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ECE 3301
General Electrical Engineering
Section 19
Maximum Power Transfer Theorem
1
Maximum Power Transfer
• It is often desired to transfer maximum
power out of a network into a load
resistance.
• Since a Thevenin Equivalent Circuit may be
found for any network we may consider a
voltage source in series with a resistance.
RS

VS
IL
RL

2
Maximum Power Transfer
• The current through the load resistance is:
VS
IL =
RS + RL
RS

VS
IL
RL

3
Maximum Power Transfer
• The power dissipated in the load resistance
is :
VS2RL
PL =
(RS + RL)2
RS

VS
IL
RL

4
Maximum Power Transfer
• When RL = 0, there is zero power dissipated
in the load. All of the power available is
dissipated in the source resistance.
VS2RL
PL =
(RS + RL)2
RS

VS
IL
RL

5
Maximum Power Transfer
• When RL = , IL = 0 and There is again zero
power dissipated in the load resistance.
VS
IL =
,
RS + RL
PL = IL2 RL
RS

VS
IL
RL

6
Power Dissipated in
Load Resistance
Maximum Power Transfer
Load Resistance
• For what value of RL is maximum power
delivered to RL?
7
Maximum Power Transfer
• The power dissipated in the load resistance
is:
VS2RL
2
–2
PL =
2 = VS RL(RS + RL)
(RS + RL)
8
Maximum Power Transfer
• To find the maximum power transferred, the
derivative of this quantity with respect to RL
is placed equal to zero.
dPL
= VS2 [RL(– 2)(RS + RL) – 3 + (RS + RL) – 2] = 0
dRL
9
Maximum Power Transfer
• The quantity in brackets is set equal to zero:
2RL(RS + RL)
–3
= (RS + RL)
–2
• Solving for RL reveals
2RL = RS + RL
RL = RS
10
Maximum Power Transfer
• Maximum Power is transferred when the
Load Resistances matches the Source
Resistance.
RS

VS
IL
RL = RS

11
Power Dissipated in
Load Resistance
Maximum Power Transfer
Load Resistance
RS = RL
12