Analytical Models for Calculating the Time Response of a Four-Conductor Transmission Lines in Differential and Common Modes

Abstract

The paper considers the solution of one of the problems of electromagnetic compatibility to perform analysis of signal propagation in interconnections. An analytical approach is presented that is based on the method of modal analysis to calculate the time response in a four-conductor transmission line (TL) in differential and common modes. For the first time, analytical models have been derived to calculate the time response at the output of such a TL. The models take into account the asymmetry of the TL cross section along one plane and multiple signal re-reflections in the TL. Based on these models, we obtained the analytical condition for equalizing the pulse amplitudes of modes 3 and 4 for differential and modes 1 and 2 for common mode, provided that the loads on both ends are the same. Testing this analytical condition showed that it allows finding such values of termination loads separately for differential and common mode, which provides equality of amplitudes. In this case, it is necessary to know only the matrices of primary parameters, while the calculation of the time response is not required.