A Hybrid Method to Study the Substrate Integrated Waveguide Circuit

A hybrid method is proposed to study the substrate integrated waveguide circuit. It combines the eigen function expansion method and the method of moments. The field scattered by a cylinder, either dielectric of metalic, is expanded by a series of cylindrical eigen functions. Those field due to a given cylinder can be easily transformed onto the surface of another cylinder by applying the additional theorem of the Hankel or Bessel functions. The waveguide port is treated in a method of moments way. It is divided into many sub-ports, each with a constant current density. The evaluation of the field observed on a sub-port and due to a sub-port is the same as the traditional method of moments. The evaluation of the field observed on a cylinder surface due to a sub-port is done by dividing the sub-port into many line sources at different locations, and applying the coordinate system transformation. A rectangular matrix is constructed after applying the boundary conditions and the orthogonality of the exponential functions, and the final S matrix can be obtained using matrix partitioning and manipulations. As examples, two substrate integrated waveguide filters are successfully studied by using the proposed method, and the results are verified by using HFSS.