DC power-bus modeling and design with a mixed-potential integral-equation formulation and circuit extraction

Application of a circuit extraction approach based on a mixed-potential integral equation formulation (CEMPIE) for dc power-bus modeling in high-speed digital designs is detailed herein. Agreement with measurements demonstrates the effectiveness of the approach. Dielectric losses are included into the calculation of Green's functions, and thus, incorporated into the rigorous first principles formulation. A SPICE model is then extracted from the discretized integral equation. A quasistatic approximation is used for Green's functions to keep the extracted circuit elements frequency independent. Previous work has established a necessary meshing criterion in order to ensure accuracy for a given substrate thickness and dielectric constant to a desired frequency. Several power-bus design issues, such as surface mount decoupling and power-plane segmentation, were investigated using the modeling approach. The results and discussions illustrate the application of the method to dc power-bus design for printed circuit and multi-chip module substrates.