Modeling of multiple vias with a shared anti-pad in an irregular plate pair using domain decomposition approach

An irregular plate pair with multiple vias sharing an anti-pad is decomposed into top/bottom plate-thickness domain and parallel-plate domain whose admittance matrices are calculated by three-dimensional (3D) finite element method (FEM) and hybrid 3D/2D FEM. Combined admittance matrix algorithm is used to obtain the final admittance matrix of the plate pair including finite thickness plates. The widely-used assumption of transverse electromagnetic (TEM) modes on anti-pads is carefully investigated by comparing the combined admittance matrix algorithm with hybrid 3D/2D FEM. It is found that higher-order modes are excited on anti-pads and in practical printed circuit board, the higher-order modes can penetrate from one layer of plate pair to another layer. This may provide guidance for future research for multiple vias in a shared anti-pad.