ECE 201 Circuit Theory I 1

Maximum Power Transfer

Maximize the power delivered to a resistive load

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?

ECE 201 Circuit Theory I 3

General Case (continued)

ECE 201 Circuit Theory I 4

Take the Thevenin equivalent of the circuit

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

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

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

ECE 201 Circuit Theory I 8

Example 4.12

• a) Find the value of RL for maximum power transfer to RL.

ECE 201 Circuit Theory I 9

Determine the Thevenin Equivalent

150V = (360) = 300VTh

180

(150)(30)R = = 25Ω

Th150 + 30

ECE 201 Circuit Theory I 10

R = 25ΩL

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

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

ECE 201 Circuit Theory I 13

Example 4.12 continued

• Percentage of source power delivered to the load

900× 100% = 35.71%

2520