An efficient analysis of lossy substrate integrated waveguide resonators

An efficient and accurate technique to determine resonant frequencies and quality factors of lossy Substrate Integrated Waveguide (SIW) resonators is presented. The SIW structure is modeled as a set of metalized via holes placed into an infinite parallel plate waveguide. The characterization of the resonators is obtained considering the mutual scattering by metallic via holes. Field inside the parallel plates is expanded in terms of cylindrical vector wave functions and resonances are determined considering the system of equations relevant to the scattering by the vias and locating the frequencies for which the corresponding homogeneous system of equations has non trivial solution. Resonant frequencies and quality factors have been evaluated using an efficient technique based on an estimate of the minimum singular value (SVD) of the system, combined with a Muller search in the complex plane. Results relevant to rectangular resonators are presented and compared with results obtained with a commercial code.