Estimation of Time-Domain Frequency Stability Based on Phase Noise Measurement; Conference paper

摘要

The time domain characterization of the frequency fluctuations is usually expressed in terms of the Allan variance, sigma squared sub y (tau), or the modified Allan variance, Mod sigma squared sub y (tau) . Both variances can be accurately determined by the integral relations to S sub y (f) , the power spectral density of fractional frequency fluctuations, which include five types of noise: White PM, Flicker PM, White FM, Flicker FM and Random Walk FM. These noise types are distinguished by the integer powers (alpha) in their functional dependence on Fourier frequency f. Because the noise is inherent to all kinds of oscillators and measurement systems, specifying their contributions to the time domain frequency stability is important and meaningful. In this paper, both the numerical integral and the curve-fitting methods are presented to estimate the frequency stability from the results of phase noise measurement of oscillators, amplifiers, etc. The numerical integral is a direct way to use and we calculate the integral approximation after smoothing some spike points. In addition, owing to the properties of power-law noise processes, the weighting coefficient h sub alpha of each type of noise component could be estimated when curve-fitting skills are adopted. Cutler's formula is used to calculate the integral approximation using these coefficients. The approximations of frequency stability from these two ways are compared and analyzed. Lastly, the limitations and possible errors from the estimating methods are also discussed.