Design of cross-coupled substrate integrated waveguide filters with the mode-matching and finite element methods

A mode-matching (MM) formulation based on rectangular waveguide mode expansion is presented for the fast and accurate analysis of circular via hole rows in substrate integrated waveguide (SIW) filters. To ensure the full flexibility in positioning of the via holes this method is combined with the two-dimensional finite element method (2D FEM) without significant reduction in speed and accuracy. This numerical technique is applied to cross-coupled SIW filters utilizing TE₂₀₁/TE₁₀₁-mode cavities for the generation of additional transmission zeros (TZ). A five-pole filter design with three TZs is taken as example and verified by the three-dimensional finite element method (3D FEM).