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This paper is a review of frequency stability measurement techniques and of noise properties of frequency sources.

First, a historical development of the usefulness of spectrum analysis and time domain measurements will be presented. Then the rationale will be stated for the use of the two-sample (Allan) variance rather than the classical variance. Next, a range of measurement procedures will be outlined with the trade-offs given for the various techniques employed. Methods of interpreting the measurement results will be given. In particular, the five commonly used noise models (white PM, flicker PM, white FM, flicker FM, and random walk FM) and their causes will be discussed. Methods of characterizing systematics will also be given. Confidence intervals on the various measures will be discussed. In addition, we will point out methods of improving this confidence interval for a fixed number of data points.

Topics will be treated in conceptual detail. Only light (fundamental) mathematical treatment will be given.

Although traditional concepts will be detailed, two new topics will be introduced in this paper: (1) accuracy limitations of digital and computer-based analysis and (2) optimizing the results from a fixed set of input data.

The final section will be devoted to fundamental (physical) causes of noise in commonly used frequency standards. Also transforms from time to frequency domain and vice-versa will be given.

Key Words

frequency stability; oscillator noise modeling; power law spectrum; time-domain stability; frequency-domain stability; white noise; flicker noise.


Precision oscillators play an important role in high speed communications, navigation, space tracking, deep space probes and in numerous other important applications. In this paper, we will review some precision methods of measuring the frequency and frequency stability of precision oscillators. Development of topics does not rely heavily on mathematics. The equipment and set-up for stability measurements are outlined. Examples and typical results are presented. Physical interpretations of common noise processes are discussed. A table is provided by which typical frequency domain stability characteristics may be translated to time domain stability characteristics and vice-versa.

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Summary and Introduction I II III IV V VI VII VIII IX X XI XII Conclusion References