NIST Technical Note 1337: Characterization of Clocks and Oscillators

More documents

Recommendations

Info

Rep. 580-2 145r f\ \:\.\ f":\.\r\,'.'\~\.~,-.~......... ,-.'i-.. "Fourier frequency 'Y ('1")r "IT-''\."T"'\."""" T'V' "./~ T' /'Sampling time -FIGURE 1 -Slope characteriftics ofthe five independent noiu processes(log scale)Specifically, for the power law model given by equation (5), the time-domain measure also follows thepower law as derived by Cutler from equations (5) and (9).Note. - The factor 1.038 in the fourth term of equation (to) is different from the value given in most previouspublications.IN-165
146 Rep. 580-2The values of ha are characteristics of oscillator frequency noise. One may note for integer values (as oftenseems to be the case) that 11 = -a - 1, for -3 $ ex $ 1, and 11'" -2 for ex ~ I where OHt) - "[I'.These conversions have been verified experimentally [Brandenberger et 01., 1971] and by computation[Chi, 1977J. Table II gives the coefficients of the translation among the frequency stability measures from timedomain to frequency domain and from frequency domain to time domain.The slope characteristics of the five independent noise processes are plotted in the frequency and timedomains in Fig. 1 (log log scale).S. Measurement techniquesThe spectral density of phase Iluctuations S",{f) may be approximately measured using a phase-locke4loop and a low frequency wave analyzer [Meyer, 1970; Walls et al., 1976J. A double-balanced mixer is used as thephase detector in a lightly coupled phase lock loop. The measuring system uses available state-of-the-art electroniccomponents; also a very high quality oscillator is used as the reference. For very low Fourier frequencies (wellbelow I Hz), digital techniques have been used [Atkinson et 01., 1963; De Prins et 01., 1969; Babitch andOliverio, 1974]. New methods of measuring time (phase) and frequency stabilities have been introduced withpicosecond time precision [Allan and Daams, 1975J, and of measuring the Fourier frequencies of phase noise with30 dB more sensitivity than the previous state of the art [Walls et al., 1976J.Several measurement systems using frequency counters have been used to determine time-domain stabilitywith or without measurement dead time [Allan, 1974; Allan and Daams, 1975J. A system without any counter hasalso been developed [Rutman, 1974; Rutman and Sauvage, 1974J. Frequency measurements without dead time canbe made by sampling time intervals instead of measuring frequency directly. Problems encountered when deadtime exists between adjacent frequency measurements have also been discussed and solutions recommended[Blair. 1974; Allan and Daams, 1975; Ricci and Peregrino. 1976]. Discrete spectra have been measured byGroslambert et al. [1974].6. Confidence limits of time domain measurementsA method of data acquisition is to measure time variations Xi at intervals to. Then Oy{t) can be estimatedfor any t -n"[o (n is any positive integer) since one may use those Xi values for which j is equal to nk. Anestimate for Oy{"[) can be made from a data set with M measurements of Yi as follows:(ll)or equivalent(12)Thus. one can ascertain the dependence of Oy{"[) as a function of"[ from a single data set in a very simple way.For a given data set, M of course decreases as n increases.To estimate the confidence interval or error bar for a Gaussian type of noise of a particular value Oy{t)obtained from a finite number of samples [Lesage and Audoin. 1973] have shown that:Confidence Interval fa "'" Oy{"[) . Ka' M-1 /2 for M > 10 (13)where:M: total number of data points used in the estimate,a: as defined in the previous section,K2 ... KI "" 0.99.KO ,.. 0.87,IC_I 0.77.K_2 0.75.TN-166
Page 1 and 2:
Characterization ofClocks and Oscil
Page 3 and 4:
PREFACEFor many years following its
Page 5 and 6:
0 • • • • • • • •
Page 7 and 8:
0 •• 0 •• 0 •• 0 •
Page 9 and 10:
TOPICAL INDEX TO ALL PAPERSThe foll
Page 11 and 12:
of the wide range of measurement si
Page 13 and 14:
The first of these (D.l) by Lesage
Page 15 and 16:
Table 1. Guide to Selection of Meas
Page 17 and 18:
10- 1410- 15c-een10- 1610- 1710- 18
Page 19 and 20:
Table 2. Ratio of mod a~('r) to a~(
Page 21 and 22:
of the frequency measured in this m
Page 23 and 24:
From: Proceedings of the 35th Annua
Page 25 and 26:
where V0 ;: nomi na I peak vo Itage
Page 27 and 28:
ports of the pair of double balance
Page 29 and 30:
fluctuations prior to the bias box
Page 31 and 32:
up an interesting hierarchy of kind
Page 33 and 34:
is determi ned by the measurement s
Page 35 and 36:
Since each average of the fractiona
Page 37 and 38:
Thus. with 9~ probability the calcu
Page 39 and 40:
in fact. Also for n=l the "experime
Page 41 and 42:
1n tenns of the typical performance
Page 43 and 44:
and eq (1.1) we get2m>(t) = ~T(t) =
Page 45 and 46:
varactor control in th@ reference o
Page 47:
V nn5(45 Hz) = 100 nV por root hort
Page 50 and 51:
We can use the convolution theorem
Page 52 and 53:
though the concept of harmonics in
Page 54 and 55:
and wz(t) is now the si!npled versi
Page 56 and 57:
10.7 Time Domain-Frequency Domain T
Page 58 and 59:
o/(t). In the table, the left colum
Page 60 and 61:
Weean make the following general re
Page 62 and 63:
-flO• r.1OSP1 t(f2-,~ 1Ci~-/'10 f
Page 64 and 65:
frequency extent of the analysis ba
Page 66 and 67:
28. P. Kartaschoff and J. Barnes, "
Page 68 and 69:
_--_._~--~II..gIIIIII1.......oIIIII
Page 70 and 71:
From: Precision FrequenC)' Control,
Page 72 and 73:
12 FREQUENCY AND TIME MEASUREMENT 1
Page 74 and 75:
12 FREQUENCY AND TIME MEASUREMENT19
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
12 FREQUENCY AND TIME MEASUREMENT 2
Page 82 and 83:
12 FREOU::NCY AND TIME MEASUREMENT2
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
12 FREQUENCY AND TIME MEASUREMENTI~
Page 92 and 93:
Page 94 and 95:
12 FREOUENCV AND TIME MEASUREMENT21
Page 96:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
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 and 122:
408 CHAPTER BIBLIOGRAPHIESJackisch.
Page 123 and 124: 410 CHAPTER BIBLIOGRAPHIESlesage. P
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
Page 173: i44 Rep. 580-2If the initial sampli
Page 177 and 178: 148 Rep. SSO-2TABLE II - Translalio
Page 179 and 180: ISO Rep. 580-2, 738-2BIBLIOGRAPHYAL
Page 181 and 182: 522 LESAGE AND AUDOIN01., 1971J:S,I
Page 183 and 184: 524 LESAGE AND AUDOINKl- 1410- 11 \
Page 185 and 186: 526LESAGE AND AUDOINQuartz ClJstalF
Page 187 and 188: 528 LESAGE AND AUDOINMinrFrequent,r
Page 189 and 190: 530 LESAGE AND AUOOINsuch as c:r;(T
Page 191 and 192: 532 LESAGE AND AUDOINl.l-TEquations
Page 193 and 194: 534 LESAGE AND AUDOINof measurement
Page 195 and 196: 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 225 and 226:
7. PHASE NOISE AND AM NOISE MEASURE
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
7. PHASE NOISE AND AM :>lOISE MEASU
Page 245 and 246:
_~ ~A _7. PHASE NOISE AND AM NOISE
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
average frequency over the interval
Page 253 and 254:
and frequency stability of precisio
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
Page 289 and 290:
andG == N (N - 1) (N - 2)Also, the
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'
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::
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 and 350:
22. page TN-160In eqs (101), (102),
Page 351 and 352:
29. page TN-180If the ratio of T/ T
Page 354:
NIST-114A(REV. 3-89)4. TITLE AND SU
show all

NIST Technical Note 1337: Characterization of Clocks and Oscillators

Create successful ePaper yourself

Delete template?

Save as template?