NIST Technical Note 1337: Characterization of Clocks and Oscillators

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Table 1. Asymptotic forms of a~( r) for various power-law types and two filter types. Note: wh./2'ff = f his the measurementsystem bandwidth, often called the high-frequency cutoff. In =loge.Name of Noise ex S/O a/(T)w hr»l wh. r »l Whr <
29. page TN-180If the ratio of T/ T is constant and greater than 1 (the usual case), the problem describedis eliminated. However, in taking data for a plot of Oy( T) versus T, it is difficult toachieve this in the hardware and not possible to do it with software processing alone. Forfurther discussion see paper D.8 (page TN-296).30. page TN-197The most recent definitions and concepts for spectral density are given in a new IEEEstandard (paper CIon page TN-B8). This new standard should be consulted as the latestauthority on definitions and terminology.31. page TN-198The newly accepted definition of ~(f) is given in paper Cl. This new definition, ~(f) ==Y2Sif), was always valid for Fourier frequencies far from the carrier. It has now beenextended to cover all frequencies.32. page TN-217Equation (73) should read 20 log (final frequency/original frequency).33. page TN-239On page TN-198 the authors refer to a paper by Glaze (1970). The reference, apparentlylost in printing, is: Glaze, D.J. (1970). "Improvements in Atomic Beam Frequency Standardsat the National Bureau of Standards, "IEEE Trans. Instrum. Meas. IM-19(3), 156-160.34. page TN-257There are two errors in Table 2. Under R(n) the first entry should be l/n rather than 1.The second item in the same column is not single valued (1), but takes on different valuesfor different measurement bandwidths. The reader is referred to section A.6 (page TN-9)for a discussion of this topic.35. pages TN-261 and TN-262Subsequent work on moda~T) and R(n) is reported in section A.6 (page TN-9) of thisreport. There are some differences between the results in A.6 and the ones reported inTables I and II and Figure 4 in this paper.36. page TN-264To be consistent with other papers in the literature, ¢(t) in eq (1) should probably bewritten as xl(t).37. page TN-268The term e(t) in eq (3) is normally used to represent the amplitude fluctuations in theoutput voltage of an oscillator. This term might be better designated Y1(t).TN-342
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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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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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Page 301 and 302: FREQUENCY DRIFT AND WHITESTANDARD D
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Page 307 and 308: By definition, white noise has a po
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Page 311 and 312: Some useful asymptotic forms of B 3
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Page 315 and 316: Stability Using Non-zero Dead-Time
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Page 325 and 326: BUN,r,IItJI for r =/tl\ !'I= 8 16 3
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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::
Page 343 and 344: B3(2,"',r,ail for r = 1024MIl \ I'l
Page 345 and 346: E. APPENDIX - Notes and ErrataThe n
Page 347 and 348: Influence of Pressure and Humidity
Page 349: 22. page TN-160In eqs (101), (102),
Page 354: 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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