EENG 2610: Circuits Analysis

Class 9: Thevenin’s and Norton’s Theorems, Maximum Power Transfer

Oluwayomi Adamo Department of Electrical Engineering College of Engineering, University of North Texas

Example 5.9: Determine Thevenin’s equivalent of the network at terminals A-B.

Circuits containing only dependent sources © Dr. Xinrong Li EENG 2610, Class 9

V

2

V

3 2

R Th

Circuits containing only dependent sources © Dr. Xinrong Li

V

3 EENG 2610, Class 9 3

Example 5.11: Use Thevenin’s theorem to find Vo Circuits containing both independent and dependent sources © Dr. Xinrong Li EENG 2610, Class 9 4

Example 5.12: Use Thevenin’s theorem to find Vo Circuits containing both independent and dependent sources © Dr. Xinrong Li EENG 2610, Class 9 5

Source Transformation/Source Exchange

    

v oc

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.

R Th i

A

v oc



R Th i sc i

A

v o i sc R Th v o

B Circuit B (Load) EENG 2610, Class 9 B Circuit B (Load) 6 © Dr. Xinrong Li

Example 5.14: Use source transformation to find Vo 3 k  2 k  4 k  12 V 6 k  2 mA 8 k  V O © Dr. Xinrong Li EENG 2610, Class 9 7

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 8

Maximum Power Transfer

v i R R L P L



i

2

R L

 (

R



v R L

) 2

R L d P L d R L

 0

R L



R

Maximum power transfer takes place

R L

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

L Th

© Dr. Xinrong Li EENG 2610, Class 9 9

Example 5.16: Find out

R L

for maximum power transfer and the maximum power that can be transferred to this load.

© Dr. Xinrong Li EENG 2610, Class 9 10

Example 5.17: Find out

R L

for maximum power transfer and the maximum power that can be transferred to this load.

© Dr. Xinrong Li EENG 2610, Class 9 11

Example 5.18: Plots © Dr. Xinrong Li EENG 2610, Class 9 12