Electromagnetics, Microwave Circuit, and Antenna Design for Communications Engineering, Second Edition

A multiconductor transmission-line is a transmission-line with more than two parallel cylindric conductors as shown in Figure 7.13. In a multiconductor transmission-line all conductors are mutually coupled and signals are coupled from one conductor to the other. If the coupling is unintended this effect is referred to as crosstalk. Multiconductor transmission-lines play a role in flat cables for high-speed data transfer, in printed circuit boards, and in monolithic integrated circuits. Multiconductor transmission-lines are treated in detail in [6 10].
In this section the tem modes of multiconductor transmission-lines filled with homogeneous isotropic dielectric are treated. It will be shown that in the homogeneous multiconductor transmission-line with n +1 conductors n TEM modes can propagate. All these modes propagate with the same velocity, that is, the TEM plane wave velocity c for the dielectric material given in (2.75).
Figure 7.13 gives a schematic view of the general cylindric multiconductor transmission-line. The current flowing in the kth conductor in positive z-direction is i k( z, t) and the voltage from conductor k to conductor l is v k 1 ( z, t). Usually a transmission-line is operated in such a way that the sum of the currents through all conductors vanishes. Therefore, for a multiconductor transmission-line with n +1 conductors only n currents can be chosen independently. Also from the
( n +1) n voltages v k 1( z, t