Fitting strategy of resonance curves from microwave resonators with non-idealities

Microwave resonators are of widespread use in technological applications as well as in many research fields. In all cases, as microwave filters or as material characterisation devices or as sensors, their use requires the accurate measurement of their quality factor Q and resonance frequency ν
₀
, which are the main parameters shaping their response. The most accurate measurements are obtained through a full determination of all the complex scattering coefficients S
_ij
of a two-port coupled resonator, through a Vector Network Analyzer, and subsequent fitting in the complex plane. These approaches allow also to compensate for resonator non-idealities which alter the resonator response and thus impact on Q and ν
₀
accuracies. On the other hand, cost effective and fast measurement setups rely on power sensors which allow scalar measurements only. In these cases, the resonator ideal response takes the shape of a lorentzian curve. It is therefore of interest to optimise the fitting strategy of scalar measurements in order to obtain the better fit goodness and robustness against perturbations. In this work we study the most common sources of perturbation and their models, in order to assess which fitting strategy yields the best results when the perturbation cause is not known a-priori. We perform both numerical simulations and tests on actual experimental data. We find that the fit model describing a cross-coupling between two resonator ports is the most robust approach.