Transmission line

Definition

A transmission line is a two-conductor structure, uniform along an axis with coordinate $z$, that carries a TEM or quasi-TEM mode. It is modelled by four constants per unit length. They are the series resistance $R \ge 0$, series inductance $L > 0$, shunt conductance $G \ge 0$ and shunt capacitance $C > 0$. The voltage $V(z, t)$ between the conductors and the current $I(z, t)$ along them satisfy the telegrapher's equations $$\frac{\partial V}{\partial z} = -R I - L \frac{\partial I}{\partial t}, \qquad \frac{\partial I}{\partial z} = -G V - C \frac{\partial V}{\partial t}.$$ Consider time-harmonic signals with time factor $e^{j\omega t}$. The propagation constant of the line is $\gamma = \sqrt{(R + j\omega L)(G + j\omega C)}$. Its characteristic impedance is $Z_0 = \sqrt{(R + j\omega L)/(G + j\omega C)}$. Both square roots are taken with positive real part.