Hybrid-mode analysis of a microstrip-slot resonator

A hybrid-mode analysis is presented for obtaining resonant frequencies of a microstrip resonator with a tuning slot; namely, a microstrip-slot resonator, which has a microstrip and a tuning slot on each side of the substrate, respectively, and whose special case is a microstrip resonator. The analysis is based upon Galerkin's method in the Fourier transform domain. The sensitivity of the solution is investigated with respect to the basis functions. The computed resonant frequencies, using simple basis functions, are compared with the experimental values on alumina substrate in the frequency range 3?7 GHz.