A Surface Integral Equation Formulation for Efficient Simulation of Finite-Sized Multilayered Parallel-Plate Structure

The multilayered parallel-plate structure (MPPS) is a typical structure in microwave engineering. In numerical simulation, MPPS is usually modeled by an infinitely large planarly layered medium (PLM) to simplify the computation. For a realistic microwave circuit, however, the substrate is always finite in spatial extent, i.e., it is a finite-sized MPPS (FS-MPPS). To address this issue, a novel surface integral equation (SIE) formulation is proposed for the efficient simulation of FS-MPPS. In this article, the surface equivalence principle is first revisited. For the exterior and interior problems, different Green's functions are utilized. In particular, the common homogeneous-medium Green's function is used for the exterior homogeneous region, whereas the layered-medium Green's function (LMGF) is applied for the interior multilayered structure. In this manner, FS-MPPS is no longer directly approximated by the infinite PLM model, but instead, it is modeled accurately by SIE whose integration kernel is derived from PLM. Finally, a PMCHWT SIE is established for the electromagnetic analysis of FS-MPPS. Due to the finite nature of the inner problem, the setting of PLM and LMGF is not unique. This nonuniqueness is studied in theory and verified by numerical simulation. It is revealed that such a nonuniqueness of the setting of the inner problem does not change the uniqueness of the final solution. To validate the proposed approach, a multidomain FS-MPPS and an FS-MPPS with embedded dielectric structures are investigated. Compared with the conventional brute-force SIE methods for FS-MPPS, where all the interfaces of the layered structure should be discretized and assigned with degrees of freedom (DOFs), the proposed method is more succinct and efficient.