Frequency Stability Measurement of Cryogenic Sapphire Oscillators with a Multichannel Tracking DDS and the Two-Sample Covariance

TL;DR

This paper demonstrates a novel measurement approach for ultra-stable cryogenic sapphire oscillators using a multichannel tracking DDS and two-sample covariance, achieving unprecedented precision in frequency stability analysis.

Contribution

It introduces a new measurement technique combining multichannel tracking DDS and two-sample covariance to accurately assess frequency stability of cryogenic sapphire oscillators.

Findings

Achieved frequency stability measurements from 2E-16 to parts in 1E-15.

Demonstrated the covariance method outperforms the Three-Cornered Hat in background noise rejection.

Validated the approach with traditional TCH comparisons and discussed applications to frequency comb outputs.

Abstract

This article shows the first measurement of three 100 MHz signals exhibiting fluctuations from 2E-16 to parts in 1E-15 for integration time tau between 1 s and 1 day. Such stable signals are provided by three Cryogenic Sapphire Oscillators (CSOs) operating at about 10 GHz, also delivering the 100 MHz output via a dedicated synthesizer. The measurement is made possible by a 6-channel Tracking DDS (TDDS) and the two-sample covariance tool, used to estimate the Allan variance. The use of two TDDS channels per CSO enables high rejection of the instrument background noise. The covariance outperforms the Three-Cornered Hat (TCH) method in that the background converges to zero "out of the box," with no need of the hypothesis that the instrument channels are equally noisy, nor of more sophisticated techniques to estimate the background noise of each channel. Thanks to correlation and averaging, the instrument background (AVAR) rolls off with a slope 1/sqrt(m), the number of measurements, down to 1E-18 tau = 1E4 s. For consistency check, we compare the results to the traditional TCH method beating the 10 GHz outputs down to the MHz region. Given the flexibility of the TDDS, our methods find immediate application to the measurement of the 250 MHz output of the FS combs.