NIST Technical Note 1337: Characterization of Clocks and Oscillators
NIST Technical Note 1337: Characterization of Clocks and Oscillators NIST Technical Note 1337: Characterization of Clocks and Oscillators
12 FREOUENCV AND TIME MEASUREMENT215x(t),.!.., ,~~ I"IIIII ,! l' I I I !---..lI I ' :t ~:a .. 5 • 7'.. • 10 11 12 13 14'"Tl I NONOYERLAPPING y~ :~....."I--;"i FULLY OYERLAPPING i~..."aIt'TIMEFIG. 12-14 Illustration of the case of ': = 4'0_ for which the ralio of the number of fullyoverlapping to nonoverlapping estimates of the variance is more than 8 for the Si phase pointsshown. When the averaging time for the computation of mean frequencies 1 exceeds thesampling time 10. the number of fully overlapping mean frequencies is far larger than the numberof nono'·erlapping frequencies. In general. for large N approximately 2m times as manyestimates of the sample variances.can be computed using the fully overlapping technique.* TABLE12-4Number of Degrees of Freedom for Calculation of the Confidence of theEstimate of a Sample Allan Variance'!'ioise typeWhite phaseFlicker phaseWhite frequencydfIN + lX.'I/ - 2m)2lN - m)eX{In('\: I) In«1m + I~X,\j -I))J3(N - 1) 2(N - 21J 4m'[ ~ - --N-- 4m 2 + 52(N - 21Flicker freq uency for m = 12.3N - 4.9Random-walk frequency5N'4rrnN ~ 3mlfor m :2: 2N - 2 (N - 1)2 - 3m(.'V - I) + 4m 2m (N - 31=• For': = mro from .'1 phase points spaced '0 apart.* See Appendix Note # 39IN-85
216 SAMUEL R. STEINTABLE 12-5Number of Degrees of Freedom for Calculation of the Confidence of the Estimate of a SampleAllan Variance for the Major Noise Types·White Flicker White Flicker Random-walkN m phase phase frequency frequency frequency9 1 3.665 4.835 4.900 6.202 7.0002 3.237 3.537 3.448 3.375 2.8664 1.000 1.000 1.000 1.000 0.999129 1 65.579 79.015 84.889 110.548 127.0002 64.819 66.284 71.642 77.041 62.5244 63.304 52.586 42.695 36.881 29.8228 60.310 37.306 21.608 16.994 13.56716 54.509 22.347 9.982 7.345 5.63132 44.761 9.986 4.026 2.889 2.04764 1.000 1.000 1.000 1.000 1.0001025 1 526.373 625.071 682.222 889.675 1023.0002 525.615 543.863 583.621 636.896 510.5024 524.088 459.041 354.322 316.605 253.7558 521.038 366.113 186.363 156.492 125.39~16 514.952 269.849 93.547 76.495 61.24132 502.839 179.680 45.947 36.610 29.21064 478.886 104.743 21.997 16.861 13.288128 432.509 50.487 10.003 7.281 5.516256 354.914 17.419 4.003 2.861 2.005512 1.000 1.000 1.000 1.000 1.000• N is the number of equally spaced phase points that are taken m at a time to form the averagingtime.12.1.9 Separating the Variances of the Oscillator and the ReferenceA measured variance contains noise contributions from both the oscillatorunder test and the reference. The individual contributions are easily separatedif it is known a priori that the reference is much less noisy than thedevice under test or equal to it in performance. Otherwise, the individualcontributions can be estimated by comparing three devices (Barnes, 1966).The three possible joint variances are denoted by 0"&. UJb and ufk' while theindividual device variances are uf, uf, and u~.The joint variances arecomposed of the sum of the individual contributions under the assumptionthat the oscillators are independen t:2 2 2Uij = O"j + Uj.UJk = uJ + u~. (12-43)O";k = 15; + 15;.TN-86
- 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: 12 FREQUENCY AND TIME MEASUREMENT19
- Page 78 and 79: 12 FREQUENCY AND TIME MEASUREMENT19
- Page 80 and 81: 12 FREQUENCY AND TIME MEASUREMENT 2
- Page 82 and 83: 12 FREOU::NCY AND TIME MEASUREMENT2
- Page 84 and 85: 12 FREQUENCY AND TIME MEASUREMENT20
- Page 86 and 87: 12 FREQUENCY AND TIME MEASUREMENT20
- Page 88 and 89: 12 FREQUENCY AND TIME MEASUREMENT20
- Page 90 and 91: 12 FREQUENCY AND TIME MEASUREMENTI~
- Page 92 and 93: 12 FREQUENCY AND TIME MEASUREMENT21
- Page 96: 12 FREQUENCY AND TIME MEASUREMENT21
- Page 100 and 101: 12 FREQUENCY AND TIME MEASUREMENT22
- Page 102 and 103: 12 FREQUENCY AND TIME MEASUREMENT22
- Page 104 and 105: 12 FREQUENCY AND TIME MEASUREMENT22
- 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
216 SAMUEL R. STEINTABLE 12-5Number <strong>of</strong> Degrees <strong>of</strong> Freedom for Calculation <strong>of</strong> the Confidence <strong>of</strong> the Estimate <strong>of</strong> a SampleAllan Variance for the Major Noise Types·White Flicker White Flicker R<strong>and</strong>om-walkN m phase phase frequency frequency frequency9 1 3.665 4.835 4.900 6.202 7.0002 3.237 3.537 3.448 3.375 2.8664 1.000 1.000 1.000 1.000 0.999129 1 65.579 79.015 84.889 110.548 127.0002 64.819 66.284 71.642 77.041 62.5244 63.304 52.586 42.695 36.881 29.8228 60.310 37.306 21.608 16.994 13.56716 54.509 22.347 9.982 7.345 5.63132 44.761 9.986 4.026 2.889 2.04764 1.000 1.000 1.000 1.000 1.0001025 1 526.373 625.071 682.222 889.675 1023.0002 525.615 543.863 583.621 636.896 510.5024 524.088 459.041 354.322 316.605 253.7558 521.038 366.113 186.363 156.492 125.39~16 514.952 269.849 93.547 76.495 61.24132 502.839 179.680 45.947 36.610 29.21064 478.886 104.743 21.997 16.861 13.288128 432.509 50.487 10.003 7.281 5.516256 354.914 17.419 4.003 2.861 2.005512 1.000 1.000 1.000 1.000 1.000• N is the number <strong>of</strong> equally spaced phase points that are taken m at a time to form the averagingtime.12.1.9 Separating the Variances <strong>of</strong> the Oscillator <strong>and</strong> the ReferenceA measured variance contains noise contributions from both the oscillatorunder test <strong>and</strong> the reference. The individual contributions are easily separatedif it is known a priori that the reference is much less noisy than thedevice under test or equal to it in performance. Otherwise, the individualcontributions can be estimated by comparing three devices (Barnes, 1966).The three possible joint variances are denoted by 0"&. UJb <strong>and</strong> ufk' while theindividual device variances are uf, uf, <strong>and</strong> u~.The joint variances arecomposed <strong>of</strong> the sum <strong>of</strong> the individual contributions under the assumptionthat the oscillators are independen t:2 2 2Uij = O"j + Uj.UJk = uJ + u~. (12-43)O";k = 15; + 15;.TN-86
Change language