Analysis and Simulation of the Effects of Distributed nonlinearities in microwave superconducting devices

Abstract—This paper presents a comprehensive study of mi-crowave nonlinearities in superconductors, with an emphasis on intermodulation distortion and third-harmonic generation. It contains the analysis of various resonant and nonresonant test devices and its validation using numerical simulations based on harmonic balance (HB). The HB simulations made on test devices show that the closed-form equations for intermodulation and third-harmonic genera-tion are only valid at low power levels. The paper also contains examples of application of HB to illus-trate that this technique is useful to simulate superconductive de-vices other than simple test devices, and that the validity of the simulations is not restricted to low drive power levels. Most of the analyses and simulations of this paper are based on electrical parameters that describe the nonlinearities in the super-conducting material. These parameters are compatible with many existing models of microwave nonlinearities in superconductors. We discuss the particulars on how to relate these electrical param-eters with one of the existing models that postulates that the non-linear effects are due to a dependence of the penetration depth on the current density in the superconductor. Index Terms—Harmonic balance (HB), intermodulation, nonlin-earities, superconductors. I