# 9

# TIME-DOMAIN ANALYSIS OF MULTICONDUCTOR LINES

In the previous chapter, we examined the time-domain solution of the transmission-line equations and the incorporation of the terminal constraints for two-conductor lines. We will extend those results to the case of lines composed of more than two conductors or multiconductor transmission lines (MTLs) in this chapter. We will find that the results of the preceeding chapter for two-conductor lines can be extended to the case of MTLs consisting of *n* + 1 conductors with *n* > 1 in a very straightforward manner using matrix notation.

## 9.1 THE SOLUTION FOR LOSSLESS LINES

In this section, we will examine the time-domain solution of the MTL equations for a *lossless line*:

where **L** and **C** are the per-unit-length inductance and capacitance matrices, respectively, and are of dimension *n* × *n*. The line voltages and currents are contained in the *n* × 1 vectors **V** and **I**. The uncoupled, second-order equations are

Note that the order of multiplication of **L** and **C** in these second-order equations must be strictly observed. The objective in this section is ...