# 6

# FREQUENCY-DOMAIN ANALYSIS OF TWO-CONDUCTOR LINES

In this chapter, we will examine the solution of the transmission-line equations for two-conductor lines, where the line is excited by a single-frequency sinusoidal signal and is in steady state. The analysis method is the familiar phasor technique of electric circuit analysis [A.2, A.5]. The excitation sources for the line are single-frequency sinusoidal waveforms such as *x*(*t*) = *X*cos (*ωt* + *θ*_{X}). Again, as explained in Chapter 1, the reason we invest so much time and interest in this form of line excitation is that we may decompose any other *periodic* waveform into an infinite sum of sinusoidal signals that have frequencies that are multiples of the basic repetition frequency of the signal via the Fourier series. We may then obtain the response to the original waveform as the superposition of the responses to those single-frequency harmonic components of the (nonsinusoidal) periodic input signal (see Figure 1.21 of Chapter 1). In the case of a nonperiodic waveform, we may similarly decompose the signal into a continuum of sinusoidal components via the Fourier transform and the analysis process remains unchanged. An additional reason for the importance of the frequency-domain method is that losses (of the conductors and the surrounding dielectric) can easily be handled in the frequency domain, whereas their inclusion in a time-domain analysis is problematic as we will see in Chapters 8 and 9. The per-unit-length resistance of the ...