Harmonic balance algorithms for the nonlinear simulation of HTS devices

This paper describes the application of Harmonic Balance algorithms to predict nonlinear effects in planar High Temperature Superconductors (HTS) microwave circuits. The resulting algorithms are fast and efficient and can be used both for the characterization of the nonlinearities in the HTS material, and for the prediction of the behavior of an HTS circuit given the parameters of these nonlinearities (such as a dependence of the surface impedance on the current density). Most previously published nonlinear HTS models can be used, because the algorithms are not restricted to a specific model of HTS nonlinearities. Two different types of algorithms are described: (1) algorithms specific for one-dimensional resonators (transmission lines and TM010 disk resonators) and (2) an algorithm based on the combination of Method of Moments and Harmonic Balance, applicable to 2D planar structures with few restrictions in their shape. Several cross-checks with theory and measurements are presented.