In many low-power circuits, often the aim is getting the maximum power output from the circuit. In such a case, efficiency is not a matter of concern. For example, an instrumentation circuit may get its input from a transducer and it may be required to get the maximum signal strength from the transducer. Another example can be presented. We may have an audio amplifier and the aim may be to get the maximum power delivered to the loudspeaker.
When maximum power transfer occurs, the efficiency of the system is poor. The ratio of power delivered to the load to power generated by the source is defined as the efficiency. There are many systems which have efficiency as their prime goal and maximum power transfer may be an irrelevant concept for such a system. For example, in a power system delivering the utility mains supply, efficiency is the goal and maximum power calculated according to maximum power transfer theorem is an impractical objective.
The application of maximum power transfer theorem to a dc circuit is illustrated now.
Maximum power transfer theorem is explained with the help of the circuit in Fig. 41. Let a network consisting of one or more independent sources and other resistive elements be represented by its Thevenin's equivalent circuit as shown in Fig. 41. We find out now the value of load resistance for which the power transferred to it is the maximum.
The current through the load resistor is obtained using equation (62).
The power absorbed by the load resistor is obtained using equation (63). We can find out the condition for maximum power transfer to the load as described below.
We get equation (64) from equation (63), by replacing IL by its expression in equation (62).
When maximum power is transferred to the load resistor, the rate of change of power delivered with respect to load resistance is zero, as expressed by equation (65). We can get the expression for the derivative in equation (65) from equation (64).
Equation (66) is obtained from equation (64) by the use of differentiation by parts.
Equating the derivative to zero, we find that the power transferred to the load is maximum, when the load resistor equals the source resistance. For this load resistance, the efficiency of the circuit is only 50 percent.
To find the load resistance for maximum power transfer, reduce the given network to its Thevenin's equivalent. Then maximum power transfer occurs when the load resistance equals the Thevenin's resistance.
We can see that the power transferred to the load resistor is the maximum when the load resistor has the same value as Thevenin's resistance. Let the power delivered by the source be called as Pm, as shown by equation (68). Let the load resistor be RL , and let ratio of power delivered to load resistor to power Pm be called as the normalized power PN, as shown by equation (69). Let the ratio of load resistor RL to the Thevenin's resistance be called y. Then the normalized power PN can be expressed as a function of y. The values of normalized power is computed for values close to unity. It can be seen that the normalized power has the maximum value of 0.5, when the load resistor equals the Thevenin's resistance. The plot of normalized power is shown below.
The plot of normalized power is shown above. It can be seen that normalized power is nearly flat, for values of y close to unity. It has a peak value of 0.5 when y is 1.
This page has described what the maximum power transfer theorem is and how it can be applied. The worked examples presented illustrate the use of maximum power transfer theorem.