Characterization of resonances by polar expansion of Generalized Admittance Matrix

An algorithm for the computation of resonances of lossless electromagnetic problems segmented into elementary blocks is presented. The method is based on the pole expansion of the Generalized Admittance Matrix (GAM) of each elementary block. Two quasi-static terms are extracted from the expansion in order to obtain a better convergence. The connection of all blocks composing a geometry can be realized in pole expansion format efficiently, without requiring a frequency sweep. This algorithm is used in the frame of the Transverse Resonance Method (TRM) in order to solve for the mode resonances of a radial waveguide. The procedure reduces to the solution of a linear eigenvalue problem instead of a transcendental equation. Once the results of the mode resonances are available the proposed algorithm is used to solve for the resonances of a dielectric resonator.