A Mixed Approach for Solving Volume-Surface Integral Equations in the Analysis of Microstrip Antenna and Packaging Structures

Electromagnetic analysis for microstrip antenna and packaging structures is formulated by volume-surface integral equations (VSIEs). The conducting microstrip and ground are described with SIEs, while the dielectric substrate is governed by volume integral equations (VIEs), and they are coupled to each other to form VSIEs. Using VIEs instead of SIEs for dielectric substrate can improve the conditioning of system matrix related to the multiscale property of antenna and packaging structures. The VSIEs are usually solved by the method of moments (MoM) with well-designed basis functions defined over conforming meshes, resulting in much inconvenience of implementation. We propose a mixed approach to solve the VSIEs by combining the traditional MoM for the conducting part and a point-matching scheme for the dielectric part together. The approach uses cuboids to discretize the dielectric substrate and does not require conforming meshes between the conducting and dielectric parts. Also, the approach considers the thickness of metallic microstrip and ground, which is usually neglected. Typical numerical examples are presented to demonstrate the proposed approach, and its effectiveness has been verified.