# Transmission Line - Input Impedance of Lossless Transmission Line

Input Impedance of Lossless Transmission Line

The characteristic impedance of a transmission line is the ratio of the amplitude of a single voltage wave to its current wave. Since most transmission lines also have a reflected wave, the characteristic impedance is generally not the impedance that is measured on the line.

For a lossless transmission line, it can be shown that the impedance measured at a given position from the load impedance is

$Z_mathrm{in} (l)=Z_0 frac{Z_L + jZ_0tan(beta l)}{Z_0 + jZ_Ltan(beta l)}$

where is the wavenumber.

In calculating, the wavelength is generally different inside the transmission line to what it would be in free-space and the velocity constant of the material the transmission line is made of needs to be taken into account when doing such a calculation.