2.10 : Maximum Power Transfer

Numerous practical applications within engineering disciplines, such as telecommunications, necessitate optimizing power delivery to a connected load. This pursuit, however, entails inherent internal losses, which can either equal or exceed the power supplied to the load. The Thevenin equivalent circuit is helpful in finding the maximum power a linear circuit can deliver to a load. It is assumed in this context that the load resistance can be adjusted.

By substituting the entire circuit with its Thevenin equivalent while preserving the load as shown in Figure 1,

Figure 1:Circuit used for maximum power transfer

the power delivered to the load is given by

.................(1)

For a given circuit, Thevenin equivalent resistance and voltage are fixed. The variation of power delivered to the load with load resistance is small for small or large values of load resistance but maximum for some value load resistance between zero and infinity. The maximum power occurs when the load resistance equals the Thevenin's resistance expressed as

.................(2)

This is known as the maximum power transfer theorem. Using equations 1 and 2, the expression for maximum power transferred is obtained and is expressed as

..................(3)

This Equation applies only when equation 2 is valid, otherwise, the power delivered to the load is determined using Eq. 1.