NIST Technical Note 1337: Characterization of Clocks and Oscillators

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CHAPTER 17. 401Arnoldl. M. (1974). A frequency counter with time-multiple indication. L Funk· Tech. 20721-724. In German.Arnoldt, M, (1977), Frequency counter for ultra short wave radio receivers. Funk· Tech. 32,237-242, 244-245, In German,Arnoldt, M. (1979), A frequency counter for YHF receivers with frequency control loops.Fundschau 51,1371-1374, In German.Artyukh, Yu. N., Amit, M"A" Gotlib. G. Land Zagurskii, Y, Ya, (1978), Instrument formeasuring time intervals to an accuracy of 2 nsee, Instrum. Exp. Tech, (Engl. Transl,) 20,1039-1041.Ashley. 1. R.. Searles, C. B.. and Palka, F, M. (1968), The measurement of oscillator noise atmicrowave frequencies. IEEE Trans. Microv,are Theory Tech, MIT-16. 753-760.Auchterlonie. L J., and Bryant. D, L (1978), A direct method ofmeasuring small frequency shiftsusing two open resonators at millimetre wavelengths. Int, J, Electron. 45, 113-122.Ausejo, R. (1976), Frequency and time meters, Mundo Electron, 50, 59-66, In Spanish,Azoubib. L Granveaud, M., and Guinot. B. (1977), Estimation of the scale unit duration of timescales, Metrologia 13. 87-93,Raev, A. V"~ Rozkina, M, 5" and Torbenkov, G, R (1973), Capacitive method for measuringfrequency. Meas. Tech, (Engl, Transl,) 16. 1034-1036,Bahadur. H.. and Parshad. R. (1977), Measurement of time. J, Inst, Electron Telecommun, Eng.(;Vel>' Delhi) 17. 103-108,Baidakov, I. G .. Pushkin, S, B.• and Titov, Y, P. (1973), Securing unanimity oftime and frequencymeasurement in the USSR at the highest section of the reference system, ,'>leas, Tech, (Engl,Trans/,) 16. 60-63,Baird, K. M .. Hanes, G, R,. Evenson, K, M .. Jennings. D. A" and Petersen, F, R. (1979),Extension of absolute·frequency measurements to the visible: frequencies of ten hyperfinecomponents of iodine, Opt. Lerr, 4, 263-264,Balph. T (1976). A 200 MHz autoranging frequency counter. Electron, Equip, News, April. p. 17,Barber, R. E. (l9711. Short-term frequency stability of precision oscillators and frequencygenerators. Bell Syst, Tech, J, 50, 881-915.Barnaba, J. F. (1972). USAF time and frequency calibration program. Proc. 26th Annu, Freq.Control Symp.. pp. 260-263,Barnes. J, A. (1966), Atomic timekeeping and the statistics of precision signal generators, Proc,IEEE 54. 207-219,Barnes, J, A. (1969). Tables of bias functions B I and B 1 for variances based on finite samples ofprocesses with power law spectral densities. ,'IiBS Tech, Note (C.S.) 375.Barnes. J. A. (1972), Problems in the definition and measurement of frequency stability. Proc.26th Annu. Freq. Conrrol Symp .. p. 20.Barnes, J. A. 11976a). A simulation of the fluctuations of International Atomic Time. ,IiBS Tech.Sote ( l'.S,) 609, ::0 pp.Barnes, J. A. (1976b), Models for the interpretation of frequency stability measurements. NBSTech. ,Vote (L'S) 689,39 pp.Barnes. J. A., and Allan. D. W. (1966), A statistical model of flicker noise. Proc. IEEE 54,I ~6-178,Barnes, J. A.. and Winkler. G. M. R, 119~2). The standard of time and frequency in the IJSA,Prof. :!6th Annu. Freq. Control Symp .. pp 269-::78.Barnes, J A.. Chi, A, R .. Cutler. L S, Healey, D. 1. Leeson, D. B. McGunigal, T. E.. Mullen,J. A, Jr, Smith, W. L.. Sydnor. R. L.. Vessot. R. C F.. and Winkler, G, M. R. (\9711.Characterization of frequency stability. IEEE Trans. Instrum, J/eus. D·I·20. 105-120.B:lrrier. B.. and Humbert. J .-P, (197 3). ~umericaI frequency meters from A to Z, Int. Elecrron. 28.33-39. In French,Bastelberger. J. 11%8). Normal frequencies, their investigation and measurement. Fernme/de·1",
402 CHAPTER BIBLIOGRAPHIESBaugh. R. A. (1971). Frequency modulation analysis with the Hadamard variance. Proc. 25/hAnnu. Freq. Control Symp.. pp. 222-225.Baugh. R. A. (1972). Low noise frequency multiplication. Proc. 26/h Annu. Freq. Control Symp..pp.50-54.Bava. E.. De Marchi. A.. and Godone. A. (1977). A narrow outputlinewidth multiplier chain forprecision frequency measurements in the I THz region. Proc. 3!s/ Annu. Freq. ControlS.I'mp.. pp. 578-582.Bay. Z.. and Luther. G. G. (1968). Locking a laser frequency to the time standard. App!. Phys.Lett. 13. 303-304.Becker. G. (1976). The second as standard unit of time. L'msch. Wiss. Tech. 76. 706-707. InGerman.Becker. G .. and Hubner. C. (1978). The generation of time scales. Radio Sci. 14.593-603.Beckman. D. (1974). How accurate is your timer-counter? E1ec/ron. Equip. News IS. 32-33.Begley. W. W.. and Shapiro. A. H. (1970). Precision timing systems. I. Standard scales. Ins/rum.Control Sys/. 43. 87-89.Behnke. H. (1973). Standard frequency comparison by error multiplication. Radio FernsehenElektron. 22. 642-643. In Gennan.Beisner. H. M. (19S0). Clock error With a Wiener predictor and by numerical calculation. IEEETrans. Ins/rum. !>leas. IM-29. 105-113.Belenov. E. M .. and Uskov. A. V. (1979). Measurement oflaser frequencies using superconductingpoint contacts. SOL'. J. Quantum Electron. (Engl. Transl.) 9. 1519-1522.Belham. N. D. N. (1980). How accurate is a digital frequency meter? Radio Commun. 56. 368-371.Belomestnov. G. L. Dmitrienko. A. D .• Emakov. A. S.• and Korzh. V. F. (1976). Automaticsystem fvr acquiring. recording. and processing information by computer for secondarytime-and-frequency standards. !>feas. Tech. (Engl. Transl.) 19. 1572-1574.Belotserkovskii. D. Yu.. lI·in. V. G .. and Stepanova.l. V. r1976). International cooperation in thefield ofe.~act time and frequency measurements. Meas. Tech. (Engl. Transl.) 18. 517-519.Berger. F. (1975). Time metrology and quartz application.!. Time metrvlogy. Rer. Gen. Eleetr.8-1.907-918. In French.Bezdrukov. S. M.. and Preobrazhenskii. N. I. (1979). Increased accuracy in audio-frequencymeasurements with the 54- I 2 and S4-53 spectrum analyzers. Ins/rum. Exp. Tech. (Engl.Transl.) 21. 714~716.Bichler. H.. and Fenk. J. (1981 a). Simple universal 0 to 30 M Hz frequency counter with SDA5680A. Siemens Components (Engl. Transl.) 16. 21-24.Bichler. H.. and Fenk. J. (1981 b). The IC unit. SDA 5680A. universal frequency counter covering100 kHz to 30 MHz. E1ektron Int. 3--4. 89-92. In Gennan.Blachman. I\. M. (1976). The elfect of noise upon polar-display instantaneous frequencymeasuremenl.lEEE Trans. Instrum. .Heas.I"I-25. 214-21.Blair. B. E. (1974). Time and frequency: theory and fundamentals. .vBS .Honogr. ([:.S.) 1-10.460 pp.Blaney. T. G. Cross. N. R.. Knight. D. J. E.. Edwards. G. 1.. and Pearce. P R (1980). Frequencymeasurement at 4.25 THz (70.5 Ilm) using Josephson harmonic mi.'er and phase-locktechniques. J. Phys. D 13. 1365-1370.Bodea. M.. and Danila. T. (19'79). Autoranging. digital time-interval meter. Bull. Inst. Politelt.Gheorghe Gheorglriu-Dej Bucuresti Ser. E1ec/roteh. -10. 57-63. In Rumanian.Body. l.. and Szemok. L (1974). General problems of frequency measurement .\feres AUlOm. 22.422-428. In Hungarian.Bologlu..-\. ( 1975). Automatic 4.5-G Hzcounter provides I-Hz resolution. He\\'lett-PackllrJ1. 27.14-18.TN-106
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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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0 •• 0 •• 0 •• 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
Page 64 and 65: frequency extent of the analysis ba
Page 66 and 67: 28. P. Kartaschoff and J. Barnes, "
Page 68 and 69: _--_._~--~II..gIIIIII1.......oIIIII
Page 70 and 71: From: Precision FrequenC)' Control,
Page 72 and 73: 12 FREQUENCY AND TIME MEASUREMENT 1
Page 74 and 75: 12 FREQUENCY AND TIME MEASUREMENT19
Page 80 and 81: 12 FREQUENCY AND TIME MEASUREMENT 2
Page 82 and 83: 12 FREOU::NCY AND TIME MEASUREMENT2
Page 90 and 91: 12 FREQUENCY AND TIME MEASUREMENTI~
Page 94 and 95: 12 FREOUENCV AND TIME MEASUREMENT21
Page 96: 12 FREQUENCY AND TIME MEASUREMENT21
Page 107 and 108: 228 SAMUEL R. STEIN9.3 GHzOSCILLATO
Page 109 and 110: 230 SAMUEL R. STEINThe combination
Page 111 and 112: 232 SAMUEl R STEINHowever, the spec
Page 113: 400 CHAPTER BIBLIOGRAPHIESAllan. D.
Page 117 and 118: 404 CHAPTER BIBLIOGRAPHIESConway. A
Page 119 and 120: 406 CHAPTER BIBLIOGRAPHIESGardner.
Page 121 and 122: 408 CHAPTER BIBLIOGRAPHIESJackisch.
Page 123 and 124: 410 CHAPTER BIBLIOGRAPHIESlesage. P
Page 125 and 126: 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
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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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