Computation of the Resonant Frequency and Quality Factor of Lossy Substrate Integrated Waveguide Resonators by Method of Moments

This paper presents a technique for the efficient and accurate determination of resonant frequencies and quality factors of Substrate Integrated Waveguide (SIW) resonators. To consider resonators of a general shape the SIW structure is modelled as a parallel plate waveguide populated with metalized via holes. The field into the SIW cavity is found solving the scattering problem for the set of vias into the parallel plate. Resonances are determined searching for the complex frequencies for which the determinant of the system of equations pertinent to the scattering is zero. To speed up the search, a first guess for the resonance frequency is found using an estimate of the minimum singular value of the system of equations. A Muller search in the complex plane is later used to accurately determine both frequencies and quality factors. Results relevant to resonators of various shapes are presented and compared with results obtained with a commercial code.