Nonlinearity in superconducting metamaterial structures, including spirally coupled lines

Superconducting devices can indicate nonlinear behaviors such as harmonic generation and intermodulation distortion (IMD) with regard to nonlinear Meissner effect even at low input powers. Firstly in this paper, a new method for nonlinear modelling of Superconducting Transmission Lines (SMTLs) with complex coupling is proposed. Then, based on the proposed new method, nonlinear equivalent circuit model for Superconducting Spirally Coupled Lines (SSCLs) is suggested. A numerical approach based on three-dimensional finite element method (3D-FEM) is used to compute the current distribution in SSCLs. Closed-form expressions for quadratic and modulus geometrical nonlinear factors (GNFs) of SSCLs are proposed. The proposed model can be analyzed nonlinearly by using of Harmonic Balance (HB) method to predict nonlinear behaviors. To validate the accuracy of the proposed nonlinear model, we modeled a superconducting metamaterial filter consisting of two SSCLs in this paper. Good agreement between calculated results and measured ones was found. Thereafter, based on the proposed model, effects of nonlinearity on main parameters of the superconducting metamaterial structure such as phase constant (β) and attenuation factor (α) are analyzed.