EENG 2610: Circuits AnalysisClass 9: Thevenin’s and Norton’s Theorems, Maximum Power Transfer

Oluwayomi AdamoDepartment of Electrical EngineeringCollege of Engineering, University of North Texas

© Dr. Xinrong Li EENG 2610, Class 9 2

Example 5.9: Determine Thevenin’s equivalent of the network at terminals A-B.Circuits containing only dependent sources

2V 3V

© Dr. Xinrong Li EENG 2610, Class 9 3

Example 5.10: Determine at terminals A-B.Circuits containing only dependent sources

ThR

3V

© Dr. Xinrong Li EENG 2610, Class 9 4

Example 5.11: Use Thevenin’s theorem to find VoCircuits containing both independent and dependent sources

© Dr. Xinrong Li EENG 2610, Class 9 5

Example 5.12: Use Thevenin’s theorem to find VoCircuits containing both independent and dependent sources

© Dr. Xinrong Li EENG 2610, Class 9 6

Source Transformation/Source Exchange If we have embedded within a network a current source i(t) in parallel with a

resistor R, we can replace this combination with a voltage source of value v(t) = i(t)R in series with the resistor R.

The reverse is also true; that is, a voltage source v(t) in series with a resistor R can be replaced with a current source of value i(t) = v(t)/R in parallel with the resistor R.

Parameters within the circuit are unchanged under these transformations. We can use source transformations back and forth to simplify circuits. Important: the two equivalent circuits are equivalent only at the two

external nodes.

A

B

ov

i

Circuit B(Load)

ocv

ThR A

B

ov

i

Circuit B(Load)

sciThR

scThoc iRv

© Dr. Xinrong Li EENG 2610, Class 9 7

Example 5.14: Use source transformation to find Vo

mA 2

k 3

V 12k 6

k 2 k 4

k 8OV

© Dr. Xinrong Li EENG 2610, Class 9 8

General Rules for Circuit Analysis Try to select a simple technique for a given problem,

First, count the number of nodes and loops. Next, examine the type and number of sources. Select a technique based on this information, your objective, and

your experiences. Loop analysis and nodal analysis are straightforward and as

good as any technique that you have learned. What about other techniques?

Equivalency, Linearity, Superposition, Thevenin’s and Norton’s Theorems

The real value of these techniques is the insight and understanding that they provide about the physical nature of the network.

© Dr. Xinrong Li EENG 2610, Class 9 9

Maximum Power Transfer

Thevenin’s theorem provides a way to determine the maximum power that a circuit can supply; that is, .

v

i

LR

RL

LLL R

RR

vRiP 22 )(

0L

L

Rd

PdRRL

Maximum power transfer takes place when the load resistance . RRL

ThL RR

© Dr. Xinrong Li EENG 2610, Class 9 10

Example 5.16: Find out RL for maximum power transfer and the maximum power that can be transferred to this load.

© Dr. Xinrong Li EENG 2610, Class 9 11

Example 5.17: Find out RL for maximum power transfer and the maximum power that can be transferred to this load.

© Dr. Xinrong Li EENG 2610, Class 9 12

Example 5.18: Plots