A line has a characteristic impedance of 400 Ω and a terminating resistance of 600 Ω. Assuming that the incident voltage wave is 100 kV, determine the following: (a) The reflection coefficient of the voltage wave; (b) The reflection coefficient of the current wave; (c) The backward-traveling

Question

A line has a characteristic impedance of 400 Ω and a terminating resistance of 600 Ω. Assuming that the incident voltage wave is 100 kV, determine the following: (a) The reflection coefficient of the voltage wave; (b) The reflection coefficient of the current wave; (c) The backward-traveling voltage and current waves; (d) The voltage across and current through the resistor.

Accepted Answer

(a) [latex]\rho_{rV}=\frac{R_T−Z_c}{R_T+Z_c} =\frac{600-400}{600+400}=0.2. [/latex]

(b) [latex]\rho _{ri} =\frac{i_b}{i_f}=-\frac{\upsilon_b}{Z_c}/\frac{\upsilon_f}{Z_c} =-\frac{\upsilon _b}{\upsilon _f}=-\rho _{rV}=−0.2. [/latex]

(c) [latex] \upsilon _b=\rho _{rV}\upsilon _f=0.2\cdot 10^3=20 kV[/latex]

[latex]- i_b=\frac{\upsilon _b}{Z_c}=-\frac{20·10^3}{400}=-50A. [/latex]

(d) [latex]\upsilon _T =\upsilon _f+\upsilon _b=100+20=120 kV[/latex]

[latex]i_T=\frac{\upsilon _T}{R_T}=\frac{120·10^3}{600}=200A. [/latex]

Question 7.3: A line has a characteristic impedance of 400 Ω and a termina...

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