Modeling and simulation in multiconductor transmission line theory

Multiconductor transmission lines (MTLs) are an indispensable part in the treatment of complex EMC problems. A numerical model for transmission lines can be based to a large extent on analytical solutions. This has the great advantage that computing time is reduced. Usually analytical solutions for uniform and nonuniform MTLs are incorporated in the analysis of networks of different kinds. This may be networks occurring in Electromagnetic Topology on the basis of a generalized BLT equation as well as usual networks with lumped elements, including nonlinear ones. Our representation is divided into two parts: The first part deals with EM-Topology, invented by Baum, Liu and Tesche, and further developed by Parmantier et al. The second one includes nonuniform MTLs into a network analysis which roots in contributions from Singer et al. We begin with EM-Topology, explaining the breakdown of a complex electromagnetic problem into several smaller problems, using an aircraft which is excited from outside. Topological and interaction graphs for the different coupling steps from outside to inside the system are described, finally resulting into a very general structure equation (the generalized BLT equation). In this equation two supermatrices play an important role: the scattering- and propagation-supermatrices. It is emphasized that the junction characterization with the aid of the scattering matrix can be performed with various methods, e.g. MoM, FDTD, analytical solutions or experiments, to name only a few of those methods. On the other hand, the tube characterization to obtain the propagation matrix still takes place in the framework of MTL theory. But also in this context more generalized ansaetze are in preparation. The solution of the BLT equation with the CRIPTE code applied to an example concludes the first part of our paper. In the second part of our presentation we focus on the treatment of nonuniform MTLs in time- and frequency domain network simulations. In both cases the solution of the telegrapher equations are used to establish equivalent networks. In time domain controlled current sources are added to the network at both ends of the lines, whereas in frequency domain the line is taken into account by a two-port with three impendances in II-arrangement. A generalized Bergeron-procedure is applied to calculate lossy and nonuniform lines in time-domain. In frequency-domain the matrizant approximation for nonuniform MTLs is related to the corresponding chain matrix of the line which in turn is used as basis to estimate the ingredients of the equivalent network. Examples in both domains are studied and serve as elucidation of our procedure.