Analysis of Multiconductor Transmission Lines, 2nd Edition

3

THE TRANSMISSION-LINE EQUATIONS FOR MULTICONDUCTOR LINES

In Chapter 1, we discussed the general properties of all transmission-line equation characterizations. The transverse electromagnetic (TEM) field structure and associated mode of propagation is the fundamental, underlying assumption in the representation of a transmission-line structure with the transmission-line equations. These were developed in the previous chapter for two-conductor lines. In this chapter, we will extend those notions to multiconductor transmission lines (MTLs) consisting of n + 1 conductors.

The development and derivation of the MTL equations parallel the developments for two-conductor lines considered in the previous chapter. In fact, the developed MTL equations have, using matrix notation, a form identical to those equations. There are some new concepts concerning the important per-unit-length parameters that contain the cross-sectional dimensions of the particular line.

3.1 DERIVATION OF THE MULTICONDUCTOR TRANSMISSION-LINE EQUATIONS FROM THE INTEGRAL FORM OF MAXWELL'S EQUATIONS

Figure 3.1 shows the general (n + 1)-conductor line to be considered. It consists of n conductors and a reference conductor (denoted as the zeroth conductor) to which the n line voltages will be referenced. This choice of the reference conductor is not unique. Applying Faraday's law to the contour c_i that encloses surface s_i shown between the reference conductor and the ith conductor gives

FIGURE 3.1 Illustration of the ...