Consider an underground cable line 1.6 km long with a characteristic impedance of 50 Ω and a wave propagation velocity of 1.6·10^8 m/s. The line is connected to the d.c. ideal Zs = 0 voltage source V0 = 1000 V and terminated in a 200 Ω resistor. (a) Determine the reflection coefficients at the

Question

Consider an underground cable line 1.6 km long with a characteristic impedance of 50 Ω and a wave propagation velocity of [latex]1.6·10^8 m/s[/latex]. The line is connected to the d.c. ideal [latex]Z_s = 0[/latex] voltage source [latex]V_0 = 1000 V[/latex] and terminated in a 200 Ω resistor. (a) Determine the reflection coefficients at the sending- and receivingends; (b) Draw the appropriate lattice diagram for voltage and current; (c) Determine the value of voltage and current at [latex]t=5.5t_r and x = (1/4)\ell; [/latex] (d) Plot the voltage and current versus time at line point [latex]x=(1/2)\ell. [/latex]

Accepted Answer

(a) The reflection coefficients are

[latex] \rho _s=\frac{Z_s−Z_c}{Z_s+Z_c}=\frac{0-50}{0+50} =-1, \rho _r=\frac{Z_T-Z_c}{-Z_T-Z_c}=\frac{200-50}{200+50}=0.6. [/latex]

(b) The traveling time is

[latex]t_r =\frac{1.6·10^3}{1.6·10^8}=10 \mu s [/latex]

The lattice diagram is shown in Fig. 7.21(a). The values of the voltage/current traveling waves are written above the arrows.

(c) From the lattice diagram the voltage at the point A is

[latex]\upsilon \left(\frac{1}{4}\ell ,5.5t_r \right) = 1000 + 600 − 600 − 360 + 360 = 1000 V, [/latex]

and the current is

[latex]i\left(\frac{1}{4}\ell ,5.5t_r \right) = \frac{1}{50} (1000 − 600 − 600 + 360 + 360) = 10.4 A. [/latex]

(d) The plot of the voltage and current at the line point [latex]x=1/2\ell [/latex] versus time is shown in Fig. 7.21(b) and (c).

Question 7.5: Consider an underground cable line 1.6 km long with a charac...

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