Circuit synthesis techniques of rational models of electromagnetic systems: A tutorial paper

This work aims to review the state of the art of the most important circuit synthesis techniques of rational approximation of electromagnetic multiport systems in order to incorporate them into a circuit simulator. In particular, equivalent circuits for the state‐space or for the pole/residue representation of impedances, admittances, and scattering parameters are reviewed in details. Furthermore, a novel contribution is given to show how it is possible to migrate from a state‐space (S,Y,Z) representation to another one by applying different matrix transformations. The resulting equivalent circuits can then be connected to linear/nonlinear devices or lumped elements in a Spice‐like framework allowing to analyze mixed electromagnetic/circuit problems. The validity of all the presented equivalent circuits and state‐space transformation is tested through two pertinent numerical examples. Pseudocodes are provided in order to make the reader able to easily implement the revised synthesis techniques.