Efficient Integral Equation Analysis of Arbitrarily Shaped Rectangular Waveguide Discontinuities Including Conducting Objects

In this contribution, an Integral Equation (IE) formulation is proposed for the analysis of microwave circuits, based on the junction of two different rectangular waveguides coupled by an arbitrarily shaped zero thickness discontinuity. These rectangular waveguides could include an unlimited number of conducting elements with arbitrary shapes inside them. To solve the IE, the problem is split into two equivalent subproblems, each of which is related to a rectangular waveguide. Subsequently, an equivalent surface magnetic current density ($\vec{\mathrm{\mathbf{M}}}_{\text{ap}}$) defined at the discontinuity is used to connect the equivalent problems of each rectangular waveguide. In order to reduce the number of unknowns, the Lorenz gauge Green's functions of rectangular waveguides and their spatial derivatives are used to model the boundary conditions. In addition, the Ewald method has been employed to significantly speed up the evaluation of these rectangular waveguide Green's functions. Therefore, the use of this surface magnetic current density can reduce in some configurations the number of unknowns compared to an alternative Electric Field Integral Equation (EFIE). In addition, it allows a simpler analysis of some kind of discontinuities with respect to an EFIE method. Finally, the proposed technique has been validated by comparison with the results provided by commercial full-wave software tools such as Ansys HFSS and CST Studio Suite, showing good agreement and a better numerical efficiency.