Modeling Nonlinearity in Superconducting Interdigital Capacitors and Its Effects on Metamaterial Structures

Superconducting devices are known to indicate nonlinear behaviors such as harmonic generation and intermodulation distortion even at low input powers. In this paper, a nonlinear equivalent circuit model for a superconducting interdigital capacitor (SIDC) is proposed. A numerical approach based on a 3-D finite-element method is used to compute the current distribution in SIDCs. Then, closed-form expressions for kinetic inductance, resistance, and geometrical nonlinear factor of SIDCs are proposed. The proposed model can be analyzed nonlinearly by using a harmonic balance method to predict nonlinear phenomena. To validate accuracy of the proposed nonlinear model, nonlinearity in a superconducting metamaterial structure consisting of two SIDCs is predicted. A good agreement between calculated results and measured ones was found. Thereafter, based on the proposed model, other nonlinear behaviors of the considered structures are predicted, and based on our new method, effects of nonlinearity on main parameters of the superconducting metamaterial structure such as phase constant, attenuation factor, plasma frequency, permittivity, and permeability are analyzed.