Resonance parameter estimation for low-Q microwave cavities

Microwave cavity resonators are commonly used to investigate material parameters because the latter strongly influence the cavity resonances. This approach involves the extraction of resonance curve features such as the resonance frequency or the quality factor Q from measured n-port matrices. In our application, we work with 2-port S-matrices measured by automatic vector network analyzers (VNA). Well-known feature extraction methods include magnitude-only approaches (3-dB method, transformed linear approximation, nonlinear approximation) and fits of the magnitude and phase of the complex-valued S-parameters. These methods are commonly applied to high-Q resonators, and their suitability for the low-Q case is not obvious a priori. We have encountered this low-Q case in the in-situ observation of electrochemical systems such as automotive catalysts and now discuss the associated parameter estimation problem. We address the issues of which S-parameters should be measured, how they should be evaluated and what errors due to, e. g., discretization and embedding of the resonator in its environment are to be expected. It is found that the best results are achieved on the basis of the complex transfer coefficient S₁₂ because this allows a certain amount of de-embedding and works for all values of Q examined.