Analysing and modelling non‐linearity in superconducting metamaterial filter based on stepped impedance resonators

Abstract

There are non‐linear behaviours in superconductive circuits such as superconducting metamaterial filter. In this study, the authors propose a distributed non‐linear equivalent circuit model for the superconducting metamaterial filter based on the stepped impedance resonator. This model can be used to predict the non‐linear behaviours like the third‐order intermodulation distortion and the harmonic generation. In the proposed non‐linear model, to have an accurate prediction, the authors considered both quadratic and modulus non‐linearity dependence on the current. Thereafter, this model analyses the non‐linearly using harmonic balance (HB) method at different temperatures and different input powers. There are good agreements between non‐linear simulation results and the measured ones. Moreover, based on the proposed model, the authors consider effects of the non‐linear behaviours on main parameters in the metamaterial structures such as phase constant, attenuation factor, plasma frequency, relative permittivity and permeability. Finally, the results related to variation of these parameters at different temperatures and specific input power are presented in linear and non‐linear regimes.