ECE 201 Circuit Theory I1 Maximum Power Transfer Maximize the power delivered to a resistive load.
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Transcript of ECE 201 Circuit Theory I1 Maximum Power Transfer Maximize the power delivered to a resistive load.
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ECE 201 Circuit Theory I 1
Maximum Power Transfer
Maximize the power delivered to a resistive load
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ECE 201 Circuit Theory I 2
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?
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ECE 201 Circuit Theory I 3
General Case (continued)
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ECE 201 Circuit Theory I 4
Take the Thevenin equivalent of the circuit
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ECE 201 Circuit Theory I 5
Look at the power developed in the load
2
V2 Thp = i R = R
L LR + R
Th L
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ECE 201 Circuit Theory I 6
Find the value of Rload that maximizes power
2(R + R ) - 2R (R + R )dp 2 Th L L Th L
= V = 04Th
dR (R + R )L Th L
2(R + R ) = 2R (R + R )
Th L load Th L
R = RL Th
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ECE 201 Circuit Theory I 7
The maximum power delivered to the load
2V2 Th
p = I R = Rmax 2L L
(2R )L
2VTh
p =max
4RL
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ECE 201 Circuit Theory I 8
Example 4.12
• a) Find the value of RL for maximum power transfer to RL.
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ECE 201 Circuit Theory I 9
Determine the Thevenin Equivalent
150V = (360) = 300VTh
180
(150)(30)R = = 25Ω
Th150 + 30
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ECE 201 Circuit Theory I 10
R = 25ΩL
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ECE 201 Circuit Theory I 11
Example 4.12 continued
• b) Calculate the maximum power that can be delivered to RL.
2
3002p = i R = (25)
L50
p = 900W
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ECE 201 Circuit Theory I 12
Example 4.12 continued
• What percentage of the power delivered by the 360 V source reaches RL?
Isource
+
Vab
-
V = 150Vab
360 - 150I = = 7Asource
30
p = -I (360) = -2520Ws s
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ECE 201 Circuit Theory I 13
Example 4.12 continued
• Percentage of source power delivered to the load
900× 100% = 35.71%
2520