Waveguide circuits with nearly arbitrary cross-sections

A new method is presented to compute the eigenmodes of rectangular waveguides with rounded corners. The boundary condition, the trigonometric and the Bessel functions in the solution of the wave-equation are all expanded in a Fourier series. The products of these series are reduced by convolution to a single series of periodic functions, which represents the eigenmodes. The coupling between subsequent sections of such waveguides is calculated by the mode-matching method. This leads to the design of optimized transitions of short length between rather different waveguides. Examples show excellent agreement between simulation and measurement