Transmission Line Problem

[jakob]

Say you have a circuit where a signal-generator Vg(t) is in series
with a generator impedance Zg. A transmission line of length k is in
series with Zg. At the end of the transmission line an impedance load
ZL is connected.

This is a sketch of the circuit:

|-----Zg-----___________________________________------
| |
Vg(t) |
| ZL
| |
-------------___________________________________------


Say you know the basic parametres for the transmission line C,G, L and
R

And you also know the signals angular frequency w

How do you calculate v(x,t) which is the voltage at position x at time
t
on the transmission line?

As far as I understand the solution is:

v(x,t) = real part of the complex number V(x)*exp(-jwt)

where V(x) = Vp * exp (jgx) + Vm * exp (-jgx) is the phasor and g is
the propagation constant

If this is correct, how do I calculate all the necessary constants
like Vp and Vm ?

 

[jakob]

for some reason the diagram changes when I commit it...

so I will try to describe it like this instead:

GND --- Vg --- Zg ---(transmissionline)---ZL---GND