Generalized Scattering Matrix of the discontinuity between an equilateral triangular waveguide and a rectangular, circular or elliptical waveguide

The full-wave analysis of the discontinuity between an equilateral triangular waveguide and other analytical larger waveguide with rectangular, circular or elliptical cross-section is presented. The equilateral waveguide can be shifted and/or rotated with respect to the other waveguide, providing a great flexibility for the design of microwave components such as transformers, filters or double-polarization components. Furthermore, the presented quasi-analytic formulation, unified for the three cases throughout the use of plane wave series, is very efficient and can be integrated in hybrid solvers for full-wave optimization. The Mode-Matching technique is employed for analyzing the basic discontinuity and the inner cross products between the modes are computed by means of their plane wave representation in the different waveguides. The simulation results are compared with those obtained by other numerical techniques.