Fast S-Parameter TAN Model of n-Port Lumped Structures

Abstract

This paper deals with the fast S-parameter modeling of multi-port lumped structures. The developed model is based on unfamiliar formalism using the tensorial analysis of networks (TAN). The modeling methodology is described with the general abstract topology and different application cases. The methodology consists, first, in elaborating the equivalent graph topology of the considered problem. Then, it is followed by the TAN mathematical abstraction, including, successively, the branch and mesh space analyses. The problem metric can be written with the tensorial Ohm's law expressed in function of the covariant voltage, contravariant current, and the twice covariant impedance in the mesh spaces. The equivalent Z-matrix of the considered multi-port structure is established from an innovative reduction method of the mesh impedance. The S-parameter model is extracted from the Z-to-S matrix transform. The effectiveness of the established fast S-parameter TAN modeling is validated with three cases of proof of concept constituted by TT-cell, the TTT-cell two-port circuit, and four-port structure inspired from the 3D coaxial shielded cable. As expected, an excellent agreement between the S-parameters calculated from the TAN model and simulated from the commercial tools from DC to some hundred's megahertz is obtained. In the future, the developed model is outstandingly beneficial for fast and accurate applications notably for the conduced shielded cable electromagnetic compatibility analysis.