Electrical Engineering Analog Signals, Network and Measurement Virtual Laboratory Experiments

Verification of Maximum Power Transfer Theorem            

Theory

Maximum power is transferred from a source of given voltage and an internal impedance to the load impedance ZL in the following circuit shown in figure 1, under three conditions.



[Fig 1: Circuit diagram with source and load impedance(i.e. ZS and ZL )]


 1. When only XL is adjustable:

Under this condition the power consumed by the load (I2*RL) is maximum, when I is maximum, since RL is constant.

I=VsRs+jXs+RL+jXL...(1)

|I|max=VsRs+RL...........(2)

when XL=−Xs

 

 This means that if the load reactance(XL)  is made equal magnitude and opposite in sign to the internal reactance(Xs), the power transferred is maximum.


2. When only RL is adjustable:

From equation (1) in section (1), one may write, 


P=|I2|∗RL=Vs2∗RL(Rs+RL)2+(Xs+XL)2...(3)

Differentiating the equation (3) w.r.t  RL and equating to zero, one obtains.

RL=Rs2+(Xs+XL)2...................(4)

3. When both RL and XL are adjustable:

Under this condition both equation (2) and (4) are valid simultaneously and one obtains.

RL=Rs

XL=−Xs