Analysis of PCB level EMI phenomena using an adaptive low-frequency plane wave time domain algorithm

A novel integral equation based algorithm is proposed that permits the analysis of PCB-level EMI phenomena. The algorithm is based on the multilevel plane wave time domain algorithm (PWTD). For a problem of N _T temporal and N_S spatial unknowns involving no sub-wavelength features, the multilevel PWTD algorithm reduces the O(N _TN_S²) computational cost of a classical marching-on-in-time (MOT) algorithm to O(N_TN_Slog ²N_S). However, PCB structures with fine geometrical details such as very thin slots, closely spaced vias or pins, etc., call for a highly non-uniform spatial discretization of the problem domain. In such cases, a straightforward implementation of the multilevel PWTD scheme cannot achieve a reduced computational complexity. Here, an adaptive low-frequency PWTD algorithm is described to solve this problem. Numerical results are presented to demonstrate the applicability of the scheme to the EMI analysis of complex PCB problems