Equivalent network synthesis for via holes discontinuities

A methodology is presented for the synthesis of passive equivalent circuit of via holes in multilayers printed circuit boards. The paper describes the network synthesis starting from the extraction of the poles and residues from the driving point transfer functions for two ports networks. The via hole is partitioned into elementary structures assumed not electromagnetically coupled and the scattering parameters for each one of them are evaluated by using a numerical approach suitably validated by comparison with results computed by other independent numerical methods. The equivalent circuit of the complete via hole is given by the cascading of the circuits of the elementary structures. The proposed technique is validated by comparing the computed scattering parameters with those coming from the measurements for a real test boards.