A loss-less transmission line having characteristic impedance Z₀ is terminated in a load of Z_R. If the value of Z_R is exactly half of Z_0­ then reflection coefficient Γ_L is  

Reflection coefficient:

• The reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium.
• It is equal to the ratio of the amplitude of the reflected wave to the incident wave, with each expressed as phasors.

Simple circuit configuration showing a measurement location of the reflection coefficient:

Where,

Γ is the reflection coefficient

ZL is the load impedance

Z0 is the Characteristic Impedance

Relation to load impedance:

The reflection coefficient corresponds directly to a specific impedance as seen at the point it is measured.

A load impedance of Z_L (using a reference impedance Z₀) corresponds to a reflection coefficient of

\({\rm{Γ }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}\)

Calculation:

Given,

Z_L = Z_R = Z₀ / 2

Reflection coefficient Γ,

\({\rm{Γ }} = \frac{{\frac{{{Z_0}}}{2} - {Z_0}}}{{\frac{{{Z_0}}}{2} + {Z_0}}}\)

Therefore the reflection co-efficient Γ is - 1/3