Maximum Power Transfer Theorem

For any power source, the maximum power transferred from the power source to the load is when the resistance of the load RL is equal to the equivalent or input resistance of the power source (Rin = RTh or RN).

The process used to make RL = Rin is called impedance matching.

Suppose we have a voltage source or battery that's internal resistance is Ri and a load resistance RL is connected across this battery. Maximum power transfer theorem determines the value of resistance RL for which, the maximum power will be transferred from source to it. Actually the maximum power, drawn from the source, depends upon the value of the load resistance.

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To solve:

1.Take the Thevenin equivalent of the circuit.

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2. Look at the power developed in the load

2

V2 Thp = i R = R

L LR + RTh L

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3. Find the value of Rload that maximizes power.

2(R + R ) - 2R (R + R )dp 2 Th L L Th L

= V = 04ThdR (R + R )

L Th L

2(R + R ) = 2R (R + R )

Th L load Th L

R = RL Th

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4. The maximum power delivered to the load

2V2 Th

p = I R = Rmax 2L L(2R )

L

2VTh

p =max4R

L

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Example 1:a) Find the value of RL for maximum power transfer to RL.

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Determine the Thevenin Equivalent

150V = (360) = 300VTh

180

(150)(30)R = = 25ΩTh

150 + 30

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R = 25ΩL

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Example 2:Calculate the maximum power that can be delivered to RL.

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3002p = i R = (25)

L50

p = 900W

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Example 2:What percentage of the power delivered by the 360 V source reaches RL?

Isource

+Vab-

V = 150Vab

360 - 150I = = 7Asource

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p = -I (360) = -2520Ws s

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Example 2Percentage of source power delivered to the load

900× 100% = 35.71%

2520