09"04 '

N

+ 7 9° 3 9 ' W OMNI- DIRECTIONAL

1 50 (EST.) 1 24 1 ±0.5

CW TIME

PULSES

5 EVERY EVEN h EXCEPT 2400

UTC 7 24

L NDT

(4) JAPAN

34'58 '

N

137-01 'E

NPG/ NLK {4} WASHINGTON

U. S. A.

+48*12'N

+1 21 -55 - W OMNI- DIRECTIONAL

250 (EST.) 18.6 NIL +0.5 NIL NIL UTC 7 24

N NPM

(4) Lualualei

.

HAWAII

U. S. A.

+ 21 "25'N

+1 58-09 ( W OMNI- DIRECTIONAL

140 (EST.) - 23.4 NIL ±0.5 NIL NIL UTC 7 24

MARYLAND

U. S. A.

+38*59'N

+ 76-27 'W OMNI- DIRECTIONAL

100 (EST.) • 21 .4 1 ±0.5

CW TIME PULSES

6 EVERY h UTC 7 24

Q NHC

(4) AUSTRAL I

A

- 21-49'S

-1 14*10 ' E OMNI- DIRECTIONAL

1000 (EST.) 22.3 ±0.5 FSR PULSES

2 BEFORE 0430,1630

(EXPERIMENTAL)

UTC 7 24

OMA Podebrady

,

CZECHOSLOVAK

S . R

.

+ S0°08 'N -15-08'E T 5 50 ±10

CARRIER INTERRUPTION

Al TYPE

23 h PER DAY UTC 7 24

s RWM - RES Moskva

,

U.S.S.R.

+ 55°46 'N -37*18'E

20 100 1 ±50 Al TYPE

5 EVERY h EXCEPT 2000 UTC 7 21

SAZ

Enkb'pi ng

,

SWEDEN +59-35-N

-17 B 08'E

YAGI

(12 db)

0.1 (EST.) ID

5 NIL ±50 NIL NIL ZERO OFFSET CARRIER 7 24

u SAJ Stockholm , SWEDEN

+ 59*20 ' N -18-03 'E OMNI- DIRECTIONAL0 .

1

(EST.) 1.5 X 10

5 NIL ±1 NIL NIL ZERO OFFSET CARRIER (FRIDAY)

2 (0930-

1 1 30 UT)

VE9GBS

(3) Ottawa

,

CANADA

+ 45'22 'N +76'53'W TOP-LOADED

VERTICAL

0.006-1 .4 (DEPENDENT

ON FREQ.)

16.9, 23-200 NIL ±0.3 NIL NIL UTC 7 24

VNG

Lynd hur st

,

VICTORIA AUSTRALIA

- 38-03'S -145-16'E

OMNI- DIRECTIONAL 10 45O0;75OO

1 2000 1 -.1000 YES CONTINUOUS

EXCEPT FOR SILENT PERIODSUTC 7 24 (VARIES BY FREQUENCY)

wwve Fort Col 1 ins, COLORADO

U. S. A.

+ 40*40'N

+105*03 , W TOP -LOADED VERTICAL 1 3 60

t> ±0.1 TIME CODE CONTINUOUS UTC 7 24

zuo Johannesburg

,

REPUBLIC OF SOITH AFRICA

-26-11 'S -28°04 'E OMNI- DIRECTIONAL 0. 05 ID

5 ±0.5 CONTINUOUS UTC 7 24{SILENT

15-25 MIN PAST h)

NOTES: (1) INFORMATION OBTAINED AS IN ANNEX B; IN ADDITION FROM REF. [74].

(2) AS NOTE (2) IN ANNEX B.

(3) EXPERIMENTAL LF STATION USED PRIMARILY FOR PROPAGATION STUDIES. FOR SCHEDULE OF FREQUENCIES BROADCAST, CONTACT DR. J. BELROSE, DEPARTMENT OF COMMUNICATIONS, SHIRLEY BAY, ONTARIO, CANADA.

(4) THESE STATIONS ARE USED PRIMARILY FOR COMMUNICATION. TRANSMISSIONS ARE REFERENCED TO C s FREQUENCY STANDARDS AND ARE USEFUL FOR FREQUENCY SYNCHRONIZATION. STATION CH ARAC ERT I ST I C S ARE SUBJECT TO CHANGE;

HOWEVER, CHANGES ARE ANNOUNCED IN ADVANCE TO INTERESTED USERS BY USNO, WASHINGTON, D.C., U.S.A.

(5) FORMAT IN PLANNING STAGE.

312
ANNEX 10.D. CHARACTERISTICS OF FREQUENCY STABILIZED NAVI

GATION SYSTEMS USEFUL FOR TIME/FREQUENCY COMPARISON'1 '

STATI0N

{2) TRANSMITTER CARRIER

(3 j TIME SIGNALS

(3) PERIOD OF OPERATION

CALL SIGN

CHAIN DESIGNATION

(4)

APPROXIMATE

LOCATION LONGITUDE

LATITUDE ANTENNA

TYPE

CARRIER

POWER

kW

(5)

STABILIZED

FREQUENCIES

GROUP REPETITION

PERIODS

(GRP)

ACCURACY

PTS IN lo'°

TIME PULSES

pps UURAT I ON METHOD

OF ADJUSTMENT

DAYS

PER WEEK

HOURS

PER

DAY

LORAN-C SS7-H

EAST COAST

U. S. A.

Carol ina Beach N . C

.

u. s! a! 34"Q3 '46"N +77°54 '46"W OMNI- DIRECTIONAL

99,300

CONTINUOUS

LORAN-C SS7-W FLORIDA*

U. S. A.

+27*01 '59"N +80°06'53"W

OMNI- DIRECTIONAL 400 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C

SS7-X Cape Race, NEWFOUNDLAND

+46*46 '32"N +53"10'29"W

OMNI- DIRECTIONAL 3000 100 ±0.05 YES CONTINUOUS 1 ui STEPS 7 24

LORAN-C

SS7-Y

Nantucket

U. S. A.

+41 C 15'12"N +69*58'39"W

OMNI- DIRECTIONAL

LORAN-C

SS7-Z

Dana

,

INDIANA

U. S. A.

+39*51 '08"N +87 0 29'11"W

' OMNI- DIRECTIONAL 400 100 ±0,05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C SL3-M

NORWEGIAN

SEA

Ejde. Faroe Is. +62°17'57"N

+ 7°04-15"W

OMNI- DIRECTIONAL 400 100

79,700

±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C SL3-H

Sylt. GERMANY +54°48'29"N

- 8

0

1 7

' 4 1 " E OMNI- DIRECTIONAL 300 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C SL3-X

Bo. NORWAY +68°38'05"N

-14*27 '54"E OMNI- DIRECTIONAL 200 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C

SL3-Y Sandur

,

ICELAND

+64°54 '31 "N +23°55"08"W

OMNI- DIRECTIONAL 3000 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C SL3-Z

Jan Mayen, NORWAY +70°54'S6"N

+ 8"43'59"W

OMNI- DIRECTIONAL 200 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C SH4-M CENTRAL

PACIFIC

Johnston

Is .

+ 16°44'44"N +169°30'32"WOMNIDIREC riONAL 300 100

59 ,600

±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C

SH4-X

Upolo Pt .

,

HAH A I I

+ 20°14'S0"N

+155*53 '09"W OMNI- DIRECTIONAL 300 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C SH4-Y MIDWAY is.

+ 28*23 ' 4

1 "

N

+178*17 -30"W OMNI- DIRECTIONAL 300 1 00 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C

SS3-M

PACIF IC

I wo J1ma, JAPAN

+ 24*48'04"N

-141*19'29"E

OMNI- DIRECTIONAL 4000 1 00

99.700

±0.05 YES CONTINUOUS 1 us STEPS 7 24

SS3-W Marcus Is.

+ 24*1 7' 08"N -153*S8'51"EOMNI - DIRECTIONAL 4000 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C

SS3-X

H °JAPAN°'

+ 42*44'33"N

-143*43 '05"E OMNI- DIRECTIONAL 400 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C Gesasht

,

OK I NAWA

+ 26*36*21 "N

- 1 28*08 ' 54 "E OMNID I RECT I ONAL 400 100 ±0.05 YES CONTINUOUS 1 us STEPS 7 24

LORAN-C

SS3-Z

Yap CAROLINE^ IS.

+ 9*32'46"N -138°09'55"E

OMNI- DIRECTIONAL 4000 100 ±0.05 YES CONTINUOUS 1 us" STEPS 7 24

NIL NORWAY -13°09'E

TOP - LOADED FJORD SPAN

4 E (6),

10.2-A

i3.6-e

(7)

NIL ±0.5 NIL

(8) CONTINUOUS (3) 7 24

OMEGA

(1/NO (REPLACES

ONY-)

NIL

N . D . .U.S.A. +46*22 ' N +98*20 'W

TOP-LOAOED

V ERT I CAL UMBRELLA

1 0 ( E RP )

10.2-0

11-1/3-F

1 3 . 6-E !i:f

5 }<»>

N I L NU

(8) CONTINUOUS

(9)

(3} 7 24 (ABOUT APRIL 1972)

OMEGA

tl/T NIL Trinidad,WEST INDIES

+ 10*42 'N +31 *38'W

TOP- LOADED

VALLEY -SPAN 1 (ERP)

10.2-B 11-1/3-0

12.0(u) 13.6-C

NIL ±0.5 NIL

(8) CONTINUOUS

(9}

(3) 7 24

OMEGA

(1/H NIL HAW A I

!

U. S. A.

+ 21'24'N

+1 57*50 'W TOP-LOADED

VALLEY -SPAN 2{ERP)

10.2-C

1 1 -1/3-E

12.2(u) 13.6-D

NIL ±0.5 NIL

(8)

i 0 NT I NL 0 U

', (9)

(3) 7 24

(1) INFORMATION OBTAINED AS IN ANNEX B.

(2) LOCATION OF LORAN-C STATIONS SHOWN IN FIGURE 10.18; OMEGA PROPOSED LOCATIONS ARE SHOWN IN FIGURE 10.16.

(3) THESE BROADCASTS WILL BE TRANSMITTED WITH ZERO OFFSET AFTER JAN. 1, 1972; OMEGA SYSTEM WILL NOT MAKE

LEAP SECOND ADJUSTMENTS.

(4) THESE LORAN -C CHAINS ARE TIME SYNCHRONIZED AND PHASE CONTROLLED WITHIN ±1

5

M s OF UTC(USNO). (M DESIGNATION

INDICATES MASTER; W, X, Y, Z INDICATE SLAVE STATIONS.) FOUR ADDITIONAL CHAINS ARE USED FOR LORAN-C NAVIGATION AND EMPLOY Cs STANDARDS FOR FREQUENCY CONTROL, BUT ARE NOT MAINTAINED WITHIN ±15ys OF UTC . OF THESE, THE MEDITERRANEAN AND NORTH ATLANTIC ARE , T IME -MON I TORED AND CORRECTIONS IN TERMS OF UTC(USNO) ARE PUBLISHED WEEKLY; THE NORTH PACIFIC (ALASKA) AND SOUTHEAST ASIA ARE UNSYNCHRON I ZED AND ARE NOT RELATED TO

UTC. THESE LATTER FOUR CHAINS ARE SUBJECT TO TIME JUMPS AND EQUIPMENT FAILURES. SYNCHRONIZATION OF STATIONS WITHIN A CHAIN USUALLY HELD WITHIN ±0.2ps.

(5) PEAK POWER EXCEPT AS NOTED ESTIMATED RADIATED POWER (ERP).

(6) EIGHT WORLDWIDE OMEGA NAVIGATION STATIONS ARE PLANNED FOR FULL IMPLEMENTATION IN THE 1970's. GLOBAL COVERAGE IS ANTICIPATED WITH EACH STATION RADIATING 15 kw OF POWER AT STABILIZED FREQUENCIES BETWEEN

10.2 and 13.6 kHz. FOUR INTERIM STATIONS ARE NOW IN OPERATION AND ARE IN PROCESS OF BEING UPGRADED. ADDITIONAL OMEGA STATIONS WILL BE CONSTRUCTED IN JAPAN, AUSTRALIA-NEW ZEALAND AREA, LA REUNION (INDIAN

OCEAN) , AND ARGENTINA.

(7) LETTERS REFER TO SEGMENTS OF OMEGA FORMAT EXCEPT u_ WHICH INDICATES UNIQUE ASSIGNED FREQUENCY TO GIVEN STATION.

(8) DAY, h, min, LOW-BIT RATE TIME CODE PROPOSED FOR FUTURE INCLUSION IN OMEGA FORMAT.

(9) OMEGA FORMAT IS TIME MULTIPLEXED.

313

CHAPTER 11

THE STANDARDS OF TIME AND FREQUENCY IN THE USA**

James A. Earnest and Gemot M. R. Winkler $

Contents

Page 11.1. Introduction 317

11.2. Time Scales — Terms of Reference 317

11.2.1. Compromise Time Scales 318

11.3. Time and Frequency (T&F) Activities of the National Bureau of Standards and the U.S. Naval Ovservatory 318

11.3.1. The Formal Missions of the T&F Activities of the NBS and USNO 318

a. T&F Activities of NBS 318

b. The Position of the U.S. Naval Observatory in the Federal Government.. 319

(1) The USNO Time Service Division, Background 320

(2) Organizations of the USNO Time Service Division 320

11.3.2. T&F Activities of NBS and the USNO Compared 321

11.3.3. Coordination of T&F 322

11.4. International Organizations Involved in Standard Time and Frequency 323

11.4.1. Organizations of the Treaty of the Meter (Standards) 324

11.4.2. Scientific Organizations 324

11.4.3. International Radio Consultative Committee (CCIR) (Regulatory) 324

11.5. The Legal Definition of "Standard Time" 325

11.6. Summary 325

11.7. References 325

Annex 11. A. NBS Enabling Legislation 329

Annex ll.B. USNO Authorizing Documents 347

Annex 11. C. NBS Time and Frequency Responsibilities 359

Annex 11. D. USNO Precise Time and Time Interval (PTTI) Responsibilities 363

Annex 11. E. NBS/USNO Time Coordination/Services 377

Annex 11. F. Treaty of the Meter 385

Annex 11. G. Legal Documents Concerning "Standard Time" 389

*This chapter is a slightly modified version of a paper of the same title presented at the 26th Annual Symposium on Frequency Control (Atlantic City, NJ, June

6-8, 1972). •Manuscript received February 23., 1973. tTime and Frequency Division, Institute for Basic Standards, National Bureau of Standards, Boulder, CO 80302. tTime Service Division, U.S. Naval Observatory, Washington, D.C 20390.

315
"Let us raise a standard to which the wise and honest can repair . . ."

George Washington Speech to the Constitutional Convention,

1787.

This chapter describes the national responsibilities for standards of time and frequency in the U.S.A. The National Bureau of Standards (NBS) and the U.S. Naval Observatory (USNO) are the two

organizations chiefly involved in distributing accurate and precise time and frequency information

within the USA. The NBS is responsible for the "custody, maintenance, and development of the

national standards" of frequency and time (interval) as well as their dissemination to the general public. The mission of the USNO includes the "provision of accurate time" for electronic navigation systems, communication, and space technology. This is an integral part of its work concerned with the publication of ephemerides which are used in support of navigation and in the establishment of a fundamental

reference system in space. Both agencies provide the U.S. contribution to the Bureau International de l'Heure (BIH) [Inter- national Time Bureau], which has the responsibility of publishing definitive values of Universal Time

(UT), International Atomic Time (TAI), and Coordinated Universal Time (UTC).

Key words: Astronomical time measurements; clock synchronization; clocks; Coordinated Universal Time (UTC); frequency; frequency standards; International Atomic Time (TAI); International Radio

Consultative Committee (CCIR); International Scientific Radio Union (URSI); International Time

Bureau (BIH); international time organizations; leap seconds; national time/frequency standards; NBS time and frequency; Precise Time and Time Interval (PTTI); time; time coordination; time

interval; time scales; treaty of the meter (standards); U.S.A. standard time zones; USNO time and

frequency.

316
11.1. INTRODUCTION

The national responsibilities for the provision of

standards of time and frequency (T&F) in the U.S.A.

rests with two organizations of widely different background, professional traditions, and outlook (NBS

enabling legislation and USNO authorizing documents (annexes 11. A and 11. B)). The measurement

of T&F permeates all scientific observations. It is fundamental to any system of measurement standards, and it is an indispensable element in fundamental astronomy, geodesy, and navigation. It follows from this wide range of applications and

interfaces with all disciplines of science and tech- nology that requirements for standards of T&F can

only be satisfied in some form of compromise.

A short discussion of principles and terminology,

followed by a minimum of historical accounts, will

facilitate the review of the present distribution of

work and responsibilities of the two agencies in- volved, the National Bureau of Standards (NBS)

and the United States Naval Observatory (USNO).

International organizations with time and frequency

responsibilities in the areas of standards, scientific groups, and regulatory bodies are described. A

brief section outlines the status of the legal defini- tion of "standard time" in the U.S.A. Seven Annexes

document various aspects of the contents of this chapter.

11.2. TIME SCALES —TERMS OF

REFERENCE

A time scale is any system which allows the

unambiguous ordering of events. Calendars are

(rather coarse) time scales. Indeed, the daily move- ment of the sun, stars, and the moon provides the

Time Scale prototype, even though the standard

intervals are not uniform. Uniformity is a requirement which is becoming increasingly more important

for two reasons, one scientific and the other operational. The widespread application of manifestly

nonuniform time scales is impractical without cor- rections which render the scales uniform. Wide

applications of time scales require synchronization

of clocks. Once synchronized, such clocks become

the vehicle of access to all kinds of time scales. Thus, the study of synchronization also would be

properly said to belong to the broader study of time

in general.

As pointed out in Chapter 1, a time scale is a system which allows one to assign "dates" to events,

where date refers to some designated mark on a time scale. (Some people use "epoch" for our

designation of "date" — see a detailed discussion

of these words in chap. 1.) We prefer to use the

word "date" if both day and time of day are given

for the event. There are many astronomical and

clock time scales. The unrestricted word "time"

can embody various aspects of time scales, time

measurement, as well as time interval or duration. Thus, one cannot say that "time" is determined

solely by astronomical means, since different time

scales exist in biology, geology, and physics. On

the other hand, the calendar and fraction of a day

is the legal standard to which we ultimately refer most events for "dating."

Clocks are devices capable of generating and

counting time intervals. In order to do this in a most

uniform manner, modern atomic clocks derive their frequency (rate) reference from inner atomic

processes, shielded as much as possible from

external disturbing influences. Such clocks must

also contain counters and displays of accumulated

time intervals. Since repetitive phenomena are involved here, time, in one way or another, is always identified with angles whether we deal with

the rotating earth or with 1-MHz signals from a frequency standard. Our conventional hours,

minutes, and seconds are angular measures ("hour

angle") of astronomy ("Universal" Time, UT).

In reviewing the historical development of time

scales,1 one becomes aware that, with the rapidity

and far-reaching consequences of communication,

the greater are the demands for an all-pervasive

and unifying convention of synchronizing clocks. That is, it is a matter of convenience and importance

that they read the same time, but not necessarily on an absolute time base. An accuracy of a few

seconds is perhaps important and sufficient in the

operation of railroads. Now, however, sophisticated

telecommunications equipment exists which can send and receive several million alphanumeric

characters each second; thus, there are accuracy

requirements for clock synchronizations to microseconds and better. Celestial navigators require earth-based time

signals to establish their position as determined

from the angular orientation of the earth. Since the

earth rotates on its axis about once every 24 hours,

a navigator can determine his longitude by means

of a sextant (which gives him local solar time) and

the knowledge of solar time at Greenwich. Approximately 200 years ago the first chronometers were

built which allowed the accurate determination of

longitude while at sea. Until radio made its appearance, navigation at sea was very dependent upon

good clocks. Nowadays, there are many standard

time broadcast stations in the world. The best

known standard time broadcast stations in North

America are operated by the National Bureau of

Standards (USA) and the National Research Council

(Canada); WWV (NBS) is located in Fort Collins,

Colorado; and CHU(NRC) is near Ottawa, Ontario.

Recently, more sophisticated uses of UT have come into being as in geodetic astronomy, star and

satellite tracking, and very-long-baseline radio

interferometry (VLBI) which require (and can also provide) UT with millisecond accuracy. Since the

rotation of the earth is not strictly uniform (varia1 For a more detailed account of time concepts, time scales and uses of time scales, the reader is referred to Chapter 1.

317
tions in the length of the day are of the order of a

part in 108

) a problem exists in relation to clock time

which can be kept stable to about one part in 1013

. Additional difficulties with clock time arise if used in the prediction of cosmic phenomena as, for example, orbital position of celestial bodies or times of arrival of signals from "pulsars." These

latter signals can be resolved today with a precision

of better than 5 /as [l] 2

. It is clear that such uses demand a clock time offering more than simply the means for synchronization such as required for electronic system applications.

11.2.1. Compromise Time Scales

We have identified very different uses for time.

One use allows very high speed and extended

electronic systems to function. The needs here are

for extremely accurate and/or precise synchronization and measurements of time interval. Another use was for celestial navigation and astronomy. Here

the need for precision is less but there are now

additional requirements for "epoch" which cannot

be set arbitrarily. If Universal Time (UT) could be

measured with sufficient accuracy and convenience,

the UT could also be used for time systems syn- chronization. In actuality, Universal Time is difficult to measure, and accuracies at this time are limited

to one millisecond (after the fact). Conflicting requirements imposed on time scales

by such varied categories of time scale users pro- vided impetus to form a compromise time scale

which would adequately reflect the needs and

relative importance of system synchronization as well as navigation and astronomy. With the growing importance and sophistication of communications systems and the implementation of electronic

navigation systems (to supplement direct celestial navigation), the trend in the compromise time

scales has turned from time scales based solely on

the earth's rotation (i.e., astronomical time scales)

to those referenced to atomic resonance. In particular, it is quite instructive to explain here briefly

the new compromise time scale (called UTC) which

became effective internationally on January 1, 1972 [2] (see chap. 1 - ann. LB).

As we mentioned previously, the spinning earth

does not make a very good clock. In point of fact,

commercial atomic clocks in common use today are about one hundred thousand times more uniform

than the spinning earth. Nonetheless, navigators

need earth time (i.e., earth position relative to the

stars) in real time no matter how erratic and

unpredictable it might be. We find ourselves in a rather familiar situation. There is not a whole

number of days in the year, and we don't want the

calendar to get badly out of step with the seasons.

Similarly, there is not a whole number of seconds in a solar day, and we don't want our clocks to get

2 Figures in brackets refer to the literature references at the end of this chapter.

badly out of step with the sun. The solution is analogous to the leap year with its extra day; we

have an extra second — a leap second.

In fact, since January 1, 1972, the internationally

accepted and used clock time scale can, on occasion,

incorporate leap seconds to keep our clocks in approximate step with the sun, thus satisfying the

needs of the navigators [3]. In contrast to leap years

which occur at defined intervals, the need for leap

seconds is not precisely predictable but there

should not be more than one in about a year's time.

This lack of predictability arises because the earth

doesn't spin at a constant rate. In any event leap

seconds are going to be with us for a while. They

allow a time scale (UTC) running at a constant rate, but whose time still approximates a clock defined

by the rotating earth. The compromise time scale,

by international agreement, thus provides UTC

(atomic) which will be kept within about 700 ms of UT1 (earth), the navigators time scale.

11.3. TIME AND FREQUENCY (T&F)

ACTIVITIES OF THE NATIONAL

BUREAU OF STANDARDS AND

THE U.S. NAVAL OBSERVATORY

11.3.1. The Formal Missions of T&F Activities

of the NBS and USNO

a. T&F Activities of NBS

In Title 15 of the United States Code § 272,

(see ann. ll.A.l), it states: "Sec. 2." The Secretary of Commerce is authorized to undertake the

following functions:

"(a) The custody, maintenance, and development

of the national standards of measurement, and the

provision of means and methods for making

measurements consistent with those standards,

including the comparison of standards used in

scientific investigations, engineering, manufacturing,

commerce, and educational institutions with the

standards adopted or recognized by the Government." In particular the authorization specified:

"(11) the broadcasting of radio signals of standard

frequency" [4]. In Department of Commerce Order,

DO 30-2A (June 19, 1972), the above authority is delegated to the Director of the National Bureau of Standards (ann. 11.A.2).

The four independent base units of measurement

currently used in science are length, mass, time,

and temperature. In certain fields of science such as cosmology, geology, navigation, and astronomy,

time interval and (astronomical) date are both

important concepts. However, with respect to the

fundamental foundations of science, time interval

is the most important concept. This is true because

the "basic laws" of physics are differential in nature and usually involve small time intervals. Based on these laws and extensive experimentation, scientists have been able to demonstrate that

318
frequency can be controlled and measured with the

smallest percentage error of any physical quantity.

Since most clocks depend on some periodic phenomenon (e.g., a pendulum) in order to "keep time,"

and since one can make reliable electronic counters

to count the "swings" of the periodic phenomena, we can construct clocks with an elapsed time ac- curacy of the frequency standard.

In fact, the international definition of the second

(unit of time interval) is based on the resonance

frequency of the cesium atom. The present definition, approved by the 13th General Conference of Weights and Measures (CGPM) in 1967, states [5]:

"The second is the duration of 9 192 631 770 periods of the

radiation corresponding to the transition between the two

hyperfine levels of the ground state of the cesium-133 atom."

The second must therefore be considered as one of the most important base units of the "Systeme

International" (SI), the measurement system used

for all scientific and technological measurements

[6].In response to this state of affairs, there is a Time

and Frequency Division within the National Bureau

of Standards. This Division has 3 major thrusts as shown in figure 11.1.

1) One of these is concerned with basic standards

of time and frequency. Presently, it consists of

two program areas; i.e., Quantum Electronic Fre- quency Standards and Atomic Time Standards.

Their prime responsibilities are shown in figure 11.1. Principally, they are engaged in research and de- velopment of both primary and backup frequency

standards, and associated time scales [7, 8], innovation of state-of-art T&F processes [9, 10], and

operation of the NBS primary standards of fre- quency and time interval. (Their work is documented also in many chapters of this Monograph.)

U.S. DEPARTMENT OF COMMERCE

N8S TIME & FREQUENCY DIVISION (Z73.00) Boulder, Colorado 80302

Develops, evaluates. & improves

NBS frequency standards. Operati

2) The Frequency and Time Dissemination Re- search Group conducts research and development

activities on new methods of disseminating time

and frequency information. As examples, this Section developed the TV line-10 synchronization

pulse technique [11] based on the work of Tolman

et al. [12]; devised and perfected a more extensive

TV time system [13, 14] which actively encodes

time signals in the vertical interval; and developed some satellite timing techniques [15, 16]. 3) The Frequency and Time Broadcast Services

Group disseminates the NBS standard frequencies

and time scales via radio (WWV, WWVH, and WWVB), and via telephone (303-499-7111). More

detailed information about these services may be

obtained by requesting NBS Special Publication

236 [17] from:

Frequency and Time Broadcast

Services Section, 273.02

National Bureau of Standards

Boulder, Colorado 80302.

This section also publishes a monthly Bulletin

giving NBS time scale information, phase deviations

of standard frequency transmissions, and TV and

satellite information (see ann. 11.E.4). All of the activities of these groups are coordinated both nationally and internationally through

the Time and Frequency Division Office. In a formal

sense, the mission of the Division and the individual

Sections and Program Areas are summarized in Annex ll.C. This Annex also includes a brief

description of postdoctoral research associateships

assigned to the Division with the cooperation of the

National Research Council.

b. The Position of the U.S. Naval Observatory in the Federal Government

The U.S. Naval Observatory performs the same

public functions as the national observatories of the

principal countries of the world. Its nearest counterparts are the Royal Greenwich Observatory (United

Kingdom), the Pulkovo Observatory (USSR), and

the Paris Observatory (France). It is the sole authority in the United States for astronomical

data required for public and legal purposes, such as times of sunrise and sunset, moonrise and moonset, and almanacs required for marine and air navigation, and for land surveying [18, 19]. By virtue of its official mission,3 the primary

function of the U.S. Naval Observatory is to pro- vide accurate time and other astronomical data

which are essential for safe navigation at sea, in the

air, and in space. To carry out this function, it is necessary for the Observatory to maintain continual

observations of the positions and motions of the

Figure 11.1. The Time and Frequency Division of the NBS.

3 "Make such observations of celestial bodies, natural and artificial, derive and

publish such data as will afford to United States Naval vessels and aircraft as well as

to al! availing themselves thereof, means for safe navigation, including the provision

of accurate time, and while pursuing this primary function, contribute material to the general advancement of navigation and astronomy '(20] (see ann. 11. B. 3).

319
sun, moon, planets, and principal stars. From

some of these observations astronomical time is determined.

The determination and dissemination of precise

clock time, which the Observatory has developed to very high precision, is essential to many military

operations, especially the fields of electronic navigation, communications, and space technology. In response to these needs, the Department of Defense

has charged the USNO with single management

responsibilities for T&F in the Department of

Defense [21] (see ann. 11. D). The Naval Observatory also concentrates on astrometry (precise meas- urements of angular distances between celestial objects), celestial mechanics (theories and calculations of the motions of celestial bodies), and astro- physics. It operates the most modern and precise

special-purpose astronomical equipment in the

world, most of which has been designed by its staff, and is comprised of about 20 telescopes of various

kinds at its stations in Washington D.C., Arizona,

Florida, in the U.S.A. and Argentina [22]. The Observatory is also a computing center and

publishing house, calculating and publishing each

year 1,000 pages of navigational data, 500 pages of

astronomical predictions, and averaging 250 pages

of research papers, all of which are published in book form, as well as numerous research papers in astronomical periodicals.

(1) The USNO Time Service Division, Background

There has been a continuous evolution from the

first public "time service," the dropping of the

USNO time ball at noon (1844), to the many services

rendered today (ann. 11. E.). Many of these services

and operations were the first of their kind; for example:

1) In 1904 the first worldwide radio time signals were broadcast from a U.S. Navy station based on

a clock provided and controlled by the Observatory.

2) A "Photographic Zenith Tube" (PZT) has been

used by the Observatory since 1915 for the deter- mination of latitude and since 1933 for the deter- mination of latitude and Universal Time (UT).

3) The "Dual Rate Moon Camera" was invented

by William Markowitz in 1951, and it became the

instrument with which the frequency of cesium

(which today is the basis for the definition of the

second) was determined with respect to the ephemeris second. This assured a clock rate which allows

the use of atomic time (A.l and now TAI) as an

extrapolation of ephemeris time [23]. 4) The first atomic time scale (A.l) using the value

for the Cesium frequency (later adopted inter- nationally) also applied the principle of an "average

clock" [24]. Originally, A.l was determined from

all available cesium clocks throughout the world.

The USNO clock time scale is still derived from

a set of "standard" clocks (selected commercial

cesium standards). In contrast, the NBS atomic

time scale is based on a laboratory cesium standard

and a set of commercial cesium standards which

serve as a memory of the rate of the primary

standard. Only USNO clocks are used today for the USNO clock time reference [25, 26]. There

are also other substantial differences in basic

philosophy between NBS and USNO which may be

resolved only after much more experience becomes

available [27].

(2) Organizations of USNO Time Service Division

There are four sections within this Division as shown in figure 11.2:

1) Control of Time/Time Interval Section. This

section is responsible for all electronics support

and instruments. It monitors T&F transmissions

of United States Naval electronic systems and other

precise T&F transmissions (WWVL, GBR, foreign

time signals, etc.) and prepares control messages

to stations controlled directly by the USNO. It prepares Time Service Announcements, Series 2,

3, 4, 5, 8, 9, and 16 (see ann. 11.E.5).

2) Precise Time Operations Section. This section is responsible for external liaison and portable

clock operations used for national and international

coordination. It carries the main load of PTTI

management responsibilities as assigned by the

Department of Defense Directive [21]. 3) Astronomy — Washington, DC. This section

is responsible for observations with the PZT,

Astrolabe and Moon Camera in Washington. It is responsible for all computer software including

automatic data acquisition and control system,

and is responsible for the atomic clock time scale

under direct supervision of the Assistant Director.

U.S. NAVAL OBSERVATORY

USNO TIME SERVICE DIVISION Washington. 0C 20390

ates and Maintains PTTI Fun

onal and Inte

CONTROL OF TIME/TIME INTERVAL

ctronic Instruments S System Oesigi Monitoring of T/F Transmissions

Control Messages

T.S. Announcements Series 2, 3. 4, 5. 8. g. & 16

PRECISE TIME OPERATIONS

PTTI Management Functions Liaison Portable Clock Operations

ASTRONOMY WASHINGTON, DC Observation with PZT, Astrolabe (Determination of UT) Observation with Moon Camera (Determination of ET) Computer and OAS Software

Atomic Clock Time Scales

T.S. Announcement Series 1. 6, 7,

10, 11 , 12, 13 , & 17

ASTRONOMY RICHMOND, Fl

Figure 11.2. The USNO Time Service Division.

320
It is also responsible for Time Service Announcements, Series, 1, 6, 7, 10, 11, 12, 13, and 17 (see ann. 11. E. 5). 4) Astronomy — Richmond, Florida (near Miami).

This is a largely independent Observatory capable

of all Washington time operations on a smaller

scale. It is a station with one of the most favorable

climatic conditions anywhere (320 clear nights

per year, compared to 210 at Washington, DC).

In addition, background radio noise is low, and this makes the station valuable as a monitor site. The above listed activities produce only part of

the information which is published daily, weekly,

monthly, and irregularly by the USNO Time Service

Division (see ann. ll.E). A great number of messages and notes are received regularly from cooperating stations all over the world whose contri- butions make it possible to achieve today a truly

"worldwide continuity of precision" in time meas- urements with which the USNO is specifi cally

charged [21]. In addition, the USNO initiates annual PTTI meetings for T&F specialists to consider new and improved techniques in the field [28].

11.3.2. T&F Activities of NBS and USNO

Compared

As listed in the previous section, the main inter- actions of the two agencies can be summarized as shown in figure 11.3. Both agencies provide input

to the BIH (at the Paris Observatory) which is charged to provide a central international reference

point for time and related matters. NBS and USNO

are both substantial contributors to the Inter- national Atomic Time Scale, TAI, constructed by

the BIH and now serving as reference for UTC. NBS

provides input in regard to absolute accuracy of the

rate of TAI (and the U.S. clock time scales as well). USNO provides UTO and latitude information. In conformance with the specific mission state- ments, as cited above, time and absolute frequency

are central but not exclusive areas of concern, competence, and responsibility of the USNO and NBS

respectively. Both areas are very closely linked,

which requires equally close cooperation between

the two agencies (see ann. ll.E. 3). For example,

the NBS broadcasts of standard frequency have as a most logical extension a 24-hour standard time

signal emission. Commensurate with the NBS

introduction of these and similar services (a TV and

a satellite T&F dissemination are being actively

investigated by NBS), the USNO has reduced or eliminated some of its own dissemination services.

Today, the Naval time signals are on the air for only

5 minute periods every 1, 2, or more hours (but on

about 30 frequencies) [29]. They are intended to supplement the WWV and WWVH emissions. These

HF services of NBS are very important to the USNO

and its "customers" (navigators, geodesists, astrono- mers, etc.).

It is noteworthy that table 11.1, which summarizes the main points of this discussion, repre- sents only an historical ideal. Clock coordination

has diminished the direct significance of USNO's

role as a national time standard since the

UTC(NBS)-UTQUSNO) time difference is less than 6 pis since June 1968 [30] and since both

agencies provide independent clock time input to the BIH. On the other hand, the real standard of

frequency is now the cesium atom and there is no

longer a U.S. frequency standard (or a U.S. second)

just as there is no U.S. meter. However, there is U.S. input to the absolute SI second from a primary

frequency standard at the NBS.

T&F CONTROL

OF NAVY BROADCASTS

& LORAN C (DOT)

T&F CONTROL

OF NBS BROADCASTS

Figure 11.3. NBS, USNO, and BIH interactions.

321
Table 11.1. T&F Responsibilities of NBS/USNO

NBS USNO

National Standard of Frequency; Standard Frequency (and Time) Broadcast; Fundamental Research in T&F as related to Clock Time and Frequency Measurements,

Synchronization; Consultation and Education; USNO Precise Time Reference Station.

National Standard of Time (Epoch, Date); Control of Naval T&F Transmissions; Applied Research in Time as related to Clock applications, Astronomy, Geophysics, Navigation; Consultation and Management of PTTI activities as related to DOD.

11.3.3. Coordination of T&F

Each agency, NBS and USNO, derives an entirely independent local atomic time scale: AT(NBS)

and A.l(USNO). AT(NBS) is based on (occasional)

calibrations of its operational standards (8 commercial cesium clocks) with the NBS primary frequency

standard. A.l(USNO) is based on a set of 16 best

commercial cesium clocks selected as "standards"

from about 70 cesium clocks available to the USNO.

A.l(USNO) results from an adjusted, iterated

averaging procedure which makes the average

rate of the time scale independent of the particular

clocks used and assures very great reliability.

Both of these inputs are used by the BIH to compute

the TAI and UTC scales. The agencies' coordinated clocks are derived

with a deliberate coordination offset (*£ 1012

). The International Radio Consultative Committee

(CCIR) and the International Astronomical Union

(IAU) recommend 1 ms as the maximum tolerance

[2, 31]. As noted previously, UTC(NBS) and

UTC(USNO) have been closer than 6^s since

1968; also they are now within a few microseconds

of UTC(BIH). It is the intent to achieve even closer

coordination in the future. Figure 11.4 depicts the

coordination of time scales within the USA with

input to the BIH (see ann. 11. E).

OTHER NATIONS

INTERNATIONAL

COORDINATION U.S. CONTRIBUTIONS USERS

A

COORDINATION

USNO

TIME DETERMINATION

UT1 (USNO) , ET

A . 1 (USNO) "MEAN" ADJUSTED

LOCAL TIME SCALE

UTC(USNO)

\ WITHIN 6 us

UTC(NBS)

LOCAL TIME SCALE

AT ( NBS

)

NBS FREQUENCY STD

NAVIGATORS

GEODESISTS

SPACE TRACKING

NAVAL COMM. STA TRANSIT

OMEGA LORAN-C (DOT)

PORTABLE CLOCKS

DCA SYSTEMS

WESTERN UNION

LOCAL TV

WWV WWVH

WWVB

AT SATELLITE

TV TIMING (NATIONAL)

TELEPHONE : 303-499-71 1

1

Figure 11.4. Time scales in the United States of America.

322
In addition to clock time, UT1 and the coordinates

of the pole are furnished internationally by the

BIH[32] and in the USA by the USNO[33]. (The pole

coordinates are given at various times and at the

three levels of "Predicted," "Preliminary" (BIH

"Rapid Service"), and "Final.") In view of the fact that the BIH values are averages of some 50 observatories, its values are precise to better than 1 ms in UT1 and about 0".01 in x and y (polar coordinates).

The results of the International Latitude Service

(ILS, now IPMS) can be considered more accurate

but less precise than BIH in the polar coordinates

since the definition of the Standard Pole (OCI)

refers to the 5 latitude stations and not to the BIH

observatories [34]. With the increase of participating

observatories, the relative importance of these U.S.

contributions has decreased. We can expect similar

developments with respect to the U.S. local atomic

time scales as more national timekeeping agencies

contribute to the TAI.

11.4. INTERNATIONAL ORGANIZATIONS INVOLVED IN STANDARD

TIME AND FREQUENCY

The general subject of time and frequency is important in three fundamentally different ways.

Firstly, it is important as one of the 4 independent

base units in metrology (i.e., length, mass, time, and

temperature); that is, it is important to the Systeme

International (SI) of units of measurement. Secondly, time and frequency are important scientifically in their own right, not just as they influence

measurements; and thirdly the methods of dis- semination of standard time and frequency are important from a regulatory aspect such as the

assignment of radio spectrum for broadcast purposes

of standard time and frequency. Correspondingly, one can find three separate chains of international

involvement with time and frequency as shown in figure 11.5; i.e., standards, scientific, and regulatory.

STANDARDS SCI ENTI FIC REGULATORY

CONSULTATIVE

COMMITTEES

SUPPORT

FOR TAI

UNESCO

SG VII

STUDY GROUPS

Figure 11.5. International organizations involved with standard frequency and time.

323
11.4.1. Organizations of the Treaty of the

Meter (Standards)

The USA was one of the original signers of the

Treaty of the Meter in 1875 [35] (see ann. ll.F).

This treaty established an international standards

laboratory (Bureau International des Poids et Mesures, BIPM) which is governed by an international committee (Comite International des Poids et Mesures, CIPM) composed of representatives of the

member nations. Advisory to the CIPM are various

technical consultative committees (e.g., the Consultative Committee for the Definition of the Second

(CCDS), the Consultative Committee for the Definition of the Meter (CCDM), etc.). Policy decisions

such as financial assessments of the member nations

and final endorsements of new definitions of standards are handled by a General Conference of

Weights and Measures (CGPM).

11.4.2. Scientific Organizations

Scientific involvement occurs through the Inter- national Council of Scientific Unions (ICSU)

which receives support and financial assistance

from the United Nations Educational, Scientific,

and Cultural Organization (UNESCO). Also, in our area, threre are four scientific unions (see table

11.2 for abbreviations): URSI, IAU, IUPAP, and

IUGG. Within these scientific unions. T & F

matters are primarily confined to URSI-Commission

1 and IAU-Commission 31. ICSU has established a number of permanent

services administered by the Federation of Astro- nomical and Geophysical Services (FAGS). These

permanent services include the Bureau International

de l'Heure (BIH), the International Polar Motion

Service (IPMS), and others. Historically, the BIH

has had the responsibility of coordinating and

calculating the final and formally adopted measure- ments of time. With the advent of atomic clocks

and with the recommendations of the IAU, the BIH

established its own atomic time scale (TAI) which is based, ultimately, on a weighted average of various

local atomic time scales [36]. The CGPM has

endorsed the TAI scale for defining International

Atomic Time (date) [37], and the CGPM will also provide some financial assistance to the BIH (see

chap. 1 — ann. 1.A.3).

11.4.3. International Radio Consultative

Committee (CCIR) (Regulatory)

Advisory to the International Telecommunications Union (ITU) is the CCIR with its numerous

Study Groups. Study Group 7 of the CCIR is con- cerned with standard frequency and time broadcasts. The recommendations of CCIR specify the

acceptable formats for standard frequency and time

broadcasts as well as the tolerances of the broadcast

scales relative to the time scales of the BIH [2]. Although these recommendations do not have the

force of international law, almost all countries

carefully adhere to them (see chap. 1 — ann. l.B). For each of the international organizations cited

above there exist either national delegates or national committees which formulate the national

policy to be presented to the international

organizations.

Table 11.2. Abbreviations of International Organizations

Abbreviation Organization

BIH International Bureau of Time. BIPM International Bureau of Weights and Measures. CCDM Consultative Committee for the Definition of the Meter. CCDS Consultative Committee for the Definition of the Second. CCIR :. International Radio Consultative Committee. CGPM General Conference of Weights and Measures. CIPM International Committee of Weights and Measures.

FAGS Federation of Astronomical and Geophysical Services.

IAU International Astronomical Union. ICSU International Council of Scientific Unions. ITU International Telecommunications Union. IUGG International Union of Geodesy and Geophysics.

IUPAP International Union of Pure and Applied Physics.

UN United Nations. UNESCO United Nations Educational, Scientific, and Cultural Organization.

URSI International Science Radio Union.

324
11.5. THE LEGAL DEFINITION OF

"STANDARD TIME"

The legal basis of Standard Time in the USA is contained in the "Uniform Time Act of 1966"

(Public Law 89-387) [38] and the U.S. Code, Title 15 [39] (see ann. 11. G). This act reiterates the policy

of the United States to "promote the adoption and

observance of uniform time within prescribed

Standard Time Zones . . ." and establishes the

annual advancement and retardation of standard

time by 1 hour the last Sunday of April and October

respectively. The Department of Transportation

(DOT) is the agency designated for enforcement of

the law. The "Uniform Time Act" establishes 8 Standard

Time Zones for the USA (see fig. 11.6) and notes

that Standard Time is based on the mean solar time of specified longitudes. The reference meridi- ans are spaced 15° apart in longitude beginning

with the meridian through Greenwich, England.

Time zones extend 7V2° in longitude on each side

with considerable variation in boundaries to con- form to political and/or geographic boundaries.

Since the time zones are 15° apart, the time differ- ence between two adjacent zones is one hour.

Mean solar time (related to UTO and not UT1) is simply apparent solar time, corrected for the effects of orbital eccentricity and the tilt of the earth's axis

relative to the ecliptic plane; i.e. corrected by the

equation of time.

The 8 USA Standard Time Zones are designated

as follows:

1) Atlantic Standard Time

2) Eastern Standard Time

3) Central Standard Time

4) Mountain Standard Time

5) Pacific Standard Time

6) Yukon Standard Time

7) Alaska-Hawaii Standard Time

8) Bering Standard Time.

A comprehensive delineation of these zones is given in the Code of Federal Regulations, entitled

"Standard Time Zone Boundaries" (see ann.

11.G.3). This code indicates also the various exceptions and time zones for the operating railroads

within the USA.

11.6. SUMMARY

Time and Frequency is a complex field with

widely different requirements. Historically, two

agencies have provided the standards of time and

frequency in the USA; they are the USNO and the

NBS, respectively. Their roles have evolved, however, into more diversified interests. The need to coordinate with the rest of the world and the new

"natural" standards of time (the second) and

length (the meter) produce a strong pressure for adjustment in the interest of improving our public

services. This, together with the different professional backgrounds of the two agencies, has emphasized different thrusts of action. Operations

and worldwide organization of resources have

always been favored by astronomers, particularly

those who use clocks as a means and not as an end.

On the other hand, questions of absolute accuracy

in the realization of a measurement standard,

research in the physics of clocks, and education in the use of standards is emphasized at NBS. Both

agencies conduct research which is complementary

rather than competitive not only because management wants it, but because of their different pro- fessional outlook and resources.

11.7. References

[I] Allan, D. W., "Time transfer using near-synchronous

reception of optical pulsar signals," Proc. IEEE (Lett.), 60, No. 5, pp. 625-627 (May 1972).

[2] CCIR, "Detailed instructions by Study Group 7 for the implementation of Recommendation 460 concerning the improved coordinated universal time (UTC) system, valid from 1 January 1972," in XHth Plenary Assembly CCIR,

III, pp. 258 a-d (ITU, Geneva, Switzerland, 1970) (see chap. 1 — ann. l.B.l).

[3] Smith, H. M., "International time and frequency coordination," Proc. IEEE, 60, No. 5, pp. 479-487 (May 1972).

[4] Committee on Judiciary of House of Representatives, United States Code: 1970 Edition, Title 15, 3, Chapter 7, "The National Bureau of Standards," sec. 271-290, pp. 3231-3240 (USGPO, 1971).

[5] CGPM, Comptes Rendus des Seances de la Treizieme Conference General des poids et Mesures (Proceedings of the Sessions of the 13th General Conference of Weights

and Measures) (Paris, France, October 1968), p. 103

(Gauthier-Villars, Paris, France, 1968) (in French — see chap. 1 — ann. l.A.l).

[6] Page, C. H., and Vigoureux, P. (Editors), "The International System of Units," (American translation of "Le Systeme

International d'Unites") 1970 OFFILB, 48 rue GayLussac, F. 75, Paris 5 (Revised Edition 1972), Nat. Bur. Stand. (U.S.) Spec. Publ. 330, 1972 Ed., p. 3 (USGPO,

April 1972).

[7] Brandenberger, H., Hadorn, F., Halford, D., and Shoaf, J. H., "High quality quartz crystal oscillators: frequencydomain and time domain stability," Proc. 25th Ann. Symp. on Frequency Control (U.S. Army Electronics Command, Ft. Monmouth, NJ 07703, April 26-28, 1971), pp. 226-230 (NTIS, AD 746211, 1971).

[8] Allan, D. W., "Statistical modeling and filtering for optimum

atomic time scale generator," Proceedings ofthe Frequency

Standards and Metrology Seminar (Quebec, Canada,

August 30, 31-September 1, 1971), pp. 388-410 (Quantum

Electronics Lab., Dept. of Elect. Eng., Laval University,

Quebec, Canada, 1972).

[9] Halford, D., Hellwig, H., and Wells, J. S., "Progress and

feasibility for a unified standard for frequency, time, and

length," Proc. IEEE (Lett.), 60, No. 5, pp. 623-625 (May

1972).

[10] Hellwig, H. (Ed.), Proceedings of the Frequency Standards and Metrology Seminar, (Quebec, Canada, August 30, 31-September 1, 1971) (Quantum Electronics Lab., Dept.

of Elect. Eng., Laval University, Quebec, Canada. 1972).

[II] Davis, D. D., Blair, B. E., and Barnaba, J., "Long-term

continental U.S. timing system via TV networks," IEEE

Spectrum, 8, No. 8, pp. 41-52 (August 1971).

[12] Tolman, J., Ptacek, V., Soucek, A., and Stecher. R., "Micro- second clock comparison by means of TV synchronizing

pulses," IEEE Trans, on Instrum. and Meas., IM-16,

No. 3, pp. 247-254 (September 1967).

[13] Davis, D. D., Jespersen, J. L., and Kamas, G., "The use of

television signals for time and frequency dissemination."

Proc. IEEE (Lett.), 58, No. 6, pp. 931-933 (June 1970).

325

[14] Howe, D. A., "Nationwide precise time and frequency

distribution utilizing an active code within network tele- vision broadcasts," IEEE Trans, on Instrum. and Meas., IM-2 1 , No. 3, pp. 263-276 (August 1972).

[15] Hanson, D. W., and Hamilton, W. F., "Clock synchronization from satellite tracking," IEEE Trans, on Aerosp. and

Electron. Syst., AES-7, No. 5, pp. 895-899 (September

1971).

[16] Hanson, D. W., Hamilton, W. F., and Gatterer, L. E., "The

NBS frequency and time satellite experiment using

ATS-3," Proc. 3rd Ann. Precise Time and Time Interval (PTTI) Strategic Planning Meeting (November 16-18,

1971) (U.S. Naval Observatory, Washington, DC 20390),

pp. 155-165 (USNO, Washington, DC 20390, 1972 (NTIS,

AD 758739).

[17] Viezbicke, P. P. (Ed.), "NBS frequency and time broadcast

services," Nat. Bur. Stand. (U.S.) Spec. Publ. 236, 1972

Ed., 14 pages (USGPO, March 1972) (Updated annually).

[18] USNO/HMSO, The Nautical Almanac for the Year 1973

(Issued jointly by Nautical Almanac Office/USNO-USA

and H-M's Nautical Office/RGO-United Kingdom) 276

pages and Annexes (USGPO, 1971).

[19] USNO/HMSO, The Air Almanac-1973 (January- April) (Issued jointly by Nautical Almanac Office/USNO-USA

and H — M's Nautical Office/RGO — United Kingdom)

276 pages and Annexes (USGPO, 1971).

[20] U.S. Navy/CNO, "Mission and functions of the U.S. Naval

Observatory," U.S. Naval Operations Instruct. 5450.90B,

1 page (December 16, 1969) (see ann. 11. B. 3). [21] U.S. Department of Defense (DOD), "Precise time and time

interval (PTTI) standards and calibration facilities for use by Department of Defense Components," DOD

Directive No. 5160.51, 6 pages (August 31, 1971); also Code of Federal Regulations (CFR), Title 32 (National Defense), Chap. 1, "Part 275 — Precise time and time

interval (PTTI) standards and calibration facilities for use by Department of Defense components," pp. 550—552 (USGPO, January 1, 1972). (NOTE: The CFR essentially

codifies agency regulations and should not be confused

with the United States Code (USC) which codifies legal statutes, Presidential Orders, etc.) (see ann. ll.D.l).

[22] USNO, United States Naval Observatory, 18 pages (USNO,

Washington, DC 20390, 1972).

[23] Markowitz, W., Hall, R. G., Essen, L., and Parry, J. V. L., "Frequency of cesium in terms of ephemeris time,"

Phys. Rev. Letters, 1, pp. 105-106 (August 1962).

[24] Markowitz, W., "The atomic time scale," IRE Trans, on

Instrum., 1-11, Nos. 3 and 4, pp. 239-242 (December

1962).

[25] Winkler, G. M. R., Hall, R. G., and Percival, D. B., "The

U.S. Naval Observatory clock time reference and the performance of a sample of atomic clocks," Metrologia,

6, No. 4, pp. 126-134 (October 1970).

[26] Putkovich, K., "Automated timekeeping," Trans, on In- strum. and Meas., IM-21, No. 4, pp. 401-405 (November

1972).

[27] Allan, D. W., and Gray, J. E., "Comments on the October

1970 Metrologia paper, 'The U.S. Naval Observatory

clock time reference and the performance of a sample of atomic clocks'," Metrologia, 7, No. 2, pp. 79-82 (April 1971). [28] USNO/NASA, Proc. 4th Ann. NASA and DOD Precise Time

and Time Interval (PTTI) Meet. (NASA Goddard Space

Flight Center, Greenbelt, MD 20771, November 14-16,

1972) , 371 pages (NASA, X-814-73-72, Greenbelt, MD

20771, 1973).

[29] USNO, "Worldwide primary VLF and HF transmissions,"

Time Service Announcement, Series 1, No. 1, 20 pages (USNO, Washington, DC 20390, July 1971).

[30] NBS, "Nation gets unified time system," Nat. Bur. Stand.

(U.S.) Tech. News Bull., 53, No. 2, p. 34 (USGPO,

February 1969).

[31] De Jager, C, and Jappel, A., (Editors), "Commission 31: Time (l'Heure) — Session 4" (Proc. 14th General Assembly, Brighton, England 1970) Trans. IAU,X1VB, p. 198 (D. Reidel Publishing Co., Dordrecht, Holland, 1971).

[32] BIH, Monthly Circulars B, C, and D and Annual Reports

(BIH, Paris, France).

[33] USNO, Time Service Announcements, Series 7 and 11 (USNO, Washington, DC 20390).

[34] Mueller, I. I., Spherical and Practical Astronomy, pp. 80-84 (Frederick Ungar Publishing Co., New York, NY

10003, 1969).

[35] Schwarz, K. M., Federal and State Weights and Measures

Laws, "Metric Convention — 1875," Nat. Bur. Stand.

(U.S.) Circular 501, pp. 3-5 (USGPO, December

1951) (see ann. ll.F).

[36] Guinot, B., Feissel, M., and Granveaud, M., Bureau Inter- national d l'Heure Annual Report for 1971, pp. A9-A20

(BIH, Paris, France, 1972).

[37] CGPM, Comptes Rendus des Seances de la Quatorzieme

Conference Generate des poids et Mesures (Proceedings

of the Session of the 14th General Conference of Weights and Measures) (Paris, France, October 4-8, 1971), pp. 77-78 (BIPM, Sevres, France, 1972) (See chap. 1-ann.

1.A.3).

[38] USA, "Uniform Time Act of 1966," Public Law 89-387, 89th

Congress, S. 1404, 3 pages (USGPO, April 13, 1966) (see ann. ll.G.l).

[39] Committee on Judiciary of House of Representatives, United States Code: 1970 Edition, Title 15, 3, Chap. 6, "Weights and Measures and Standard Time," sec. 260-

267, pp. 3228-3231 (USGPO, 1971) (see ann. 11.G.2).

[40] NBS/NRC, "Postdoctoral research associateships — 1973

tenable at National Bureau of Standards (Washington,

DC and Boulder, CO)," in association with the National Research Council, pp. 31-32 (NRC, Washington, DC

20418, 1972).

[41] Fizell, W. E., "On the determination of universal time and

the use of the U.S. Naval Observatory Time Service

Bulletins, Notices, and Announcements," NASA Report X-521-70-188 , 28 pages (NTIS, N70 41890, 1970).

327

Annex 11.A.

NBS ENABLING LEGISLATION

Contents

Page ll.A.l. NBS Legislative Authority— U.S. Department of Commerce, Nat. Bur. Stand. (U.S.) Ad.

Man. Chapter 1. April 30, 1968 (sec. 1.01.01 to 1 .01 .10). [See U.S. Code, Title 15, 3, Chap.

7, sec. 271-290. pp. 3231-3240, 1970 Edition (USGPO, 1971)] 331

11.A.2. U.S. Department of Commerce—Department Organization Order 30—2A — National

Bureau of Standards Mission Statements, 4 pages, June 19, 1972 335

11.A.3. U.S. Department of Commerce—Department Organization Order 30-2B — National

Bureau of Standards Mission Statements, 8 pages, June 12, 1972 339

329

ANNEX ll.A.l.

U. 5. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS Chapter 1 Authority

ADMINISTRATIVE MANUAL Subchapter l Legislative Authority

LEGISLATIVE AUTHORITY

Sections

1.01.01 Basic Legislation

1.01.02 Bureau Established

1.01.03 Functions of Secretary.

1.01.04 Functions: For Whom Exercised

1.01.05 Director: Powers and Duties

1.01.06 Appointment of Officers and Employees

1.01.07 Service Charges

1.01.08 Ownership of Facilities

1.01.09 Regulations

1.01.10 Visiting Committee

1.01.11 Gifts and Bequests

1.01.12 Working Capital Fund

1.01.13 Acquisition of Land for Field Sites

1.01.14 Construction and Improvement of Buildings and Facilities

1.01.15 Functions and Activities

1.01.16 Fire Research and Safety

1.01.17 Multiyear Appropriation Authority

1.01.18 Testing Materials for District of Columbia

1.01.19 National Hydraulic Laboratory

1.01.20 Other Legislation

a. Standards of Electrical and Photometric Measurement

b. Research Associates

1.01.01 BASIC LEGISLATION

The National Bureau of Standards was established on March 3, 1901, by "An Act to Establish the National Bureau of Standards"

(31 Stat. 1449). Extensive amendments were made in 1950 by passage of Public Law

81-619 (64 Stat. 371); in 1956 by Public

Law 84-940 (70 Stat. 959); and in 1958 by

Public Law 85-890 (72 Stat. 1711). The provisions of the organic act and amend- ments are merged in the following statement

of basic legislation quoted from Title 15 of the United States Code.

1.01.02 BUREAU ESTABLISHED

(15 U.S.C. 271) "The Office of Standard Weights and Measures

shall be known as the National Bureau of

Standards .

1.01.03 FUNCTIONS OF SECRETARY

(15 U.S.C 272) "The Secretary of Commerce (hereinafter

referred to as the "Secretary") is authorized to undertake the following

functions

:

November 28, 1972

(Trans. 181) 1.01.01 - 1.01.03

331
Legislative Authority 2 11-28-72

(Trans. 181)

"(a) The custody, maintenance, and development of the national standards of measurement, and the provision of means and methods

for making measurements consistent with

those standards, including the comparison

of standards used in scientific investigations, engineering, manufacturing, commerce, and educational institutions with the standards adopted or recognized by the Government

.

"(b) The determination of physical con- stants and properties of materials when

such data are of great importance to scientific or manufacturing interests and* are not to be obtained of sufficient accuracy

elsewhere

.

"(c) The development of methods for testing materials, mechanisms, and structures,

and the testing of materials, supplies, and

equipment, including items purchased for use of Government departments and independent establishments.

"(d) Cooperation with other governmental

agencies and with private organizations in the establishment of standard practices,

incorporated in codes and specifications.

"(e) Advisory service to Government

agencies on scientific and technical

problems

.

"(f) Invention and development of devices

to serve special needs of the Government.

"In carrying out the functions enumerated

in this section, the Secretary is authorized

to undertake the following activities and

similar ones for which need may arise in the operations of Government agencies,

scientific institutions, and industrial

enterprises:

"(1) the construction of physical standards;

"(2) the testing, calibration, and certification of standards and standard measuring

apparatus

;

"(3) the study and improvement of instru- ments and methods of measurements;

"(4) the investigation and testing of

railroad track scales, elevator scales, and

other scales used in weighing commodities

for interstate shipment;

"(5) cooperation with the States in securing uniformity in weights and measures

laws and methods of inspection;

"(6) the preparation and distribution of

standard samples such as those used in checking chemical analyses, temperature,

color, viscosity, heat of combustion, and

other basic properties of materials; also

the preparation and sale or other distribution of standard instruments, apparatus and

materials for calibration of measuring

equipment

;

"(7) the development of methods of chemical

analysis and synthesis of materials, and

the investigation of the properties of rare substances;

"(8) the study of methods of producing and

of measuring high and ldw temperatures; and

the behavior of materials at high and at low temperatures;

"(9) the investigation of radiation,

radioactive substances, and X-rays, their

uses, and means of protection of persons

from their harmful effects;

"(10) the study of the atomic and molecular

structure of the chemical elements, with

particular reference to the characteristics

of the spectra emitted, the use of spectral

observations in determining chemical

composition of materials, and the relation

of molecular structure to the practical

usefulness of materials;

"(11) the broadcasting of radio signals

of standard frequency;

MBS Administrative Manual (1.01.03)

332
Legislative Authority 3 11-28-72

(Trans. 181)

"(12) the investigation of the conditions

which affect the transmission of radio waves from their source to a receiver;

"(13) the compilation and distribution of

information on such transmission of radio waves as a basis for choice of frequencies

to be used in radio operations;

"(14) The study of new technical processes

and methods of fabrication of materials

in which the Government has a special

interest; also the study of methods of measurement and technical processes used

in the manufacture of optical glass and

pottery, brick, tile, terra cotta, and

other clay products;

"(15) the determination of properties of

building materials and structural elements,

and encouragement of their standardization

and most effective use, including investigation of fire-resisting properties of

building materials and conditions under

which they may be most efficiently used,

and the standardization of types of

appliances for fire prevention;

"(16) metallurgical research, including

study of alloy steels and light metal

alloys; investigation of foundry practice,

casting, rolling, and forging; prevention

of corrosion of metals and alloys; behavior

of bearing metals; and development of

standards for metals and sands;

"(17) the operation of a laboratory of

applied mathematics;

"(18) the prosecution of such research in engineering, mathematics, and the physical

sciences as may be necessary to obtain

basic data pertinent to the functions

specified herein; and

"(19) the compilation and publication of

general scientific and technical data

resulting from the performance of the functions specified herein or from other

sources when such data are of importance

to scientific or manufacturing interests or to the general public, and are not available elsewhere, including demonstration of the results of the Bureau's work

by exhibits or otherwise as may be deemed

NBS Administrative Manual

most effective, and including the use of

National Bureau of Standards scientific or technical personnel for part-time or intermittent teaching and training activities at educational institutions of higher learning

as part of and incidental to their official

duties and without additional compensation

other than that provided by law."

1.01.04

FUNCTIONS: FOR WHOM EXERCISED

(15 U.S.C. 273) "The Bureau is authorized to exercise its

functions for the Government of the United

States and for international organizations

of which the United States is a member; for governments of friendly countries; for any

State or municipal government within the United States; or for any scientific society,

educational institution, firm, corporation,

or individual within the United States or friendly countries engaged in manufacturing

or other pursuits requiring the use of

standards or standard measuring instruments:

Provided, That *:he exercise of these functions

for international organizations, governments

of friendly countries and scientific societies,

educational institutions, firms, corporations,

or individuals therein shall be in coordination

with other agencies of the United States Government, in particular the Department of State

in respect to foreign entities. All requests

for the services of the Bureau shall be made

in accordance with the rules and regulations

established in sections 276 and 277 of this

title (15 U.S.C.)."

1.01.05 DIRECTOR: POWERS AND DUTIES

(15 U.S.C. 274) "The director shall be appointed by the President, by and with the advice and consent of the Senate. He shall have the

general supervision of the bureau, its

equipment, and the exercise of its functions. He shall make an annual report

to the Secretary of Commerce, including an abstract of the work done during the year

and a financial statement. He may issue,

when necessary, bulletins for public

distribution, containing such information

as may be of value to the public or facilitate the bureau in the exercise of

its functions."

1.01.04 - 1.01.05

333
Legislative Authority 4 11-28-72

(Trans. 181)

1.01.06

APPOINTMENT OF OFFICERS AND EMPLOYEES

(15 U.S.C. 275)

"The officers and employees of the bureau,

except the director, shall be appointed by

the Secretary of Commerce at such time as their respective services may become necessary ."

1.01.07 SERVICE CHARGES

(15 U.S.C. 275a)

"The Secretary shall charge for 'services

performed under the authority of section

273 of this title, [15 U.S.C] except in cases where he determines that the interest

of the Government would be best served by

waiving the charge. Such charges may be based upon fixed prices or costs. The appropriation or fund bearing the cost of

the services may be reimbursed, or the Secretary may require advance payment

subject to such adjustment on completion

of the work as may be agreed upon."

1.01.08 OWNERSHIP OF FACILITIES

(15 U.S.C. 276)

',' In the absence of specific agreement to the contrary, additional facilities,

including equipment, purchased pursuant to the performance of services authorized

by section 273 of this title [15 U.S.C]

shall be come the property of the Department

of Commerce."

to be attained in standards submitted for verification, the sealing of standards,

the disbursement and receipt of moneys,

and such other matters as he may deem necessary for carrying into effect sections

271-278b of this title [15 U.S.C.]."

1.01.10 VISITING COMMITTEE

(15 U.S.C. 278)

"There shall be a visiting committee of

five members to be appointed by the Secretary of Commerce, to consist of men

prominent in the various interests

involved, and not in the employ of the Government. This committee shall visit

the bureau at least once a year, and

report to the Secretary of Commerce upon

the efficiency of its scientific work and

the condition of its equipment. The members of this committee shall serve without

compensation, but shall be paid the actual expenses incurred in attending its meetings.

The period of service of the members of

the committee shall be so arranged that one member shall retire each year, and the appointments to be for a period of five years. Appointments made to fill vacancies

occurring other than in the regular manner

are to be made of the remainder of the

period in which the vacancy exists."

1.01.09 REGULATIONS

(15 U.S.C 277)

"The Secretary of Commerce shall, from

time to time, make regulations regarding

the payment of fees, the limits of tolerance

NBS Administrative Manual 1.01.06 - 1.01.11

334
ANNEX 11.A.2.

TRANSMITTAL 12L

United States of America

DEPARTMENT OF COMMERCE

DEPARTMENT

ORGANIZATION ORDER 30-2A

DEPARTMENT

ORGANIZATION

ORDER SERIES

DATE OF ISSUANCE EFFECTIVE DATE

June 19, 1972 June 19, 1972

SUBJECT NATIONAL BUREAU OF STANDARDS

SECTION 1. PURPOSE.

This order delegates authority to the Director of the National Bureau of Standards, and prescribes

the functions of the National Bureau of Standards

.

SECTION 2. STATUS AND LINE OF AUTHORITY.

.01 The National Bureau of Standards, established by Act of March 3, 1901, (31 Stat. 1449

15 U.S.C. 271) is continued as a primary operating unit of the Department of Commerce.

.02 The Director, who is appointed by the President by and with the advice and consent of the Senate, shall be the head of the Bureau. The Director shall report and be responsible

to the Assistant Secretary for Science and Technology.

.03 The Director shall be assisted by a Deputy Director, who sha'l be the principal assistant to the Director and shall perform the functions of the Director during the latter' s ab- sence or disability He shall also serve as Acting Director whenever the position of Director

is vacant, unless and until the Secretary shall make a further designation. In the absence

of both the Director and Deputy Director, an employee of the Bureau designated in writing

by the Director shall act as Director.

SECTION 3. DELEGATION OF AUTHORITY.

.01 Pursuant to authority vested in the Secretary of Commerce by law (including Reorganization Plans No. 3 of 1946, No. 5 of 1950, and No. 2 of 1965), and subject to such policies

and directives as the Secretary of Commerce or the Assistant Secretary for Science and

Technology may prescribe, the Director is hereby delegated the authority to perform the functions vested in the Secretary of Commerce by the following Chapters of Title 15, United

States Code:

a. Chapter 6 (Weights and Measures);

b. Chapter 7 (The Bureau of Standards, except for subsections 272(f) 12 and 13, which pertain to the investigation of the conditions which affect the transmission of radio waves, and

the compilation and distribution of information on such transmission, which activities have

been delegated to the Office of Telecommunications .);

c. Chapter 25 (Flammable Fabrics);

d. Chapter 26 (Household Refrigerators); and

e. Chapter 39 (Fair Packaging and Labeling)

.

.02 The above delegations of authority are subject to the following limitations:

a. The Director may issue such regulations as he considers necessary to carry out his responsibilities, except that procedural regulations pertaining to the formulation, adoption,

or publication of voluntary or mandatory product standards, as provided for or authorized by

Chapters 7, 25, 26, and 3 9 of Title 15, U.S. Code, are to be issued by the Assistant

Secretary for Science and Technology.

335
DOO 30-2A -2-

b. With respect to Chapter 25 of Title 15, U.S. Code, the authorities to adopt final flammability standards, to appoint members of, and deal with, the National Advisory Committee

for the Flammable Fabrics Act, and to transmit an annual report of the results of the Department's activities in carrying out the Flammable Fabrics Act, as amended, are reserved

to the Secretary, The authority to make determinations of possible need for, and to institute proceedings for the determination of, a flammability standard or other regulation is delegated to the Assistant Secretary for Science and Technology.

c. The authority to prescribe and publish commercial standards, pursuant to Section 1213,

Chapter 26, Title 15, U.S. Code, is reserved to the Secretary.

d. With respect to Chapter 39 of Title 15, U.S. Code, the authority delegated in this order excludes the authority to make determinations of (1) an undue proliferation of weights, measures, or quantities, pursuant to 15 U.S.C. 1454 (d) , and (2) the non-adoption of standards

or the non-observance of adopted standards, pursuant to 15 U.S.C. 1454 (e) , which authority is delegated to the Assistant Secretary for Science and Technology. The authorities

to submit reports to the Congress concerning non-adoption or failure to observe voluntary

product standards, pursuant to 15 U.S.C. 1454 (e) , and to transmit an annual report to the Congress, as required by 15 U.S.C. 1457, are reserved to the Secretary.

.03 The Director is further delegated the authority to perform the functions assigned to the Secretary by Section 759(f), Chapter 16, Title 40, United States Code, pertaining to the conduct of research and the provision of scientific and technological advisory services relating to automatic data processing (ADP) and related systems, except that recommendations

to the President concerning the establishment of uniform Federal ADP standards are reserved

to the Secretary.

.04 The Director is further delegated the authority to perform the functions vested in the Secretary by:

a. Public Law 90-396 (82 Stat. 339), called the Standard Reference Data Act; and

b. Public Law 85-934 (72 Stat. 1793; 42 U.S.C. 1891-3) to make grants for the support of basic scientific research to nonprofit institutions of higher education and to nonprofit

organizations whose primary purpose is the conduct of scientific research.

.05 Pursuant to the authority delegated to the Secretary by the Administrator of the General

Services Administration (Temporary Regulation E-10, July 11, 1967, Federal Property Management Regulations) , and subject to such policies and directives as the Secretary or the Assistant Secretary for Science and Technology may prescribe, the Director is hereby delegated

authority to operate an automatic data processing service center.

.06 The authority delegated to the Secretary by the Administrator of the General Services

Administration, dated August 15, 1967, (32 F.R. 11969), to appoint uniformed guards as

special policemen and to make all needful rules and regulations for the protection of those

parcels of property at National Bureau of Standards installations which are not protected by

GSA guards, and over which the Federal Government has exclusive or concurrent jurisdiction,

is hereby redelegated to the Director. This authority shall be exercised in accordance with

the requirements of the Federal Property and Administrative Services Act of 1949 (63 Stat. 377), as amended, and the Act of June 1, 1948 (62 Stat. 281), as amended, and policies, procedures,

and controls of the General Services Administration.

.07 The authority vested in the Secretary of Commerce, by Executive Order 11654, dated

March 13, 1972, which pertains to the Federal Fire Council, is hereby delegated to the

Director. This delegation shall include authority to serve as Chairman of the Council or to designate an employee of the National Bureau of Standards to serve in that capacity.

.08 The Director may exercise other authorities of the Secretary as applicable to performing

the functions assigned in this order.

336
-3- DOO 30-2A

.09 The Director may redelegate his authority to any employee of the National Bureau of Standards subject to such conditions in the exercise of such authority as he may prescribe.

SECTION 4. FUNCTIONS.

.01 The National Bureau of Standards shall perform the following functions:

a. Develop and maintain the national standards of measurement, and provide means for making measurements consistent with those standards;

b. Determine the physical constants and properties of materials;

c. Develop methods for testing materials, mechanisms, and structures, and conduct such

tests thereof as may be necessary, with particular reference to the needs of Government

agencies;

d. Cooperate with and assist industry, business, consumers, and governmental organizations in the establishment, technical review, determination of acceptability, and publication of voluntary standards, recommended specifications, standard practices, and model

codes and ordinances;

e. Provide advisory service to Government agencies on scientific and technical problems;

f. Conduct a program for the collection, compilation, critical evaluation, publication, and

dissemination of standard reference data;

g. Invent and develop devices to serve special scientific and technological needs of the Government;

h. Conduct programs, in cooperation with United States business groups and standards

organizations, for the development of international standards of practice;

i. Conduct a program of research, investigation, and training with respect to the flammability characteristics of textiles and fabrics;

j . Conduct research and provide technical services designed to improve the effectiveness

of use by the Federal Government of computers and related techniques;

k. Conduct a national fire research and safety program, (as provided for by Public Law

90-259 (82 Stat. 34-39) amending Chapter 7 of Title 15, United States Code);

1. Conduct a program to provide an experimental basis for formulation of Government policy

to stimulate the development and use of technology by industry; and

m. Coordinate the activities of the Federal Fire Council.

.02 The Bureau shall perform the following functions, pursuant to the Fair Packaging and

Labeling Act (Chapter 39, Title 15, United States Code):

a. Ascertain the number and other characteristics of the weights, measures, and

quantities in which commodities are packaged for retail sale;

b. Conduct studies of the relationship between the weights, measures, and quantities in which commodities are packaged and the ability of consumers to make value comparisons;

c. Conduct studies concerning the extent to which voluntary product standards adopted

pursuant to 15 U.S.C. 1454 are being followed by industry;

337
DOO 30-2A -4-

d. Distribute copies of regulations and standards promulgated under this chapter, and

provide information and assistance to appropriate State officials, to promote uniformity in State and Federal regulation of the labeling of consumer commodities; and,

e. Conduct such other studies, investigations, and standards development activities as

are necessary to achieve the objectives of the Act.

.03 The Bureau, as appropriate, shall request the views of, and provide an opportunity for participation by, the Bureau of Domestic Commerce in the development and execution of its responsibilities for conducting investigations and analyses, and for developing or appraising

product standards , under the Flammable Fabrics Act , the Fair Packaging and Labeling

Act, or other Bureau legislative authorities.

SECTION 5. EFFECT ON OTHER ORDERS.

This order supersedes Department Organization Order 30-2A of October 1, 1968 (formerly

DO 90-A), as amended.

Secretary of Commerce

338
ANNEX 11.A.3. TRANSMITTAL 124

United States of America

DEPARTMENT OF COMMERCE

DEPARTMENT

ORGANIZATION ORDER 30-2B

DEPARTMENT

ORGANIZATION

ORDER SERIES

DATE OF ISSUANCE

June 12, 1972

SUBJECT NATIONAL BUREAU OF STANDARDS

SECTION 1. PURPOSE.

This order prescribes the organization and assignment of functions within the National Bureau of Standards (NBS) . This revision establishes a Center for Building

Technology under the Institute for Applied Technology, (paragraph 11.11) and makes

certain other changes of a minor nature. SECTION 2. ORGANIZATION.

The organization structure and line of authority of the National Bureau of Standards shall be as depicted in the attached organization chart.

SECTION 3. OFFICE OF THE DIRECTOR.

.01 The Director determines the policies of the Bureau and directs the development and

execution of its programs

.

.02 The Deputy Director assists the Director in the direction of the Bureau and performs

the functions of the Director in the latter 1 s absence.

SECTION 4. STAFF UNITS REPORTING TO THE DIRECTOR.

.01 The Office of Academic Liaison shall serve as the focal point for the Bureau's cooperation with the academic institutions , and serve as liaison office for cooperative

research activities between the Bureau and other Government agencies.

.02 The Office of Legal Adviser shall, under the professional supervision d the Department's General Counsel and as provided in Department Organization Order 10-6, serve

as the law office of and have responsibility for all legal services at the National Bureau

of Standards

.

SECTION 5. OFFICE OF THE ASSOCIATE DIRECTOR FOR PROGRAMS.

The Office of the Associate Director for Programs shall perform the functions of policy

development, program analysis, and program promotion; sponsor and coordinate the performance of issue and impact studies; relate Bureau programs to national needs;

generate planning formats and develop information on NBS program plans and status

for internal and external audiences; administer evaluation panels; and define alternatives

for the allocation of resources and advise Bureau management on their implications.

SECTION 6. OFFICE OF THE ASSOCIATE DIRECTOR FOR ADMINISTRATION.

.01 The Associate Director for Administration shall be the principal assistant and

adviser to the Director on management matters and is responsible for the conduct of administrative management functions, including the management of NBS buildings, plants,

and non-scientific facilities. He shall carry out these responsibilities primarily through

the organization units specified below, which are under his direction.

.02 The Accounting Division shall administer the official system of central fiscal records, payments and reports, and provide staff assistance on accounting and related matters

.

339
DOO 30-2B -2-

.03 The Administrative Services Division shall be responsible for security, safety,

emergency planning, and civil defense activities; provide mail, messenger, communications, duplicating, and related office services; manage use of auditorium and conference

rooms; conduct records and forms management programs; operate an NBS records holding

area; manage the NBS motor vehicle fleet; and provide janitorial service.

.04 The Budget Division shall provide advice and assistance to line management in the preparation, review, presentation, and management of the Bureau's budget encompassing its total financial resources

.

.05 The Personnel Division shall advise on personnel policy and utilization; administer re- cruitment, placement, classification, employee development and employee relations activities; and assist operating officials on these and other aspects of personnel management.

.06 The Plant Division shall maintain the physical plant at Gaithersburg , Maryland, and per- form staff work in planning and providing grounds, buildings, and improvements at other Bureau locations

.

.07 The Supply Division shall procure and distribute material, equipmert , and supplies pur- chased by the Bureau, keep records and promote effective utilization of property, act as the Bureau coordinating office for research, construction, supply and lease contracts of the Bureau, and administer telephone communications services and travel services.

.08 The Management and Organization Division shall provide consultative services to line management in organization, procedures, and management practices; develop administrative

information systems; maintain the directives system; and perform reports management functions.

.09 The Instrument Shops Division shall design, construct, and repair precision scientific instruments and auxiliary equipment.

SECTION 7. OFFICE OF THE ASSOCIATE DIRECTOR FOR INFORMATION PROGRAMS.

.01 The Associate Director for information Programs shall promote optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal

Gevernment; promote the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader aspects of the National Measurement System; provide appropriate services to ensure that the NBS staff has optimum

accessibility to the scientific information of the world; and direct public information activities of the Bureau.

.02 The Office of Standard Reference Data shall administer the National Standard Reference Data System which provides critically evaluated data in the physical sciences on a national

basis. This requires arrangement for the continuing systematic review of the national and

international scientific literature in the physical sciences, the evaluation of the data it contains, the stimulation of research needed to fill important gaps in the data, and the compilation and dissemination of evaluated data through a variety of publication and refer- ence services tailored to user needs in science and industry.

.03 The Office of Technical Information and Publications shall foster the outward communication of the Bureau's scientific findings and related technical data to science and industry

through reports , articles , conferences and meetings , films , correspondence and other appropriate mechanisms; and assist in the preparation, scheduling, printing and distribution of Bureau publications

.

.04 The Library Division shall furnish diversified information services to the staff of the Bureau, including conventional library services, bibliographic, reference, and translation services; and serve as a reference and distribution center for Congressional legislative

materials and issuances of other agencies.

340
-3- DOO 30-2B

.05 The Office of International Relations shall serve as the focal point for Bureau activities

in the area of international scientific exchanges

.

SECTION 8. CENTER FOR COMPUTER SCIENCES AND TECHNOLOGY.

.01 The Center for Computer Sciences and Technology shall conduct research and provide

technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment (Public Law 89-306); and serve as the principal focus

within the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages.

.02 The Director s hall direct the development, execution, and evaluation of the programs of the Center.

.03 The functions of the organizational units of the Center are as follows:

a. The Office of Information Processing Standards shall provide leadership and coordination

for Government efforts in the development of information processing standards at the Federal,

national, and international levels.

b. The Office of Computer Information shall function as a specialized information center for computer sciences and technology.

c. The Computer Services Division shall provide computing and data conversion services to NBS and other agencies on a reimbursable basis; and provide supporting problem analysis and

computer programming as required.

d. The Systems Development Division shall conduct research in information sciences and

computer programming; develop advanced concepts for the design and implementation of data processing systems; and provide consultative services to other agencies in software aspects

of the design and implementation of data processing systems.

e. The Information Processing Technology Division shall conduct research and development

in selected areas of information processing technology and related disciplines to improve

methodologies and to match developing needs with new or improved techniques and tools.

SECTION 9. INSTITUTE FOR BASIC STANDARDS.

.01 The Institute for Basic Standards shall provide the central basis within the United States

of a complete and consistent system of physical measurement; coordinate that system with measurement systems of other nations; and furnish essential services leading to accurate and

uniform physical measurements throughout the Nation's scientific community, industry, and commerce

.

.02 The Office of the Director.

a. The Director shall direct the development, execution, and evaluation of the programs of the -Institute

.

b. The Deputy Director shall assist in the direction of the institute and perform the functions

of the Director in the latter' s absence.

c. The Deputy Director, Institute for Basic Standards/Boulder shall assist in the direction

of the Institute's programs at Boulder and report to the Associate Director for Administration

through the Director, IBS, in supervising the administrative divisions at Boulder.

d. The administrative divisions reporti ng to the Deputy Director, Institute for Basic

Standards/Boulder include:

341
DOO 30-2B t4-

Supply Services Division

Instrument Shops Division

Plant Division

These divisions and units within his office shall provide staff support for the technical program and administrative services for the NBS organization at Boulder, Colorado. The

administrative units and divisions shall also service, as needed, National Oceanic and

Atmospheric Administration and Office of Telecommunications units at Boulder, Colorado, and

associated field stations.

.03 The Office of Measurement Services shall coordinate the Bureau's measurement services program, including development and dissemination of uniform policies on Bureau calibration practices

.

.04 The Center for Radiation Research shall constitute a prime resource within the Bureau

for the application of radiation, not only to Bureau mission problems, but also to those of other agencies and other institutions. The resulting multipurpose and collaborative functions

reinforce the capability of the Center for response to Bureau mission problems.

a. The Director shall report to the Director, Institute for Basic Standards, and shall direct the development, execution, and evaluation of the programs of the Center. The Deputy

Director shall assist in the direction of the Center and perform the functions of the Director

in the absence of the latter.

b. The organizational units of the Center for Radiation Research are as follows:

Linac Radiation Division

Nuclear Radiation Division

Applied Radiation Division

Each of these Divisions shall engage in research, measurement, and application of radiation to the solution of Bureau and other institutional problems, primarily through collaboration.

.05 The other organization units of the Institute for Basic Standards are as follows:

Located at Bureau Hdqrs

.

Located at Boulder, Colorado

Applied Mathematics Division Quantum Electronics Division

Electricity Division Electromagnetics Division

Mechanics Division Time and Frequency Division Heat Division Laboratory Astrophysics Division

Optical Physics Division Cryogenics Division

a . Each Division except the Applied Mathematics Division shall engage in such of the following functions as are appropriate to the subject matter field of the Division:

1. Davelop and maintain the national standards for physical measurement, develop

appropriate multiples and sub-multiples of prototype standards, and develop transfer standards and standard instruments;

2. Determine important fundamental physical constants which may serve as reference standards, and analyze the self-consistencies of their measured values;

3. Conduct experimental and theoretical studies of fundamental physical phenomena of interest to scientists and engineers with the general objective of improving or creating new

measurement methods and standards to meet existing or anticipated needs;

342
-5- DOO 30-2B

4. Conduct general research and development on basic measurement techniques and

instrumentation, including research on the interaction of basic measuring processes on the properties of matter and physical and chemical processes;

5. Calibrate instruments in terms of the national standards, and provide other measurement

services to promote accuracy and uniformity of physical measurements;

6. Correlate with other nations the national standards and definitions of the units of measurement; and

7. Provide advisory services to Government, science, and industry on basic measurement

problems

.

b. The Applied Mathematics Division shall conduct research in various fields of mathematics important to physical and engineering sciences, automatic data processing, and

operations research, with emphasis on statistical, numerical and combinatorial analysis and

systems dynamics; provide consultative services to the Bureau and other Federal agencies; and

develop and advise on the use of mathematical tools, in checking mathematical tables, handbooks, manuals, mathematical models, and computational methods.

SECTION 10. INSTITUTE FOR MATERIALS RESEARCH.

.01 The Institute for Materials Research shall conduct materials research leading to improved

methods of measurement, standards, and data on the properties of materials needed by

industry, commerce, educational institutions, and Government; provide advisory and research

services to other Government agencies; and develop, produce, and distribute standard

reference materials.

,02 The Director shall direct the development, execution and evaluation of the programs of the Institute. The Deputy Director shall assist in the direction of the Institute and perform

the functions of the Director in the latter' s absence.

.03 The Office of Standard Reference Materials shall evaluate the requirements of science

and industry for carefully characterized reference materials which provide a basis for calibration of instruments and equipment, comparison of measurements and materials, and aid in the

control of production processes in industry; and stimulate the Bureau's efforts to develop

methods for production of needed reference materials and direct their production and distribution.

.04 The other organization units of the Institute for Materials Research are as follows: Analytical Chemistry Division

Polymers Division

Metallurgy Division

Inorganic Materials Division Reactor Radiation Division

Physical Chemistry Division

Each Division shall engage in such of the following functions as are appropriate to the subject matter field of the Division:

a. Conduct research on the chemical and physical constants, constitution, structure, and

properties of matter and materials;

b. Devise and improve methods for the preparation, purification, analysis, and characterization of materials;

c. Investigate fundamental chemical and physical phenomena related to materials of importance to science and industry, such as fatigue and fracture, crystal growth and imperfections, stress, corrosion, etc.;

343
DOO 30-2B -6-

d. Develop techniques for measurement of the properties of materials under carefully controlled conditions including extremes of high and low temperature and pressure and exposure to different types of radiation and environmental conditions;

e. Assist in the development of standard methods of measurement and equipment for evaluating the properties of materials;

f . Conduct research and development methodology leading to the production of standard

reference materials, and produce these materials;

g. Provide advisory services to Government , industry, universities, and the scientific and technological community on problems related to materials;

h. Assist industry and national standards organizations in the development and establish- ment of standards; and

i. Cooperate with and assist national and international organizations engaged in the development of international standards.

SECTION 11. INSTITUTE FOR APPLIED TECHNOLOGY.

.01 The Institute for Applied Technology shall provide technical services to promote the use of available technology and to facilitate technological innovation in industry and Government; cooperate with public and private organizations leading to the development of technological standards (including mandatory safe standards) , codes and methods of test; and

provide technical advice and services to Government agencies upon request. The Institute shall also monitor NBS engineering standards activities and provide liaison between NBS and

national and international engineering standards bodies.

.02 The Director shall direct the development, execution, and evaluation of the programs of the Institute. The Deputy Director shall assist in the direction of the Institute and perform

the functions of the Director in the latter' s absence.

.03 The Office of Engineering Standards Services shall cooperate with and assist producers,

distributors, users and consumers, and agencies of the Federal, State, and local govern- ments in the establishment of standards for products, and shall administer the Department

of Commerce's Voluntary Product Standards program as set forth in Part 10 of Title 15, Code of Federal Regulations, "Procedures for the Development of Voluntary Product Standards".

.04 The Office of Weights and Measures shall provide technical assistance to the States with regard to model laws and technical regulations, and to the States, business, and

industry in the areas of testing, specifications, and tolerances for weighing and measuring

devices, to design, construction, and use of standards of weight and measure of associated

instruments, and the training of State and local weights and measures officials. The office includes the Master Railway Track Scale Depot, Clearing, Illinois.

.05 The Office of Invention and Innovation shall analyze the effect of Federal laws and

policies (e.g. , tax, anti-trust, and regulatory policies) on the national climate for invention

and innovation; undertake studies in related areas with other agencies; and assist and encourage inventors through inventors' services and programs, including cooperative activities with the States

.

.06 The Product Evaluation Technology Division shall develop the technology, standards, and

test methods for evaluating products including their systems, components, and materials.

.07 The Electronic Technology Division shall develop criteria for the evaluation of products

and services in the general field of electronic instrumentation; cooperate with appropriate

public and private organizations in identifying needs for improved technology in this field; and cooperate in the development of standards, codes and specifications. Further, it shall apply the technology of electronic instrumentation to the development of methods of practical measurement of physical quantities and properties of materials.

344
- 7 - DOO 30-2B

.08 The Technical Analysis Division shall conduct benefit-cost analyses and other basic

studies required in planning and carrying out programs of the Institute. This includes the development of simulations of industrial systems and of Government interactions with industry, and the conduct of studies of alternative Institute programs. On request, the Division shall provide similar analytic services for other programs of the Department of Commerce, in particular, those of the science-based bureaus, and, as appropriate, for other agencies of the executive branch.

.09 The Measurement Engineering Division shall serve the Bureau in an engineering

consulting capacity in measurement technology; and provide technical advice and apparatus

development supported by appropriate research, especially in electronics, and in the combination of electronics with mechanical , thermal , and optical techniques

.

.10 The Fire Technology Division shall (a) conduct data gathering, research, education

and demonstration programs on fire, its causes, prevention, and control, and on the flammability of products, fabrics, and materials; (b) develop test methods and standards in flammability; and (c) coordinate all other fire research and safety activities of the National Bureau of Standards

.

.11 The Center for Building Technology shall consult with industry, government agencies,

professional associations, labor organizations, consumers, and such organizations as the National Conference of States on Building Codes and Standards in developing test methods

for evaluating the performance of buildings including their materials and components, the

support and stability characteristics of their elements and systems, the effects of new design strategies, their fire safety and environmental characteristics, and their service and

communication systems; formulating performance criteria for building design and urban systems; and performing research, including research on safety factors, in the systems approach

to building design and construction, in improving construction and management efficiency,

in building material characteristics, in structural behavior, and in building environmental systems.

a. The Director shall report to the Director, Institute for Applied Technology and shall direct the development, execution and evaluation of the programs of the Center. The Deputy Director shall assist in the direction of the Center and perform the functions of the Director in the

latter' s absence.

b. The organizational units of the Center for Building Technology shall be:

Office of Housing Technology

Office of Federal Building Technology

Office of Building Standards and Codes Services

Building Environment Division

Structures, Materials and Life Safety Division

Technical Evaluation and Application Division.

SECTION 12. EFFECT ON OTHER ORDERS.

This order supersedes Department Organization Order 30-2B of November 16, 1970, as amended.

Acting Director, National Bureau o: Standards

Assistant Secretary for Science and

Approved: Technology

USCOMM-DC - 50368

345
346
Annex ll.B.

USNO AUTHORIZING DOCUMENTS

Contents

Page

ll.B.l. Executive Order 9126, April 1942 — Organizational Location 349

11.B.2. Reorganization Plan No. 3, May 1946 350

11.B.3. U.S. Naval Operations Instruction 5450.90B, Dec. 16. 1969 - Mission and

Functions of the U.S. Naval Observatory 357

347

ANNEX ll.B.l.

The White House,

April 7, 1942. EXECUTIVE ORDER 9126*

Transferring Cognizance of the Duties

and Functions of the Hydrographic

Office and the Naval Observatory

From the Bureau of Navigation, Navy

Department, to the Chief of Naval

Operations

By virtue of the authority vested in me

by Title I of the First War Powers Act,

1941, approved December 18, 1941 (Public

Law 354, 77th Congress) , and for the more

effective exercise and more efficient administration of my powers as Commander

in Chief of the Army and Navy, it is hereby ordered as follows:

1. The duties and functions of the Hydrographic Office and Naval Observatory,

Bureau of Navigation, Navy Department,

are hereby transferred to the cognizance

and jurisdiction of the Chief of Naval

Operations under the direction of the

Secretary of the Navy.

2. All personnel, together with the

whole of the records and public property now under the cognizance of the Bureau

of Navigation in the Hydrographic Office and the Naval Observatory are assigned

and transferred to the Office of Chief of Naval Operations.

Franklin D Roosevelt

The White House,

April 8, 1942.

Page 1137

* Office of Federal Register, Code of Federal Regulations, Title 3 (The President, 1938-1943 Compilation), "transferring cognizance of

the, duties and functions of the Hydrographic Office and the Naval Observatory from the Bureau of Navigation, Navy Department, to the Chief of Naval Operations," Executive Order 9126, Franklin D. Roosevelt, April 1942, page 1137 (USGPO, 1968).

349
ANNEX 11.B.2.

[118] May 16 Public Papers of the Presidents

118 Special Message to the Congress Transmitting Reorganization

Plan 3 of 1946. May 16, 1946*

To the Congress of the United States:

I transmit herewith Reorganization Plan

No. 3 of 1946, prepared in accordance with

the provisions of the Reorganization Act of

1945. The Plan contains reorganizations affect- ing a number of departments and establish- ments. Some continue on a permanent basis changes made by Executive order under authority of the First War Powers Act. A

few make adjustments in the distribution of functions among agencies. The remainder

deal with problems of organization within

individual agencies. All are concerned with

improving and simplifying particular phases

of Government administration. Each proposal is explained in more detail under the appropriate heading below.

I have found, after investigation, that each

reorganization contained in the Plan is neces- sary to accomplish one or more of the purposes set forth in section 2(a) of the Reorganization Act of 1945.

DEPARTMENT OF THE TREASURY The functions of the Bureau of Marine In- spection and Navigation were transferred from the Department of Commerce to the Coast Guard and the Bureau of Customs in 1942 by Executive order under the First War

Powers Act. This arrangement has been

proved successful by the experience of the

past four years. Part I of the Reorganization Plan continues the arrangement on a permanent basis.

United States Coast Guard

The principal functions of the Bureau of Marine Inspection and Navigation were

those of the inspection of vessels and their

260

equipment, the licensing and certificating of officers and seamen, and related functions designed to safeguard the safety of life and

property at sea. Thus these functions are

related to the regular activities and general purposes of the Coast Guard. The Coast Guard administered them successfully dur- ing the tremendous expansion of wartime

shipping, by virtue of improvements in or- ganization and program, many of which

ought to be continued.

The Plan also transfers to the Coast Guard

the functions of the Collectors of Customs

relating to the award of numbers to un- documented vessels. These functions, too, were temporarily transferred to the Coast Guard in 1942.

Bureau of Customs

The Plan transfers to the Commissioner

of Customs the functions of the Bureau of Marine Inspection and Navigation and the

Secretary of Commerce relating to the documentation of vessels, measurement of vessels, administration of tonnage tax and tolls, entry and clearance of vessels and aircraft, regulation of coastwise trade and fisheries, recording of conveyances and mortgages of

vessels, and protection of steerage passengers. These functions have always been

performed at the ports by the Customs Service, although legal responsibility for their supervision was vested in the Bureau of Marine Inspection and Navigation and the

Secretary of Commerce until transferred temporarily to the Commissioner of Cus- toms under the wartime reorganization power. The proposed transfer will permit more

efficient administration by ending divided

responsibility.

*Grover, W. C. (Archivist), Public Papers of the Presidents of the United States— Harry S Truman — 1946, "No. 118, Special message

to the Congress transmitting reorganization plan 3 of 1946," pp. 260-267 (TJSGPO, 1962).

350
Harry S. Truman, 1946 May 16 [118]

DEPARTMENT OF WAR AND DEPARTMENT OF THE NAVY

Functions with Respect to Certain Insane Persons

Prior to World War I practically all mental patients for whom the Federal Government was legally obligated to provide

hospital care and treatment, including per- sonnel of the armed forces, were hospitalized

in St. Elizabeths Hospital, Washington,

D.C. In addition, this hospital served as the mental hospital for the District of Columbia Government. Following World

War I, the responsibility for hospital care of mentally ill war veterans was assigned to the Veterans Administration. Somewhat

later, specialized hospital facilities were pro- vided by the Bureau of Prisons of the Department of Justice to enable that agency to care for prisoners suffering from mental

disorders. With the growth in the population of the

District of Columbia and the wartime ex- pansion of the armed forces, the facilities of St. Elizabeths Hospital became inadequate. The War Department therefore es- tablished its own mental hospitals at the

outset of World War II. Furthermore it became necessary a year ago for the Navy

Department to discontinue the use of St. Elizabeths and to assume the responsibility for the care of its mental patients. Since the return of the Coast Guard to the Treasury Department, the Public Health

Service now provides care in its mental hospitals for personnel of the Coast Guard in accordance with the basic responsibility dele- gated to it in the Public Health Service Code

enacted in 1944. The Plan abolishes the functions of St. Elizabeths Hospital with

respect to insane persons belonging to the Coast Guard which are provided for by Sec. 4843 of the Revised Statutes (24 U.S.C. 191).

Responsibility for the care of mental patients has been allocated on the basis of the four broad categories of beneficiaries,

namely, (1) veterans, to be cared for by the Veterans Administration; (2) military and

naval personnel, to be cared for by the War

and Navy Departments; (3) prisoners, for whom the Department of Justice will be

responsible; and (4) other civilians, to be

cared for by the Federal Security Agency.

The Reorganization Plan, in order to carry out this policy, provides for the transfer or

abolition of certain functions and legal

responsibilities now resting with the Federal

Security Administrator and Superintendent

of St. Elizabeths Hospital.

NAVY DEPARTMENT

Hydrographic Office and Naval Observatory

The Plan transfers the Hydrographic Office and the Naval Observatory from the Bureau of Naval Personnel to the Office of

the Chief of Naval Operations. The Plan

would confirm and make permanent the

action taken in 1942 by Executive Order

No. 9126 under the First War Powers Act. The functions performed by both the Hydrographic Office and the Naval Observatory

relate primarily to operational matters and

thus are more appropriately placed in the

Office of the Chief of Naval Operations than

in the Bureau of Naval Personnel. This

fact was recognized in the realignment of naval functions at the outbreak of the war. The Plan merely confirms an organizational

relationship which has existed successfully for the past four years.

Supply Department of the United States Marine Corps

The Plan consolidates the Paymaster's Department and the Quartermaster's Department of the United States Marine Corps into

261

351
[118] May 16 Public Papers of the Presidents

a single Supply Department. This consoli- dation will establish in the Marine Corps an

integrated supply organization which parallels that of the Navy Department's Bureau

of Supplies and Accounts. The consolidation will make possible a more efficient and more economical organization of the companion functions of supply

and disbursement, eliminating the present

handling of related items by two separate

departments of the Corps.

DEPARTMENT OF THE INTERIOR The Fran\lin D. Roosevelt Library at Hyde

?ar\

At the present time, the National Park

Service, the Public Buildings Administration, and the Archivist of the United States

all perform "housekeeping" functions at the Franklin D. Roosevelt Library and home at Hyde Park. The Plan unifies in the National Park Service responsibility for activities of this character at Hyde Park—that is, the maintenance and protection of buildings

and grounds, the collection of fees, and the handling of traffic and visitors. Because of

its wide experience in the administration of

historic sites, the National Park Service is the logical agency to assume the combined

functions. Transfer of these functions does not affect the responsibility of the Archivist for the

contents and professional services of the Li- brary proper. It also does not affect the

present disposition of the receipts, which is provided by law.

Functions Relating to Mineral Deposits in Certain Lands

The Plan transfers to the Department of the Interior jurisdiction over mineral deposits on lands held by the Department of Agriculture.

262

The Department of the Interior now ad- ministers the mining and mineral leasing

laws on various areas of the public lands,

including those national forests established on parts of the original public domain. The

Department of Agriculture, on the other hand, has jurisdiction with respect to mineral deposits on (1) forest lands acquired

under the Weeks Act, (2) lands acquired in connection with the rural rehabilitation pro- gram, and (3) lands acquired by the Department as a part of the Government's

effort to retire submarginal lands. Accordingly this Reorganization Plan

provides that these mineral deposits on lands

of the Department of Agriculture will be administered by the Department of the Interior, which already has the bulk of the Federal Government's mineral leasing pro- gram. The Plan further provides that the administration of mineral leasing on these lands under the jurisdiction of the Department of Agriculture will be carried on subject to limitations necessary to protect the surface

uses for which these lands were primarily

acquired.

Bureau of Land Management

The Plan consolidates the General Land

Office and the Grazing Service of the Department of the Interior into a Bureau of Land Management.

The General Land Office and the Grazing

Service now divide responsibility for the major portion of the multiple-use Federallyowned lands now held by the Department of

the Interior. The lands under jurisdiction of the two agencies are comparable in character and in use. In some functions, the two agencies employ the same type of per- sonnel and use the same techniques. Other

functions are divided between the agencies

so that both are engaged in management of

352
Harry S. Truman, 1946 May 16 [118]

various aspects of the same land. Consoli- dating these two agencies will permit the development of uniform policies and the

integration of two organizations whose

responsibilities now overlap.

Integration of the activities of the two

agencies will make possible greater utiliza- tion and thus more economic use of expert

skills. The same practical experience embraced in range administration on public lands in grazing districts will be available

for public lands outside the districts. Utilization of lands within grazing districts for non-grazing purposes will be subject to only one classification examination,

rather than dual examination as is now

necessary. Economy will be possible in the

construction of range improvements, wherever feasible, to serve lands both in and out

of districts. Legal procedures such as adjudication of issues relating to licenses and

leases, hearings on appeal from administrative decisions, and the processing of trespass

cases will benefit from unified administration and handling.

In such activities as fire protection, soil and moisture conservation, management of public lands under agreement with other

agencies (e.g., Bureau of Reclamation), range surveys, maintenance and improvement of stock driveways, and stabilization of range use on all public domain, the

benefits of consolidation will become in- creasingly apparent. Further, records re- lating to grazing lands can be concentrated

in fewer field offices and hence administered more effectively.

While the establishment of a new Bureau

of Land Management under a Director in- volves the abolition of the Commissioner

and Assistant Commissioners of the General Land Office, the Director and Assistant Directors of Grazing, the Registers of District Land Offices, and the United States

83738—62 20

Supervisor of Surveys, the statutory functions now discharged by these officers are

in no way modified. This plan will place

final responsibility for these functions in the

Secretary of the Interior and make him re- sponsible for their performance in coordination with the other land activities of his Department. Officers whose offices are

specifically abolished, but whose experience

will make them valuable to the Department,

should be available for appointment in the new Bureau.

I have found and declare that by reason

of the reorganization made by the Plan the

responsibilities and duties of the Bureau of Land Management are of such nature as to require the inclusion in the Plan of provisions for the appointment and compensation

of a Director, an Associate Director, and

Assistant Directors.

DEPARTMENT OF AGRICULTURE

Functions of Certain Agencies of the Department of Agriculture

To enable the Department of Agriculture

to meet its responsibilities for food production and distribution during the war, there was early and continuing coordination of

its programs directly concerned with these phases of the food problem. Beginning with

Executive Order No. 9069 of February 23, 1942, those programs and agencies dealing

with food production and distribution were

gradually consolidated by a series of Executive orders issued under the authority of the

First War Powers Act. By Executive Order

No. 9934 of April 19, 1943, they were all grouped into a War Food Administration,

under a War Food Administrator.

When the fighting was drawing to a close and the emergency purposes of the War

Food Administration had been largely ac- complished, this Administration was ter263

353
[118] May 16 Public Papers of the Presidents

minated by Executive Order No. 9577 of June 29, 1945; and its functions and agencies were transferred back to the jurisdiction of the Secretary of Agriculture. Executive

Order No. 9577 also authorized the Secretary of Agriculture to organize and administer

the transferred functions and agencies in the manner which he deemed best. Under this authority, the Secretary estab- lished the Production and Marketing Administration in August 1945. Into this Administration, he consolidated the functions of many of the production and marketing agencies which were transferred back from the War Food Administration. Included were

the functions of the Agricultural Adjustment Administration and the Surplus Marketing Administration and the administration of the programs of the Federal Crop

Insurance Corporation and the Commodity

Credit Corporation.

The Plan transfers these functions to the

Secretary of Agriculture in order to permit

him to continue the consolidation already

effected in the Production and Marketing

Administration. This provision makes it possible to maintain the close coordination

and integration of food production and dis- tribution programs, with the resulting benefits that were achieved during the war. It also provides the Secretary with the necessary

flexibility to make adjustments in the coor- dination and administration of these pro- grams to meet changing conditions and new

problems, a flexibility which he particularly needs at this period of acute food shortages

throughout the world.

DEPARTMENT OF COMMERCE

Certain Functions of National Bureau of Standards

The Plan transfers the functions of two

divisions of the National Bureau of Stand264

ards in the Department of Commerce,

namely, the Division of Simplified Trade

Practices and the Division of Commercial

Standards, to the Secretary of Commerce.

The transfer will permit the Secretary to re- assign these functions to the Office of Domestic Commerce, which is the focal point

of the Department's general service functions for American business. These two divisions were established as a

result of the standardization work initiated in World War I. Both divisions have fol- lowed the same basic procedure of assisting the producers and the consumers of particular products to agree among themselves on

certain standards or on a certain limited number of varieties. Each such voluntary

agreement is then published by the National Bureau of Standards and, although not compulsory, has tended to become the generally

accepted practice in the trade. Standardization again proved to be an

important device for accelerating production

in World War II; and industry has shown

renewed interest in continuing these wartime conservation and rationalization pro- grams on a voluntary basis in the production

of peacetime products.

The desirability of the proposed transfer was emphasized only a few months ago by

the report of a committee of prominent

businessmen appointed by the Secretary of Commerce to review the entire question of

the Government's activities in this field. These studies indicate that two major

benefits will result from the transfer.

First, the association of the two divisions with the National Bureau of Standards has perhaps tended to give the impression in some quarters that voluntary standards and

trade practices worked out by industry with

the help of these two divisions are in some

sense Government standards which are en- forced on the basis of scientific and objective

354
Harry S. Truman, 1946 May 16 [118]

tests. The transfer of these two divisions to the Department proper would reduce any

such misconceptions, and make it clear that

these standards and simplified practices are voluntary industry agreements in the making of which the Government acts merely in an advisory capacity.

Second, the other general services of the Department to American business, such as marketing, management, and economic and

statistical services, are now concentrated in the Office of Domestic Commerce. The as- sociation of these two divisions with these other services to business will facilitate their work and enable them to make use of the wide industrial and business contacts of the

Office of Domestic Commerce.

NATIONAL LABOR RELATIONS BOARD

Stride Ballots Under the War Labor

Disputes Act The Plan abolishes the function of con- ducting strike ballots which was vested in the National Labor Relations Board by Section 8 of the War Labor Disputes Act (57

Stat. 167, ch. 144). Experience indicates that such elections under the act do not serve

to reduce the number of strikes and may

even aggravate labor difficulties. The Congress has already forbidden the Board to expend any of its appropriations for the current fiscal year for this activity (First

Deficiency Appropriation Act of 1946). I believe that the function should now be

permanently abolished.

SMITHSONIAN INSTITUTION

Canal Zone Biological Area The Plan transfers responsibility for the Canal Zone Biological Area to the Smithsonian Institution. At present, the Canal

Zone Biological Area is an independent

agency of the Government, having as its function the administration of Barro Colo- rado Island in Gatun Lake as a tropical wildlife preserve and research laboratory.

The Board of Directors of this agency consists of the President of the National

Academy of Sciences as Chairman, the Sec- retary of the Smithsonian Institution, three members of the Cabinet—the Secretaries of War, Interior, and Agriculture—and three

biologists.

The transfer will locate this function with

comparable and related functions already

assigned to the Smithsonian Institution whose staff members have participated since the beginning in developing the island as a research center. It will reduce by one the number of Government agencies. It will

relieve three Cabinet members of routine

duties not important enough to warrant their personal attention. Under its existing authority the Smithsonian Institution may constitute an advisory

board of biologists and departmental rep- resentatives if it finds such action necessary.

UNITED STATES EMPLOYMENT SERVICE

Placement Functions Under Selective Training and Service Act of 1940

The Plan transfers to the United States Employment Service the functions of the

Selective Service System and its Director

with respect to assisting ex-servicemen in obtaining new positions. These functions direcdy overlap the regular placement activities of the United States Employment Service, which is required to provide a special

placement service for veterans both by its basic act and by the Servicemen's Readjustment Act of 1944. The transfer is in line with the policy of the Congress on the placement of veterans as most recendy expressed

in the 1944 Act. The shift will prevent

265

355
[118] May 16 Public Papers of the Presidents

needless duplication of personnel and facili- ties and will assure the best service to veterans. Harry S. Truman

note: Reorganization Plan 3 of 1946 is published

in the U.S. Statutes at Large (60 Stat. 1097) and

in the 1943-1948 Compilation of title 3 of the Code

of Federal Regulations (p. 1065). It became effec- tive July 16, 1946.

356
ANNEX 11.B.3.

OPNAVINST 5450. 90B

Dec 16 1969

Mission and Functions of the

U. S. Naval Observatory

Mission : To make such observations of celestial bodies, natural and

artificial, derive and publish such data as will afford to United States

Naval vessels and aircraft as well as to all availing themselves thereof, means for safe navigation, including the provision of accurate time; and

while pursuing this primary function, contribute material to the general

advancement of navigation and astronomy.

Functions : In carrying out this mission, the Superintendent, U. S. Naval

Observatory, shall perform the following functions:

1. Supervise and direct all functions, programs, and activities of the

U. S. Naval Observatory, and command shore activities as assigned by the

Chief of Naval Operations.

2. Recommend policies, plans, and programs deemed necessary or appropriate

to promote the operational effectiveness or efficiency of the Naval Observatory.

3. Make continuous observations of the sun, moon, planets, stars, and

other celestial bodies, natural and artificial, to determine their positions and motions.

4. Compile and publish the astronomical publications required for safe

navigation and fundamental positional astronomy.

5. Derive, maintain and coordinate precise time and time interval

(frequency), both astronomical and atomic, for the Department of Defense;

and control distribution of, and provide single management service and

interservice support for precise time and time interval within the Department of Defense

o

6. Collaborate worldwide with astronomers through the exchange of astronomical data in order to obtain information required for the publications

of the Naval Observatory.

7. Contribute to the advancement of astronomy and navigation by the

conduct of research in celestial mechanics and astronomy and the publication of the results thereof.

8. Discharge other responsibilities which may be assigned by the Chief

of Naval Operations.

357

ANNEX ll.C.

NBS TIME AND FREQUENCY RESPONSIBILITIES

Contents

Page ll.C.l. Time and Frequency Division (273.00 — Institute for Basic Standards — IBS) 361

a. Atomic Frequency and Time Standards Program Areas (273.00/PA).

b. Frequency-Time Dissemination Research Section (273.01).

c. Frequency-Time Broadcast Services Section (273.02).

359

ll.C.l. Time and Frequency Division

(2 73.00 -Institute for Basic Standards)

Provides custody and maintenance for NBS

frequency and time interval standards and time

scales. Conducts fundamental and applied research

to establish such standards. Disseminates inter- nationally coordinated frequency and time through

radio broadcasts, portable clocks, and other

advanced techniques. Engages in research and

development on new dissemination techniques

that improve accuracy and increase coverage. Develops improved instrumentation for dissemination of time and frequency. Coordinates time and

frequency nationally and internationally and pro- vides NBS time scale input to the BIH for formulation of TAI. Conducts fundamental physical

research in which the techniques used in time and

frequency standards are of critical importance.

Disseminates information through consultation

and publication.

a. Atomic Frequency and Time Standards Program Areas (273.00/PA)

Provides atomic frequency standards for the

United States and develops and improves such

standards. Provides, develops, and improves

atomic time scales based on the frequency standards, and evaluates such time scales for consideration as a standard. Pursues fundamental research

to maintain state of the art expertise in frequency

standard and time scale work. Furnishes time and

frequency signals to other Boulder Laboratory

activities. Performs frequency and time calibration

services for science, industry, commerce, and

government users who require reference to the

national standards.

b. Frequency-Time Dissemination Research Section

(273.01)

Conducts research and development on new and

improved methods of dissemination of frequency

and time standards including satellites, television, very low frequency (VLF) radio signals, portable

clocks, and other advanced techniques; investigates

propagation errors of time signals; provides consultation on methods of frequency and time dissemination; compares and evaluates methods of frequency

and time dissemination; and makes recommendations for improvements in monitoring techniques

and other mission components.

c. Frequency-Time Broadcast Services Section (273.02)

Provides wide dissemination of frequency and

time standards primarily by radio broadcasts;

investigates and develops techniques for improving

the accuracy with which frequency and time can

be distributed by broadcasting electromagnetic

signals; measures distortion involved in the radio

broadcast of time and frequency standards, particularly with regard to electronic transmitting and

receiving equipment; provides consultation relative

to the frequency and time broadcast services;

evaluates the effectiveness of the frequency and

time broadcast services; recommends improvement

or modification of existing services or additions of new services; and monitors frequency and time

broadcasts from various sources.

Postdoctoral Research Awards

From time to time the National Bureau of Standards, in cooperation with the National Research

Council, offers postdoctoral research awards for study in a broad spectrum of interests in basic

and applied science, engineering, and technology

involving many disciplines. Currently there are four specific research areas in the Time and Fre- quency Division as follows:

1) Fundamental Noise Studies in Frequency

Standards,

2) New Quantum Electronic Frequency

Standards,

3) Statistical Control and the Theory of Measurement,

4) The Unified Time-Length Standard.

Further information is given in reference 140].

361

Annex ll.D.

USNO PRECISE TIME AND TIME INTERVAL (PTTI) RESPONSIBILITIES

Contents

Page

ll.D.l. U.S. Department of Defense (DOD) Directive 5160.51, PTTI Standards and Calibration

Facilities for Use by DOD Components; 6 pages (August 31, 1971) 365

11.D.2. U.S. Sec. Navy Instruction 4120.4, PTTI Standards and Calibration Facilities for Use

by Department of Navy; 5 pages (June t», 1972) 371

i

363

ANNEX ll.D.l.

August 31, 1971

NUMBER 5160.51

ATSD(T)

Department of Defense Directive

SUBJECT Precise Time and Time Interval (PTTI) Standards and

Calibration Facilities for Use by Department of Defense

Components'

Refs.: (a) DoD Directive 5160.51, "Time and Time Interval

Standards and Calibration Facilities for Use by

Department of Defense Components," February

1, 1965 (hereby cancelled)

(b) DoD Instruction 4630.4, "Support and Management

Services for Precise Time and Time Interval

Standards, " June 22, 1966 (hereby cancelled)

(c) DoD Directive 4000.19, "Basic Policies and

, Principles for Interservice and Interdepartmental Logistic Support, " August 5, 1967

I. REISSUANCE

This Directive reissues reference (a) and consolidates

references (a) and (b) which are hereby cancelled. Revisions

occasioned by organizational and administrative changes are

also included. There are no substantive changes.

II. PURPOSE AND APPLICABILITY

This Directive establishes policy and assigns responsibility

to a single Department of Defense Component for establishing,

coordinating, and maintaining capabilities for time and time

interval (astronomical and atomic) for use by all DoD Components, DoD contractors, and related scientific laboratories.

III. DEFINITIONS

For purposes of this Directive, the following definitions

will apply.

l»W " ynAd!0n (;". . mmmmm*

p.s # .

365
Continuation of III.

A. Time signifies epoch, that is, the designation of an instant on a selected time scale, astronomical or atomic. It is

used in the sense of time of day.

B. Time Interval indicates the duration of a segment of time

without reference to when the time interval begins and ends.

Time interval may be given in seconds of time.

C. Standards signifies the reference values of time and time

interval. These standards are determined by astronomical

observation and by the operation of atomic clocks. They are disseminated by transport of clocks, radio transmissions,

and by other means.

D. Precise Frequency signifies a frequency requirement to

within one part in 109 of an established time scale.

E. Precise Time signifies a time requirement within ten

milliseconds.

IV. POLICY

A. Resources for uniform and standard time and time interval

operations and research shall be the responsibility of a

single DoD Component.

B. The maximum practicable interchange of time and time

interval information shall be effected throughout the DoD.

C. Maximum practical utilization of interservice support will

be achieved as prescribed in reference (c).

V. RESPONSIBILITIES

A. The U. S. Naval Observatory (hereafter referred to as the

"Observatory") is assigned the responsibility for insuring:

1. Uniformity in precise time and time interval operations

including measurements.

2. The establishment of overall DoD requirements for time

and time interval.

2

366
Aug 31, 71 5160. 51

Continuation of V.

3. The accomplishment of objectives requiring precise time

and time interval with minimum cost.

B. In carrying out the above responsibilities, the Observatory

shall:

1. Derive and maintain standards of time and time interval,

both astronomical and atomic.

2. Provide coordination of such standards with recognized

national and international standards to insure world-wide

continuity of precision.

3. Monitor conferences concerning time and time interval

standards.

4. Advise and provide guidance to DoD Components, contractors, and scientific laboratories on matters concerning time and time interval, and their measurement.

C. All DoD Components which require, utilize, or distribute

time and time interval information or have a need for a

specific time scale shall:

1. Refer time and time interval to the standards established

by the Observatory.

2. Maintain specific time scales such that relationship to the standard established by the Observatory is known.

3. Prescribe technical requirements for the coordination of

techniques, procedures and periodic calibrations of systems.

4. Promote economy by prescribing requirements for precise

time that are consistent with operational and research

needs for accuracy.

3

367
DELINEATION OF FUNCTIONS

A. The Observatory is the single DoD Component responsible

for PTTI management control functions. This responsibilityencompasses overall activities requiring time to within ten

milliseconds and frequency to within one part in 10^ of an

established time scale. In carrying out these PTTI functions on a common-servicing basis, the Observatory will:

1. Issue detailed information concerning reference values

for PTTI and distribute them by means of controlled

radio transmissions and portable atomic clocks.

2. Promote (a) operational uniformity of PTTI functions,

including measurements; (b) establishment of overall

DoD PTTI requirements; and (c) accomplishment of

objectives requiring PTTI at minimum cost.

3. Monitor DoD research programs concerning PTTI

(frequency), in coordination with the Office of the

Director of Defense Research and Engineering.

4. Review (a) existing and future PTTI (frequency) requirements of the DoD user components in order to establish

overall DoD requirements and to provide adequate supporting services; and (b) existing PTTI operations conducted

by DoD user components to provide guidance and recommendations to the Assistant to the Secretary of Defense

(Telecommunications).

5. Establish relationships between the DoD and other Federal

Government agencies on PTTI matters.

6. Provide advice and guidance concerning requests for

unilateral PTTI (frequency) programs at the direction

of Assistant to the Secretary of Defense (Telecommunications).

7. Participate in PTTI policy negotiations between the DoD

and other Federal Government agencies and international

organizations

.

4

368
Aug 31, 71 5160. 51 Continuation of VI. A.

8. Maintain records of PTTI (frequency) arrangements

between the DoD and its contractors and other Federal

Government agencies, with the exception of radio

frequency assignments.

B. DoD User Components

1. DoD Components presently conducting Precise Time and

Time Interval operations and research may continue

these activities unless otherwise instructed by the

Assistant to the Secretary of Defense (Telecommunications).

2. The Military Departments will assist the Observatory

by (a) providing technical information on current and

prospective programs involving PTTI applications; and

(b) distributing, monitoring and controlling PTTI services on request, subject to the provisions of this Directive

and the availability of funds.

C. DoD User Components and contractors will:

1. Consult the Observatory on any technical and logistic

problems arising from obtaining a particular accuracy

through radio transmissions and portable atomic clocks.

2. Use DoD -controlled transmissions to the maximum

extent practicable. Other transmissions of time and

frequency which have been coordinated with the

Observatory may be used when DoD transmissions do

not provide adequate coverage.

3. Refer measurements and contract specifications to DoD

standards determined by the Observatory.

4. Use techniques and procedures described in information

documents issued by the Observatory in all cases where

such documents satisfy the need.

5. Notify the Observatory of:

a. Existing and planned PTTI requirements, including

information as to accuracy and stability of needs,

5

369
Continuation of VI. C. 5. a.

measurement techniques planned or in operation,

and continuity of service required of the applicable

distribution transmission.

b. PTTI (frequency) arrangements between DoD user components and contractors and other Federal

Government agencies (see paragraph VI. A. 8. above)

and

c. Scheduled scientific and technical meetings on PTTI

(frequency).

6. Consult the Observatory prior to entering into contracts

for equipment, research, studies, or services involving

PTTI (frequency) in order that maximum use of existing

facilities may be assured.

VII. EFFECTIVE DATE AND IMPLEMENTATION

This Directive is effective immediately. It shall be given full

distribution by all DoD Components. Two copies of each

implementing document shall be forwarded to the ATSD(T)

within 90 days. ^ s~"v /)

Deputy Secretary of Defense

6

370
ANNEX 11.D.2.

DEPARTMEN I OF THE NAVY

OFFICE OF THE CHIEF OF NAVAL OPERATIONS

WASHINGTON, D. C. 20350 'N o«*ly >[rcn to OPNAVINST 4120.4

NAVOBSY

6 JUN 1972

OPNAV INSTRUCTION 4120.4

From: Chief of Naval Operations

Subj : Precise Time and Time Interval (PTTI) Standards and

Calibration Facilities for use by Department of the

Navy

Ref: (a) DoD Directive 5160.51 of 31 Aug 1971 (NOTAL)

(b) SECNAV Instruction 4355. 11B of 16 Jul 1969 (NOTAL)

1. Purpose . To implement reference (a) within the Department of the Navy.

2. Scope and Applicability . The scope of this instruction

includes : the generation of operational and research requirements for PTTI (frequency); the establishment, coordination,

maintenance, distribution, and utilization of standard values

for time and frequency; and the coordination of the Department

of the Navy with other components of the Department of Defense

with respect to precise time and frequency operations , techniques, procedures, measurements, and calibrations.

3. Definitions . For purposes of this instruction, the following definitions will apply:

a. Time signifies epoch, that is, the designation of

an instant on a selected time scale, astronomical or atomic.

It is used in the sense of time of day or date.

b. Time Interval indicates the duration of a segment of

time without reference to when the time interval begins and

ends. Time interval may be given in seconds of time.

c. Standards signify the reference values of time and

time interval. These standards are determined by astronomical

observation and by the operation of atomic clocks. They are

disseminated by transport of clocks, radio transmissions, and

by other means.

d. Precise Frequency signifies a frequency requirement

to within one part in 10* of an established time scale.

e. Precise Time signifies a time requirement within ten

milliseconds.

371
OPNAVINST 4120. 4

6 Junp -"97?

4 . Policy

a. The epoch and the interval of time (frequency) as determined by the U. S. Naval Observatory (NAVOBSY) shall be

utilized as standards within the Department of the Navy.

b. Designated Department of the Navy facilities and

systems which are capable of distributing precise time or frequency information, such as radio communications, satellites, and radio navigation systems, shall transmit the

standards determined by the NAVOBSY.

c. Addressees requiring precise time and frequency shall

make their requirements known to the Superintendent, NAVOBSY

or the Chief of Naval Material (CNM) , and shall obtain guidance

as appropriate in preparing Specific Operational Requirements

(SOR) , Advanced Development Objectives (ADO) , Proposed Technical

Approaches (PTA) , Technical Development Plans (TDP) , and similar

planning instruments.

d. Organizations with future requirements for precision

or geographic coverage exceeding those provided by existing

distribution systems shall make these requirements known to

the Superintendent, NAVOBSY.

5 . Responsibilities

a. The NAVOBSY is assigned the responsibility for insuring

uniformity in PTTI (frequency) operations for DoD including

measurements. The CNM is responsible for assuring this uniformity within the Department of the Navy.

b. The CNM is assigned the responsibility for insuring:

(1) The establishment of overall Department of the

Navy requirements for time and time interval.

(2) The accomplishment of objectives requiring PTTI

(frequency) with minimum cost.

c. In carrying out the above responsibilities,

(1) The NAVOBSY shall:

(a) Derive and maintain standards of time and

time interval, both astronomical and atomic.

2

372
OPNAVINST 4120. A

6 Junr 1 97?

(b) Provide coordination of such standards with

recognized national and international standards to insure

worldwide continuity of precision.

(c) Issue detailed information concerning reference values of PTTI (frequency) and distribute them by

means of controlled radio transmissions, portable atomic

clocks, and other appropriate means.

(d) Establish relationships between the Department of the Navy and other DoD agencies on PTTI (frequency)

matters

.

(e) Provide advice and assistance as required.

(2) The CNM shall:

(a) Sponsor and monitor conferences concerning

time and time interval standards in coordination with the

NAVOBSY

.

(b) Advise and provide guidance to Department of

the Navy components, contractors, and scientific laboratories

on matters concerning time and time interval , and their measurement .

(c) Prescribe technical requirements for the coordination of techniques, procedures, and periodic calibration

of systems.

d. All Department of the Navy components which require,

utilize, or distribute time and time interval information or

have a need for a specific time scale shall:

(1) Refer time and time interval to the standards

established by the NAVOBSY.

(2) Maintain specific time scales such that relationship to the standard established by the NAVOBSY is known.

(3) Promote economy by prescribing requirements for

precise time that are consistent with operational and research

needs for accuracy.

373
OPNAVINST 4120 . 4

6 June 1972

6 . Delineation of Functions

a. The CNM is the single Department of the Navy manager

responsible for PTTI (frequency) management control functions.

This responsibility encompasses overall activities requiring

time to within ten milliseconds and frequency to within one

part in 10 9 of an established time scale. In carrying out

these PTTI (frequency) functions, the CNM will:

(1) Promote (a) operational uniformity of PTTI (frequency) functions; and (b) establishment of overall Department of the Navy PTTI (frequency) requirements.

(2) Monitor Department of the Navy research programs

concerning PTTI (frequency) , in coordination with the NAVOBSY.

(3) Sponsor Department of the Navy research and development programs for PTTI (frequency) and PTTI applications,

in coordination with the NAVOBSY.

(4) Review (a) existing and future PTTI (frequency)

requirements of the Department of the Navy user components in

order to establish overall Department of the Navy requirements

and to provide adequate supporting services; and (b) existing

PTTI (frequency) operations conducted by Department of the

Navy user components to provide guidance and recommendations

to the NAVOBSY.

(5) Provide training, maintenance, repair, and calibration services for Department of the Navy PTTI (frequency)

equipment and systems.

(6) Provide advice and guidance concerning requests

for unilateral PTTI (frequency) programs at the direction of

the NAVOBSY.

(7) Participate in PTTI (frequency) policy negotiations in coordination with the NAVOBSY, between the Department

of the Navy and other DoD agencies.

(8) Maintain records of PTTI (frequency) arrangements

between the Department of the Navy and its contractors, with

the exception of radio frequency assignments.

b. Department of the Navy user components will assist

the CNM by (1) providing technical information on current and

prospective programs involving PTTI (frequency) applications;

and (2) distributing, monitoring, and controlling PTTI (frequency) services on request.

4

374
OPNAVINST 4120.4

6 June 1972

c. Department of the Navy User Components and Contractors will:

(1) Consult the CNM on any technical and logistic

problems arising from PTTI (frequency) operations or research.

(2) Use DoD-controlled transmissions to the maximum

extent practicable. Other transmissions of time and frequency which have been coordinated with the NAVOBSY may be

used when DoD transmissions do not provide adequate coverage.

(3) Refer measurements and contract specifications

to DoD standards determined by the NAVOBSY.

(4) Use techniques and procedures described in information documents issued by the NAVOBSY in all cases where such

documents satisfy the need.

(5) Notify the CNM of existing and planned PTTI (frequency) requirements, including information as to accuracy

and stability of needs, measurement techniques planned or in

operation, and continuity of service required of the applicable

distribution transmission.

(6) Consult the CNM prior to entering into contracts

for equipment, research, studies, or services involving PTTI

(frequency) in order that maximum use of existing facilities

may be assured.

7 . Action

a. The Chief of Naval Operations (CNO) designates and

places operational requirements upon those naval facilities

and systems which will transmit the time and frequency standards determined by the NAVOBSY. The CNO also provides and

maintains suitable facilities for the NAVOBSY to carry out

the responsibilities assigned.

b. The CNM, as directed by the CNO and in accordance with

reference (b) , will coordinate compliance, as necessary.

DISTRIBUTION ; T.F. DEDMAN See page 6 . Assistant Vice Chief of Naval Operations

Director of Naval Administration

5

375

Annex ll.E.

NBS/USNO TIME COORDINATION/SERVICES

Contents

Page ll.E.l. USNO Time Reference Stations, USNO Time Service Announcement, Series 14, No. 1, 17 April 1968 379

ll.E. 2. Coordination of Clock Time Scales, USNO Time Service Announcement, Series 14, No. 3,

8 October 1968 381

11.E.3. NBS- "Nation Gets Unified Time System," Nat. Bur. Stand. (U.S.) Tech. News Bull.,

53, No. 2. p. 34, February 1969 382

ll.E. 4. NBS Time and Frequency Publication Services 383

11.E.5. USNO Time Service Publications 384

377

ANNEX ll.E.l.

Uo S. NAVAL OBSERVATORY

WASHINGTON, D.C„ 20390

17 April 1968

TIME SERVICE ANNOUNCEMENT, Series 14 NO. 1

U. S. Naval Observatory Time Reference Stations

1. Precise time measurements against the Master Clock maintained by the

U. S. Naval Observatory in Washington, D.C., may also be made at the

locations listed below. Reference atomic clocks have been set up, or designated at these locations, and their time differences with the U. S. Naval Observatory Master Clock are measured regularly and are known to an accuracy of better than +2.5 microseconds.

Present locations of Time Reference Stations:

Master Clock:

U. S. Naval Observatory

Time Service Division

Washington, Do Co 20390

Tel: AUTOVON

Commercial: 202 696-8423

TWX: 710 822 1970

Time Reference Stations:

(a) National Bureau of Standards

Boulder, Colorado

Tel: FTS

Commercial: 303 449-1000

TWX

:

(b) U. S. Naval Observatory Time Service Substation

Miami (Perrine) , Florida

Tel: Commercial: 305 235-0515

TWX: 305 238 3451

379
(c) U. S. Navy Astronautics Group

Detachment CHARLIE

Wahiawa, Oahu, Hawaii

Tel: AUTOVON

Commercial: 4315523

TWX:

(d) Uo S. Coast Guard Loran Monitoring Station

Building 683

Fuchu Air Station

Fuchu-Shi, Tokyo-To, Japan

Te 1 : AUTOVON

Commercial: 45700 or 47188

TWX:

(e) Hewlett Packard Company

Palo Alto, California

Tel: Commercial: 415 326-7000

TWX : HEWPACK

(f) Hewlett Packard Company

Geneva, Switzerland

Tel: Commercial: 022 42.81.50

TWX : HEWPACKSA

2. Recent measurements are reported in the U. S. Naval Observatory Phase

Value Bulletins and messages.

3. For further information, contact the:

Superintendent

U. S. Naval Observatory

Washington, Do C. 20390

j. m. Mcdowell

Superintendent

380
ANNEX 11.E.2.

U. S. NAVAL OBSERVATORY

WASHINGTON, D.C„ 20390

8 October 1968

TIME SERVICE ANNOUNCEMENT, SERIES 14 NO. 3

Coordination of Clock Time Scales

1. In the interest of improved coordination between the National Bureau

of Standards, the U. So Naval Observatory, and international timekeeping

centers, the frequency of the U„ S. Naval Observatory clock time scales

was lowered 4 parts in 10 13 on 1 October 1968 at 0h UT.

2. Effective 1 October 1968 all daily phase values and clock measurements published by the U. S. Naval Observatory will be given with respect

to these improved coordinated time scales. Clocks which were running

perfectly with respect to UTC(USNO) before 1 October 1968 will now show

an apparent daily rate of 34.56 nanoseconds (fast).

3. For most timing applications this change will be insignificant since

it is less than the random fluctuations of individual atomic clocks.

J. MAURY WERTH

Superintendent

381
ANNEX 11. E. 3.

The Nation's two "time keepers"—the National Bureau of Standards. Boulder, Colo, (top) and the U.S. Naval Observatory, Washington, D.C.—recently synchronized their clocks

to provide the country with a unified time system

of unsurpassed accuracy.

NATION GETS

Unified Time System

NBS and Naval Observatory Synchronize Time

to About 1 Microsecond

A Unified Time System of unsurpassed accuracy for the entire country was achieved recently when the Nation's two "time keepers"—the National Bureau of Standards and the U.S. Naval Observatory ( USNO ) —synchronized

their clocks. On October 1, 1968, these agencies cooperated to effect a much more precisely coordinated time system than has ever before existed. The action taken by

these agencies was the synchronization of their Coordinated Universal Time ( UTC I clocks to within about 1 microsecond of each other. Synchronization was achieved when the NBS Time and Frequency Division (Boulder.

Colo.) increased the rate of its UTC (NBS) clock by 4

parts in 10'\ while the Naval Observatory (Washington,

D.C.I decreased the rate of its UTC (USNO) clock by 4

parts in 10". The Bureau and the USNO have been cooperating under

regulations of the International Radio Consultative Committee (CCIR). which for the past several years has re- quired synchronization of standard time broadcasts to one

thousandth of a second. This has been adequate for most

users, but as technology has advanced, many precise timing needs have developed that cannot be met by this tolerance. More than a year ago, the desirability of synchronizing

the USNO and NBS frequency and time standards to much

finer tolerances than 1 millisecond was recognized.

In anticipation of a coordinated coordinate rate for USNO and NBS, on August 24. 1967. the Coordinated

Universal Time clock of the Bureau. UTC (NBS I. and all

I TC transmissions of NBS were advanced by 200 microseconds. This left NBS about 35 microseconds early rela- tive to USNO.

As the rate of the USNO clock has been high relative to the NBS clock by about 1 part in 101J

. the two clocks

drifted toward each other. Their time lines converged on about October 1. 1968. and the time difference between

the USNO clock, UTC (USNO). and the NBS clock, UTC

( NBS ) . became zero. At that time USNO reduced the rate of its clock by 4 parts in 10", and NBS increased the rate of its clocks controlling NBS standard transmissions by 4

34

parts in 101 (A clock running fast by 4 parts in 10TM

accumulates about 35 billiontbs of a second error per day. This rate of error would require about 80 000 years to accumulate one second in error. ) The present specified absolute accuracy of the rate of the NBS clock is ±5

parts in 1012

. Measurements made after October 1 with portable

clocks indicate that the time difference between the USNO

and the NBS coordinated clocks is within one microsec- ond. By mutual agreements between USNO and NBS, small frequency adjustments ( <10"1J

) will be made infrequently

to assure that this time difference remains less than about

three microseconds.

Among scientists requiring more precise time measure- ments are geodesists, who, in attempting to measure the Earth very accurately, must sight on an artificial satellite from distant locations at very nearly the same instant of

time. The sightings must be made within about 100 micro- seconds of each other, but the geodesists would prefer that the time error be within 10 microseconds. There are also military and NASA requirements that require synchronization accuracies in the microsecond range. It should be emphasized that this is synchronization accuracy and not

absolute time-of-day accuracy. Meanwhile, there is a general trend in technology to- ward tighter tolerances on synchronization. For example,

the planned Aircraft Collision Avoidance System ( ACAS)

specifies worldwide synchronization accuracy of 0.5 microsecond, which is possibly beyond the current state-of-theart.To meet such needs, the National Bureau of Standards and U.S. Naval Observatory are engaged in a joint effort

to provide a unified time service to all the United States. The new system is near the limit of the present state-of-theart in its ability to provide accurate time and time syn- chronization to remote locations. This synchronization

system is expected to provide a working model of a co- ordinate time system suitable for extension to worldwide

coverage at some later date.NBS Technical News Bulletin

382
ANNEX 11.E.4.

NBS Time and Frequency Publication Services*

A. Publishes a monthly Time and Frequency Services Bulletin. Typical table of contents as follows: (Sec. 273.01)

CONTENTS

1. TIME SCALE INFORMATION"

Relations of some time scales to the AT(NBSI and UTC(NBSI Time

Scales.

2. ADJUSTMENTS IN NBS BROADCAST TIME PULSES

Listed are adjustments in broadcast time pulses dated from January 1, 1972. Notices of future adjustments will be made when they are avail- able from the BIH. These adjustments are made to maintain the broadcast pulses within about ±0.7 seconds of the UT1 scale. The UT1

scale is slightly non-uniform due to variations in the rotation of the earth about its axis.

3. DAILY PHASE DEVIATIONS FOR NBS STATIONS*

Day-by-day transmitted phase deviations measured from 1800 UT to 1800 UT, referred to the UTC(NBS) time marker, are listed for station WWVB. General time and freouency information is listed for stations WWV and WWVH.

4. PHASE DEVIATIONS FOR NON-NBS STATIONS"

Listed are day-by-day phase deviations measured with respect to the UTC(NBS) time marker and obtained by monitoring non-NBS stations. 5A. OUTAGES OF NBS RADIO BROADCASTS

Interruptions in service from NBS radio stations. 5B. SCHEDULED OUTAGES OR ALTERATIONS IN NBS RADIO BROADCASTS

Advance notice of scheduled interruptions or changes in service. 6A. DAILY TELEVISION TIME TRANSFER MEASUREMENTS

Daily readings for the three major U. S. networks of the difference between UTC(NBS) and the trailing edge of the next line 10 (odd) horizontal synchronization pulse as received in Boulder, Colorado.

6B. DAILY TELEVISION FREQUENCY TRANSFER MEASUREMENTS*

Listed are the average fractional frequencies with respect to the NBS

primary frequency standard for each of the three rubidium gas cell frequency standards used at each of the corresponding major network

originating studios.

7. NBS FREQUENCY AND TIME SATELLITE EXPERIMENT

Antenna pointing angles to the satellite and propagation delays from NBS Boulder to the user via the satellite are presented. General in- formation important to the users of the experimental service is also

given.

8. EXPLANATION OF TIME SCALES AND DEFINITIONS OF TERMS

(not in every issue) - The NBS Time Scales- -their derivation and relation to each other and to those of other laboratories. Definitions of all terms used in this bulletin.

9. NOTES (not in every issue) Corrections, additions, deletions, and special announcements.

' The sign convention used in this bulletin follows the recommendations of the CCIR.

'See notes, part 9-

No. 177, August 1972

B. Sends advance notice of revisions to NBS standard frequency broadcasts to users on basis of need. (Sec. 273.01)

C. Periodically sends a bibliographic listing of NBS published documents per- taining to frequency and time standards or related metrology to interested

users. (273.00/PA)

D. Services a mailing list for current scientific and technical publications maintained in Atomic Frequency and Time Standards Program Area. Forwards

reprints of papers as they become available. (273.00/PA)

•Material available upon request to NBS Time and Frequency Sections involved or to Chief Time and Frequency Division. National Bureau of Standards. Boulder. Colorado 80302.

383
ANNEX 11.E.5.

USNO Time and Frequency Publications*

A. Publishes Time Service Publications (see ref. [41]) as follows:

Series Title

1 List of Worldwide VLF and HF Transmissions suitable for Precise Time Measurements. Includes: Call sign, geographic lo- cation, frequencies, radiated power, etc. (Time Signal Transmissions).

2. Schedule of U.S. Navy Time Signal Transmissions in VLF and HF bands. Includes:

Times of broadcast, frequencies, etc.

3. Schedule of U.S. Navy VLF Transmissions

including Omega system. Includes: Location, frequencies, power radiated, mainte- nance periods, type of transmission, etc.

4. Daily Relative Phase Values (Issued weekly).

Includes: Observed phase and time differ- erences between VLF, LF, Omega, Television, Portable Clock measurements,

and Loran-C stations and the UTQUSNO

Master Clock). Propagation disturbances

are also given.

5. Daily Teletype Messages (sent every working

day). Includes: Daily relative phase and

time differences between UTQUSNO MC)

and VLF, LF, Omega, Loran-C stations. Propagation disturbances and notices of immediate concern for precision timekeeping.

6. USNO A.1-UT1 Data. Preliminary daily

values distributed monthly with final data

issued as available.

7. Preliminary Times and Coordinates of the Pole (issued weekly). Includes: General time

scale information; UT1 — UTC predicted 2

weeks in advance; time difference between A.l. UT1, UT2, UTC(BIH) and

UTC(USNO), provisional coordinates of the

pole; DUT1 value; and satellite information.

*Available upon request to Director, Time Service Division USNO, Washington, DC 20390.

Series Title

8. Time Service Announcements pertaining to synchronization by television. Includes:

times of coincidence (NULL) ephemeris

tables.

9. Time Service Announcements Pertaining to Loran-C. Includes: Change in transmissions

and repetition rates, times of coincidence

(NULL) ephemeris tables, coordinates and

emission delays, general information, etc. 10. Astronomical Programs (issued when available). Includes: Information pertaining to results, catalogs, papers, etc., of the Photographic Zenith Tube (PZT), Danjon Astrolabe, and Dual-Rate Moon Position Camera.

11. Time Service Bulletins. Includes: Time

differences between coordinated stations

and the UTC Time Scale; earth's seasonal

and polar variations (as observed at Washington, D.C. and Florida); Provisional coor- dinates of the pole; adopted UT2 — A.l, etc.

12. Time Service Internal Mailing.

13. Time Service Internal Mailing.

14. Time Service General Announcements.

Includes: General information pertaining

to time determination, measurement, and

dissemination. Should be of interest to all Time Service Addressees.

15. Bureau International de I'Heure (BIH)

Circular D: Heure Definitive et Coordonnees du Pole a 0

h TU. Includes: Coordi- nates of the pole; UT2-UTC, UT1-UTC,

and TA (AT) -UTC; UTC -Signal. NOTE:

USNO Time Service will distribute Circular

D of the BIH to U.S. addressees only.

16. Communication Satellite Reports giving

the differences UTC(USNO)-SATCOM

Clock for each of the available SATCOM

stations.

17. Transit Satellite Reports. Includes Satellite Clock -UTCrtJSNO) and the frequency

offset for each of the operational satellites.

B. Publishes Proceedings of Annual PTTI Meetings (e.g. [28]).

384
ANNEX ll.F.

TREATY OF THE METER*

Metric Convention: Signed at Paris, May 20, 1875; ratification advised by the Senate, May 15, 1878; ratified by the President, May 28, 1878; ratifications exchanged, August 2, 1878; pro- claimed, September 27, 1878. As amended by the convention

signed at Sevres, October 6, 1921; ratification advised by the

Senate, January 5, 1923; ratified by the President, September

19, 1923; ratification of the United States, deposited with the Government of the French Republic, October 24, 1923; pro- claimed, October 27, 1923. His Excellency the President of the United States of America. His Majesty the Emperor of Germany, His Majesty the Emperor of Austria-Hungary, His Majesty the King of the

Belgians, His Majesty the Emperor of Brazil, His Excellency

the President of the Argentine Confederation, His Majesty the King of Denmark. His Majesty the King of Spain, His Excellency the President of the French Republic, His Majesty the King of Italy, His Excellency the President of the Republic of Peru, His Majesty the King of Portugal and the Argarves, His

Majesty the Emperor of all the Russias, His Majesty the King

of Sweden and Norway, His Excellency the President of the

Swiss Confederation. His Majesty the Emperor of the Otto- mans, and His Excellency the President of the Republic of Venezuela, desiring international uniformity and precision in standards of weight and measure, have resolved to conclude

a convention to this effect, and have named as their plenipotentiaries the following: • • • Who, after having exhibited their full powers, which were

found to be in good and due form, have agreed upon the following articles: Article 1. The high contracting parties engage to establish and maintain, at their common expense, a scientific and

permanent international bureau of weights and measures, the

location of which shall be at Paris. Art. 2. The French Government shall take all the necessary measures to facilitate the purchase, or, if expedient, the construction, of a building which shall be especially devoted to

this purpose, subject to the conditions stated in the regulations which arc subjoined to this convention.

Art. ). The operation of the international bureau shall be under the exclusive direction and supervision of an international committee of weights and measures, which latter shall be under the control of a general conference for weights and

measures, to be composed of the delegates of all the contract- ing Governments.

Art. -f. The general conference for weights and measures

shall be presided over by the president for the time being of

the Paris Academy of Sciences. Art. 5. The organization of the bureau, as well as the formation and the powers of the international committee, and

of the general conference for weights and measures, are estab- lished by the regulations subjoined to this convention.

Art. 6. The international bureau of weights and measures

shall be charged with the following duties:

First. All comparisons and verifications of the new prototypes

of the meter and kilogram.

Second. The custody of the international prototypes. Third. The periodical comparison of the national standards with the international prototypes and with their test copies, as well as comparisons of the standard thermometers.

Fourth. The comparison of the prototypes with the funda- mental standards of nonmetrical weights and measures used in

different countries for scientific purposes.

Fifth. The sealing and comparison of geodesic measuring

bars. Sixth. The comparison of standards and scales of precision,

the verification of which may be requested by governments or by scientific societies, or even by constructors or men of science. Art. 7. After the committee shall have proceeded with the work of coordinating the measures relative to electric units and

when the general conference shall have so decided by a unani- mous vote, the bureau will have charge of the establishment and keeping of the standards of the electric units and their

test copies and also of comparing with those standards, the

national or other standards of precision. The bureau is also charged with the duty of making the determinations relative to physical constants, a more accurate knowledge of which may be useful in increasing precision and

further insuring uniformity in the provinces to which the above-mentioned units belong (article 6 and first paragraph

of article 7)

.

It is finally charged with the duty of coordinating similar determinations effected in other institutions. Art. 8. The international prototypes and standards and

also their test copies shall be deposited in the bureau; access

to the deposit shall be solely reserved for the international committee.

Art. 9. The entire expense of the construction and outfit of the international bureau of weights and measures, together with the annual cost of its maintenance and the expenses of

the committee, shall be defrayed by contributions from the contracting states, the amount of which shall be computed in proportion to the actual population of each.

Art. 10. The amounts representing the contributions of each of the contracting States shall be paid at the beginning

of each year, through the ministry of foreign affairs of France,

into the Caisse de dSpots et consignations at Paris, whence they

may be drawn as occasion may require, upon the order of the

director of the bureau.

Art. 11. Those Governments which may take advantage of

the privilege, open to every State, of acceding to this convention shall be required to pay a contribution, the amount of which shall be fixed by the committee on the basis established

in article 9, and which shall be devoted to the improvement

of the scientific apparatus of the bureau.

Art. 12. The high contracting parties reserve to themselves

the power of introducing into the present convention, by com- mon consent, any modifications the propriety of which may

have been shown by experience.

Art. 13. At the expiration of twelve years this convention mav be abrogated by any one of the high contracting parties, so far as it is concerned. Any Government which may avail itself of the right of terminating this convention, so far' as it is concerned, shall be

required to give notice of its intentions one year in advance, and by so doing shall renounce all rights of joint ownership in

the international prototypes and in the bureau. • • •.

Appendix No. 1, Regulations.

Article 1. The international bureau of weights and measures shall be established in a special building, possessing all the necessary safeguards of stillness and stability.

It shall comprise, in addition to the vault, which shall be

devoted to the safe-keeping of the prototypes, rooms for mounting the comparators and balances; a laboratory, a library, a room for the archives, workrooms for the employes, and lodgings for the watchmen and attendants.

Art. 2. It shall be the duty of the international committee to acquire and fit up the aforesaid building and to set in operation the work for which it was designed. In case of the committee's inability to obtain a suitable

•Schwartz, K. M., Federal and State Weights and Measures Laws. "Metric Convention- 1875," Nat. Bur. Stand. (U.S.) Circular 501. pp. 3-5 (USGPO, December 1951).

385
Federal and State Weights and Measures Laws

building one shall be built under its directions and in accord- ance with its plans. Art. 3. The French Government shall, at the request of the

international committee, take the necessary measures to cause

the bureau to be recognized as an establishment of public

utility. Art. 4. The international committee shall cause the necessary instruments to be constructed, such as comparators for the standards of line and end measures, apparatus for the de- termination of absolute dilatations, balances for weighing in

air and in vacuo, comparators for geodetic measuring bars, etc. Art. 5. The entire expense incurred in the purchase or

construction of the building, and in the purchase and placing

of the instruments and apparatus, shall not exceed 400,000

francs. Art. 6. The annual appropriation for the international bureau consists of two parts, one of which is fixed, the other complementary.

The fixed part is, in principle, 250.000 francs, but on the unanimous vote of the committee may be raised to 300,000

francs. It is borne by all the States and autonomous colonies

that adhered to the meter convention before the sixth general

conference. The complementary part is made up of contributions from

the States and autonomous colonies that joined the convention

after the aforesaid general conference. The committee is charged with the duty of drawing up on the motion of the

director the annual budget, but without exceeding the amount

computed in accordance with the provisions of the two para- graphs above. The budget is made known every year by means

of a special financial report to the Governments of the high

contracting parties.

If the committee find it necessnry either to increase beyond

300,000 francs the fixed part of the annual appropriation or to modify the computation of the contributions as determined by

article 20 of these regulations, it should lay the matter before

the Governments so as to enable them to issue in good time

the needed instructions to their delegates to the next general conference in order that the said conference may deliberate to good purpose. The decision will stand only in the case that no opposition shall have been expressed before or in the conference by any of the contracting States.

If the State should let three years go without paying its contribution, that contribution shall be divided among the other States proportionally to their own contribution. The

additional sum thus paid by the States to make up the whole

of the appropriation of the bureau shall be regarded as an

advance to the delinquent State and shall be reimbursed to them if that State should make good its arrears. The advantages and prerogatives conferred by adhering to the meter

convention are suspended in the case of States that have been

delinquent three years. After three more years the delinquent State shall be ex- pelled from the convention and the reckoning of the contri- butions restored in accordance with the provisions of article 20 of these regulations.

Art. 7. The general conference mentioned in article 3 of

this convention shall be at Paris, upon the summons of the

international committee, at least once every six years.

It shall be its duty to discuss and initiate measures necessary

for the dissemination and improvement of the metrical sys- tem, and to pass upon such new fundamental metrological determinations as may have been made during the time when

it was not in session. It shall receive the report of the inter- national committee concerning the work that has been accomplished, and shall replace one-half of the international committee by secret ballot. The voting in the general conference shall be by States; each State shall be entitled to one vote. Each of the members of the international committee shall be entitled to a seat at the meetings of the conference. They

may at the same time be delegates of their Governments.

Art. 8. The international committee mentioned at article 3

of the convention shall be composed of 18 members all from

different States.

At the time of the renewal by halves of the international committee the outgoing members shall be first those who may

have been provisionally elected to fill vacancies between two

sessions of the conference; the others will be drawn by lot. Outgoing members may be reelected. Art. 9. The international committee organizes itself by elect- ing by its own secret vote its chairman and secretary. Those

appointments are notified to the Governments of the high

contracting parties. The chairman and the secretary of the committee and the

director of the bureau must belong to different countries. Once organized, the committee can not hold other elections or make other appointments until three months shall have

elapsed after the notice of a vacancy calling for a vote shall have been given to all the members.

Art. 10. The international committee directs all the metrological works that the high contracting parties shall decide to have carried on jointly.

It is also charged with the duty of seeing to the conservation

of the international prototypes and standards.

It may, lastly, institute the cooperation of specialists in questions of metrology and coordinate the results of their work.

Art. 11. The committee shall meet at least once in two

years. An. 12. The balloting in the committee is by a majority

vote; in case of a tie vote the chairman has the casting vote. Decisions are only valid if the members present are at least one half of the elected members forming the committee.

Subject to that condition absent members have a right to delegate their votes to present members who must prove that they have been so delegated. This also applies to appointments

by secret ballot. The director of the bureau is a nonvoting member of the committee.

Art. 13. During the interval occurring between two ses- sions the committee shall have the right to discuss questions

by correspondence. In such cases, in order that its resolutions may be consid- ered to have been adopted in due form, it shall be necessary

for all the members of the committee to have been called upon

to express their opinions.

Art. 14. The international committee for weights and

measures shall provisionally fill such vacancies as may occur

in it; these elections shall take place by correspondence, each

of the members being called upon to take part therein.

Art. 15. The international committee will draw up a detailed set of regulations for the organization and work of the bureau and will fix the dues to be paid for the extraordinary works provided by articles 6 and 7 of the convention. Those dues will be applied to improving the scientific equip- ment of the bureau. A certain amount may be drawn annually

for the retirement fund from the total dues collected by the bureau.

Art. 16. All communications from the international committee to the Governments of the high contracting parties

shall take place through the diplomatic representatives of

such countries at Paris. For all matters requiring the attention of the French authorities, the committees shall have recourse to the ministry

of foreign affairs of France.

Art. 17. A regulation drawn up by the committee will de- termine the maximum staff for each category of the personnel

of the bureau. The director and his assistants shall be elected by secret ballot by the international committee. Other appoint- ments shall be notified to the Governments of the high contracting parties. The director will appoint the other members

of the personnel within the bounds laid by the regulation mentioned in the first paragraph above.

Art. 18. The director of the bureau shall have acceso to the

place where the international prototypes are deposited only in pursuance of a resolution of the committee and in the pres- ence of at least one of its members. The place of deposit of the prototype shall be opened only by means of three keys, one

of which shall be in the possession of the director of archives

386
Introduction

of France, the second in that of the chairman of the committee, and the third in that of the director of the bureau. The standards of the class of national prototypes alone

shall be used for the ordinary comparing work of the bureau.

Art. 19. The director of the bureau shall annually furnish

to the committee: First, a financial report concerning the ac- counts of the preceding year, which shall be examined, and if found correct, a certificate to that effect shall be given him;

second, a report on the condition of the apparatus; third, a

general report concerning the work accomplished during the course of the year just closed. The international committee shall make to each of the Governments of the high contracting parties an annual report concerning all its scientific, technical, and administrative operations, and concerning those of the bureau. The chairman of

the committee shall make a report to the general conference concerning the work that has been accomplished since its last session. The reports and publications of the committee shall be in the French language. They shall be printed and furnished to the Governments of the high contracting parties. Art. 20. The scale of contributions spoken of in article 9

of the convention is established for its fixed part on the basis of the appropriation referred to in article 6 of the present

regulations and of the population; the normal contribution of each State can not be less than five to a thousand nor more

than 15 per cent of the whole appropriation, regardless of the

population. In order to establish that scale, it shall first be found which are the States that are in the conditions required

for the minimum and maximum and the remainder of the quota shall be distributed among the other States in the direct

ratio of their population.

The quota thus reckoned stands for the whole time included between two consecutive general conferences and can only be

modified in the meanwhile in the following cases:

(a) If one of the adhering States allows three successive years to pass without making its payments;

(b) When, on the contrary, a State which had been previously delinquent for more than three years pays up its arrears, and the occasion arises to return to the other Governments the advances made by them. The complementary contribution is computed on the same

basis of population and is like that which the States that have

long belonged to the convention pay under the same conditions.

If after adhering to the convention a State declares it would

like to extend the benefits thereof to one or more of its colo- nies that are not autonomous, the number of the population

of the said colonies would be added to that of the State in reckoning the scale of contributions. When a colony that is recognized as autonomous shall desire to adhere to the convention, it will be regarded with re- spect to its admission into the convention and as the mother

country may decide, either as a dependency of that mother

country or as a contracting State. Art. 21. The expense of constructing the international prototypes and the standards and test copies which are to accom- pany them shall be defrayed by the high contracting parties in accordance with the scale fixed in the foregoing article. The amounts to be paid for the comparison and verification of standards required by States not represented at this con- vention shall be regulated by the committee in conformity with the rates fixed in virtue of article 15 of the regulations.

Art. 22. These regulations shall have the same force and

value as the convention to which they are annexed.* • • On January 2, 1890, "meter No. 27" and "kilo- gram No. 20", being copies of the international pro- totype meter and kilogram preserved at the International Bureau of Weights and Measures, were op- ened at the White House and accepted by President

Harrison as national standards. Duplicates of these,

being "meter No. 21" and "kilogram No. 4", were

received later in the same year. These standards were

given into the custody of the Office of Standard

Weights and Measures of the Coast and Geodetic

Survey of the Treasury Department.

In 1893 a ruling of fundamental importance with

respect to standards was made by T. C. Mendenhall,

the Superintendent of Standard Weights and Measures. This ruling, which subsequently came to be

known as the "Mendenhall Order", was approved

April 5, 1893, by the Secretary of the Treasury; its essential part is as follows:

Bulletin No. 26, "Fundamental Standards of Length and Mass", United States Coast and Geodetic Survey, Treasury Depart- ment, April 5, 1893.

• • • the Office of Weights and Measures, with the ap- proval of the Secretary of the Treasury, will in the future, regard the International Prototype Metre and Kilogramme as fundamental standards, and the customary units, the yard

and the pound, will be derived therefrom in accordance with

the Act of July 28, 1866. • • •

Bulletin No. 26 also carried a "Note", as follows: Note.—Reference to the Act of 1866, results in the establish- ment of the following:

Equations

3600

1 yard = metre. 3937

1

1 pound avoirdupois = kilo. 22046 A more precise value of the English pound avoirdupois is

1 kilo., 220462

differing from the above by about one part in one hundred

thousand, but the equation established by law is sufficiently accurate for all ordinary conversions. As already stated, in work of high precision the kilogramme

is now all but universally used and no conversion is required.

The National Bureau of Standards continues to consider the relation

3600

1 yard= meter

3937

which may also be expressed

1 meter=39.37 inches

as an exact equivalent. In the case of the relation

between the avoirdupois pound and the kilogram,

however, the National Bureau of Standards now

recognizes as the fundamental relation

1 avoirdupois pound=0.453 592 427 7 kilogram

which corresponds with

1 kilogram=2.204 622 341 avoirdupois pounds.

387

ANNEX ll.G.

LEGAL DOCUMENTS CONCERNING "STANDARD TIME"

Contents

Page ll.G.l. "Uniform Time Act'"' -Public Law 89-387, 89th Congress S. 1404, April 13. 1966... 391

11.G.2. "Standard Time." U.S. Code, Title 15, 3, Chap. 6, sec. 260-267, pp. 3228-3231,

1970 Edition (USGPO, 1971) 394

11.G.3. "Standard Time Zone Boundaries," Code of Federal Regulations, Title 49 — Transportation, Subtitle A, Part 71, issued July 31, 1970, pp. 83-90 (USGPO, January 1, 1972) 398

11.G.4. "Standard Time Zone Boundaries — Relocation of Eastern-Central Time Zone

Boundary in the State of Michigan," Federal Register, Title 49 — Transportation,

Subtitle A, Part 71, 38, No. 70, pp. 9228-9229 (April 12, 1973) 406

11.G.5. "Emergency Daylight Saving Time — Procedures and Criteria for Implementation," Federal Register, 38, Title 49 -Transportation, Subtitle A, Part 73, No. 244,

pp. 34876-34878 (December 20, 1973)- Added in proof 408

ll.G.5.a. "Emergency Daylight Saving Time" — DOT exemption and realignment to Certain

States, Federal Register, 39, No. 7 (Transportation), pp. 1524-1526 (January 10,

1974)- Added in proof 411

389
I
ANNEX ll.G.l.

Public Law 89-387

89th Congress, S. 1404

April 13, 1966

an act

To promote the observance of a uniform ayttam of time thmagmont the Doited

States, Be it enacted by the Senate and House of Representative* of the United States of America m Congress assembled, That this Act may uniform Tine be cited ss the "Uniform Time Act of 1966". Aot or 1966. Sec. 2. It is the policy of the United States to promote the adoption

and observance of uniform time within the standard time zones prescribed by the Act entitled "An Act to save daylight and to provide

standard time for the United States", approved March 19, 1918 (40

Stat 450; 15 U.S.C. 261-264), as modified by the Act entitled "An

Act to transfer the Panhandle and Plains section of Texas and Oklahoma to the United States standard central time zone", approved

March 4, 1921 (41 Stat. 1446 ; 15 U.S.C. 265) . To this end the Interstate Commerce Commission is authorised and directed to foster and

promote widespread and uniform adoption and observance of the same

standard of time within and throughout each such standard time zone. Sac. 3. (a) During the period commencing at 2 o'clock antemeridian on the last Sunday of April of each year and ending at 2 o'clock antemeridian on the last Sunday of October of each year, the standard

time of each zone established by the Act of March 19, 1918 (15 U.S.C.

261-264), as modified by the Act of March 4, 1921 (15 UJ3.C. 265),

shall be advanced one hour and such time as so advanced shall for the purposes of such Act of March 19, 1918, as so modified, be the standard

time of such zone during such period ; except that any State may by

law exempt itself from the provisions of this subsection providing

for the advancement of time, but only if such law provides that the

entire State (including all political subdivisions thereof) shall observe

the standard time otherwise applicable under such Act of March 19, 1918, as so modified, during such period.

(b) It is hereby declared that it is the express intent of Congress

by this section to supersede any and all laws of the States or political subdivisions thereof insofar as they may now or hereafter provide for advances in time or changeover dates different from those specified in this section.

(c) For any violation of the provisions of this section the Inter- violations,

state Commerce Commission or its duly authorised agent may apply

to the district court of the United States for the district in which

such violation occurs for the enforcement of this section; and such

court shall have jurisdiction to enforce obedience thereto by writ of

injunction or by other process, mandatory or otherwise, restraining ao stat. 107. against further violations of this section and enjoining obedience feo stat. ios. thereto /

1 Sec. 4. (a) The first section of the Act of March 19, 1918, as Standard tlae amended (15 U.S.C. 261), is amended to read as follows: zones. "That for the purpose of establishing the standard time of the United States, the territory of the United States shall be divided into eight zones in the manner provided in this section. Except as pro- vided in section 3(a) of the Uniform Time Act of 1966, the standard

time of the first zone shall be based on the mean solar time of the

120

391
Pub. Law 89-387 - 2 - April 13, 196o

ftO STAT. 106 sixtieth degree of longitude west from Greenwich: that of the second zone on the seventy fifth degree; that of the third zone on the ninetieth degree; that of t he fourth zone on the one hundred and fifth degree;

that of the fifth zone on the one hundred and twentieth degree; that of the sixth zone on the one hundred and thirty-fifth degree; that of the seventh zone on the one hundred and fiftieth degree; and that of the eighth zone on the one hundred and sixty-fifth degree. The limits of each zone shall be defined by an order of the Interstate Commerce

Commission, having regard for the convenience of commerce and the

existing junction points and division points of common carriers engaged in interstate or foreign commerce, and any such order may

"Interstate or be modified from time to time. As used in this Act, the term 'inter- foreign oomi roe." state or foreign commerce' means commerce between a State, the District of Columbia, the Commonwealth of Puerto Rico, or any posses- sion of the United States and any place outside thereof/' (b) Section 2 of such Act is amended to read as follows: "Sec. 2. Within the respective zones created under the authority of

this Act the standard time of the zone shall insofar as practicable (as determined by the Interstate Commerce Commission) govern the

commerce. In all statutes, orders, rules, and regulations relating to the time of performance of any act by any officer or department of

the United States, whether in the legislative, executive, or judicial

branches of the Government, or relating to the time within which any

rights shall accrue or determine, or within which any act shall or

shall not be performed by any person subject to the jurisdiction of

the United States, it shall be understood and intended that the time

shall insofar as practicable (as determined by the Interstate Commerce

Commission) be the United States standard time of the zone within which the act is to be performed."

(c) Section 4 of such Act is amended to read as follows: "Sec. 4. The standard time of the first zone shall be known and

designated as Atlantic standard time; that of the second zone shall be known and designated as eastern standard time; that of the third zone shall be known and designated as central standard time; that of

the fourth zone shall be known and designated as mountain standard

time; that of the fifth zone shall be known and designated as Pacific standard time; that of the sixth zone shall be known and designated

as Yukon standard time: that of the seventh zone shall be known and

designated as Alaska-Hawaii standard time; and that of the eighth zone shall be known and designated as Bering standard time." Sec. 5. The Administrative Procedure Act (5 U.S.C. 1001-1011)

shall apply to all proceedings under this Act, the Act of March 19, 1918 (15 U.S.C. 261-264), and the Act of March 4, 1921 (15 UJS.C.

265).

Effective date. Sec. 6. This Act shall take effect on April 1, 1967 : except that if any

State, the District of Columbia, the Commonwealth of Puerto Rico, or any possession of the United States, or any political subdivision

thereof, observes daylight saving time in the year 1966, such time

shall advance the standard time otherwise applicable in such place by

one hour and shall commence at 2 o'clock antemeridian on the last

movement of all common

121

392
April 13, 1966 - 3 - Pub. Law 89-387

80 STAT. 109 .Sunday ill April of t lie year 1U66 and slinll end at 1 o'clock ante- meridian oi\ tne last Sunday in October of the year 1966. Sec. 7. As used in this Act, the term "State'' includes the District "state, of Columbia, the Commonwealth of Puerto Rico, or any possession of

the United States. Approved April 13, 1966.

LEGISLATIVE HISTORY ;

HOUSE REPORTS : No. 1315 accompanying H. R. 6785 (Comm. on Interstate 4 Foreign Commeroe) and No. 1365 (Coin, of Conferenoe). SENATE REPORT No. 266 (CoTM, on Comae roe). CONGRESSIONAL RECORD:

Vol. Ill (1965): June 3, considered and passed Senate.

Vol. 112 (1966): Mar. 16, oonsldered and passed House, amended,

in lieu of H. R. 6785. Mar. 22, Senate concurred in House amendment with amendments*

Mar. 29, Senate agreed to oonferenoe report. Mar. 30, House agreed to oonferenoe report.

122

GPO 90-13*

393
ANNEX 11.G.2.

§ 242 TITLE 15. —COMMERCE AND TRADE Page 3228

STANDARD TIME

§260. Congressional declaration of policy; adoption and observance of uniform standard of time; authority of Secretary of Transportation.

It is the policy of the United States to promote

the adoption and observance of uniform time within

the standard time zones prescribed by sections 261 to 264 of this title, as modified by section 265 of this

title. To this end the Secretary of Transportation is authorized and directed to foster and promote wide- spread and uniform adoption and observance of the same standard of time within and throughout each

such standard time zone. (Pub. L. 89-387, § 2, Apr. 13, 1966, 80 Stat. 107.) Effective Date

Section 6 of Pub. L. 89-387 provided that: "This Act (which enacted sections 260, 260a, 266, and 267 of

this title and amended sections 261—263 of this title] shall take effect on April 1, 1967; except that if any State, the District of Columbia, the Commonwealth of Puerto

Rico, or any possession of the United States, or any politi- cal subdivision thereof, observes daylight saving time in the year 1966, such time shall advance the standard time

otherwise applicable in such place by one hour and shall commence at 2 o'clock antemeridian on the last Sunday

in April of the year 1966 and shall end at 2 o'clock ante- meridian on the last Sunday in October of the year 1966." Short Title

Section 1 of Pub. L. 89-387 provided: "That this Act

| which enacted sections 260, 260a, 266, and 267 of this

title, and amended sections 261-263 of this title, and

enacted provisions set out as notes under this section] may be cited as the 'Uniform Time Act of 1966'." Transfer of Functions

Reference to the Interstate Commerce Commission was changed to the Secretary of Transportation pursuant to Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931, which created the Department of Transportation and vested all powers,

duties and functions of the Interstate Commerce Commission and of the Chairman, members, offices, and offi- cers thereof relating generally to standard time zones and

daylight savings time under this section in the Secretary

of Transportation. See section 1655(e)(5) of Title 49, Transportation. Section Referred to in Other Sections

This section is referred to in sections 266, 267 of this

title.

I

*Comrnittee oo Judiciary of Hquse of Representatives. United States Code: 1970

Edition, Title 15, 3, Chap. 6, "Weights and Measures and Standard Time," sec. 260-

267, pp. 3228-3231 (USGPO, 1971). 394
Page 3229 TITLE 15 —COMMERCE AND TRADE § 262

§ 260a. Advancement of time or changeover dates.

(a) Duration of period; State exemption.

During the period commencing at 2 o'clock ante- meridian on the last Sunday of April of each year and ending at 2 o'clock antemeridian on the last Sunday of October of each year, the standard time

of each zone established by sections 261 to 264 of this

title, as modified by section 265 of this title, shall be advanced one hour and such time as so advanced shall for the purposes of such sections 261 to 264, as so modified, be the standard time of such zone during such period; except that any State may by law exempt itself from the provisions of this subsection providing for the advancement of time, but only if such law provides that the entire State

(including all political subdivisions thereof) shall observe the standard time otherwise applicable under such sections 261 to 264, as so modified during such period.

(b) State laws superseded.

It is hereby declared that it is the express intent

of Congress by this section to supersede any and

all laws of the States or political subdivisions thereof

insofar as they may now or hereafter provide for advances in time or changeover dates different from

those specified in this section.

(c) Violations; enforcement. For any violation of the provisions of this section the Secretary of Transportation or his duly authorized agent may apply to the district court of the United States for the district in which such

violation occurs for the enforcement of this section; and such court shall have jurisdiction to enforce obedience thereto by writ of injunction or by other

process, mandatory or otherwise, restraining against

further violations of this section and enjoining obedience thereto. (Pub. L. 89-387, § 3, Apr. 13, 1966, 80 Stat. 107.) Transfer of Functions

Reference to the Interstate Commerce Commission was

changed to the Secretary of Transportation pursuant to Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931, which created the Department of Transportation and vested all powers,

duties and functions of the Interstate Commerce Commission and of the Chairman, members, offices, and offi- cers thereof relating generally to standard time zones and

daylight savings time under this section In the Secretary

of Transportation. See section 1655(e)(5) of Title 49, Transportation. Section Referred to in Other Sections

This section Is referred to in section 261 of this title.

§261. Zones for standard time; interstate or foreign commerce. For the purpose of establishing the standard time

of the United States, the territory of the United

States shall be divided into eight zones in the manner provided in this section. Except as provided in section 260a(a) of this title, the standard time of the first zone shall be based on the mean solar time

of the sixtieth degree of longitude west from Greenwich; that of the second zone on the seventy-fifth

degree; that of the third zone on the ninetieth

degree; that of the fourth zone on the one hundred

and fifth degree; that of the fifth zone on the one hundred and twentieth degree; that of the sixth zone on the one hundred and thirty-fifth degree: that of

the seventh zone on the one hundred and fiftieth degree; and that of the eighth zone on the one hundred and sixty-fifth degree. The limits of each zone

shall be defined by an order of the Secretary of Transportation, having regard for the convenience

of commerce and the existing junction points and

division points of common carriers engaged in inter- state or foreign commerce, and any such order may

be modified from time to time. As used in sections 261—264 of this title, the term "interstate or foreign commerce" means commerce between a State, the District of Columbia, the Commonwealth of Puerto Rico, or any possession of the United States and any place outside thereof. (Mar. 19, 1918, ch. 24,

§ 1, 40 Stat. 450; Apr. 13, 1966, Pub. L. 89-387, § 4(a)

,

80 Stat. 108.) Amendments

1966—Pub. L. 89-387 increased the number of time

zones from five for the territory of continental United

States to eight for the territory of the United States, Inserted the "exception phrase", substituted "solar" for "astronomical" time, established the first zone on basis

of the 60th degree of longitude west from Greenwich,

redesignated as the second through the fifth zones based on the 75th, 90th, 105th, and 120th degrees former zones one through four based on such degrees, established the

sixth zone based on the 135th degree, redesignated as the seventh zone based on the 150th degree former fifth zone based on such degree, and established the eighth zone based on the 165th degree, substituted "interstate

or foreign commerce" for "commerce between the several States and and with foreign nations" and defined "interstate or foreign commerce."

Repeals

Section 5 of act Mar. 19, 1918, repealed all conflicting

acts and parts of acts. District of Columbia

Act March 31, 1949, ch. 43, 63 Stat. 29, authorized the Board of Commissioners [now the District of Columbia

Council] to establish daylight-saving time In the District of Columbia.Return to Standard Time

Act Sept. 25, 1945, ch. 388, 59 Stat. 537, provided, that, notwithstanding the provisions of act Jan. 20, 1942, ch. 7, 56 Stat. 9, which provided for war time, the standard time

for each zone as provided for In sections 261 —264 of this

title should again become effective as of Sept. 30, 1945, at 2:00 A. M. Transfer of Functions

Reference to the Interstate Commerce Commission was

changed to the Secretary of Transportation pursuant to Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931, which created the Department of Transportation and vested all powers,

duties and functions of the Interstate Commerce Commission and of the Chairman, members, offices, and offi- cers thereof relating generally to standard time zones and

daylight savings time under this section In the Secretary

of Transportation. See section 1655(a)(5) of Title 49, Transportation. Section Referred to in Other Sections

This section is referred to in sections 260, 260a, 262,

266, 267 of this title.

§ 262. Duty to observe standard time of zones. Within the respective zones created under the

authority of sections 261 to 264 of this title the stand- ard time of the zone shall insofar as practicable (as determined by the Secretary of Transportation) govern the movement of all common carriers en- gaged in interstate or foreign commerce. In all statutes, orders, rules, and regulations relating to the time of performance of any act by any officer or department of the United States, whether in the

395
§ 263 TITLE 15.—COMMERCE AND TRADE Page 3230

legislative, executive, or judicial branches of the Government, or relating to the time within which any rights shall accrue or determine, or within which any act shall or shall not be performed by any person subject to the jurisdiction of the United

States, it shall be understood and intended that the time shall insofar as practicable (as determined

by the Secretary of Transportation) be the United

States standard time of the zone within which the

act is to be performed. (Mar. 19, 1918, ch. 24, § 2, 40

Stat. 451; Apr. 13, 1966, Pub. L. 89-387, §4(b), 80

Stat. 108.) Amendments

1966—Pub. L. 89-387 inserted "Insofar as practicable

(as determined by the Interstate Commerce Commission) " in two instances and substituted "engaged in

interstate or foreign commerce" for "engaged in commerce between the several States or between a State and any one of the Territories of the United States, or between a State or the Territory of Alaska and any one

of the Insular possessions of the United States or any

foreign country".Transfer of Functions

Reference to the Interstate Commerce Commission was

changed to the Secretary of Transportation pursuant to Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931, which created the Department of Transportation and vested all powers,

duties and functions of the Interstate Commerce Commission and of the Chairman, members, offices, and offi- cers thereof relating generally to standard time zones and

daylight savings time under this section in the Secretary

of Transportation. See section 1655(e)(5) of Title 49, Transportation

.

Section Referred to in Other Sections

This section is referred to in sections 260, 260a, 261,

266. 267 of this title.

§ 263. Designation of zone standard times. The standard time of the first zone shall be known and designated as Atlantic standard time;

that of the second zone shall be known and desig- nated as eastern standard time; that of the third zone shall be known and designated as central standard time; that of the fourth zone shall be known and designated as mountain standard time; that of the fifth zone shall be known and desig- nated as Pacific standard time; that of the sixth zone shall be known and designated as Yukon

standard time; that of the seventh zone shall be known and designated as Alaska-Hawaii standard

time; and that of the eighth zone shall be known

and designated as Bering standard time. (Mar. 19, 1918, ch. 24, § 4, 40 Stat. 451; Apr. 13, 1966, Pub. L. 89-387, § 4(c) , 80 Stat. 108.) Amendments

1966—Pub. L. 89-387 added Atlantic standard time

as first zone designation; redesignated as eastern standard time, central standard time, mountain standard

time and Pacific standard time for second through fifth zones former designation of United States standard east- ern time, United States standard central time, United

States standard mountain time and United States standard Pacific time for former zones one through four; added Yukon standard time as sixth zone designation; redesig- nated as Alaska-Hawaii standard time for seventh zone

former designation of United States standard Alaska time

for fifth zone; and added Bering standard time as eighth zone designation. Transfer of Functions

All functions, powers, and duties of this Interstate Commerce Commission and the Chairman, members,

offices, and officers thereof relating generally to standard

time zones and daylight savings time under this section were transferred to and vested in the Secretary of Transportation by Pub. L. 89-670. Oct. 15, 1966, 80 Stat. 931, which created the Department of Transportation. See

section 1655(e) (5) of Title 49, Transportation. Section Referred to in Other Sections

This section Is referred to in sections 260, 260a, 261, 262, 266, 267 of this title.

g 264. Part of Idaho in third zone. In the division of territory, and in the definition

of the limits of each zone, as provided in sections 261 to 264 of this title, so much of the State of Idaho

as lies south of the Salmon River, traversing the

State from east to west near forty-five degree thirty

minutes latitude, shall be embraced in the third zone: Provided, That common carriers within such

portion of the State of Idaho may conduct their operations on Pacific time. (Mar. 19, 1918, ch. 24,

§ 3, as added Mar. 3, 1923, ch. 216, 42 Stat. 1434, and

amended June 24, 1948, ch. 631, § 1, 62 Stat. 646.) Amendments

1948—Act June 24, 1948, added proviso relating to common carriers. Effective Date of 1948 Amendment

Section 2 of act June 24, 1948, provided that: "This Act [act June 24, 1948] shall take effect at 2 o'clock antemeridian of the second Monday following the date

of its enactment [June 24, 1948]." Repeals The original section 3 of act Mar. 19, 1918, providing

for daylight-savings, was repealed by act Aug. 20, 1919, ch.

51, 41 Stat. 280. Transfer of Functions

All functions, powers, and duties of the Interstate Commerce Commission and the Chairman, members,

offices, and officers thereof relating generally to standard

time zones and daylight savings time under this section were transferred to and vested in the Secretary of Transportation by Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931, which created the Department of Transportation. See

section 1655(e) (5) of Title 49, Transportation. Section Referred to in Other Sections

This section is referred to in sections 260, 260a, 261, 262, 266 of this title.

§ 265. Transfer of certain territory to standard cen- tral-time zone. The Panhandle and Plains sections of Texas and

Oklahoma are transferred to and placed within the United States standard central-time zone. The Secretary of Transportation is authorized and directed to issue an order placing the western boundary line of the United States standard central- time zone insofar as the same affect Texas and Okla- homa as follows: Beginning at a point where such western boundary time zone line crosses the State boundary line between Kansas and Oklahoma; thence westerly

along said State boundary line to the northwest

corner of the State of Oklahoma; thence in a

southerly direction along the west State boundary

line of Oklahoma and the west State boundary line of Texas to the southeastern corner of the State of New Mexico; thence in a westerly direction along

the State boundary line between the States of Texas and New Mexico to the Rio Grande River; thence down the Rio Grande River as the boundary line between the United States and Mexico: Provided,

396
TITLE 15.—COMMERCE AND TRADE § 267

That the Chicago, Rock Island and Gulf Railway

Company and the Chicago, Rock Island and Pacific Railway Company may use Tucumcari, New Mexico,

as the point at which they change from central to mountain time and vice versa; the Colorado Southern and Port Worth and Denver City Railway Companies

may use Sixela, New Mexico, as such changing

point; the Atchison, Topeka and Santa Fe Railway

Company and other branches of the Santa Pe system

may use Clovis, New Mexico, as such changing point, and those railways running into or through El Paso may use El Paso as such point: Provided further, That this section shall not, except as herein provided, interfere with the adjustment of time zones

as established by the Secretary of Transportation.

(Mar. 4, 1921, ch. 173, § 1, 41 Stat. 1446.) Repeals

Section 2 of act Mar. 4, 1921, repealed all conflicting laws and parts of laws. Transfer of Functions

Reference to the Interstate Commerce Commission was

changed to the Secretary of Transportation pursuant to Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931, which createc the Department of Transportation and vested all powers,

duties and functions of the Interstate Commerce Commission and of the Chairman, members, offices, and offi- cers thereof relating generally to standard time zones and

daylight savings time under this section In the Secretary

of Transportation. See section 1655(e)(5) of Title 49, Transportation. Transfer of El Paso and Hudspeth Counties, Texas, to Mountain Standard Time Zone

Pub. L. 91-228, Apr. 10, 1970, 84 Stat. 119, provided: "That, notwithstanding the first section of the Act of March 4, 1921 (15 U.S.C. 265) [this section], the Secretary of Transportation may, upon the written request of the County Commissioners Court of El Paso County,

Texas, change the boundary line between the central standard time zone and the mountain standard time

zone, so as to place El Paso County In the mountain

standard time zone. In the manner prescribed In section 1 of the Act of March 19, 1918, as amended (15 U.S.C. 261), and section 5 of the Act of April 13. 1966 (15 U.S.C. 266). In the same manner, the Secretary of Transportation may

also place Hudspeth County, Texas, In the mountain

standard time zone. If the Hudspeth County Commissioners Court so requests In writing and If El Paso County

Is to be placed In that time zone." Section Referred to in Other Sections

This section Is referred to In sections 260, 260a, 266 of

this title.

§ 266. Applicability of Administrative Procedure Act. The Administrative Procedure Act shall apply to

all proceedings under sections 260 to 267 of this title. (Pub. L. 89-387, § 5, Apr. 13, 1966, 80 Stat. 108.) References in Text The Administrative Procedure Act, referred to In text,

Is classified to sections 551 et seq. and 701 et seq. of Title

5, Government Organization and Employees.

Codification

"Sections 260 to 267 of this title" read In the original

"this Act [meaning Pub. L. 89-387], the Act of March 19, 1918 (15 U.S.C. 261-264) , and the Act of March 4, 1921 (15 U.S.C. 265)", which are classified to sections 260—263,

266, 267; 261—264; and 265 of this title, respectively, Transfer of Functions

All functions, powers, and duties of the Interstate Commerce Commission and the Chairman, members,

offices, and officers thereof relating generally to standards

time zones and daylight savings time under this section

were transferred to and vested In the Secretary of Transportation by Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931, which created the Department of Transportation. See

section 1655(e) (5) of Title 49, Transportation. Section Referred to in Other Sections

This section is referred to In section 267 of this title.

§ 267. State defined. As used in sections 260 to 263, 266 and 267 of this

title, the term "State" includes the District of Columbia, the Commonwealth of Puerto Rico, or any

possession of the United States. (Pub. L. 89-387,

§ 7. Apr. 13, 1966, 80 Stat. 109.) Transfer of Functions

All functions, powers, and duties of the Interstate Commerce Commission and the Chairman, members,

offices, and officers thereof relating generally to standard

time zones and daylight savings time under this section were transferred to and vested In the Secretary of Transportation by Pub. L. 89-670, Oct. 15, 1966, 80 Stat. 931. which created the Department of Transportation. See

section 1655(e) (5) of Title 49, Transportation. Section Referred to in Other Sections

This section Is referred to In section 266 of this title.

397
ANNEX 11.G.3.

PART 71—STANDARD TIME ZONE

BOUNDARIES *

Sec.

71.1 Limits denned; exceptions authorized

for certain rail operating purposes

only.

71.2 Annual advancement of standard

time.

71.3 Atlantic zone.

71.4 Eastern zone.

71.5 Boundary line between eastern and

central zones.

71.6 Central zone.

71.7 Boundary line between central and

mountain zones.

71.8 Mountain zone.

71.9 Boundary line between mountain and

Pacific zones.

71.10 Pacific zone.

71.11 Yukon zone.

71.12 Alaska-Hawaii zone.

71.13 Bering zone. Authority: The provisions of this Part 71 Issued under sees. 1-4, 40 Stat. 450, as amended, sec. 1, 41 Stat. 1446, as amended,

sees. 2-7, 80 Stat. 107-109, sec. 6(e)(5), 80

Stat. 937, sec. 1, 84 Stat. 119; 15 U.S.C. 260-

267, 49 U.S.C. 1655(e)(5), unless otherwise

noted. Source: The provisions of this Part 71 appear at 35 F.R. 12318, Aug. 1, 1970, unless otherwise noted.

§ 71.1 Limits defined; exceptions authorized for certain rail operating purposes only.

(a) This part prescribes the geo- graphic limits of each of the eight standard time zones established by section 1 of the Standard Time Act, as amended by

section 4 of the Uniform Time Act of 1966 (15 U.S.C. 261) . It also contains lists of operating exceptions granted for

specified rail carriers, whose operations

cross the time zone boundaries prescribed by this part, authorizing them to carry the standard of time on which the

major portion of a particular operation

is conducted into an adjoining time zone.

(b) Any rail carrier whose operations

cross a time zone boundary prescribed

by this part may apply for an operating

exception to the General Counsel, Department of Transportation, Washington, D.C. 20590. However, each rail carrier for which an operating exception

is granted shall, in its advertisements,

time cards, station bulletin boards, and

other publications, show arrival and

departure times in terms of the standard

time for the place concerned.

(c) The time zones established by the

Standard Time Act, as amended by the

•Office of Federal Register, Code of Federal Regulations, Title 49 (Transportation) "Part 71 -Standard Time Zone Boundaries," pp. 83-90 (USGPO, January 1, 1972). 398
§ 71.2 Title 49—Transportation

Uniform Time Act of 1966, are Atlantic, eastern, central, mountain, Pacific,

Yukon, Alaska-Hawaii, and Bering.

§ 71.2 Annual advancement of standard

time.

(a) Section 3(a) of the Uniform Time

Act of 1966 (15 U.S.C. 260a(a)) requires

that "the standard time of each

zone * * * shall be advanced 1 hour

[during the period beginning at 2:00

a.m. on the last Sunday in April of each

year and ending at 2:00 a.m. on the last Sunday in October] * * * and such

time as so advanced shall be the standard time of such zone during such

period." The section further authorizes

any State to exempt itself from this requirement. For these reasons, all times

(including the period of advanced time)

in the United States, whether in an ex- empted State or not, shall be cited as "standard time" during the entire year.

(b) Section 3(b) of the Uniform Time

Act of 1966 (15 U.S.C. 260a(b)) provides

that "it is the express intent of Congress * * * to supersede any and all laws of the States or political subdivisions thereof insofar as they may now

or hereafter provide for advances in time

or changeover dates different from those

specified in [section 3(a) of that Act]",

which are those specified in paragraph

(a) of this section. §71.3 Atlantic zone. The first zone, the Atlantic standard

time zone, includes that part of the

United States that is between 52°30' W.

longitude and 67°30' W. longitude and

that part of the Commonwealth of Puerto Rico that is west of 67°30' W. longitude,

but does not include any part of the State of Maine.

§ 71.4 Eastern zone. The second zone, the eastern standard

time zone, includes that part of the

United States that is west of 67*30' W.

longitude and east of the boundary line described in § 71.5, and includes all of the State of Maine, but does not include any

part of the Commonwealth of Puerto

Rico.

§ 71.5 Boundary line between eastern and central zones.

(a) Minnesota - Michigan - Wisconsin.

Prom the junction of the western boundary of the State of Michigan with the

boundary between the United States and

Canada southerly and easterly along the

western boundary of the State of Michigan to a point in the middle of Lake

Michigan opposite the main channel of Green Bay; thence southerly along the western boundary of the State of Michigan to its junction with the southern

boundary thereof and the northern

boundary of the State of Indiana.

(b) Indiana-Illinois. From the junction of the western boundary of the State

of Michigan with the northern boundary

of the State of Indiana easterly along

the northern boundary of the State of Indiana to the east line of La Porte County; thence southerly along the east

line of La Porte County to the north line of Starke County; thence east along the

north line of Starke County to the east

line of Starke County; thence south

along the east line of Starke County to the south line of Starke County; thence

west along the south line of Starke

County to the east line of Jasper County

;

thence south along the east line of Jasper County to the south line of Jasper County; thence west along

the south lines of Jasper and Newton

Counties to the western boundary of the

State of Indiana; thence south along the western boundary of Indiana to the

north line of Gibson County; thence east along the north lines of Gibson and Pike

Counties to the east line of Pike County;

thence south along the east lines of Pike

and Warrick Counties to the north line of Warrick County; thence east along the

north lines of Warrick and Spencer

Counties to the east line of Spencer

County; thence south along the easi

line of Spencer County to the IndianaKentucky boundary.

(c) Kentucky. From the junction of the east line of Spencer County, Ind.,

with the Indiana-Kentucky boundary

easterly along that boundary to the west

line of Meade County, Ky.; thence southeasterly and southwesterly along the west

lines of Meade and Hardin Counties to the southwest corner of Hardin County;

thence along the south lines of Hardin

and Larue Counties to the northwest

corner of Taylor County; thence southeasterly along the west (southwest) line of Taylor County and northeasterly along

the east (southeast) line of Taylor

County to the west line of Casey County;

and thence southerly along the west and

south lines of Casey, Pulaski, and McCreary Counties to the Kentucky-Tennessee boundary.

(d) Tennessee. From the junction of the west line of McCreary County, Ky.,

399
Subtitle A—Office of the Secretary of Transportation § 71.5

with the Kentucky-Tennessee boundary

westerly along that boundary to the west

line of Scott County, Tenn.; thence

southerly along the west line of Scott County, the north and west lines of Morgan County, and the north line of Roane County to the north line of Rhea

County; thence northwesterly along the

north line of Rhea County; and thence

southwesterly along the west lines of Rhea and Hamilton Counties to the Tennessee-Georgia boundary.

ce) Georgia-Alabama. From the junction of the west line of Hamilton County,

Tenn., with the Tennessee-Georgia

boundary westerly along that boundary to its junction with the AlabamaGeorgia boundary; thence southerly

along that boundary and the FloridaGeorgia boundary to the southwest cor- ner of the State of Georgia.

(f) Florida. From the southwest cor- ner of the State of Georgia to the midpoint of the Apalachicola River on the

downstream side of Jim Woodruff Dam;

thence southerly along the middle of the

main channel of the Apalachicola River

and Apalachicola Bay to the Gulf of Mexico.

(g) Operating exceptions—(1) Lines

east of boundary excepted from eastern

zone. Those parts of the following lines of railroad located east of the zone boundary described in this section, are, for operating purposes only, excepted

from the eastern standard time zone and

included within the central standard

time zone:

Railroad From

To—

Railroad FromTo—

Baltimore &

Ohio.

Do.

Do.

Chicago, Mil- waukee, St. Paul&

Pacific. Do

Chicago &

Northwestern.

East line of La

Porte County,

Ind. (west of Walkerton,

Ind.). Illinois-Indiana State line (west

of Dana, Ind.). Illinois-Indiana State line (west

of Vincennes,

Ind.). Illinois-Indiana State line (northwest of Dana, Ind.). Michigan-Wisconsin State line (south of Iron Mountain,

Mich.). Michigan-Wisconsin State line.

Erle-Lacka- South line of wanna. Starke County,

Ind. (near Ora,

Ind.). See footnotes at end of table.

West yard limits

of Garrett, Ind.

West yard limits

of Indianapolis, Ind. Washington,

Ind.

Seymour, Ind.

Champion,

Ontonagon, and Iron River, Mich.i

East lines ol Marquette and

Delta Counties, Mich.' Marion, Ohio.

Grand Trunk

Western.

Do

Illinois Central.

Do

East line of La

Porte County,

Ind. (east of Mill Creek). Michigan-Indiana

State line (near Granger, Ind.). Illinois-Indiana State line (west

of Riverton,

Ind.). West line of Hardin County, Ky. (west of Summit, Ky.).

Louisville & West line of Nashville. Meade County, Ky. (west of Guston, Ky.). Do South line of Hardin County, Ky. (south of Dombey, Ky.). Do West line of Hamilton

County, Tenn.

(west of Hooker, Ga.). Do Apalachicola

River. Norfolk & East line of Western. Starke County,

Ind. (west of Burr Oak,

Ind.). Do East line of La

Porte County,

Ind. (east of Dillon, Ind.) Do. Illinois-Indiana State line (west

of State line, Ind.)

Do Ohio-Michigan

State line (near Munson, Mich.). Do East line of La

Porte County,

Ind. (west of Walkerton, Ind.) Do Illinois-Indiana State line (west

of Ambia, Ind.). Do Illinois-Indiana State line (west

of Cayuga,

Ind.). Penn Central Michigan-Indiana

State line (south

of Grand Beach,

Mich.). Do East line of La

Porte County,

Ind. (west of Elkhart, Ind.). Do East line of Starke County, Ind. (west of Donaldson, Tnd.). Do South line ot Starke County,

Ind. (north of Denham, Ind.). Do East line oi Jas- per County,

Ind. (east of Remington,

Ind.).

Michigan-Indi- ana State line (near Granger,

Ind.). Battle Creek,

Mich.i South yard

limits of Indianapolis, Ind. Hodgenville, Ky., and south yard limits of Louisville, Ky.

Strawberry, Ky.

Lebannon Junction, Ky.

Western limits of Chattanooga, Tenn.

River Junction,

Fla. East yard limits

of Fort Wayne,

Ind.

Toledo, Ohio.

Toledo, Ohio, and Ohio- Michigan

State line (near Munson,

Mich.). Oakwood

Junction,

Mich.i South yard

limits of Peru,

Ind. East yard limits

of Frankfort.

Ind. Frankfort, Ind.

Nile*, Mich.i

Tower B (4.9 miles) east ol the west line of Elkhart County, Ind. Fort Wayne,

Ind.

Logansport,

Ind.

Logansport,

Ind.

400
§ 71.5 Title 49—Transportation

Railroad From— To—

Perm Central— The intersection Continued of the north

line of Benton

County, Ind., and Illinois- Indiana State

line (northwest

of Sheff, Ind.). Do South line of Newton County, Ind. (north

of Sheff, Ind.). Do Illinois-Indiana State line (west

of St. Marys of the Woods,

Ind.). Do Illinois-Indiana State line (east of Farrington,

111.). Peoria & Eastern. Illinois-Indiana State line (east of Danville,

111.). Soo Line Michigan-Wisconsin State

line.

Southern. East line of Pike County, Ind. (west of Stapleton, Ind.).

Shefl, Ind.

Illinois-Indiana State line (northeast of Danville,

111.). Ringo Tower,

Ind.

(Terre Haute).

Ringo Tower,

Ind. (Terre Haute). West yard limits

of Indianapolis, Ind. United States- Canada

Boundary

(near Sault

Ste. Marie, Mich.) ' Junction with

Baltimore &

Ohio near Vincennes

Street, New

Albany, Ind.

1 Effective only from 2 a.m. on the last Sunday in October to 2 a.m. on the last Sunday in April; exception unnecessary during the remainder of year because during

that period Michigan time is not advanced and therefore is the same as central standard time (advanced). (2) Lines west of boundary included

in eastern zone. Those parts of the follow- ing lines of railroad located west of the zone boundary line described in this section, are, for operating purposes only, ex- cepted from the central time zone and

included within the eastern standard

time zone:

Railroad From— To—

Apalachicola Northern.

Central of Georgia. Chesapeake 4

Ohio.

Do.

Louisville &

Nashville.

Apalachicola.

Fla., and

Apalachicola

River.

Georgia-Alabama

State line (west

of Hilton, Ga.). South line of Starke County,

Ind. (north of Beardstown,

Ind.). Michigan-Indiana

State line (south

of New Buffalo, Mich.). West line of Taylor County, Ky. (east of Whitewood,

Ky.). See footnotes at end of table.

Port St. Joe,

Fla.

Dothan, Ala.

Griffith, Ind.

Porter and La

Crosse, Ind.'

Greensburg, Ky.

i\Ra \] rnn fi a. ilk uu ' i From To—

IVfrtrinn North line of Michigan CAtv

Pulaski County, Ind. and

Ind. (south of Hammond

Sftn FMorrp^ Ind. Do West line of White Hammond Ind.

l"!nnnt.TT TnH on/"l \J\ \r* \t \cra r\ (west of Leo City, Ind.

Ind.).

P*»nri f!flnt", ftl 9aii r h lino .if '-!!!> y | '11'! Davitss County,

Ind (north of X 1 *

1

j 1 1 '

1 '

.

, Ind.) Seaboard Coast Georgia*Alabama "Ri> iiirmminf/hn iii j; i ia iii, m

State line (west

of Esom Ga.V

Ala. Do Georgia-Alabama 1*1 Mr»yjlln tIgvlUCL c? <i in amJr , State line (west Ala.

nf r^mftha Oft ^ Do _ flftnrt/i-A-A wdui g \(i n. lftKnmft lot itxnia i al&VVUUU, Ala.

State line (near Pyne, Ga.). Do Georgia-Alabama Abbeville, Elba,

State line (west and Montgomof Saffold, Ga.). ery, Ala. Tennessee, Georgia-Alabama Gadsden, Ala. Alabama State line & Georgia. (southwest of Mcnlo, Ga.).

i Effective only from 2 a.m. on tho last Sunday in October to 2 a.m. on the last Sunday in April; exception unnecessary during the remainder of the year because

during that period Michigan time Is not advanced and

therefore is the same as central standard time (advanced). (3) Indiana and Ohio operations in- cluded in Michigan nonadvanced time. Those parts of the following lines of railroad located east of the zone boundary described in this section, are, for operating purposes only, excepted from

the eastern standard time zone to permit

operations in accordance with Michigan

nonadvanced eastern standard time during the period from 2 a.m. on the last Sunday in April to 2 a.m. on the last Sunday in October:

Railroad From— To -

Chesapeake & Michigan-Ohio Alexis, Ohio.

Ohio. State line (north

of Alexis, Ohio).

Detroit & Toledo Michigan-Ohio Toledo, Ohio. Shore Line. State line (north

of Toledo, Ohio). Penn Central Michigan-Indiana Tower B, ElkState line (north hart, Ind.

of Vistula, Ind.). Do Michigan-Ohio Alexis, Ohio.

State line (north of Alexis, Ohio). Do Michigan-Indiana South Bend,

State line (south Ind.

of Niles, Mich.). Do Michigan-Indiana Fort Wayne,

State line (south Ind.

of Sturgis, Mich.).

(4) Michigan operations excepted

from Michigan nonadvanced eastern

401
Subtitle A—Office of the Secretary of Transportation §71.7

standard time. Those parts of the follow- ing lines of railroad located within the

State of Michigan and east of the zone boundary described in this section, are, for operating purposes only, excepted

from the requirement to operate in ac- cordance with Michigan's nonadvanced

eastern standard time and are authorized

to operate on eastern standard time

(advanced) during the period from 2 a.m. on the last Sunday in April to 2 a.m. on

the last Sunday in October.

Bailrofid ITrom— To

Ann A rhnr Ohio-Michigan Owosso, Mich.

State line (north of Alexis,

Ohio.). D6troit, Toledo Ohio-Michigan Detroit and & Tronton. State line Dearborn,

(north of Meta- Mich. mora. Ohio). Do _ Ohio-Michigan Tecumseh,

State line Mich.

(north of Denson, Ohio). Do _ Ohio-Michigan

State line (north of Alexis, Ohio)

(over the tracks

of the Ann

Arbor Railroad).

Diann, Mich.

Perm Central Indiana-Michigan

State line (north of Ray,

Ind.).

Jackson. Mich.

Do White Pigeon Jonesvllle, Mich.

Junction, Mich. Do.... Litchfield, Mich.. Osseo, Mich. Do Bankers, Mich North Adams,

Mich. Do . Morenci, Mich Palmyra, Mich. Do Clayton, Mich Ida, Mich. Do Ohio-Michigan

State line (south of Ottawa Lake,

Mich.).

Clinton, Mich.

Do Ohio-Michigan Jackson, Mich.

State line (north of Alvordton,

Ohio. Do Cement City, Mich. Brooklyn, Mich.

(h) Municipalities on boundary line. All municipalities located upon the zone boundary line described in this section are in the central standard time zone, except Apalachicola, Fla., which is in the

eastern standard time zone. §71.6 Central zone. The third zone, the central standard

time zone, includes that part of the

United States that is west of the boundary line between the eastern and central standard time zones described in § 71.5 and east of the boundary line between

the central and mountain standard time

zones described in § 71.7.

§71.7 Boundary line between central and mountain zones.

(a) Montana-North Dakota. Beginning at the junction of the MontanaNorth Dakota boundary with the boundary of the United States and Canada

southerly along the Montana-North

Dakota boundary to the Missouri River;

thence southerly and easterly along the

middle of that river to the midpoint of the confluence of the Missouri and Yel- lowstone Rivers; thence southerly and

easterly along the middle of the Yellowstone River to the north boundary of T. 150 N., R. 104 W.; thence east to the northwest corner of T. 150 N., R. 102 W.;

thence south to the southwest corner of T. 149 N., R. 102 W.; thence east to the northwest corner of T. 148 N., R. 102 W.;

thence south to the northwest corner of T. 147 N., R. 102 W.; thence east to the southwest corner of T. 148 N., R. 101 W.;

thence south to the middle of the Little Missouri; thence easterly and northerly

along the middle of that river to the midpoint of its confluence with the Missouri River; thence southerly and easterly along the middle of the Missouri

River to the north line of Morton

County; thence west along the north line of Morton County to the northwest cor- ner of T. 140 N., R. 83 W.; thence south

to the southwest corner of T. 140 N., R.

83 W. ; thence east to the southeast cor- ner of T. 140 N., R. 83 W.; thence south

to the middle of the Heart River; thence

easterly and northerly along the middle

of that river to the southern boundary of

T. 139 N., R. 82 W.; thence east to the middle of the Heart River; thence southerly and easterly along the middle of that river to the midpoint of the confluence of the Heart and Missouri Rivers;

thence southerly and easterly along the middle of the Missouri River to the northern boundary of T. 130 N., R. 80 W.; thence west to the northwest corner

of T. 130 N., R. 80 W.; thence south to the North Dakota-South Dakota boundary; thence easterly along that boundary

to the middle of the Missouri River.

(b) South Dakota. From the junction

of the North Dakota-South Dakota

boundary with the Missouri River southerly along the main channel of that river

to the crossing of the Chicago & North

Western Railway near Pierre; thence

southwesterly to the northeast corner of T. 1 S., R. 28 E. in Jones County; thence

south along the range line between Rs.

402
§71.7 Title 49 — Transportation

28 and 29 E. to the north line of Mellette County; thence east along the north line of Mellette County to the west line of Tripp County; thence south along the west line of Tripp County to the North

Dakota-Nebraska boundary.

(c) Nebraska. From the junction of the west line of Tripp County, South

Dakota with the South Dakota-Nebraska

boundary west along that boundary to the west line of R. 30 W.; thence south

along the range line between Rs. 30 and

31 W. to the southwest corner of sec. 19, T. 33 N., R. 30 W.; thence easterly along

section lines to the northeast corner of

sec. 29, T. 33 N., R. 30 W.; thence southerly along section lines with their offsets to the northeast corner of sec. 17, T. 32

N., R. 30 W.; thence westerly along sec- tion lines to the northwest corner of sec.

18, T. 32 N., R. 30 W.; thence southerly

along the range line to the southwest

corner of T. 31 N., R. 30 W.; thence

easterly along the township line to the

northeast corner of T. 30 N., R. 30 W.;

thence southerly along the range line to the southwest corner of T. 29 N., R. 29 W.; thence westerly along the township

line to the northwest corner of sec. 4, T. 28 N., R. 30 W.; thence southerly along

section lines to the southwest corner of

sec. 33, T. 28 N., R. 30 W.; thence easterly along the township line to the northeast corner of sec. 4, T. 27 N., R. 30 W.;

thence southerly along section lines to the southwest corner of sec. 22, T. 26 N., R. 30 W.; thence easterly along section

lines to the southeast corner of sec. 24, T. 26 N., R. 30 W.; thence southerly along

the range line to the north line of Thomas County; thence westerly along

the north line of Thomas County to the west line of Thomas County; thence

south along the west line of Thomas

County to the north line of McPherson

County; thence west along the north line of McPherson County to the west line of McPherson County; thence south along

the west line of McPherson County to the north line of Keith County; thence

east along the north line of Keith County

to the west line of Lincoln County;

thence south along the west line of Lincoln County to the north line of Hayes

County; thence west along the north line of Hayes County to the west line of Hayes

County; thence south along the west line of Hayes and Hitchcock Counties to the

Nebraska-Kansas boundary.

(d) Kansas-Colorado. From the Junction of the west line of Hitchcock County,

Nebr., with the Nebraska-Kansas boundary westerly along that boundary to the

northwest corner of the State of Kansas

;

thence southerly along the Kansas-Colorado boundary to the north line of Sherman County, Kans.; thence easterly

along the north line of Sherman County

to the east line of Sherman County;

thence southerly along the east line of Sherman County to the north line of Logan County; thence westerly along the

north line of Logan County to the east

line of Wallace County; thence southerly along the east line of Wallace County to the north line of Wichita County;

thence westerly along the north line of Wichita County to the east line of Greeley County; thence southerly along the

east line of Greeley County to the north

line of Hamilton County ; thence easterly

along the north line of Hamilton and

Kearny Counties to the junction of the

east line of R. 36 W.; thence southerly

along the range line between Rs. 35 and 36 W. with its offset to the south

line of Kearny County; thence westerly

along the south line of Kearny and

Hamilton Counties to the Kansas-Colorado boundary; thence southerly along

the Kansas-Colorado boundary to the

junction of that boundary with the north

boundary of the State of Oklahoma.

(e) Oklahoma-Texas-New Mexico.

From the junction of the Kansas-Colorado boundary with the northern boundary of the State of Oklahoma westerly

along the Colorado-Oklahoma boundary

to the northwest corner of the State of Oklahoma; thence southerly along the west boundary of the State of Oklahoma

and the west boundary of the State of Texas to the southeast corner of the State

of New Mexico; thence westerly along

the Texas-New Mexico boundary to the

east line of Hudspeth County, Tex.; thence southerly along the east line of Hudspeth County, Tex., to the boundary

between the United States and Mexico.

(f) Operating exceptions—(1) Lines

east of boundary excepted from central

zone. Those parts of the following lines of railroad, located east of the zone boundary line described in this section,

are, for operating purposes only, ex- cepted from the central standard time

zone and are included within the mountain standard time zone:

403
Subtitle A—Office of the Secretary of Transportation § 71.9

Railroad From

To- Railroad From

To

Atchison, Topeka, &

Santa Fe. Do.

DoEast line of T.

24 S., R. 36 W., Kearny County,

Kans.

Kansas-Colorado

State line. Colorado-Okla- homa State

line.

Chicago, Burl- East line of ington, & Hooker County,

Quincy. Nebr. Do East line of Perkins County, Nebr. Do East line of Chase

County, Nebr. Do East line of Dundy County,

Nebr.

Chicago, Mil- Missouri River, waukee, St. S. Dak.

Paul & Pacific. Chicago &

Northwestern.

Great Northern.

Do.

Northern

Pacific.

Do.

Do.

Union Pacific Do

West line of T. 34 N., R. 30 W., Cherry County,

Nebr. Montana-North Dakota State

line. Yellowstone

River, N. Dak.

East line of T.

138 N., R. 83 W., Morton

County, N. Dak. North line of T.

140 N., R. 81 W., Morton

County, N. Dak.

South line of T.

139 N., R. 81 W., Morton

County, N. Dak.

East line of Keith County, Nebr.

East line of Wallace County, Kans.

Scott City and Dodge City, Kans.

Satanta, Kans. Dodge City, Kans., via Boise City, Okla. Ravenna, Nebr.

Holdrege, Nebr;

McCook, Nebr; Do.

Mobrldge,

S. Dak. Long Pine, Nebr.

Wllllston, N. Dak.

Waterford City, N. Dak. Mandan, N. Dak.

Do.

Do.

North Platte, Nebr.

Ellis, Kans.

(2) Lines west of boundary included

in central zone. Those parts of the follow- ing lines of railroad located west of the zone boundary line described in this sec- tion are, for operating purposes only, ex- cepted from the mountain standard time

zone and are included within the central standard time zone:

Railroad Frorn- To—

Atchison, Topeka, &

Santa Fe.

Chicago, Rock

Island &

Pacific.

Texas-New

Mexico State

line (near Texico, N.

Mex.). Texas-New

Mexico State

line.

Clovis, N. Mex.

Tucumcari, N. Mex. Do West line of Thomas

County. Kans.

Goodland,

Kans.

Missouri.

Soo Line.

Southem

Pacific. Texas &

Pacific. Texas-New

Mexico.

West line of Wichita County, Kans. Montana-North Dakota State

line. East line of Hudspeth

County, Tex. do Texas-New

Mexico State

line.

Pueblo, Colo.

Whltetail, Mont.

El Paso, Tex.

Do.

Lovlngton, N. Mex.

(g) Points on boundary line. All municipalities located upon the zone boundary line described in this section are in the mountain standard time zone, except Murdo, S. Dak., which is in the

central standard time zone. §71.8 Mountain zone. The fourth zone, the mountain standard time zone, includes that part of the

United States that is west of the boundary line between the central and mountain standard time zones described in

§ 71.7 and east of the boundary line between the mountain and Pacific standard time zones described in § 71.9. § 71.9 Boundary line between mountain

and Pacific zones.

(a) Montana-Idaho-Oregon. From the junction of the Idaho-Montana boundary with the boundary between the

United States and Canada southerly

along the Idaho-Montana boundary to the boundary line between Idaho County,

Idaho, and Lemhi County, Idaho; thence

southwesterly along the boundary line between those two counties to the main

channel of the Salmon River; thence

westerly along the main channel of the Salmon River to the Idaho-Oregon

boundary; thence southerly along that

boundary to the boundary line between

Baker County, Oreg., and Malheur

County, Oreg.; thence westerly along the north line of Malheur County to the

northwest corner of Malheur County;

thence southerly along the west line of Malheur County to the southwest corner

of T. 35 S., R. 37 E.; thence east to the Idaho-Oregon boundary; thence south

along that boundary to the southwest comer of the State of Idaho; thence

easterly along the Idaho-Nevada boundary to the northeast corner of the State

of Nevada.

(b) Utah-Nevada-Arizona-California.

Prom the northeast corner of the State

404
§ 71.10 Title 49—Transportation

of Nevada southerly along the UtahNevada boundary, the Nevada-Arizona

boundary, and the Arizona-California

boundary to the boundary between the

United States and Mexico.

(c) Operating exceptions—(1) Lines

east of boundary excepted from mountain zone. Those ports of the following

lines of railroad located east of the zone boundary line described in this section,

are, for operating purposes only, ex- cepted from the mountain standard time zone and are included within the Pacific standard time zone

:

Railroad From- To—

Great Northern.. Troy, Mont Montana-Idaho

State line. Northern Pacific. Paradise, Mont Do.

Southern Pacific. Ogden, Utah Utah-Nevada

State line. Western Pacific.-- Salt Lake City, Do.

Utah. Do Burmester, Utah.. Warner, Utah.

(2) Lines west of boundary included

in mountain zone. Those parts of the fol- lowing lines of railroad located west of the zone boundary line described in this

section, are, for operating purposes only,

excepted from the Pacific standard time zone and are included in the mountain

standard time zone:

§71,12 Alaska-Hawaii zone. The seventh zone, the Alaska-Hawaii

standard time zone, includes that part of the United States that is between 141° W.

longitude and 162° W. longitude and in- cluding all of the State of Hawaii.

§71.13 Bering zone. The eighth zone, the Bering standard

time zone, includes that part of the United States that is between 162° W.

longitude and 172°30' W. longitude and

that part of the Aleutian Islands that is west of 172°30' W. longitude, but does not

include any part of the State of Hawaii.

Railroad From— ToAtchison, Topeka, &

Santa Fe. Chicago, Milwaukee, St. Paul & Pacific. Union Pacific...

Colorado River... Southern limits of Needles, Montana-Idaho

State line. Idaho-Nevada

State line near Idavada, Idaho. Do West line of Malheur

County, Oreg.

Calif. Avery, Idaho.

Wells, Nevada.

Burns, Oreg.

(d) Points on boundary line. All municipalities located upon the zone boundary line described in this section are in the mountain standard time zone. §71.10 Pacific zone. The fifth zone, the Pacific standard

time zone, includes that part of the

United States that is west of the boundary line between the mountain and Pacific standard time zones described in

§ 71.9 and east of 137° W. longitude.

§71.11 Yukon zone. The sixth zone, the Yukon standard

time zone, includes that part of the

United States that is between 137° W.

longitude and 141° W. longitude.

405
ANNEX 11.G.4.

Title 49—Transportation

Subtitle A—Office of the Secretary of Transportation

[Docket No. 21; Amdt. 71-13] PART 71—STANDARD TIME ZONE

BOUNDARIES *

Relocation of Eastern-Central Standard Time Zone Boundary in the State of Michigan

The purpose of this amendment to part

71 of title 49 of the Code of Federal Regulations is to change the existing boundary line between the eastern time zone and the central time zone as it relates to the State of Michigan.

On March 15, 1973, the Department of Transportation published in the Federal

Register (38 FR 7009) , a notice of pro- posed rulemaking to relocate a segment

of the boundary between the eastern and

central time zones from its present location along the border between the State

of Wisconsin and the Upper Peninsula

of the State of Michigan northward in order to include four Upper Peninsula

counties along the Wisconsin border (Menominee, Dickinson, Iron, and Gogebic) in the central time zone. The proposal was based on a petition

from the Board of County Commissioners

of each of the four counties. The peti- tions cited two reasons for seeking the change—closer commercial relations with

neighboring communities in the State of Wisconsin, which Is in the central zone, than with the rest of the State of Michigan; and the recent decision of the State

of Michigan to observe advanced (daylight, or "fast") time beginning in 1973. From 1969 to 1972, the State of Michigan

exercised its option under section 3(a)

of the Uniform Time Act of 1966 (15 U.S.C. § 260a) and exempted Itself from

the observance of advanced time. Thus,

eastern standard (slow) time was observed throughout the year in Michigan.

All or part of the four counties concerned are further west than Chicago,

HI., which is in the central zone; the westernmost of the counties, Gogebic, is as far west as St. Louis, Mo., which Is also In the central zone. (In fact, the westernmost part of Gogebic County Is farther west than the 19th meridian west

of Greenwich, which Is the standard meridian of the central zone.) Under

eastern advanced time, during the summer, areas that far west have daylight on some days as late as 10:30 p.m.; under

central advanced time (which is the same

time on the clock as eastern standard

time) there is daylight on those days

only as late as 9 : 30 p.m. Under the Uniform Time Act of 1966, the Secretary of Transportation is authorized to modify the boundaries of time zones "having regard for the convenience of commerce and the existing Junction points and division points of common carriers engaged in interstate or foreign commerce."

Interested persons were given a 22-day

period within which to comment in writ- ing on the proposed change. In addition, a representative of the Department conducted a public hearing on the proposal

in each of the four counties, during

which interested persons had opportunity to comment on the proposal either

orally or in writing, or both. Although

percentages varied county by county, comments received from each county

overwhelmingly favor the proposal. Of

the total of approximately 1.500 persons who submitted comments, approximately

90 percent favor the proposal, and docu- ment commercial relations with both the State of Wisconsin and other areas in the central time zone close enough to demonstrate that the convenience of commerce would be served by including the four counties in the central time

zone. Among those favoring the proposal

is North Central Airlines, Inc., the only

certificated air carrier engaged in inter- state commerce in the four-county area. The Department also Invited comments on whether any counties in the Upper Peninsula contiguous to the four named should be placed In the central

zone. Since very few persons addressed

themselves to this, only the four counties named are being placed in the central zone at this time. Many persons, however, urged the Department to locate the boundary line farther east in the Upper

Peninsula, between the counties of Alger

and Schoolcraft In the west and the

counties of Luce and Mackinac in the

east. These counties meet In a straight north-south line approximately 86* west

of Greenwich. These persons contend

that

(1) There are two discernible economic

areas in the Upper Peninsula;

(2) The 12 Upper Peninsula counties west of this north-south line (Alger, Baraga, Delta, Dickinson, Gogebic, Houghton, Iron, Keweenaw, Marquette, Menominee, Ontonagon, and Schoolcraft)

form an area closely tied economically to the State of Wisconsin;

(3) The three Upper Peninsula counties east of this line (Chippewa, Luce, and Mackinac) form another, closely

tied economically to the Lower Peninsula

of Michigan;

(4) This north-south line runs through

a sparsely populated section of the Upper

Peninsula and relocating the time zone boundary along it would Inconvenience

relatively few people.

Although the Department recognizes the validity of these contentions, relocation of the boundary that far east was

not within the scope of the proposal

which led to this rulemaking. These contentions will, however, be considered as the Department evaluates the effect of the relocation which is being made.

Advanced time begins this year at 2

a.m., Sunday, April 29. Making the relo- cation of the boundary effective at that time will serve both the convenience of

*Federal Register, Title 49 (Transportation), "Part 71— Standard Time Zone Boundaries," 38, No. 70, pp. 9228-9229 (April 12. 1973). 406
Title 49 — Transportation

commerce and the convenience of the persons living in the area affected by the change (since eastern standard time is the same time on the clock as central advanced time, they will not have to change their clocks). I therefore find that good cause exists for making this amendment effective in fewer than 30 days after publication in the Federal

Register. In consideration of the foregoing, effect at 2 a.m. on April 29, 1973, para- graph (a) of S 71.5 of title 49 of the Code

of Federal Regulations is amended to read as follows: §71.5 Boundary line between eastern and central zones.

(a) Minnesota-Michigan-Wisconsin.—

From the junction of the western boundary of the State of Michigan with the boundary between the United States and

Canada northerly and easterly along the

west line of Gogebic County to the west

line of Ontonagon County; thence south

along the west line of Ontonagon County

to the north line of Gogebic County;

thence southerly and easterly along the north line of Gogebic County to the west

line of Iron County; thence north along

the west line of Iron County to the north

line of Iron County; thence east along

the north line of Iron County to the east

line of Iron County; thence south along

the east line of Iron County to the north

line of Dickinson County; thence east along the north line of Dickinson County

to the east line of Dickinson County;

thence south along the east line of Dickinson County to the north line of Menominee County; thence east along the north line of Menominee County to the

east line of Menominee County; thence

southerly and easterly along the east line of Menominee County to Lake Michigan;

thence east to the western boundary of the State of Michigan ; thence southerly

and easterly along the western boundary of the State of Michigan to a point in the middle of Lake Michigan opposite the main channel of Green Bay; thence

southerly along the western boundary of the State of Michigan to its junction with

the southern boundary thereof and the northern yboundary of the State of Indiana. This amendment does not concern ad- herence to or exemption from advanced

time. The Uniform Time Act of 1966 re- quires observance of advanced time from

2 a.m. on the last Sunday in April to 2 a.m. on the last Sunday in October of each year, but permits any State to ex- empt itself from this requirement by law

applicable to the entire State. A State

that has parts in more than one time

zone may exempt the entire area within one time zone without exempting the entire State. Thus, that part of the State

of Michigan which is hereby placed in the central time zone must, under exist- ing law in the State of Michigan, observe

central advanced time from 2 a.m. on

the last Sunday in April to 2 a.m. on the

last Sunday in October of each year. That

entire part may, however, be exempted

from such observance by act of the Michigan legislature. The Department of

Transportation does not have any administrative authority with respect to

this requirement.

(Aot of March 19, 1918, as amended by the Uniform Time Act of 1966. 15 U.8.C. 260-267;

sec. 6(e)(5), Department of Transportation

Act, 49 U.S.C. 1655(e)(5).) Issued in Washinngton, D.C., on

April 10, 1973. Claude S. Brinegar,

Secretary of Transportation.

(FR Doc.73-7199 Piled 4-ll-73;8:45 am]

407
ANNEX 11.G.5.

Title 49—Transportation SUBTITLE A—OFFICE OF THE SECRETARY OF TRANSPORTATION

[OST Docket No. 34] PART 73—EMERGENCY DAYLIGHT

SAVING TIME

Procedures and Criteria for Implementation

The Emergency Daylight Saving Time

Energy Conservation Act of 1973 (De- cember 15, 1973, Pub. L. 93-182) ("the Act") advances the standard time by one hour in all eight standard time zones of the United States continuously from

2:00 a.m. Sunday, January 6, 1974, to 2:00 a.m. Sunday, April 27, 1975, and

provides that the time as so advanced

shall be standard time. The purpose of the regulations which appear below is to

set forth procedures and criteria for implementation of the Act. Two classes of States are permitted to exempt themselves from advanced time:

(1) Any State which is entirely within one time zone and not contiguous to any

other State (Hawaii, Puerto Rico, and

the Virgin Islands) ; and (2) any State with parts thereof in more than one time

zone (Alaska, Florida, Idaho, Indiana, Kansas, Kentucky, Michigan, Nebraska, North Dakota, Oregon, South Dakota,

Tennessee, and Texas). (Section 3(a)).

If a State elects to exempt itself, the ex- emption must apply to the entire area

of the State lying within one time zone, and the effect of the exemption must be

to put the entire State on uniform time

(i.e. the exemption can only apply to that part of the State in the more easterly zone) (see H. Rep. No. 93-709 at 5)

.

While this limitation could not be lit- erally applied to Alaska, which is in four time zones, any exemption for that State would have to take account of this intent

of Congress. Section 3(c) of the Act provides that any law in effect on October 27, 1973, ex- empting a State from advanced time under section 3(a) of the Uniform Time Act

of 1966 (15 U.S.C. S 260a(a)> shall re- main in effect as the exercise by the State

of the exemption permitted by section 3(a) of the Act unless the State by law

provides that such exemption shall not

apply during the effective period of the

Act. Thus, the effect of section 3(c) of the Act is to continue exemptions enacted by Indiana, Hawaii, Puerto Rico and the Virgin Islands, unless the legis- lature passes a law providing that the exemption shall not apply. (The State of Arizona has also enacted an exemption

pursuant to section 3(a) of the Uniform

Time Act which was in effect October 27, 1973; however, that exemption does not remain in effect and Arizona may not

otherwise exempt Itself because, although

It lies entirely within one time zone', It la contiguous to another State and therefore does not satisfy the statutory re- quirements for exemption.

)

States permitted exemptions by section 3(a) may exempt themselves from ad- vanced time anytime during the period

*Federal Register, Title 49 (Transportation) "Part 73 — Emergency Daylight Saving Time", 38, No. 244, pp. 34876-34878 (December

20, 1973)- Added in proof. 408
Title 49 — Transportation

the Act is In effect. The exemption must, however, be complete; a State may not

elect to exempt itself from advanced time

during winter months but observe ad- vanced time during summer months.

Section 3(b) of the Act permits the

President to grant a State an exemption from the advanced time established by

section 3(a) of the Act or a request for realignment of the existing limits of time

zones, if the State, by proclamation of

its Governor, makes a finding prior to Sunday, January 6, 1974—the effective date of the Act—that such exemption or realignment is necessary to avoid undue

hardship or to conserve fuel in such State or part thereof. ("(The President's! decision should be based on the appropriateness of all aspects of any exemption,

including convenience of commerce, possible energy savings, or undue hardship to large segments of the population, as well as the possible impact on the success of and cooperation with the national energy conservation program." S. Rept. No. 93-504 at 3.) By Executive Order 11751, issued De- cember 15, 1973, the President has desig- nated and empowered the Secretary of Transportation to exercise the authority

vested In him by section 3(b) to grant

the exemptions or realignments.

The last regular Federal workday before the effective date of the Act Is Fri- day, January 4, 1974. Therefore, procla- mations should be received by the Department of Transportation not later than 5:30 p.m. eastern standard time on

that date. Section 2 of the Executive Order es- tablishes the following criteria to guide

the Secretary in the exercise of the authority delegated by the Order:

1. The policy of the United States, as .expressed In section 2 of the Uniform

Time Act of 1966 (15 U.S.C. 260) , to pro- mote the adoption and observance of uniform time within the standard time

zones of the United States. This means

that an exemption will not ordinarily be

granted to an area if the effect would be

to put it on a time different from all contiguous areas.

2. The convenience of commerce. This

is the primary standard in section 4 of the Uniform Time Act of 1966 (15 U.S.C.

261) guiding the Secretary's decisions whether to modify time zone limits under that section. This means that the problems of carriers engaged in inter- state and foreign commerce and of the

broadcast media will be given considerable weight in determining whether an

exemption or realignment will be

granted.

3. Possible energy savings. The rationale behind the Act is that year-round advanced time will conserve energy. Since any exemption or realignment may

interfere with the testing of this rationale, a Governor claiming that an exemption or realignment will conserve fuel must produce evidence substantiating the effect on fuel use in the subject area and in related power-consumption areas.

4. Undue hardship to large segments

of the population. Included within this criterion are considerations of the commerce and industry in the area covered by the proclamation, weather conditions, problems of school children that cannot be dealt with adequately by State and

local authorities, motor vehicle traffic patterns and densities, commercial and

energy relationships with surrounding

areas, and location on the western edges

of a time zone which has a severe west- ward extension. For a showing of "undue" hardship, the effects must substantially exceed those consequences presumably recognized by the Congress

as necessarily Incident to advanced time

during winter months.

5. Possible impact on the success of and cooperation with the national energy

conservation program. Many of the measures being taken or planned as part

of the national energy conservation pro- gram are directed, among other things, to the reduction and shift of peak energy demands, increased use of mass transportation and car pools, increased load factors in commercial aviation, and conversion of heating and power plants to

alternative fuels. Any exemption or re- alignment Inconsistent with, or counterproductive to the success of, any of these measures will be denied unless specific evidence Is presented that an overriding reason exists for granting the exemption

or realignment. In deciding whether to grant an ex- emption or realignment the Secretary may, by virtue of section 3 of the Executive Order, seek Information and advice from any appropriate Federal agency. Any exemption enacted pursuant to section 3(a) and any exemption or re- alignment granted pursuant to section 3(b) expires contemporaneously with

the expiration of the Act at 2:00 a.m. Sunday, April 27, 1975, at which time

only those exemptions enacted pursuant

to section 3(a) of the Uniform Time Act

of 1966, as amended, and time zone limits as they existed on October 27, 1973, will be effective. In addition to the foregoing, the Act

contains other significant provisions:

1. Section 5 suspends for the duration

of the Act the authority of the Secretary under section 4 of the Uniform Time Act

of 1966 (15 U.S.C. 261) to modify the

limits of time zones. During the effective period of the Act, time zone limits may be

realigned only In accordance with section 3(b) of the Act and only for the duration of the Act.

2. Section 3(d) makes applicable to the Act the preemption provision in sec- tion 3(b) of the Uniform Time Act of 1966 (15 UJS.C. 260a(b) ) , superseding all laws of States and their political subdivisions insofar as they are inconsistent with the six months of advanced

time established by section 3(a) of the Uniform Time Act. Thus, during the

effective period of the Act, all laws of States and their political subdivisions are superseded to the extent they are in- consistent with the Act.

3. The authority of the Secretary under section 3(c) of the Uniform Time

Act of 1966 (15 U.S.C. 260a(c)) to seek enforcement in the appropriate United

States District Courts of the advanced

" time provision of the Uniform Time Act

of 1966, as amended, is made applicable

to the Act by section 3(d) of the Act

4. The Secretary, with the cooperation

of all appropriate Federal agencies, is required to study the full range of effects of the year-round advanced time established by the Act and to submit two re- ports to Congress thereon. In order to limit the number of variables affecting the operation of the Act and Improve the

reliability of the study, an exemption or realignment granted by the Secretary

may not be revoked or modified during

the effective period of the Act except with the prior written approval of the

Secretary. Because of the emergency nature of the Act and the short period of time between Its enactment December 15, 1973, and Its taking effect January 6, 1974, I find that notice and public pro- cedure on these regulations is contrary

to the public interest and that good cause

exists for making them effective in fewer than 30 days after publication in the Federal Register. In consideration of the foregoing. Title 49 of the Code of Federal Regulations is amended by adding thereto a new Part

73, to read as follows:

Subpart A—Gsnaral

Sec.

73.1 Purpose.

73.3 Definitions, 734 State exemption for State In two time

zones.

73.7 Grant of exemption or realignment by

the Secretary.

73.9 Reduction In number of time zones.

73.11 Restrictions on exemptions and re- alignments.

73.13 Expiration of exemptions and realign- ments.

Subpart B—Procedures and Criteria 73.21 Submission of proclamation of a Governor.

73.23 Decision of the Secretary. 73.26 Criteria. Authority : Pub. L. 03-182, December 15, 1973; Executive Order 11761, December 15, 1973; 6 UJS.C. 662(a) (1). Subpart A—General

§ 73.1 Purpose. This part sets forth the procedures and

criteria for implementation of the Emergency Daylight Saving Time Energy Conservation Act of 1973 (December 15, 1973, Pub. L. 93-182) rthe Act")

.

§ 73.3 Definitions. As used in this part

"Governor of a State" and "Governor"

Include the Commissioner of the District of Columbia, the Governor of the Commonwealth of Puerto Rico, and the Governor of the Virgin Islands. "Secretary" means the Secretary of Transportation. "State" includes the District of Columbia, the Commonwealth of Puerto Rico, and any possession of the United States. § 73.5 State exemption for State in two

time zones. An exemption enacted pursuant to sec- tion 3(a) of the Act by a State with parts thereof In two time zones may apply only

FEDERAL REGISTER, VOL 38, NO. 244—THURSDAY, DECEMBER 20, 1973

409
Title 49 — Transportation

to all that part of the State which is in the more easterly time zone.

§ 73.7 Grant of exemption or realign- ment by the Secretary.

(a) A request for exemption or re- alignment pursuant to section 3(b) of the Act may be granted in whole or In

part.

(b) An exemption will not ordinarily be granted pursuant to section 3(b) of the Act to an area if the effect would be to put that area on a time different from

the time observed in all contiguous areas.

§ 73.9 Reduction in number of time

zones. No realignment of time zone limits

will be granted pursuant to section 3(b)

of the Act if the effect of such realign- ment would be to reduce the number of time zones in the United States.

§ 73.11 Restrictions on exemptions and

realignments.

( a) An area exempted from the observ- ance of advanced time or affected by a

realignment pursuant to section 3(b) of the Act shall observe continuously from

2:00 a.m. Sunday, January 6, 1974, to 2:00 a.m. Sunday, April 27, 1975, the standard time applicable January 5, 1974, to the standard time zone in which the area is located. Exemptions or realign- ments may be revoked or modified only with the approval of the Secretary.

(b) A State may not exercise the ex- emption authority contained in section 3(a) of the Act in a manner which would

frustrate the Intent of the Act that either advanced time or non-advanced time will be observed on a year-round basis by

each State.

§ 73.13 Expiration of exemptions and

realignments.

Exemptions enacted pursuant to section 3(a) of the Act, and exemptions

from advanced time or realignments of time zone limits granted pursuant to sec- tion 3(b) of the Act, expire contemporaneously with the expiration of the Act

at 2:00 a.m. Sunday, April 27, 1975. At

that time, only those exemptions enacted pursuant to section 3(a) of the Uniform

Time Act of 1966, as amended, and align- ments of time zone limits as they existed October 27, 1973, will be effective. Subpart B—Procedures and Criteria § 73.21 Submission of proclamation of a Governor.

(a) A certified copy of a proclamation

issued by the Governor of a State pur- suant to section 3(b) of the Act must be forwarded to the Docket Clerk, Office of the General Counsel, TGC, Department

of Transportation, 400 Seventh Street SW„ Washington, D.C. 20590, and should

be mailed In time to be received by 5:30

p.m. eastern standard time Friday, January 4, 1974.

(b) For proclamations transmitted by

telecopier, the telephone number is Area Code 202, 426-4193. A certified copy of a

proclamation transmitted in this manner

shall be forwarded to the Docket Clerk in accordance with paragraph (a) of this section immediately upon completion of transmission.

(c) A proclamation must Include, or be accompanied by, a statement of the

claims of undue hardship or fuel conservation on which the proclamation Is based, and supporting facts. Additional information may be requested by the

Secretary and the proclamation should

be accompanied by the name, title, address, and telephone number of the offi- cial of the State to be contacted by the Secretary for that purpose.

§ 73.23 Decision of the Secretary. Proclamations received in accordance

with § 73.21 of this part will be acted upon as expeditiously as practicable. The

decision of the Secretary will be communicated to the Governor by telegram

and confirmed by letter. § 73.23 Criteria. Consistent with the legislative history

of section 3(b) of the Act, the Secretary's

decision will be based on consideration of the appropriateness of all aspects of the exemption or realignment. This will involve, necessarily, a consideration and

balancing of the objectives sought to be achieved by the Act, including:

(1) The policy of the United States, as expressed in section 2 of the Uniform

Time Act of 1966 (15 U.S.C. 260), to promote the adoption and observance of uniform time within the standard time

zones of the United States.

(2) The convenience of commerce.

(3) Possible energy savings.

(4) Undue hardship to large segments

of the population.

(5) Possible impact on the success of and cooperation with the national energy

conservation program.

Effective date: This Part is effective December 20, 1973. Issued in Washington, D.C, on De- cember 19, 1973.Claude S. Brinecar, Secretary of Transportation.

[PR Doc.73-27018 Piled 12-19-73:12:40 pm]

410
ANNEX ll.G.5.a.

Office of the Secretary [OST Docket No. 34. Notice No. 74-9J ARIZONA

Emergency Daylight Saving Tim*

Exemption

The Emergency Daylight Saving Time

Energy Conservation Act of 1973 (December 15. 1973. Pub. Law 93-182) ("the

Act") advances the standard time by one

hour In all eight standard time zones of the United States continuously from 2

a.m. Sunday. January 6, 1974, to 2 a.m. Sunday. April 27. 1975. and provides that

the time as so advanced shall be standard time. Section 3(b) of the Act permits the

President to grant a State an exemption from advanced time established by section 3(a) of the Act or a request for re- alignment of the existing limits of time

zones, if the State, by proclamation of

Its Governor, makes a finding prior to Sunday. January 6, 1974—the effective date of the Act—that such exemption

or realignment is necessary to avoid undue hardship or to conserve fuel in such State or part thereof. ("[The President's] decision should be based on the

appropriateness of all aspects of any exemption. Including convenience of commerce, possible energy savings, or undue hardship to large segments of the

population, as well as the possible impact on the success of and cooperation with the national energy conservation program." 8. Rept. No. 93-604 at 3.) By Executive Order 11751, issued December 15. 1973, the President has desig- nated and empowered the Secretary of Transportation to exercise the authority

vested in him by section 3(b) to grant

exemptions or realignments. Procedures and criteria for Implementation were is- sued by the Secretary (49 CFR Part 73, 38 PR 34876). The Governor of the State of Arizona,

the Honorable John R. (Jack) Williams,

by proclamation Issued December 19, 1973, requests that the State of Arizona

be exempted from observance of ad- vanced time during the effective period

of the Act. The proclamation and supporting data

submitted establish that Arizona had

legislatively exempted Itself from observ- ance of advanced time under the Uniform

Time Act of 1966; that the summer mean

temperatures in the more populous areas

of the State are such as to cause severe

discomfort, and that observance of advanced time would severely Increase this discomfort; that if Arizona were to observe year-round advanced time, greater power consumption would likely occur

during summer months, without corre- sponding savings during winter months; and that much of the State's agricultural commerce with Mexico would be dis- rupted by observing advanced time. Several residents of Arizona have submitted views in opposition to the Governor's proclamation. They did not, however, present specific data responsive to

the criteria set forth In either the Act

or the regulations' promulgated there- under. Upon consideration of the proclamation and supporting data, and all comments received. I find the requested ex- emption is consistent with the objectives

sought to be achieved by the Act, and

should be granted. I further find that the

State of Arizona shall observe mountain

nonadvanced (standard) time as stand- ard time during the effective period of the Emergency Daylight Saving Time Energy Conservation Act of 1973. Because of the emergency nature of the Act; the Congressional intent that It be Implemented quickly *; the short period of time between its enactment December 15, 1973, and its taking effect January 6. 1974; and the short period

of time between the date of the proclamation—December 19, 1973—and January 6, 1974, 1 find that notice and public

procedure on this action are contrary to the public interest and that good cause

exists for making it effective in fewer than 30 days after publication in the Federal Register. For these same rea- sons it has not been possible to assess the need for, and, if necessary, to prepare an

environmental impact statement on this action. See section 102. National Environ- mental Policy Act of 1969 (January 1, 1970. Public Law 91-190, sec. 102, 83 Stat. 853; 42 U.8.C. 4332)

.

This action is taken pursuant to sec- tion 3(b) of the Emergency Daylight

Saving Time Energy Conservation Act of 1973 (December 15, 1973, Public Law

93-182. 13(b). 87 Stat. 708); Executive Order 11751 (38 FR 34725) ; and Part 73

of the Regulations of the Office of the

Secretary of Transportation (49 CPR

Part 73). Effective date. This action is effective 2 ajn. mountain nonadvanced (standard) time Sunday January 6, 1974. Issued In Washington, D.C., on January 4, 1974. Clauds S. Bunkoar. Secretary of Transportation.

[FR Doc.74-786 Filed l-fr-74;S:4S am]

[OST Docket No. 84, Notice No. 74-1) KENTUCKY

Emergency Daylight Saving Time? RssngnnMnt

The Emergency Daylight Saving Time

Energy Conservation Act of 1973 (December 15, 1973, Pub. Law 93-182) ("the

Act") advances the standard time by one hour in all eight standard time zones of the United States continuously from 2 am, Sunday, January 6, 1974, to 2 ajn.

Sunday, April 27, 1975, and provides that

the time as so advanced shall be stand- ard time. Two classes of States are permitted to exempt themselves from advanced time:

(1) Any State which is entirely within one time zone and not contiguous to any

1 " [The Secretary) should act quickly and

expeditiously. Failure to do m wfll risk serious inconvenience and uncertainty." See

Senate Report No. 93-604 at 3.

other State (Hawaii, Puerto Rico, and

the Virgin Islands) ; and (2) Any State with parts thereof in more than one time zone (Alaska. Florida. Idaho. Indiana. Kansas. Kentucky. Michigan, Nebraska. North Dakota. Oregon, South Dakota.

Tennessee, and Texas). (Section 3(a)).

If a State elects to exempt Itself, the exemption must apply to the entire area

of the State lying within one time zone, and the effect of the exemption must be

to put the entire State on uniform time

(I.e., the exemption can only apply to that part of the State In the more easterly zone) (see H. Rept. No. 93-709 at 5)

.

States permitted exemptions by sec- tion 3(a) may exempt themselves from

advanced time anytime during the period the Act Is In effect. The exemption

must, however, be complete; a State may

not elect to exempt Itself from advanced

time during winter months but observe advanced time during summer months.

Section 3(b) of the Act permits the

President to grant a State an exemption

from the advanced time established by

section 3(a) of the Act or a request for realignment of the existing limits of time zones, if the State, by proclamation

of its Governor, makes a finding prior to Sunday. January 6, 1974—the effec- tive date of the Act—that such exemption or realignment is necessary to avoid undue hardship or to conserve fuel in such State or part thereof. ("[The President's] decision should be based on the

appropriateness of all aspects of any ex- emption, including convenience of commerce, possible energy savings, or undue

hardship to large segments of the population, as well as the possible Impact on

the success of and cooperation with the

national energy conservation program."

S. Rept. No. 93-504 at 3.) By Executive Order 11751, issued De- cember 15, 1973, the President has desig- nated and empowered the Secretary of Transportation to exercise the authority

vested in him by section 3(b) to grant the exemptions or realignments. Procedures and criteria for implementation were promulgated by the Secretary (49 CPR Part 79. 38 FR 34876). The Governor of the Commonwealth

of Kentucky, the Honorable Wendell H.

Ford, by proclamation issued January 3, 1974, requests the limits of the division between the eastern and central time

zones In Kentucky be realigned during

the effective period of the Act, to Include within the central time zone all of the Commonwealth except twelve northeastern counties (Boone, Kenton, Campbell, Grant, Pendleton, Bracken, Mason,

Lewis, Greenup, Carter, Boyd, and Lawrence) . The twelve counties which would

remain in the eastern time zone are proximate to the Ohio and West Virginia State lines. The proclamation and supporting data

submitted by the Governor of Kentucky

establish that more than 75 percent of the population of Kentucky live in the extreme western edge of the eastern time zone (as presently delineated) ; that observance of eastern advanced time

within most of that portion of Kentucky

in the eastern time zone would cause

'Federal Register (Transportation)- "Emergency Daylight Saving Time" — DOT Exemption and Realignment to Certain States-39, No. 7, pp. 1524-1526 (January 10, 1974.)- Added in proof. 411
Title 49 — Transportation

extreme hardship to school children,

agriculture, and Industry requiring daylight working conditions; that the convenience of commerce would be served by western Kentucky counties observing

the same time as adjacent areas in Tennessee and Indiana; and that the pro- posed realignment would not be detri- mental to the national energy conservation program. The data submitted also establish that the twelve counties which

would remain in the eastern time zone

are commercially related to adjacent

areas in Ohio and West Virginia, and

that the convenience of commerce would

best be served by their continued observance of the same time as those areas. Although section 3(a) of the Act contemplates State legislative action to achieve an exemption from observance

of advanced time within one time zone

of a State with parts in more than one

zone, the proposed realignment may be

obtained only under section 3(b). Upon consideration of the proclamation and supporting data, I find the re- quested realignment of the limits of the

eastern and central time zones within Kentucky is consistent with the objectives sough to be achieved by the Act. During the effective period of the Act,

therefore, the limit between the eastern and central time zones in the Commonwealth of Kentucky shall be denned as

follows: Prom the junction of the east line of Spencer County, Indiana, with the Indiana- Kentucky boundary northerly and easterly along that boundary to the vert line of Boone

County, Kentucky; thence southerly along

the west line of Boone County to the north

line of Grant County; thence west along the north line of Grant County to the west line of Grant county; thence southerly along the west line of Grant County to the south line of Grant County, thence easterly along the south lines of Grant and Pendleton Counties to the west line of Bracken County;

thence south along the west line of Bracken County to the south line of Bracken County; thence easterly along the south lines of Bracken, Mason, Lewis, and Carter Counties

to the west line of Lawrence County; thence

south along the west line of Lawrence County to the south line of Lawrence County:

thence easterly and northerly along the south

line of lAwrence County to its junction with

the Kentucky-West Virginia boundary;

thence southerly along the Kentucky-West

Virginia ' boundary to the Kentucky-Tennessee boundary; thence west along the Kentucky-Tennessee boundary to its junction with the west line of Scott County, Tennessee. Because of the emergency nature of the Act; the Congressional Intent that It be Implemented quickly; 1 the short period of time between its enactment December 15, 1973, and its taking effect January 0, 1974; and the short period

of time between the date of the proclamation—January 3, 1974—and January 8, 1974, 1 find that notice and public procedure on this action are contrary

to the public Interest and that good cause

1 "[The (Secretary] should at quickly and

expeditiously. Failure to do win risk ssrtous Inconvenience and uncertainty." See Senate Beport Ho. 08-BOft at 8.

KOERAL

exists for making it effective in fewer than 30 days after publication in the Federal Register. For these same reasons it has not been possible to assess the need

for, and, if necessary, to prepare an en- vironmental Impact statement on this action. See section 102, National Environ- mental Policy Act of 1969 (January 1. 1970. Public Law 91-190, section 102, 83

Stat. 853; 42 U.S.C. 4332)

.

This action Is taken pursuant to sec- tion 3(b) of the Emergency Daylight

Saving Time Energy Conservation Act of 1973 (December 15, 1973, Pub. Law 93-

182, section 3(b) , 87 Stat. 708) ; Executive Order 11751 (38 PR 34725); and Part

73 of the Regulations of the Office of the

Secretary of Transportation (49 CFR

Part 73). Effective date. This action Is effective 2 a.m. central nonadvanced (standard) time Sunday, January 6. 1974. Issued in Washington, D.C., on Jan- uary 4, 1974. Claude S. Brinegar,

Secretary of Transportation.

[PR Doc.74-767 Piled l-©-74;8:46 am]

[OST Docket No. 34, Notice No. 74-3] IDAHO AND OREGON

Emergency Daylight Saving Time

Exemptions

The Emergency Daylight Saving Time

Energy Conservation Act of 1973 (December 15, 1973. Pub. Law 93-182) ("the Act") advances the standard time by one hour in all eight standard tune zones of the United States continuously from 2:00

a.m. Sunday. January 8, 1974, to 2 a.m. Sunday, April 27, 1975, and provides that the time as so advanced shall be stand- ard time. Two classes of States are permitted to exempt themselves from advanced time:

(1) any State which is entirely within one time zone and not contiguous to any

other State (Hawaii, Puerto Rico, and

the Virgin Islands) ; and (2) any State with part thereof in more than one time zone (Alaska, Florida, Idaho, Indiana, Kansas, Kentucky, Michigan, Nebraska,

North Dakota, Oregon, South Dakota,

Tennessee, and Texas). (Section 3(a)).

If a State elects to exempt itself, the ex- emption must apply to the entire area of the State lying within one time zone, and the effect of the exemption must be

to put the entire State on uniform time

(I.e., the exemption can only apply to that part of the State in the more easterly zone) (see H. Rept. No. 93-709 at 5)

.

Section 3(a) permits States to exempt

themselves from advanced time by law

enacted anytime during the period the Act la in effect. The »»»mpti«n must, however, be complete; a State may not

elect to exempt Itself from advanced time

during winter months but observe ad- vanced time during summer months.

Section 3(b) of the Act permits the

President to grant a State an »ra»p««n

from the advanced time established by

section 3(a) of the Act or a request tor realignment of the existing limits of time

zones, If the State, by proclamation of

t, VOL 39, NO. 7—THUtSOAY, JANUARY

its Governor, makes a finding prior to Sunday. January 6, 1974—the effective date of the Act—that such exemption or realignment is necessary to avoid undue

hardship to large segments of the popula-

-State or part thereof. ("[The President's] decision should be based on the appropriateness of all aspects of any ex- emption, including convenience of commerce, possible energy savings, or undue

hardship to large segments of the population, as well as the possible impact on

the success of and cooperation with the national energy conservation program."

S. Rept. No. 93-504 at 3.) By Executive Order 11751, issued December 15, 1973, the President has

designated and empowered the Secretary

of Transportation to exercise the authority vested in him by section 3(b) to grant the exemptions or realignments. Procedures and criteria for implementation were issued by the Secretary

(49 CFR Part 73. 38 FR 34876). The Governor of the State of Idaho, the Honorable Cecil D. Andrus, by

proclamation issued December 28, 1973, requests that the entire area of Idaho

located within the mountain time zone be exempted from observance of ad- vanced time during the effective period

of the Act. The Governor of the State of Oregon,

the Honorable Tom McCall, by proc- lamation issued January 2. 1974, requests that any determination made with

respect to the mountain time zone sec- tion of Idaho apply equally to that sec- tion of Oregon which is in the mountain

zone (northern Malheur County), since

failure to apply any Idaho exemption to

this County would create an "island" one

hour ahead of all surrounding areas. The proclamation and supporting data submitted by the Governor of Idaho

establish that the State is located on the boundary between the mountain and

Pacific time zones; that the northern

portion of Idaho Is located in the Pacific time zone and the southern portion in the mountain time zone; that permitting the requested exemption would result In observance of a single time throughout

the State; that energy conservation would not occur were advanced time observed in the southern portion; that winter daylight time observance would

severely disrupt outdoor Industry, such

as forestry, and school operations in the southern portion of the State; and that commerce would not be disrupted. Several television broadcasting companies operating within southern Idaho

state that their services would be adversely affected If the requested exemption is granted. Their network program- ming is received through the mountain

time zone, and they note that "prime

time" broadcasts would occur between

6 and 9 pm., If advanced time Is not

observed, rather than between 6 and 10

p.m., if advanced time Is observed. The

broadcasters state that purchase and use

of tape delay equipment would not be

economically feasible. Other comments have been received from several Idaho residents generally

supporting or opposing the requested ex- emption.

10, 1*74

412
Title 49 — Transportation

extreme hardship to school children,

agriculture, and industry requiring daylight working conditions; that the convenience of commerce would be served by western Kentucky counties observing the same time as adjacent areas In Tennessee and Indiana; and that the pro- posed realignment would not be detri- mental to the national energy conservation program. The data submitted also

establish that the twelve counties which

would remain in the eastern time zone

are commercially related to adjacent

areas In Ohio and West Virginia, and

that the convenience of commerce would

best be served by their continued observance of the same time as those areas. Although section 3(a) of the Act contemplates State legislative action to achieve an exemption from observance

of advanced time within one time zone

of a State with parts In more than one

zone, the proposed realignment may be

obtained only under section 3(b). Upon consideration of the proclamation and supporting data, I find the re- quested realignment of the limits of the

eastern and central time zones within Kentucky is consistent with the objectives sough to be achieved by the Act. During the effective period of the Act,

therefore, the limit between the eastern and central time zones In the Commonwealth of Kentucky shall be denned as

follows: From the junction of the east line of Spencer County, Indiana, with the Indiana- Kentucky boundary northerly and easterly along that boundary to the wee* line of Boone

County, Kentucky; thence southerly along

the west line of Boone County to the north

line of Grant County; thence west along the north line of Grant County to the west line

of Grant County; thence southerly along the

west line of Grant County to the south line of Grant County; thence easterly along the

south lines of Grant and Pendleton Counties to the west line of Bracken County;

thence south along the west line of Bracken County to the south line of Bracken County;

thence easterly along the south lines of Bracken, Mason, Lewis, and Carter Counties

to the west line of Lawrence County, thence

south along the west line of Lawrence County to the south line of Lawrence County;

thence easterly and northerly along the south

line of Lawrence County to Its junction with

the Kentucky-West Virginia boundary;

thence southerly along the Kentucky-West

Virginia boundary to the Kentucky-Tennessee boundary; thence west along the Kentucky-Tennessee boundary to Its Junction with the west line of Scott County, Tennessee. Because of the emergency nature of the Act; the Congressional Intent that It be Implemented quickly; 1 the short period of tune between its enactment December 15, 1973, and its taking effect January 6, 1974; and the short period

of time between the date of the proclamation—January 3, 1974—and January 8, 1974, 1 find that notice and public procedure on this action are contrary

to the public interest and that good cause

»-|The secretary] should at quickly and

expeditiously. Failure to do will risk serious Inconvenience and uncertainty." See Senate

Report No. 93-604 at g.

exists for making It effective in fewer than 30 days after publication In the Federal Register. For these same reasons it has not been possible to assess the need

for, and, If necessary, to prepare an en- vironmental Impact statement on this action. See section 102, National Environ- mental Policy Act of 1969 (January 1. 1970, Public Law 91-190, section 102, 83

Stat. 853; 42 U.S.C. 4332)

.

This action is taken pursuant to sec- tion 3(b) of the Emergency Daylight

Saving Time Energy Conservation Act of 1973 (December 15, 1973, Pub. Law 93-

182, section 3(b) , 87 Stat. 708) ; Executive Order 11751 (38 PR 34725) ; and Part

73 of the Regulations of the Office of the

Secretary of Transportation (49 CPR

Part 73). Effective date. This action is effective 2 a.m. central nonadvanced (standard) time Sunday, January 6, 1974. Issued in Washington, D.C., on Jan- uary 4, 1974. Claude S. Brihegar,

Secretary of Transportation.

(PR Doc.74-767 FUed l-»-74;8:4fl am]

(OST Docket No. 34, Notice No. 74-3) IDAHO AND OREGON

Emergency DayHght Saving Time

Exemptions

The Emergency Daylight Saving Time

Energy Conservation Act of 1973 (December 15, 1973, Pub. Law 93-182) ("the Act") advances the standard time by one hour In all eight standard time zones of the United States continuously from 2 : 00

a.m. Sunday, January 8, 1974, to 2 ajn.

Sunday, April 27, 1975, and provides that

the time as so advanced shall be stand- ard time

Two classes of States are permitted to exempt themselves from advanced time:

(1) any State which is entirely within one time zone and not contiguous to any

other State (Hawaii, Puerto Rico, and

the Virgin Islands) ; and (2) any State with part thereof In more than one time zone (Alaska, Florida, Idaho, Indiana,- Kansas. Kentucky, Michigan, Nebraska,

North Dakota. Oregon, South Dakota,

Tennessee, and Texas). (Section 3(e)).

If a State elects to exempt Itself, the ex- emption must apply to the entire area of the State lying within one time zone, and the effect of the exemption must be

to put the entire State on uniform time

(i.e., the exemption can only apply to that part of the State In the more easterly zone) (see H. Rept. No. 93-709 at 5). Section 3(a) permits States to exempt

themselves from advanced time by law

enacted anytime during the period the Act Is in effect. The exemption must,

however, be complete; a State may not

elect to exempt itself from advanced time

during winter months but observe ad- vanced time during summer months.

Section 3(b) of the Act permits the

President to grant a State an exemption

from the advanced time established by

section 3(a) of the Act or a request for realignment of the existing limits of time

zones, if the State, by proclamation of

its Governor, makes a finding prior to Sunday, January 6, 1974—the effective date of the Act—that such exemption or realignment Is necessary to avoid undue

hardship to large segments of the populaState or part thereof. ("[The President's] decision should be based on the appropriateness of all aspects of any ex- emption, including convenience of commerce, possible energy savings, or undue

hardship to large segments of the population, as well as the possible Impact on

the success of and cooperation with the national energy conservation program."

S. Rept. No. 93-504 at 3.) By Executive Order 11751, issued December 15, 1973, the President has

designated and empowered the Secretary

of Transportation to exercise the authority vested In him by section 3(b) to grant the exemptions or realignments. Procedures and criteria for Implementation were Issued by the Secretary

(49 CFR Part 73, 38 FR 34876). The Governor of the State of Idaho, the Honorable Cecil D. Andrus, by

proclamation issued December 28, 1973. requests that the entire area of Idaho

located within the mountain time zone be exempted from observance of ad- vanced time during the effective period

of the Act. The Governor of the State of Oregon,

the Honorable Tom McCall, by proc- lamation Issued January 2, 1974, requests that any determination made with

respect to the mountain time zone sec- tion of Idaho apply equally to that sec- tion of Oregon which is in the mountain

zone (northern Malheur County), since

failure to apply any Idaho exemption to

this County would create an "island" one hour ahead of all surrounding areas. The proclamation and supporting data submitted by the Governor of Idaho

establish that the State is located on the boundary between the mountain and

Pacific time zones; that the northern

portion of Idaho is located in the Pacific time zone and the southern portion in the mountain time zone; that permitting the requested exemption would result in observance of a single time throughout

the State; that energy conservation would not occur were advanced time observed In the southern portion; that winter daylight time observance would

severely disrupt outdoor Industry, such

as forestry, and school operations in the southern portion of the State; and that commerce would not be disrupted. Several television broadcasting companies operating within southern Idaho

state that their services would be adversely affected If the requested exemption Is granted. Their network program- ming is received through the mountain

time zone, and they note that "prime

time" broadcasts would occur between

5 and 9 pm.. If advanced time Is not

observed, rather than between 6 and 10

p.m., If advanced time Is observed. The

broadcasters state that purchase and use

of tape delay equipment would not be

economically feasible. Other comments have been received from several Idaho residents generally

supporting or opposing the requested ex- emption.

FEORAl tfOISTft, VOL. 39, NO. 7—THURSDAY, JANUARY 10, 1*74

413

SUBJECT INDEX

A Page A. 1 time (USNO) 320

Abbreviations

international organizations 324

time and frequency listing 458

Absolute frequency 321 Absorption 72, 131 beam 131, 132

cell , 84,130

frequency, electromagnetic 128

laser radiation, simple 131 microwave 97

probability 78

saturated 129, 133, 134, 142

iodine 131 methane 107, 131 A—C power utilities in the continental U.S 298 ACAS (Aircraft Collision Avoidance System), T/F 288 commercial 289

evaluation for TFD 289 ground timing system 289

walk-in T/F service 289

Acceleration, stress, vibration (crystal units) 50, 61

Accessibility, UTC(NBS) 221,222

Accuracy 81, 103, 124, 153 AT-NBS time scale 219, 220

atomic time scale 4, 219

algorithms 215 AT(NBS) 220, 322

construction and maintenance 207 NBS 113,219 TAI 27, 207, 223 USNO (A. 1) 322

capability

frequency standards 124, 127, 133

historical developments 139 NBS-III (1969) 115 NBS-5 (preliminary error budget 1973) 124

SI base units 140 cesium 81,95,104,113,124

clock 277, 317

date transfer 300

definition 139, 153, 238, 317

dissemination (T/F) techniques 300

frequency

standards 96, 104, 113, 124, 139

synchronization 300

laboratory cesium standards and precision of clock rate or frequency standards 104, 208

levels of service (satellite) 277

operation skill required for T/F comparisons 302 primary frequency standards 113, 121, 127, 146

rate of AT(NBS) time scale 219, 223

received, radio broadcast carrier 282

synchronization 208 TAI time scale 223

time 153 WWV broadcast transmissions 247 Accuracy users (TFD)-low, intermediate, high.. 299

Acoustic loss (crystal) 46, 59

Active device 72, 78

Active-line TV 265

capabilities and limitations for TFD 267 experiment 267

Activer maser oscillator 128

Additive noise 54, 240 Advanced T/F systems using radio techniques 284 415
Page Advantages of T/F dissemination techniques

a-c power (60-Hz) 299

aircraft flyover 294 commercial (stabilized) broadcasts 282 hardwire distribution systems (telephone, coax line) 297 HF broadcasts 251 LF broadcasts 246 Loran-A navigation system 257 Loran-C navigation system 256 MBTS system 287 microwave system (SHF) 282 Omega navigation system 253

portable clock method 292

pulsar optical time transfer 296

satellites 280

television methods 264, 265, 267 TF-ACAS 289 VHF reflection from meteor trails 284 VLBI clock synchronizations 285 VLF broadcasts 244 AEP (American Electric Power) Co 298 Aging 48,49.61.167

clock 208

crystal 48,49,61,290

frequency 158

rate 49, 167

time 48

Aircraft Collision Avoidance System (see ACAS)

Aircraft flyover synchronization 293

evaluation for TFD 294 one-way method 294 two-way method 294

Algorithms

atomic time scale 215

first and second order time scale 216 mini-computer program 227

time prediction 214

Allan variance 114, 123, 157, 165, 209 computing counter program 182 discussion 165 equation 166, 178 sample calculation 181 Ambiguity 238,300

cycle (VLF) 243

position, navigation 251 power system (60-Hz) 299 American Electric Power (see AEP)

Ammonia

beam maser 92, 131, 133

clock 93, 140

inversion transition 92 maser 92

Amplifiers, operational 169 low noise 169 Amplitude distribution 46 Analog

spectrum analyzers (frequency domain) 164

to digital converter 168

voltage 164 Angular momentum

electron 69, 71, 73

total 76 Anharmonic overtone, quartz 60 Antenna pointing charts (satellite) 277 APC (Automatic Phase Corrector) telephone lines 297 Apparent solar time 5

Applications, line of sight radio dissemination 240

Astronomical time 13 scale 5

416
Page Astronomy stations (USNO)

Richmond, Florida (near Miami)

Washington, D.C

Asymmetry, spectral AT(atomic time) AT(NBS)

accuracy rate calibration with NBS-5 frequency standard

clock ensemble

rate measurement system (chronograph) time scale

errors of 6 selected cesium clocks overview system

block diagram AT-cut plates, quartz crystal units Atomic

beam , cesium

Dunoyer's apparatus frequency standards

Frisch-Segre technique

magnetic resonance techniques

techniques

thallium devices tubes (cesium) clock cesium

world's first (ammonia)

worldwide synchronization

frequency

control of HF radio broadcasts (emissions) energy levels standards

availability capability

historical development

increasing use major examples

physical basis recent progress in development

side by side comparison

state of the art hydrogen

hyperfine splitting maser

properties spectra

state, change of time

time scales

(also see Time scales)

differing techniques for construction and maintenance

NBS-generation, stability, accuracy and accessibility.. NBS system, AT(NBS) TAI (see TAI)

unit of time interval

velocities Atomichrons Atoms n.^i

alkali metals barium oxide cesium

change of state

criteria for choosing

electrical charge energy helium hydrogen

energy level for ground electronic state interrogation of magnetic moments

mercury

nuclear

321 320

128

7, 223

207, 214, 222, 262

219, 220, 224

220

215

215

207, 214, 223, 264

219

207

214 214

44, 59

67, 83, 87, 88

80, 87, 121 87

67, 71, 83, 93, 96, 103, 113 88

878887,96

127

4, 207, 317

140

93, 140

290, 294

251 67,69

67, 72, 83, 87, 113, 121, 127

103

143, 302

87, 103

103

7867

103

95, 290

104, 113, 121, 214

91

87, 97, 105, 113

70

73

71, 88

7, 95

7, 207, 320

207

207

214, 320

95, 208

122

95

67, 71 77

131

77, 95, 153, 319

71, 90

73, 77

67

68. 69, 73. 75-77

68

70. 73, 74, 92, 98 69,91

127

72, 77, 89

90, 131 69 417
Pase orbital angular momentum number 73 potassium 75, 88 energy level diagram for emission electron 75

properties 70 rubidium 77,81,97

silver 87, 88 sodium 87, 91, 96

spectra 73

thallium 96

velocity 72 ATS-1 (Applications Technology Satellite-1), NASA 272 VHF transponders 270 ATS-3 272

experimental work with satellite 276

timing studies 277 Audio tones (HF radio broadcasts) 248

Auto-correlation functions 209 Automatic Phase Corrector (see APC)

Automation system (time scales) 219 Average

clock ; 320

frequency 165 one second (frequency stability) 133 sample, independent estimate of Sj/(/) 165 time 157

variance 165 B

Balmer series 73 Bandwidth

frequency measuring equipment 159

servo 169, 170

Baselines, widely separated (VLBI) 284 Base units of measurements 10, 139, 140, 318 comparison of accuracy capability 140

Basic standards '. 127. 145, 319

Battery bias box

(frequency stability measurements) 169 Beam

absorption in 131, 135 atomic (see atomic beam)

atomic frequency standard 93, 131 broken-technique 92 cesium 80. 87. 94, 95, 107. 113, 121, 127

clock 290

laboratory device 93-95. 104, 214

particle 143 cryogenic source 107 double-system 116 hybrid optics 108 hydrogen standard 79, 94. 95, 105, 106, 131, 132

intensity 121 long 95 maser, storage 132 molecular 87

multiple 107

optics 105, 122 alignment 124

hybrid 108

particle system 141

reversal 104, 113, 114. 121

storage, principle 132. 135 tube 131, 133 barium oxide 131 cesium 87. 121. 127, 131. 133. 143 helium 131 hydrogen, storage 131-132 mercury 131

particle 143

smaller 107

storage 106, 131. 132, 135

thallium 87, 96, 131

traveling 131, 132

418
Beat-frequency technique 162 Bias 110, 123. 124, 127, 218

cavity phase difference 121, 123

collisions 130

corrections 134

deterministic 153 frequency 123, 130

correction 115

functions 160, 190

B, and B 2 (tables) 192-204

general 161 variances 176

uncertainties 124. 128. 129

wall shift 134

Bibliography (also see reference listings at end of each chapter) atomic frequency standards 84 frequency stability r. 182

future trends in accurate frequency/time metrology 148 time scales and their formation 230

time/time scales 14 BIH (International Time Bureau) 10, 19, 23, 33, 207, 223. 324 NBS/USNO interactions 321 UTC 10.23,25,220,322

BIPM (International Bureau of Weights and Measures) 324

Black body radiation 68. 71 Bloch-Siegert

effect 141 frequency shift 129 Bohr's model 67, 68

theory 70. 71, 74 Broadcasts 240, 319

atomic frequency control of HF 251

carrier, received accuracy 282

format of WWV, WWVB, WWVH 246, 249

location of stations for TFD service 241 NBS, standard frequency 247, 321

reference for NBS T/F 207, 248. 319

stabilized carrier (commercial) 282

standard time and frequency (emissions) 31, 238

allocated band (chart) ( 311

outside allocated band (chart) 312

U.S. Navy time signal 321 Broken-beam technique 92

Buffer gas 82. 96. 132, 142 techniques 91,97 Bureau International de l'Heure (see BIH)

Bureau International des Poids et Mesures (see BIPM)

c

c (velocity of light), denned value 127, 145

C-fields 79-81. 89. 115 Calendars 317

Calibration AT(NBS) time scale with NBS-5 220

cost 301

delay 238

frequency 114 standard 214

local standard 267 microwave frequency stability 173. 187 NBS-III primary frequency standard 113. 214 NBS-5 primary frequency standard 121, 215

precision 218 PTTI standards/facilities 365. 371 remote oscillator 267

Capabilities, time dissemination techniques 300 Cathode ray experiment (electron) 67

Carrier-to-noise ratio.... 161

419
Cavity

coupling

discriminator

phase-difference bias phase shift

offsets.. pulling

effects frequency shift Q

Ramsey type resonance CCDS (Consultative Committee for the Definition ol the Second) , recommendations at 6

th session CCIR (International Radio Consultative Committee)

Recommendation 460 Study Group 7 Celestial navigation motion of bodies

Cell, absorption

Cesium

accuracy atom

atomic beam

commercial

device

transition tube beam diagram

clock performance

time errors gas cell standard

oscillator particle beam tube resonance frequency

reference standard

transition frequency

Cesium beam standard commercial improvements

early forms

electronic systems

frequency

high-performance tube

laboratory device accuracy trends (1956-1973)

state-of-the-art C-fields errors longitudinal structure CGPM (General Conference of Weights and Measures)

Chains, frequency multiplier

Change of state-atoms

Characteristics broadcasts (F/T) in allocated bands

emissions (F/T) outside allocated bands

frequency stabilized navigation systems Loran-C stations radio frequency bands 4 to 10 Characterization of frequency stability Charge distribution for ground states of several elements

.

Charge to mass ratio , Chief of U.S. Naval Operations, transferring responsibility. Chronograph-AT(NBS) rate measurement

Chronometer CIPM (International Committee of Weights and Measures).

Page

81, 128

173 173

121, 123

104. 124

130

98, 128. 129

106 98

173

113, 121, 130

129

10, 324

39

323. 324

31324

6, 11. 317 320

84. 130

77, 80, 94-96, 103, 122 81,96, 104, 113, 121, 133, 146

77, 95, 153, 319

80. 87. 94, 98. 127. 145

95. 96, 107 87

81, 95, 319

127, 134 80

218. 290

140 219

96263

143

81, 127. 319

87. 267

95, 113, 121

81, 95. 122. 127

80, 87, 103, 107, 127, 145, 214

95, 96, 107, 114, 290

95. 108 93-95

105. 114. 121

67. 87, 113. 145

108

94, 103, 121, 145, 214

104

104. 121 79-81. 89

105

105

108

10, 17, 323

114, 122

71

311 312

313

254, 313 310a

154

7567,69

349

215

13323

420
Page

Circuit, electrical equivalent (quartz crystal) 44. 59

Circular slide rule (satellite propagation delay) 277, 278

Classification of time and frequency users 299 Clock • 3, 4, 93, 94, 114, 140, 153. 208, 290, 317

aging 208 ammonia 93, 140 atomic 140, 317

scale, international comparison 291, 294

average 320 cesium commercial . *- ly time errors 219 performance 14G, 223

characterization 216 commercial cesium 95, 218

coordination 321, 381

definition r. 153, 208, 235, 317 ensemble 215 AT(NBS) 215 frequency stability 216, 218 NBS 114 primary function 219

time dispersion 219

errors 161.209

first atomic 93, 140

"flying experiment" 95, 290

frequency drift 209 master 240, 271, 379 USNO 272,379

modeling 208, 224

noise characterization 212

on-board, satellite 269, 271. 273

on-line 216

on-site visits 292 "paper" 227

portable 95. 290

quartz crystal 218. 290

first 290 random perturbation of time 209

rate/frequency, accuracy and precision 208

resynchronization of remote 253

slave 254, 271

synchronization 153, 208, 238, 295. 317 accuracy 208, 277

basic techniques of system 238

initial 243

intercontinental precision 285 remote locations 259, 262, 277

widely separated 271. 290

transition 128 Coax

cable distribution, T/F signals 297

evaluation of hardwire systems for TFD 297, 298

transmission of phase data over lines 297 Codes IRIG-H time 250

transmission of DUT1 34 WWV-lOOHz 248 WWVB-time 246 Coherent communications systems 237

Collimator, oven 121

Collision-narrowing effect (buffer gases) 91 Color subcarrier (see television) Commercial-radio broadcast TFD technique 282

evaluation for TFD 282 Commercial frequency standard cesium 95,96.107,114,290

rubidium 97, 108 Communication satellites 276 Compromise time scale 13, 318

421
Page Computer (frequency stability measures)

analysis, time data 170

on-line processing 215 program (Allan variance) 182 Concepts

dissemination, T/F 235 frequency stability 156 primary frequency standards 133 time 4 time and frequency 10, 208 Confidence of the estimate 164 Confinement techniques 129,141

Confining particles (effects on frequency) 129. 130 Conservation of charge 71 Conservation of electromagnetic spectrum 257, 302

Consultative Committees (International) 324

Continental drift 284

Contours, satellite path delay 277 Convergence, power law spectral densities 165 Conversion

chart-stability measures (Frequency domain-time domain) 166

fractional frequency to time stability 222 Converter

analog to digital 168

voltage to frequency 170 Coordinate time scale, UTC(NBS) 207, 220

Coordinate Universal Time (see UTC)

Coordinates of the pole 323. 384

Coordination agreement (NBS/USNO time scales) 220. 381, 382 Corpuscular theory 71 Corrections

lunar topography (TFD) 287 VLF broadcasts 243

Cost, users' effectiveness (dissemination techniques) 222. 238 Counters

computing-time domain measurements 174 frequency 157, 163, 167 Crab Nebula Pulsar 294

Criteria, frequency standard characteristics 77 Cryogenic beam source 107

Crystalline body vibration 60

Crystals (also see Quartz crystals) 43. 59 Cycle

identification (VLF) 243, 252

per second (Hertz) 10, 70, 140

slip (low frequency radio) 245 D

Data

analysis (T/F) statistical 153, 181 concepts for primary frequency standards 133

filtering 216

simulation 212

translation from frequency domain to time domain 178 uniform methods of reporting 175 Date 4,153.208,235,317

accuracy of transfer 300

events of a leap second 34 DC resistance-phase sensitivity (hardwire TFD) 297 Dead time in the frequency stability measurement process 164 Decoders. IRIG time code 250 Dedicated telephone lines (TFD) 297 Defense Satellite Communication System (see DSCS)

Definitions accuracy 139, 153. 238

clock 3.153,208.317

date 4. 153. 208, 317

deviations, random/non-random 153 epoch 4, 153, 208, 317

422
equation of time frequency

frequency stability measures of hertz

identification (TFD)

leap second

precision

reproducibility second

simultaneity

stability

statistical models

synchronization time

astronomical atomic r ephemeris

GMT

interval sidereal SI unit TAI UTO

UT1

UT2

UTC

UTC(BIH)

time scale Delay

computer, satellite differential path

radio propagation

satellite motion variability path contours

theoretical prediction (propagation)

time, propagation Demodulator (FM)

Densities, spectral (also see spectral density)

Description of radio frequency bands 4 through 10 Detection of particles Deterministic

biases

properties Deviations frequency, quartz crystal random/non-random

Dielectric constants, quartz material Difference frequency

Differential delay measurements (TV, line-10) path delay

phase noise measurements

Digital time dissemination

Dipole transitions Director of NBS, responsibilities Discriminator

cavity '. frequency

Dispersion

frequency

time

Dissemination compromises in choosing a service concepts

system

characteristics

Page 6

10. 70, 140, 153, 237

154

156

10, 70, 140 238

9, 34, 220

154

154

11, 17, 127, 139, 140. 153, 209, 319

4, 153. 208

154, 155

155

4, 153, 208

5, 153, 371

5, 13

76

6

10. 208. 371 6

17, 208

10, 19, 27 5

6

6

8

10, 26

4, 207, 317

277

298

270. 277

240, 259

271 277

243

237, 238, 269

173

156, 157, 177, 178 310a

78, 128

173 208

50

153 45

167. 243

298

260

259

171 266

130

318. 335

173 164

244

219, 220

302

235

239

237

423
Page Dissemination (T/F) techniques 221, 222. 235

Aircraft Collision Avoidance System (ACAS) 288

aircraft flyover 293 coax cable 296 commercial radio broadcasts 282 HF radio broadcasts 247 LF radio broadcasts 245 Loran — A navigation system 257 Loran — C navigation system 222. 253 meteor trail 283 microwave signals 281 Moon Bounce Time Synchronization (MBTS) 286 Omega navigation system 251

portable clock 290 power line (60 Hz) system 222.298

pulsar optical time transfer 294

radio methods 239

satellites 222. 223. 269

telephone lines 296

television systems (TV) 222, 259 Very Long Base Interferometry (VLBI) 284 VLF radio systems 241 Dissemination (T/F) techniques, comparison-evaluation 301

fractional frequency stability vs function of sample time 221 Dissymmetric modes, crystal 48

Distance gap between T/F source and user 235

Diurnal changes

phase, low frequency 242, 245, 310a

resistance of phone line 296

Diversity techniques, radio reception 247 DOD directive No. 5160 (T/F responsibilities) 320, 365 Doppler

effect 98.141,143.269

first order : 81.130,133,141,142

second order 121-124, 141 measurements 273

radar 161 ranging 288

shift 80,115,130,271

second order 105, 115, 130, 131. 142 Double-beam system (atomic frequency standard) 116, 121 Double resonance techniques 90. 96

Drift 43,48

compensation, quartz crystal 50. 61

continental 284

correction 290 frequency 167, 210

linear 158, 167

long-time, quartz crystal 48

rates 43, 158, 209

Drive level, crystal frequency stability 50, 61 DSCS (Defense Satellite Communication System) 276 network 281

timing tests 276 Dual rate moon camera 320

Dunoyer's atomic beam apparatus 87 DUT1 33, 245

transmission code 35

E

Earth

coverage by satellites 269 magnetic field 79

orbital motion 285

rotation rate 7

satellite (TFD) 269

sun, moon relationships 5 Einstein

photoelectric effect 68

theory of special relativity 71

424
Elastic constants, crystal Electrical charge-atoms

equivalent circuit, quartz Electromagnetic (EM)

absorption frequency

field, energy of radiation spectrum, conservation of wave

Electron angular momentum

collisions emission

intrinsic magnetic moment

mass

spin

velocity Electronic frequency standards, quantum

problems, laboratory cesium beam standards systems

Electrostatic magnetic forces

state separator Emergency daylight saving time Emission

electrons

probability

spectral, lines spontaneous

Enclosures, crystal Energy

atoms

difference electromagnetic (EM) field levels atomic frequency cesium

hydrogen atom

lithium many-electron atom

mercury

potassium rubidium

shifts spin-additional

transitions

states

total E

transition states trapping, crystal units Ensemble

clock devices AT(NBS) clock

time, calculation Envelope timing measurements (VLF)

Environment (oscillator signal generators)

Ephemeris reference tables, time of coincidence (TOC)

Loran-C TV

Ephemeris Time (see ET)

Epoch

Equation of time

Equatorial satellite Erogodicity Errors clock Loran-C timing

signal processing equipment

wall shift

Page 45

67

44, 59

71, 128

68, 71

68, 71 257

71

67, 69, 70, 74, 130

71, 73

130

75

70, 71 69

71, 73, 88

69

127, 131

105, 121

95. 114

74

92

408. 411

75

78

88

72, 128

44, 45, 61

67, 129-131

68, 69

76

68, 72

73, 75. 76, 78, 88, 130

67, 69

81

69, 73, 76, 79, 98

89

7390

75, 88

82, 97

129

70

69, 71, 72, 74, 88, 90

67. 131, 141 69

88

46, 48, 60

215, 218-220

154, 155 215

216

252

52, 155

255, 384

263, 384

4, 153, 208, 317

6269

155

161, 219

256

164

79. 98. 106. 134

425
Page ET (Ephemeris time) 6, 95, 317

Evaluable primary frequency standards 207, 219, 223

Evaluation NBS-III 113 NBS-5 121, 215

time and frequency users and systems 300 Exchange spin 129, 130

Excitation frequency 89, 93

pulsed microwave 104

state levels 90 Experimental work ATS -3 satellite 277

Exponential

prediction 213,218

weighting filter 212 F

Factors affecting radio propagation 310a FAGS (Federation of Astronomical and Geophysical

Services) 324

FC-cut (crystal) 60

Federation of Astronomical and Geophysical Services (see FAGS)

Figure of merit 116, 128

Filter adjustable RC 169

exponential weighting 212 low pass 162, 171 optimum 210, 212

flicker 226

various noise processes 225

recursive 226

First ammonia clock 93, 140

order Doppler shift 98, 130, 133, 142 time scale algorithm 216 minicomputer program 227

quartz crystal clock 290

Flexure (crystal units) shear modes 44, 59

type 49

Flicker-frequency noise 114, 178

Flicker noise 62, 158, 226

flicker of phase and DC 62, 114 frequency modulation (FM) 7, 158, 210-213, 298

time dispersion with recursive filter 226

predictors for 213

Fluctuations measure of phase (frequency domain) 114

oscillator frequency 54 random 166 Flux of signal particles 128 "Flying clock measurements" 95, 290 FM noise 164 Foamed mounting (quartz units) 52 Focusing magnets 104 Formats HF radio broadcasts 247 Loran-C navigation system 255 Omega (proposed) 253 WWV, WWVH broadcasts 249 WWVB one-minute time code 246

Fourier frequencies 156

transformations 158, 179. 210

426
Fractional frequency

conversion to time stability differential deviation, pulsars

fluctuation spectral density

offsets

stability power line (60 Hz) data

relative versus sample time for several TFD techniques.... TAI

television color subcarrier measurements

line- 10 data Frequency

absolute

stabilization of a TV transmission accurate measurements

survey

aging

averaging

basic concepts

beat or difference

biascorrection broadcasts (standard)

calibration cesium beam

transition characteristics criteria clock drift comparison

zero-beat method

control (HF broadcasts) counters

cutoff dependence of various "noise" types

deviation

error expander

difference discriminators

dispersion time scale memory

dissemination (also see Dissemination T/F techniques)

domain

measures of phase fluctuations

translation to time domain

drift electromagnetic absorption

excitation

flicker noise

fluctuations

fractional measurement

spectral density variances

free atom

hertz (unit of frequency)

high transition hydrogen

resonance terms of cesium

transition frequency

infrared synthesis

lock, servo system measurements (also see measurement freq.) accurate

significance and impact

survey of selected throughout EM spectrum

Pane

222

295

166

8, 209

114-116, 128, 156, 216. 217

299

114 265

223

265

261. 262

10. 43. 60. 70. 127, 140. 153. 208. 237

321 263 140-142 142-144

158

165

10. 208

162. 167 123 115

240. 241

114, 121

93. 113

81. 95, 122, 319

77209 292

250

248

157, 163, 167 159 167 50

168

116, 243

164 244

220

235

157, 211

114, 155, 167, 168 159

167, 210

128 89

114. 178

164, 167

177

167

54. 156. 165. 178

164

78

10. 70. 140

130. 134

106 98

107

142

95, 114

139

144

143

427
Page microwave 71, 99, 142, 173 modulation (FM) 114 demodulator 173 white noise 210

multiplication 114,167

multiplier chains 94

noise (see Noise) 158

offset 210 UTC from 1960 to 1972 8 output 127 permanent change (crystal) 51

radiation 72

radio (RF) bands 4 to 10, description 310a

response 164 rubidium transition 82

shift keying (FSK) 244

shifts 97,142

short-term changes 49

signal (carrier) variable 178

sources, high precision-state of the art 62

stability (see Frequency stability) stabilization commercial broadcast stations 282 TV color subcarrier 263 TV transmissions 262

standards (see Frequency standards)

step 220

survey-accurate measurements 144

synchronization, accuracy of 300

temperature drift compensation 50

time

Division (NBS) 319. 361 metrology 127, 140. 145, 148, 237

performance, precision quartz oscillators 49

signal emissions CCIR recommendation 460 31, 32

in allocated bands 241, 311

outside allocated bands 312

transformation 128, 132

transition 77, 130, 141

unified standard 127, 145 white noise 115 window 164

zero-beat method of comparison 250 Frequency and time metrology 127, 140. 148, 195, 237 NBS Division responsibilities 319, 322, 361 USNO (Time Service) Division responsibilities 320, 322. 371 Frequency band, RF transmissions 310a Frequency domain 155, 157, 168 analog spectrum analyzers 164

characteristics of various power laws 211 frequency stability 166 measurements, 168 time domain 168

translation to time domain 159, 178 measures

phase fluctuations 114

stability 178 Frequency stability 43, 60, 61, 105, 114, 123, 128, 154, 159, 165

applications of specifications and measurements 165

bibliography 182

calibration procedure, microwave 173

characterization of 154

clock ensemble 220

color subcarrier (TV) 265

concepts of 156

428
Page crystal oscillators 43,48,62

definition 154

fractional (see Fractional stability) measure (spectral density) 165 measurements

definitions 157 hazards in 164 HF regions 168 microwave region 171, 188

calibration procedure 173, 187 techniques 162 X-band 174 one-second averaging 133

quartz crystal 43, 48, 62

statistical models 155. 209 summary of measures 165

systematic trends - 158

variations 158 terminology specifications 165

translations among measures 159

chart-time domain

frequency domain 166. 178 Frequency standards 62. 72. 77, 78, 87. 103, 113, 121. 127, 146, 208. 209 accuracy 95, 105, 113, 121, 214

capability 115. 124. 127. 133, 146 primary 121. 146 atomic (see Atomic frequency standards) beam 73.80.81.88,96

basic 144. 146. 319 cesium (see Cesium beam standard)

characteristics criteria 77 commercial 95. 96. 98. 107

effects on frequency

particle confinement 129

interrogation 128

preparation 131 frequency/temperature drift compensation (quartz) 50

future areas of promise for development 127

historical development 87 hydrogen (see Hydrogen)

international comparisons 95, 290

laboratory 93. 94, 103. 113. 121, 146. 214

accuracy trend, 1956-1973 104

stability performance data 105 Mean Time Between Failure (MTBF) 9. 96

National Bureau of Standards (NBS) 93 94 113 121 214 NBS-III 113 accuracy capability (1969) 115 NBS-5

accuracy budget 124

(preliminary 1973) fiequency stability 122 primary

calibration 95. 97, 113, 121. 214

candidates for 146 concepts for 78, 133

evaluable 207, 223 improvements in 103, 113. 121 memory of the rate 223 NBS and measurement system 121, 214 quantum electronic 127, 131 secondary 78

stability 62, 105. 122

state of the art 104, 113, 121, 127. 214

thallium 87. 96 rubidium 82,97

commercial 97, 108 USA 315

429
Frequency-time domain 157

Characteristics of various power law 211

chart translation 166, 178 measures of frequency stability 157, J68 techniques 168

translation among measures 159, 166, 178

Frequency-transitions (also see applicable atoms) 77, 130, 140 coupling 130

particles 130, 134

Frisch-Segre atomic beam technique 88

Functions, auto-correlation 209 Fundamental constants base set of 139, 145 knowledge of 145 Future

developments-crystal oscillators 55. 62 primary frequency standards 107, 127, 139

trends, accurate F/T metrology (Bibliography) 148

G

Gas cell 81, 87, 89-91. 97, 131-133 cesium 96

factors limiting performance 97

optically pumped 82, 90, 97, 132 maser 132

passive 132 rubidium 81. 89, 97, 131-133

standards 97, 132 temperature 97 General Conference of Weights and Measures (see CGPM)

General theory of relativity 144

Generators, power utilities 237 Geometry of VLBI receiving sites 284 GEOS-II (satellite) 272

Geostationary satellite 223. 271

Global geodesy 284

time synchronization 290, 294

Glossary of time and frequency symbols 176 GMT (Greenwich Mean Time) 6, 11 Gradients, magnetic field 106

Gravitational

potential, difference in 220

shifts, relativistic 271 Greenwich. England-meridian 11 Greenwich Mean Time (see GMT)

Ground state, electron 69. 75. 90 Ground stations (ACAS)

(walk in T/F service) 289

synchronization 289 Groundwave radio signals 251. 282

range, Loran-C signals 256

stability, Loran-C signals 254, 256 Group Repetition Period (GRP), Loran-C 254.256 H

Hardwire systems, aerially mounted 298 Hazards in frequency stability measures 164 Helium ion storage technique 131 Hertz, unit of frequency 10. 70, 140 Heterodyne techniques 162

period measurements 163 HF (High Frequency) radio 247

atomic frequency control of broadcasts 251

430
broadcast formats

evaluation for TFD

optimum radio measurement procedures

propagation delay of radio signals skywave radio signals telecommunications systems, performance prediction

time/frequency dissemination High accuracy T/F users High performance cesium beam tube Hops, skywave radio signals Hybrid beam optics

Hydrogen

atom

emission spectrum

energy level atomic hyperfine splitting beam standard frequency

difference between standards

in terms of cesium

magnetic dipole transition masers

atomic comparisons with cesium beam

deformable storage bulb Harvard

large bulb

historical development

inaccuracies NP3 (NASA)

clock ensembles comparison NP3/AT(NBS)

Ramsey

spectrum

spin exchange shifts stability standard

storage bulbs

transition frequency

wall shift storage beam

standard

transition curves

tube Hyperfine interaction

splitting transition

I

IAU (International Astronomical Union) 323. 324 IBS (Institute for Basic Standards), NBS 341 ICSU (International Council of Scientific Unions) 323, 324

Identification (TFD) 238. 244 Image rejection, predetection bandwidth 164 Improvements

NBS cesium frequency standards 104, 113, 121. 220 phase noise characteristics, crystal oscillators 105 TAI scale 39, 223

Infrared

effects 129 frequency synthesis 142

region (EM spectrum) , 127

Initial synchronization of clocks 243

Injection of T/F information into TV format 265

Instabilities 156

evaluation of a primary rate standard 219-220

frequency measures 167

Institute for Basic Standards (see IBS)

Instruments, long-beam frequency standards 95

Interaction time-storage technique 91 Intercomparisons, hydrogen masers and cesium beam standards.. 98 Interconnected power systems 298

Intercontinental synchronization of precise clocks 285. 291. 294

rage 247

251 250

250

251 251 247 299

108 250

108

68. 77. 97. 113

74

69. 73. 76

91

97. 105. 106

285

98

98

79, 97. 98. 105, 113. 132. 216. 285. 296

97, 113 216

106 98

99, 105 92106

216

217 98

70. 73

106 106

97. 105. 285

79. 92. 97. 105. 134

79

79. 98. 105

105

106

106. 132 76

91

127. 130

431
Page Intermediate T/F accuracy users 299

International Astronomical Union (see IAU)

International Atomic Time Scale (see TAI)

International Council of Scientific Unions (see ICSU)

International Latitude Service (ILS) 323

International organizations, standard time and frequency 323

International Polar Motion Service (see IPMS)

International Radio Consultative Committee (see CCIR)

International Science Radio Union (see URSI)

International System of Units of Measurement (see SI) International Telecommunications Union (see ITU)

International Union of Geodesy and Geophysics (see IUGG)

International Union of Pure and Applied Physics (see IUPAP)

Inter-Range Instrumentation Group (see IRIG)

Interrogation atoms or molecules 127 electromagnetic (EM) field 127. 128

particle 127, 141 time 129

Intrinsic reproducibility 154

Iodine absorption of laser radiation 131 saturated absorption 131

transition 143

Ion storage 107 helium 131, 143 mercury 131

principle 133 Ionospheric propagation anomalies 240, 310a IPMS (International Polar Motion Service) 323, 324 IRIG (Inter-Range Instrumentation Group)

decoders for time codes 250

time code 248 ITU (International Telecommunications Union) 323. 324 IUGG (International Union of Geodesy and Geophysics) 324 IUPAP (International Union of Pure and Applied Physics) 324

J

Josephson

effect 127 phenomenon 145

Julian Day

modified number 221 K

Kirsch hyperfine-structure level separations 89

Laboratoire Suisse de Recherches Hologeres (see LSRH)

Laboratory frequency standards cesium 94, 96, 103, 113, 121, 214 accuracy trend, 1956 to 1973 104

stability performance data 105 performance, stability 105, 116, 123

state-of-the-art 104. 113, 121 Lacey's method (frequency stability) 122 Lane identification (navigation) 252 Laser

oscillator 129, 143

radiation simple absorption 131

sulfurhexaflouride 131 Latitude stations (International— see IPMS) 323

Lattice distortions in crystals 46

432
Page Leap second 9, 32, 220. 318

adjustments 32-34, 221 dating of events 34 Leap year 8, 318

"Legal" volt 145

Legislative Authority, NBS responsibilities 331 LES-6 (satellite) 272, 276 LF (low frequency) radio signals 245

evaluation for TFD 246

pulse decay time measurements 246

single-frequency phase tracking 245

time and frequency dissemination 245 Length

standard of 144

unified standard 145, 237

Librations of moon (effect on TFD) 287

Light

intensity (optical pumping) 97

quantilization 68

shift 97, 132 spectroscopy 71 wave theory 71

Light, speed of 127, 145

Limitations of dissemination techniques for TFD (see evaluation under various techniques).

Line-of-sight applications 240

radio frequency propagation 269, 310a

transmission 240

Line-Q, particle confinement 129 Linear drift, crystal oscillators 43. 61, 158. 167 Linewidths 142 narrow 95 resonance curve 72

transition 78 Lithium nucleus 89

Local standard calibration 267 Local TV service areas 264 Long beam instruments (Cesium standard) 95, 113 Long term stability, NBS-III 114 Long time drift, quartz crystals 48

Longitudinal C-fields 105 Loose phase-lock loop 169 Loran-A navigation system (HF) 257

baseline of pairs 257

clock synchronization via 257 coverage map for stations 258

evaluation for TFD 257

pulse envelope 259 Loran-C navigation system (LF) 253

basic and specific rates 256

basic unit 254

chains 254

characteristics of stations 254, 313

clock synchronization techniques 223, 256

coverage map of system 255

evaluation for TFD 256 groundwave range 256

null ephemeris table (TOC) 255, 384

pulse-coded format 254

pulse group format 255 skywave propagation 256

synchronization of 254

time of coincidence (TOC) of signals 255 Loran triad 257 Low-accuracy T/F users 299

Low-altitude orbiting satellites 271 LSRH (Swiss Laboratory of Clock Research) 98 Lunar

topography, corrections for TFD 287

radar time synchronization (see MBTF)

433
M

M, sample time Magnetic

dipole transition forces moment

nuclear resonance technique, atomic beam

shielding

Magnetic field earth's gradient

properties

Magnets, focusing

Magnification factor Maintenance of synchronization at remote sites Majorana transitions Mapping of exponents, /a — a Maps

Loran-A (navigation system) coverage Loran-C (navigation system) coverage Omega (navigation system) stations time zone USA

world

world-location of broadcasting stations useful for TFD.

Masers

active oscillator ammonia

Harvard, large bulb hydrogen (see Hydrogen maser) rubidium

self-stimulation emission

stability storage beam

techniques Mass, electron Master

clock

station, Loran-C

Maxwell's theory (EM radiation) MBTS (Moon Bounce Time Synchronization)

evaluation for TFD

Mean solar time Mean-square time error Mean Time Between Failure (see MTBF)

Measurements

accurate frequency

survey AT(NBS) rate system

comparison techniques

differential, TV line-10 data Doppler (radio) envelope timing (YLF)

"flying clock" frequency (also see Frequency measurements)

domain (time domain)

computing counter

fluctuations

stability conversion chart

operational systems-microwave region

translations TV color subcarrier microwave

period

phase (TV)

power-shift process "dead time"

pulse-velocity distribution quantum transitions

relativity single-oscillator system

Page 165

98

74

70-72, 77, 88, 89 89

88. 89

92. 108, 121

79106 124

104 243

292

130

160

258

255

252

326

12241

77, 79, 92, 97, 105, 132, 144, 146. 216

128

92. 131. 133. 144 105

131. 132 79106

132

92, 132 69

240, 271, 379

254

69, 71 286

287

5, 6 210

140, 144

143 214

167 260

273

252

95, 290

167-171

174

167 154-159

166, 178

171

159, 160 263

173, 188

163 268

123 164

123 140 284

173

434
Page techniques for frequency stability 162 time 3 differences 218

physical 81 time devices since ~ 1000 AD 3

unified standard 127, 145 X-band frequency • 171-173 Mechanical

design of cesium beam standards 108, 121

vibration, crystal units 50, 61 Medium-altitude satellites 269 Memory-rate of NBS primary frequency standard 223 Mercury

atom 90

ion storage 131 Meridian of Greenwich, England 11 Merit, figure of....._ 116, 128 Meteor trail (burst) system 283

evaluation for TFD 284 phase stability 283

scatter, forward reflection 283 Methane

saturated absorption 107, 131, 144

cell 84 Metrology (see Frequency and time) Microwave

absorption 97

effects 71, 129 frequency 71, 99, 142 frequency stability measurements 171, 187, 188

calibration procedure 173

input power 104 optimum power 116 pulsed excitation 104

relay routing of TV networks 260

resonances 4

signal changes 107 spectrum 123 system drift 281 TD-2 system 260, 281

time and frequency transfer 281

evaluation for TFD 282 Mini-modem equipment (DSCS) 276 Minimum-squared error of time prediction 212 Mise en pratique du temps atomique international (putting into usetheTAI) 21,22

Mission responsibilities NBS 318, 331 USNO 319,357

Mixer, double balanced 168 Modeling, clock 208 Models

idealized 155 mathematical, propagation media 240

statistical 155 Modes, crystal units dissymmetric 48

flexure and shear 44, 59, 60 motion 42, 46, 59

Modified Julian Day number 221 Modulation

frequency 114

sinusoidal 173 time pulse 246 Molecular beam technique (Stern) 87 Moment (electron) 70 magnetic 71,77,89

nuclear magnetic 89 Momentum

particle 70

total angular 76

435
Page Monotonic function of time 153 Moon Bounce Time Synchronization (see MBTS)

Moon

earth, sun relationships 5

librations affecting TFD 287 Motions of celestial bodies 320 Mounting systems, crystal vibrator 45 MTBF (Mean Time Between Failure), cesium standards 9, 95

Multipair-telephone lines (TFD) 296

Multipath effects, radio propagation 269, 310a

Multiple

beams (frequency standards) 107

frequency-VLF techniques 243, 253

Multiplication, frequency 167

Multiplier chains, frequency 96, 114, 122 Mutual reciprocity of reflected VHF signals 283

N

Narrow linewidths 95 NASA-Application Technology Satellites (ATS) 276 NASA orbital elements (satellite positions) 277

National Bureau of Standards (see NBS)

National Physical Laboratory (see NPL)

National reference standards 104

National Research Council (see NRC)

National Research Laboratory of Metrology (see NRLM)

Natural quartz 45 Naval time signals 321

Navigation

capability of present day communication system 302

celestial 6, 317

characteristics of frequency stabilized systems useful

for time/frequency comparisons 313 Loran systems for TFD 253, 257

radio systems for TFD 239 Radux system 242

rho-rho system 251

timing relationship 252

Navigators time scale 318 Navy Navigation Satellite System (see NNSS)

NBS (National Bureau of Standards)

AT clock ensemble 215

atomic time scale 214, 320

broadcasts of standard frequency 321 cesium beam frequency standard 94, 105, 113, 121 clock ensemble 114, 217

coordination with USNO 220, 321, 377

enabling legislation 329

function 335

Institute for Basic Standards (IBS) 341

mission 318, 331

organization and assignment of functions 339

organization chart 346

primary standards frequency and time 319

frequency measurement system 214

radio station WWV. WWVH 247

time and frequency

activities 318

Division 319, 361

organization chart 319

publications 183, 383

responsibilities 361 TV time system 266 UTC, accessibility and coordinated time scales 207, 220, 221, 319

436
Page NBS-III cesium standard 113, 214, 223 NBS-5 cesium standard 105, 121, 215, 220

calculated and measured stability 121, 123, 221

evaluation (1973 preliminary) 124, 215 system description 121 NBS-X4 105, 121, 124, 215, 221 Needs, time and frequency 300, 302 Network (TV) reroutes 261 NNSS (Navy Navigation Satellite System) 273 Noise 54, 62, 72, 128, 156, 159. 207, 244

additive 54, 240 AM 164 bandwidth, system 159

clock, characterization 212

contribution to frequency fluctuations 54 dependence of various types 167

differential phase measurements 171

flicker 158, 211, 226 FM 7, 210, 226, 298

frequency 114, 178 phase 62, 114, 167 FM 164, 226

frequency 158 improved phase characteristics (crystal oscillators) 105

non-deterministic 159 power 159 power law processes 211 process 159, 220 a = -l 160,212

optimum filters 225 random 167

shot 54, 114, 123, 128 spectrum 207

types, frequency dependence 167 white 115, 167, 226 FM 210, 226 frequency 115 Non-random deviations 153

Non-reciprocity of propagation path 271, 310a

North Atlantic Synchronization (Synchron) aircraft flyover 294 NP-0532 pulsar time transfer 294

evaluation for TFD 296

fractional frequency deviations vs sample time 295 NPL (National Physical Laboratory), England 94 NRC (National Research Council), Canada 95, 103 NRLM (National Research Laboratory of Metrology), Japan 104 Nuclear atoms 69

effect, frequency stability (crystal units) 51 magnetic moments 89

spin 71,76

Nucleus atom 67, 69, 71

lithium 89

Null ephemeris table- Loran-C 255, 384 Number of users TFD systems serve 301 o

Offset, frequency 8, 210 Omega navigation system 251

basic pattern 252

evaluation for TFD 253

10-second proposed format 253 On-board clock (satellite) 269, 271, 273

On-line clock 216 computer processing 215

On-site clock visit 292 One-sided spectral density 179 One-way satellite system 270

Operational amplifier 169

437
Optical pulsars (see Pulsars) Optical pumping.. 82, 89-91, 97, 130, 132, 141 Optics

beam

alignment 124

hybrid 108 system 116 Optimum

filter 210, 225 HF radio measurement procedures 250

Orbit

predictions 273

satellite 269 "Orbit" television system (USSR) 277

Orbital angular momentum number 73

elements, satellite 270

motion, earth 5, 6

Organization

chart NBS-Department of Commerce 346 NBS-Time and Frequency Division 319 USNO-Time Service Division 320

functions NBS 318,329

USNO 319,347

Oscillators 43, 62, 93, 95. 267

active maser 79, 128

calibration of remote 267 cesium 81, 263

design circuit 53 environment 52, 155 frequency

fluctuations 54

fractional, stability/function of sample time 211

stability measurement system 173

laser 129, 143

precision 52

quartz 43,83,115.158,211

crystal (see quartz crystal oscillator) crystal controlled 52,62

flicker of phase and DC flicker noise 62 frequency-time performance 49

future developments 55, 62

general purpose 52

short term stability 54,62

severe environment 52

slave 115, 128 temperature compensated 52,60

thermal shot noise 54

voltage controlled 52,163 Oven 80

collimator 121 detector 121 P

"Paper clock" 227

Particle 127-130, 141 beam apparatus 141 cesium beam tube 143

collisions 142 confinement 129, 141 • detection 78, 128

flux of signal 128

interrogation 127, 141 momentum 70

preparation 130, 141 pulsed 131

storage 129, 141, 142 wavelength 70

438
Page Passive

device 78 method, particle interrogation 129 technique 134

television 259 Path delay 222, 240. 250, 259, 270

contours (satellite) 277

differential 259

propagation 240

Pauli exclusion principle 74

Period measurement 163

Periodicity 74

Perturbation, random (clocktime) 209 Phase

anomalies 244, 310

automatic correction (APC), telephone lines 297

difference instability 113

bias (cavity) 121, 123

fluctuations 166, 180 frequency domain measure 114, 166 phase sideband power, related 180

spectral density 166

lock loop 169

loose 169

tight 170

noise

characteristics (crystal oscillators) 62, 105

flicker 62,114,167

quadrature 162, 167, 171, 180 random walk (time) 166, 167, 211, 226

records (VLF) 242

residual error 243

shift cavity 104, 121, 130

diurnal 242, 245, 296, 310a problems 104

shifter, adjustable 171 sideband power-fluctuations 180

stability of the meteor burst trail 283

tracking

LF signals 245 VLF signals 242

trans-Atlantic comparisons 242

values, daily 252, 383, 384 Photo cell 78, 83

detector 91 Photoelectric effect Einstein explanation 68

theory (Shrbdinger and Heisenberg) 70 Photographic integration, LF time pulse measurements 246 Photographic Zenith tube (PZT) 320 Photon 91, 129

recoil effects 141, 142

Physical

basis-atomic frequency standards 67 measurements of time 81 Physikalisch Technische Bundesanstalt (see PTB)

Planck's constant 68, 70, 88, 142, 144

Planetary motion 69

Plate strain, vibrating crystal 46, 48, 59

Plates (quartz) AT-cut 44, 59 FC-cut 60

Polar motion 6, 284

Portable clocks 95, 290

evaluation for TFD 292

Position ambiguity (navigation) 251

Post-detection bandwidth 164

Postdoctoral research awards (NBS) 361 Potassium atoms 88

emission electrons 75

439
Page Power

grids

synchronization of interconnected 246

U.S. coast to coast interconnected 298 law

frequency and time domain characteristics 211

noise processes 211

spectral densities 156, 165

line (60 Hz) signal-time transfer 298

evaluation for TFD 299

fractional frequency stability 299

noise 159 optimum microwave 116

shift measurement 123

spectral density (crystal units) 54

Precision clock rate or frequency 208

clocks, international comparisons 294, 295

definition 140, 154 frequency

sources, state-of-the-art 62

standards, calibration 98, 218 NBS-III 113

oscillator 43, 52, 62

synchronization, time scale 208

Precise Time and Time Interval (see (PTTI)

Prediction exponential 213

routine 218

long-term performance-HF communications systems 251 minimum-squared error of time 212

orbit (satellite) 273

oscillator aging 158, 159

theory, clock errors 162 time algorithms 214

Pressure-temperature shifts (gas cells) 97 Primary standards 78, 79, 127, 214

candidates for 133, 146 concepts 133

evaluable 219, 223

frequency (see Frequency standard, primary)

frequency and time interval 208, 319

future-areas of promise 127

inaccuracies in evaluation of rate 219

state-of-the-art 104, 140, 214

Probability distribution 158 Propagation

characteristics of various RF bands 310a

delay

radio 240, 256

path 259

theoretical predictions 243

factors affecting 310a

ionospheric anomalies 240

mathematical models 240 media 240

vagaries 252

Properties, deterministic 158, 208 PTB (Physikalisch Technische Bundesanstalt) 104 CS-1 (cesium standard) 223 PTTI (Precise Time and Time Interval) 363 meetings 321

standards and calibration facilities 365, 371 USNO responsibilities 363

Publications NBS time and frequency 183, 383

Special Publication 236 319 USNO time and frequency 384

Pulsars 294

differential fractional frequency deviations 295 NP-0532 294

time transfer system (optical signals) 294

evaluation for TFD 296

440
Page Pulse coded Loran-C format 255 LF decay time measurements 246 methods, accuracy evaluation of NBS-5 123 modulation, time 246

repetition rates Loran-A navigation systems 257 Loran-C navigation systems 256 sync (TV) 259, 262

transfer standard 259

time (WWV, WWVH) 249 VLF methods 243 Pulsed microwave excitation 104

preparation, particle 131 Pumping, optical (see Optical pumping)

Q

Q values 92, 94, 96

cavity 173

line 107, 121, 129

quartz 45, 59 Quadrature

condition 173, 180 phase 162, 167, 171 Quantization 68

spatial 88 Quantum

electronic frequency standards 127, 131, 319

historical development 139 mechanics, theory 70, 72 numbers 70, 73

transition 128, 129, 140 Quartz 43, 59

crystal 43, 59

aging 48,49,61,290

ambient temperature changes 48 amplitude distribution 46

amplitude of vibration 50, 53 anharmonic overtone in 60 AT-cut plates 44, 59

characteristics 43

clock 218,290

crystalline body vibration 60

crystallographic axes 44

dielectric constants 45 dissymmetric modes 48

drift rates 43,48,54,290

drive level (frequency stability) 50, 61

elastic constants 45

electrical equivalent circuit 44, 59

enclosures 44, 61 energy trapping 46-48, 60

FC-cut plate 60

first clock 290

flexure-type, shear modes 47, 49, 59 foamed mounting 52 frequency

deviations 50

stability 43, 48, 52, 54, 60

temperature drift compensation 50, 52

glass units 49

imperfections 48, 50

lattice distortion 46

long-time drift 48

metal units 49 modes of motion 44, 46, 59

nuclear effects on 51

441
oscillators 43, 52, 62, 81, 83, 93, 95, 115, 123, 158, 211

aging '. 49,61,158

characteristics 43

controlled 62

design circuit 53

flicker of phase and DC flicker noise 62 frequency

fluctuations 54

stability 43, 48, 60

future developments 55, 62 improved phase noise characteristics 62 low frequency types 49

output phase noise 62 performance, precision 49, 62

precision 52, 53

severe environment 52

short-term stability 54

state-of-the-art 43, 59, 62 temperature compensated 51-53. 60

thermal and shot noise 54 TRANSIT (satellite) stability 273, 274

voltage-controlled 52

plates dispersion curves for thickness shear and flexure 60 mode shapes 60

Q-values 45, 59 resonance patterns 46, 59 shock and vibration, effects on 50-52, 61 short-term frequency changes 49

stability 54, 62

stress distribution 46

stress-strain relationship 50, 51

synthetic 45, 59

units acceleration 50, 61 high-frequency aging..' 49 power spectral density 54

triple, ribbon supported 52

vibration, mechanical 48, 50, 61 width-shear vibrators 48. 49

vibrating

mounting systems 44

plate strain 46, 52, 60

impurities 50

material 45, 59

natural 45

noise 54

resonators 59

strain in vibrating plates 60

thermally induced strain (non-aging) 50

vibration 50, 61

vibrators acoustic loss 46

basic modes 44

designations 44

distribution of strain 48

frequency-time performance 49 mounting systems 45

quality factor 54 resonance pattern 46

stress distribution 46

surface strain 48 temperature/frequency effects 48, 52, 53, 60

thermal shock 50

width-shear 48, 49 R

Rabi magnetic resonance method 88, 94 Radar (Doppler) signal instabilities 161 Radiation barium oxide 131 black-body 68, 71

442
Page electromagnetic 68, 71 frequency 72

iodine absorption, laser 131 methane 131

optical resonance 90

sulfurhexafluoride laser 131 Radio astronomy stations, worldwide net 285

broadcast stations for TFD (map) 241

characteristics of frequency bands 310a commercial for TFD 282

delay path (satellite) 269

dissemination of time and frequency 239

dissemination techniques 240

evaluation of methods for TFD 244, 246, 251, 282 HF broadcasts 247 LF broadcasts 245 VLF broadcasts 241 frequency bands 4 through 10, characteristics 310a

frequency (RF) spectral density 156 HF skywave signals 251 microwave systems for TFD 281

navigation systems for TFD 251

propagation

factors 240, 310a

path delay 240, 259 Radux navigation system 242 Ramsey

cavity 113, 116, 130

fields 89, 92 resonance 94, 105 separated oscillating fields 92 spectrum 123 type cavity 121 Random

deviations 153

fluctuations 166, 207

perturbation of a clock's time 209

uncertainty 133 walk 153, 166 walkFM 211,226

walk of phase (time) 167, 226 Range-range (navigation system) 251 Ranging

Doppler 288

navigation 252 Rate

accuracy of AT (NBS) scale 219, 220

time correction 220

Ratio

carrier to noise 161 charge to mass 69

Real-time synchronization

stabilized TV sync pulses 262

transfer in local TV service area 264 Received accuracy of broadcast carrier 282 Receiver cost for stated accuracy (TFD) 301

Recoil effect (particle interrogation) 129, 141, 142 Recursive filter (Flicker noise FM) 226 Redundancy 9 cesium frequency standards (Omega) 256 Reference NBS T/F broadcasts 207

stable 218

standards, national 95, 104, 317

stations (USNO time) 379

t3.fc)lcS Loran-C,TOC 254,384

television, TOC 263,384

Refractive index (radio signals) 269

443
Relative

fractional frequency stability time difference AT(NBS)-AT(USNO) time scales

Relativistic gravitational shifts Relativity Einstein theory of special

general theory measurements

tests Relaxation time RELAY-II (satellite) Relay transponder, satellite Reliability Reorganization Plan 3 of 1946 (USNO)

Repeatability, signal arrival time

Repetitive resynchronizations

Reporting data, uniform methods of Reproducibility, intrinsic Reroutes, TV networks

Residuals phase error VLF

Resistance-phase sensitivity (telephone TFD)

Resonance ammonia

atomic beam magnetic techniques

cavity cesium

curves

double, techniques

frequency

hydrogen

line width of curve

lithium nucleus microwave

optical radiation pattern (crystal vibrators) quartz plates (AT-cut) Rabi magnetic method

Ramsey curves rubidium hyperfine Resonator, quartz Resynchronization of remote clocks Rho-rho navigation technique

Rotation of the earth Routing of TV signals in USA

Rubidium

commercial standards

gas cell diagram

hyperfine resonance maser

oscillator frequencies (TV standards)

transition frequency

Russell-Saunders coupling Rutherford experiment

s

Sample averaging of independent estimates of S y

(f) Sample size, M

Sampling time

interval

oscillator frequency fluctuations SAT (Stepped Atomic Time)

Satellite, orbiting elements

low-altitude medium-altitude

Satellites

Page

114, 116, 262, 265, 295, 299

262

271

103

71144 284

106

92, 128 272 269

9, 103, 238, 301 350

238

289

175 154

261 208

243 297

72, 105, 106 92

87

129

81, 94, 319

89, 90

90, 96 319

98. 106

7289

4

9046

59

88, 89

105, 106

82, 97

59253

251

7, 317

260

77

97, 108

81, 89, 97, 131, 133

82

81, 97

131, 132 263

82

7467

165

165

178 54

8

270

269. 271

269, 275

223, 269

444
antenna pointing charts ATS-1

ATS-3

basic concepts for TFD

classification communications

delay (path) computer

DSCS

earth coverage of evaluation for TFD

GEOS-II

geostationary

LES-6

low altitude orbiting medium altitude motion variability (path delay changes) movement NASA-ATS

Navy Navigation Satellite System (NNSS).

on-board clock one-way mode

orbit predictions RELAY-II

relay transponder

selected T/F comparisons (1962-1973)

side tone ranging technique

stationary

synchronous (equatorial) TACSAT

TELSTAR

TIMATION

TRANSIT

transponder

two-way mode

Saturated absorption device

iodine methane

Scales (see Time scales) Schottky barrier diodes mixer

Script £ (f) sample calculation of versus frequency

Schrbdinger's theory Second

atomic

definition ephemeris

leap TAI

Second-order Doppler shift time scale algorithm

Secondary standards

Selective pumping

Self-stimulation emission masers

Series limit (energy levels) Service areas, local TV

Servo bandwidth

loopresponse system

frequency lock (NBS-III)

solid state VLF tracking system

time constant

Setting of remotely located clocks (TV) Severe environment oscillator Sextant

Shields, magnetic

Page 277

270, 272

272, 277 269 269

276

277

272, 276 270

280

272

223, 302

272, 276

271, 273

269, 275

271

271, 277 276

273

269, 271, 273 270 269

273

272 269

272 270

302

269, 280

272, 276

272

272, 275

272, 273 269 270

129, 133, 134

142

131, 144

84, 107, 133, 144

168 215

114, 167, 169, 176 180

170

70

11, 95, 121, 127

140, 319

11, 17, 127, 139, 140, 153, 208, 319

6

9, 34, 220, 318

7, 9

105, 115, 121, 123, 141 216

79

97

79

73

263, 264

169, 170

169

163

114 116 242

116 262

52317

108, 121

445
Shift Page cavity phase 104, 124

diurnal 242, 245, 296, 310a Doppler 80,115,130.271

energy level 129 frequency (wall collison) 142

light 97, 132

relativistic gravitational 271

wall 79, 98, 105, 134 Shock and vibration, quartz units 50, 52

Short-term stability 49, 54, 62, 267 Shot noise 54, 114, 123, 128

SI (International System) of units 140, 207, 319, 323 accuracy capability 140 base units 140

unit of time 19, 23, 27, 140, 207

Side-by-side comparisons, atomic frequency standards 95, 290

Side-tone ranging technique (satellite) 270

Sidereal time 6 sigma versus tau 167, 170

Signal

frequency (carrier) variable 178

particles, flux 128 power line (60 Hz) 223, 298

processing equipment, errors caused by 164 source 164

Silver atoms 87

Simulation, data 212

Simultaneity (time) 4, 153, 208

Single-frequency phase tracking

LF signals 245 VLF signals 242

Sinusoidal modulation 173

Skill (operator) required for TFD systems 302 Skywave

hops (HF radio transmissions) 250

signals HF radio 251 Loran-C 256

Slave

clock 271

oscillator 115, 128 Sodium atoms 87, 91, 96

Solar time apparent 5 mean 5, 6, 325

Spatial

quantization 88,89

state selection 130, 141

Specification of frequency stability terminology 165 Spectra, atomic 73 Spectral density 54, 115, 157, 165 asymmetry 128 concepts 156

estimation from time domain data 164

fluctuations

fractional frequency 166 frequency 177 phase 166, 177

voltage 177 frequency domain measures of stability 178 measure of frequency stability 165

one-sided; two sided 179 power 54, 115

radio frequency (RF) 156

types of 179

Spectral emission lines 88 Spectroscopy 71 Spectrum

analyzers, analog 164

conservation of electromagnetic 257, 302 microwave 123 Ramsey 123 Speed of light (unified standard) 127, 145

446
Spin

additional energy levels electron exchange, collisions hydrogen, exchange shifts nuclear Spontaneous emission

Stability atomic standards

characterization of frequency

clock ensemble

color subcarrier frequency (TV)

Commercial

cesium standards rubidium standards

definition fractional frequency —

conversion to time stability TV system long-term

frequency (see Frequency stability) hydrogen maser standards

laboratory cesium standards

long-term measures

applications of frequency domain

time domain

performance of various frequency standards

short-term

statistical models

temperature control Stabilized commercial broadcast stations emissions outside allocated frequency assignments

navigation systems

television sync pulses

Stable time scale and reference Standards

atomic beam frequency (also see Atomic standard).

historical development

basic

calibration (local) cesium (see Cesium beam standard) frequency cesium

hydrogen

rubidium

thallium frequency and time broadcasts

signal emission — CCIR Recommendation 460

signals in allocated bands

gas cell length

measurement, unified national reference primary (see Primary standards) quantum electronic frequency

secondary

"The"

time

interval, frequency

scale

unified (frequency, length, time) Standard time

adoption and observance advancement, annual emergency daylight saving time

legal definition Standard time and frequency

basic emissions

international organizations involved in radio assignments (international) responsibilities in the USA

Pape 71, 106

70

73, 88

129, 130

106 76

72, 128

52, 54, 62, 153

103, 108, 114, 123 154

218, 220

263, 265

107 108

154

116, 128 222 267

105 106

114

161

157, 178

157, 165 105-108, 113. 121

54, 62, 128, 267 209

48, 52. 60

282 312

313

262 218

67, 87, 103, 145, 235

67, 93, 96, 127

87, 103

127, 145 267

17, 80, 95, 103. 107, 140

79, 97, 105

81, 97, 108 96

240, 241

31

241, 311

90, 97, 132 144

127, 145, 237

104, 317

127, 131 78145

17, 145, 207, 237, 394

144

207, 214, 223

127, 145, 237

394

399 408

325

319

31. 240, 241, 311 323

241 317 447
Page Standard time zones USA (map) 326

boundaries 325, 398

relocation — Michigan (1973) 406

world 12 State (energy)

selection 78,80

separator, electrostatic 92

spatial 130

State-of-the-art laboratory cesium beam 104, 113, 121 primary standards 214

Stationarity 155

Stations

latitude 323

location of broadcasting (for TFD) 241 master 254 NBA, NSS (USNO) 243

radio astronomy net 285 USNO time reference 379 WWV, WWVH (NBS) 247 WWVB 245

Statistical analysis, T/F data 153, 207 models

frequency stability 155, 209

time dispersion 210

smoothing, VLF data 243

Step, frequency 220 Stepped Atomic Time (see SAT)

Stern-Gerlach experiment 88

Stern molecular beam technique 87

Storage

beam 79, 131, 135, 142 tube 132 box principle 92 bulbs 79 deformable 106 hydrogen 79, 97

principle, particles 141, 142 technique — interaction time 91 Storage of ions 143 helium 131 mercury 131

principle 133

Strain (quartz crystal) 48, 50

surface (vibrators) 48

thermally induced 50

vibrating plate 60

Stress

distribution, vibrating quartz 46

vibration and acceleration (quartz) 50, 61

Structure, C-field 108 Study Group 7 (CCIR) 324

Subcarrier (TV color) 263

Sub-radar reflection point (MBTS) 287

Sulfurhexafluoride laser radiation 131 Sun-earth-moon relationships 5, 319, 357

Sundial 5 Survey, accurate frequency measurements 144 Sync pulses (TV) 259, 262

transfer standard 259 SYNCHRAN (North Atlantic Synchronization) aircraft flyover... 294

Synchronization 4, 238 ACAS ground stations 289 accuracy and precision of 208

aircraft flyover 293

clock 153, 238, 256

initial 243, 262 remote site 259, 277, 285, 290 maintenance of time 292 day to day (60-Hz system) 298

definition 4, 292

global time 242, 290, 293

448
Pani' interconnected power grids 246

intercontinental of precise clocks 285, 293 Loran-C navigation system 256

system-. 11 worldwide-atomic clocks 242, 290 Synchronous

satellite „ 269,302

altitude (equatorial) H '. 269

detection 116

Synthesis, infrared frequency 142 Synthetic quartz 45 System

AT (NBS) rate measuring 215

clock ensemble 215

coherent communication 237

coverage of a T/F 238, 300 fundamental constants and basic standards 144

navigation for TFD 251

noise bandwidth 159

operational for measurement frequency 168. 171

single oscillator measuring 173

stability descriptions at HF region 168 microwave region 171 Systematic variations and trends (frequency stability) 158 Systeme International d'Unites (International System of Units —

see SI) T

TABLES

Accuracy budget for NBS-5 (1973 preliminary) 124 Accuracy capability of NBS-III (1969) 115 Bias Functions B, and B2 192-204

Characteristics: frequency stabilized navigation systems useful for time/ frequency comparisons 313 Loran-C stations 254, 313

radio frequency bands 4 through 10 310a

stabilized frequency and time signal emissions outside

allocated frequency assignments 312

standard frequency and time signals in allocated bands 311 Data on different concepts for primary frequency standards 133 Designation of "quartz vibrators" 44 Frequency dependence of various noise types 167 Frequency offsets of UTC from 1960 to 1972 8 Organization chart: NBS — Department of Commerce 346 NBS Time and Frequency Division 319 USNO Time Service Division 320 Promising candidates for primary frequency standards 146 Selected time/frequency comparisons via satellites (1962-

1973) 272,276

Stability measure conversion chart (frequency domain-time domain) 166 Standard Time and Frequency radio assignments (WARC) 241 Survey of accurate frequency measurements 144 TACSAT (satellite) 272 TAI (International Atomic Time) 7, 19, 22, 27, 207, 321 accuracy 223

construction 10, 223, 321

current determination 39

fractional frequency 223. 224 improvement 39

rate 223

resolutions 27

scale 10, 321, 324

adoption 223

annual frequency drift 223 Tau (r) parameter (ACAS) 288 Techniques

active line TV for TFD 265

449
Page atomic beam, magnetic resonance 87

beat-frequency 162 broken-beam 92

buffer gas 82, 91 clock modeling 208

clock synchronization Loran-C 256 system 238 confinement 129, 141 constructing and maintaining atomic time scales 207

dissemination (see T/F dissemination techniques)

diversity (radio reception) 247 double-resonance 90. 96 frequency and time domain 168 frequency stability measurements HF region 168 microwave 171 X-band 171, 174

Frisch-Segre atomic beam 88 heterodyne 162 maser 92 measurement for frequency stability 162

multiple frequency. VLF 243

optical detection 91, 96 pumping 82.89-91,97

radio T/F dissemination 240,284

satellite for TFD 269

side-tone ranging (satellite) 270

Stern molecular beam 87

television for TFD 259

trilateration 277 Telephone lines 296

dedicated 297

evaluation for TFD 297

resistance, phase change 296 underground 297 Telephone time signals (WWV) 298

Television 259

active line NBS TV system 265 frame repetition rate 262

local service area 263, 264 microwave relay system (USA) 260 network reroutes 261 "Orbit" system (USSR) 277

passive for TF comparisons 259

real time synchronization via stabilized TV sync pulses 262

routing of signals 260

sync pulses 259,262

sync pulse "transfer standard" 259 system long-term stability 267 TD-2 microwave system 260 TFD techniques 259

active line injection of T/F information into TV format 265 NBS TV system 266

color subcarrier 263

calibration system 264

frequencies 263

stability, stabilization 263

evaluation 264, 265, 267

line-10 (passive technique)

differential measurements 260

fractional frequency stability 262

transfer standard 260 USNO, line-10 (real time) measurement system 262

vertical blanking interval format 261 TELSTAR (satellite) ' 272 Temperature 48, 52, 60

ambient changes (crystal) 48 compensated quartz oscillator 52, 60 compensation advantages/methods 48, 52. 60

450
Page frequency effects (quartz crystals) 48

gas cell 97

rhaser . v 106 Temps Atomique International (see TAI)

Terminology

specification of frequency stability 165 time scale 208 TFD (Time and Frequency Dissemination) (see Dissemination,

T/F techniques)

TF-ACAS (see ACAS)

Thallium atom beam devices 96 beam tube 131 Theoretical predictions of propagation delay 243 Thermal

equilibrium 130 induced strains 50

shock, crystal 50

shot noise 54

Tidal oscillations 284

Tight phase-lock loop 170 TIMATION II, III (satellites) 275 Time 4-11,81,145,153,208,235

accuracy 153 requirements 299

Act. Uniform (1966) 325, 391

algorithms prediction 214 announcements (radio) 248

apparent solar 5 aspects 153 astronomical 5, 13, 95

atomic 7, 95 NBS 207, 214, 320 TAI 7, 27, 223, 257, 321 USNO 320,322

basic concepts 4, 10, 208

bibliography 14, 230

closure (portable clock) 291

coarse check , 277 code 253

generator 266 IRIG-H (modified) 248 WWV, WWVH (100 Hz) 248 WWVB 245 comparisons 250

constant of phase-lock loop 169

coordinated Universal (UTC) 8 frequency offsets (1960 to 1972) 8

correction rate 220

definition (also see Definitions, time) 5, 208

delay 237

difference 215, 218 between clocks 219

dispersion 226

clock ensemble 219, 220

frequency (VLF) 244

statistical models for 210

dissemination (also see Dissemination, T/F techniques) 319, 361

capabilities of techniques 300

digital 266

overview of principles and techniques 235

time scale UTC(NBS) 221, 222 domain

characteristics of various power laws 170, 211 computing, counter measurements 174

data, spectral density estimation 164 frequency stability 166 measurements 170

translation-frequency domain 159, 166, 178

duration 4

ensemble, calculation of 216 ephemeris (ET) 6, 95

451
equation of

errors in AT(NBS) scale frequency (also see Time and frequency)

length, unified standard metrology

performance, precision quartz oscillators global synchronization

Greenwich Mean Time (see GMT)

interrogation

interval astronomical atomic unit sampling

standard mean solar mean-square error measurements

envelope monotonic function of Naval signals (radio) NBS broadcasts ordered format

physical measurement of prediction

algorithms

minimum squared error pulse broadcasts from WWV, WWVH

modulation random walk of phase

reference stations (USNO)

relaxation sampling

oscillator frequency fluctuations scales (see Time scales)

SI, unit sidereal

signal repeatability

signals (allocated bands)

simultaneity

stability, conversion from fractional frequency stability standard

basic broadcasts in allocated bands USA

system, nation unified

ticks transfer mode

optical pulsar signals power line (60 Hz) signal technique

precise

system description

television techniques

VLF radio signals

unit of

unified standard for Time and frequency (also see Frequency; time) abbreviations accuracy levels of service (satellite TFD)

activities NBS (Time and Frequency Division) USNO (Time Service Division)

classification of users , dissemination (also see Dissemination T/F techniques) overview of principles and techniques

Division (NBS)

DOD

location of broadcasting stations used for T/F dissemination metrology -

Page 6219

127, 145

140, 145 52-54

285, 290, 294

129

4, 11, 95, 139, 153, 208, 237, 319

95

95

178 139

5, 6, 325 210

3252

163 321

319, 383 288

81

214, 215 212

249

246

226

292, 379

91, 128 178 54

27, 203, 139, 208

6238

311 4222

17, 145, 207, 237, 394

319

311 317

382 248

239, 276, 294, 298

222 294

298

285 239

259

243

23, 153

127, 145

458

277

318, 361

320, 357 299

233, 236, 237

318, 361 365

241

127, 140, 145, 148, 237

452
Page NBS activities 318,359

NBS/USNO responsibilities 321, 322, 377

publications

NBS 183, 383 USNO 384

radio dissemination 240

standard radio broadcasts 241, 311

standards in the USA 207, 317 system coverage 238, 300

technology , 302

transfer, basic considerations 235

user and system evaluation 300

user needs 299 Time domain 155, 157, 159. 170, 178, 211 conversion to frequency domain 159 frequency stability 166 measurement 170 computing counter 174

spectral density estimation 164

stability measure 165

translations among measures 160 Time of Coincidence (TOC)

Loran-C reference tables 255, 384 TV reference tables 263, 384 Time-ordered format 288 Time Reference Stations (USNO) 292, 379 Time scale 3, 4, 8, 11, 23, 207, 223, 317, 322

A. 1 (USNO) 320

algorithms 214, 215

first order 216

mini-computer program 227 second order : 216

astronomical 5, 11 AT (NBS). 205,214

block diagram 214

generation, stability, accuracy and accessibility 205

long-term accumulated time, errors of 6 selected cesium

clocks 219

overview 207

relative fractional frequencies of 5 selected clocks 219 system 214,322

AT (NBS) — AT(USNO) 262,321

atomic , 4, 205, 320

algorithms 215

construction and maintenance 207 NBS 205, 320 TAI (see TAI)

USNO (A. 1) 320

automation system 219

bibliography 14, 230

celestial navigation 11 comparisons 9,291,294,321

compromise 13, 318

coordinate, UTC (NBS) 207, 220

coordination 322 agreement, NBS and USNO 220. 382

clock time scales 220, 381 frequency dispersion in the memory 220

navigators 318

relative time difference AT (NBS)- AT (USNO) 262

simultaneity 4

stable 219

synchronization 4 systems 11 TAI (also see TAI) 10, 27, 220, 223, 321, 324

unit of (BIH) 23, 321 USA 322 USNO and NBSI UTC,^^coordination......!!!!!!!!!^!!!!!!"!"!!^! 292, 322, 381, 382 USNO clock 272, 320

453
Page UTC 8, 220 UTC (NBS) 220, 221, 261, 320 Time Service Division (TSD-USNO) 320, 363 Time, Universal 6, 7. 32 UTO 6 UT1 6 UT2 6 UTC(BIH) 10, 23, 220 Time zones USA standard 325, 326

world map 12 Timekeeping 3 accuracy progress (1000 to 1973 AD) 3 accuracy via Loran-C 256

Total angular momentum 76

energy, E 69 TRANET tracking network 275 Trans Atlantic phase comparisons 242, 294

Transfer

clock 271

standard 239, 259 Transform, Fourier 158, 210

Transformation, frequency 128, 132 TRANSIT satellite 272-274

crystal oscillator stability 273, 274

Transitions (atomic) 69, 71, 72, 88, 129 ammonia inversion 92 cesium 81,95,122

clock 128

coupling 130

dipole, magnetic 98, 130 energy levels 67-70, 72, 88 frequency 77, 130, 141 high frequency 130, 134 hydrogen 79, 98, 106

hyperfine .' 98, 107. 127, 130

iodine 141 linewidth 78 majorana 130

probability 72 quantum 128. 129. 140 rubidium 81, 97

Translations frequency stability measures 159 time domain measures 160 Transmissivity optical 132 Transmission phase data-coax cable 297 Transmissions (radio) descriptions RF bands 4 through 10 310a Transponder (satellite). 270

Traveling beam tube 131 Treaty of the Meter (Standards) 324, 385

Trend, UT-ET 7 Trilateration 223, 277, 289

Triple ribbon supported HF crystal unit 52 Tube

cesium beam (atomic) 121, 127, 131, 143 hydrogen storage beam 131,132

Photographic Zenith (PZT) 320

thallium beam 131 TV (see Television) TV-time (NBS active TFD system) 266 Two-way mode

aircraft flyover 294

satellite 271 Types of spectral densities 179 u

Uncertainties

bias 124, 128, 129 random 133

454
Page UNESCO (United Nations Educational, Scientific and Cultural Organization) 324

Unified standard

(frequency, length, time) 127, 145, 237

Unified time

adoption and observation (time zones) 394

nation gets system (accurate) 382 Uniform methods of reporting T/F data 175 Uniform Time Act of 1966 325, 391

Units frequency-Hertz 10, 70, 140 measurement, SI 17, 27, 139, 208

time interval astronomical 95 atomic 95, 139

time/time scale (BIH) 23, 25, 153

Universal Time (UT) (see Time, Universal) URSI (International Science Radio Union) 324 USA

standard time zones 325, 326

standards of time and frequency 317

time scales 322

Users, T/F dissemination

cost to 222, 238, 301

evaluation of selected techniques 300 number that can be served 301

U.S. Naval Observatory (see USNO)

USNO (U.S. Naval Observatory) 317, 319, 349, 351

A. 1 time scale 320

authorizing documents 347

clock time scale 320

functions and missions 319, 322, 357

line-10 (real time) TV measurements 262 Naval time signals (radio) 321 NBS coordination 220, 292, 321, 381, 382

organization chart (TSD) 320

publications, time and frequency 384 PTTI responsibilities 363 Time Reference Stations 379 Time Service Division (TSD) 320 UTC time scale 292, 321 UT (see Time, Universal) UTC (BIH) 10, 220, 322 new system 8 UTC (Coordinated Universal Time) 10, 32, 220, 318

frequency offsets 8 UTC (NBS) 261, 321, 382

accessibility 221, 222, 245, 248

coordinated time scales 220

time scale 207 UTC(USNO) 261,321,382

coordination with NBS 220, 321, 381, 382

time scale 207, 220, 261

V

Variability in path delay, satellite motion 271

Variance, Allan (see Allan variance)

Variations, systematic 158

Velocities, atoms 72, 122 Maxwellian distribution 72 Veractor tuning 169

Vertical blanking interval-TV format..... 26], 267 Very Long Baseline Interferometry (see VLBI)

VHF radio signals

signals reflected from meteor trails 283

transponders (satellite) 270

455
Page Vibration (quartz crystals) 50, 61 amplitude 50, 53 mechanical 50. 61 shock 52

Vibrators (see Quartz crystal vibrators) Vibratory plates (synthetic quartz) 45 VLBI (Very Long Baseline Interferometry) 284

evaluation for TFD 285 geometry of receiving sites 284 VLF radio signals 241

corrections to broadcasts 243, 384

evaluation for TFD 244 Frequency Shift Keying (FSK) of carriers 244

multiple-frequency techniques 243

pulse methods 243

single frequency comparison 242

statistical smoothing of data 243 time transfer 243 use in TFD 244

Voltage

controlled oscillator 52, 53 frequency converter 170 w

Walk-in service, T/F comparisons (ACAS) 289 Wall

coatings 92, 98

collisions 129,142

shift 98, 105

bias 134

error 106 Wave

analyzer 169

electromagnetic (EM) 71 function 70

theory 71 Weighting

factors 218

filter, exponential 212 White noise 166,167,211,225

FM-random walk of phase (time) 167, 226 frequency (cesium beam standards) 115 Width-shear vibrators, quartz crystal units 48, 49 World Administrative Radio Council (WARC) 240 Worldwide

net of radio astronomy stations 285

synchronization of atomic clocks 285, 290, 294 WWV/WWVH (NBS standard HF-T/F stations) 247 accuracy of WWV transmissions, 1923-1973 247

broadcast format 249

telephone signals (WWV) 297

timecode 248

pulse broadcast characteristics 249 WWVB (NBS frequency stabilized LF station) 245

time code 246 X

X-band frequency measurements 173 source 173 techniques for frequency stability measurements 174

Y

Year, leap 8 Yearly UTC adjustments 8

456
Pane z

Zeeman

spectral lines 88

splitting 90

Zero-beat method of comparing frequencies 250

Zero-coefficient (crystals) 48

Zenith Photographic Tube (PZT) 320

457
TIME AND FREQUENCY ABBREVIATIONS LISTING

ACAS

AEP

APC

AT

ATS-1 &

BIH

BIPM

CCDS

CCDM

CCIR

CGPM

CIPM

DOC

DOD

DSCS

DUT 1

EM

ET

FAGS

FM

FSK

GEOS

GOES

GMAT

GMT

GRI

HF

Hz

Aircraft Collision Avoidance System

American Electric Power Company

Automatic Phase Corrector

Atomic Time

Applications Technology Satellites 1 & 3 (NASA)

Bureau International de l'Heure 1 (International Bureau of Time)

Bureau International des Poids et Mesures (International Bureau of Weights and Measures)

Comite Consultatif pour la Definition

de la Seconde (Consultative Committee for the Definition of the Second)

Comite Consultatif pour la Definition

de la Metre (Consultative Committee

for the Definition of the Meter)

Comite Consultatif International des

Radiocommunications (International

Radio Consultative Committee)

Conference Generale des Poids et Mesures (General Conference of

Weights and Measures)

Comite International des Poids et Mesures (International Committee of

Weights and Measures)

Department of Commerce (USA)

Department of Defense (USA)

Defense Satellite Communication

System

The approximate value of the differ- ence UT1 minus UTC as transmitted

(may be regarded as a correction to be

added to UTC to obtain an approximation of UT1 DUT1 = UT1 - UTC)

Electromagnetic

Ephemeris Time

Federation of Astronomical and Geophysical Services

Frequency Modulation

Frequency Shift Keying

Geodetic Earth Orbiting Satellite (NASA)

Geostationary Operational Environmental Satellite (DOC/NOAA)

Greenwich Mean Astronomical Time

Greenwich Mean Time

Group Repetition Interval

High Frequency

Hertz (cycles per second)

IAU

IBS

ICAO

ICSU

IFRB

IMCO

IPMS

IRIG

ITU

IUGG

IUPAP

IWP

LES-6

LF

LSRH

MBTS

MF

MTBF

NASA

NBS

NNSS

NOAA

NPL

NRC

NRL

NRLM

PCM

PTB

PTTI

PZT

RELAY II RF

RGO

International Astronomical Union

Institute for Basic Standards (NBS)

International Civil Aviation Organization

International Council of Scientific

Unions

International Frequency Registration

Board

Intergovernment Maritime Consultative Organization

International Polar Motion Service

(formerly International Latitude Service, ILS)

Inter-Range Instrumentation Group

(USA)

International Telecommunications

Union

International Union of Geodesy and

Geophysics

International Union of Pure and

Applied Physics

Interim Working Party

Lincoln Experimental Satellite No. 6

Low Frequency

Laboratoire Suisse de Recherches

Hologeres (Swiss Laboratory of Clock

Research)

Moon Bounce Time Synchronization

Medium Frequency

Mean Time Between Failure

National Aeronautics and Space

Administration (USA)

National Bureau of Standards (USA)

Navy Navigation Satellite System

National Oceanographic and Atmospheric Administration (DOC)

National Physical Laboratory (England)

National Research Council (Canada)

Naval Research Laboratory (USA)

National Research Laboratory of Metrology (Japan)

Pulse Code Modulation

Physikalisch-Technische Bundesanstalt (Physical Technical Federal

Laboratory — Germany)

Precise Time and Time Interval Photographic Zenith Time

'The original language is given for the abbreviation followed by the English translation.

Satellite Radio Frequency

Royal Greenwich

land)

Observatory (Eng458
SAT Stepped Atomic Time

SHF Super High Frequency

SI Systeme International d'Unites (International System of Units) — officially

abbreviated SI — is a modernized ver- sion of the metric system. It was

established by international agree- ment (CGPM) to provide a logical and

interconnected framework for all practical measurements in science,

industry, and commerce. SI is built upon a foundation of base units and

their definitions, from which all other

units are derived

TACSAT Tactical Communication Satellite (DOD)

TAI Temps Atomique International (International Atomic Time) (It is the coor- dinate of time reference established

by the BIH on the basis of data from

atomic clocks functioning in several

establishments conforming to the definition of the second, the unit time of

the SI.) TD-2 USA Microwave Network System

(TV)

_ TELSTAR Satellite (first reported clock comparison—see table 10.9)

T/F Time and Frequency

TF/CAS Time and Frequency — Aircraft Collision Avoidance System

TFD Time and Frequency Dissemination

TIMATION Time Navigation Satellite (US Navy)

TOC Time of Coincidence (Loran-C and

TV Tables)

TRANET

TRANSIT

TV

UHF

UNDP

UNESCO

URSI

USNO

UT

UTO

UT1

UT2

UTC

VHF

VLBI

VLF

WARC

Tracking Network

NNSS Satellite (US Navy)

Television

Ultra High Frequency

United Nations Development Pro- gram

United Nations Educational, Scientific, and Cultural Organization

Union Radioscientifique Internationale (International Science Radio

Union)

United States Naval Observatory

(USA)

Universal Time.

Universal Time — An apparent solar time corrected for the earth's orbital and inclination effects Universal Time 1 — UTO corrected for polar motion based on astronomical

measurements from worldwide ob- servatories

Universal Time 2 — UTl corrected for periodic seasonal fluctuations

Universal Time Coordinated (a time

scale coordinated by the BIH relating

to TAI by time differences of an inte- gral number of seconds and tracking

UTl by leap seconds)

Very High Frequency

Very Long Baseline Interferometry.

Very Low Frequency

World Administrative Radio Conference

459

* U. S. GOVERNMENT PRINTING OFFICE : 1974 O - 523- 512
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR RF.PORT NO. NBS-MONOGR. 140

2. Gov't Accession

No.

4. TITLE AND SUBTITLE

Time and Frequency: Theory and Fundamentals

3. Recipient's Accession No.

5. Publication Date May 1974

6. Performing Organization Code

7. AUTHOR(S)

Byron E. Blair, Editor

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2 73 0101

11. Contract/Grant No. EIIIM-6

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Partial Support by:

Richards Gebaur AFB, MO 64030

13. Type of Report & Period Covered N/A

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Number: 73-600299

se

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a sig aspects

bibliography or literature survey, mention it here.) This is a tutorial Monograph describing VariOUS'-Of

time and frequency (T/F). Included are chapters relating to elemental concepts of preci

time and frequency; basic principles of quartz oscillators and atomic frequency standards; historical review, recent progress, and current status of atomic frequency standards; promising areas of developing future primary frequency standards; relevance of

frequency standards to other areas of metrology including a unified standard concept;

statistics of T/F data analysis coupled with the theory and construction of the NBS atomic

time scale; an overview of T/F dissemination techniques; and the standards of T/F in

the USA. This Monograph addresses both the specialist in the field as well as thosejlesiring basic information about time and frequency. The authors trace the development and

scope of T/F technology, its improvement over periods of decades, its status today, and

its possible use, applications, and development in days to come.

Key words: Accuracy; Allan variance; atomic frequency standards; atomic time scales;

AT(NBS); BIH; buffer gases; CCIR; clock ensembles; clocks; crystal aging; Cs frequency

standard; dissemination techniques; figure of merit; flicker noise; frequency stability;

frequency standards; frequency /time metrology; hydrogen maser; leap seconds; Loran-C

magnetic resonance; masers; NBS-III; NBS-5; NBS /USNO time coordination; Omega;

optical pumping; precision; quartz crystal oscillators; radio T/F dissemination; Rb

frequency standards; satellite T/F dissemination; short-term stability; SI Units;TAI; tele

vision T/F dissemination; thallium beam standards; time; time dispersion; time domain;

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

time /frequency statistics; time scale algorithm; time scales; "unified standard"; URSI;

USA standard time zones; UTC(NBS); UTC(USNO).

18. AVAILABILITY Unlimited

|

1 For Official Distribution. Do Not Release to NTIS

|X ! Order From Sup. of Doc, U.S. Government Printing Office Washington. D.C. 20402. SD Cat. No. C13 44:140

^\ Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

470

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

$8.65

USCOMM.DC 29042-P74