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 180⁰ 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|