Fast nonlinear eigenvalues analysis of arbitrarily shaped substrate integrated waveguide (SIW) resonators

In this paper, the problem of evaluating resonant frequencies of arbitrarily shaped substrate integrated waveguide resonators is considered. Resonances are found regarding them as nonlinear eigenvalues of the operator describing the scattering by metallic posts in a parallel plate waveguide. Nonlinear eigenvalues are usually computed by singular value decomposition. In order to save computational time, we propose an alternative approach derived by some general consideration on the theory of nonlinear eigenvalue problems in the discrete case. Results on rectangular, circular, and elliptical cavities are presented and compared with High Frequency Structure Simulator software package simulations. It is shown that the proposed method is efficient and accurate. Index Terms--Microwave resonators, nonlinear eigenvalue problems, singular value decomposition (SVD), substrate integrate waveguide (SIW).