What is the Solution for a Lossless Transmission Line with Given Parameters?

[Mali]

Homework Statement

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.

Homework Equations

V(z) = V₊(e^-jβz + \Gammae^jβz

\Gamma = (Z_L - Z₀)/(Z_L + Z₀)

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

V₊ = V_GZ_input/((e^jβL+\Gammae^-jβL)(Z_input+Z_G))

The Attempt at a Solution

\Gamma = (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?

 

[Mali]

I'd like to add that I'm very, very confused by the concepts, and I'm basically just juggling the equations derived in class.

 

[rude man]

There is a simple equation for E2 for a lossless transmission line, involving only β, l, Z₀ and load impedance Z_Land E1.

What is tanh(jx) ) in terms of a non-hyperbolic trig function?

Unfortunartely for you, E1 is the voltage at the driven end of the line so you have to take care of the source impedance Z_G. Hint: Z_G forms a voltage divider with Z_input.

I can't post the equation for E2. Would violate the terms of use of this forum. It can be found in many places.

BTW the nice way to handle this problem is with ABCD matrices but I take it you haven't had those yet.