Allan Variance Estimated by Phase Noise Measurements

P.C. Chang, H.M. Peng, S.Y. Lin

Abstract: For short measurement times, the Allan (or two-sample) variance can be determined from the phase noise using the mathematical conversion between time and frequency domain. This provides us with a useful tool to obtain the very short-term frequency stability (t<0.5 second) in the time domain, which is difficult for a time-interval counter to measure because of its resolution limitations. Before carrying out the conversion, bias from the measurement system and uncorrelated noises to the DUT (device under test), e.g. ac power noise and environmental perturbations are considered and corrected in the raw data. By doing this, the proper characteristic of the DUT seems to be revealed reasonably. If the above-mentioned bias and noises were not corrected, the generated variance would be apart from the corrected one irregularly, depending on the sampling time t. In this paper, both the numerical integration and the power-law model are used to practice the conversion. The numerical integration is a straightforward way to use and we can get the integral approximation easily. In addition, a common model for the phase noise is linear combinations of power law processes, which are distinguished by the integer powers (a) in their functional dependence on Fourier frequency f with the appropriate coefficients ha. Fitting experimental data with standard regression techniques could have the values of these coefficients. Thereafter, we obtain the variance with Cutler’s equation using these values. The variances from these two ways are compared and inspected. Finally, because ac power noise is always inevitably getting into the measurement system and the DUT, we also make some discussions on the role it plays in the calculations of the Allan variance.
Published in: Proceedings of the 36th Annual Precise Time and Time Interval Systems and Applications Meeting
December 7 - 9, 2004
Hyatt Regency Washington on Capitol Hill
Washington, D.C.
Pages: 165 - 172
Cite this article: Chang, P.C., Peng, H.M., Lin, S.Y., "Allan Variance Estimated by Phase Noise Measurements," Proceedings of the 36th Annual Precise Time and Time Interval Systems and Applications Meeting, Washington, D.C., December 2004, pp. 165-172.
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