NIST Technical Note 1337: Characterization of Clocks and Oscillators

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CHAPTER 12 409Kobayashi. M.. Osawa. H.. Morinaga. N.. and Namekawa. T. (1976). Mean frequency and meanpower measurement using correlation detection. Trans. Soc. Instrum. Control Eng. 12.613-618. In Japanese.Kocaurek. R. (1968). Frequency comparison receiver EF 151 k. Ne"..s Rohde and Sch •.-ar: 8.23-24.Koch. E. (1979). An all-waveband receiver with a digital frequency display and a quartz clock.Funkschau 51.236-239. In German.Koga. I. (1970). Precision measurement of crystal Frequency by means of" center line method."Proc. 24th Annu. Freq. Control Symp.. pp. 168-171.Kogan. L. R. (1970). Oscillator stability requirements in radio interFerometers. Radiotekh.Eleklron. 15. 1292-1294. In Russian.Kolbasin. A. I.. and Pavlenko. Yu. F. (1978). TransFer of the dimension of a unit deviation ofFrequency from the special state standard to prototype means of measurement. Meas. Tech.(Engl. Trans'.) 21. 806-809.Koppe. H. (1979). Frequency measurement using a microcomputer-a program and aninstruction program. Elekrron. Prax. 14. 30. 35-36. 39. In German.Kotel'nikov. A. V.• Rubailo. G. T.. and Uvarov. N. E. (1975). An instrument For measuring theratio of time intervals. Te!ecommun. Radio Eng. (Engl. Transl.), ParI 129.60-61.Kourigin. E. I.. Chemyshev. V. S.. and Shumkin. Yu. V. (1979). High-speed device for timeinterval measurement. Inslrum. Exp. Tech. (Engl. Transl.) 22. 484-486.Kramer. G. (1970). An electronic time intervalometer with high resolution. Nachrichlentech. Z.23.433-436. In German.Krause. W. H. U. (1968). Accurate time and frequency measurement. Frequen: 22. 178-182. InGerman.Kuchynka. K.. and Preuss. A. (1981). Electronic counters facilitate time measurement. SiemensPower Eng. 3.179-182.Kul'gavchuk. V. M. (1975). Frequency meters using devices with S-shaped volt-amperecharacteristics. Inslrum. Exp. Tech. (Engl. Transl.) 18. 514-516.Kuznetsov. V. P.. and Reznikov. A. L (1974). Adjacent time intervals measured by two Frequencymeters. Meas. Tech. (Engl. Transl.J 17.474-475.Laker. K. R.• and Slobodnik. A. 1.. Jr. (1975). "Impact of SAW Filters on RF. Pulse FrequencyMeasurement by Double Detection." Report AFCRL-PSRP-621. Air Force CambridgeResearch Laboratories. Hanscom Air Force Base. Massachusetts. 194pp. Available fromthe National Technical InFormation Service. Springfield. Virginia.Lance. A. L.. Seal. W. D .. Mendoza. F. G .. and Hudson. N. H. (1977). Automating phase noisemeasurements in the frequency domain. Proc. 31s1 Annu. Freq. Control Symp.. pp. 347-358.Leah. P. (1977). Frequency counter timer. Pracl. Elalron. 14.22-28.Leikin. A. Ya.. and Orlov. E. Z. (1973). Equipment for comparing frequencies of highly-stablegenerators. JIeas. Tech. (Engl. Transl.) 16. 1469-1470.Leikin. A. Ya .. Tomashenko. I. V.. and Fertik. N. S. (\974). Application of a rubidiumdiscriminator for the measurement of frequency flucluations. 1:1'. Vl·ssh. Cchehn. ZaredRadlO(i:. 17.851-854. In Russian.Lemesev. S. G.. Rachev. B. T .. Strugach. V. G .. and Shub. S. M. (1975). Statistical method formeasuring a recurrent time interval using a random pulse signal. 1:1'. Vyssh. Uchebn. Zared.Priboroslr. 18. 16-21. In Russian.Lesage. P. (1982). Characterization oFfrequency stability: bias due to the addition of time intervalmeasureme:nts. CPEJf Dig.. pp. M.8-9.Lesage. P. (1983). Characterization of frequency stability: bias due to the: juxtaposition of tlmeintervalmeasurements. IEEE Trans. Inslrum. l.leas. 1:\-1-32. 204-207.TN-113
410 CHAPTER BIBLIOGRAPHIESlesage. P.. and Audoin. C. (1973). Characterization of frequency stability: uncertainty due to thefinite number of measurements. IEEE Trans. Instrum. Meas. IM-22. 157-161. withcorrections from IEEE Trans. Instrum. Ideas. IM-25. 270.lesage. P.. and Audoin. C. (1975a). A time domain method for measurement of the spectraldensity of frequency fluctuations at low Fourier frequencies. Proc. 29th Annu. Freq. ControlSymp.. pp. 394-403.Lesage. P.. and Audoin. C. (1975b). Comments on "Characterization of frequency stability:uncertainty due to the finite number of measurements," IEEE Trans. Instrum. Meas. 1:\1-24.86.lesage. P.. and Audoin. C. (1977). Estimation of the two-sample variance with a limited numberof data [signal generator frequency stability]. Proc. 31st Annu. Freq. Control Symp.. pp.311-318.Lesage. P., and Audoin. C. (1979a). Characterization and measurement of time and frequencystability. Radio Sci. 14, 521-539.lesage. P.• and Audoin C. (1979b). Effect of dead time on the estimation of the two-samplevanance. IEEE Trans. Instrum. Meas. 1:\1·28.6-10.Lo Faso, G. (1968a). Digital frequency meter and chronometer in RTL micrologic. Int. £lekrron.Rundsch. 22. 63-66. In German.Lo Faso. G. (l968b). RTL Micrologic in a digital frequency and time counter. Int. Elektron.Rundsch. 22.47-50. In German.Lomas, G. (1974). Signal-frequency meter. Wireless World 80, 429-434.Loose. P. (1979). Modern electronic-based timing systems. Electron. Eng. 51. 81. 83-84.Lubentsov. V. F. (1973). The errors of the absolute method for measuring difference-signalfrequency. TeIecommun. Radio Eng. (Eng/. Transl.), Part 2 28. 96-99.Lubentsov. V. F., and Ashitkov. I. N. (1968). Device for measuring the frequencies and errors ofcrystal oscillators. Meas. Tech. (Engl. Transl.) (7), 906-911.Lukas. M. (1968). An intermediate frequency measuring equipment with an unusual frequencyindication. Siaboproudy Ob;. 29.323-326. In Czech.MacLeod. K. J. (1973). A portable high-resolution counter for low-frequency measurements.Hewlell-Packard J. 25. 10-15.Malell. W. (1974).100 MHz universal counter FET 100. News Rohde & Schwar; 14. 5-7.Markowitz. W. (1968). Time and frequency measurement. atomic and astronomical. Proc. 5thAnnu.ISA Test Meas. Symp.. lnstrument Society ofAmerica. Pittsburgh. Pennsylvania. p. 6.~larlin. D. (1971). Frequency stability measurements by computing counter system. He ....lellPackard 1. 23. 9-14.Martin. D. (1974). Measure time interval precisely. Electron. Des. 22. 162-167.Martin. J. D. (1972). Digital methods of frequency measurements: a comparison. Radio Electron.Eng. 42. 285-294.Maton. G. W. (1978). Thoughts on frequency meters and counter-timers. Electron (134),24,27.Maxwell. B. J. (1980). Perception of errors in instruments and applications. L Time, our mostaccurate measurement. Autom. Control (Ne... Zealand) 10, 27-29.McCarthy, E. P. (1979). A digital instantaneous frequency meter. IEEE Trans. Instrum. ;\feas.1\-1-28.224-226.McCaskill. T. B.. and Buisson. J. A. (1975). NTS,/ (TIMATION IIIl [satellite] quartz andrubidium oscillator frequency stability results. Prot'. 29th Annu. Freq. Controi Symp., pp.425-428.McCaskill. T.. White. 1.. Stebbins. S. and Buisson, J. (1978). NTS-2 cesium frequency stabilityresults. Proc. 32nd Annu. Freq. Control Symp.. pp. 560-566.',;fcCellan, G. (1978\. Prescaler and LSI chip form 135-MHz counter. Electronics SI. 97. 99.~leer. P. (1977). Four fune'tlon calculator can measure time. Electron. Eng. 49. 35.TN-114
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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
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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,
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 and 116: 402 CHAPTER BIBLIOGRAPHIESBaugh. R.
Page 117 and 118: 404 CHAPTER BIBLIOGRAPHIESConway. A
Page 119 and 120: 406 CHAPTER BIBLIOGRAPHIESGardner.
Page 121: 408 CHAPTER BIBLIOGRAPHIESJackisch.
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
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
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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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