NIST Technical Note 1337: Characterization of Clocks and Oscillators

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Rep. 580-2 149BLAIR, B. E. (Ed.) [May, 1974) Time and frequency: theory and fundamentals. NBS Monograph No. 140. (US GovernmentPrinting Office, Washington, D.C. 20402).BOILEAU, E. and PICINBONO, B. [March, 1976) Statistical study of phase nuctuations and oscillator stability. IEEE Trans.Insrr. Meas., Vol. 25, I, 66-75.BRANDENBERGER, H., HADORN, F., HALFORD, D. and SHOAF, J. H. (1971) High quality quartz crystal oscillators:frequency-domain and time-domain stability. Proc. 25th Annual Symposium on Frequency Control, 226-230.CHI, A. R. [December, 1977) The mechanics of translation of frequency stability measures between frequency and time-domainmeasurements. Proc. 9th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, Greenbelt,MD, USA.CUTLER, L. S. and SEARLE, C. L. [February, 1966] Some aspects of the theory and measurement of frequency Ouctuations infrequency standards. Proc. IEEE, Vol. 54, 136-154.DE PRINS, J. and CORNELISSEN, G. [October, 1971] Analyse spectrale discrete. Eurocon (Lausanne, Switzerland).DE PRINS, J., DESCORNET, G., GORSKI, M. and TAMINE, J. [December, 1969] Frequency-domain interpretation ofoscillator phase stability. IEEE Trans. Ins/r. and Meas., Vol. IM-18, 251-261.GROSLAMBERT, J., OLIVIER, M. and UEBERSFELD, J. [December, 1974] Spectral and short-term stability measurements.IEEE Trans. Ins/r. Meas., Vol. IM-23 4, 518-521.HOWE, D. A., ALLAN, D. W. and BARNES. J. A. [May, 1981] Properties of signal sources and measurement. Proc.35th Annual Symposium on Frequen,y Control, Philadelphia, PA, USA (US Army Electronics Command,Ft. Monmouth, NJ 07703), 669-717 (Electronics Industries Association, Washington, DC 20006, USA).IEEE [May, 1972J Special issue on time and frequency. Proc. IEEE, Vol. 60, 5.IEEE [1983J Frequency S/abili/y: Fundamen/als and Measurement, 77-80. Ed. V. F. Kroupa. IEEE Press Books.IEEE-NASA [1964] Proceedings of Symposium on short-term frequency stability. NASA Publication SP 80.JONES, R. H. and TRYON, P. V. [January-February, 1983] Estimating time from atomic clocks. NBS Res., Vol. 88, I, 17-24.LESAGE, P. [1983J Characterization of frequency stability: Bias due to the juxtaposition of time interval measurements. IEEETrans. Ins/r. Meas., Vol. IM-32, I, 204-207.LESAGE, P. and AUDOIN, F. [June, 1973J Characterization of frequency stability: uncertainty due to the finite number ofmeasurements. IEEE Trans. Insrr. Meas., Vol. IM-22, I, 103.LESAGE, P. and AIJDOIN, C. [March, 1974J Correction to: Characterization of frequency stability: uncertainty due to finitenumber of measurements. IEEE Trans. Ins/r. Meas., Vol. IM-23, I, 103.LESAGE, P. and AUDOIN, F. [May, 1975J A time domain method for measurement of the spectral density of frequencyOuctuations at low Fourier frequencies. Proc. of the 29th Annual Symposium on Frequency Control, 394-403.LESAGE, P. and AUDOIN, C. [September, 1976J Correction to: Characterization of frequency stability: uncertainty due to thefinite number of measurements. IEEE Trans. Instr. Meas., Vol. IM-25, 3.LESAGE, P. and AYI, T. [December, 1984J Characterization of frequency stability: analysis of modified Allan variance andproperties of its estimate. IEEE Trans. Insrr. Meas., Vol. IM-33, 4,332-336.LINDSEY, W. C. and CHIE, C. M. [De~mber,Proc. IEEE, Vol. 64, 1662-1666. 1976J Theory of oscillator instability based upon structure functions.MEYER, D.G. [November, 1970J A test set for the accurate measurements of phase noise on high-quality signal sources. IEEETrans. Ins". Meas., Vol. (M-19, 215-227.PERCIVAL, D. B. [June, 1976J A heuristic model of long-term atomic clock behavior. Proc. of the 30th Annual Symposium onFrequency Control.RICCI, D. W. and PEREGRINO, L. [June, 1976J Phase noise measurement using a high resolution counter with on-line dataprocessing. Proc. of the 30th Annual Symposium on Frequency Control.RUTMAN, J. [February, 1972J Comment on characterization of frequency stability. IEEE Trans. Ins". Meas., Vol. IM-21, 2, 85.RUTMAN, J. [March, 1974J Characterization of frequency stability: a transfer function approach and its application tomeasurements via filtering of phase noise. IEEE Trans. Insrr. Meas., Vol. (M-23, I, 40-48.RUTMAN, J. [September, 1978J Characterization of phase and frequency instabilities in precision frequency sources: fifteenyears of progress. Proc. IEEE, Vol. 66, 9, 1048-1075.RUTMAN, J. and SAUVAGE, G. [December, 1974J Measurement of frequency stability in the time and frequency domains viafiltering of phase noise. IEEE Trans. Ins/r. Meas., VoL (M-23, 4, 515, 518.SAUVAGE, G. and RUTMAN, J. [July· August, 1973] Analyse spectrale du bruit de frequence des oscillateurs par la variance deHadamard. Ann. des Telecom., Vol. 28, 7-8, 304-314.VON NEUMANN, J., KENT, R. H., BELLINSON, H. R. and HART, B. L [1941] The mean square successive difference. Ann.Math. S/ar., U, 153-162.WALLS, F. L., STEIN, S. R., GRAY, J. E. and GLAZE, D. J. [June, 1976] Design considerations in state-of-the·art signalprocessing and phase noise measurement systems. Proc. of the 30th Annual Symposium on Frequency Control.WINKLER, G. M. R. [December, 1976) A brief review of frequency stability measures. Proc. 8th Annual Precise Time and TimeInterval (PTTI) Applications and Planning Meeting (US Naval Research Laboratory, Washington, DC), 489-528.YOSHIMURA, K. [March, 1978] Characterization of frequency stability: Uncertainty due to the autocorrelation of the frequencyfluctuations. IEEE Trans. Ins/r. Meas., IM-27 I, 1-7.TN-169
ISO Rep. 580-2, 738-2BIBLIOGRAPHYALLAN, D. W., ~t at. (1913) Performance, modelling, and simulation of some caesium beam clocks. Proc. 21th AnnualSymposium on Frequency Control, 334-346.FISCHER, M. C. (December, 1916] Frequency stability measurement procedures. "Proc. 8th Annual Precise Time and TimeInterval (PTTI) Applications and Planning Meeting (US Naval Research Laboratory, Washington, DC), 515~18.HALFORD, D. (March, 1968J A general mechanical model for 1/1« spectral density noise with special reference to flicker noise1/1/1. hoc. IEEE (Corres.), Vol. 56,3, 2SI·2S8.MANDELBROT, B. [April, 1961] Some noises with II/spectrum, a bridge between direct current and white noise. IEEE TrailS.In! 17I~ory, Vol. IT·l3, 2, 289·298.RUTMAN, J. and UEBERSFELD, J. [February, 1972] A model for flicker frequency noise of oscillators. hoc. IEEE, Vol. 60, 1,233-235.VANIER, J. and TETU, M. (1918] Time domain measurement of frequency stability: a tutorial approach. Proc. 10th AnnualPrecise Time and Time Interval (PTTI) Applications and Planning Meeting, Washington, DC, USA, 247·291.VESSOT, R. (1916] Frequency and Time Standards. Chap. 5.4 Methods of Experimental Physics, Academic Press, 198·221.VESSOT, R., MUELLER, L. and VANIER, J. (February, 1966] The specification of oscillator characteristics from measurementsmade in the frequency domain. hoc. IEEE, Vol. 54, 2, 199-201.WINKLER, G. M. R., HALL. R. G. and PERCIVAL, D. B. (October, 1970] The US Naval Observatory clock time reference andthe performance of a sample of atomic clocks. Ml'lrotogia, Vol. 6, .., 126-134.TN-170
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Characterization ofClocks and Oscil
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PREFACEFor many years following its
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0 • • • • • • • •
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TOPICAL INDEX TO ALL PAPERSThe foll
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of the wide range of measurement si
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The first of these (D.l) by Lesage
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Table 1. Guide to Selection of Meas
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10- 1410- 15c-een10- 1610- 1710- 18
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Table 2. Ratio of mod a~('r) to a~(
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of the frequency measured in this m
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From: Proceedings of the 35th Annua
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where V0 ;: nomi na I peak vo Itage
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ports of the pair of double balance
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fluctuations prior to the bias box
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up an interesting hierarchy of kind
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is determi ned by the measurement s
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Since each average of the fractiona
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Thus. with 9~ probability the calcu
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in fact. Also for n=l the "experime
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1n tenns of the typical performance
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and eq (1.1) we get2m>(t) = ~T(t) =
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varactor control in th@ reference o
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V nn5(45 Hz) = 100 nV por root hort
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We can use the convolution theorem
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though the concept of harmonics in
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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.
Page 127 and 128: 414 CHAPTER BIBLIOGRAPHIESSorden. J
Page 129 and 130: 416 CHAPTER BIBLIOGRAPHIESYoshimura
Page 131 and 132: 648IEEE TRANSACTIONS ON ULTRASONICS
Page 133 and 134: 650 IEEE TRANSACTIONS ON ULTRASONIC
Page 135 and 136: 652 IEEE TRANSACTIONS ON ULTRASONIC
Page 137 and 138: IEEE TRANSACTIONS ON ULTRASONICS. F
Page 139 and 140: Powet spectral analysis of the outp
Page 141 and 142: major difficulty is designing a mix
Page 143 and 144: The phase noise in the source can c
Page 145 and 146: detail elsewhere [12]. The low pass
Page 147 and 148: NJ:",--0~.8~..(/)-110-1:20-130-140m
Page 149 and 150: is ~he preferred measure, since, un
Page 151 and 152: 2. Copy.r,ion Beeween Frequency and
Page 153 and 154: All.n, D. Y., .nd D...s, H., Picose
Page 155 and 156: 105Characterization of Frequency St
Page 157 and 158: B'R:sES et ai.: ClHR.,CTY.RIZHIO:-r
Page 159 and 160: e4.RNES et al.: CH."R.ACTERrZ.4.TIO
Page 161 and 162: MII.NES et al.. CHAIl.ACfERlZATlO:-
Page 163 and 164: :l frequcllcy ~eparatioll froll1 th
Page 165 and 166: MRNES et al.: CHARACTERIZATION OF F
Page 167 and 168: B\R~f:S eL al.: CIHRACTERIZ.,TIOI<
Page 169 and 170: 8IR:-IES et al.: CH.'R.'CTER[Z.
Page 171 and 172: 142 Rep. 580--2Reprinted, with perm
Page 173 and 174: i44 Rep. 580-2If the initial sampli
Page 175 and 176: 146 Rep. 580-2The values of ha are
Page 177: 148 Rep. SSO-2TABLE II - Translalio
Page 181 and 182: 522 LESAGE AND AUDOIN01., 1971J:S,I
Page 183 and 184: 524 LESAGE AND AUDOINKl- 1410- 11 \
Page 185 and 186: 526LESAGE AND AUDOINQuartz ClJstalF
Page 187 and 188: 528 LESAGE AND AUDOINMinrFrequent,r
Page 189 and 190: 530 LESAGE AND AUOOINsuch as c:r;(T
Page 191 and 192: 532 LESAGE AND AUDOINl.l-TEquations
Page 193 and 194: 534 LESAGE AND AUDOINof measurement
Page 195 and 196: LESAGE AND AUDOIN2 - Vo )]53610- 1
Page 197 and 198: 538 LESAGE AND AUWINstability measu
Page 199 and 200: Copyright Ie) 1984 Academic Press.
Page 201 and 202: 7. PHASE NOISE AND AM NOISE MEASURE
Page 207 and 208: 7. PHASE ~OISE AND AM NOISE MEASURE
Page 211 and 212: 7. PHASE :'-iOrSE AND AM NOISE MEAS
Page 213 and 214: or, in rms radians,7. PHASE !'rOISE
Page 215 and 216: i. PHASE :-JOISE AND AM NOISE MEASU
Page 221 and 222: 7. PHASE ~OISE AND AM NOISE MEASVRE
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7. PHASE NOISE AND AM NOISE MEASURE
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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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