Power-to-Frequency Conversion in Cryogenic Sapphire Resonators

TL;DR

This paper investigates how cryogenic sapphire resonators convert microwave power variations into frequency shifts, revealing a low-pass filter behavior and enabling phase noise prediction for microwave oscillators.

Contribution

It provides the first detailed measurement of power-to-frequency conversion in cryogenic sapphire resonators and models it as a first-order low-pass filter.

Findings

Power-to-frequency conversion follows a first-order low-pass filter with a specific corner frequency.

Measured transfer function allows accurate phase noise prediction.

Cryogenic sapphire resonators exhibit predictable power-to-frequency behavior at 6 K.

Abstract

We studied how the cryogenic sapphire resonator responds to fast variations of the dissipated microwave power. The experiments were carried out with sapphire resonators cooled to 6 K at frequencies around 11 GHz. We found that the power-to-frequency conversion of the resonator depends on Fourier frequency as the transfer function of the 1st-order low-pass filter with corner frequency close to the resonator loaded half-bandwidth. Having measured the power-to-frequency conversion of the cryogenic sapphire resonator, we predicted the phase noise of the microwave oscillator based on such resonator.