Modeling Method for Analysis of the Current Density Distribution and IR Drop in Traces of the Printed Circuit Board

The proposed modeling method is based on the vertex-centered finite volume method. The vertex-centered strategy is used to generate control volumes after analyzing the pixel information of the trace layout, particularly for identifying the solutions at the boundary region. By applying Gauss's Divergence Theorem and Taylor series truncation with 2
^nd
order precision, the integration form of the continuity equation is approximately simplified to a linear relationship between the electric potentials of cell vertices. After the electric potential distribution is identified, the current density distribution can be further derived using finite difference approximation. The 45° inclined linear boundary can be implicitly reconstructed through modeling. Based on the modeling method, a test solver was programed in MATLAB. To verify the method's feasibility, a trace layout was simulated using both the test solver and COMSOL Multiphysics.