Handbook of frequency stability analysis

2008·9.2 MB·English

by  Riley, W.J.

NATL INST OF STAND & TECH
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NIST Special Publication 1065
Handbook Frequency
of
Analysis
Stability
W.J. Riley
Nisr
National Institute of Standards and Technology • U.S. Department of Commerce
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NIST Special Publication 1065
Handbook of Frequency
Stability Analysis
W.J. Riley
Under contract with:
Time and Frequency Division
Physics Laboratory
National Institute ofStandards and Technology
325 Broadway
Boulder, CO 80305
July 2008
U.S. DepartmentofCommerce
Carlos M. Gutierrez, Secretary
NationalInstitute ofStandards and Technology
James M. Turner Deputy Director
Certain commercial entities, equipment, or materials may be identified in this document in order to describe an
experimental procedure or concept adequately. Such identification is not intended to imply recommendation or
endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities,
materials, or equipment are necessarily the best available for the purpose.
National Institute of Standards and Technology Special Publication 1065
Natl. Inst. Stand. Technol. Spec. Publ. 1065, 136 pages (July 2008)
CODEN: NSPUE2
U. S. GOVERNMENT PRINTING OFFICE
Washington: 2008
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Dedication
This handbook is dedicated to the memory of Dr. James A. Barnes (1933-2002), a pioneer in the statistics of
frequency standards.
James A. Barnes was born in 1933 in Denver, Colorado. He received a Bachelor's degree in engineering physics from
the University of Colorado, a Masters degree from Stanford University, and in 1966 a Ph.D. in physics from the
MBA
University ofColorado. Jim also received an from the University ofDenver.
After graduating from Stanford, Jimjoined the National Institute ofStandards, now the National Institute ofStandards
and Technology (NIST). Jim was the first Chiefofthe Time and Frequency Division when it was created in 1967 and
set the direction for this division in his 15 years of leadership. During his tenure at NIST Jim made many significant
contributions to the development ofstatistical tools for clocks and frequency standards. Also, three primary frequency
standards (NBS 4, 5, and 6) were developed under his leadership. While he was division chief, closed-captioning was
developed (which received an Emmy award) and the speed oflight was measured. Jim received the NBS Silver Medal
in 1965 and the Gold Medal in 1975. In 1992, Jim received the I.I. Rabi Award from the IEEE Frequency Control
Symposium "for contributions and leadership in the development of the statistical theory, simulation and practical
understanding ofclock noise, and the application ofthis understanding to the characterization ofprecision oscillators
and atomic clocks." In 1995, he received the Distinguished PTTI Service Award. Jim was a Fellow ofthe IEEE. After
retiring from NIST in 1982, Jim worked for Austron.
Jim Barnes died Sunday, January 13, 2002, in Boulder, Colorado after a long struggle with Parkinson's disease. He
was survived by a brother, three children, and two grandchildren.
Note: This biography is published with permission and taken from his memoriam on the UFFC web site at:
http://www.ieee-uffc.org/fcmain.asp?page=barnes.
Ill
Preface
I have had the great privilege of working in the time and frequency field over the span of my career. I have seen
atomic frequency standards shrink from racks of equipment to chip scale, and be manufactured by the tens of
thousands, while primary standards and the time dissemination networks that support them have improved by several
orders of magnitude. During the same period, significant advances have been made in our ability to measure and
analyze the performance ofthose devices. This Handbook summarizes the techniques offrequency stability analysis,
bringing together material that I hope will be useful to the scientists and engineers working in this field.
I acknowledge the contributions ofmany colleagues in the Time and Frequency community who have contributed the
analytical tools that are so vital to this field. In particular, I wish to recognize the seminal work ofJ.A. Barnes and
D.W. Allan in establishing the fundamentals at NBS, and D.A. Howe in carrying on that tradition today at NIST.
Together with such people as M.A. Weiss and C.A. Greenhall, the techniques of frequency stability analysis have
advanced greatly during the last 45 years, supporting the orders-of-magnitude progress made on frequency standards
and time dissemination.
I especially thank David Howe and the other members of the NIST Time and Frequency Division for their support,
encouragement, and review ofthis Handbook.
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Contents
INTRODUCTION
1 1
2 FREQUENCY STABILITY ANALYSIS 2
2.1 Background 2
3 DEFINITIONS AND TERMINOLOGY 5
3.1. Noise Model 5
3.2. PowerLawNoise J
3.3. StabilityMeasures 6
3.4. DifferencedandIntegratedNoise 6
3.5. Glossary 7
STANDARDS
4 8
5 TIME DOMAIN STABILITY 9
5.1. Sigma-TauPlots 9
5.2 Variances 10
5.2.1. Standard Variance 13
5.2.2. Allan Variance 14
5.2.2. OverlappingSamples 15
5.2.4. OverlappingAllan Variance 16
5.2.5 ModifiedAllan Variance 17
5.2.6. Time Variance 18
5.2.7. Time ErrorPrediction 19
5.2.8. Hadamard Variance 20
5.2.9. OverlappingHadamard Variance 20
5.2.10. ModifiedHadamard I'ariance 21
5.2.11. Total Variance 23
5.2.12. ModifiedTotal Variance 25
5.2.13. Time Total Variance 26
5.2.14. HadamardTotal Variance 26
5.2.15. Theol 29
5.2.16 TheoH 31
5.2.17 MTIE 33
5.2.18. TlErms 34
5.2.19. IntegratedPhaseJitterandResidualFM 34
5.2.20. DynamicStability 36
5.3. Confidence 1>4TERVALS 37
5.3.1. Simple Confidence Intervals 37
5.3.2 Chi-SquaredConfidence Intervals 38
5.4. DegreesOFFreedom 38
5.4.1. AVAR. MVAR. TVAR. andHVAREDF 38
5.4.2. TOTVAREDF 41
MTOTEDF
5.4.3. 41
5.4.4. Thiol /TheoHEDF 42
5.5. NoiseIdentification 43
5.5.1. PowerLawNoiseIdentification 43
5.5.2. Noise Identification UsingB, andR(n) 44
5.5.3. TheAutocorrelationFunction 44
5.5.4. The Lag I Autocorrelation 45
5.5.5. Noise Identification Usingri 45
5.5.6. Noise IDAIgorithm 46
5.6. BiasFunctions 48
5.7. B BiasFunction 48
I
5.8. B2 BiasFunction 48
5.9. B3BiasFunction 49
5.10. R(N)BiasFunction 49
5.11. TOTVARBiasFunction 49
V
5.12 MTOTBiasFunction 49
5.13 TheoI Bias 50
5.14 TheoHBias 50
5.15 DeadTime 51
5.16 UnevenlySpacedData 54
5.17 Histograms 55
5.18 FrequencyOffset 56
5.19 FrequencyDrift 57
5.20 DriftAnalysisMethods 57
5.21 PhaseDriftAnalysis 57
5.22 FrequencyDriftAnalysis 58
5.23 AllTau 59
5.25 EnvironmentalSensitivity 60
5.26 Parsimony 61
5.27 TransferFunctions 64
6 FREQUENCY DOMAIN STABILITY 67
6.1 NoiseSpectra 67
6.2 PowerSpectral Densities 68
6.3 PhaseNoisePlot 69
6.4 SpectralAnalysis 69
6.5 PSD Windowing 70
6.6 PSDAveraging 70
6.7 MuLTiTAPERPSDAnalysis 70
6.8 PSDNotes 71
7 DOMAIN CONVERSIONS 73
7.1. PowerLawDomainConversions 73
7.2. ExampleofDomainConversions 74
8 NOISE SIMULATION 77
8.1. WhiteNoiseGeneration 78
8.2. FlickerNoiseGeneration 78
8.3. FlickerWalkandRandomRunNoiseGeneration 78
8.4. FrequencyOffset, Drift,andSinusoidalComponents 78
9 MEASURING SYSTEMS 80
9.1. TimeIntervalCounterMethod 80
9.2. HeterodyneMethod 80
9.3. Dual MixerTimeDifferenceMethod 81
9.4. MeasurementProblemsandPitfalls 82
9.5. MeasuringSystemSummary 82
9.6. DataFormat 83
9.7. DataQuantization 83
9.8. Timetags 84
9.9. ArchivingANDAccess 84
ANALYSIS PROCEDURE
10 86
10.1. DataPrecision 89
10.2. Preprocessing 89
10.3. Gaps,Jumps,ANDOutliers 89
10.4. GapHandling 90
10.5. UnevenSpacing 90
10.6. AnalysisOFDataWITHGaps 90
10.7. Phase-FrequencyConversions 90
10.8. DriftAnalysis 91
10.9. VarianceAnalysis 91
10.10. SpectralAnalysis 91
10.11. OutlierRecognition 91
10.12. DataPlotting 92
10.13. VarianceSelection 92
10.14. Three-CorneredHat 92
10.15. Reporting 96
vi
11 CASE STUDIES 97
11.1. FlickerFloorofaCesiumFrequencyStandard 97
11.2. HadamardVarianceofaSourcewithDrift 99
11.3. Pr^seNoiseIdentification 100
11.4. DetectionofPeriodicComponents 101
11.5. StabilityUnderVibrationalModulation 103
11.6. WhiteFMNoiseofaFrequencySpike 104
1 1.7. CompositeAofngPlots 104
12 SOFTWARE 106
12.1. SoftwareValidation 106
12.2. TestSuites 106
12.3. NBSDataSet 106
12.4. 1000-PoiNTTestSuite 107
12.5. IEEEStandard 1139-1999 109
13 GLOSSARY 110
14 BIBLIOGRAPHY 112
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