Hybrid of Scattering Matrix Method and Integral Equation used for Co-simulation of Power Integrity and EMI in Electronic Package with Large Number of P/G Vias

The paper presents the development of a coupled scattering matrix method (SMM) with integral equation method for analyzing the power integrity (PI) of multilayered package structure with large number of power/ground vias. Analysis of the entire signal traces and the associated vias, connected between the power and ground, (named as P/G vias) is treated as analyzing the coupling between the external signal traces and the inside vertical vias, and analyzing the scattering effects between the vertical vias. A pair of the layered power/ground planes is considered as the parallel-plate waveguide structure. The scattering matrix method for the parallel-plate waveguide modes is developed by using the Foldy-Lax equations to analyze the scattering effects between the vertical P/G vias. The equivalent layered vias are modeled for the vertical vias connected between the power/grounds planes. The scattering matrices for coupling between the P/G vias including the signal vias are computed, and hence the outgoing wave coefficients for each via are calculated for power integrity analysis. The admittance (Y) matrix of a two-port network is modeled to represent the multiple scattering of the vertical P/G vias with the signal vias. The integral equation method is used to extract the equivalent circuit models for coupling between the external signal traces and the vertical vias. The extracted models are simulated together with the Y-matrix for signal response.