NIST Technical Note 1337: Characterization of Clocks and Oscillators

More documents

Recommendations

Info

where the coefficients A. B, C, etc., are given by:A 3 [3N (N + 1) + 2]B = -18 (2N + 1)C 30D 12 (2N + 1) (8N + 11) I [(N + 1) (N + 2)]E -180 I (N + 2)F = 180 I [(N + 1) (N + 2)]andG N (N - 1) (N - 2).In matrix form, the error variance for forecast values is:where Nk' = [1 no no] and TO no is the date for the forecast point, Xk' Thatis, no = N + K and K is the number of lags past the last data point at lag N.A568TN-28I
APPENDIX BREGRESSIONS ON LINEAR AND CUBIC FUNCTIONSThe matrixes (N'N)-1 for the linear fit and cubic fit, which correspond to Eq.A6 in Appendix A are as follows:For the linear fit:(N'N)-1[: :] lIDwhereA 2 (2N + 1)B -6C 12 I (N + 1)andD = N (N - 1)For the cubic fit:A B C D(N'N)-1BCEFFHGI1 I KD G I JwhereA 8 (2N + 1) (N + N + 3)B = -20 (6N2 + 6N + 5)C 120 (2N + 1)D -140EFG200 (6N4 + 27 N3 + 42 N2 + 30 N + 11) I L-300 (N + 1) (3N + 5) ON + 2) I L280 (6N2 + lSN + 11) I L569TN-282
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 and 174:
i44 Rep. 580-2If the initial sampli
Page 175 and 176:
146 Rep. 580-2The values of ha are
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 203 and 204:
Page 205 and 206:
Page 207 and 208:
7. PHASE ~OISE AND AM NOISE MEASURE
Page 209 and 210:
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 217 and 218:
Page 219 and 220:
Page 221 and 222:
7. PHASE ~OISE AND AM NOISE MEASVRE
Page 223 and 224:
Page 225 and 226:
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: 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
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: andG == N (N - 1) (N - 2)Also, the
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?