Modelling nonlinearity in superconducting split ring resonator and its effects on metamaterial structures

•Proposing nonlinear circuit models of the superconducting split ring resonator to predict nonlinear behaviours.•Analytical formulation for each parameter in our proposed model.•Create fast and accurate analysis of the nonlinearity in superconducting microwave structures consist of split ring resonators such as superconducting meta-material filters.•We analyzed the effects of nonlinearity on main parameters of the superconducting meta-material structure such as phase constant (β), attenuation factor (α).•Obtaining very good results in comparison with measured ones which shows this model can predict nonlinear behaviour. Superconducting materials are intrinsically nonlinear, because of nonlinear Meissner effect (NLME). Considering nonlinear behaviors, such as harmonic generation and intermodulation distortion (IMD) in superconducting structures, are very important. In this paper, we proposed distributed nonlinear circuit model for superconducting split ring resonators (SSRRs). This model can be analyzed by using Harmonic Balance method (HB) as a nonlinear solver. Thereafter, we considered a superconducting metamaterial filter which was based on split ring resonators and we calculated fundamental and third-order IMD signals. There are good agreement between nonlinear results from proposed model and measured ones. Additionally, based on the proposed nonlinear model and by using a novel method, we considered nonlinear effects on main parameters in the superconducting metamaterial structures such as phase constant (β) and attenuation factor (α).