3.7 Maximum Power Transfer Theorem

Consider the circuit shown in Figure 3.51. We want to find the value of R _LOAD which will absorb maximum power from the voltage source v _S whose internal resistance is R _S.

Figure 3.51: Circuit for computation of maximum power delivered to the load R _LOAD

The power p _LOAD delivered to the load is found from

or

To find the value of R _LOAD which will make p _LOAD maximum, we differentiate (3.53) with respect to R _LOAD. Recalling that

and differentiating (3.53), we get

and (3.54) will be zero if the numerator is set equal to zero, that is,

or

or

Therefore, we conclude that a voltage source with internal series resistance R _S or a current source with internal parallel resistance R _P delivers maximum power to a load R _LOAD when R _LOAD = R _S or R _LOAD = R _P. For example, in the circuits of 3.52, the voltage source v _S and current source i _N deliver maximum power to the adjustable ^[*] load when R _LOAD = R _S = R _P = 5 ?

Figure 3.52: Circuits where R _LOAD is set to receive maximum power

We can use Excel or MATLAB to see that the load receives maximum power when it is set to the same value as that of the resistance of...