The effect of power-drive level on the calibration of the bridge instrument for the measurement of the quartz stability
Résumé
In space application, the demand for high-stability quartz oscillators is ever increasing. The highest stability, of the order of 5×10–14 Allan deviation at 5–30 s measurement time, has been achieved with 5–10 MHz bulk acoustic-wave resonators, yet only after careful selection from a significantly larger production. The small improvement obtained at great effort in the past 15 years seems to indicate that the target stability of 10–14 is still not around the corner. In this quest, some discrepancies between the measurement of oscillators and resonators indicates that metrology is a critical point. At the state of the art, the experimental investigation on the resonator's frequency stability relies on the bridge (interferometric) method1, in which the quartz is used as a passive device, with no sustaining amplifier. The instrument is based on the synchronous detection of the noise sideband after suppressing the carrier by vector sum of an equal and opposite reference signal. The detected noise is measured with a fast Fourier transform analyzer. Since a reference source of noise lower than that of the resonators under test is not available, we use a symmetric scheme that compares two equal resonators, rejecting the noise of the source. An advanced version of this instrument has been implemented at FEMTO-ST, in collaboration with the CNES and with the major European manufacturers of high stability resonators2. The usual way to calibrate the system is to inject in one arm of the bridge a sideband of known frequency and amplitude. The instrument gain is calculated from the amplitude of the detected signal. We observed that this practice may be incorrect. The reason is that the non-linearity, inherent in the quartz lattice, warps the shape of the frequency response, breaking the symmetry between upper and lower sidebands. Consequently, the quartz is no longer described by a 2nd-order linear differential equation. This phenomenon is definitely not negligible at the power levels of interest. The measurement of a few batches from different manufacturers reveals inconsistencies correlated to power. After reviewing the state of the art, this article proposes a new calibration method.