Transmission Lines

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.


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


where                            Vr=Reflection voltage

Vi= 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 1800 phase shift at the receiving end while the reflected voltage does not.

Thus                                         p=- Ir/Ii

Where                                       Ir=Reflected Current

Ii= 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                              |Vmax|=|Vi|+|Vr|                                  (1)

Where Vi is the r.m.s value of incident voltage and

Vr is the r.m.s value of the reflected voltage.

Also                           |Vmin|=|Vi|-|Vr|                                           (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=|Vmax|/|Vmin|

Substituting the value of Vmax and Vmin from equation (1) and (2) in above equation,we get


Dividing numerator and denominator by Vi,we have

VSWR = (1+Vr/Vi)/(1-Vr/Vi)                                          (3)

As reflection co-efficient,


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|

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