# 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 *i*th conductor gives

**FIGURE 3.1** Illustration of the ...