Hybrid of Method of Moments and Cylindrical Eigenfunction Expansion to Study Substrate Integrated Waveguide Circuits

A hybrid method that combines method of moments (MOM) and cylindrical eigenfunction expansion is presented to study a substrate integrated waveguide circuit that consists of metallic and dielectric circular cylinders. The problem is considered as a 2-D electromagnetic problem assuming no field variation normal to the dielectric substrate. The scattered field from each circular cylinder is expanded by cylindrical eigenfunctions, and the equivalent current densities at a waveguide port are expanded using the MOM. After enforcing boundary conditions and applying the additional theorem of Bessel and Hankel functions, a set of linear equations are constructed using the orthogonality of the exponential function. With matrix manipulation and sub-ports combination, the S matrix can then be obtained. Four examples are analyzed by using the hybrid method and verified by using Ansoft Corporation´s commercial High Frequency Structure Simulator (HFSS) software package. It is shown that the hybrid method runs faster than HFSS and requires less memory. It is also pointed out that the method can be used to study a circuit with noncircular cylinders.