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Characterization of Phase and Frequency Instabilities in Precision Frequency Sources: Fifteen Years of Progress

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Characterization of Phase and Frequency Instabilities in Precision Frequency Sources: Fifteen Years of Progress 1048 PROCEEDINGS OF THE IEEE, VOL. 66, NO. 9, SEPTEMBER 1978 Characterization of Phase and Frequency Instabilities in Precision Frequency Sources: Fifteen Years of Progress Abstmct-Recision freuuencv sources such as auartz oscillators. cations; frequency instabilities are harmful in all cases because masers, and passive atodc fre&ency standards are kfected by phase‘ they degrade system performance. andfrequency instabilities including both random and deterministic 3) In range measurementswhere ranging signals are phase components. It is ofprime importance to haveacomprehensive characterization of these instabilities in order to be able to assess the compared relative to a reference signal, instabilities in any of potential utility of each source. For that purpose, many parameters the bscillators involved introduce an uncertainty in the range have been proposed especially for dealing with random fluctuations. estimate. Some of them have been recommended by the IEEE Subcommittee 4) In communication systems, interference is reducedand onFrequency Stability and later by Study Group 7 on “Standard Frequencies and Time Signals” of the International Radio Consultative performance is improved by better frequency control of the Committee (CCIR). Others are not so widely used but show interesting carrierfrequencies. In digital communications, emphasis is capabilities. This paper aims at giving a broad review of parameters put on the timing capability of the network clocks: an ade- proposed for phase and frequency instability characterization, includingquate performance measure, the maximum time interval both classical widely used concepts and more recent less familiar ap- error, is related to clocks phase andfrequency instabilities. proaches.Transfer functions that link frequency-domainand time- domainparameters are emphasized because they provide improved For long-term frequencyfluctuations, afractional value of understanding of the properties of a given timedomain parameter or 1 part in 10” or better is recommended by the International facilitateintroducing of new parameters. As far as newapproaches Telegraphand Telephone Consultative Committee (CCITT) are concerned, an attempt has been made to demonstrate’cleady their for the interconnection of several synchronous networks on respectiveadvantages. To this end, some developments that did not the international level. appear in the original references are presented here, e.g, the modified 5) Of course, one should not forget the field of time and three sample variance Z$(T),the expressions of the interpreta- GB$), frequency metrologywhere sophisticated laboratory-type tion of structure functionsof phase and its relations withZ;(T) and the Hadamard variance. The effects of polynomial phase and frequency time and frequency standards are designed, constructed and drifts on various parameters have also been pointed out in pdelwith operated, e.g., long cesium-beam andhydrogen devices. In those of random processes modeled by power-lawspectral densities. fact, with few exceptions, most of the widely used stability measures have beendeveloped by scientists working in the I. INTRODUCTION field. HASE AND FREQUENCYinstability characterization Apractical problem is that several groups of people with has become of great concern to many engineers working different backgrounds have had to find a common language Pin various fields since an increasing number of systems rely for oscillator specifications. upon high-quality time and frequency sources such as quartz- The question was how to develop a useful and comprehen- crystaloscillators, frequency synthesizers, atomicfrequency sive characterization of phase and frequency instabilities that standards and clocks; also, the advent of frequency stabilized can be understood and applied by everyone. More specifically, lasers has provided us with frequency standards in the optical in each field, everyone wanted to know how instabilities affect range. system performance and how the possible instability measures The following nonexhaustive list of systems illustrates the can be used to assess system performance. Of course, nosingle wide range of users [ 11 [ 21 : answer can be given and much work has beencarried out during 1) Doppler radar systems with a narrow bandwidth receiver the last fifteen years to provide some useful answers. tunedto detect the shifted frequency return need high- Frequency stability was already recognized as an important performance transmitter oscillators and receiver local oscillators problem at thebeginning of the sixties: the special IEEE-NASA since any instability limitsrange resolution and sensitivity. Symposium on Short-Term Frequency Stability held at God- 2) Oscillators are used in missiles and spacecrafts for a dard Space Flight Center on November 23-24, 1964 [ 1] ap variety of purposes including guidance?tracking, ind communi- peared as the Fit opportunity for cross-fertilization of ideas. Following this Symposium,an IEEE Subcommittee on Fre- Manuscript received April 15, 1978; revised May 25,1978. The sub- quency Stability of the Technical Committee on Frequency mission of this paper was encouraged after submission of an advanced and Time was created with the ultimateaim of providing a set proposal.This paper is an expandedversion of “Oscillatorspecifica- tions: A review of classical and new ideas,” which appearedin Proceed- of recommendationsfor standards and definitions on both ings of the31st Annual FrequencyControl Symposium, June 1-3, short-termand long-term stability.A Special Issue of the 1977 [47]. PROCEEDINGSOF THE IEEE was devoted to frequency sta- Theauthor is withthe LaboratoirePrimaire du Temps et des Fri- quences, BureauNational de Mitrologie, Observatoire de Paris, Paris bility in February 1966 [ 21 to promote further exchange of 75014, France. information, the Subcommitteeserving as Editorial Committee. 0018-9219/78/0900-1048$00.75 O 1978 IEEE RUTMAN:PHASE FREQUENCYAND INSTABILITIES PRECISIONFREQUENCY IN SOURCES 1049 Several basic papers dealing explicitly with frequency stability other words, frequency stability is the degree to which a source characterization in both frequency and time domains and in- produces a constant frequency over a specified time interval. cluding thetranslations between them, were then published In practice, one often speaks of stability whereas applications [ 31 - [ 71. Of particular interest, the use of sample variances arelimited by instabilities; also, the measurementresults for time-domain characterizationwas developed in [ 71. which are much smaller than unity, e.g., lo-” and so on, are In May, 1971, the Subcommittee issued a paper’ [ 81 pre- indeed values of fractional (or relative or normalized) fre- sented as technical background for an eventual IEEE standard quency instability. definition(not yet adopted): two definitions of frequency The problem is hence the characterization of the unwanted stability were given together withtranslation relationships frequencydepartures which are time-dependent because of that play an importanttheoretical andpractical role. Both the various physical mechanisms to be presented in this have gained wide acceptance among manufacturers and users section. of precision frequency sources. A mathematical model is required for the oscillator quasi- In the present paper, following a description of the mathe- sinusoidal output signal since the mere concept of frequency matical models and basic definitions given in Section 11, the instability immediately implies that the signal is no longer a parametersproposed as frequencystability measures will be pure sinewave. Before establishing this model, it is useful to studied in Section I11 (Fourier frequency domain) and Section emphasizefirst thedichotomy betweendeterministic and IV (time domain). random variations of the oscillator output frequency. In Section V, emphasis will be put on the role of the transfer A. Deterministic Versus Random Frequency Variations. functions which allow one tocalculate the time-domainparam- eters(the variances) fromthe knowledge of thefrequency- Due to several physical mechanisms, the output frequency domain parameters (the spectraldensities). of any real source (even of the best quality) is continuously Up to now, we have mentioned only the basic concepts in changing with time. Typical changes are as follows. wide use today namely thespectral densities of phase and 1)Systematic variations, also known as driftsor trends: frequency fluctuations and the two sample variance of aver- they may be due to the aging of the resonator material (e.g., aged (fractional) frequency fluctuations. But in the mean- in quartz oscillators), but are also found in atomic frequency time, other researchers have proposed new concepts leading to standards (e.g., somecommercial cesium units exhibit a fre- new time domain measures which are believed to exhibit some quency drift of a few parts in 1013 per year). These extremely specific advantages relatively to thetwo-sample variance. These slow changes are often referred to as “long-term instability” approaches will be presented in Sections VI-VI11 with special and expressed in terms of parts in 1 of frequency change per emphasis on the relevant transfer functions relating these new hour, day, month, or year, according to the device or the ap- parameters to the spectral densities. The links with more con- plication. No statistical treatment is needed for the evaluation ventional concepts will be also outlined. It must be recognized of these deterministic
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