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Maximum Power Transfer Theorem

The maximum power transfer theorem is used for determining the condition for which a source delivers maximum power to the load. The maximum power theorem states that the maximum power is delivered to the load if the load impedance is equal to the source impedance. The maximum power transfer theorem is applicable for AC and DC circuits. To obtain the maximum power from the source, load resistance matching with the source impedance is done.

Explanation of Maximum Power Transfer Theorem

In case of DC source, it  has certain resistance. In case of AC source it has certain impedance. The source feeds current to the load. The voltage drop takes place in the source impedance when current flows through the circuit.The power lost in the source resistance must be minimum to get the maximum power delivery of the source.

If the power loss in the source resistance is more, the maximum power delivery from source can not be ensured. There is certain relationship between the source impedance and load impedance for which maximum power delivery from the source can be achived. The maximum power theroem states that if the load resistance is equal to the source resistance, the maximum power will be deliverd by the source.

The source resistance is the resistance viewed from the load side. The source resistance can be found by Thevenin theorem. The source resistance is also called Thevenin resistance.We take DC circuit to understand the maximum power transfer theorem.

The source resistance viewed from the load side is RTH and the Thevenin voltage is V0. According to maximum power transfer theorem, the maximum power transfer occurs when the source resistance is equal to the load resistance.
Derivation of Maximum Power Transfer Theorem

We take the following DC circuit to derive the condition of maximum power delivery.

The DC source supply current to the load. The power dissipation in the load resisor RL is P= I2R. The current I flowing through the  circuit is:






The power dissipation in the resistor RL is:






Putting the value of I from equation (1) in equation(2),we get:


The maximum power is delivered if :






Equation(3) can be solved as follows.























Thus, the source delivers maximum power to load, if the source resistance is equal to the load resistance.The efficiency of the system under condition of maximum power transfer can be calculated as follows.


Efficiency Calculation under Maximum Power Transfer Condition


To calculate the efficiency, we first calculate the maximum power transfer when the load resistance is equal to the source resistance.

Maximum Power Delivered to the Load
Total power transferred from source is:
Efficiency can be calculated by Dividing equation(4) by equation(5):












Hence, at the condition of maximum power transfer the efficiency is 50%. At maximum power transfer condition 50 % of generated power is delivered to the load and at other conditions small percentage of power is delivered to the load.












Application of  Maximum Power Transfer Theorem

The efficiency of the electrical system is 50 %  when the load resistance is equal to the source resistance. It means 50 % power is delivered to the load and remaining 50% lost in the circuit. The MPTT is not applicable where large power transfer is taking place.In view of this MPTT is not applicable for power transmission. In communication circuit, the magnitude of power transfer is very small and low efficiency is not a problem in communication circuit. The MPTT is used in the communication circuit.

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