Characterization of phase and frequency instabilities in precision frequency sources: Fifteen years of progress

Precision frequency sources such as quartz oscillators, masers, and passive atomic frequency standards are affected by phase and frequency instabilities including both random and deterministic components. It is of prime importance to have a comprehensive characterization of these instabilities in order to be able to assess the potential utility of each source. For that purpose, many parameters have been proposed especially for dealing with random fluctuations. Some of them have been recommended by the IEEE Subcommittee on Frequency Stability and later by Study Group 7 on "Standard Frequencies and Time Signals" of the International Radio Consultative Committee (CCIR). Others are not so widely used but show interesting capabilities. This paper aims at giving a broad review of parameters proposed for phase and frequency instability characterization, including both classical widely used concepts and more recent less familiar approaches. Transfer functions that link frequency-domain and time-domain parameters are emphasized because they provide improved understanding of the properties of a given time-domain parameter or facilitate introducing of new parameters. As far as new approaches are concerned, an attempt has been made to demonstrate clearly their respective advantages. To this end, some developments that did not appear in the original references ate presented here, e.g, the modified three sample variance Σ y 2 (τ), the expressions of 〈δy - T 2 〉, the intetpretation of structure functions of phase and its relations with Σ y 2 (τ) and the Hadamard variance. The effects of polynomial phase and frequency drifts on various parameters have also been pointed out in parallel with those of random processes modeled by power-law spectral densities.