Can someone explain to me how to use the transmission line (TL) formula (from telegrapher's equations) to calculate the DC resistance of the TL?
Here's my work so far:
V(x,s) = A * exp(-gamma*x) + B * exp(gamma*x)
where A and B = complex amplitudes of forward going and backward going waves, respectively
gamma = sqrt((R+sL)(G+s*C))
- Telegrapher's model (L,C,R,G constants)
- A DC source (Vs) is attached at one end of the transmission line, and the output of transmission line is a shorted.
- G = 0 (no shunt resistance)
I expect the DC resistance of the transmission line to be equal to R*(length of transmission line).
I should be able to calculate the constants A and B from the boundary conditions (voltage = Vs at one end, 0V at other).
However, when I plug s = 0 (DC) and G = 0 into formula for gamma, I get gamma = 0. When using gamma = 0 in transmission line equation, I get V(x,s) = A + B
This implies that V(x,s) is not a function of x at all, which contradicts the boundary conditions.
Please help me figure out where my reasoning went wrong. Do TL equations not apply at DC, and if so, why not?