2.10:
Maximum Power Transfer
In practical applications, a circuit is designed to deliver maximum power from a source to a load.
A Thevenin equivalent circuit can determine the maximum power that a linear circuit can deliver.
The delivered power is the product of the load resistance and the square of the current. It varies as the load resistance changes.
To identify the load resistance value that maximizes power, differential calculus is used. Simplifying this equation provides the optimal load resistance value.
This resistance value is substituted into the second derivative of power, resulting in a negative value, confirming the condition for maximum power.
The obtained resistance value allows the calculation of the maximum power. If the load resistance does not match the Thevenin resistance, the actual power delivered will deviate from this maximum.
According to the Maximum Power Transfer Theorem, the highest power transfer occurs when the load resistance matches the Thevenin resistance.
Consider a battery of known parameters, connected with two resistors of known values. The resistance that matches the internal resistance of the battery receives the maximum power.
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.