Accurate measurements of very small coupling coefficients of electromagnetic resonators at microwave frequencies

Accurate characterization of weakly coupled electromagnetic resonators is often required when considering cryogenic applications of such resonators. In the case of a sapphire loaded cavity resonator, the dielectric loss of sapphire is a strong function of temperature, and coupling to such a resonator must be set below 10−4 at room temperature in order to obtain a critical coupling at the temperature of liquid helium. The current work describes an experimental technique for high resolution measurements of very small coupling coefficients. The measurement process involves frequency modulation of the microwave signal incident on the resonator with the subsequent synchronous demodulation of the reflected signal. The immunity of synchronous demodulation to the technical noise sources associated with the microwave signal processing permits the high fidelity measurements of coupling coefficients at the level unattainable by microwave network analysers.