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Analysis of Multiconductor Transmission Lines, 2nd Edition by Clayton R. Paul

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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]:

images

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 images. A differential surface area of surface s is denoted by images, where is a unit normal to the surface. The direction of the contour c and ...

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