When trying to solve a basic transmission line problem, I was making the mistake of using voltage divider across the input load. Why is this wrong?
What I mean is, assume there is a generator impedance Zg and a load ZL on a lossless transmission line. I can find the input impedance Zin at the generator, but to find the voltage across the load, I can't simply do
\$V_g\frac{Z_L}{Zg + Zin}\$.
Why is that wrong?
simulate this circuit – Schematic created using CircuitLab
Schematic isn't that good. Basically some impedance Zg and some impedance Zl on a transmission line.
Best Answer
One way to calculate Zin as the input impedance to the line with load is $$ Z_{in} = Z_0 (\frac{Z_L + j Z_0 \tan{\beta l}}{Z_0 + j Z_L \tan{\beta l}}) $$ which is a non-linear function of \$Z_L\$ and \$Z_0\$, and wavelength and line length.
The whole transmission line plus the load can therefore be modeled as one lumped impedance as \$Z_{in}\$. But you cannot use this model yet isolate \$Z_L\$ out to form a voltage divider, which would require you to assume \$Z_{in} = Z_0 + Z_L\$ (which is wrong).