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S. Jayaram June 27th 2005 GenE 123 Continuation of Network Theorems Maximum Power Transfer Theorem: This theorem allows one to find the maximum power that a circuit (source) can supply, and the manner in which to adjust the load to effect maximum power transfer from the circuit to the load. Consider the following circuit, 2 Pload V = i RL = RL + R R L 2 By differentiating the equation for power with respect to RL , we can find a condition for which the power across the load (RL) is maximum. 2 2 dPload ( R + RL ) V − 2V ( R + RL ) RL ∴ = =0 dRL (R + RL )4 2 Simplifying yields, RL = R When the load resistance is equal to the source resistance, maximum power is transferred Any complex network can be reduced to the form considered above by using Thevenin’s Equivalent circuit. Hence combining these two theorems, many devices can be evaluated to find their performance. S. Jayaram Source Transformation: GenE 123 Continuation of Network Theorems June 27th 2005