Numerical solution of the continuous waveguide transition problem

A simple transition between two sizes of rectangular waveguide is analyzed using the generalized telegraphist's equation. Solutions are obtained using a new moment method technique, a Runge-Kutta algorithm, and an iterative numerical integration technique. The results are compared to previously published experimental and numerical data. It is found that the numerical stability, accuracy, and consistency of the results are critically dependent on the choice of weighting and expansion functions. The best results for a simple rectangular-to-rectangular transition were obtained when Galerkin's method and triangle expansion functions were applied to several short sections which were then cascaded. Unlike the Runge-Kutta technique or the integration technique, the Galerkin's method procedure did not result in instabilities with the inclusion of evanescent modes. The programs can, in fact, be extended to any number of modes, the only apparent limitations being the obvious ones of computer time and memory.>