circuit theorem

1BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Chapter 4 : Circuit Theorem

4.1 Superposition Theorem4.2 Source Transformation, Thevenin’s and Norton’s Theorem4.3 Maximum Power Transfer

2BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Learning Outcomes

1. Discuss the Superposition Principles

2. Solve circuit problems using Superposition

theorem

3. Apply the Source Transformation in the circuits

4. Carry out the Thevenin's and Norton's Theorem

in the circuits

5. Describe Maximum Power Transfer

3BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

SUPERPOSITION THEOREM

4BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Superposition Theorem

Superposition : the voltage across (or current through) an element in a linear circuits is the algebraic sum of the voltage across (or current through) that element due to each independent source acting alone.

Current Source open circuit(0 A)

Voltage Source short circuit (0 V)

5BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Step to apply:

1. Turn off all independent sources except one source. Find the output (voltage or current) due to that active source.

2. Repeat step 1 for each other independent sources.

3. Find the total contribution by adding algebraically all the contribution due to the independent source.

Superposition Theorem

6BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine I0 using superposition

Example 1

(-0.4706 A)

7BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine vx using superposition

Exercise 1

(12.5 V)

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SOURCE TRANSFORMATION

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Source Transformation

Source transformation :

replacing a voltage source vs in

series with a impedance Z by a

current source is in parallel with a

impedance Z, or vice versa.

10BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Source Transformation

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Determine v0 using source transformation

Example 2

(3.2 V)

12BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine Ix using source transformation

Exercise 2

(1.176 A)

13BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

THEVENIN’S THEOREM

14BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Thevenin’s Theorem

Thevenin’s theorem : a linear two terminal circuit can be replaced by an equivalent circuit consisting of a voltage VTh in series with an impedance ZTh ,

where VTh is the open circuit voltage at

the terminals and ZTh is the input or

equivalent impedance at the terminals when the independent source are turned off.

15BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Thevenin’s Theorem

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Finding VTh and ZTh

Thevenin’s Theorem

17BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Finding ZTh when circuit has dependent sources

Z

Thevenin’s Theorem

18BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Circuit with load

Thevenin’s Theorem

ThLTh

LLLL

LTh

ThL V

RR

RIRV

RR

VI

19BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine the Thevenin equivalent at terminals a-b

Example 3

(RTh=6Ω, VTh=20 V)

20BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine the Thevenin equivalent at terminals a-b

Exercise 3

(RTh=0.44Ω, VTh=5.33 V)

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NORTON’S THEOREM

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Norton’s Theorem : a linear two-terminal circuit can be replaced by an equivalent

circuit consisting of a current source IN in

parallel with an impendence ZN, where IN is

the short circuit current through the

terminals and ZN is the input or equivalent

impedance at the terminals when the independent source are turned off.

Norton’s Theorem

23BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Norton’s Theorem

ThN RR

24BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Finding Norton current IN.

Norton’s Theorem

Th

ThN

scN

R

VI

iI

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Thevenin and Norton Equivalent

NN

Th

sc

ocTh

scN

ocTh

RI

V

i

vR

iI

vV

26BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine the Norton equivalent at terminals a-b

Example 4

(RN=5Ω, IN=7 A)

27BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine the Norton equivalent at terminals a-b

Exercise 4

(RN=1Ω, IN=10 A)

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MAXIMUM POWER

TRANSFER

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Maximum power : transferred to the load when the load resistance equals the Thevenin resistance as seen from the load (RL = RTh)

Maximum Power Transfer

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Maximum Power Transfer

Th

ThThL R

VpRR

4

2

max

31BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine a) The value or RL for maximum power transfer b) The maximum power transfer

Example 5

(RL=9Ω, pmax=13.44 W)

32BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine a) The value or RL for maximum power transfer b) The maximum power transfer

Exercise 5

(RL=4.22Ω, pmax=2.901 W)

33BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

1. Q & A

2. Outcomes : • Discuss the Superposition Principles

• Solve circuit problems using Superposition theorem

• Apply the Source Transformation in the circuits

• Carry out the Thevenin's and Norton's Theorem in the

circuits

• Describe Maximum Power Transfer

3. Reflection