2D-FDFD with integrated via model for accurate simulation of PCBs and packages

This paper proposes a novel approach to directly integrate equivalent circuit models of vias in a 2D finite-differences frequency-domain method for the simulation of PCB and package structures. The via model serves two main purposes. First, it improves the accuracy of simulation results by modeling the modification of the local electric field in the vicinity of the via barrel. Second, it provides the coupling between different cavities, thus allowing to represent and solve a multilayer structure in a single 2D-FDFD system. In comparison to a related approach recently suggested in the literature, the procedure in this paper has two main advantages: First, it allows taking into account via barrel-to-plane capacitances at the proper positions in the equivalent circuit model, thus providing modeling accuracy. Second, its application to arbitrary numbers of cavities is straightforward. Both points are demonstrated with examples, showing good agreement to full-wave results up to 25 GHz.