NBSIR 74-396

SPECIFICATION AND MEASUREMENT OF FREQUENCY STABILITY

John H. Shoaf

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

November 1974

NBSIR 74-396

SPECIFICATION AND MEASUREMENT OF FREQUENCY STABILITY

John H. Shoaf

Time and Frequency Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

November 1974

The results of this report are not to be used for

advertising or promotional purposes, or to

indicate endorsement or disapproval of the

product(s) by the National Bureau of Standards.

This report is, with minor revisions, a reprint

of an unpublished NBS Report bearing the same

title and author, issued September 7, 1971

u s DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS Richard W Roberts Director

C ontent s

1. INTRODUCTION AND BACKGROUND 1

2. TERMINOLOGY FOR SPECIFICATION OF

FREQUENCY STABILITY 3

3. COMPARISON OF MEASUREMENT TECHNIQUES 6

4. OPERATIONAL SYSTEMS FOR MEASUREMENT

OF FREQUENCY STABILITY AT NBS 9

5. MEASUREMENTS OF FREQUENCY STABILITY

AT MICROWAVE FREQUENCIES 19

6. SUMMARY 20

REFERENCES 21

APPENDIX A, Glossary of Symbols 22

APPENDIX B, A Sample Calculation of Script a? 24

APPENDIX C, A Sample Calculation of Allan Variance 25

APPENDIX D, Stability Measure Conversion Chart 27

APPENDIX E, General References and Selected Papers .... 29

BIBLIOGRAPHY 32

iii
List of Figures

Page

Figure 1 Frequency domain measurement of frequencystability o . . o . 10

Figure 2 Stepped- gain operational amplifier , . , 11

Figure 3 Low-noise amplifier , . 12

Figure 4 Adjustable RC filter 13

Figure 5 Battery bias box ,. . 13

Figure 6 Plot of Script af(f) versus frequency f 14

Figure 7 Time domain measurement of frequency

stability 15

Figure 8 Plot of sigma versus tau , . . , 16

Figure 9 Differential phase noise measurement ....... 17

Figure 10 Adjustable phase shifter (5-MHz delay line) .... 17

iv
SPECIFICATION AND MEASUREMENT

OF FREQUENCY STABILITY

John H. Shoaf

Atomic Frequency and Time Standards Section

National Bureau of Standards

Boulder, Colorado 80302 USA

Abstract

This report gives concise definitions for specifying

frequency stability for measurements in the frequency

domain and tim.e domain. Standards of terminology and

of measurement techniques are r ecoromended. Measurement systems are described in adequate detail so that the

apparatus may be duplicated. Proposed extension of the

measurement systems through 12.4 GHz is discussed.

Key Words : Allan variance , Frequency stability

measurements, Measurement system

description, Phase noise, Spectral density,

Terminology standards.

1. INTRODUCTION AND BACKGROUND

At the beginning of FY 71 the Department of Defense Joint

Services Calibration Coordinating Group (DoD/CCG), Ray Y, Bailey

(Chairman), Newark Air Force Station, Newark, Ohio, initiated a proposal with the National Bureau of Standards (NBS) to write a survey

paper pertaining to the specification and measurement of frequency

stability. The project was under the jurisdiction of the DoD/CCG Time

and Frequency Working Group. The members of this group are E. L.

Kirkpatrick (Chairman), Aerospace Guidance and Metrology Center,
Newark Air Force Station, Newark, Ohio; Lloyd H. Daniels, U, S.

Army Metrology and Calibration Center, Redstone Arsenal, Alabama;

and Peter Strucker, Metrology Engineering Center, Pomona, California.

A widely-accepted, well-defined set of standards for the

specification and measurement of frequency stability has been long

overdue. A manuscript by the Institute of Electrical and Electronics

Engineers Subcommittee on Frequency Stability appears to be the most

comprehensive treatment of the subject to date. The manuscript [1],

"Characterization of Frequency Stability" by Barnes et al. , may be

considered an authoritative paper on the subject; it has been used

extensively in the preparation of this survey report.

This report gives recommended standards of terminology and

measurement techniques in addition to comparison of other widely used

contemporary measurement methods for determination of frequency

stability. Operational systems for frequency stability measurement at

the National Bureau of Standards are described in detail and extension

of these systems to 12.4 GHz is discussed. An extensive bibliography

on frequency measurement is also included.

A comprehensive knowledge of the definitions and relations

outlined below is necessary in order to understand the practical systems

that are useful for measurement of frequency stability. It is the objective in this report to place the emphasis on details of useful working

systems (apparatus) that may be duplicated by others in the field of

frequency stability measurements. Uniformity of data presentation is

recommended to facilitate interpretation of stability specifications and

to enable one to communicate and compare experimental results more

readily.

Experience in the use of these measurement systems and these

concepts will be the best teacher; this report is at most the teacher's

as sistant.

2
2. TERMINOLOGY FOR SPECIFICATION

OF FREQUENCY STABILITY

A general definition of frequency stability has been stated as

"the degree to which a signal source (e. g„ , oscillator) produces the

same value of frequency throughout a specified period of time, " Measurement of stability can be accomplished in both the frequency

domain (e, g. , spectrum analysis) and the time domain (e. g. , gated

frequency counter). In the aforementioned manuscript [1] the authors

chose to use two independent definitions, each related to different,

useful methods of measurement. In addition to the following comments

on definitions, a complete glossary of symbols for this paper is found

in Appendix A.

The first definition of frequency stability (frequency domain) is

the one-sided spectral density of the fractional frequency fluctuations,

y, on a per hertz basis:

S (f) H spectral density of y, (1)

y

where y represents the fractional frequency fluctuations, y = bv/^

o This measure of stability has the dimensions of inverse hertz. The

spectral density of phase fluctuations is related by the identity,

S.^(f) S (f) O'i y

2, ,2

V /f o The second definition of frequency stability (time domain) uses

the type of sample variances called the Allan variance [2] of y:

n=l k=l

This measure of stability is dimensionles s . The bar over the y indicates

that y has been averaged over a time interval T. The angular brackets

indicate an average of the quantity over time.

3
Further explanation of these definitions will be given later.

A very coraplete discussion may be found in reference [1].

Frequency drift is defined as a systematic, typically linear

increase or decrease of frequency with time. This is characterized as

"aging rate" in crystal oscillators and is expressed in fractional parts

per period of time. This report on frequency stability does not include

a discussion of this so-called "linear drift. "

In all known signal sources the output frequency is affected by

noises of various types. The noises can be characterized by their frequency dependence. The random noises [1] include white thermal and

shot noises (f°), flicker noise (f and integrals of these noises.

It is the examination of these noise spectra with which we are concerned

in the first definition of frequency stability given in eq (1). The fractional frequency fluctuation spectral density S (f) is not to be confused

with the radio frequency power spectral density S (v) which is not a

6 V

good primary measure of frequency stability because of fluctuations in

amplitude and for other reasons [1].

Since S (f) of eq (1) is expressed in terms of the spectral density

of phase fluctuations S (f )

, a convenient laboratory method of determining the phase noise would be useful. Phase noise spectral density

plots are used for presenting frequency stability information in the

frequency domain.

Script 5£(f) is a frequency domain measure of phase fluctuations

(noise, instability, modulation) used at NBS. Script a?(f) is defined as

the ratio of the power in one phase noise sideband, referred to the

input carrier frequency, on a per hertz of bandwidth spectral density

basis, to the total signal power, at Fourier frequency f from the

carrier, per one device.

4
^(f) = Power density (one phase modulation sideband)

Power (total signal) (3)

For small §0,

m = 2=£(f) . (4)

A practical system for the measurement of s£(f) or Sg^(f) will be

described in detail later.

2

In the time domain a useful determination of (ct^ (N, T,T)) of eq (2)

may be accomplished by utilization of the particular Allan variance [2]

where specifically N = 2 and T = T such that

a^T) . /a (N=2,T=T, T))= < ^

). (5)

y y 2

Plots of CT versus T on a log-log scale are commonly used as a presentation of frequency stability in the time domain. Convenient

suitable systems and techniques used at NBS for obtaining time domain

measurements of frequency stability will be discussed extensively later.

5
3. COMPARISON OF MEASUREMENT TECHNIQUES

In this discussion we shall not concern ourselves with accuracy

of a frequency. The primary concern shall be the measurement of

fluctuations of frequency, i. e. , instability or stability . It is sometimes

convenient to refer to the instability as fractional frequency deviation.

The measurement of frequency fluctuations can be accomplished

by one or more of several methods. In each method a precise (stable

in time) reference is essential. In the case of measuring excellent

sources an equally excellent reference source is needed.

The first method, direct counting of frequency by the use of

counters , is straightforward. Here, successive values of frequency

are read out directly and recorded. (The reference signal controls the

counter gate. ) Statistical analysis of the results are usually made.

High resolution is not possible by this method when measuring the lower

frequencies unless frequency multiplication is used. Two disadvantages

of frequency multipliers are- -one, a pair of specialized multiplier

chains may be needed for each different carrier frequency range and,

two, not only does the signal noise get multiplied but noise from the

multiplier itself may be introduced.

A second method involves mixing the two frequencies and

recording the beat . When the reference and signal frequencies are

close in value, this requires determination of the fluctuations in very

long beat periods. A quantitative measure of short-term frequency

stability is not practical in this case. However, when a large offset

frequency is introduced, the method is feasible for assessing stability

when a readout device such as a period counter is used for observing

fluctuations in the period of the beat.

6
A somewhat similar method uses a phase sensitive detector for

determining phase fluctuations between two signals which are approximately in phase quadrature (and hence must be at the same frequency).

Short-term (or long-term) phase fluctuations may be recorded. In

order to facilitate statistical analysis it is advantageous to drive an

analog-to-digital converter and a counter with a printer. This method

is related to the NBS system (time domain) which is described in detail

in Section 4.

An interesting and fast method used for comparison of

frequencies and also applicable to stability measurement (time domain)

is the commercially available frequency error expander . Since frequency multiplication is used, the same disadvantages are present as in

the first method where multipliers are employed. The principle of the

error expander is that one of the signals is synthesized to a convenient

offset frequency which is then mixed and multiplied in stages to obtain

higher and higher resolution. Eventually, however, the region is

reached where the noise becomes very great and frequency comparison

is no longer possible.

It is noted that none of the above-mentioned conventional methods

of measuring frequency stability utilize frequency domain techniques.

As indicated previously, in order to have a comprehensive and sufficient

measure of frequency stability it is preferred that the measurements

involve both frequency and time domain techniques. This is recommended even though it is possible to compute time domain performance

from frequency domain results and often conversely [1]. Appendix D

contains a table which allows translation from one domain to the other.

At least one man\xfacturer has made it convenient to determine frequency

stability in the time domain with the results computed automatically [3], [4].

7
others outside NBS have reported on excellent systems for frequencydomain and for time domain measurements of frequency stability [5],

[6], [7], [8]. Some of these resemble in principle the systems used at

NBS. The techniques described by Van Duzer [5] and Meyer [6] best

describe those used in the NBS systems.

Fortunately, frequency domain and time domain methods for

measuring frequency stability require similar apparatus except that:

to make measurements in the frequency domain you must have a frequency window (spectrum analyzer) following the detector; for the

time domain you must have a time window (gated counter) following the

detector. .

8
4. OPERATIONAL SYSTEMS FOR MEASUREMENT

OF FREQUENCY STABILITY AT NBS

It was the introduction of good double -balanced mixers that

permitted measurement of frequency stability by improved techniques.

The double -balanced mixer, considered as a phase sensitive detector,

makes possible meaningful frequency stability measurements of

high-quality signal sources in both the frequency domain and the time

domain. The results are quantitative and may be obtained from a measurement system which is reasonable in cost.

The frequency stability measurement systems described below

have been used at NBS since 1967. The functional block diagrams in

figures 1, 7, and 9 are referred to in the detailed descriptions of the

particular systems. Certain commercial components utilized in the

systems are referred to by brand name and model number. * Substitute

components with similar specifications will give equivalent results.

Certain commercial equipment, instruments, or materials are

identified in this paper in order to adequately specify the experimental

procedure. In no case does such identification imply recommendation

or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best

available for the purpose.

9
1)

OSCILLATOR

(4)

MI XER

(3)

PAD

750mH

'

T

'

0 . 001 uF

AS PHASE

2) 7) OSCILLATOR VOLT

BOX

VERY LOOSE PHASE LOCK

LOOP. VOLTAGE VARIES

1 mi

I OuF

TIME DOMAIN

(OPTIONAL)

CHART RECORDER

COMPUTER

PRINTER

COUNTER

CONVERTER

FREQUENCY DOMAIN

FIGURE 1: FREQUENCY DOMAIN MEASUREMENT OF FREQUENCY STABILITY

( 1 ) OSCILLATOR UNDER TEST

(2) REFERENCE OSCILLATOR OF HIGH SPECTRAL PURITY (VARACTOR TUNING)

(3) ADJUSTABLE ATTENUATOR (TYPICALLY lOdB)

(4) DOUBLE-BALANCED MIXER, HP MODEL 10514A (SCHOTTKY BARRIER DIODES)

(5) NBS LOW-NOISE dc AMPLIFIER (SEE FIGURE 3) (6) OPERATIONAL AMPLIFIER, PHILBRICK MODEL P65AU OR P25AU (SEE FIGURE 2' (7) BATTERY BIAS BOX (SEE FIGURE 5) (8) SPECTRUM ANALYZER, QUAN-TECH MODEL 304

Figure 1 illustrates the measurement system typically used

at NBS for frequency domain measurements. It should be noted that

time domain data can also be obtained simultaneously, although usually

this system is used only for frequency domain measurements. (For

tinie domain measurements it is often more convenient to use a slightly

modified measurement setup to be described later, i In this freqLiency

domain setup the oscillator under test is fed into one side of a low-noise

double - balanc ed mixer (HP Model 105 14A), which utilizes Schottky

barrier diodes. The reference oscillator is fed into the other side of

the mixer through an attenuator, typicallv 10 dB. The mixer acts as

a phase sensitive detector so that when the two signals are ifU.ntical m

10
frequency and are in phase quadrature the output is approximately zero

volts dc . When this output is sent back to the reference oscillator via

the varactor tuning, phase lock is achieved. The phase lock loop contains proper terraination at theoutput of the mixer follov^^ed by operational

amplifiers v/ith adjustable gain. The time constant of the loop may be

adjusted as needed by varying the amplifier gain within the loop and by

use of the RC filter indicated in the diagram. Finally, a battery bias box

is included at the varactor input in order to operate in a suitably linear

portion of the varactor's frequency versus voltage curve. A ve ry loo s

phase lock loop is indicated inasmuch as the voltage varies as phase (in

short term), and in this frequency domain measurement vv^e are observing

the small phase variations directly. Philbrick Model P65AU or P25AU

operational amplifiers which are used are arranged in a circuit as shown

in figure 2 for convenience of adjusting the gain and for self-contained

OUTPUT

FRONT REAR

INPUT

XI 00 r

X30

XIO

1—

X3

XI

1 cOPEN

FIGURE 2: STEPPED-GAIN OPERATIONAL AMPLIFIER

battery supply voltage. Special NBS low-noise dc amplifiers used in

certain precision measurements are shown in figure 3. At NBS we

1 1
EACH

D MERCURY

CELLS IN

!^ PARALLEL

•

• , FIGURE 3: LOW ilOISE AflPLIFIER

have arranged in a small chassis the adjustable RC or CR filters

utilizing low-noise components, with rotary switches for various

combinations of R and C (see fig. 4). The battery bias box is arranged

with a vernier as shown in figure 5, facilitating fine frequency adjustments via the varactor frequency adjustment in one oscillator. A wave

analyzer (Quan-Tech Model 304) is used to obtain the noise plot

information relevant to stability (frequency domain). The phase noise

sideband levels are read out in rms volts on the analyzer set to certain

chosen values of frequency, f. This corresponds to measuring only

those phase noise sidebands which are separated from the carrier by

the various f intervals chosen. Script a? (f ) may be calculated with the

assumption that both sources contribute equally; however, if one source

were the major contributor, then the noise of that source would be no

worse than 3 dB greater than the value of /(f) so calculated.

12
FIGURE 4; ADJUSTABLE RC FILTER

SI: FILTER MODE SWITCH (ROTARY, 3 WAFER)

S2: RESISTOR SWITCH (ROTARY, SHORTING TYPE)

S3: CAPACITOR SWITCH (ROTARY, PROGRESSIVE SHORTING)

1 .OijF

. OuF

OPEN

® @-

FRONT FRONT

+ REAR REAR

NON-SHORTING

SWITCH

1 kw

10 TURN HELIPOT 1 k', V

A 1 .4V MERCURY CELL

FIGURE 5; BATTERY BIAS BOX

THE UNITS ARE BUILT ON SEPARATE CHASSIS AND CONNECTED IN SERIES

TO FACILITATE FINE ADJUSTMENT BETWEEN STEP VOLTAGES

FRONT

+ REAR

13
A typical plot is shown in figure 6. A sample calculation may be

found in Appendix B.

mmrrmm Scmnpt ^ (0 i-^ --i tre'|iie

}>lia-.« llui luations (no

lion), .script ^(1) IS d power in .'iit phase no

u y cloinain measure of

;-e, instritnlity. moduldlined is the ratio of Ihe ye side'jaiid, referred to"

the input tarrier frequency, on a per hertz of bandwidth spectral density basis, to the total signal power, at Fourier frequency f from the carrier, per one d<-vice.

It) ill ht s

f NBS n

l; I I" 3: - f I Hz i TOT rmr

li. ttrrr

1 0 Don

FIGURE 6; SCRIPT ^(f) VERSUS FREQUENCY f

14
In figure 7 a measurement system typically used at NBS for

stability measurements in the time domain is shown. It will be noted

(14)

(1)

OSCILLATOR

(4)

COMPUTER

MIXER

7 50uH

SOU

(3)

PAD

Jo.OOluF

J

(2)

VERY TIGHT PHASE

LOCK LOOP. VOLTAGE

VARIES AS FREQUENCYX AMPL

OSCILLATOR

VOLT

BOX

13)

PRINTER

COUNTER

(12

(11

CONVERTER

(8)

SPECTRUM

ANALYZER

OpF

10)

CHART

RECORDER

TIME DOMAIN

FREQUENCY

DOMAIN

(OPTIONAL)

L _l

FIGURE 7: TIME DOflAIN nEASUREHENT OF FREQUENCY STABILITY

ITEMS (1) THROUGH (8) SAME AS FIGURE 1 (9) OPERATIONAL AMPLIFIER, PHILBRICK P65AU OR P25AU

(10) STRIP CHART RECORDER FOR QUALITATIVE OBSERVATION

(TYPE NOT SPECIFIED)

(11) VOLTAGE-TO-FREQUENCY CONVERTER, VIDAR MODEL 240

(12) FREQUENCY COUNTER WITH LOW DEAD TIME, HP MODEL 5325B

(13) DIGITAL RECORDER WITH FAST RECORDING SPEED, HP MODEL 5050B

(INHIBIT TIME COMPATIBLE WITH COUNTER DEAD TIME)

(14) COMPUTER (OPTIONAL METHOD OF DATA ANALYSIS)

that the principle of operation is similar to that used in the frequency

domain measurement wherein the reference oscillator is locked to the

test oscillator. However, for the time domain measurement we use a very tight phase lock loop and the correction voltage at the oscillator

varies as frequency. This is a very convenient setup for observing fre

quency fluctuations in longer term. However, with the time constant

appropriately adjusted and the means for taking sufficiently fast sample

15
the system is readily used for short term measurements, as well as

the longer term measurements, in the time domain. For qualitative

observations any suitable oscilloscope or strip chart recorder may be

used. For quantitative measurements the system at NBS utilizes a voltage-to-frequency converter (Vidar Model 240), a counter (HP

Model 5325B), and printer (HP Model 5050B Digital Recorder) capable

of recording rapid samples of data with very short dead time. The data

are analyzed typically by computer via a program designed to compute

the appropriate Allan variance [1], [2]. In our computer program it automatically plots on microfilm log o" versus log T along with the

associated confidence in the (j . For small batches of data a desk

calculator could be used and the computer analysis would not be

necessary. An example of a specific Allan variance computation is

shown in Appendix C. A typical plot of log (j versus log T is shown in

figure 8. The dashed lines indicate the slopes which are characteristic

of the types of noise indicated.

2 3 4 567891 5 6 7 8 9 1

1.0 1000

FIGURE 8: SIGMA VERSUS TAU

16
An additional useful system illustrated in figure 9 is used for

differential phase noise measurements of various discrete components

which are frequently used in stability measurement systems. In this

system only one frequency source is used. Its output is split so that

part of the signal passes through the component to be tested,

(14)

REFERENCE

OSCILLATOR COMPUTER

(4)

MIXER

750yH

(3)

son

_|o.001yF

PAD

(15) (16) DEVICE OR COMPONENT

UNDER TEST SHIFTER

13! PRINTER COUNTER (12:

(8) ^ SPECTRUM ANALYZER

FREQUENCY DOMAIN

FIGURE 9 : DIFFERENTIAL PHASE NOISE nEASUREHENT

(11 ) CONVERTER

(9)

(10) CHART >—

RECORDER

TIME DOMAIN

ITEMS (1) THROUGH (14) SAME AS FIGURES 1 AND 7 „..,nrn

(15) ANY DEVICE OR COMPONENT UPON WHICH NOISE MEASUREMENTS ARE DESIRED

(AMPLIFIERS, FILTERS, CAPACITORS, CABLES, PADS, ETC.)

(16) NBS ADJUSTABLE PHASE SHIFTER, 5MHz (SEE FIGURE 10)

The signal is adjusted via a phase shifter (fig. 10) so that it is in phase

quadrature with the other part of the original signal and is downconverted in the Schottky barrier diode mixer as described in previous

FIGURE 10: ADJUSTABLE PHASE SHIFTER (5MHz DELAY LINE)

RG174/U CABLE WAS USED FOR EACH SEGMENT OF PHASE SHIFT

CALCULATED AT ~ 1 0 cm PER DEGREE AT 5 MHz.

17
systems. A low-pass filter is included before the signal is amplified

in special low-noise, low-level dc amplifiers and observed on the

spectrum analyzer. Script ^ {() values are calculated at various frequency values, f, and plotted. A sample calculation is shown in

Appendix B.

The measurement system noise level (e. g. , see fig. 6) is easily

evaluated. Using the differential phase noise measurement system

shown in figure 9, let the "device under test" be a short length of

coaxial cable (which is itself not a source of noise). The small amount

of noise observed on the spectrum analyzer represents the system

noise, mainly due to the mixer (4) or the first amplifier (5). The

calculation of the system noise is then the procedure illustrated in

Appendix B.

By the phrase very loose phase lock loop , we mean that the

bandvi/idth of the servo response is small compared to the lowest frequency f at which we wish to measure (i. e. , the response time is very

slow). By the phrase very tight phase lock loop , we mean that the

bandwidth of the servo response is relatively large (i. e. , the response

time is much smaller than the smallest time interval T at which we

wish to measure).

A convenient chart for translating between frequency domain and

time domain is given in Appendix D.

Appendix E lists several important references for measurement

of frequency stability. In addition to several general references a number of specific papers are given. These may be useful for better

understanding of the problems and principles involved in frequency

stability measurements.

An extensive bibliography is given. It includes all references

listed elsewhere in the paper.

18
5. MEASUREMENTS OF FREQUENCY STABILITY

AT MICROWAVE FREQUENCIES

All of the systems described above have been used extensively

for determining frequency stability of 1 to 100 MHz sources. It is in

that frequency range, principally, that the most stable, spectrally pure

signal sources have been available. However, the measurement systems as described above are not limited to that range. Measurements

can be performed readily on sources in the range 0. 2 MHz to 500 MHz

using the identical systems illustrated in figures 1 and 7. (For the

system in fig. 9 the only component which would be different is the

phase shifter which must be one capable of functioning at the source

frequency. ) Similar measurement systems can be used in frequency

ranges up to 12 GHz without employing waveguide mixers or other

waveguide components. A wider range mixer (instead of the one

specified) must be substituted and possibly some isolation of the sources

would be needed. Several commercial double -balanced mixers with

coaxial connectors are available using Schottky barrier diodes [9].

The techniques of measurement are basically the same as described

previously. In general, waveguide components may be used for these

frequency stability or phase noise measurements between 5 GHz and

12.4 GHz (and higher). Balanced mixers can be made using a 180°

hybrid (magic tee) as the coupling, device with two diodes mounted either

in series or in shunt with the output. Our interest (or experience) in

this frequency range has not been extensive partly because of the lack of

spectrally pure sources at higher frequencies. However, the measurements which have been made employ the previously described techniques

primarily.

19

I
The results of our measurements indicate that the precision

capabilities are better than what is necessary for determining stability

on the relatively noisy sources available (i.e. , klystrons, Gunn oscillators, sources derived from lower frequency by multiplication, etc. ).

i .

6. SUMMARY

Concise definitions for specifying frequency stability have been

given for measurements in the frequency domain and time domain.

The attempt is to be basic so that a person without extensive knowledge

in the field can quickly grasp the concepts involved (extended derivations and theory are left to the appendices or references). Several

contemporary measurement techniques are reviewed and compared.

Operational systems for measurement of frequency stability are

described in detail sufficient to facilitate duplication of the apparatus

used. Uniform methods of reporting data and techniques of measurement are recommended as advantageous and desirable so that better

interpretation of specifications for frequency stability can be

accomplished. The measurement systems and techniques may be

utilized well into the microwave region.

The author is particularly indebted to Dr. Donald Halford for his

valuable assistance and comments in the preparation of this document.

20
REFERENCES

[1] J. A. Barnes, A. R. Chi, L. S. Cutler, et al. , "Characterization

of Frequency Stability, " NBS Technical Note 394 (October 1970);

also published in IEEE Trans, on Instr. and Meas. IM- 20 , No. 2,

pp. 105-120 (May 1971).

[2] D. W. Allan, "Statistics of Atomic Frequency Standards, " Proc.

IEEE 54, No. 2, pp. 221-230 (February 1966).

[3] Hewlett-Packard, "Precision Frequency Measurements , "

Application Note 116 (July 19 69).

[4] Hewlett-Packard, "Computing Counter Applications Library,"

Nos. 7, 22, 27, 29 (1970).

[5] V. Van Duzer, "Short-Term Stability Measurements , " Proc. of

the IEEE-NASA Symposium on the Definition and Measurement of

Short-Term Frequency Stability, NASASP-80, pp. 269-272 (19 65).

[6] D. G. Meyer, "A Test Set for Measurement of Phase Noise on

High Quality Signal Sources, " IEEE Trans, on Instr. and Meas.

IM- 19 , No. 4, pp. 215-227 (November 1970).

[7] R. B. Shields, "Review of the Specification and Measurement of

Short-Term Stability, " Microwave Journal, pp. 49-55 (June 1969).

[8] L. S. Cutler and C. L. Searle, "Some Aspects of the Theory and

Measurement of Frequency Fluctuations in Frequency Standards, "

Proc. IEEE 54, No. 2, pp. 136- 154 (February 1966).

[9] G. R. Reeve, "Signal Detection Systems ," NBS Report 9767

(October 1967), sponsored by Army/Navy/ Air Force

JTCG-METCAL/CCG on Contract 69-25b.

21
6v_

APPENDIX A

Glossary of Symbols

Carrier frequency

Fourier frequency of fluctuations

Nominal frequency of source

Frequency fluctuation

Fractional frequency fluctuations,

dx Time interval fluctuations, —— r y

dt ^

Average of y over a time interval T

Defined as B, high frequency cutoff (bandwidth)

Spectral density of y

Radio frequency power spectral density

Phase fluctuation

2

Spectral density of phase fluctuations; S. (f) = S (f) ——

b<t> y

Frequency domain measure of phase fluctuations;

Script (f ) is defined as the ratio of

Power density (one phase modulation sideband)

Power (total signal)

For small 6^, S {{) = 2j^(f)

6®

Number of data values used in obtaining a sample variance

Total number of data values available (usually M » N)

Time interval between the beginnings of two successive

measurements

22
APPENDIX A cont .

T Sampling time interval

r Parameter related to dead time; r = T/t

t Time variable

Cj-^(N, T, t) Sample variance of N averages of y(t) each of duration T, and repeated every T units of time (Allan variance)

k,n Integers (used as index of summation)

2

(T (t) Specific Allan variance where N = 2, T = T

y

(J Square root of a variance

A Peak-to-peak voltage of a beat frequency at output of mixer

V Root-mean- square (noise) voltage at output of mixer as measured by a spectrum analyzer

23
APPENDIX B

A Sample Calculation of Script af

For convenience of computation and plotting it often is

advantageous to set the beat frequency voltage (before locking) to —X=r=r volts (0. 316 V) peak-to-peak at the mixer output. Then (after

v/10

lock) with the output of the phase detector expressed in rms nanovolts

per root hertz, direct plotting is facilitated for j£(f) in decibels versus

frequency in hertz. In this case 1000, 100, and 10 nanovolts per root

hertz correspond to -110, -130, and -150 dB respectively. A sample

calculation demonstrating this convenience is shown below.

Given:

A' = 0. 316 V (i. e. , V)

ptp 710

v = lOOnVHz"'^ @ f = 20 Hz

rms

100nVHz"'^\ / lO'"" \ -1 10"^'',, -1 Hz = Hz

0. 316 V

'

\ rrr^ J ,n-i

10'^^ Hz"^ = -130 dB

or u^ing logarithms:

'^rms\ , (10-'' V- Hz' ''^) ^'ZQ Hz) = 20 log = 20 log ^ -j^ = 20(-7 + C.5)

3-130 dB

If the phase noise follows flicker law, at f = 1 Hz it is 20 times worse

(or 13 dB greater), that is

af(l Hz) = -130 dB + 13 dB = -117 dB.

24
APPENDIX C

A Sample Calculation of Allan Variance, cr (t)

y

ay(T) (a^{N= 2,T= T,T))= (^^^ 1 M-l

2(M- 1) 1 'Vk+1 " '^k k=l

in the example below:

Number of data values available, M = 9

Number of differences averaged, M - 1 = 8

Sampling time interval T = Is

Data values

(y)

892

809

823

798

671

644

883

903

677

First differences

83

14

25

127

27

239

20

226

M-l

1

k=l

(yk+l

First differences squared

6889

196

625

16129

729

57121

400

51076

h3165

Based on these data:

a^(T)

y

133165

2(8)

=: 8322.81,

[%(T)] y 8322. 81 = 91. 23, N = 2, T = T = 1

In this example, the data values may be understood to be expressed in

parts in 10 ^ ^.

25
APPENDIX Ccont

Using the same data as in the above example it is possible to calculate

the Allan variance for T = 2s by averaging pairs of adjacent data values

and using these averaged values as new data values to proceed with the

calculation as before. Allan variance values may be obtained for

T = 3 s by averaging three adjacent data values in a similar manner,

etc. , for larger values of T.

Ideally the calculation is done via a computer and a large

number, M, of data values should be used. (Typically M = 256 data

values are used in the NBS computer program. ) The statistical confidence of the calculated Allan variance improves nominally as the square

root of the number, M, of data values used. For M - 256, the confidence of the Allan variance is not expected to be better than approximately —/

X 100% ^ 7% in the rms sense. The use of M 1 /256

is logically similar to the use of B • T » 1 in spectrum analysis

a a measurements, where B is the analysis bandwidth (frequency window)

of the spectrum analyzer, and T is the post-detection averaging time"^

of the spectrum analyzer.

26
APPENDIX D

27
28
APPENDIX E

Some Important References

for

Measurement and Specification of Frequency Stability

General References

1. November or December of even-numbered years IEEE

Transactions on Instrumentation and Measurement (Conference

on Precision Electromagnetic Measurements, held every 2 years).

2. February 1966 Proceedings of the IEEE , special issue on

frequency stability (IEEE-NASA Symposium).

3. Proceedings of the IEEE-NASA Symposium on the Definition

and Measurement of Short-Term Frequency Stability at

Goddard Space Flight Center, Greenbelt, Maryland,

November 23-24, 1964. Prepared by Goddard Space Flight

Center (Scientific & Technical Information Division, National

Aeronautics and Space Administration, Washington, D, C. , 1965). Copies available for $1.75 from the U. S. Government

Printing Office, Washington, D.C. 20402.

4. The annual proceedings of the Symposium on Frequency Control

(Ft. Monmouth). These papers are not edited nor reviewed.

J. A. Barnes, A. R. Chi, L. S. Cutler, et al. , "Characterization

of Frequency Stability, " NBS Technical Note 394 (October .970);

also published in IEEE Trans, on Instr. and Meas. IM-20 , No. 2,

pp. 105-120 (May 1971). This is the most definitive discussion

to date of the characterization and measurement of frequency

stability. It was prepared by the Subcommittee on Frequency

Stability of the Institute of Electrical and Electronic Engineers.

29
APPENDIX E cont.

Some Specific Papers

6. D. W. Allan, "Statistics of Atomic Frequency Standards, " Proc. IEEE, vol. 54, pp. 221-230, February 1966.

A thorough understanding of this paper is important for

everyone who wishes to measure and quote performance of

frequency standards in the time domain, e. g. , cr versus T

plots. The data analysis must take into account the number

of samples taken and how they are used.

7. David W. Allan, B. E. Blair, D. D. Davis, and H. E.

Machlan, "Precision and Accuracy of Remote Synchronization via Portable Clocks, Loran C, and Network Television

Broadcasts, " Proc. 25th Annual Symposium on Frequency

Control, Fort Monmouth, N. J. , 2 6- 28 April 197 1 , to be

published.

8. E. J. Baghdady, R. N. Lincoln, and B. D. Nelin, "ShortTerm Frequency Stability: Characterization, Theory, and

Measurement, " Proc. IEEE, vol. 53, pp. 704-722, July

19 65. Among many other topics, the possible problem of

AM noise is discussed.

9. Helmut Brandenberger , Frederic Hadorn, Donald Halford,

and John H. Shoaf, "High Quality Quartz Crystal Oscillator

Frequency Domain and Time Domain Stability, " Proc. 25th

Annual Symposium on Frequency Control, Fort Monmouth,

N. J. , 26-28 April 1971, to be published. An example of

1970 "state-of-the-art" measurements.

10. L. S. Cutler, "Present Status in Short Term Frequency

Stability," Frequency, vol. 5, pp. 13-15, SeptemberOctober 1967. This is a well- written, concise progress

report with indications for future effort. Caution: His

examples I and 11 were not in fact state-of-the-art, while

example IV has some factor-of-ten typographical errors as

given„

30
APPENDIX E cont.

11. L. S. Cutler and C. Searle, "Some Aspects of the Theory

and Measurement of Frequency Fluctuations in Frequency

Standards," Proc. IEEE, vol. 54, pp. 136-154, February

19 66. This is a useful treatment of some of the theory, mathematics, and measurement techniques - -with physical insight

into the noise processes of practical concern.

12. W. A. Edson, "Noise in Oscillators, " Proc. IRE, vol. 48,

pp. 1452-1466, August I960. This paper is an "old classic."

13. C. Finnie, R. Sydnor, and A. Sward, "Hydrogen Maser

Frequency Standard, " Proc. 25th Annual Symposium on

Frequency Control, Fort Monmouth, N. J. , 26-28 April

1971, to be published.

14. D, J. Glaze, "Improvements in Atomic Beam Frequency

Standards at the National Bureau of Standards, " IEEE Trans,

on Instr. and Meas. IM-19, No. 3, pp. 156- 160, August 1970.

15. D. B. Leeson, "A Simple Model of Feedback Oscillator

Noise Spectrum," Proc. IEEE (Letters), vol. 54, pp. 329-

330, February 1966. Descriptive, in a simple, practical

manner

16. J. A. Mull en, "Background Noise in Nonlinear Oscillators, " Proc. IRE, vol. 48, pp. 1467- 1473, August I960. An "old

classic. "

17. H. P. Stratemeyer, "The Stability of Standard- Frequency

Oscillators," General Radio Experimenter, vol. 38, pp. 1-16,

June 1964. Easy reading.

18. V. Van Duzer, "Short-Term Stability Measurements, " IEEE-NASA Symposium on Short-Term Frequency Stability,

Washington, D. C. : U. S. Government Printing Office,

pp. 269-272, NASA-SP80. The basic method described by

Van Duzer is simple, elegant, easily instrumented, easily

modified, extremely versatile, and capable of the best

resolution which is attained at today's state-of-the-art.

31
BIBLIOGRAPHY

1. D. W. Allan, "Statistics of Atomic Frequency Standards, " Proc.

IEEE, vol. 54, pp. 221-230, February 1966.

2. David W. Allan, B. E. Blair, D. D. Davis, and H. E. Machlan,

"Precision and Accuracy of Remote Synchronization via Portable

Clocks, Loran C, and Network Television Broadcasts, " Proc.

25th Annual Symposium on Frequency Control, Fort Monmouth,

N.J. , 26-28 April 1971, to be published.

3. A. E. Anderson and H. P. Brower, "A Tunable Phase Detector

for Short-Term Frequency Measurement, " Proc. IEEE-NASA

Symposium on the Definition and Measurement of Short-Term

Frequency Stability, NASASP-80, pp. 295-302, 1965.

4. J. R. Ashley and C. B. Searles, "Microwave Oscillator Noise

Reduction by a Transmission Stabilizing Cavity, " IEEE Trans, on

Microwave Theory and Techniques MTT-16, pp. 743-748,

September 1968.

5. J. R. Ashley, C. B. Searles, and F. M. Palka, "The Measurement

of Oscillator Noise at Microwave Frequencies, " IEEE Trans, on

Microwave Theory and Techniques MTT-16, pp. 753-760,

September 1968.

6. W. Atkinson and L, Fey, "Statistical Aspects of Clock Errors,"

NBS Report 6085, January 5, I960.

7. W. R. Atkinson, L. Fey, and J. Newman, "Spectrum Analysis of

Extremely Low Frequency Variations of Quartz Oscillators, " Proc. IEEE (Correspondence), vol. 51, p. 379, February 1963.

8. E. J. Baghdady, R. D. Lincoln, and B. D. Nelin, "Short-Term

Frequency Stability: Theory, Measurement, and Status," Proc.

IEEE-NASA Symposium on Short-Term Frequency Stability,

NASASP-80, pp. 65-87, 1965; also Proc. IEEE, vol. 53,

pp. 704-722, 2110-2111, 1965.

9. J. J. Bagnall, Jr. , "The Effect of Noise on an Oscillator

Controlled by a Primary Reference, " NEREM 1959 Record,

pp. 84-86.

32
BIBLIOGRAPHY cont.

10. J. A. Barnes, "Studies of Frequency Stability, " Unpublished NBS

Report, August 15, 1969.

11. J. A. Barnes, "Frequency Measurennent Errors of Passive

Resonators Caused by Frequency-Modulated Exciting Signals, " IEEE Trans, on Instrumentation and Measurement IM-19, No. 3,

pp. 147-152, August 1970.

12. J. A. Barnes, "Atomic Timekeeping and the Statistics of Precision

Signal Generators, " Proc. IEEE, vol. 54, pp. 207-220, February

1966.

13. J. A. Barnes, "Tables of Bias Functions, Bj and B2, for

Variances Based on Finite Samples of Processes with Power Law

Spectral Densities," NBS Technical Note 375, January 1969.

14. J. A. Barnes and D. W. Allan, "A Statistical Model of Flicker

Noise, " Proc. IEEE, vol. 54, pp. 176- 178, February 1966.

15. J. A. Barnes and D. W. Allan, "Effects of Long-Term Stability

on the Definition and Measurement of Short-Term Stability, " Proc. IEEE-NASA Symposium on Short-Term Frequency Stability,

NASASP-80, pp. 119-123, 1965.

16. J. A. Barnes, A. R. Chi, L. S. Cutler, et al, , "Characterization

of Frequency Stability, " NBS Technical Note 394, October 1970;

also published in IEEE Trans, on Instrumentation a.nd Measurement IM-20, No. 2, pp. 105- 120, May 1971.

17. J. A. Barnes and L. E. Heim, "A High- Resolution Ammonia

Maser Spectrum Analyzer, " IRE Trans, on Instrumentation I- 10.

No. 1, pp. 4-8, June 1961.

18. J. A, Barnes and R. C. Mockler, "The Power Spectrum and Its Importance in Precise Frequency Measurements, " IRE Trans, on

Instrumentation 1-9 , pp. 149-155, September I960,

19. J. S, Bendat, Principles and Applications of Random Noise Theory . New York: John Wiley and Sons, p. 79, 1958.

33
BIBLIOGRAPHY cont.

20. W. R. Bennett, Electrical Noise . New York: McGrav/-Hill, I960.

21. W. R. Bennett, "Methods of Solving Noise Problems," Proc. IRE,

vol. 44, pp. 609-638 (Eq. 223 ff. ), May 1956.

22. I. Berstein and G, Gorelik, "Frequency Modulation Noise in

Oscillators," Proc. IRE (Correspondence), vol. 45, p. 94,

January 1957.

23. C. Bingham, M. D. Godfrey, and J. W. Tukey, "Modern

Techniques of Power Spectrum Estimation, " IEEE Trans. AU,

vol. 15, pp. 56-66, June 1967.

24. R. B. Blackman and J. W. Tukey, The Measurement of Power

Spectra . New York: Dover, 1958.

25. Helmut Brandenberger, Frederic Hadorn, Donald Halford, and

John H. Shoaf, "High Quality Quartz Crystal Oscillators:

Frequency Domain and Time Domain Stability, " Proc. 25th

Annual Symposium on Frequency Control, Fort Monmouth, N.J. , 26-28 April 1971, to be published.

26. E. O. Brigham and R. E. Morrow, "The Fast Fourier Transform,"

IEEE Spectrum, vol. 4, pp. 63-70, December 1967.

27. J. R. Buck and D. J. Healey, in, "Calibration of Short-Term

Frequency Stability Measuring Apparatus, " Proc. lEEF L. , vol. 54, p. 305, February 1966.

28. J. R. Buck and D. J. Healey, III, "Short Term Frequency Stability

Measurement of Crystal Controlled X-Band Source, " Proc.

IEEE-NASA Symposium on Short-Term Frequency Stability,

NASASP-80, pp. 201-209, 1965.

29. J. R. Buck, D. J. Healey, III, and M. Meiseles, "Measurement

of Phase Stability of Quartz Crystal Oscillators for Airborne Radar

. Applications," IEEE International Conv. Rec. , pt. 8, pp. 34-42,

March 1964.

34
BIBLIOGRAPHY cont.

30. G, A. Campbell and R. M. Foster, Fourier Integrals for

Practical Applications . Princeton, N. J. : D. Van Nostrand, 1948.

31. R. A. Campbell, "Stability Measurement Techniques in the

Frequency Domain, " Proc. IEEE-NASA Symposium on the

Definition and Measurement of Short-Term Frequency Stability,

NASASP-80, pp. 231-235, 1965.

32. E. R. Chenette, "Low Noise Transistor Amplifiers, " Solid State

Design, vol. 5, pp. 27-30, February 1964.

33. J. Chramiec, "Noise Properties of a Super regenerative

Parametric Amplifier, " Proc IEEE, vol. 54, p. 704, April 1966.

34. E. L. Crow, "The Statistical Construction of a Single Standard

from Several Available Standards, " IEEE Trans, on Instrumentation and Measurement IM- 1 3 , pp. 180-185, December 1964.

35. L. S. Cutler, "Some Aspects of the Theory and Measurement of

Frequency Fluctuations in Frequency Standards, " Proc.

IEEE-NASA Symposium on the Definition and Measurement of

Short-Term Frequency Stability, NASASP-80, pp. 89- 100, 1965.

36. L. S. Cutler, "Present Status in Short Term Frequency Stability, " Frequency, vol. 5, pp. 13-15, September-October 1967.

37. L. S. Cutler and C. L. Searle, "Some Aspects of the Theory and

Measurement of Frequency Fluctuations in Frequency Standards, " Proc. IEEE, vol. 54, pp. 136-154, February 1^66.

38. W. B. Davenport and W. L. Root, Random Signals and Noise . New York: McGraw Hill, Ch. 6, 1958.

39. E. V. Dvornikov, E. A. Mavrin, and N. V. Morkovin, "A HighStability Transistorized Crystal Oscillator, " Pribory i Tekhn.

Eksperim. (USSR), No. 4, July-August 1963. For English

translation see Instr. Exper. Tech. (USSR), pp. 672-674, JulyAugust 1963.

40. W. A. Edson, "Noise in Oscillators, " Proc. IRE, vol. 48,

pp. 1454-1466, August I960.

35
BIBLIOGRAPHY cont.

41. W. A. Edson, "Progress and Problems in Short Term Stability, " Proc. 19th Annual Symposium on Frequency Control, Fort

Monmouth, N. J. , pp. 43-48, 20-22 April 1965.

42. Esposito and J. A. Mullen, "Noise in Oscillators with General

Tank Circuits, " IRE International Conf. Rec. , pt. 4, pp. 202-208,

March 1961.

43. C. Finnic, R. Sydnor, and A. Sward, "Hydrogen Maser Frequency

Standard, " Proc. 25th Annual Symposium on Frequency Control,

Fort Monmouth, N.J. , 26-28 April 1971, to be published.

44. L. Fey, W. R. Atkinson, and J. Newman, "Obscurities of

Oscillator Noise, " Proc. IEEE (Correspondence), vol. 52,

pp. 104-105, January 1964.

45. E. A. Gerber and R. A. Sykes, "State of the Art--Quartz Crystal

Units and Oscillators. " Proc. IEEE, vol. 54, pp. 103-116,

February 1966.

46. E. A. Gerber and R. A. Sykes, "Quartz Frequency Standards,"

Proc. IEEE, vol. 55, pp. 783-791, June 1967.

47. D. J. Glaze, "Improvements in Atomic Beam Frequency

Standards at the National Bureau of Standards, " IEEE Trans, on

Instrumentation and Measurement IM-19, No. 3, pp. 156-160,

August 1970.

48. M.J. E. Golay, "Monochromaticity and Noise in a Regenerative

Electrical Oscillator, " Proc. IRE, vol. 48, pp. 1473-1477,

August I960.

49. C. H. Grauling, Jr. and D. J. Healey, III, "Instrumentation for

Measurement of the Short-Term Frequency Stability of Microwave

Sources," Proc. IEEE, vol. 54, pp. 249-257, February 1966.

50. P. Grivet and A. Blaquiere, "Nonlinear Effects of Noise in

Electronic Clocks," Proc. IEEE, vol. 51, pp. 1606-1614,

November 1963.

36
BIBLIOGRAPHY cont.

51. J. D, Hadad, "Basic Relation Between the Frequency StabilitySpecification and the Application, " Proc. IEEE-NASA Symposium

on the Definition and Measurement of Short-Term Frequency

Stability, NASA SP- 80, pp. 11- 18, 19 65.

E. Hafner, "The Effects of Noise on Crystal' Oscillator s , " Proc.

IEEE, p. 179, February 1966.

Donald Halford, "A General Mechanical Model for |f Spectral

Density Random Noise with Special Reference to Flicker Noise

l|f|, " Proc. IEEE, vol. 56, No. 2, pp. 25 1-258, March 1968.

54. Donald Halford, A. E. Wainwright, and James A. Barnes,

"Flicker Noise of Phase in RF Amplifiers and Frequency

Multipliers: Characterization, Cause, and Cure, " (Summary)

Proc. 22nd Annual Symposium on Frequency Control, Fort

Monmouth, N. J. , pp. 340-341, April 1968.

55. Hewlett-Packard, "Frequency and Time Standards, " Application

Note 52, 1965.

56. Hewlett-Packard, "Precision Frequency Measurements , " Application Note 116, July 19 69.

57. Hewlett-Packard, "Computing Counter Applications Library, " Nos. 7, 22, 27, 29; 1970.

58. R. H. Holman and L. J. Paciorek, "Short-Term Stability

Measurement Techniques and Results, " Proc. IEEE-NASA

Symposium on the Definition and Measurement of Short-Term

Frequency Stability, NASASP-80, pp. 237-252, 1965.

59. S. L. Johnson, B. H. Smith, and D. A. Calder, "Noise Spectrum

Characteristics of Low-Noise Microwave Tubes and Solid-State

Devices," Proc. IEEE, vol. 54, pp. 258-265, February 1966.

60. P. Karta£choff, "Shot- Effect Influence on the Frequency of an

Oscillator Locked to an Atomic Beam Resonator, " Proc.

IEEE-NASA Symposium on the Definition and Measurement of

Short-Term Frequency Stability, NASASP-80, pp. 303-308, 1965.

37
BIBLIOGRAPHY cont.

61. R. F. Lacey, A. L. Helgesson, and J. H. Holloway,

"Short-Term Stability of Passive Atomic Frequency Standards, " Proc. IEEE, vol. 54, pp. 170-176, February 1966.

62. R. W. Larson, "Power Spectrum of Oscillator and Frequency

Multiplier Phase Jitter," Proc. IEEE, vol. 54, p. 796, May 1966.

63. D. B, Leeson, "A Simple Model of Feedback Oscillator Noise

Spectrum, " Proc. IEEE L. , vol. 54, pp. 329-330, February 1966.

64. D. B. Leeson and G. F. Johnson, "Short-Term Stability for a Doppler Radar: Requirements, Measurements, and Techniques,"

Proc. IEEE, vol. 54, pp. 244-248, February 1966.

65. R. M. Lerner, "The Effects of Noise on the Frequency Stability

of a Linear Oscillator, " Proc. Natl. Electr. Conf. , vol. 7,

pp. 275-280, 1951.

66. L. Mailing, "Phase-Stable Oscillators for Space Communications,

including the Relationship between the Phase Noise, the Spectrum,

the Short-Term Stability, and the Q of the Oscillator, " Proc. IRE,

vol. 50, pp. 165 6-1664, July 19 62.

67. J. C. McDade, "Measurement of Additive Phase Noise Contributed

by the Step-Recovery Diode in a Frequency Multiplier, " Proc.

IEEE L. , vol. 54, pp. 292-294, February 1966.

68. D. G. Meyer, "A Test Set for Measurement of Phase Noise on

High Quality Signal Sources, " IEEE Trans, on Instrumentation

and Measurement IM- 19, No. 4, pp. 215-227, November 1970.

69. A. H. Morgan and J. A. Barnes, "Short-Time Stability of a Quartz-Crystal Oscillator as Measured with an Ammonia Maser, " Proc. IRE (Letter), vol. 47, No. 10, p. 1782, October 1959.

70. J. A. Mullen, "Background Noise in Nonlinear Oscillators, " Proc. IRE, vol. 48, pp. 1467-1473, August I960.

71. J. A. Mullen, "Background Noise in Oscillators with R. F. Pushing

J. Electronics and Control, vol. 10, pp, 127-138, February 1961.

38
BIBLIOGRAPHY cont.

72. J. G. Ondria, "A Microwave System for Measurements of AM

and FM Noise Spectra, " IEEE Trans, on Microwave Theory and

Techniques MTT-16, pp. 767-78(1, September 1968.

73. R.. E. Paradysz and W. L. Smith, "Measurement of FM Noise

Spectra of Low-Noise VHF Crystal Controlled Oscillators, " IEEE Trans, on Instrumentation and Measurement IM-15, pp. 202-

211, December 1966.

74. V. Prabhu, "Noise Performance of Abrupt- Junction Varactor

Frequency Multipliers, " Proc. IEEE L. , vol. 54, pp. 285-287,

February 1966.

75. J. Rarity, L. Saporta, and G. Weiss, "Study of Short Term

Stability of Crystal Oscillators, " New York University, New York,

N. Y., Tech. Rpt. Cont. DA36-039 -SE- 87450, DA Project

3A-99-15-02, 02-02.

76. G. R. Reeve, "Signal Detection Systems, " NBS Report 9767,

October 19 67, sponsored by Army/Navy/ Air Force

JTCG-METCAL/CCG on Contract 69-25b.

77. C. L. Searle, R. D. Posner, R. S. Badessa, and V. J. Bates,

"Computer- Aided Calculation of Frequency, " Proc. lEEE-N^SA

Symposium on the Definition and Measurement of Short-Term

Frequency Stability, NASASP-80, pp. 273-277, November 1964.

78. R. B. Shields, "Review of the Specification and Measurement of

Short-Term Stability," Microwave Journal, pp^ 49-55, June 1969.

79. W. L. Smith and W. J. Spencer, "Quartz Crystal Controlled

Oscillators, " B. T. L. , Final Report, Cont. DA 36-039 sc-85373,

Dept. of the Army, Proj. 3G- 2 6- 05 - 00 1 -0 1 , March 15, 1963.

80. W. J. Spencer and W. L. Smith, "Precision Crystal Frequency

Standards, " Proc. 15th Annual Symposium on Frequency Control,

Fort Monmouth, N. J. , pp. 139- 155, 19 61.

81. J. L. Stewart, "Frequency Modulation Noise in Oscillators, " Proc. IRE, vol. 44, pp. 372-376, March 1956.

39
BIBLIOGRAPHY cont.

82. H. L. Stover, "Theoretical Elxplanation for the Output Spectra of

Unlocked Driven Oscillators, " Proc. IEEE L. , vol. 54, pp. 310-

311, February 1966.

83. H. P. Stratemeyer , "The Stability of Standard- Frequency

Oscillators," General Radio Experimenter, vol. 38, pp. 1-16,

June 1964.

84. R. Sydnor, J. J. Caldwell, and B. E. Rose, "Frequency Stability

Requirements for Space Communications and Tracking Systems, " Proc. IEEE, vol. 54, pp. 231-236, February 1966.

85. R. A. Sykes, W. L.. Smith, and W. J. Spencer, "Performance of

Precision Quartz -C rystal Controlled Frequency Generators, " IRE Trans, on Instrumentation I- 1 1 , pp. 243-247, December 1962.

86. V. Troitsky, "Certain Problems of the Theory of Fluctuations in

Oscillators. The Influence of Flicker Noise, " Izv. Vysshikh

Uchebn. Zavedenii, Radiofiz. , vol. 1 , -pp. 20-33, 1958.

87. A. Tykulsky, "Spectral Measurements of Oscillators, " Proc.

IEEE L. , vol. 54, p. 306, February 1966.

88. V. Van Duzer, "Short-Term Stability Measurements, " Proc.

IEEE-NASA Symposium on the Definition and Measurement of

Short-Term Frequency Stability, NASASP-80, pp. 269-272, 1965.

89. R.F.C. Vessot, L. F. Mueller, and J, Vanier, "A CrossCorrelation Technique for Measuring the Short-Term Properties

of Stable Oscillators, " Proc. IEEE-NASA Symposibm on the

Definition and Measurement of Short-Term Frequency Stability,

NASASP-80, pp. 1 1 1- 1 18, 1965.

9C. R.F.C. Vessot, L. Mueller, and J. Vanier, "The Specification of

Oscillator Characteristics from Measurements made in the

Frequency Domain," Proc. IEEE, p. 199, February 1966.

91. A. L. Whitwell and A. N. Williams, "A Microwave Technique for

Determining Noise Spectra at Frequencies Close to the Carrier, " Microwave J., vol. 2, pp. 27-32, November 1959.

-J, <JU 'r ^ T'

40
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12. Sponsoring Organization Name and Complete Address (Street, City. State, ZIP)

Same as Item 9.

13. 1 ype of Report & Period C oV e r e d

14. Sponsoring Agency C ode

15. SUPPLEMENTARY NOTES ^BS Report 9794 6/30/71

NBS Report 9794 (revised) 9/7/71

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.)

This report gives concise definitions for specifying frequency

stability for measurements in the frequency domain and time domain.

Standards of terminology and of measurement techniques are recommended.

Measurement systems are described in adequate detail so that the

apparatus may be duplicated. Proposed extension of the measurement

systems through 12.4 GHz is discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons ) » i -i • « Allan variance. Frequency stability measurements.

Measurement system description. Phase noise. Spectral density. Terminology standards.

18. AVAILABILITY Unlimited 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

1

' For Official Distribution. Do Not Release to NTIS UNCL ASSIFIED

1

' Order From Sup. of Doc, U.S. Government Printing

Washington, D.C. 20402. SD Cat. No. C13

Office 20. SECURITY CLASS

(THIS PAGE)

22. Price

1

^ Order From National Technical Information Service

Springfield, Virginia 22151

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UNCLASSIFIED

USCOMM-DC 29042-P74

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