Combination approach of FEM and circuit system in IR drop analysis and its applications

A method was developed to solve the combined system of the current field and the circuit. The “super-node” was used to transform the matrix for conventional nodal analyses of a circuit system from non-positive definite to positive definite. Then, a positive definite matrix for the overall system was obtained by combining the matrix from the circuit nodal analysis method and the matrix resulted from finite element method (FEM) formulation to solve the FEM fields. This approach has been successfully applied to simulate the electrical potential and current distributions on each metal layer of printed circuit boards (PCBs) and integrated circuit (IC) packages for a given power supply. The simulation results can then be used to analyze the properties of the PCBs and IC packages such as the port resistances and IR drops. The results can also be used to optimize PCB and IC package designs, such as by adjusting the power/ground distribution networks.