# Relation Voltage Standing Wave Ratio and Reflection Coefficient

Last time I have discussed the standing wave ratio and voltage standing wave ratio. Today we will discuss the reflection coefficient and relation of voltage standing wave ratio with the reflection coefficient.

**REFLECTION COEFFICIENT**

**Definition:- **Reflection co-efficient is defined as the ratio of the reflected voltage to the incident voltage.

p=V_{r}/V_{i}

where V_{r}=Reflection voltage

V_{i}= Incident Voltage

The reflection co-efficient can also be defined in terms of the ratio of reflected current and incident current. However , it is observed that p as defined from current ratio is negative with respect to that defined from voltage ratio. The reason being that the reflected current suffers a 180^{0} phase shift at the receiving end while the reflected voltage does not.

Thus p=- I_{r}/I_{i}

Where I_{r}=Reflected Current

I_{i}= Incident Current

It is a vector quantity having magnitude and direction both.

**Relation Between Voltage Standing Wave Ratio and Reflection Coefficient**

The points of voltage maximum are those ,where the incident and reflected voltage are in phase and add up,

That is |V_{max}|=|V_{i}|+|V_{r}| (1)

Where V_{i} is the r.m.s value of incident voltage and

V_{r} is the r.m.s value of the reflected voltage.

Also |V_{min}|=|V_{i}|-|V_{r}| (2)

Because the points of voltage minimum are those ,where the incident and reflected voltage are out of phase and thus ,will have opposite sign

From definition of VSWR , VSWR=|V_{max}|/|V_{min}|

Substituting the value of V_{max} and V_{min} from equation (1) and (2) in above equation,we get

VSWR=|V_{i}|+|V_{R}|/|v_{I}|-|v_{R}|

Dividing numerator and denominator by V_{i},we have

VSWR = (1+V_{r}/V_{i})/(1-V_{r}/V_{i}) (3)

As reflection co-efficient,

P=V_{r}/V_{i}

By substituting value of p in equation (3),we get

VSWR=1+|p|/1-|p| (4)

Or VSWR (1-|p|)=1+|p|

Or VSWR-1=|p|(VSWR+1)

Thus |p|=VSWR-1/VSWR+1 (5)

Expressions (4) and (5) represents the relation between voltage standing wave ratio and reflection coefficient.

**For current standing wave ratio **

CSWR= 1-|p|/1+|p|