Ungleichförmige und zufällig geführte Mehrfachleitungen in komplexen, technischen Systemen

Abstract

Multiconductor transmission lines have an important influence on the electromagnetic com-patibility (EMC) and signal integrity of complex technical systems. In real life systems mostof these cables are nonuniform. These nonuniformities lead to differences if compared tothe properties of a uniform transmission line. This thesis describes numerical and semi-analytical methods to solve the transmission line equation for nonuniform lines which is anon-homogeneous system of first order differential equations with non-constant parameters.Formulas are given to obtain the matrizant (product integral) and the equivalent sourcevector. Transformations to scattering, propagation and admittance matrices are formulatedto use the results in network descriptions of complex cable harnesses. But for the applicationof these deterministic methods the geometric positions of all wires along the cable tube mustbe known. In the majority of cases these data are not available and may significantly varyalong the cable tube and between samples of a production series. These variations lead todeviation of transmission and EMC characteristics if compared to an ideal, deterministicsituation. In this thesis a Markov-model for a random multiconductor transmission line ispresented. For this model the first and second stochastic moments of voltages and currentscan be analytically calculated. On the basis of these moments the expected values, standarddeviations and covariances of (interference) voltages and currents or scattering parameterscan be computed.