Lossless Transmission Line

1. The problem statement, all variables and given/known data



A lossless transmission line with



characteristic impedance Z₀ = 50Ω , β = 5∏x10^-3,

and length l =80 meters, is terminated into a load Z_L = 80Ω. The transmission line is powered by a source with 120 V and Z_G = 12 Ω. Calculate the load voltage.







2. Relevant equations



V(z) = V₊(e^-jβz + [itex]\Gamma[/itex]e^jβz



[itex]\Gamma[/itex] = (Z_L - Z₀)/(Z_L + Z₀)



Z_input = Z₀(Z_L+Z₀tanh(jβL))/(Z₀+Z_Ltanh(jβL))



V₊ = V_GZ_input/((e^jβL +[itex]\Gamma[/itex]e^-jβL )(Z_input+Z_G))



3. The attempt at a solution



[itex]\Gamma[/itex] = (80-50)/(80+50) = 3/13



Z_input = 50(80+50tanh(j*.4*pi)/(50+80tanh(j*.4*pi)



I can't find the input independence because my calculator can't evaluate the imaginary argument in the tanh function. I also have to same problem with solving for V₊ and the imaginary exponents in the denominator. Does anyone know a way around this, or am I completely doing the wrong thing here?