# 2

# THE TRANSMISSION-LINE EQUATIONS FOR TWO-CONDUCTOR LINES

In this chapter, we will show the derivation of the transmission-line equations for two-conductor lines from two points of view. First, they will be derived from the integral form of Maxwell's equations, and second they will be derived from the per-unit-length distributed parameter equivalent circuit. Both methods allow the incorporation of conductor losses. In Chapter 3, we will repeat this for a general (*n* + 1)-conductor multiconductor transmission line (MTL). The process will be identical to that for a two-conductor line, but the details will be a bit more tedious. Nevertheless, the transmission-line equations for an MTL, written using matrix notation, will be identical in *form* to those for a two-conductor line.

## 2.1 DERIVATION OF THE TRANSMISSION-LINE EQUATIONS FROM THE INTEGRAL FORM OF MAXWELL'S EQUATIONS

Recall Faraday's law in integral form [A.1,A.6]:

This is illustrated in Figure 2.1. The differential path length around the closed contour *c* that bounds the open surface *s* is denoted by . A differential surface area of surface *s* is denoted by , where is a unit normal to the surface. The direction of the contour *c* and ...