Non-linearity in superconducting coplanar waveguide rectangular-spiral resonators

In the present work, a non-linear distributed circuit model for superconducting rectangular-spiral resonators is proposed. This is based on an accurate non-linear circuit model for superconducting parallel coupled lines, which is simultaneously considered both quadratic and modulus non-linear dependencies. The non-linearity in superconducting devices depends on the current distribution, which is mainly determined by the geometrical structure of the device. The current distribution in the superconducting spiral resonators can be computed by a numerical approach based on three-dimensional finite element method. This computed current distribution is used to produce a non-linear circuit model for the superconducting spiral resonator. Numerical technique based on harmonic balance approach is used for non-linear analysis of the proposed equivalent non-linear circuit. The model is proposed for coplanar waveguide (CPW) resonators, which can easily be extended for microstrip resonators. To confirm the accuracy of the proposed model, non-linearity in a 6-pole superconducting CPW spiral bandpass filter has been measured. Measurement results show good agreement with the ones from the model. This proposed technique is found to be a major approach for fast and efficient non-linear analysis of the superconducting spiral resonators and filters.