Transcript Maximum Power Transfer Maximize the power delivered to a resistive load

Maximum Power Transfer
Maximize the power delivered to a
resistive load
ECE 201 Circuit Theory I
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Consider the General Case
• A resistive network contains independent
and dependent sources.
• A load is connected to a pair of terminals
labeled a – b.
• What value of load resistance permits
maximum power delivery to the load?
ECE 201 Circuit Theory I
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General Case (continued)
ECE 201 Circuit Theory I
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Take the Thevenin equivalent of the circuit
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Look at the power developed in the load
2
p = i R
L
 VTh 
= 

R
+ R
 Th L 
ECE 201 Circuit Theory I
2
R
L
5
Find the value of Rload that maximizes power
dp
=
dR
(R
R
L
 (R Th
V
Th 

2
+ R )
Th
L
L
= R
2
= 2R
+ R )
L
2
- 2R (R
+ R )
L Th
L
4
(R
+ R )
Th
L
load
(R

=0

+ R )
Th
L
Th
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The maximum power delivered to the load
2
p
2
max
= I R
L
=
V
Th
(2R )
L
2
R
L
2
p
max
=
V
Th
4R
L
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Example 4.12
• a) Find the value of RL for maximum
power transfer to RL.
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Determine the Thevenin Equivalent
150
V
=
Th
(360) = 300V
180
(150)(30)
R
Th
=
= 25Ω
150 + 30
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R
ECE 201 Circuit Theory I
L
= 25Ω
10
Example 4.12 continued
• b) Calculate the maximum power that can
be delivered to RL.
 
300
2
p = i R
2
L
=
(25)
50
p = 900W
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Example 4.12 continued
• What percentage of the power delivered
by the 360 V source reaches RL?
V
= 150V
ab
+
Vab
Isource
-
360 - 150
I
source
=
= 7A
30
p
s
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= -I (360) = -2520W
s
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Example 4.12 continued
• Percentage of source power delivered to
the load
900
× 100% = 35.71%
2520
ECE 201 Circuit Theory I
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