Phenomenological theory of intermodulation in HTS resonators and filters

Recent work on nonlinear effects in microwave resonators and filters from high temperature superconductors, focusing on intermodulations, is reviewed. We calculate the intrinsic nonlinear response of s-wave and d-wave superconductors. A phenomenological description of the lowest order nonlinear behavior in high-T-c films in terms of a single parameter, j(IMD), is proposed. We show how this description can be used to calculate the intermodulation power arising in realistic microstrip resonators. These calculations show good agreement with measurements on hairpin resonators. This description can also be used for the modeling of nonlinear behavior of complex microwave filters.