Understanding Reflection Coefficient

Reflection coefficient is a parameter closely associated with VSWR indicating the portion of the signal that is reflected at the end of a feeder, etc.

VSWR & Transmission Line Theory Tutorial Includes:
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The reflection coefficient is a parameter that describes how much of an electromagnetic wave is reflected by an impedance discontinuity in the transmission medium.

The reflection coefficient is a very useful quality when determining VSWR or investigating the match between, for example, a feeder and a load.

Reflection coefficient definition

When looking at the reflection coefficient it is very useful to have a definition so that the basis of the concept can be understood.

Reflection coefficient definition:

In the context of antennas and feeders, the reflection coefficient is defined as the figure that quantifies how much of an electromagnetic wave is reflected by an impedance discontinuity in the transmission medium. The reflection coefficient is equal to the ratio of the amplitude of the reflected wave to the incident wave.

The Greek letter Γ is typically used for reflection coefficient, although σ is also often seen.

Calculating reflection coefficient

There are many ways in which the reflection coefficient can be calculated.

Using the basic definition of the reflection coefficient, it can be calculated from a knowledge of the incident and reflected voltages.

Reflection coefficient voltages
Voltages used for calculating the reflection coefficient
Γ   =   V ref V fwd

Where:
    Γ = reflection coefficient
    Vref = reflected voltage
    Vfwd = forward voltage


It is also possible to express the reflection coefficient in terms of the load and line or feeder impedances:

Reflection coefficient - feeder and load impedance definitions
The feeder and load impedance definitions
Γ   =   | Z L - Z 0 Z L + Z 0 |

Where:
    Γ = reflection coefficient
    ZL = load impedance
    Z0 = feeder charcteristic impedance


It is also useful to be able to calculate the refelction coefficient in terms of the forward and reverse power levels. As the power is proportional to V2 [ watts = V2 / R], we can deduce that:

Γ = P ref P fwd

Where:
    Γ = reflection coefficient
    Pref = reflected power
    Pfwd = forward power


The reflection coefficient is different to the VSWR. The reflection coefficient is a figure that quantifies the level of the incident waveform that is reflected, whereas the standing wave ratio, be it a current standing wave ratio or a voltage standing wave ratio looks at the ratio of the peak and minimum voltage or current levels within the feeder arising from the forward and reflected power.

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