The single-phase, two-wire lossless line in Figure 13.3 has a series inductance \(\mathrm{L}=0.999 \times 10^{-6} \mathrm{H} / \mathrm{m}\), a shunt capacitance \(\mathrm{C}=1.112 \times 10^{-11} \mathrm{~F} / \mathrm{m}\), and a \(60-\mathrm{km}\) line length. The source voltage at the sending end is a \(\operatorname{ramp} e_{\mathrm{G}}(t)=\mathrm{E} t u_{-1}(t)=\mathrm{E} u_{-2}(t) \mathrm{kV}\) with a source impedance equal to the characteristic impedance of the line. The receiving-end load consists of a \(150-\Omega\) resistor in parallel with a \(1-\mu \mathrm{F}\) capacitor. The line and load are initially unenergized. Determine

(a) the characteristic impedance in \(\Omega\), the wave velocity in \(\mathrm{m} / \mathrm{s}\), and the transit time in \(\mathrm{ms}\) for this line;

(b) the sending- and receiving-end voltage reflection coefficients in perunit;

(c) the Laplace transform of the sending-end voltage, \(\mathrm{V}_{S}(s)\); and

(d) the sending-end voltage \(v_{\mathrm{S}}(t)\) as a function of time.

Figure 13.3

Transcribed Image Text:

Eg(s) Z(s) X = 0 Za -1(x, s) V(x, s) X-! ZAIS)