High-resolution measurement of the temperature-dependence of the Q, coupling and resonant frequency of a microwave resonator

An automated system is described which facilitates fast high-resolution measurements of Q, coupling and resonant frequency of modes in a microwave resonator. We demonstrate measurements of Q and coupling with a resolution of 6 x 10(-4) and a fractional frequency measurement resolution of 3 x 10(-13). The system is used to measure the temperature-dependence of the mode Q, coupling and resonant frequency for modes in two high-Q cryogenic sapphire resonators. Measurement of the temperature variation of Q is used to estimate the geometric factor, which is a measure of the mode energy confinement to the sapphire element distribution. Measurement of the mode frequency temperature-dependence can be used to determine the effect of paramagnetic impurities in the sapphire.