NIST Technical Note 1337: Characterization of Clocks and Oscillators

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CHAPTER 12 403Bologlu. A. (1980). A new method of measuring the frequency of microwave signals. usingmicroprocessors. Nachr. E/eklron. 34. 149-152. In German.Bologlu. A.. and Barber. V. A. (1978). Microprocessor-controlled harmonic heterodynemicrowave counter also measures amplitudes. Hew/ell-Packard J. 29. 2-4. 6-7. 9-12. 14-16.Bordt. A. (1973a). Universal digital counter for frequencies up to 12 MHz. I. Radio FernsehenE/eklron. 22. 365-368. In German.Bordt. A. (l973b). Universal digital counter for frequencies up to 12 MHz. II. Radio FernsehenE/eklron. 22. 402-406. In German.Borisochkin. V. V. (1972). Checking the frequency of highly stable generators. Meos. Tech. (Eng/.Trans/.) 15.460-463.Bosnjakovic. P. (1976). A new solution of the precision line frequency measurement. AUlOma/ika17. 194-196. In Serbo-Croatian.Bowman. 1. A. (1973). Short and long term stability measurements using automatic data recordingsystem. Proc. 27/h Annu. Freq. Control Symp.. pp. 440-445.Bowman. M. J .. and Whitehead. D. G. (1977). A picosecond timing system. IEEE Trans. Ins/rum.Meas. IM-26. 153-157.Brandenberger. H.. Hadom. F.. Halford. D .• and Shoaf, J. H. (1971). High quality quartz crystaloscillators: frequency domain and time domain stability. Proc. 25/h Annu. Freq. Con/rolSymp.. pp. 226-130.Brown. D. E. (1957). Frequency measurement of quartz crystal oscillators. Marconi Ins/rum. 11.12-15.Budreau. A. J.. Siobodnik. A. 1.. Jr.. and Carr. P. H. (1982). Fast frequency hopping achievedwith SAW synthesizers. Micro .....au J. 25. 71-73. 76-80.Burgoon. R.. and Fischer. M. C. (1978). Conversion between time and frequency domain ofintersection points of slopes of various noise processes. Proc. 32nd Annu. Freq. ControlSymp.. pp. 514-519.Buchuev. F. I.. and Ivakin. V. M. (1979). Electronic converter of the unit time dimension. .~{eas.Tech. (Eng/. Trans/.) 21. 788-789.Buxton. A. J. (1976), Digital frequency meter. Prac/. E/ecrron. 12.376-382.Buzek. 0 .. Cermak. J.. Smid. 1.. and Medellin. H. (1980a). A time base controlled by the OMA50 kHz transmitter. Sde/ovaci Tech. 28. 362-365. In Czech.Buzek. 0 .. Cermak. 1.. and Tolman. J. (I 980b). Accurate time and frequency. S/ahoproudy Ob=.41. 263-266. In Czech.Cantero. J. A.. Pollan. T.. and Barquillas. 1. (1978). Digital frequency meter uses variablemeasuring and automatic scale conversion. Mundo E/ecrron. 71. 34-35. In Spanish.CardwelL W. T.. Jr. (1978). Frequency counter in a probe. Radio E/ec1ron Eng. 49. 67. 72-73.100-10I. 103.Charriere. J.-J. (1977). A digital chronometer. I. Ret'. Poly/echo (6). 585. 587. In French.Chebotayev. V. P.. Goldort. V. G .. Klementyev. V. M.. Nikitin. M. V .• Timchenko. B.A.. andZakharyash. V. F. (1982). Development of an optical time scale. App/. Phys. B 29.63-65.Coates. P. B. (1968). Fast measurement of short time intervals. 1. Sci. [nsrrum. l. 1123-1127.Cochran. W. T .. Cooley. J. W.. Fallin. D. L.. Helms. H. D.. Kaenel. R. A .• Lang. W. W., Maling.G. c., Jr.. i\ielson, D. E., Rader. C. M.. and Welch. P. D. (1967). What is the fast Fouriertransform? I££E Trans. Audio E/ec/roacousr. .-\V-15. 45-55.Colburn, J.. and Owen. B. (1979).600 MHz portable frequency counter. Radio E/ecrron. Eng. 50.39-43.90.Cole. H. ;v!. (1975). Time domain measurements. E/ecrron. E/ecrro-Opric In! Counrermeas. l.38-42. 55.Con.... ay. A .. and L'rdaneta. N. (l978a). Considerations in selecting a frequency counter.CommumCQfions 15. 22-:3.TN-to?
404 CHAPTER BIBLIOGRAPHIESConway. A.. and Urdaneta. N. (1978b). Selecting a frequency counter. T"I"ph. Eng. Jlalltlg"m"nt82.77-78.Cordwell. C. R. (1968)... Frequency Measurements." Vacation school on electrical measurementpractice. Institution of Electrical Engineers. London. 13 pp.Cordwell. C. R. (1969). Frequency measurements. Electron. Radio Tech. 3. 95-103.Cosmelli. C. and Frasca. S. (1979). Fast new technique for measuring the resonance frequenciesof high Q systems. Ret·. Sci.lnstrum. SO. 1650-/651.Cutler, L. S.• and Searle. C. L. (1966). Some aspects of the theory and measurement of frequencyfluctuations in frequency standards. Proc. IEEE 54. 136-154.Czarnecki. A. (19801. Test set for the comparison of standard frequencies. type FZ-530. Pro Inst.Tele-Radiotech. (83). 27-32. In Polish.Danilevich. V. V.. Chernyavskii. A. F.. and Yakushev. A. K. (1977a). Seleclro-type time intervalanalyzer with a measurement range of 10- 10 to 10- 2 sec. Instrum. Exp. Tech. (Engl. Trans!.)20.326-327.Danilevich. V. V.. Kvachenok. V. G .. Priimak. M. A.. Chernyavskii. A. F.. and Yakushev. A. K.(1977b). Signal generator for adjusting and calibrating time measurement systems. Instrum.Exp. Tech. (Engl. Transl.) 20. 600.Danzeisen. K. (1977). Remote frequency measurement using VHF-UHF receivers. Funk-Tech.32.196-197. In German.Davis. D. D. (1975). Calibrating crystal oscillators with TV color-reference signals. Electronics48.107-112.De Costanzo. L. (1979). Radio receiver frequency counter clock. Electron. Ind. 5. 16-17.De Jong. G .. and Kaarls, R. (1980). An automated time-keeping system. IEEE Trans. Instrum.!tieas. Il\I·29. 230-233.Denbnovetskii, S. V.. and Kovtun. A. K. (1970). Time measurements. Digital time-intervalmeters. I:mer. Tekh. 10. 29-31. In Russian.Denbnovetskii. S. V.. and Shkuro. A. N. (1975). Principles of eliminating ambiguity in digitaltime·interval meters (review). Instrum. Exp. Tech. (Engl. Transl.) 18.1659-1670.De Prins. J. (1974). Timing systems. In .. ELF-VLF Radio Wave Propagation Spatind. Norway,"pp. 385-398. Reidel. Dordrecht. The Netherlands.De Prins. J. (1977). Aspects of time and frequency measurement. Ret·. HFIO. 123-134. In French.De Prins. 1.. and Cornelissen. G. (1974). Critique and discussion about frequency slabilitydefinitions with respect to various kinds of noises. CPEJf 74 Dig., pp. 54-56.Dietzel. R. (1975). Passive resonators with noise feeding in frequency-analogue measuringsystems. Jfess.. Steuern. Regeln 18. 389-393. In German.Dombrovskii. A. S.. Zaitsev. V. N .. and Pashev. G. P. (1974). Apparatus for time and frequencymeasurement. .\1eas. Tech. (Engl. Trans!.) 17.919-9:1.Domnin. Y. S.. Kosheljaevsky. N. B.. Tatarenkov. V. M .. and Shumjatsky. P. S. (1980a). Precisefrequency measurements in submillimeter and infrared region. IEEE Trans. Instrum. Meas.1:\-1-29.264-26'Damnin. Yu. S.. Kosheljaevsky. N. B.. Tatarenkov. V. M .. and Shumjatsky. P. S. (1980bl Precisefrequency measurements in submililmeter and infrared region [lasers]. CPE.H Dig .. p. 85.Doring. F. W. and Hollenberg. K. (1981). Eight.channel time measurement system with 2 nsresolution. J. Phys. E 14. 638-640.Doronina. O. M .. and Petukh, A. M (1980). Interpolation method of increasing measurementaccuracy for low frequencies. A.L"(ometriya IS). 89-9:. In RUSSIan.Drake. J. M.. and Rodriguez-Izquierdo. G. (1978). Analogue setup for fast-response frequencymeasurement. Electron. Eng. SO. 41. 43.Drake. 1. M .. ROdriguez-Izquierdo. G. (1980). Fast analogue measurement oflow frequencies.ReI'. Tdegr. Electron. 69. 1359-1360. In Spanish.TN-lOB
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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
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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 and 114: 400 CHAPTER BIBLIOGRAPHIESAllan. D.
Page 115: 402 CHAPTER BIBLIOGRAPHIESBaugh. R.
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
Page 165 and 166: 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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