1

Lecture 6: Equivalent Circuits, Max Power Transfer, SuperpositionNilsson & Riedel 4.10-4.13

ENG17 (Sec. 1): Circuits I

Summer 1 2014

July 1, 2014

2

Overview

• Thevenin Equivalent• Norton Equivalent• Special Cases• Maximum Power

Transfer• Superposition

3

Thevenin Equivalent Circuit

• Independent voltage source in series with resistor

• Provides simplified equivalence to more complex circuit

4

Finding Thevenin Equivalent

5

Example

Find equivalent w.r.t. a-b. Then, find I.

6

Overview

• Thevenin Equivalent• Norton Equivalent• Special Cases• Maximum Power

Transfer• Superposition

7

Norton Equivalent Circuit

• Independent current source in parallel with resistor• Provides simplified equivalence to more complex circuit• Relates to Thevenin Equivalent (source transformation)

8

Finding Norton Equivalent

9

Overview

• Thevenin Equivalent• Norton Equivalent• Special Cases• Maximum Power

Transfer• Superposition

10

With Dependent Source

11

Alternate Method

12

ExampleFind RN and IN

13

Overview

• Thevenin Equivalent• Norton Equivalent• Special Cases• Maximum Power

Transfer• Superposition

14

Power Transfer

• Two issues:– Efficiency of Power Transfer– Amount of Power Transfer

15

Maximum Power Transfer

16

Example

• Find value of RL that results in maximum power transfer.

• Use Thevenin Equivalent circuit.

17

Example

Find the value of RL for maximum power transfer. Find the maximum power.

18

Overview

• Thevenin Equivalent• Norton Equivalent• Special Cases• Maximum Power

Transfer• Superposition

19

Superposition

• Applies to linear system• Defined: when linear system is excited by >1

independent energy sources, the total response is the sum of individual responses.

• Clarified– Deactivate 1st source, find response from 2nd

source– Deactivate 2nd source, find response from 1st

source– Add these responses

20

In practice

• May not help so much right now…

21

w/Dependent Sources

22

Example

Use superposition to find vo.

23

Overview

• Thevenin Equivalent• Norton Equivalent• Special Cases• Maximum Power

Transfer• Superposition