A reflection coefficient is the complex ratio of a reflected wave amplitude to the corresponding incident wave amplitude. For voltage waves on a transmission line,
let 
travel toward a load of impedance 
and let 
travel away from it. If the line has real positive characteristic
impedance 
,
then the voltage reflection coefficient at the load is
 |
The complex modulus 
is the reflected-to-incident voltage-amplitude ratio,
while the complex argument of 
is the phase shift on reflection. For a lossless line,
the reflected-to-incident power ratio is 
. A Smith chart represents
while simultaneously displaying the corresponding normalized load impedance (Pozar
2012).
