Determine the voltage and current waves due to the connection of the resistive load RL = 300 Ω at the arbitrary point of the TL shown in Fig. 7.6(a). The characteristic impedance of TL is 400 Ω and it is charged with initial voltage V_0 = 20 kV and initial current I0 = 50 A.

Question

Determine the voltage and current waves due to the connection of the resistive load [latex]R_L = 300 \Omega[/latex] at the arbitrary point of the TL shown in Fig. 7.6(a). The characteristic impedance of TL is 400 Ω and it is charged with initial voltage [latex]V_0 = 20 kV[/latex] and initial current [latex]I_0 = 50 A.[/latex]

Accepted Answer

Since both directions of wave propagation (to the left and right from the connection point) are symmetrical, both current waves will be equal to each other, i.e., [latex]i_f = i_b and \upsilon_f = \upsilon_b[/latex]. Applying KCL and Ohm’s law,

[latex] i_L=−(i_f+i_b)=−2i_f=−2i_b, \upsilon_L=R_Li_L=V_0+ \upsilon_f=V_0+ \upsilon_b[/latex]

Solving equation 7.41 with the relation [latex]\upsilon_f = Z_c i_f[/latex], we obtain

[latex]i_L=−(i_f+i_b)=−2i_f=−2i_b, \upsilon_L=R_Li_L= V_0+\upsilon_f = V_0+\upsilon_b. [/latex] (7.41)

[latex]i_b =i_f=−\frac{V_0}{2R_L+Z_c} =-\frac{20·10^3}{600+400} =−20 A [/latex]

and

[latex]\upsilon_b =\upsilon_f =Z_c i_f=−\frac{V_0 Z_c}{2R_L+Z_c} =-20\frac{400}{1000}=-8 kV. [/latex]

The voltage and current distribution along the TL is shown in Fig. 7.6(b).

Question 7.2: Determine the voltage and current waves due to the connectio...

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