The previous chapter was devoted to the analysis of two-conductor lines excited by an incident electromagnetic field that was generally in the form of a uniform plane wave. In this chapter, we will extend that analysis to multiconductor transmission lines (MTLs). Virtually all of the two-conductor line results in the previous chapter can be extended rather straightforwardly to the case of MTLs using matrix notation.

The derivation and solution of the MTL equations was considered in [H.1–H.5] and in [1–5]. A SPICE model for their solution was given in [H.10]. The MTL equations that we will obtain will be solved and the termination networks incorporated into that general solution in the usual fashion in order to determine the line currents *at the ends of the line*. The currents that are modeled with these MTL equations are, once again, *differential-mode* or *transmission-line currents* in that the sum of the currents directed in the +*z* direction on all *n* + 1 conductors is *zero* at any line cross section. In other words, the differential-mode currents of *n* of the conductors “return” on the reference conductor. In addition to these differential-mode currents, there can exist certain common-mode or antenna-mode currents that are not modeled by the MTL equations, as discussed in Chapter 1 [6]. So at points along the line there will be a combination of both currents, only one component of which (the differential mode) will be modeled by ...

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