NIST Technical Note 1337: Characterization of Clocks and Oscillators

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360 (2N + 1) (9N + 13) I LH ..I .. -4200 (N + 1) I LJ2800 I LandK = N (N - 1) (N - 2) (N - 3)L (N + 1) (N + 2) (N + 3).The restrictions on these equations are that the data is evenly spaced beginningwith n = 1 to n = N. and no missing values. For error estimates (and theirdistributions) to be valid. the residuals must be random. uncorrelated, (i.e.,white) •570TN-283
REFERENCES1. D.W. Allan, "The Measurement of Frequency and Frequency Stability of PrecisionOscillators," Proc. 6th PTTI Planning Meeting, p109 (1975).2. J.A. Barnes, et al., "Characterization of Frequency Stability," Proc IEEETrans. on lnst. and Meas., lM-20, pl0S (1971).3. NoR. Draper and H. Smith, "Applied Regression Analysis," John Wiley andSons, N. Yo, (1966).4. GoE.P. Box and G.M. Jenkins, "Time Series Analysis," Holden-Day, SanFrancisco, p294, (1970).s. P.V. Tryon and R.H. Jones, "Estimation of Parameters in Models for CesiumBeam Atomic Clocks," NBS Journal of Research, Vol. 88, No.1, Jan-Feb. 1983.6. R.H. Jones and P.V. Tryon, "Estimating Time from Atomic Clocks," NBS Journalof Research, Vol. 88, No.1, Jan-Feb. 1983.7. J.A. Barnes and S. Jarvis, Jr., "Efficient Numerical and Analog Modeling ofFlicker Noise Processes," NBS Tech. Note 604, (1971).571TN-284
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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
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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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Page 241 and 242: 7. PHASE NOISE AND AM NOISE MEASURE
Page 243 and 244: 7. PHASE NOISE AND AM :>lOISE MEASU
Page 245 and 246: _~ ~A _7. PHASE NOISE AND AM NOISE
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
Page 259 and 260: to a g
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: APPENDIX BREGRESSIONS ON LINEAR AND
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Page 297 and 298: 100%CUMULATIVE PERIODOGRAM -50%U'
Page 299 and 300: 100%CUMULATIVE PERIODOGRAM50%(J'l..
Page 301 and 302: FREQUENCY DRIFT AND WHITESTANDARD D
Page 303 and 304: MR. McCASKILL:Well, let me go furth
Page 305 and 306: NIST Technical Note 1318, 1990.VARI
Page 307 and 308: By definition, white noise has a po
Page 309 and 310: where aZ(N,T,r) is the expected sam
Page 311 and 312: Some useful asymptotic forms of B 3
Page 313 and 314: Since the time-domain definition fo
Page 315 and 316: Stability Using Non-zero Dead-Time
Page 317 and 318: I!II.....I~I.....cIQ)IEQ) I~I~(J)
Page 319 and 320: -2,THE BIAS FUNCTION, 8 2 (r,p.)Fig
Page 321 and 322: AppendixWith reference to figure 1,
Page 323 and 324: 8lIN,r,lll) for r = .011\1\ N= ~ 81
Page 325 and 326: BUN,r,IItJI for r =/tl\ !'I= 8 16 3
Page 327 and 328: 81 (N,r,lIUl for r =ItJ \ IF 4 8 16
Page 329 and 330: __ ....... ~...........__ .........
Page 331 and 332: BllN,r,kl) for r = 1024It! \ N= 4 B
Page 333 and 334: B2(r,llU)It! \ r = .0001 .0003 .001
Page 335 and 336: B3( 2, P1,I", IIU) far r '" .01~\ ~
Page 337 and 338: 83(2,I'f,r,~)for r '"""'III \ 2 4 B
Page 339 and 340: B312.I'I,r,llU) for r " 4I\J \ pt::
Page 341 and 342: 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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