Power-to-Frequency Conversion in Cryogenic Sapphire Resonators

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.