,.*" NBS TECHNICAL NOTE 616

(2d Revision)

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

FREQUENCY STANDARDS AND CLOCKS:

A TUTORIAL INTRODUCTION

c,2
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and

technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to pro- mote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the

Office of Experimental Technology Incentives Program. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consist- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center for Radiation Research — Laboratory Astrophysics 2 — Cryogenics 2 — Electromagnetics 2 — Time and Frequency*. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed by industry, commerce, educational insti- tutions, and Government; provides advisory and research services to other Government agencies; and develops, produces, and

distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials, the Office of Air and Water Measurement, and the following divisions:

Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor Radiation — Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services developing and promoting the use of avail- able technology; cooperates with public and private organizations in developing technological standards, codes, and test methods; and provides technical advice services, and information to Government agencies and the public. The Institute consists of

the following divisions and centers: Standards Application and Analysis — Electronic Technology — Center for Consumer Product Technology: Product Systems Analysis; Product Engineering — Center for Building Technology: Structures, Materials, and Safety; Building Environment; Technical Evaluation and Application — Center for Fire Research: Fire Science; Fire Safety Engineering. THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides 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; and serves as the principal focus wthin the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer

languages. The Institute consist of the following divisions: Computer Services — Systems and Software — Computer Systems Engineering — Information Technology.

THE OFFICE OF EXPERIMENTAL TECHNOLOGY INCENTIVES PROGRAM seeks to affect public policy and process

to facilitate technological change in the private sector by examining and experimenting with Government policies and practices in order to identify and remove Government-related barriers and to correct inherent market imperfections that impede

the innovation process. THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS; promotes the development of the National Standard Reference Data rSystem and a system of in- formation analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services

to ensure that the NBS staff has optimum accessibility to the scientific information of the world. The Office consists of the following organizational units:

Office of Standard Reference Data — Office of Information Activities — Office of Technical Publications — Library —

Office of International Standards — Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

1 Located at Boulder, Colorado 80302.
Frequency Standards and Clocks:

A Tutorial Introduction

k

NATIONAL BUREAC

OF STANDARDS

LIBRARY AUG : 3 B77

H. Hellwig

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

•*»,AU 0« *

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued June 1977
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 616 (2d Revision)

Nat. Bur. Stand. (U.S.), Tech Note 616 (2d Rev.) , 70 pages (June 1977)

CODEN: NBTNAE

Tech. Note 616 (2d Revision) dtd June 1977 supersedes:

Tech. Note 616 (Revised) dtd March 1974

Tech Note 616 dtd April 1972

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1977

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

Page

1

.

INTRODUCTION 1

2

.

BASIC CONCEPTS 6

2 .

1

Accuracy, Reproducibility, Stability 6

2 .

2

Time Accuracy 9

2.3 Clocks 12

3

.

FREQUENCY STANDARDS , GENERAL ASPECTS 13

3.1 Resonators 13

3 . 2 Primary and Secondary Standards 18

4

.

QUARTZ CRYSTAL DEVICES 19

4 .

1

Quartz Crystal Resonator 19

4.2 Effects on the Crystal Resonator Frequency 25

4.3 Quartz Crystal Oscillator Performance 29

5

.

ATOMIC RESONANCE DEVICES 31

5 .

1

Atomic Resonators 31

5.2 State Selection 34

5 .

3

Interrogation of the Atoms 35

5.4 Signal Detection 35

5 .

5

Atomic Frequency Standard 39

5.6 Effects on the Atomic Resonator Frequency 41

6

.

AVAILABLE ATOMIC FREQUENCY STANDARDS 43

6 .

1

Cesium Beam Frequency Standard 46

6.2 Rubidium Gas Cell Frequency Standard 49

6 .

3

Atomic Hydrogen Maser 52

7

.

SUMMARY AND COMPARISON OF AVAILABLE FREQUENCY STANDARDS ... 54

8. TRENDS 58

iii
LITERATURE 60

ACKNOWLEDGMENTS 62

APPENDIX 1 63

APPENDIX II 64

LIST OF FIGURES

Page

Fig. 1. Definition of time and frequency. 3

Fig. 2. Frequency standard and clock. 5

Fig. 3. Relationships between clock accuracy, frequency

stability, and frequency offset. 10

Fig. 4. Example of a clock system. 11

Fig. 5. Examples of resonators. 14

Fig. 6. Decay time, linewidth, and Q-value of a resonator. 15

Fig. 7. Hierarchy of frequency standards. 17

Fig. 8. The piezoelectric effect. 20

Fig. 9. Principal vibrational modes of quartz crystals. 21

Fig. 10. Typical quartz crystal mount. 22

Fig. 11. Block diagram of a quartz crystal oscillator. 23

Fig. 12. Fundamental and overtone resonance frequencies. 24

Fig. 13. Frequency stability of the better quartz crystal

oscillators. 28

Fig. 14. Spatial state selection. 32

Fig. 15. Optical state selection. 33

Fig. 16. Atom detection. 36

Fig. 17. Optical detection. 37

Fig. 18. Microwave detection. 38
Fig. 19. Atomic frequency standard. 40

Fig. 20. Schematic of a cesium beam tube. Typically, a cavity

with separated interrogation regions is used. This

design offers certain advantages over a simple cavity

of a length equivalent to the separation of the two

regions. See Appendix II. 44

Fig. 21 Frequency stability of commercial cesium beam frequency standards.

a) typical performance

b) typical performance of high beam intensity tubes

Individual units may perform slightly worse or better

than shown. Modern laboratory standards perform still

better. 45

Fig. 22. Schematic of a rubidium gas cell 47

Fig. 23. Frequency stability of commercial rubidium gas cell

frequency standards. 48

Fig. 24. Schematic of a hydrogen maser oscillator. 50

Fig. 25. Frequency stability of a hydrogen maser oscillator. 51

LIST OF TABLES

Page

1. Summary and Comparison of Available Frequency Standards 54-57

2. Additional Promising Items Under Investigation 59

FREQUENCY STANDARDS AND CLOCKS;

A TUTORIAL INTRODUCTION

The topic of frequency standards and clocks is treated in

a tutorial and non-mathematical way. The concepts of time,

frequency, frequency stability, and accuracy are introduced.

The general physical principles and design features of frequency

standards and clocks are described. The design, performance,

and limitations of quartz crystal oscillators and atomic devices

(cesium, hydrogen, rubidium) are discussed in detail and critically

compared for laboratory devices as well as for devices intended

for field usage.

Key words: Cesium beam; clocks (atomic); crystal

oscillator; frequency accuracy; frequency stability;

frequency standards; hydrogen maser; quartz crystal;

rubidium gas cell; timekeeping.

1 . INTRODUCTION

Frequency standards and clocks: what do they have in common? A more complete answer will be given later. We note for the moment that most

clocks and in particular the very accurate and precise ones are based on frequency standards. The reason for this is the intimate relationship

between frequency (symbol v> "nu") and time (symbol t) . If we look at

a series of events which are occurring in a somewhat regular fashion,

e.g., the rise of the sun every morning, we can state how many of these

events occur in a given time period: this number would be the frequency

of this series of events. In our example we could say that the frequency

of sunrises is v = 7 events per week or v = 365 events per year. "Events

per week" or "events per year" would be called the unit which we used

for our frequency number; this frequency number is different for different units. In our example we assumed that we know somehow what a week

or a year is, i.e., we relied on some external definition for our unit

of time.
We can now ask, what is the time between the events? The answer

for our example is simple, one sunrise succeeds the other after

t = — week or t = —— year where we used "week" and "year" as two

/ 365

possible choices for our unit of time. We can rely on the regularity

and precision of the occurrence of the events, in other words, on their precise periodicity. Hence, we could define: the unit of time

is one week; one week is the time elapsed at the seventh sunrise

following an initial sunrise.

We learned two things: (a) For periodic events, the time between

the events t is related to the frequency V of their occurrence in the

following simple way

V = I (1)

and (b) that periodic events can be used to define time, i.e., the

generator of the periodic events - the frequency standard - can be used

as a clock. The frequency standard becomes a clock by the addition of

a counting mechanism for the events.

In our example above, the frequency standard is the rotating earth.

The time between recurring events is one day. This frequency standard

served mankind for thousands of years and remained until very recently

the source for the definition of time. The counting mechanism which

made it a clock was the recording of years and days.

The needs to interpolate time from day to day, to get along for

many days without celestial observations, and to more precisely measure

time-intervals which are very much shorter than a day brought about the

invention of clocks. Although there are other types of clocks like the

sand-clock or the decay in radiation intensity of a radioactive substance, we shall confine ourselves to the discussion of clocks based

on frequency standards (i.e., systems based on periodic events).

The first clocks based on a frequency standard (a pendulum) were

invented about 400 years ago. This type of clock is most widely used

today. The pendulum may be a suspended weight (gravitational pendulum)

like in "grandfather" clocks or the balance (torsion pendulum) or quartz
II

LU^

>- CJ O o ^ _l LU c_) rjcr Q

LU LU

en 1— o cr: o

oo 1— Q <c O cr; i—i

LU

DC s

LU LU D_ CD

a: >

LU LU COO U_ i—i LU

u_

a

Q_ LU

00 3

<C <C o

a)O

a; Q

60

:z> 00 o 00 o o < a.
crystal of modern wristwatches. The objects of our discussion in this

report are today's most advanced frequency standards and clocks; however, a close look at our traditional clocks will show all the essential

features which we will recognize again in our later discussion of

quartz crystal and atomic clocks.

The pendulum in our clock is the frequency determining element. In order to arrive at a frequency standard the pendulum has to be set in

motion and to be kept in motion: A source of energy is necessary

together with means to transfer this energy to the frequency determining

element. In a wristwatch this source of energy is typically the winding

spring, and the energy is transferred by mechanical means which are controlled by the pendulum itself in order to cause energy transfer in

the proper amount at the proper time in synchronism with the movement of

the pendulum. This is called "feedback" in electronic systems. We now

have a frequency standard; the tick- frequency of its pendulum could be

picked up acoustically, for example, and used as a standard frequency.

This is actually being done commercially when adjusting the rate of a clock: the tick-frequency is compared to some (better) standard frequency.

In order to arrive at a clock, a read-out mechanism is necessary which

counts and accumulates the ticks (more accurately: the time between the

ticks) and displays the result. In our example of a wristwatch, this is

accomplished by a suitably dimensioned set of gears and the moving hands on the clockface.

The unit of time today is the second (symbol s) . Very much in

analogy to our sunrise example, the second is defined in reference to

a frequency determining element. Since 1967 by international agreement

this "natural pendulum" is the cesium atom. One second is defined in

the official wording as "the duration of 9192 631 770 periods of the

radiation corresponding to the transition between the two hyperfine levels

of the ground state of the cesium-133 atom". Accordingly, the frequency

of the cesium pendulum is 9192 631 770 events per second (the cesium atom

is a very rapidly oscillating pendulum) . Following our eq (1) the unit

of frequency is then defined as hertz (symbol Hz) . One hertz equals the
REQUENC

TANDAR OUTPUT

[Z<"1 1

<L3 ^ o z uo

1—1u

CLO OUN UMUL ISPL ' 1 a 'o

T3 ts

(_> i—1 1—

«=C c

Z.-Z.-ZL

d i i i t—l LU 4-J 3S2 CO o-o; lu >> ' 1 LU LU _l

C£ \— LU

UC ^ LU LUO

0)3 (J a1 1 1 ID ca U Q \m LU

LU

Lu '

>- C£ O o Z I— LU <C CTLU

VNJ

>- LU O (_> OH CH

LU ZD LU Z Z O

LU GO

o: lu

Ll_ t3
repetitive occurrence of one event per second. The use of "hertz" is

preferred to the older term "cycle per second", cps,and was assigned

in recognition of the exceptional contributions of the 19th century

physicist Heinrich Hertz.

2. BASIC CONCEPTS

2.1 Accuracy, Reproducibility, Stability

The performance of frequency standards is usually described in

terms of accuracy, reproducibility, and stability. We will use these

terms in the sense of the following definitions:

Accuracy: the degree of conformity of a measured and/or calculated

value to some specified value or definition.

Reproducibility: the degree of agreement across a set of independent devices of the same design after adjustment of appropriate specified

parameters in each device. Alternately, it is the ability to reproduce,

independently, a previous frequency value.

Stability: the frequency and/or time domain behavior of a process.

In the time domain (i.e., the measurement time or duration is the varied

quantity) a frequently used measure of stability is the pair-variance

(or Allan variance) (to be explained later) or its square root (the

pair-stability)

It is obvious from these definitions that frequency accuracy will be

largely of interest in scientific measurements and in the evaluation and

intercomparison of -the most advanced devices, but of little or no interest to the average user of frequency standards. A good reproducibility

is an asset in applications where it is of importance to rely on some degree of conformity of the output frequency of several devices such as

a factory-guaranteed frequency value. The characterization of the

stability of a frequency standard is usually the most important information to the user. The frequency stability (symbol a, "sigraa") of a freL In this paper, for tutorial purposes, only the time domain stability

is used. We note, however, that for many scientific applications the

frequency domain stability measure is more useful.
quency standard will depend on a variety of physical and electronic

influences both internal and external to the device which cause frequency fluctuations. The frequency stability depends also on the

exact measurement procedure which was used to measure the stability.

We shall explain this in the following: Frequency stability can be measured by taking a reasonably large number of successive readings

of an electronic counter which counts the frequency of the device to be evaluated. Each counter reading (in hertz) is obtained by measuring or sampling the counted frequency for some specified time, the

sampling time (symbol T, "tau") - This sampling time can usually be

chosen by simply adjusting a knob on the counter; for example, a sampling time of 0.1s or Is or 10s may be chosen. Everyone has had the

experience that fluctuations tend to average out if observed long enough;

however, this is not always so. Sigma will therefore usually depend on the sampling time of the measurement and tends to get smaller with

longer sampling times; again, there are many exceptions to this.

It may be that the fluctuations at some later time are partially

caused by, or depend to some degree on, the previous fluctuations. In this case, the actual value of a will also depend on the particular way

in which the many counter readings are averaged and evaluated. Also,

it will be of influence whether the counter starts counting again

immediately after completion of the preceeding count or if some time

elapses ("dead-time") before counting commences again.

Finally, electronic circuits will have a finite response time, e.g.,

they cannot follow fluctuations faster than some given rate. For example, our eye can not register light fluctuations which occur faster

than about every — of a second; using eq (1) , we say that the eye has

a frequency response of 10 Hz, or that its bandwidth is only 10 Hz, i.e.,

the eye can not follow frequencies higher than 10 Hz. In order to measure frequency stabilities for sampling times larger than some value , we have to provide for an electronic frequency bandwidth which is larger

than about —

T"
We summarize : a recommended way of properly measuring and describing

frequency stability is the following: (a) make sure that the frequency

bandwidth of the total measuring set-up is larger than — . where T . T mm min

is the smallest desired sampling time; (b) use a counter with a deadtime as small as possible ; (c) take a sufficiently large number of readings at a given sampling time which is held constant and compute

•V

addition of the squares of the differences between successive readings

2 x total number of differences used

In the scientific literature this O is called the square root of the

pair (or Allan) variance; (d) repeat (c) at other sampling times x and

tabulate or plot a as it depends on x. See Appendix I (fig. 26).

Commonly, a will be given as a fractional or normalized value, i.e.,

the value obtained for the frequency stability is divided by the carrier

frequency. For example, if a frequency stability of 0, = 10 Hz were measured at a carrier frequency of V = 5 MHz (MHz = megahertz = million Hz)

then the fractional frequency stability would be

10

a = - 6 = 2 x 10 6. y 5 x 10

We denote the kind of a by a subscript, 6v ("delta nu") referring to frequency fluctuations (measured in Hz) or — = y referring to fractional

or normalized frequency fluctuations (dimensionless) . A stability of one part in a million is thus

and one part in a trillion is written as

2 The dead-time should be less than the reciprocal bandwidth; if not,

computation procedures exist to account for larger dead-times.

3 The counter readings can be taken in Hz, O will then have the

dimension of Hz.
The common usage of the fractional frequency stability <J instead

of the frequency stability a» (given in Hz) has its good reasons. In many applications of frequency standards their nominal output frequency

is used after multiplication or division, i. e. , the standard frequency is

used to synthesize electronically other frequencies. Also, frequency

standards themselves already synthesize several output frequencies, and

different frequency standards offer different output frequencies. In such

a usage of frequency standards as well as in the comparison of their performances it would be extremely inconvenient to state 0~ because this

number (in Hz) would change with any alteration in frequency due to

synthesis. This is not the case with because 6v as well as V change

in the same way in synthesizing procedures. Of course, we assume here

that synthesis does not cause additional instabilities, an assumption

which is mostly valid with today's electronic capabilities.

2.2 Time Accuracy

In clocks, time accuracy is of importance. In accordance with the

definition for accuracy at the beginning of this section, the accuracy

of a clock is the conformity of its reading (the date shown) with the

reading of a standard time scale (a standard or reference date) . A

clock can be initially set (synchronized) with respect to a reference

clock with some accuracy T . Its reading then gradually deviates by an amount T(t) from the reading of the reference clock. T(t) indicates

that the deviation or error T is a function of the time t which elapsed

after synchronization with the reference. This deviation, i.e., the

accuracy of the clock, depends on the stability performance e(t)

("epsilon of t") of the frequency standard in the clock, the fractional

frequency offset R of the clock"* with respect to the reference clock,

and on the change D of the fractional frequency of the clock with time

(D = fractional frequency drift) . Other parameters may be important;

however, those mentioned are most commonly encountered. The time reading

of the clock then has a degraded accuracy T(t) which is given by

The counter readings can be taken in Hz; a will then have the

dimension of Hz.
r~~ f/ O /y in yf =d- €- i/

O

CO

' /A //CMo

*

k \/ / o

CO <Ti

I I o o

«— 13S330 A0N3n03U3 IVNOIlOVad WW= y

Ainiavis A3N3nD3cJd "WNOiiovtiJ '(i =.t)

A/

^jO

(1) en

<4-( 1<HO

5^ A o

1 e

1 (1) 3 '' s cr

I/O

<D Q ^

z. VH o T3 o C

LU nj 00

s^^ „ >s z.

J-> o r^

1—

,£5 1— a! <c

cc m en => "—

>* o z U

3: o fi en CU r— re 3 O cr z <u •>- h

oo

<«

n o: ^

LU o

h- rd Ll_ *h <c !3o

LU o S flj i—i ^

h- u

o

„

1—

CJ +-> s

0)

<D£4->(U J3

entx

.,-1 ^toc

o

• w

4-) n) 1—

CD Pi

.-I

10
o1—1 en ^c

1— c_> o o

LU _l

_l <_> LU

i i

N

ZTZ o

U3

>-O CC Z. LU

LU Q

zd >—i <=r>

LU I—

I

CH Q

Ll_

1 i N

32

s:lo

en o

^ LJt- o i— <

o z: _i

o o s: o ZD —c_> o

CO o

_i o^->

DUI N ai/ix

i— a: —LU

a.

^ =3 o a. o I—

_i ZD o o

A

o3 Qio

en LU (— Q ja MDLJ

> Q- ^

l—

l

LU Q CD

>-O Q

^ en

LU cC

zd a

o-z:

LU >=t o; i— U_ CO

Oo

I—

I

o

f

U

•r-l

11
1 2 T(t) = T +R t+— Dt + £(t) (2) o o 2

The presence of a frequency drift D can rapidly deteriorate clock accu- racy because the corresponding time error "accelerates" following the —square of the elapsed time t. If T , R and D are not present (i.e.,

o o zero), only the random fluctuations can cause a time error T(t) = £ (t)

£ (t) of course can be calculated from the frequency stability . This can be a rather complex mathematical problem and is often called "clock

modeling" or "time prediction". For most practical uses, however, a very

simple, quite good approximation may be used:

£(t) - t x a (T = t) (2a)

Y

where O (t = t) means the fractional frequency stability evaluated for

a sampling time T equal to the time t which elapsed after the last setting

of the clock. For example, a clock with a fractional frequency stability

of a = 10" for sampling times of 10 seconds (about 1 day) would be

accurate to T = ± 105 x 10-11 second = ± 1 microsecond per day (again we assume

T , R and D to be zero)

o o

' A clock with a fractional frequency offset of R = Av/V = 10~ would

be accurate to T = 100 microseconds after 1 day (assuming T , D and

o

£(t) to be zero). And, finally, a clock with D = 10

-9

per day would be

accurate to only T = 5 x 10~ 6 'day == 0.4 second, .after 100 days.

2 . 3 Clocks

In the Introduction we discussed that the addition to a frequency

standard of a mechanism, which counts and accumulates and possibly displays the result, creates a clock.

This task can be performed by a frequency divider which, for example,

derives a frequency of 60 Hz directly from a 5 MHz crystal oscillator. The

60 Hz voltage can be used to drive an electric clock similar to those

driven by the 60 Hz power line frequency which we use at home or at work.

Or, an additional electric pulse generator may be used which generates

one very sharp electrical pulse per second. The time interval of 1 second

12
between the pulses (corresponding to a frequency of 1 Hz) is directlyderived from the output of our frequency standard. The pulses can be

used in time comparisons with those of other, similar clocks; or a counter/accumulator/display (clock-face) can be driven by them.

3. FREQUENCY STANDARDS, GENERAL ASPECTS

3.1 Resonators

The performance of a frequency standard is to a considerable degree,

but not exclusively, given by its frequency determining element. It determines the frequency by its resonance behavior. Some examples

for resonance phenomena are (a) a rod, clamped only at one end, which

can vibrate, (b) a block of solid material which can contract and expand

and thus vibrate, (c) a capacitor-coil combination (tank circuit) in

which the electro-magnetic energy can oscillate back and forth between

these two elements, (d) an antenna (a dipole) where the distribution of

electric charges can oscillate back and forth, and (e) a coil in which

an electric current can create a magnetic field which can oscillate

between its two possible polarities (a magnetic dipole) . All these devices have in common that they can vibrate or oscillate if they are excited. The method of excitation may be a mechanical pulse for (a) and (b) or an electrical pulse for (c) or a sudden surge of an electric

field for (d) or of a magnetic field for (e) . The devices exhibit a resonance, i.e. , they are resonators with a well-defined frequency which

is characteristic of the physical dimensions of the device: the length of

the rod, the thickness of the block, the size of the capacitor and coil,

the length of the antennas. Once excited, the oscillations will die out

gradually with a decay time which is determined by the losses of the

resonator. Some of these losses are internal friction as in our cases

(a) and (b) , and electrical resistance for (c) through (e) ; in any case, the oscillation energy is ultimately transformed into heat. If there were

no losses, the oscillations would never stop; we would have an ideal

resonator. The more losses, the faster the oscillations decay and the resonance is less pronounced. It is now obvious that we could use the

decay t of the oscillations to describe the quality of our resonator.

The larger t, the better the resonator. Q

13
CD^ :*: h- o

«: o

Qi _i

CO 20

QO o => CD O O

21 1 Q£

1—1 CC >—

1—00

<: h- _J !-!-—» _1 O i£ m<:z uc< CO <C 1— 00^

COuu

cdCO

to (_} <u 1—

h

h- V-l LU O z 0] CD a> <c «t •—

s 2: &• 2: s

CD LU

X

2: 1—

>-• 2: 1—

W <c <

_l LU • _) _l lO >— O ^ cj a. W) CO 1—

• r-l a k

tt

14
z o

O I—

<S> i—i <c

z: f— 2:

—i < o >- _l 00 -rf cc —i uj O i—I CC

UJ o

Ql/)< o

r-l "a

u_ a: uj o o

<-> t—

z: a: <c < o ^ o>w oo =5 uj

Q£ UJ

C_)

O" h

UJ

an

«3 u_

S3o

tn4)

fH

i—

I a

C

J3

J-l

a)u

<U Q

l—l OO

<_> _l X =>

UJ Q_

15
An alternate way of measuring the resonance behavior is to use an external oscillator, to couple it to the resonator, and to sweep slowly

the frequency of the external oscillator across the resonance. We will

find again a resonance frequency at which the resonator will oscillate

most pronounced, i.e., with the greatest intensity. On both sides of

the resonance frequency, the response of the resonator will lessen until

it ceases to respond. We can define a frequency interval around resonance

in which the resonator response is relatively strong; we call it the resonance linewidth (symbol W) . There is a simple relationship 5 between

W and the decay time t

W = -i . (3) d

Again, as in the case of 0, it is of advantage to state the linewidth

W

in a fractional way. The fractional linewidth would be — where the

v

o symbol v is used for the resonance frequency. More widely used is the

quality factor of the resonance (symbol Q) which is defined as the

reciprocal fractional linewidth

v Q = -£ • (4) w

In frequency standards we obviously like to have large values for

the Q of the frequency determining element. As an example, if Q = 106

, then a fractional accuracy of 10~ 1 ° would imply that we can determine

the center of our resonance curve to a small fraction (lO

-4 or one hundredth of a percent) of its width. In the same example, a stability

of 10 for some sampling time would correspond to an ability to keep

the frequency to within 10~ 6 (one millionth) of the resonance linewidth

around a given value. It is clear, therefore, that the frequency stability

and accuracy of a frequency standard may be expected to become the better

the higher the Q-value of the frequency determining element.

Many kinds of frequency determining elements have been and are being

used in frequency standards. They can be grouped into three classes:

5Equation (3) is only an approximation. Depending on the particular

shape of the resonance curve we would have to insert a factor into

this equation; however, this factor is never far from unity, t is

defined as the decay to — of the original amplitude, e is a nuuiber, e - 2.7.

16
Q

Q

<C

>- CO Q£ o < OL Q «a: Z Q o Z o <

LlI 1— CO CO

X!oB

a) Xu

(-1 a!

!h

EN

17
Mechanical resonators;

electronic resonators;

atomic resonators.

As far as mechanical resonators are concerned we will only discuss one group in detail, the quartz crystals. Other mechanical resonators

like the pendulum and the tuning fork are of no importance in today's

high performance frequency standards although they have been historically

very important and are still used in low performance devices (e.g. , in

watches) . For similar reasons we will also omit the discussion of electronic resonators like the tank circuits (our device (c) of above) and

6 microwave cavities. Atomic resonators form the heart of our most accurate frequency standards and clocks and will, therefore, be extensively

discussed.

3.2 Primary and Secondary Standards

At this point, we should briefly discuss the frequently used terms

"primary frequency standard" and "secondary frequency standard". These

terms should refer to the systems-use of the devices; any frequency

standard, regardless of its accuracy or stability, can be a primary frequency standard, if it is used as the sole calibration reference for other

frequency sources. A secondary frequency standard is a device which is

occasionally calibrated against a primary frequency standard but operationally serves as the working reference for other frequency sources. The use of the terms "primary" and "secondary" to describe the performance and/or the design of a frequency standard itself is not helpful, often

misleading and therefore discouraged. These aspects can be described

adequately and accurately by stating accuracy, reproducibility, and

design features.

One class of frequency standards can be separated from the rest. We

call those the evaluable or "primary" frequency standards, which, by

virtue of their basic physical operation as well as their design, allow the

experimental evaluation of all known influences which might alter the output

frequency. The accuracy of the evaluable frequency standard can thus be

stated for the single device without reference to any other frequency

6We will touch on one very interesting example of a standard using a microwave cavity, the superconducting cavity oscillator, (See Section 8)

18
standard and the term "primary" is then permissible because they are by virtue

of their design the top of a calibration hierarchy. Some (but not all ) cesium

and hydrogen standards fall in this category.

4. QUARTZ CRYSTAL DEVICES

4.1 Quartz Crystal Resonator

The guartz crystal is a mechanical resonator much like our examples (a) and (b) of section 3.1 The resonator's oscillations have to be excited and

sensed externally. In the case of a guartz crystal this is done by taking

advantage of its piezoelectric properties. The piezoelectric effect is a special

property of a certain class of crystals. Compression or dilatation of the

crystal generates a voltage across the crystal, and conversely, the application

of an external voltage across the crystal causes the crystal to expand or contract depending on the polarity of the voltage. A crystal is not a homogeneous

medium but has certain preferred directions; thus, the piezoelectric effect has

a directional dependence with respect to special, preferred directions of the

crystal. In order to take advantage of the piezoelectric effect one has to cut

the crystal resonator from the crystal block in a well defined way with respect

to these crystallographic directions. The raw material today is both natural

guartz and synthetic guartz. The crystal is cut out of the raw crystal in the

desired orientation with the aid of optical technigues which allow the determination

of the crystallographic axes. The high precision final orientation of the cut

and the tuning to the desired freguency is then done by grinding and etching

under control of x-ray methods.

The guartz crystal can be cut and electrically excited in a variety of

ways. The most common types of vibrations (modes) are the longitudinal and

thickness modes, the flexure (bending) mode, the torsional mode, and the shear

mode. In order to use the piezoelectric effect, electrodes have to be put on

some of the crystal surfaces such that the desired mode is excited. The electrodes

are typically created as extremely thin metallic coatings by vacuum evaporation

of metals. Electric leads are attached to the electrodes, (e.g., by soldering),

which usually also serve as the mounting support thus suspending the guartz

crystal. In order to least perturb the mechanical vibrations of the crystal,

the electrode-support leads are attached at points where no vibrational motion

occurs (modes) . The crystal is usually encased (in metal or glass) and the

enclosure is sometimes filled with a protective gas or is evacuated.

19
M _j

h- <c

CC i— <C OO

ZD >- cr CC

<_> + " > 4 I L J

CC

a. 11 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 11

LU

O

CJ3 i—

<C I—

\—

O

—i <c o cc q o

lli o

_i oo

Q. LU

D. OO

«=c =>o

UJ C3

cc <c

=3 1— oo _i oo o

LU > Z3 cc OO a. oo

00 LU

LU

Q 1—

cc LU <C

Q_ i-i cc —1 LU

O. Z

Q_ LU <C c3

u

<L> ON

<Ua, H

20
d I 2 J toO

(0uu

crO o

CDO

GO

Co

•rHau

n)

•T-t o

•r-t uH

21
o

Q

C/5 LU

LU l/) I— QUJ< O ^ C£

e— <-> es

<_> i—i CD

lu ^ <c

_i i— x

—1 o

<C z

C_> i—i

i-H h- 1—

CtL ^ a: 1— Z3 o

<_> O Q a.

uj 2: < Do

=C to i— a

O LxJ

to

u

u

o

• H

Eh

22
ono

o

o

>-

LU

ce:

<

o

-p

-p

en>iu

N

J-> U

<TJ D

1

&l

(0 •H

a;o

o

fa

23
FUNDAMENTAL

2nd OVERTONE

3rd OVERTONE

en

<DO

c

Um

<DU

tia

co

CO

cu

a>

flo

4-1 u

>

o

C

4th OVERTONE

60

24
A frequency standard can now be built by adding an electronic

amplifier (energy transfer) , and feedback. We call such a device

a quartz crystal oscillator. Its output frequency is determined by

the quartz crystal resonator whose frequency in turn is determined by

the physical dimensions of the crystal together with the properties of

crystalline quartz. The resonance frequency thus depends on the orientation

of the cut, the particular mode, and the dimensions of the crystal. As

an example, we find that the resonance frequency for a longitudinal mode

of vibration is approximately given by

V =2.7xl0 3 X7, (5) O X,

where £ is the length of the crystal. Equation (5) is written such that

the use of meters to express £ will give the resonance frequency v in

hertz. Equation (5) allows us to estimate the size of crystals. For

example, a 100 kHz crystal has a length which is of the order of a few centimeters and a 10 MHz crystal has a length (thickness) of just

a few tenths of a millimeter. We see from this that the production of

quartz crystals with resonance frequencies much above 10 MHz is hardly

possible. However, one can excite resonators not only in their so-called

fundamental mode (which we discussed so far) but also at multiples (overtones) of this fundamental resonance frequency. The best example for this

is the violin string which also can be made to oscillate at frequencies

which are multiples of the fundamental frequency; the violinist depends on this. Quartz crystals which are designated for the excitation

of multiples of their fundamental resonance are called overtone crystals.

4.2 Effects on the Crystal Resonator Frequency

Two deleterious effects, among others, are important in the design

of crystals and crystal oscillators and limit their usefulness. The first

is the temperature dependence of the quartz crystal resonance frequency,

the second is a slow change of the resonance frequency as time goes on (frequency drift or aging)

.

25
The temperature dependence is caused by a slight change in the

elastic properties of the crystal with temperature. This can easily be

imagined from the general behavior of matter: the packing density

of atoms increases with lowering the temperature. However, certain

cuts, i.e., certain crystallographic orientations of the crystal,

minimize this effect over a rather wide range of temperatures, most

notably the so-called "AT" and "GT" cuts. Temperature coefficients of

less than one part in 100 million per degree (celsius or kelvin) are possible. In other words, the fractional frequency change is less than

-8

10 with one degree of temperature change. Nevertheless, this effect

demands certain precautions in the design of a crystal oscillator if

very high frequency stabilities over longer times (hours or days) are desired and/or if large environmental temperature fluctuations are to be

tolerated. Hence, crystals are enclosed in electronically regulated ovens which maintain a constant temperature; in certain crystal oscillators

this is done to better than -r——— of a degree. 1000 a A different solution to the temperature problem is the so-called

temperature compensated crystal oscillator or TCXO. An additional frequency determining element in the oscillator, which can essentially be

just a small capacitor (see fig. 11 and our example (c) of sec. 3.1),

gives the opportunity to tune the oscillator over a limited range by

varying this additional element. If a temperature sensor is added which

causes a change in this capacitor one can adjust the response in such a way that the change in resonance frequency of the crystal resonator is

just compensated by a suitable adjustment of the added capacitor. Bimetal

springs have been used which mechanically change the setting of the

capacitor much in the same way as the automatic choke in many automobiles

works. Today, capacitors whose value changes with an applied voltage

(varactors) are used, as shown in figure 11; the applied voltage is

derived from a temperature sensing circuit. The TCXO thus does not

necessarily require further temperature control by an oven. However, we see the drawback of this approach. In adding a further frequency

determining element, the crystal resonator has to relinquish a corres26
ponding part of its control on the output frequency of the whole oscillator. We, therefore, realize that the stability performance of a TCXO will

degrade the more, the wider the temperature range of compensation is made!

The long-term stability (days) of TCXO's is therefore below that of

crystals with a good oven control. We find TCXO's in small, usually

portable units of relatively low performance,- i.e., for applications

where frequency stabilities from day to day and frequency changes over

some tens of degrees of temperature of not better than 10 9 are needed.

The drift, or aging, is a common behavior of all crystal oscillators.

It is a nearly linear (uniform) change in resonance frequency with time,

which frequently is negative (i.e., the resonance frequency decreases).

A frequency decrease could be interpreted as an increase in the crystal

size according to eq (5) . Many physical mechanisms have been considered

as the cause: contamination of the surfaces (deposition of foreign

material) ; changes in the electrodes or the metallic plating or the

mounting; reformation of loose (from grinding and etching) surface

material; changes in the internal crystal structure; etc.; all of this

possibly caused or enhanced by the vibrating motion of the oscillating

crystal. Careful fabrication and electrode design combined with clean vacuum enclosures have led over the years to a reduction of the aging

to about 10 per day and better for the best crystals. This aging

corresponds to 10 fractional thickness change per day, as we can see from eq (5) . For a 5 MHz crystal with a thickness of a little less than

a millimeter this aging corresponds to an absolute thickness change of

only 10 11 of a millimeter or less than — °f one percent of the diameter of an atom. It seems surprising that mechanical resonators can be

built which change their dimension by so little.

Three more effects on crystal resonators are to be considered. One

is its relative sensitivity to gravitational forces and acceleration:

7 This is also true for any tuning (frequency adjustment) capability

which is added to any frequency standard. The larger the tuning range,

the less the stability. The best frequency standards and clocks

can not directly be adjusted; however, adjustment can be done external

to the device via frequency synthesizers or time steppers (phase shifters)

27
toh

4-1 ni 1—

•iH * U o to

1—

4-1 CO >s o h

t

N

4->

CM B* o 00

cr

1 Q h

z. 01

4-1 o 4-> o <D

1

LJ ,£> o O0 <D

1— ' ^5

4-1 UJ <*H s: O o

o

1—

I— 4-1 r—

en

1—

z: 2 t—

ni _J 4-J

1

Q_ to

1 2! ^ o < O

00 a1 CM 0) o h

I o

be

•i-i

Ainiavis A3N3nb3c)j ivNOiiovyj

28
frequency changes will occur because of the stresses in the crystal

caused by these forces. This influence depends on the direction of the

force relative to the crystallographic axes and thus can be minimized

for certain orientations. The magnitude of the effect is typically of

the order of 10-9 for accelerations corresponding to the earth's gravitation.

The second effect is related to intermittent operation. If a crystal oscillator is turned off and, after some time, put back into

operation it will not oscillate immediately at the original frequency but

will exhibit first a "warm-up" due to temperature stabilization of the

crystal resonator and its oven and then for some time (as long as many

days) a large but diminishing drift until it reaches its previous aging

performance. The frequency at which it will then operate might also be

substantially different (as compared to its stability and aging performance) from its frequency before the interruption. The third effect is

the sensitivity of the crystal to ionizing radiation (x-rays, nuclear

radiation) : transitory and lasting frequency changes are produced via

radiation- induced changes in the crystal lattice.

4.3 Quartz Crystal Oscillator Performance

Crystal resonators have Q-values which are typically in the range

from Q = 10 5 to almost Q = 10 7 (around room temperature; at very low

temperatures much higher Q values can be obtained) . These are very high

Q-values as compared to most other resonators except, most notably,

atomic resonators.

These high Q-values are an essential prerequisite for the excellent

stability performance of crystal oscillators. The best presently available devices show stabilities of about one part in 10 1 3 for samplinq times

from one second to hundreds of seconds. There is some experimental evidence that

some crystal resonators may perform better and that limitations are primarily caused by noise in the electronic components in the oscillator circuits. This noise (flicker noise) may possibly be reduced by a special

selection of low noise components (transistors, capacitors, etc.) and by

some special circuit design. Thus there is a reasonable chance that the

29
stability may reach values of better than 10-1 3 for sampling times of

seconds to hours. For times shorter than one second, the stability is

often determined by additive noise in the output amplifiers and can then be reduced by other better electronic circuits or by a (crystal)

filter in the output. The long-term stability beyond several hours

sampling time is determined by the aging and by external influences such

as line voltage variations, temperature fluctuations, etc. The immediate

environment of the resonator, i.e., the mounting, enclosure, etc.,

probably are of substantial influence in this regard and improvements

appear possible. A specification of accuracy is not very well possible

with crystal oscillators. Without any frequency calibration they

possibly can be fabricated via thickness-determination (not very practical) to about 10 6 frequency accuracy. If they are calibrated against

a high accuracy frequency standard they maintain this calibration

(accuracy) according to their long-term stability performance, e.g.,

a crystal with the low aging of 10-11

per day will be accurate to a few parts in 10 for the duration of a year.

We realize, therefore, that crystal oscillators require calibration,

which may be rather frequent depending on the requirements. The frequency

adjustments are being made with a small added capacitor in much the same way as we discussed before in connection with the TCXO. The most stable ones with the lowest aging rate cost more than $1000, have a volume of

a few hundred cubic centimeters, and require a power of several watts.

They have a crystal oven for temperature control, well-designed electronics, and usually several output frequencies which are derived from

the oscillator frequency with the aid of frequency dividers and multipliers.

These high performance devices presently use crystal resonators in the

1 to 10 MHz range with Q-values of more than one million.

Crystal oscillators which are cheaper and/or smaller are available

in an immense variety of designs at certain sacrifices in frequency

stability and/or environmental insensitivity. Costs can go down to

below $100, sizes to a few cubic centimeters, and power requirements

to less than 0.1 watt. The reliability of crystal oscillators is

usually not limited by the crystal, the mean time between failure

(MTBF) being that of any electronic circuit of equivalent sophistication.

30
5. ATOMIC RESONANCE DEVICES

5.1 Atomic Resonators

The basis of commercially available atomic frequency standards are resonances in atoms at microwave frequencies (range 1 to 100 GHz,

9 GHz = gigahertz = 10 hertz) . Resonances in molecules and resonances

at higher frequencies in the infrared and visible regions are being

studied for frequency standard applications but have not yet led to practical devices; however, their potential is high Csee Section 8)

.

We will confine ourselves, therefore, to the discussion of microwave

resonances in atoms. We may picture such a resonance as a little magnetic dipole antenna as was discussed in our example (e) in Section 3.1.

We typically deal with a great many of these dipole antennas (atomic

resonators), and we can separate them into two kinds 8: (1) receiving

antennas, which will absorb energy from a field at their resonance

frequency, much like our TV antenna at home, and (2) transmitting antennas

which radiate energy at their resonance frequency in a fashion analogous

to the action of the transmitting antenna of a broadcasting station. A

physicist might say that the atoms which act like a receiving antenna are in the "lower state" and those acting like a transmitting antenna are in

9 the "upper state" . In a natural ensemble of a great many atoms (a gas)

,

we find that the total number of upper state atoms is nearly equal to the

total number of lower state atoms. This has an important consequence:

if this gas is placed in an external magnetic field, which oscillates at

the atomic resonance frequency, all atoms may resonate; however, nearly

half of the atoms receive (absorb) energy from the field, the other half

emit (add) energy of an equivalent amount to the field. It is obvious

that the net effect is almost zero; the gas as a whole acts as if it

has almost no resonance although the individual atoms each may resonate.

Of course, this is a simplification

9 There is a peculiarity with atoms: an atom changes from the upper

to the lower state upon emission of a well-defined amount of energy,

and, correspondingly, an atom changes from the lower to the upper

state after receiving an equal amount of energy at the atomic resonance frequency.

31
U~) IS)- o I— I— <C

i CC

O I— I— <

<C I—

00

I DC

OvJ LU

Q.

www -•-•WW

33 LU

i—i ZD

s: o

o u~>

si)

• r-l

32
o

&

DO H

i—i UJ

_J CO

33
From this we see that in order to observe the atomic resonance we have

to change somehow the relative amounts of the two kinds of atoms; the

upper or the lower state has to be in the majority, corresponding to a net emission or absorption of energy. The way in which this is done

determines the design of an atomic resonance device, which is the

frequency determining element in our atomic frequency standard.

5.2 State Selection

We will now discuss the two most important methods to accomplish

what is called state selection: the change in the relative numbers of the

two kinds of atoms.

(a) Spatial state selection: This method relies on an actual sorting

procedure where the two atomic states are sorted into different directions

in space. One of the states can then be used, the other is discarded.

As an example, an actual system may produce an atomic gas by heating the

substance in an oven to a suitable temperature. The atoms leave the oven through a hole and form an atomic beam in an adjacent vacuum chamber.

The atomic beam is then passed through a rather strong magnet which causes

the separation of the beam into two beams, each of them containing only

one kind of atoms. We remember that our picture of an atom is that of a little magnetic dipole antenna. The magnet exerts a force on these magnetic dipoles, which acts in opposite directions for the two different

atomic states (we note this without further explanation)

(b) Optical state selection : This technique takes advantage of the fact

that the atoms have more than just one resonance. Other resonances

typically correspond to infrared or visible (light) frequencies. We can excite one of these resonances by shining intense light of the corresponding

frequency on the atoms. If the light is filtered carefully, very monochromatic (one color, i.e., a very well-defined frequency) light is obtained. If the light frequency is chosen properly, only one kind of the

atoms resonates. At the same time, this light frequency is too far away

from the corresponding light resonance of the other kind of atoms. The

light resonance can thus "remove" one kind of the atoms and provide for

the desired majority of the other kind.

34
5.3 Interrogation of the Atoms

We are now almost in a position to assemble our atomic frequency

standard. We still need some means to observe the atomic resonance. A microwave cavity is typically used. Such a cavity has microwave

resonances which are determined by its physical size. The (electrical)

losses of this cavity are given by the electrical conductivity of the

cavity material. Such a cavity may have the shape of a cylinder or that

of a box. It resonates in a way quite similar to the working of an organpipe in the case of acoustic waves. The best known example of a microwave

cavity is the microwave oven where food is heated by placing it into the resonance field of a cavity. In order to observe the atomic resonance we have to place the state selected atoms inside of this cavity and subject them for some specified time to a microwave signal at their reso- nance frequency. The microwave signal will change the relative number

of atoms in the two states, e.g. , if all atoms were initially in the

upper state we find some in the lower state after the microwave signal

acted upon them for some time (see footnote 9). If the frequency of the

external microwave signal is exactly at the atomic resonance frequency,

this transfer of atoms from one state to the other reaches a maximum.

The center of the atomic resonance is thus found by monitoring the

number of atoms in one of the two states and by varying the microwave

frequency until the number of atoms in the lower state reaches a maximum, or the number of atoms in the upper state a minimum. A proportional

electric signal can be derived which is fed back to the oscillator generating the microwave signal. Thus an automatic servo can be built which

keeps the oscillator (usually a crystal oscillator) locked to the atomic

resonance.

5.4 Signal Detection

The detection of the effect of the microwave signal on the atoms

can be done in basically three ways, two of which relate to the two

methods of state selection.

35
ts c

<c " 2: •r-i 4-3u

01 -u

<D T3a

-w LU < >

<=C >- • 3 I— v£> O 1-1 1—1

OC > O =t bio 1—1 O • H

SL

U

36
CD

CO

<

CD

i—

i

CO

o

I—o

Qo

X

o

h-o

rr: CL

O

LU

_l

_l

LUO / > i

CO

«=c CD

1 ^Ci j3l \ ip • •t-A

_l \ /To .Pl\

^:°: CD ICXO s>s>i

^°: <5jKsBs

o

CO W

z

i ^ j \

z: >- o O

co z

LU LU

a; rDo-

<_) LU

i—< q:

<c >- O i— o <C

I—I <_>

o

I—<:

_i

eC U_

z: o

CD —

i—

i

CO

LU _ 3O

OHo

J i I

fc*o*

B»o#

•Ss

•o»d

i 1 i i

c

•r-< _i -U _i U

LU CD O <D T3 COeC n) CD os

an

Q

LU

CD

Q

LU

OH I—

lu 3:

1— CD

37
MICROWAVE SIGNAL

(OF ATOMIC RESONANCE

FREQUENCY)

"O

NO ATOMS

o 1

MICROWAVE

CAVITY

MICROWAVE

RECEIVER

CONSTANT SIGNAL DUE

TO MICROWAVE SIGNAL

MICROWAVE SIGNAL

(OF ATOMIC RESONANCE

STATE SELECTED

ATOMIC BEAM

T7

FREQUENCY)

%%£«-%gy

\

MICROWAVE

RECEIVER

MICROWAVE

CAVITY

CHANGE IN SIGNAL

DUE TO ATOMS

Fig. 18. Microwave detection.

38
(a) Atom detection : The atoms which leave the cavity as an atomic beam

are passed through the field of a magnet which spatially sorts the two

states. An atom detector is placed to intercept one of these states.

The output of the detector thus indicates the number of atoms in the

upper (or lower) state.

(b) Optical detection : If the atoms are optically state selected, a detector for light (photo-detector) can be placed in a position such

that the light which has interacted with the atoms is detected. Since

the light removes atoms from one of the states, its intensity will change

if atoms which resonate at the light frequency are added. Such an addition takes place as a result of the microwave signal which, in effect,

transfers atoms from one state (with no light interaction) to the other

(taking part in the light resonance) . The light at the photo-detector

therefore is a measure of the number of atoms in one of the states.

(c) Microwave detection: In this type of detection, the microwave signal

is transmitted through the cavity to a microwave detector. Since the

atoms will either add energy to the signal (if initially in the upper

state) or subtract energy (if initially in the lower state) , the microwave power level at the detector is a measure of the number of atoms

changing state.

5 . 5 Atomic Frequency Standard

The analogy to our mechanical frequency standard, the wrist watch,

which we discussed in Section 1, may now be drawn: the frequency

determining element is the atomic resonator which consists of a cavity

containing the state selected atoms, and some means of detecting the

change in the number of atoms in the two states. A control signal,

related to the number of atoms which changed their state due to the action

of the microwave signal is fed back to the (crystal) oscillator. The

i o oscillator and the associated frequency multiplier or synthesizer

1 °As we discussed before, good crystal oscillators are available at frequencies of several MHz; the atomic resonances are at GHz

frequencies. The crystal oscillator frequency therefore has to be

multiplied by a factor of about 1000.

39
o

Il

* '

Qio

O (—

•— <=c s: 2:

! f 1— 00

=£ UJ ^ C£

J 1 CDQ

UJ

LUU_

_l >-

i— q; z cc

00 O UJ UJ >-

>- \— 13 «-« ai _i q:<o-i UJ O- O 1 UJ Q. 3 Q-

_i o; i—

i

O ID M i—i u_ (— a. u~i

<c o 2: s:

=> =£ ou

o

C

a;

o

•iH

40
correspond to the energy transferring means in our wrist watch Csee Sec. 1).

Some power supply has to provide the energy necessary to drive the

oscillator, multiplier, and possibly the atom state selector. Very high

Q-values can be achieved with atomic resonators. To understand this, we have to recall our eqs (3) and (4)

.

The Q is related to the time t , which describes the average duration

of oscillations of the resonator. In atomic resonators we find two chief

causes for the termination of oscillations. The first one is collisions of

the resonating atoms with each other and with surrounding walls; each

collision usually terminates the oscillation. The second one is a rather

obvious cause: the atoms may simply leave the region of microwave signal

interaction. In an atomic beam apparatus, the atoms enter the cavity,

traverse the cavity in a certain time, and then leave the cavity. As an

example, let us assume that we have a cavity of 1 meter length which is

traversed by atoms with an average speed of 100 meter per second (a

typical value) . We assume an atomic resonance frequency of 10 GHz. The

interaction time t., is then r—— second, the linewidth 100 Hz (from Eq (3)), d 100

and the Q-value is 10 8 (from eq (4)). We arrived at a Q-value which is

considerably better than that of a quartz crystal oscillator!

5.6 Effects on the Atomic Resonator Frequency

Before we discuss effects which might cause changes in the output

frequency of an atomic standard, we should make a very important statement: The atomic resonance frequency itself is given to us by nature,

it will not drift or age. Hence, atomic resonators with Q-values of 10 8

or higher may be expected to have accuracies of one part in 10 8 or better because we will not be able to pull the resonance frequency further

away than the linewidth of the resonance.

In the following, we are not exhaustive but list only the major

perturbing effects:

41
(a) Noise: Random noise in the crystal oscillator, the detector, the

microwave cavity, and the frequency synthesizer cause corresponding

fluctuations of the output frequency.

(b) Cavity pulling : The microwave cavity is itself a resonator. Thus

we have an additional frequency-determining element besides the

atoms. It influences the output frequency by pulling the combined

resonance frequency to a value which usually lies between the resonances of atom and cavity. This necessitates the tuning

of the cavity to the atomic resonance. The requirements for tuning

will be relaxed if the Q-value of the atomic resonance is as high

as possible and the cavity-Q as low as possible.

(c) Microwave spectrum : If the exciting microwave signal has not a symmetric but an asymmetric distribution of frequencies, a frequency pulling occurs which conceptually is related to the

mechanism of cavity pulling. By careful design in the electronics,

this effect can be made negligible.

(d) Collisions: Collisions between the atoms and between the atoms and

the walls of a vessel (gas cell) in which the atoms may be contained,

not only shorten the duration of the oscillation but also cause a frequency shift. Obviously, these effects can be minimized by

having low atom densities and no walls, if possible.

(e) Doppler effect : The apparent change in frequency if the emitter moves relative to an observer is called Doppler effect. Everybody

knows this for acoustic waves from the experience of an approaching,

whistling locomotive or from automobile racing. Here, the moving

objects are the oscillating atoms and the observer is the microwave

cavity. The Doppler effect can be highly reduced by choosing a particular direction of the atomic beam with respect to the direction

of the flow of microwave power in the cavity; in our acoustic example, this corresponds to the passing of the whistle

at some large distance instead of having the whistle move directly

The microwave signal will never be just one single frequency but

will have a certain distribution of frequencies (spectrum)

.

42
towards the observer. An alternate way of reducing the Doppler effect

is the containment of atoms in a region small compared to the wavelength

of the microwave radiation, e.g., by placing a gas cell inside of the

cavity.

(f) Magnetic field : Of the effects which we discuss here, this is the

only one which directly affects the atomic resonance. We remember that we used a small magnetic dipole antenna as the model for the atomic resonance. If this antenna is placed in an external static magnetic field

(as that of a permanent magnet) the tuning of the antenna changes, i.e.,

the atomic resonance frequency changes. This necessitates magnetic

shielding, which is a characteristic design feature of all presently used

atomic frequency standards. The shielding is usually quite elaborate and

reduces the external magnetic fields, e.g., the earth's magnetic field,

to 1%, or less of its external value. This residual magnetic field can then be measured quite precisely by using the atomic resonance itself. In fact, the associated measurement precision is so good that magnetic field

effects do not seriously impair the accuracy of atomic frequency standards.

However, fluctuations of the external magnetic field, or the movement of

the device through a varying field, e.g. , as in a relocation, may perturb

the frequency of the atomic standard. Generally speaking, one tries to

minimize all of the effects listed above, and to keep their influence as stable with time as possible. Such an approach suffices for most appli1 2 cations . For laboratory standards, however, where frequency accuracy

is the primary purpose, all effects must be evaluated in a series of

experiments, and reevaluations must be done occasionally in order to

detect, changes with time.

6. AVAILABLE ATOMIC FREQUENCY STANDARDS

We will now discuss the design and performance of, the three types

of atomic frequency standards which are currently in operational use.

1 2 The magnetic effect is an exception. The residual magnetic field inside

of the shields must be evaluated and possibly reset any time after changes

in the external field occur, e.g. , after moving the device. The magnetic

shields may also have to be demagnetized.

43
o

o
 LUCCoI—

I

oI—<

s:ro

•—

i

I/O LU

BCO -^ >- a

i— p=i i CJ ^ Q- -H 1— « =3

-p

id x: LU a- 00 Cn +J Q Cn u a p

"11

L-ii "2 r*j ^^^^^^ T ^

o uj ^_^ _o ^. C id

1 Q_ •H Q.K J

o| \ ^0\g PUM POWE

SUPP -a o p >i >- \ **^ ^^^~^ o —

I

o z LU tS

1— —I

LU 00

ITS P

3|

B \Xs '

S-l -H

IS > a <d

0) u

to

- 0) ^ a: ^ \ . h- Q

oa.

B-MAG

LU

ity

wit

a

simp

ix

II.

Q > U 'O

id 0) c

U > 0) o a c

id

tO <

>i tr> o> rH fd 0) rH P CO N o id ^ •H > . ft T3 W

_l

LU

I—

H

LU

OQ

3UENCY

YPUT .31

,770 £ id c h en

ube.

erta o

re LU ;-

, ::: * 1 <-J> a:

LU CM p o SP

_l / >- r— g to 10 u <0 LU /

(U <U £ i— xi m -p »—t /

zn /

ium n

of

of c

» Bifi

<U -H U to -H LUZ 0) -P o

LU

id t) id

L| <: m to id s: S Q- o -h a ^^^^w

VACUU

ENVELO £ (U p

DlMAGNET

ematic

ad.

T

the

s<

I X! w o \ <- O 3 P

k \ to P

y \ H C

\- \ • (L) *- \ O IB rl LU \ CN C. f(J P> -\-*> a: >- • -M -H V^\< J > < S a.

Cn t7> 3

\* 1 b ^ 11 \V—*"^1 OW°D I °- t/>

44
O

O

3- 00 o Q

1

z:o

C_> UJ 00 00 o —

o

o

to

InBic

CMo C£> U

,— Z 1)

hi _l

Q. s S

o < u

r00 >*-l

u

c

01 c J3

0) +J 3

cr" H

D ID w +J

01 P

£ a

n) u

0)

Ainiavis A0N3nt)3yj ivNOiiovyj

•H

45
6.1 Cesium Beam Frequency Standard

The atomic resonance is at 9192 631 770 Hz. The standard is based

on the atomic beam method using spatial state selection and atom

detection. An oven contains the cesium metal- If heated to about 100°C,

enough cesium gas will be produced to form an atomic beam which leaves the oven through one or many channels into a vacuum chamber. This chamber is

evacuated to a pressure of less than 10 9 of atomospheric pressure. The

beam traverses first the state selecting magnet, then the microwave cavity

where an external microwave signal acts on the beam, and finally reaches

the atom detector after passing another state selecting magnet. The atom

detector is simply a wire or ribbon (typically made from tungsten or platinum) which is heated to about 900°C by passing an electric current

through it. Cesium atoms which impinge on this wire (which is biased

with a few volts dc) become electrically charged (ionized) and can be

collected on an auxiliary electrode. The stream of electrically charged

atoms at this electrode represents an electric current which is amplified,

detected, and fed into the feedback network.

The speed of the atoms and the length of the cavity determine the

Q-value of the atomic resonator. Typical atom speeds are 100 meters per

second. In commercial devices which have to be reasonably small the

cavity is about 0.1 to 0.2 meter long; the corresponding interaction time

t is two thousandths of a~ second. From eqs (3) and (4), we calculate

a linewidth of a few hundred hertz and a Q-value of a few 10 7. In laboratory devices one can go to very long cavities. Cavities of up to 4 meter

long are used, leading to Q-values of a few 10 . The fractional frequency

stability of laboratory and commercial devices can reach one part in 10 lh

at sampling times of less than one hour to days. The frequency stability

for less than a few hours is limited by fluctuations in the atomic beam

intensity which are basic and unavoidable ("shot noise"). These fluctuations affect the frequency stability less if more intense atomic beams

are used. This approach which is becoming available in both commercial

and laboratory devices, improves the stability (compare Sec. 7). In contrast to commercial devices, the laboratory standards are designed

46
3Z

00

CD<

o

ooo

LU

OHOl—

l

s:ot-

«=c

Oh-"

co rr oo

Ss °-

isj re >- -^ o^ 1— LO

UJ => 00 n Q- uj o-z « LU i—

i

«*

cc oo

u_ CO

OH

LO LU

a: co

'-' y;

Qa: <c

ae. OO

S/1 LU z I—

ILU— HO<

I

_i 1—

1

I— _I K1

1— oo

Q_ U_ Q_ O CL oh s:

rs « o CH

oo D. oo LU

S" CO rc Q£ <

LU _j

"3 a _j o C£ 7T. __i Q. o <c LU U- <_>

1 ' X

0)o

w

(3&>S

3

-H

T3

•rH

oH

-P

(0e

uo

fa

47
U3O

o

*3-o

o

CMo

U1Q

O

o

I/O

o

I

CM

I I

03

3

o tn u X!

4-1 u o rt Tl

>> c

•iH rt

1—

1

j->rn J-l

<ri ><U

CO c

f

)

cu3

r, cr

<i> 0) i h

CO

<M

.r-t

AHU8V1S A3N3nb3yj ivnoiiovhj

48
to allow a more complete and easier evaluation of all effects on the

frequency. Cesium standards are used extensively where its high

reproducibility and long-term stability (sampling times of more than

a day) are needed. For most applications, cesium standards need not

be calibrated. They are the work horses in most of today's standard

frequency and time services. The laboratory standard serves to realize

the definition of the second Csee Sec. 1)

.

6.2 Rubidium Gas Cell Frequency Standard

The atomic resonance is at 6834 682 608 Hz. The standard is

based on the gas cell method using optical state selection and optical

detection. The gas cell contains rubidium gas at a pressure of only

-9 about 10 of atomspheric pressure. In order to reduce the effect of wall

collisions on the rubidium atoms, an inert buffer gas (e.g. , argon

or nitrogen) is introduced into the cell at a pressure of about 1/1000

of atomospheric pressure. This allows lifetimes of the rubidium atom

oscillations (the oscillation lifetime t n is still limited by atom

d

collisions) of about 1/100 second. From eqs (3) and (4) we calculate

a corresponding linewidth of about 100 Hz and a Q-value of several 10 . Atomic collisions as well as the simultaneous action of the light and the

microwave signals on the same atom cause frequency shifts of the order of

10~ 9

. These frequency shifts depend strongly on the composition,

temperature, and pressure of the buffer gas and on the intensity of the

light. As a result, rubidium gas cells vary in their resonance frequency

by as much as 10" 9 depending on the particular setting of the frequency

shifting parameters during manufacturing. Since these influences cannot

be expected to stay unchanged as time goes on, rubidium standards need not

only initial calibration but also recalibration because they exhibit a frequency drift, i.e., an aging analogous to crystal oscillators. The

stability performance of rubidium standards is nevertheless quite

spectacular. At one second sampling time they display a stability of

better than 10 and perform near the 10 level for sampling times

of up to a day. For longer times the frequency stability is spoiled by

49
u. o

CH 1— o <:

-, Li_ >- 1—

~-. l—oo

POWE

PPLY CAVI ERMO

z=> :n oo t— 1 ' oeno

LU

O

I/O o

q; i—( o i C_> < o > Q-oH- on. . cc llj u_ •—I I

^ C_5 —i t*~ O O i/i x

O0 UJ

a. o

+J

(0

•HU

COu

0)

01

(0ec

(Uen a

>io

•H

+>

nje

<DUw

50
o

ino

o ooO

o

CMO

r~ oo

CO

I Aim avis ADN3nb3cij ivnoudvcH

c

60o

!>,

O

u

c

cr 6

fcuO

fn

51
the frequency drift which is typically 1 x 10" 11 per month (but much less

than the drift of crystal oscillators) . Commercial devices with the

above mentioned performance are available. Rubidium standards are used

where excellent medium term stability (minutes to a day) is needed,

where its reduced costs, size, and weight, as compared to cesium standards,

are important, and where a crystal oscillator with its more frequent

needs for recalibrations and its greater environmental sensitivity does

not suffice.

6 . 3 Atomic Hydrogen Maser l 3

The atomic resonance frequency is at 1420 405 752 Hz. The standard

is based on the atomic beam method using spatial state selection and

microwave detection. The beam source is a radio frequency gas discharge

in molecular hydrogen 14 which produces atomic hydrogen with high efficiency.

The atomic hydrogen beam leaves the source through one or many channels

into a vacuum chamber. The beam then traverses a state selecting magnet

and enters a storage bulb in the microwave cavity. The storage bulb is

made from quartz glass which has low electric losses and thus does not

spoil significantly the cavity-Q. The storage bulb is evacuated to a pressure of less than 10-11 of atomspheric pressure. Its inner walls are lined with a fluorocarbon coating, a substance similar to the non-stick

coating in cookware. This coating allows many collisions of the hydrogen

atoms with the walls without significantly disturbing the oscillations

of the atoms. The underlying physical mechanisms are not yet fully

understood. The storage bulb is typically 0.15 meters in diameter and

dimensioned to keep hydrogen atoms for a time of about one second.

Then they leave the bulb and thus leave also the microwave

cavity. From eqs (3) and (4) we calculate a linewidth of about 1 Hz and

3 Maser is an acronym meaning "microwave amplification by stimulated

emission of radiation". Laser is a derived acronym with "light"

substituted for "microwave"

.

14 All natural hydrogen gas is composed of hydrogen molecules; each

hydrogen molecule is formed by chemical bonding of two hydrogen atoms,

52
g a Q-value of about 10 , the highest Q-value in all presently used

1 5 atomic standards. If the intensity of the hydrogen beam, which

consists only of upper state atoms (emitting atoms) , is sufficiently

large and if the cavity losses are sufficiently low, self-oscillation

will start in the cavity; i.e., the maser itself will generate a microwave

signal. We have a maser-oscillator with an output frequency directly

derived from the atomic resonance. A crystal oscillator can be locked to

this frequency by frequency comparison techniques. As compared to the

cesium standard, the hydrogen maser is not quite as accurate because

of experimental difficulties in the evaluation of the frequency shift

due to the collisions of the hydrogen atoms with the fluorocarbon sur- face of the storage bulb. In order to obtain self-oscillation the

cavity-Q must be relatively high. Thus cavity pulling is relatively

strong, and it limits the long-term stability (over times longer than

about one day) to values not better than those of cesium standards. In the region from a few seconds to nearly a day the hydrogen maser has

the best stability of all existing standards. Its application is rather

limited to uses where these stabilities are critical and where a rather bulky device is no handicap. Unlike cesium and rubidium standards,

hydrogen masers have not yet been evaluated under adverse environmental

1 6 conditions. The number of hydrogen masers in use is very small

compared to the numbers of cesium beam devices and of rubidium devices.

1 5 Higher Q-values are realized in experimental devices such as methane

stabilized helium-neon lasers and ion storage devices as well as in

microwave cavities which are cooled to the superconducting state

(compare Sec. 8)

.

1 6 Relevant data have been accumulated in 1976 in connection with the use of a hydrogen maser in a space probe in order to gain scientific

data on the general theory of relativity. This program was sponsored

by NASA and carried out by the Smithsonian Astrophysical Observatory.

53
fi •H 0) rS

T3 -P

(I) tO >l

tO rQ 3o a

to a) -H H-> T3 Idu

to •H

T3 -a

rH c

id •H • -d 01 to c c cu T3 « (0 o U

cop rC •H (d 3

to H-) >

cuC < >1 QJ a rd a u U P z c c lp W < 0) Id EH 3 £ >i

co

D1 ^ to o

cu (1)

G » in 4-1 ft cu u 4h SH >i 3 s cu P W

fa (Da CU

D £ rH rH Oi P ^-* 3 fa § m 0) CU fa tO rH u cu rQ w to rC aj J V s P h

CQ •rH

H

IS P rH CU rd

to rH > H •rH ' id < < rH & > cu u g U-t

rt! P cu u p o

fa id 4-1

a

O rH Q)

(0 rQ

p to 2 .C •H O u 0) -a rH to > CD rd H CD H CO & Ci U Cn 3 g < C

ft Id >i CD

u 2 g id rQ O u g Ti U !>1 C

in to id <d

Q Sh P g S <D •H >i

sC ft c <u rH 3 rH id >H <D rQ g

rt rC rH (C P P Id3 p

co § UH a cu D •rH rC

CO > Eh • >1 •H rH

rH H3 • id C • CU r- | H CU rH

rH

rQ

to vO

p

id Eh

id T3 CU

to

C rC

0) IT! P >

•H <*

C

Cn

cn •H

rH

C to

rH

Q) •H CU

1-1 4J ^ rQ U g

id CD 3

Eh 10 c

r>

<£) o o kO r- rH co r~

rH o o o o

rH r-t rH rH rH

id O! P s & Jh s S

CU CU cu cu CU LD MH r^ MH > H-i in Ol O o cu o

rH id rH id to id id rH

>1 rH

<-i P cn id 3 C o O •H

>i rC -H

Cn Cn & U 3 CU p C rH CU U N

N

N

N 3 Xi N N X K -0

CU +j gj § o co CN u T3 r^ o in

fa CU TS o

rH

r-~ \D r~

01 3 (d rH CN

m o P m CO o c U N p v£) vD ^

id id

X c <*H r*

N CM

T o

to 3C CD ^ rH CO CN

CU (C rC

Pi S P rH cri ^D rH

CUPhsp * rH

ra *

a) T) rH •H cu rH

K

13U CU id

u cu id CD CU C rH •H rH c ft •H

rH Id rH o cu id S o &

rH

g o rH

g

g P rH P U in CU p U <-l CU

U P o id >i E rH P 17 <u C 2 u IH -H rH g id c U rH O •H

cuu o rH cu

u P U

u

p

u Cu id ft a) id

M id c r-t o £ M t-{ cu rH o c X CU rH •H rC g o rH g X CU Oi > id ft Di rQ id g rQ u > •H g > •H O id g id Eh o K "-' w Eh K IH w u J U rH p g H C P

rH Id 3 rH cu id

cu id <-ig •H CD Cn rH

u -P rH 3 T3

U

U rH

•H

W -H •rH

g

H rH CU -H > >i O tn id rQ tn <T3 to u

CU Sj to <u cu 3 id >i id to Q 1 u D U PC « o SB S O

54
V

+Jc

o

rd

' , CO>i

rd (/" cr CO CO CO *

*

MH C

T3 £ rl r, M £ M 4-1 H rd rd rd 4J rd

CO i rdM

C

E

rd

(D

CD CD CD C

>i >i >

E

>i >i >

c c c s

rd fd rd a)

en E E E >m

izati eping

E i

i

CD>

CDCO

CDC

CDC

>ic

rdE

<U C 01 S X

P W CD M CO

rd

<u ^ e CO 3 r-| 1-1 xi u -h 3. i rd rd U C 4-1 CD >i E co m

rH

i

i X u co

CD rl M

<D to X4-1 -P 4- n

4J H fl) CD > 3 > > C C C 5 c

Eh U <U C <D O

CO X

<D rfl CO T3 E E

c <D CM E

CnC

•H .—s rji CN O m ^ ^r ^ rsi (N "sf CO C

rd

CTi

I H rH

1 1 rH

1 rH rH rH t-t r-t r-\

rd W O O O o o o O

1 O O

1 T3 o

>i

i-H r-l r-l rH rH r-{ rH rH rH rH * C

0) rH

r-l X X X X X X X X X X

4-> •rl

i-l •H

4-1 rd LO LD rH r-H CD -3- r-t o-> PO CN

•H

ft ^

ffl -P

>i o ro r-l m >* ^ ^r CM rn ^

>1

4-1 rH rH rH

I

| rH

1 H

1 H

1

r-t r-t rH rH

CO fS o O O o O O O o O

1 o

>1

T3

CD rH r-l r-l rH rH rH r-t i-H r-i rH u

c

0)C

4-1 rd X X X X X X X X X X

0)3

CD

4-1 CO in in r-l rH [^ <r rH H ro rH

M

>i o f"> r\j f> cn CO <* n n m

CM 3

rH

r-l r-i r-l rH

1 | rH

| rH rH

| rH H

1 rH rH H

rd £

fd o o o o O o o o o o u

3~T~ H r-l r-l rH r-1 rH rH r-\ r-i rH

<DcM-l •H

1 O

X X X X X X X X X X

4-1 U

a; iH r-l <N r-l r-^ co rH (N rn ro r\i — ft

rd CO 4-1 rl T3

Ph C CD CO rH ro tM rH CM N CM rH (N m xi O | rH rH rH H -1 H rH i-t rH

cu 4-1 rH o O O O O o O

1 o

1

CO O O

c E

r-l r-l rH rH rH H rH rH rH rH

CDC

c

rd u

X X X X X X X X X X u M-l r-l r\i rH o- CN " rH —I m in

c

1

Sh •H

4-1 - 4-1 rd CO rd C 4-1' ... -P ._ >1 C CO CO P -H CD » CO to H 4-1 -H

CO CD 4-1 •• 4J >i E U rH 4-1 4-1

M-4 rH

CD G O co u CD -P -H M rH O o

-H W CD 4-1 CD P <-{ r-l 3 CD CD CD ft M-l G CM C rH U cm IM

CO XI ^ § "i CD fd

CD M-l • H -H 4-1 CO IM m (d (D C <D P J3 C CO CD » CD CO 4-> 3 CO

ffl C

U -H

4-1 O emu P rd Cn

CO -! ft r-{ 4-1 M C tun C rH

>i o fd E rd CJ CO rd rji rd H rd M -H 4-1 4-> ft H 13 4-1 H 4J

CU E H C

ft 01 •H 4-1

1 C Cn H C

W

u c C U C •0 C ft H C C H C O CD CM M E

4-> C

Q) - *H E • C

P -H fd H5 CJ 4->

rd <D M £

3 <D ft-E

: U 3 > 3 U >. cn <d m 01 W Cn <D m P M B H -H C -H V rl £ C -P -H - rl -r-| 1 •h ai > H > 5 ft -P rl H > > >

I Cn c Cn C 3 E-rt cn-H e rd C

J cd| CU h 1 r< i3 CD 3 CD -H S < IM 0)

-* 3 -ri X!

CD £ CD P CO U

rd C

rl -P -H

X) H CO

•rl • rH ^ <D

rd 4J U o ai -h »" to >

IM CD

(1) IH TJ

X!p rd >1

CD O IM > C

CD CD rl 3 CD G cr Cn O CD rd

rd Sh CO m 3

1 -P CO C E

CO CD C Cn -P C to •H -H >, • -P E CO T3

rd 3 <D M tO N

rQ CO £ •rl •H rd -P rH H «— H rd 4-i -P U CD -H 3

CD in E

M 3 -H >1 Cn rH rH C -H M

CD CM 4-1 d)

CD ft S >- C

-P -P M

CD -M CO ft

-Q rH CD

•rl <D T3 X! -a M

0) rd rd M -P —

•

•M to r P

3 T3 C

cn TD CD <D

CD CD > S

iH 4-> rd ft

rd JZ H

CD -P CD 3

E W X! D1 •H 1 CD P CD rH

X! rH T(

a) 4-) <d C

x; > rd -P = p rd

tO IM -P

rd CO -H fd -a — • X)

T3 C T3

CD -P CD -P T3 ft Mh 4-1 rd M CO -H O X rd a) m -M -P Cn m 'O T3

CD rl QJ c

rl H M

ft -H

CD -p X> X &i 13 ft U C C

-rl -H rd 3

10 X Cn CO rH 3 rd T3 CO

rd a) rd >1 -P rl C U rd 3 CD

rd rd X to X

O Sh -P rd P

3 CD

rd U TS E C P U CD rd fd -P CD -a ox! T3

CD C CD

CD E C CO X -H <D rd rd

E-i -P X O 04

55
T3

4-> 3Oo

X)

id Eh

W

Q) CD •* •* l-l co > * Oi * *

rd <U -H en 3 en in p U p TS - re T3 T3 s P T3 h cox; r-{ - CD rH

CD

O en ^ CD 3 O CD en P CD in e <4-l * CD 3 rH -rt rl CD 3 •H CD c 1 ^ C O I >P -H CD MH tJi en Mh Cn o Oi C 3 -H P p p 3 in 3 p co ~- rd P en U IS 3 O rd CD O rd H P h fl nl >i H p P H £ p •H X! > o III *J CJ -P p P CD rd P u a P U s cd 3 <TJ -do CD rH p CD CD a n-i O P CD rd 3 CD CD 3 CD u 3 CD

M-l

H XS P P 3 Oiu a, enp •H Oi P H H P -H 3 -H mug rd 3 p rd 3

(0 nJ > P Oi

g rd CD E P CDg P

ft

p fa

b tn

p rd £ rd "P CD * P -rl CD • Oi Oi Oi P a Oi P U H ii 1) N tPH 3 3 CD 3 CD en 3 CD c HI U ft-H C OJ Oi ft ft H o o g 3 <d > P P P P g g P g P O ,3 Q) £ 0) P P rd P CD p P CD ft <; CQ P -H CJ H CO W rH CO P rd e/> P

>iOc

CD T3 ^D 3 * 1) 1 O1 * P o

<U >i 3 -H p o P H rH CN

n

O CN

fa rd

a

bH rH r-t rH <-i

H P cd cd 1 1 1 | | I <-i 3 MH ,C o o o o o o

(0

O 3 P >-t r-iH rH r-{ rH

C

U 3 < cd CD

X

X

X

X

X

X

•H

B en

p P en rH r- r-\ in r-{ u w o

rd < £ p

fa

>ius

0) >i 3 -P O'-H

Q) iH P -H

fa X) o r-{ CM Ol ^f ^-t ci ! •H ^o CT\ t-H rH <-t r-i <-{ r-{ rH

rH

U I 1 1 1 1 | | 1 1 rd 3 o O o o O o o o o C TS t-H T-{ rH rH rH <-i ^ H <-{ O O

tH

p

X

X

XXX

X

+J ft U 0)

H u-l CO

m

m in

rd B! P

En

p' P A 3 (D en

CJU CD ft rd >i 3 U H rd 3 g ,Qm IM g

rd- o §•H P en >, PI p P

4-1 rd rd

O

O P rd X! 3

•H

g CD rH M-l CD P •-t P <p P -H >, Q P

rd

CD

X P

"J T3 P P

CD

en

CD P

>i P CD rH CDpp rd

O 4H >i CD 01 ft

p X! CD 3 •H 3 <P P CD P X >i

CD >1 >1 P P -r|CM XI 3 P 3 -> rd (0 T) CD 3 3~ H P O1 d -a T3 ft 3 31 g S CD

CD 3 - o P ft P -rH P P en 10 -H CD rH P >o

fa Oi >1 CD CD +J CM P 4-> E P CD CD cm

rt! rd ft ft

— •Hrl rl 3 X CD ft P- [ H — Tf ro 3 1 3 rH CO to OI

(fl

OH rH 3 O 3 O

H CD <o <-{ CD

O

C P rH rH 1 rH eo 3 P-> r-{ P r-\ O CD 1 1 O CD >, II H 11)^ 1 | CD •H ft O O <-i g X 3 p *- rd • CD O o TJ X P rH r-i O rd • p XI H r-i CJ en X en rH g .3 p A3 3 CD H

rd i X

X P rd CJ

U 3 XX 3 > P o in 3 en 3 -H CD 3 O rd MH

fa i-H LO r-t «-»H rd

H S 5n E qj

U

H •H S

CD XI

CD ^J

•HrH

CDP

cd

CO 13p

cd T)3

cd p

COg3

•H

CO

CDO

-o rH

rH ^ CD crt •H

MH -33 U cfl HP 3

CD CD 3 M Oi O

rd P g -a

r^

X XI PP P

rd o

CDm3 P CD>

*r) •rl CD on y cfl ft p b cn TJ u

CD CO X < Eh* * *

56
•pCOo m P p C id •p Cw tj

ip

—' c H id CU * p

CO </>- ^

CO

T1 >i

aiC

u

+j •P c

rt CD E (1) 3

•HU ry

4J •H (i) in n p w a cw

T3

a) 3 O CU P

•P

cu ss

•H *

0) • N i-l •H O W >

id en p -P

cu -P > id cu S

en oHA

•P •pH

iH

,Q

rd H

CD

1—Pp

>i (d £1 3o

cu cu P P Ph id oom ooooooo Ioooo

ro s 1 •p

+j 1 fdp 1 cu , w

ft <D P i n

cu •p tn TJ P ft, 3 p c a 3 &• 3 3 CU 1 , CU P 6 n -a P P fi. -H id ft q

•Hg S. 3 -P > P 1 id cu p. g • ,3 P eo| p s

cu s <d, id -h m -p hlS g|

— +J

id

p

tn -P -p

(dC ~ en O <u " tn n

<u 3 pproi3C ~

•P c P o 3 -HP u idp

cu& p

>i tn3o H—H ooooo

rro I o PPc

id3 ro

en

p en P CU 3

>i ft -H

T3 P 3 (d

tn cuH

ft 3

cuu

T3 -P

en I 3

<u o P • 33 gg -P ~ 3 ^> c P CO C

tn -h o tn u -P u -p — (d TS

ft -H> 3 CU

tncu p33

•pgo

ro3

-P

ft3IgP oooo

CM

poP -H

id3 ^- o • tn tn

cu ,* P 3 • tn -p P -P

idp ooo

ana)

ft

H -P

id tn o -h u id T3 -p cu

CU -P +J iP

14-1 £t ft 3 P

tlU •" id "-

tn

a> P33

•PgO

roI O3

•HI gP

id 5 o o o o o o o o o o

CN r» 1 A c o • 3 P o £ >i c <1) H TS P rH p n CO (1 c en p in c

(1) id

m

p # p >i ,3

t) tn a) iP P

-H

p ft tn

M-l -p 3 P

CH c () U) 3 3 CI) 3 tn

(0 > C 3 3 in id p () M ,3 P H

tnP33P

ft3I PC

a)pp3UP

0) Ti33

cu" tn

id .3up3

ft

-P•H33

CU iH

tn3

•H

tnpP

•H

tn •P

•apsmu

•p

•H3

tn •H

tn

0)3P

-a

cu • t3 en 3

-P P P

•p

CU TS P 3

Id

O

en

ai >i p P 3 -P

tn iH •p -P

<w XI

(d

CU rH

tn -p

cu id -3 >

Eh id

57
8. TRENDS

All devices which were discussed in this report have improved

over the past years in one or more of the following aspects: reliability,

size, weight, stability performance, and environmental insensitivity.

A considerable amount of effort is now being expended in research and

development to go further in this direction; however, it would be

inappropriate here to try to estimate the improvement of performance

specifications which might (or might not) be achieved in the future.

There are several other devices, designs, and concepts which

have been studied or are being investigated with some potential for

future use in frequency standards. Most of these are summarized

in Table 2.

58
3 T) 4-1 CO * O cu cn g 3 cn 4-1 -~* 1 •H 1 3 o id cn O rd 3 ^ in rH 4-1 •H 3 g cu g • • cu H cn CU ^—*

in o • cn -h rH XI cu ^ cn CU rH

X \ rH

00 CTi E CU T3 3 4-1 M-l rd rH

— 3 Cn

X • rdu rH

"tf rH 4-1 0) cu 3 rH 4-> XI cn id -h •H •P • cu CU

CTl

— >i «f CU 3 CO o cu y-j .3 rH -H cn co cu rH >i

H 3 CO

u

iH' <-t -0 c 3 O CO Cn

u rH 3 -H £ id

O

g

O rd

X '—' U 0) •H H CO •H ft rd cm > 4-1 r^ 3 •H -H g cu > •P -4-) C -H cn id 5 3 •-^ cu rH 4-> X -P -H O CO C . o -a 3 CU M 3 H m in rd 3 o s 4-1 u (0 +J CU -O cn -h ^-" -H 4-1 O O r4 & r4 CU 3 3

rH (0 CM rH

U T5 4-1 4-1 4-> cn -h 3 CU cn TJ tJ cu Id 4-1 •H

X rH rH rH CM CO cu cn rH O 3 3 -H 4J — Xj • g cu 3 rH H CU T3 CM •H CI) CD c •H -H CU CU Xt O rH . rH O ^ 'O CU rH S rd M-l •H T3 H >t <-» O .H 4-1 T3 •H 4-> •rH -rH (J> O cu co 3 cu rH rd 4-1 g X O to z 3 CO U H cm cu cn 4-1 Xi C H-> Ti 3 cn X rH 3 r3 •H CU 3 Id « u X QJ cn O 4-> T3 - O rd -H - cu rH 3 M-l CU cu cn CO > rH M O

-H .-1 4-1 rH

H •H 3 rH

O cu 4-> cn 3 Q CU 4-1 rH 3 M Cn -H id 3 rH

g rH -H ft rH 4-1

X rd - CO 4J Bl IJ o -H 3 3 Cu -H rd

O

X

X S O o

>1 CU S ft rH CU

U CO

W CU r4 •H • <U CD cu ^-'

M 4-1

O 4J

O 3 p rH cn C cn H 73 rH T) • CU 4J 3 •H cu cu T) >i •H rH • cd -h

rd 0> id to

Q o 00- rH rHu > o o o o XI rH >, 3 >i

H S O rH ^^ z > g 6 cd o 4-> CU 0) cu cu td CU -H •H -H CU O -H • X CU < •H id 4J S co •H <D cn u g CO U -H 4-1 > CO 4-1 4-> 4-1 4-1 cu cn 3 TJ TS > ~ rH g rH X O 4-> 4-1 JJ 4-1 rH 3 rd <n cu cw rd rd id co CU O CU M-l > rd CU O CU X 3 rH •H 01 rH r4

co

m CO

X rH rH rH rH rH 2=

g >< 'a cu 3 3 cd rH 3 -H CO 4-) T3

O CUX

g +J id

r4 rH

Uu 3 fS CU

U

O fd 4-1 Cn CO £ O1 3 •H CU -H

O 4-1 •H >1 ft

CO •H CD

H rH -p 3 CU -H CU rH = -a

g cu <S cd cu tJ S T3 4-1 •H CO 3 r4 -^

-P Cmu &M ft CQ CU

U X, ^- 4-> Xi o cu T) 6 id cn rH 3 Cn CU ft CO |5

H cu

a CU 4-1 rH CU 4J •H > ^ 4J 3 CO cm rd 3 cn cu

u rd 3 HI > Tl

cu *" i 4J cd

Cg -h id

g i3 Cn

O •H -H 4-13 Cn cn Cn E cu £ 1 en h • X 3 C Cn 3 CO u o 3 •H .3 CU CU rH CO 3 •H • 4-1 2 u TS cu to CU -H S-i rd -H 13 CO LB +J . O -H S-i Cn 3 X 3 M-l X g CO T3 co id

CU

H +J 13 CU

g id <m id ,3 •H rH >iO -H rd cn o rd 3 -H CU

C

g rH

u 4-1 J)

X

H

O Ti 4-1 TJ <u ft cu o rH

u 4-> ,3 Xi CO cu •H 4-1 TJ id CU 4-1 3 H 01 d) 4-1 CU 3 H CU H: fl rH <Z rd 4-1 4-> 3 id 4J CU rH T3 TJ id rH CO •H MH -rH 3 •H rd 3 ft cu ft o O CO o rH >1 CU rH cn cu H rH a CU X 3 ^-^ MH cu cn ^ C M -H - 4-1 •H ^- Vi CU rH rH M S 3 Cn 3 4J X rH 3 > O O U 4-> > rH rH U U — 3 O g ft rH x: CU •H CU O 3 (d rd 3 -H rd r4 g

•H

O •H 3 O CU 3 3 cn cu 3 3 ft CU 4J

g o > cu

H

O

H rHOX ft cu

4->

U CU -rH 4-) CU 4-> 4-> Oj

H 3 | •H -H rd •H CO • rH cn cu 3 cn CU rd Tl

+J > -P •H

X rH 3 U CO 3 S T)

O <H ~ O •HX 4-1

OO o ><

CDO -H CU CO • cu cu • ft -H

O ft CU COH 3 3 g

g rd

X 1 3 CU Cn >i > d) -P C 3 co > CO -P O O -Hi CQ rd Cn O cn co MH rd CU O 4-> •rH rH -H Cn CU g •H g CU (d T) cu xii CU g C B-HH rH g -4 rH g CO rH -H P cu cn id cn cu 4-) 4-1 CU Cn rH Dl 3 4-1 Cn cu g •H CO +J rd ft cu • rd CU U —* O H

rH 3 g rH -H rH Id rH Ul rd -H rd rH 3 4-1 3 Id r4 rH ft rH Cn

O

CO ,— cu cn X! co cu ja rH "HrH

M J5

M XI •H •H id -H CU cuX

g

H M-l rH 5^ 3 H 01 H CO O 3 > O O Ol cn 4-i O rH O O T3 > goo g 4-1 SH rH o id

CDm c * cuM CU -H rH 4-1 cn o 4-1 Id -H 4-> rH CU

X CU rd CU rH

O

H 3 CU CU CU 4-1 1 "

CO 3 -H 3 rJ ft CO H-> ft

WO rH

W

— S W CM

KWX rH CO in (b

— CO

X Cu

O Eh CO

•n CO

CU 00 00 oH

inrH

rHH

Sh 3 vO o O o OO r>

ft

HO r--H rH rH rH

H in

O rH

rdH o rH rH rH • > rH O O

O

H -p 4-1 4-> 4-1 4-1 rH s r> rH

T3 +J S 1 CUO 1 C CU 0) r- r- CO 00 <n CTi MH r-^ CO H 4-> LO MH o o o O o o o v- o o rH H rH rH rH H id r-^ Ol cu H rd *3

*3 3 O O O H -H •H - 3 CT> r4 Cn rH cn

NN

->. O CU

O cu o cu DC as 4-> -H 3 U 3 rH 3 M O u N CU 3 O g N O g N N

CU >i CN CNNNN ffi rH Cn DC Cn 4-> DC Cn 4->NN DC o (N CN DC ffi X O 3 -H En 3 rd CU H 3 rd CU DC DC O 3 cu O u O CU •H •H H •H rH o O

T) -0 CU rH

nb CU T3 3 3 CU

r

O 3 3 CU 3 3 C 3 H Ol <* £ X! 3 CU X 3 CU O X 3 CU O co CN X o cr 3 3 CN H • P -H cu cn 4-> CU CO CU 4-> cn cu • • 4-1 W Q) H CO ft ft O rH ft rH CD m

0)

u r4

M 3 -H CU .3 3 CU

X

O 3 CU

X

O 3

Pn &u < < H > a o H T3 o g

H T3

Og

H c

•H >1

+J

UO cn 4-> ft •H £ •H r4 3 -H

rH rH

g rog CU \ H >

0) cu cu COMx id CQ cn 4-1 TS Xi 4-> CU rd CU o o

43 (0 rH rd

H rd Cn 3 3 g r4 cn 3 n 10 g o X rH id fl H O O O id T! CU -P g o cd 3 u CU rd -H 3 -H g 4-1 g rH 3 >

•p rd rd rd

p rH CUO 4-1 rH 4JO 4-) 3 rd rH

O rd fd •rH •H rH •H g 3 Cn 4-1 fd 3 ft 4-1 ft •H rH £ CU O S s 3 C H rH 3 O O CO rH O rH O rH T3 rH 3 O M O o O O -H H g •H CU M g 3 CU O X O H -H •H CU M

co £ g

O id 3 rH rH -a rd 3 4-1 rH cn ft COX

O CO

w ft

O

CU P g CO £ cu rd

O >i cu

O cd

O

X 1 X 3 cn CU id 3 -H

Oh S! <2

HXm

gK rQ

H

wg id cn rd PJU Cn CO

g

59
9. LITERATURE

The following references are a limited selection. They are intended

as a guide for those who wish to penetrate the subject in greater depth.

A. Introduction

(1) J. Kovalevsky, "Astronomical Time," Metrologia 1 (1965) 169.

(2) H. M. Smith, "International Time and Frequency Coordination,"

Proc. IEEE 60 (1972) 479.

(3) The American Ephemeris and Nautical Almanac, U.S. Government

Printing Office, Washington, D. C.

(4) S. L. Howe, "NBS Time and Frequency Dissemination Services,"

NBS Special Publication 432 (1976)

B. Basic Concepts

(1) D. A. Howe, "Frequency Domain Stability Measurements: A

Tutorial Introduction," NBS Tech. Note 679 (1976).

(2) D. W. Allan, "The Measurement of Frequency and Frequency

Stability of Precision Oscillators," NBS Tech Note 669 (1975).

(3) J. A. Barnes et al, "Characterization of Frequency Stability,"

IEEE Trans, on Instr. and Meas. IM-20 (1971) 105.

(4) L. S. Cutler and C. L. Searles, "Some Aspects of the Theory and

Measurement of Frequency Fluctuations in Frequency Standards ,

Proc. IEEE 54 (1966) 136.

(5) D. W. Allan, H. Hellwig, D. J. Glaze, "An Accuracy Algorithm

for an Atomic Time Scale," Metrologia 11 (1975) 133.

(6) H. Hellwig, D. W. Allan, and F. L. Walls, "Time and Frequency,"

Proc. of the V International Conference on Atomic Masses

and Fundamental Constants," Paris, France (1975), p. 305.

C. Frequency Standards, General Aspects

(1) Most general physics textbooks.

(2) A. E. Siegmann, "An Introduction to Lasers and Masers,"

Chapter 2, McGraw-Hill 1971.

D. Quartz Crystal Devices

(1) E. A. Gerber and R. A. Sykes, "State of the Art - Quartz

Crystal Units and Oscillators," Proc. IEEE 54 (1966) 103

(2) E. A. Gerber and R. A. Sykes, "A Quarter Century of Progress

in the Theory and Development of Crystals for Frequency Control

and Selection," Proc. 25th Annual Symp. on Frequency Control,

Ft. Monmouth, NJ (1971) 1 (available from Electronic Industries

Assoc. , Washington, DC)

(3) R. A. Heising, "Quartz Crystals for Electrical Circuits,"

Van Nostrand, 1946.

60
E. Atomic Resonance Devices

(1) N. F. Ramsey, "History of Atomic and Molecular Control of

Frequency and Time," Proc. 25th Annual Symp. on Frequency

Control, Ft. Monmouth, NJ (1971) 46 (available from Electronic

Industries Assoc. , Washington, DC).

(2) N. F. Ramsey, "Molecular Beams," Oxford, 1956.

(3) A. E. Siegmann, "An Introduction to Lasers and Masers,"

McGraw-Hill, 1971

(4) H. Hellwig, "Design Principles and Characteristics of

Frequency and Time Standards," IEEE Trans, on Nuclear

Science NS-23 (1976) 1629.

F. Available Atomic Frequency Standards

(1) A. 0. McCoubrey, "A Survey of Atomic Frequency Standards,"

Proc. IEEE 54 (1966) 116.

(2) D. Kleppner, H.C. Berg, S.B. Crampton, N.F. Ramsey,

R.F.C. Vessot, H.E. Peters, and J. Vanier, "Hydrogen-Maser

Principles and Techniques," Phys. Rev. 138 (1965) A972.

(3) R. E. Beehler, R. C. Mockler, and J.M. Richardson, "Cesium

Beam Atomic Time and Frequency Standards," Metrologia 1 (1965) 114.

(4) P. Davidovits and R. Norvick, "The Optically Pumped Rubidium

Maser," Proc. IEEE 54 (1966) 155.

(5) H. Hellwig, "Atomic Frequency Standards: A Survey," Proc. of

the IEEE 63 (1975) 212.

(6) C. Audoin and J. Vanier, "Atomic Frequency Standards and

Clocks," Jnl. Phys. E: Scientific Instruments 9 (1976) 697.

G. Trends

(1) H. Hellwig, "Areas of Promise for the Development of

Primary Frequency Standards," Metrologia 6 (1970) 118.

(2) H. S. Boyne, "Laser Frequency Stabilization Techniques and

Applications," IEEE Trans, on Instr. and Meas. IM-20 (1971) 19.

(3) H. Hellwig, "Clocks and Measurements of Time and Frequency,"

WESCON Technical Papers, Session 32 (1976).

General Scientific Overview

(1) Byron E. Blair, Editor, "Time and Frequency: Theory and

Fundamentals," National Bureau of Standards Monograph

140, 460 pages (January 1974) . Available from:

Superintendent of Documents, U. S. Govt. Printing Office,

Washington, DC 20402 (SD Catalog No. C13.44:140)

61
ACKNOWLEDGMENTS

The author owes much to his colleagues within and outside of

the National Bureau of Standards for many suggestions and contributions.

62
APPENDIX I SPECIFYING AN OSCILLATOR IN THE TIME-DOMAIN

A stability plot of a frequency standard typically shows the , characteristic as shown in Fig. 26. The first part, "I" with a ^ x (white frequency noise) or o % T

-1 (white or flicker of phase noise),

reflects the fundamental noise properties of the standard. This

behavior continues with increasing averaging time until the so-called

flicker "floor" is reached where O (X) is independent of the averaging

time (curve "II", flicker of frequency noise). This behavior is found

in all frequency standards; it depends on the particular frequency

standard and is not fully understood in its physical basis. Examples

for probable causes for the flicker "floor" are power supply voltage

fluctuations, magnetic field fluctuations, changes in components of

the standard, microwave power changes, etc. Finally in the third

section, "III", of the generalized curve, the stability deteriorates

with increasing averaging time. This occurs typically at times

ranging from minutes to days, depending on the particular kind of

standard. +1

A behavior O (X) ^ T usually corresponds to linear

frequency drift or aging

^

D. A slope in the range from T 0+1

to T is found in most frequency standards due to a variety of internal and

environmental parameter instabilities. Thus the third part of the curve

can be improved by better control of the standard in the laboratory

or its protection against environmental influences.

It is recommended to characterize a standard in the time-domain by

giving the following data:

1.

2.

3.

fundamental stability (curve "I") a (x) = kx stating k and u. stability limit or flicker floor (curve "II") stating a frequency drift or aging, if any, stating D (fractional frequency

change per day)

characteristic values of a (t) in the range of curve III after

subtracting linear frequency drift or aging D from the data.

°„(t)

II.

III.

TIME t

'' y ^^)~^ U v = -1; WHITE OR FLICKER OF PHASE NOISE

U = -1/2; WHITE FREQUENCY NOISE %(') = o

f

= CONST FLICKER "FLOOR" (FLICKER OF FREQUENCY)

"„(t) < v < 1 TYPICAL

1; PURE FREQUENCY DRIFT (AGING)

Fig. 26

63
APPENDIX II RAMSEY CAVITY

Figure 27 shows the cavity with two separated interaction regions

(Ramsey cavity) and a typical corresponding cesium resonance spectrum.

The broad pedestal (or "Rabi" resonance) is a result of the coherent

intereaction of the atoms with either interaction region alone; therefore,

the corresponding linewidth is W ~ v/ = -— where v is the speed of

I

dZ

the atoms , £ the length of one interaction region and t , the atomic timeof-flight through it. *

The more rapidly oscillating pattern (Ramsey pattern) on top of

the pedestal is a result of the coherent interrogation by both interaction regions. This pattern can be explained as follows (we assume

that there is no phase difference of the electromagnetic field between

the two cavity regions) : If the interrogating frequency is equal to the

cesium resonance frequency, the atomic oscillations will remain in phase

with the interrogating signal while the atom flies from the first to the

second region; the driving signal in the second region will reinforce the

action of the first cavity and we obtain maximum signal (center of the

resonance) . If the signal frequency is offset from the atomic resonance

frequency we can observe two extremes: (a) the frequency offset,A\>, is

such that Avx t = 1, 2, 3, 4, L

. where t = L/v is the

L atomic time-of-flight between the interaction regions.

(b)Av x t 1/2; 3/2; 5/2; In cases (a) the atoms arrive "in-phase" at the second interrogation

region; we obtain reinforcement and maximum signal. In cases (b) , the atoms arrive "out-of-phase" at the second region; we obtain negative

reinforcement with minimum signal as a result.

Since t depends on the atomic velocities (see above) , the cases

(a) and (b) will "wash-out" with increasing Av due to the fact that the

beam contains a spectrum of velocities (velocity distribution) and a corresponding range of t . This is the reason why the Ramsey pattern

L rapidly attenuates on either side of the central peak. As compared to a normal, single cavity of the length L, the main

advantages of the Ramsey cavity relate to the fact that the atoms are freely oscillating while flying between the two interaction regions; i.e.,

they are not subject to effects from cavity imperfections and they average

all other deleterious effects; e.g., magnetic field effects. Also, the

linewidth of the center peak of the Ramsey pattern is about one half that

of the single cavity.

W a v/L

BEAH(v)

I 8.

Fig. 27

64
rfB$-114A IHEV. 7-73)

[Ts. dept. of comm. BIBLIOGRAPHIC DATA

SHEET

U. TITLE AND SUBTITLE

1. PUBLICATION OR REPORT NO. NBS-TN-616 (2d Revision)

2. Gov't Accession

No.

3. Recipient's Accession No.

Frequency Standards & Clocks : A Tutorial Introduction

5. Publication Date June 1977

6. Performing Organization Code 277,04

7. AUTHOR(S)

Helmut Hellwig

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. 2774246

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as above

13. Type of Report & Period Covered 2nd

NBS Tech Note 616. Rev.

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) The topic of frequency standards and clocks is treated in a tutorial and

non-mathematical way. The concepts of time, frequency, frequency stability and

accuracy are introduced. The general physical principles and design features

of frequency standards and clocks are described. The design, performance, and

limitations of quartz crystal oscillators and atomic devices (cesium, hydrogen,

rubidium) are discussed in detail and critically compared for laboratory

devices as well as for devices intended for field usage.

7. 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)

Cesium beam; clocks (atomic) ; crystal oscillator; frequency accuracy;

frequency stability; frequency standards; hydrogen maser; quartz crystal; —rubidium gas cell; timekeeping.

18. AVAILABILITY [£] Unlimited

I I For Official Distribution. Do Not Release to NTIS

1x1 Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. CH . 46 :616 (2d Rev. )

I I Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

70

22. Price

$1.30

j'MM

USCOMM-DC 29042-P74

4 U.S. Government Printing Office: 19 77-777-045/1253 Region 8

NBS TECHNICAL PUBLICATIONS

PERIODICALS JOURNAL OF RESEARCH reports National Bureau

of Standards research and development in physics, mathematics, and chemistry. It is published in two

sections, available separately:

• Physics and Chemistry (Section A)

Papers of interest primarily to scientists working in these fields. This section covers a broad range of physical and chemical research, with major emphasis on

standards of physical measurement, fundamental constants, and properties of matter. Issued six times a year. Annual subscription: Domestic, $17.00; Foreign, $21.25.

• Mathematical Sciences (Section B)

Studies and compilations designed mainly for the mathematician and theoretical physicist. Topics in mathematical statistics, theory of experiment design, numerical

analysis, theoretical physics and chemistry, logical de- sign and programming of computers and computer sys- tems. Short numerical tables. Issued quarterly. Annual

subscription: Domestic, $9.00; Foreign, $11.25. DIMENSIONS/NBS (formerly Technical News Bulletin) —This monthly magazine is published to inform

scientists, engineers, businessmen, industry, teachers,

students, and consumers of the latest advances in science and technology, with primary emphasis on the work at NBS. The magazine highlights and reviews

such issues as energy research, fire protection, building technology, metric conversion, pollution abatement,

health and safety, and consumer product performance.

In addition, it reports the results of Bureau programs

in measurement standards and techniques, properties of matter and materials, engineering standards and services, instrumentation, and automatic data processing. Annual subscription : Domestic, $12.50; Foreign, $15.65.

NONPERIODICALS Monographs—Major contributions to the technical liter- ature on various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and

industrial practice (including safety codes) developed

in cooperation with interested industries, professional

organizations, and regulatory bodies. Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other

special publications appropriate to this grouping such

as wall charts, pocket cards, and bibliographies. Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists, engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides

quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a world-wide program coordinated by NBS. Program under authority

of National Standard Data Act (Public Law 90-396).

NOTE: At present the principal publication outlet for

these data is the Journal of Physical and Chemical

Reference Data (JPCRD) published quarterly for NBS

by the American Chemical Society (ACS) and the American Institute of Physics (AIP). Subscriptions, reprints, and supplements available from ACS, 1155 Sixteenth

St. N.W., Wash. D. C. 20056. Building Science Series—Disseminates technical infor- mation developed at the Bureau on building materials, components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental

functions and the durability and safety characteristics

of building elements and systems.

Technical Notes—Studies or reports which are complete

in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under proce- dures published by the Department of Commerce in Part

10, Title 15, of the Code of Federal Regulations. The

purpose of the standards is to establish nationally rec- ognized requirements for products, and to provide all concerned interests with a basis for common understanding of the characteristics of the products. NBS

administers this program as a supplement to the activities of the private sector standardizing organizations. Consumer Information Series—Practical information, based on NBS research and experience, covering areas

of interest to the consumer. Easily understandable lang- uage and illustrations provide useful background knowledge for shopping in today's technological marketplace. Order above NBS publications from: Superintendent

of Documents, Government Printing Office, Washington,

D.C. 20402. Order following NBS publications—NBSIR's and FIPS

from the National Technical Information Services,

Springfield, Va. 22161. Federal Information Processing Standards Publications (FIPS PUBS)—Publications in this series collectively constitute the Federal Information Processing Standards Register. Register serves as the official source of information in the Federal Government regarding stand- ards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended,

Public Law 89-306 (79 Stat. 1127), and as implemented

by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or final reports on work performed by NBS for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Services (Springfield, Va. 22161) in paper copy or microfiche form. BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey

bibliographies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service. A

literature survey issued biweekly. Annual subscription: Domestic, $20.00; Foreign, $25.00. Liquified Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00.

Superconducting Devices and Materials. A literature survey issued quarterly. Annual subscription: $20.00. Send subscription orders and remittances for the pre- ceding bibliographic services to National Bureau of Standards, Cryogenic Data Center (275.02) Boulder, Colorado 80302.
U.S. DEPARTMENT OF COMMERCE

National Buroau of Standard*

Washington. O.C. 20234

OFFICIAL BUSINESS

Penalty for Private Use. $300

POSTAGE AND FEES PAIO

U.S. DEPARTMENT OF COMMERCE cou.ii;

SPECIAL FOURTH-CLASS RATE . BOOK