Maximum Power Transfer theorem

Maximum Power Transfer theorem for DC excitation

Statement

A linear DC network having a resistive load connected receives maximum power when the load resistance is
equal to the internal resistance of the source network.

Explanation of Maximum power Transfer theorem

Consider the following circuit having load resistance connected to a DC source network. The DC source has been represented as a thevenin’s equivalent circuit.

Circuit for maximum power transfer theorem

To have the maximum power transferred to the load, according to the maximum power transfer theorem load resistance R_L must be equal to the source resistance R_TH.

The maximum power can be obtained by the below solution,

The load current I_L can be calculated as I_L=(V_TH)/(R_TH+R_L)

The power is given by P_L=I_L²R_L

Therefore from above two equations, P_L=[V_TH/(R_TH+R_L)]²×R_L

Since, the maximum power will be transferred when R_L=R_TH, substituting this in above equation we get,

⇒P_L(max)=[V_TH/(R_TH+R_TH)]²×R_TH

∴ P_L(max)=[V_TH²/4R_TH]

Note: The efficiency at the maximum power transfer is 50%.

Maximum Power Transfer theorem for AC excitation

Statement

In a linear network having energy sources and impedances, the maximum power is transferred to the load when the load impedance is equal to the complex conjugate of the source impedance. That is, if the source impedance is (R_S ± j X_S) Ω then load impedance must be equal to (R_S ∓ j X_S) Ω for maximum power to be transferred.