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

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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 ci that encloses surface si shown between the reference conductor and the ith conductor gives

FIGURE 3.1 Illustration of the ...

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