Lumped models for Vias in multilayered PCBs

In this paper, lumped models for vias in multilayered PCBs and their extraction are presented. Thereby, the model elements are derived from physics. It is possible to estimate the parameters of the lumped models using analytical formulas, but more precise values can be derived from vector network analyser measurements or 3d-field solver computations of a real via geometry. Two method for the extraction of the via model parameters from these reference data are presented. Thereby, calculations with two-port theory, network theory, a de-embedding algorithm and different optimisation algorithm are used.