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Transmission Lines in Digital Systems for EMC Practitioners by Clayton R. Paul

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Chapter 3

Frequency-Domain Analysis of Two-Conductor Lines

In this chapter we examine the frequency response of a two-conductor transmission line to a single-frequency sinusoidal source: img. The time-domain line voltages and currents, img and img, at each point along the line, z (generally of interest only at the line terminals), are to be determined and are similarly single-frequency sinusoids at the same frequency as the source and have a magnitude and a phase angle that are functions of their position along the line, z.

To simplify the solutions for the line voltage and current, we examine the steady-state phasor response of the line, as illustrated in Fig. 3.1. We replace the time-domain source with the complex, phasor source (denoted with a caret) as

(3.1) equation

Figure 3.1 Sinusoidal steady-state (phasor) solution.

img

Similarly, the line voltages and currents are replaced with their phasor forms:

(3.2a)

(3.2b)

3.1 The Transmission-Line Equations for Sinusoidal Steady-State (Phasor) Excitation ...

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