Accurate Field-Circuit Hybrid Modeling of High-Density Through Glass Via Arrays by Using Perfect Magnetic Conductors and Cylindrical Mode Expansion

In this paper, an accurate wideband modeling approach based on a cylindrical mode expansion of electromagnetic filed around perfect magnetic conductors (PMCs) is proposed to analyze the electrical properties of high-density through glass via (TGV) arrays. An accurate equivalent circuit of high-density TGV arrays is derived based on the results of the proposed cylindrical mode expansion method. Meanwhile, the PMC boundary used in the cylindrical mode method greatly simplifies the corresponding equivalent circuit of TGV arrays. The accuracy and the efficiency of the proposed field-circuit hybrid method are fully validated by comparing it with 2-D quasi-static, 3-D full-wave simulations, and published measurement results. As the method fully captures the scattering and multireflection effects between the vertical cylindrical vias, a very good correlation is obtained between the electrical behaviors obtained by using the proposed method and that by using the 3-D full-wave simulation.