# Maximum Power Transfer Theorem: R R = ```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
 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
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