Algorithm for Resonator Parameter Extraction From Symmetrical and Asymmetrical Transmission Responses

We describe an algorithm capable of extracting the unloaded quality factor and the resonant frequency of microwave resonators from vector S-parameters. Both symmetrical (Lorentzian) and asymmetrical (Fano) transmission responses are supported. The algorithm performs an adaptive outlier removal to discard measurement points affected by noise or distortion. It removes the effects caused by imperfections in the device (such as modes with close resonance frequencies or stray coupling between the resonator ports) or the experimental setup (such as lack of isolation or dispersion in the test set and cables). We present an extensive assessment of the algorithm performance based on a numerical perturbation analysis and the evaluation of S-parameter fitting results obtained from network analyzer measurements and resonator equivalent circuits. Our results suggest that uncertainty is mainly caused by factors that distort the frequency dependence of the S-parameters, such as cabling and coupling networks, and is highly dependent on the device measured. Our perturbation analysis shows improved results with respect to those of previous publications. Our source code is written in Python using open-source packages and is publicly available under a freeware license.