Electromagnetic Modeling of PCB Based on Darwin's Model Combined With Degenerated Prism Whitney Elements

Due to the advancement in the development of semiconductors used in the power converters, the printed circuit boards (PCBs) require an in-depth study of their electromagnetic behavior. To characterize the behavior of the PCBs, the Darwin model is employed, which can take into account all the coupled effects, namely resistive, inductive, and capacitive effects, at the intermediate frequencies. Nevertheless, the study of particular structures having a geometric dimension smaller than the others can create meshing difficulties. The modeling of thin structures by the finite element method requires the optimization of the mesh. To circumvent this issue, the shell elements for both node and edge elements are applied in this work. Finally, to validate the proposed approaches, two PCBs with different geometries are studied in both time and frequency domains, where the measurements for a single PCB are provided to compare with the numerical results.