An effective modeling method for multi-scale and multilayered power/ground plane structures

As more packages or chips are integrated into a single system in recent electronic designs, power/ground planes tend to contain numerous and diverse features than ever, such as via holes, small apertures, plane gaps, etc. Although dimensions of these features are usually very small compared to the power/ground planes, their influence on the power delivery network cannot be neglected. However, power/ground plane analysis methods using square or rectangular meshes, such as multilayer-finite difference method, can generate large number of unit cells for small features in a large design. Multi-scale structures can be effectively meshed by using triangular mesh scheme, which can then be solved using finite element method (FEM). However, it is difficult to include external circuit elements to FEM, since the equivalent circuit model of FEM is not physically intuitive. In this article, a new modeling method, multilayer triangle element method, which is efficient for solving multi-scale and multilayer power/ground plane structures with external circuit elements, is presented.