Efficient Analysis of Compact Vias in an Arbitrarily Shaped Plate Pair by Hybrid Boundary-Integral and Finite-Element Method

Abstract

The hybrid boundary-integral equation and finite-element method (BIE/FEM) is efficient for signal/power integrity analysis of multiple vias in a shared antipad (labeled as compact vias) in an arbitrarily shaped power/ground plate pair. According to field distribution between the parallel plate pair, the computation domain of plate pair is decomposed into via domains and plate domain by using a domain decomposition approach. The higher order modes in the proximity of the antipads, which attenuate exponentially along the propagating direction and are confined in the via domains, are calculated by 3-D FEM. On the other hand, in the region outside the via domains, namely, the plate domain, only the zeroorder parallel plate modes need to be considered. The network parameters of the plate domain are solved by the boundary-integral method. By enforcing the field continuity conditions along with the segmentation interfaces between via domains and plate domain, the connection of the multi-mode networks of via domains and the impedance matrix of plate domain yields the S-parameter of the entire plate pair, which characterizes the complete noise coupling path from one via structure to another one. The accuracy and efficiency of the hybrid method are verified by comparing with a commercial full-wave solver. INDEX TERMS Boundary-integral equation, finite element method, hybrid method, parallel plate pair, signal/power integrity, compact via modeling.