NIST Technical Note 1337: Characterization of Clocks and Oscillators

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288 A. L. LANCE, W. D. SEAL, AND F. LABAARAshley. J. R.. Barley, T. A., and Rast, G. J. (1977). IEEE Trans. Microwat,e Theory Tech.MTI·25(4),294-318.Baghdady, E. 1.. Lincoln, R. N., and Nelin. B. D. (1965). Proc. IEEE 53,704-722.Barnes. J. A. (1969). "Tables of Bias Functions, B, and B" for Variances Based on FiniteSamples of Processes with Power Law Spectral Densities," National Bureau of StandardsTechnical Note 375.Barnes, J. A., Chie, A. R., and Cutler, L. S. (1970). "Characterization of Frequency Stability,"National Bureau of Standards Technical Note 394; also published in IEEE Trans. Instrum.Meas.IM-20(2). 105-120 (1971).Brandenberger, H., Hadorn, F., Halford, D., and Shoaf, J. H. (1971). Proc. 25th Ann. Symp.Freq. Control, Fort Monmouth, New Jersey, pp. 226-230.Culter. L. S., and Searle, C. L. (/966). Proc.IEEE54, 136-154.Fisher. M. C. (1978). "Frequency Domain Measurement Systems," Paper presented at the10th Annual Precise Time and Time Interval Applications and Planning Meeting, GoddardSpace Flight Center, Greenbelt, Maryland. *Halford. D. (1968). Proc. IEEE 5&)),251-258.Halford, D. (1975). "The Delay Line Discriminator." National Bureau of Standards TechnicalNote 10, pp. 19-38.Halford. D., Wainwright, A. E.. and Barnes, J. A. (\968). Proc. 22nd Ann. Symp. Freq. Control.Fort Monmouth. New Jersey, 340-341.Halford. D., Shoaf, J. H., and Risley. A. S. (1973). Proc. 27th Ann. Symp. Freq. Control, CherryHill. New Jersey, pp. 421-430.Hook. W. R. (1973). "Phase Noise Measurement Techniques for Sources Having ExtremelyLow Phase Noise." TRW Defense and Space Systems Group Internal Document, RedondoBeach, California.Hewlett·Packard Company (1965).., Frequency and Time Standards." Application Note 52.Hewlett·Packard Co.. Palo Alto, California.Hewlett-Packard Company (1970). "Computing Counter Applications Library," ApplicationNOles 7, 22. 27, and 29. Hewlett·Packard Co.. Palo Alto, California.Hewlett·Packard Company (1976). "Understanding and Measuring Phase Noise in the Frequency Domain." Application Note 207. Hewlett·Packard Co., Loveland, Colorado.Labaar. F. (1982)... New Discrimi nator Boosts Phase Noise Testing." Microwat'es 21(3), 65-69.Lance, A. L. (1964). "Introduction to Microwave Theory and Measurements." McGraw·Hill,New York.Lance. A. L.. Seal, W. D., Mendoza, F. G .. and Hudson, N. W. (\977a). Microwat'e.l. 20(6).87-lOlLance, A. L.. Seal. W. D., Mendoza, F. G.. and Hudson. N. W. (I 977b). Proc. 31st Annu. S.vmp.Freq. Control. Atlantic City. New Jersey, pp. 463-48lLance, A. L.. Seal. W. D., Halford, D.. Hudson, N.. and Mendoza. F. (1978). "Phase NoiseMeasurements UsingCross·Spectrum Analysis." Paper presented at the IEEE Conference onElectromagnetic Measurements. Ottawa, Canada.Lance. A. L.. Seal. W. D., and Labaar, F. (l982).ISA Trans. 21(4), 37-44.Meyer. D. G. (1970). IEEE Trans. IM-19(4), 215-227.Ondria. J (1968). IEEE Trans. Microwave Theory Tech. MTI-I6(9), 767-781.Ondria. J. G. (\980). IEEE·MTT·S Int. Microwat'e Symp. Dig .. pp. 24-25.Payne, J. B., III (1976). Microwat'e System News 6(2),118-128.Scherer, D. (1979)... Design PrinCIples and Measurement Low Phase Noise RF and MicrowaveSources." Hewlett·Packard Co.. Palo Alto. California.Seal. W. D.. and Lance. A. L. (1981) MicrOlI'Gt'e Sysrem News 11(7). 54-61.Shoaf. J H.. Halford, D.. and Risley. A. S (1973)... Frequency Stability Specifications andMeasurement." National Bureau of Standards Technical Note 632.• See Appendix Note # 33TN-239
7. PHASE NOISE AND AM NOISE MEASUREMENTS289Tykulsky, A. (1966). Proc. IEEE 54(2), 306.Van Duzer, V. (1965). Proc. IEEE-NASA Symp. Definition Meas. Short-Term Freq. Stability.NASA SP·80. 269-272.Walls. F. L., and Stein, S. R. (1977). Proc. 31st Ann. S.vmp. Freq. Control, Atlantic City, NewJersey, pp. 335-343.Walls. F. L., Stein. S. R., Gray, J. E.. Glaze. D. J.• and Allen. D. W. (1976). Proc. 30th Ann.Symp. Freq. Co.ntrol, Atlantic City. New Jersey, p. 269.TN-240
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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,
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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
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
Page 243 and 244: 7. PHASE NOISE AND AM :>lOISE MEASU
Page 245 and 246: _~ ~A _7. PHASE NOISE AND AM NOISE
Page 247: 7. PHASE NOISE AND AM NOISE MEASURE
Page 251 and 252: average frequency over the interval
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Page 255 and 256: PHASE P~OT Clook No. ~- e I"d,....
Page 257 and 258: BL-\5ES .-\.\D \·A.Rl.-\.\CES OF S
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Page 261 and 262: while the Hanning ""!Odo"" yIelds1.
Page 263 and 264: Proc. 35th Ann. Freq. Control Sympo
Page 265 and 266: N-3n+lEj=1Mod Oy2 (t) =0 2(t) {.! +
Page 267 and 268: (a)1SIMULATED NOISE(b)1-10- 2- --10
Page 269 and 270: IEEE TRANSACTIONS ON INSTRUMENTATlO
Page 271 and 272: IEEE TRANSACTIONS ON INSTRUYlENTATI
Page 273 and 274: From: Proceedings of the 15th Annua
Page 275 and 276: where c = Dr/2. In regression analy
Page 277 and 278: '" Dr 22 = -7.507E-16 (about -6.5E-
Page 279 and 280: Coefficient of simple determination
Page 281 and 282: 100%CUMULATIVE PERIODOGRAM ~50%(,
Page 283 and 284: 100%CUMULATIVE PER I ODOGRAM50%U'10
Page 285 and 286: TABLE 6.STANDARD DEVIATIONSPROCEDUR
Page 287 and 288: APPENDIX AREGRESSION ANALYSIS(Equal
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Page 291 and 292: APPENDIX BREGRESSIONS ON LINEAR AND
Page 293 and 294: REFERENCES1. D.W. Allan, "The Measu
Page 295 and 296: 5.12 )( 10 - 7 SEC
Page 297 and 298: 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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