Scattering Matrix Description of Microwave Resonators

In this paper an analysis of the scattering matrix coefficients (reflectance and transmittances) of the microwave resonators is presented. Two general cases of resonator couplings are considered. One of them is a multiport with one port terminated by the resonator, the other is a resonator coupled, in various ways, to a number of transmission lines. The effect of external circuits on the Q and resonant frequency of the resonator has also been examined. Fundamental parameters for the commonly used microwave resonator couplings are shown in Table L