NIST Technical Note 1337: Characterization of Clocks and Oscillators

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252 A. L. LANCE, W. D. SEAL, AND F. LABAAR(2) Flicker FM (flicker of frequency). The plot goes down as l/f3. Thisnoise is typically related to the physical resonance mechanism of the activeoscillator or the design or choice of parts used for the electronic or powersupply, or even environmental properties. The time domain frequencystability over extended periods is constant. In high-quality oscillators, thisnoise may be marked by white FM (l/f2) or flicker phase modulation¢>M (1j). It may be masked by drift in low-quality oscillators.(3) White FM (white frequency, random walk of phase). The plot goesdown as I/f2. A common type of noise found in passive-resonator frequencystandards. Cesium and rubidium frequency standards have white FM noisecharacteristic because the oscillator (usually quartz) is locked to the resonancefeature of these devices. This noise gets better as a function of timeuntil it (usually) becomes flicker FM (I/f3) noise.(4) Flicker ¢>M (flicker modulation of phase). The plot goes down asl/f This noise may relate to the physical resonance mechanism in an oscillator.It is common in the highest-quality oscillators. This noise can beintroduced by noisy electronics-amplifiers necessary to bring the signalamplitude up to a usable level-and frequency multipliers. This noise canbe reduced by careful design and by hand-selecting all components.(5) White 4JM (white phase). White phase noise plot is flat f O , Broadbandphase noise is generally produced in the same way as flicker ¢>M (I/f). Latestages of amplification are usually responsible. This noise can be kept lowby careful selection ofcomponents and by narrow-band filtering at the outputThe power-law processes are illustrated in Fig. 5.F. INTEGRATED PHASE NOISEThe integrated phase noise is a measure of the phase-noise contribution(rms radians, rms degrees) over a designated range of Fourier frequencies.The integration is a process of summation that must be performed on themeasured spectral density within the actual IF bandwidth (B) used in themeasurement of b4Jrms' Therefore, the spectral density S6t1>(f) must be unnormalizedto the particular bandwidth used in the measurement. DefineSu(f), in radians squared, as the unnormalized spectral density:SuCf) = 2[10 exp(Sf(f) + 10 log B)/IO). (42)Then, the integrated phase noise over the band ofFourier frequencies (fl tofn)where measurements are performed using a constant JF bandwidth, in radianssquared, is(43)if·TN-203
or, in rms radians,7. PHASE !'rOISE AND AM NOISE MEASUREMENTS 253and the integrated phase noise in rms degrees is calculated asSB(360/21l). (45)The integrated phase noise in decibels relative to the carrier is calculated asS8 = 10 10g(tS~). (46)The previous calculations correspond to the illustration in Fig. 7, whichincludes two bandwidths (Bl and 82) over two ranges of Fourier frequencies.In the measurement program, different IF bandwidths are used as setforth by Lance et ai. (1977). The total integrated phase noise over the differentranges of Fourier frequencies, which are measured at constant bandwidthsas illustrated, is calculated in rms radians as follows:,I 2 2 (5 )2 (47)5 B'ol = V (SBI) + (SB2) + ... + Bn'where it is recalled that the summation is performed in terms of radianssquared.sFIG. 7 Integrated phase noise over Fourier frequency ranges at which measurementsperformed using conSlant bandwidth.TN-204
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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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Page 163 and 164: :l frequcllcy ~eparatioll froll1 th
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Page 171 and 172: 142 Rep. 580--2Reprinted, with perm
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Page 175 and 176: 146 Rep. 580-2The values of ha are
Page 177 and 178: 148 Rep. SSO-2TABLE II - Translalio
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Page 181 and 182: 522 LESAGE AND AUDOIN01., 1971J:S,I
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Page 185 and 186: 526LESAGE AND AUDOINQuartz ClJstalF
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Page 189 and 190: 530 LESAGE AND AUOOINsuch as c:r;(T
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Page 193 and 194: 534 LESAGE AND AUDOINof measurement
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Page 197 and 198: 538 LESAGE AND AUWINstability measu
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Page 201 and 202: 7. PHASE NOISE AND AM NOISE MEASURE
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Page 251 and 252: average frequency over the interval
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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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