Use of the finite element method for the modeling of multi-layered power/ground planes with small features

In this paper, a novel formulation for the modeling of multi-layer package power/ground planes has been proposed. The formulation is developed by first applying the finite element method (FEM) for a single plane-pair geometry, from which a SPICE-compatible equivalent circuit is extracted. Next, the admittance matrices obtained for individual plane-pairs are coupled together, to extend the technique, and to enable the modeling of multiple plane-pairs. This method, the mutli-layer finite element method (MFEM), uses an adaptive triangular mesh. This enables MFEM to capture the effects of small geometrical features that can affect the frequency response, with only a modest increase in computational cost as compared to methods that use regular square meshes. MFEM is able to correctly model the effect of apertures or voids in the planes, which cause vertical coupling of energy. Several examples have been shown to illustrate the efficacy of the method for both single and multiple plane-pair geometries.