Rigorous, multimode equivalent network representation of inductive discontinuities

The theoretical derivation of the equivalent networks has been carried out by following the rigorous procedure used by M. Guglielmi and A.A. Oliner (1989) for the case of a metal strip grating at an air-dielectric interface. Following this procedure, network representations involving multimode coupling matrices are found in terms of the solution of a singular integral equation. The solution to this equation is shown to be known so that rigorous, multimode equivalent network representations for zero-thickness inductive windows and inductive obstacles in a rectangular waveguide can be derived. The network representations developed are valid for arbitrary aperture/obstacle dimensions and offset, and can accommodate a different medium on each side of the discontinuity. The analytic expressions obtained involve double integrations which are easily evaluated numerically. Numerical results are also presented indicating that the network representations developed are rapidly convergent so that they can be easily used to carry out computations involving an arbitrary number of propagating higher-order modes