Three-dimensional modeling for electromagnetically coupled microstrip antennas of arbitrary shape

Microstrip antennas have been used widely with advanced MIC/MMIC technology. This paper focuses on the modeling of three-dimensional microstrip antennas of arbitrary shape in multilayered media. Emphasis is placed on the mutual coupling effect between the vias and the radiation elements. A combined mixed potential integral equation (MPIE) and electric-field integral equation (EFIE) technique is presented to model vias of arbitrary shape. The MPIE method combined with the triangular patch expansion function has been proven efficient to model arbitrarily shaped planar geometries. To model the vertical current along the vias, instead of using the rectangular cells, the simple pulse function with a triangular cross section is used to approximate the current density. The EFIE formulation is adopted to evaluate the interaction between vias since the integration over the vertical axis can be done analytically.