On the application of complex resistive boundary conditions to model transmission lines consisting of very thin superconductors

A resistive boundary condition for the case where the resistivity is assumed to be a complex quantity is shown to be an accurate model for a superconducting film which is thin compared to the super-conducting penetration depth. The imaginary part of the conductivity is the dominant terms and is a measure of the inductive energy stored in the superconductor. Numerical solutions of superconducting microstrip are obtained and compared to experimental results and to analytic solutions for superconducting parallel-plate waveguides. Excellent agreement is found between experimental, analytical, and numerical results