Theory of intermodulation in a superconducting microstrip resonator

The penetration depth and surface resistance of a superconductor depend upon the superfluid current density. This dependence gives rise to nonlinear mixing in a superconducting microstrip resonator. Here we discuss the problem of intermodulation in which two signals at omega(1) and omega(2), laying within the pass band of a microstrip cavity resonance, mix and generate a signal at 2 omega(1)-omega(2). An expression relating the power generated at 2 omega(1)-omega(2) to the power transmitted at omega(1) and omega(2) is given. We focus on the high-T-c superconductors where it is believed that the order parameter has d(x2-y2) symmetry. We find for a resonator with a large unloaded Q that intermodulation arises dominantly from the reactive nonlinear inductance of the superconducting film. (C) 1997 American Institure of Physics.