Multiple scattering of microwaves from septum discontinuities in a circular bend

A wave splitting method is introduced to solve the problem of multiple scattering of microwaves from septum discontinuities in a circular waveguide bend of rectangular cross section. The splitting method allows that the scattering matrices for the septum discontinuities are determined by mode-matching and cascade techniques in a stable manner. We also demonstrate that the scattering coefficients converge as the number of expansion terms increases, and give criteria for the existence of trapped modes at the septum junction in the bend. The uniqueness in the solution is lost for a discrete set of frequencies where these trapped modes are present. For this case regularization methods are applied to make the solution numerically stable. Finally, numerical results are given for a model problem of two septum discontinuities in a bend. The algorithm presented here is suitable in the design of E-plane filters, where bends are present within the band pass filter.