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

Abstract

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 by 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.

Accurate modelling of lossy SIW resonators using a neural network residual kriging approach

“…Cavity resonances f r are the real part of the complex frequencies " f r for which (1) admits a non-trivial solution when the second member is equal to zero [9]. Once that a " f r has been located, the related quality factor Q r can be easily computed as [3] …”

“…which arises by imposing the impedance boundary condition on the surfaces of each via hole realizing the cavity walls [3]. Cavity resonances f r are the real part of the complex frequencies " f r for which (1) admits a non-trivial solution when the second member is equal to zero [9].…”

“…As stated in [3], the electromagnetic field inside a lossy SIW cavity can be evaluated by using the dyadic Green's function of the lossy parallel plate waveguide (PPW), and considering the scattering phenomenon due by the metallic via holes realizing the walls of the resonator. The scattered field can be represented by means of suitable cylindrical vector wave eigenfunctions M n , N n [3] having unknown coefficients A TE m;n;l (A TE m;n;l ) (the apex TM and TE indicate the TM and the TE scattered field inside the PPW, respectively). The expansion coefficients A TM m;n;l (A TE m;n;l ) are determined through the solution of the following matrix linear system [3] …”

“…The scattered field can be represented by means of suitable cylindrical vector wave eigenfunctions M n , N n [3] having unknown coefficients A TE m;n;l (A TE m;n;l ) (the apex TM and TE indicate the TM and the TE scattered field inside the PPW, respectively). The expansion coefficients A TM m;n;l (A TE m;n;l ) are determined through the solution of the following matrix linear system [3] …”

“…Cavity SIW resonators are microstrip-like structures having walls realized by cylindrical metallic vias [1]. In [3] an effective method to handle cavity SIW with losses, based on the dyadic Green's function of the lossy parallel plate waveguide, has been presented. To reduce the computational burden associated with the design and the optimization of these devices in [4,5,6] several surrogate modelling technique able to estimate the fundamental resonant frequency f r and the related quality factor Q r for these structures, have been exploited.…”