Handbook of Frequency Stability Analysis

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(a) All Tau Stability Plot5.25. Environmental Sensitivity(b) Many Tau Stability PlotFigure 28. Comparison of all tau and many tau stability.Environmental sensitivity should be treated separately from noise when one performs a stability analysis. However, itcan be very difficult to distinguish between those different mechanisms for phase or frequency variations. It is oftenpossible to control the environmental conditions sufficiently well during a stability run so that environmental effectssuch as temperature and supply voltage are negligible. Determining how well those factors have to be controlledrequires knowledge of the device’s environmental sensitivities. Those factors should be measured individually, ifpossible, over the largest reasonable excursions to minimize the effect of noise. Environmental sensitivity can best bedetermined by considering the physical mechanisms that apply within the unit under test. Useful information aboutthe environmental sensitivity of frequency sources can be found in the references below. Some environmental factorsaffect phase and frequency differently, which can cause confusion. For example, temperature affects the phase delaythrough a cable. Dynamically, however, a temperature ramp produces a rate of change of phase that mimics afrequency change in the source. Because environmental sensitivity is highly dependent on device and application, itdoes not receive detailed consideration in this handbook. More information will be found in the following references.60
References for Environmental Sensitivity1. IEEE Standard 1193, IEEE Guide for Measurement of Environmental Sensitivities of Standard FrequencyGenerators.2. MIL-0-55310, General Specification for Military Specification, Oscillators, Crystal, Military Specificationsand Standards.3. MIL-STD-810, Environmental Test Methods and Engineering Guidelines.4. MIL-STD-202, Test Methods for Electronic and Electrical Component Parts.5. C. Audion, N. Dimarcq, V. Giodano, J. Viennet, “Physical Origin of the Frequency Shifts in Cesium BeamFrequency Standards: Related Environmental Sensitivity,” Proceedings of the 22 nd Annual Precise Time andTime Interval (PTTI) Applications and Planning Meeting, pp. 419-440, 1990.6. L.A. Breakiron, L.S. Cutler, H.W. Hellwig, J.R. Vig, G.M.R Winkler, “General Considerations in theMetrology of the Environmental Sensitivities of Standard Frequency Generators,” Proceedings of the 1992IEEE Frequency Control Symposium, pp. 816-830, 1992.7. H. Hellwig, “Environmental Sensitivities of Precision Frequency Sources,” IEEE Transactions IM-39, pp.301-306, 1990.8. E.M. Mattison, “Physics of Systematic Frequency Variations in Hydrogen Masers,” Proceedings of the 22 ndAnnual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, pp. 453-464, 1990.9. W.J. Riley, “The Physics of Environmental Sensitivity of Rubidium Gas Cell Atomic Frequency Standards,”Proceedings of the 22 nd Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting,pp. 441-452, 1990.10. F.L. Walls and J.J. Gagnepain, “Environmental Sensitivities of Quartz Crystal Oscillators,” IEEETransactions UFFC-39, no. 2, pp. 241-249, 1992.11. P.S. Jorgensen, “Special Relativity and Intersatellite Tracking,” Navigation, Vol. 35, No. 4, pp. 429-442,Winter 1988-89.12. T.E. Parker, “Environmental Factors and Hydrogen Maser Frequency Sensitivity,” IEEE Trans. UFFC-46,No. 3, pp.745-751, 1999.5.26. ParsimonyIn any measurement or analysis, it is desirable to minimize the number of extraneous parameters. This is not just amatter of elegance; the additional parameters may be implicit or arbitrary and thereby cause confusion or error if theyare ignored or misunderstood. For example, the Allan deviation has the important advantage that, because of itsconvergence characteristics for all common clock noises, its expected value is independent of the number of datapoints. Many of the techniques used in the analysis of frequency stability, however, do require that certain parametersbe chosen before they can be performed. For example, drift removal requires the choice of a model to which the datawill be fit (perhaps using the criterion of white residuals). Outlier removal is an especially difficult case, wherejudgment often enters into the decision as to whether or not a datum is anomalous. A listing of some of thesenonparsimonious parameters is given in Table 14:61
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NIST Special Publication 1065Handbo
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NIST Special Publication 1065Handbo
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PrefaceI have had the great privile
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5.12. MTOT BIAS FUNCTION ..........
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1 IntroductionThis handbook describ
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Original Allan (a)Overlapping Allan
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3 Definitions and TerminologyThe fi
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15000Random Run Noise50Random Walk
Page 19 and 20: 5 Time Domain StabilityThe stabilit
Page 21 and 22: step) are the sample period τ 0 an
Page 23 and 24: (a)(c)(b)Figure 5. (a) Simulated fr
Page 25 and 26: In terms of phase data, the Allan v
Page 27 and 28: 22 df ⋅ sχ = , (12)2σwhere χ²
Page 29 and 30: References for Time Variance1. D.W.
Page 31 and 32: M− 3m+1 j+ m−121⎧⎫Hσy( τ)
Page 33 and 34: References for Hadamard Variance1.
Page 35 and 36: 5.2.12. Modified Total VarianceThe
Page 37 and 38: Fractional Frequency Data y i, i =
Page 39 and 40: It is necessary to identify the dom
Page 41 and 42: NoiseRW FMTable 3. Thêo1 EDF Formu
Page 43 and 44: References for Thêo1, NewThêo1, T
Page 45 and 46: where S φ is the spectral density
Page 47 and 48: References for Dynamic Stability1.
Page 49 and 50: 1000100N=500250100Full EDF Algorith
Page 51 and 52: The edf for the modified Allan vari
Page 53 and 54: References for Confidence Intervals
Page 55 and 56: 5.5.4. The Lag 1 AutocorrelationThe
Page 57 and 58: The input data should be for the pa
Page 59 and 60: 5.9. B 3 Bias FunctionThe B 3 bias
Page 61 and 62: References for Bias Functions1. “
Page 63 and 64: Figure 24. Frequency stability plot
Page 65 and 66: include points at all possible tau
Page 67 and 68: x(t) = a + bt, where slope = y(t) =
Page 69: Linear frequency drift can be estim
Page 73 and 74: AllandeviationHadamarddeviationTota
Page 75 and 76: For πτf
Page 78 and 79: S(f)yS(f)=x, (59)(2π f)2where S x
Page 80 and 81: preferred, either because of measur
Page 82 and 83: References for Spectral Analysis1.
Page 84 and 85: where the h α terms define the lev
Page 86 and 87: The expected PSD values that corres
Page 88 and 89: 8.1. White Noise GenerationWhite no
Page 90 and 91: 9 Measuring SystemsFrequency measur
Page 92 and 93: factor. For example, if two 5 MHz s
Page 94 and 95: Figure 37. Random telegraph signal
Page 96 and 97: 10 Analysis ProcedureA frequency st
Page 98 and 99: 5 Remove the frequencydrift, leavin
Page 100 and 101: 10.4. Gap HandlingGaps should be in
Page 102 and 103: References for Gaps, Jumps, and Out
Page 104 and 105: Table 23. Stability data for unit u
Page 106 and 107: B1 ⎡ ⎤∑∑− , (72)⎣ ⎦M
Page 108 and 109: The total deviation canprovide bett
Page 110 and 111: The Hadamard variance isinsensitive
Page 112 and 113: Table 28. Detection of periodic com
Page 114 and 115: 11.6. White FM Noise of a Frequency
Page 116 and 117: 12 SoftwareSoftware is necessary to
Page 118 and 119: This expression produces a series o
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13 GlossaryThe following terms are
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14 Bibliography• NotesA. These re
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44. P. Lesage and T. Ayi, “Charac
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81. J. McGee and D.A. Howe, “Thê
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• Noise Identification122. J.A. B
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162. W.J. Riley, “Addendum to a T
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OOutlier . 41, 75, 106, 108, 109, 1
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Handbook of Frequency Stability Analysis

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