NIST Technical Note 1337: Characterization of Clocks and Oscillators

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PageCo2 Characterixstaon of Frequency StabilityJames A. Barnes, Andrew R. Chi, Leonard S. Cutler, Daniel 1. Healey, David B. Leeson,Thomas E. McGunigal, James A. Mullen, Jr., Warren L. Smith, Richard L. Sydnor,Robert F.e. Vessot, and Gemot M.R. WinklerIEEE Transactions all Instrnmentation and Measurement, 1971TN-146I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IN-147II. Statement of the Problem TN-148m. Background and Definitions IN-149IV. Derlnition of Measures of Frequency Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IN-149V. Translations Among Frequency Stability Measures IN-1SlVI. Applications of Stability Measures . . . . . . . . . . . . . . . . . . . . . .. IN-1S3VII. Measurement Techniques for Frequency Stability TN-IS4VIII. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. TN-IS7C.3 Characterization of Frequency and Phase NoiseComite Consultatif International Des Radiocomrnunications (CCIR)Report 580 of the CCIR, 1986TN-162L Introduction TN-1622. Fourier Frequency Domain TN-1633. Time Domain 1N-1634. Conversion Between Frequency and Time Domains TN-1M5. Measurement Techniques TN-l666. Confidence Limits of Time Domain Measurements TN-1667. Conclusion TN-167D. SUPPORTING PAPERSD.l Characteri:t8tion and Measurement of Time and Frequency StabilityP. Lesage and C. AudoinRadio Science, 1979;. TN-1711. Introduction TN-l?l2. Definitions: Model of Frequency Fluctuations TN-l713. Noise Processes in Frequency Generators TN-1734. Measurements in the Frequency Domain 1N-1745. Measurements in the Time Domain , TN-l776. Characterization of Frequency Stability in the Time Domain TN-1787. Characterization of Frequency Stability via Filtering or Frequency Noise TN-1828. Spectral Analysis Inferred From Time Domain Measurements TN-1839. Structure Functions of Oscillator Fractional Phase and Frequency fluctuations TN-l8410. Power Spectral Density of Stable Frequency Sources TN-18S11. Conclusion TN-IS7vii
0 •• 0 •• 0 •• 0 • • • • • • • • • • • ••0 0 •• 0 ••••••••••••• 0 • 0 .'Page0.2 Phase Noise and AM Noise Measurements in the Frequency DomainAlgie L. Lance, Wendell D. Seal, and Frederik LabaarInfrared and Millimeter Waves, Vol. 11, 1984. TN-1900 • 0 • 0 •••••••••••••••• 0 ••••I. Introduction TN-190II. Fundamental Concepts .. 00 •••••••• 0 ••• 0 •••• 0 •• 0 •••••••••• 0 •••••••••••••••TN-1910 •• 0 •••• 0 ••••• 0 ••••••••••••••••••••••••••••••0 •• 0 •••••••••••• 0 • 0 •••• 0 ••••• 0 ••••• 0 •• 0 0 ••••••• 0 •••0 •••• 0 0 •• 0 • 0 0 0 0 • 0 0 ••••0 •••••••••••••• 0 •••• 0 ••••• 0 ••••• 0 •••••••••0 ••••••••••••• 0 ••••A Noise Sidebands .. TN-194B. Spectral Density . TN-194C. Spectral Densities of Phase F1uctuations in the Frequency Domain 0 0 0 • 0 0 •••• 0 ••••• 0 TN-197D. Modulation Theory and Spectral Density Relationships . 0 0 •••••• 0 • 0 •• 0 • 0 •••••••• TN-199Eo Noise Processes 0 ••••••• 0 •••• 0 • 0 •• 0 ••••••••••••••• 0 • 0 •• 0 • TN-202F. Integrated Phase Noise o' 0 •••••••••••• 0 • 0 •••••• 0 ••••• 0 0 •••• 0 0 ••••••••• TN-203G. AM Noise in the Frequency Domain.. . 0 • 0 0 ••••• 0 0 • 0 • 0 •• 0 • 0 • 0 ••• 0 0 •• 0 • 0 0 • TN-20SIII. Phase-Noise Measurements Using the Two-Oscillator Technique TN-206A Two Noisy Oscillators TN-208B. Automated Phase-Noise Measurements Using the Two-Oscillator Technique 0" 0 •••••• TN-209C. Calihration and Measurements Using the Two-Oscillator System 0 •••• TN-210IV. Single-Osciliator Phase-Noise Measurement Systems and Techniques TN-218•• 0 0 • 0 0A The Delay Line as an PM Discriminator .... 0B. Calibration and Measurements Using the Delay Line as an FM Discriminator . TN-22SC. Dual Delay-Line Discriminator . 0 ••••• 0 ••• 0 ••••• 0 •••• 0 • 0 • 0 0 • 0 •• 0 •• TN-232• 0 •• 0 •••••••••••• 0 •• 0 •••• 0 •••• TN-2190 •• 0 • 0 •••••• 0 ••• 0 0 0 0 ••• 0 0 0 0 • 0 0 ••0 0 • 0 0 ••••• 0 ••• 0 ••••• 0 • 0 ••••• 0 0 •• 0 ••••••••••••• 0 ••••••••• 0 ••D. Millimeter-Wave Phase-Noise Measurements TN-234V. Conclusion TN-23803 Perlormance of an Automated High Accuracy Phase Measurement SystemS. Stein, Do Glaze, J. Levine, J. Gray, D. Hilliard, D. Howe, and L. Erb36th Annual Symposium on Fi-equency Control, 1982 ProceedingsTN-2411. Review of the Dual Mixer Time Difference Technique .. 0••••• 0 • 0 0 • 0 •••••••••••• 0 ., TN-2410 •••••••• ,0 • 0 •••• 0 0 ••• 0 ••••• 0 ••••••••••••••••• 0 •••••••• 0 .,0 •••••••••••••••••• 0 0 ••••• 0 • 0 • 0 • 0 ••••••••• 0 ••••••••• 0 0 • 0 • 02. Extended Dual Mixer Time Difference Measurement Technique TN-2423. Hardware Implementation . TN-2424. Conclusions . TN-243OA Biases and Variances of Several FliT Spectral Estimators as a Function of Noise Type andNumber of SamplesF.L. Walls, DoB. Percival and W.R. Irelan43,.d Annual Symposium on Frequency Control, 1989 ProceedingsTN-248••••••• 0 0 0 •••••••••••• 0 •••• 0 ••••••••••••••• 0 ••• 0 •••• 0 .,,,I. Introduction .. 0 TN-248n. Spectrum Analyzer Basics .... 0 ••••• 0 •••••••••••••••••• 0 •••••••••••••••••• 0 TN-248III. Expected Value and Bias of Spectral Estimates .. 0 ••••••• 0 ••• 0 • 0 •••• 0 • 0 •••• 0 •••• TN-249IV. Variances of Spectral Estimates 0 ••••• 0 ••••••• 0 •••••• 0 0 •••••• 0 • 0 ••• 0 •• 0 • 0 0 •• 0 TN-251V. Conclusions 0 ••• 0 •• 0 ••••••• 0 •••••• 0 •• 0 • 0 •••• 0 ••••••••••••• TN-252v···
Page 1 and 2: Characterization ofClocks and Oscil
Page 3 and 4: PREFACEFor many years following its
Page 5: 0 • • • • • • • •
Page 9 and 10: TOPICAL INDEX TO ALL PAPERSThe foll
Page 11 and 12: of the wide range of measurement si
Page 13 and 14: The first of these (D.l) by Lesage
Page 15 and 16: Table 1. Guide to Selection of Meas
Page 17 and 18: 10- 1410- 15c-een10- 1610- 1710- 18
Page 19 and 20: Table 2. Ratio of mod a~('r) to a~(
Page 21 and 22: of the frequency measured in this m
Page 23 and 24: From: Proceedings of the 35th Annua
Page 25 and 26: where V0 ;: nomi na I peak vo Itage
Page 27 and 28: ports of the pair of double balance
Page 29 and 30: fluctuations prior to the bias box
Page 31 and 32: up an interesting hierarchy of kind
Page 33 and 34: is determi ned by the measurement s
Page 35 and 36: Since each average of the fractiona
Page 37 and 38: Thus. with 9~ probability the calcu
Page 39 and 40: in fact. Also for n=l the "experime
Page 41 and 42: 1n tenns of the typical performance
Page 43 and 44: and eq (1.1) we get2m>(t) = ~T(t) =
Page 45 and 46: varactor control in th@ reference o
Page 47: V nn5(45 Hz) = 100 nV por root hort
Page 50 and 51: We can use the convolution theorem
Page 52 and 53: though the concept of harmonics in
Page 54 and 55: and wz(t) is now the si!npled versi
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10.7 Time Domain-Frequency Domain T
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o/(t). In the table, the left colum
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Weean make the following general re
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-flO• r.1OSP1 t(f2-,~ 1Ci~-/'10 f
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frequency extent of the analysis ba
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28. P. Kartaschoff and J. Barnes, "
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_--_._~--~II..gIIIIII1.......oIIIII
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From: Precision FrequenC)' Control,
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12 FREQUENCY AND TIME MEASUREMENT 1
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12 FREQUENCY AND TIME MEASUREMENT19
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12 FREQUENCY AND TIME MEASUREMENT 2
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12 FREOU::NCY AND TIME MEASUREMENT2
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12 FREQUENCY AND TIME MEASUREMENTI~
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12 FREOUENCV AND TIME MEASUREMENT21
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228 SAMUEL R. STEIN9.3 GHzOSCILLATO
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230 SAMUEL R. STEINThe combination
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232 SAMUEl R STEINHowever, the spec
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400 CHAPTER BIBLIOGRAPHIESAllan. D.
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402 CHAPTER BIBLIOGRAPHIESBaugh. R.
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404 CHAPTER BIBLIOGRAPHIESConway. A
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406 CHAPTER BIBLIOGRAPHIESGardner.
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408 CHAPTER BIBLIOGRAPHIESJackisch.
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410 CHAPTER BIBLIOGRAPHIESlesage. P
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412 CHAPTER BIBLIOGRAPHIESPaul. F.
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414 CHAPTER BIBLIOGRAPHIESSorden. J
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416 CHAPTER BIBLIOGRAPHIESYoshimura
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648IEEE TRANSACTIONS ON ULTRASONICS
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650 IEEE TRANSACTIONS ON ULTRASONIC
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652 IEEE TRANSACTIONS ON ULTRASONIC
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IEEE TRANSACTIONS ON ULTRASONICS. F
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Powet spectral analysis of the outp
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major difficulty is designing a mix
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The phase noise in the source can c
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detail elsewhere [12]. The low pass
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NJ:",--0~.8~..(/)-110-1:20-130-140m
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is ~he preferred measure, since, un
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2. Copy.r,ion Beeween Frequency and
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All.n, D. Y., .nd D...s, H., Picose
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105Characterization of Frequency St
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B'R:sES et ai.: ClHR.,CTY.RIZHIO:-r
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e4.RNES et al.: CH."R.ACTERrZ.4.TIO
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MII.NES et al.. CHAIl.ACfERlZATlO:-
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:l frequcllcy ~eparatioll froll1 th
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MRNES et al.: CHARACTERIZATION OF F
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B\R~f:S eL al.: CIHRACTERIZ.,TIOI<
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8IR:-IES et al.: CH.'R.'CTER[Z.
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142 Rep. 580--2Reprinted, with perm
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i44 Rep. 580-2If the initial sampli
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146 Rep. 580-2The values of ha are
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148 Rep. SSO-2TABLE II - Translalio
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ISO Rep. 580-2, 738-2BIBLIOGRAPHYAL
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522 LESAGE AND AUDOIN01., 1971J:S,I
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524 LESAGE AND AUDOINKl- 1410- 11 \
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526LESAGE AND AUDOINQuartz ClJstalF
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528 LESAGE AND AUDOINMinrFrequent,r
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530 LESAGE AND AUOOINsuch as c:r;(T
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532 LESAGE AND AUDOINl.l-TEquations
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534 LESAGE AND AUDOINof measurement
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LESAGE AND AUDOIN2 - Vo )]53610- 1
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538 LESAGE AND AUWINstability measu
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Copyright Ie) 1984 Academic Press.
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7. PHASE NOISE AND AM NOISE MEASURE
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7. PHASE ~OISE AND AM NOISE MEASURE
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7. PHASE :'-iOrSE AND AM NOISE MEAS
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or, in rms radians,7. PHASE !'rOISE
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i. PHASE :-JOISE AND AM NOISE MEASU
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7. PHASE ~OISE AND AM NOISE MEASVRE
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7. PHASE NOISE AND AM :>lOISE MEASU
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_~ ~A _7. PHASE NOISE AND AM NOISE
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average frequency over the interval
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and frequency stability of precisio
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PHASE P~OT Clook No. ~- e I"d,....
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BL-\5ES .-\.\D \·A.Rl.-\.\CES OF S
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to a g
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while the Hanning ""!Odo"" yIelds1.
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Proc. 35th Ann. Freq. Control Sympo
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N-3n+lEj=1Mod Oy2 (t) =0 2(t) {.! +
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(a)1SIMULATED NOISE(b)1-10- 2- --10
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IEEE TRANSACTIONS ON INSTRUMENTATlO
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IEEE TRANSACTIONS ON INSTRUYlENTATI
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From: Proceedings of the 15th Annua
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where c = Dr/2. In regression analy
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'" Dr 22 = -7.507E-16 (about -6.5E-
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Coefficient of simple determination
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100%CUMULATIVE PERIODOGRAM ~50%(,
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100%CUMULATIVE PER I ODOGRAM50%U'10
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TABLE 6.STANDARD DEVIATIONSPROCEDUR
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APPENDIX AREGRESSION ANALYSIS(Equal
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andG == N (N - 1) (N - 2)Also, the
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APPENDIX BREGRESSIONS ON LINEAR AND
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REFERENCES1. D.W. Allan, "The Measu
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5.12 )( 10 - 7 SEC
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100%CUMULATIVE PERIODOGRAM -50%U'
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100%CUMULATIVE PERIODOGRAM50%(J'l..
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FREQUENCY DRIFT AND WHITESTANDARD D
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MR. McCASKILL:Well, let me go furth
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NIST Technical Note 1318, 1990.VARI
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By definition, white noise has a po
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where aZ(N,T,r) is the expected sam
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Some useful asymptotic forms of B 3
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Since the time-domain definition fo
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Stability Using Non-zero Dead-Time
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I!II.....I~I.....cIQ)IEQ) I~I~(J)
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-2,THE BIAS FUNCTION, 8 2 (r,p.)Fig
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AppendixWith reference to figure 1,
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8lIN,r,lll) for r = .011\1\ N= ~ 81
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BUN,r,IItJI for r =/tl\ !'I= 8 16 3
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81 (N,r,lIUl for r =ItJ \ IF 4 8 16
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__ ....... ~...........__ .........
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BllN,r,kl) for r = 1024It! \ N= 4 B
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B2(r,llU)It! \ r = .0001 .0003 .001
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B3( 2, P1,I", IIU) far r '" .01~\ ~
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83(2,I'f,r,~)for r '"""'III \ 2 4 B
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B312.I'I,r,llU) for r " 4I\J \ pt::
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B3(2,I'I,r,lIJ) Fer r ~ MI\J\ PI::
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B3(2,"',r,ail for r = 1024MIl \ I'l
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E. APPENDIX - Notes and ErrataThe n
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Influence of Pressure and Humidity
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22. page TN-160In eqs (101), (102),
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29. page TN-180If the ratio of T/ T
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NIST-114A(REV. 3-89)4. TITLE AND SU
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NIST Technical Note 1337: Characterization of Clocks and Oscillators

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