Overview

In this chapter we model three electrical transmission systems: a coaxial cable, a strip line, and two parallel wires, which can be used to transfer both signals and power. Our models will employ familiar electrical circuit elements: inductors, capacitors, and resistors. The equations that describe the propagation of the voltage and current signals along these transmission lines are called the telegraphers' equations. These equations were obtained in the mid-to-late 1800's to describe the propagation of telegraph signals along the long copper cables connecting the United States with Europe under the Atlantic Ocean, as well as spanning the United States on poles from coast to coast. From the telegraphers' equations we can derive another important equation called the wave equation. This equation describes how waves propagate from one point to another, and will turn out to be valid whether the waves move along a transmission line or are radiated into space.

However, although we are using familiar circuit components, under certain circumstances we require several extensions to the circuit theory we have previously studied. First, the energy transfer associated with the signals moving through our circuit model takes a small, but measurable, amount of time. Thus, we need to incorporate the propagation time into our equations explicitly to account for this effect. Second, instead of using the common discrete or "lumped" electrical components that we are familiar with from circuit theory, we will be using distributed circuit elements to explain why the signals require a finite amount...