Novel spatial domain integral equation formulation for the analysis of rectangular waveguide steps close to arbitrarily shaped dielectric and/or conducting posts

In this paper, a novel integral equation formulation expressed in the spatial domain is proposed for the analysis of rectangular waveguide step discontinuities. The important novelty of the proposed formulation is that which allows to easily take into account the electrical influence of a given number of arbitrarily shaped conducting and dielectric posts placed close to the waveguide discontinuity. For the sake of simplicity, and without loss of generality, the presented integral equation has been particularized and solved for inductive rectangular waveguide geometry. In this case, the integral equation mixed-potentials kernel is written in terms of parallel plate Green's functions with an additional ground plane located on the waveguide step. Therefore, the unknowns of the problem are reduced to an equivalent magnetic surface current on the step aperture and equivalent magnetic and electric surface currents on the dielectric and conducting posts close to the discontinuity. The numerical solution of the final integral equation is efficiently computed after the application of acceleration techniques for the slowly convergent series representing the Green's functions of the problem. The numerical method has been validated through several simulation examples of practical microwave devices, including compact size band-pass cavity filters and coupled dielectric resonators filters. The results have been compared to those provided by commercial full-wave electromagnetic simulation software packages, showing in all cases a very good agreement, and with substantially enhanced numerical efficiencies.