circuit theorem

33
1 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA Chapter 4 : Circuit Theorem 4.1 Superposition Theorem 4.2 Source Transformation, Thevenin’s and Norton’s Theorem 4.3 Maximum Power Transfer

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Page 1: 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

Page 2: Circuit Theorem

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

Page 3: Circuit Theorem

3BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

SUPERPOSITION THEOREM

Page 4: Circuit 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)

Page 5: Circuit Theorem

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

Page 6: Circuit Theorem

6BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine I0 using superposition

Example 1

(-0.4706 A)

Page 7: Circuit Theorem

7BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine vx using superposition

Exercise 1

(12.5 V)

Page 8: Circuit Theorem

8BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

SOURCE TRANSFORMATION

Page 9: Circuit Theorem

9BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

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.

Page 10: Circuit Theorem

10BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Source Transformation

Page 11: Circuit Theorem

11BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine v0 using source transformation

Example 2

(3.2 V)

Page 12: Circuit Theorem

12BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine Ix using source transformation

Exercise 2

(1.176 A)

Page 13: Circuit Theorem

13BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

THEVENIN’S THEOREM

Page 14: Circuit 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.

Page 15: Circuit Theorem

15BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Thevenin’s Theorem

Page 16: Circuit Theorem

16BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Finding VTh and ZTh

Thevenin’s Theorem

Page 17: Circuit Theorem

17BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Finding ZTh when circuit has dependent sources

Z

Thevenin’s Theorem

Page 18: Circuit Theorem

18BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Circuit with load

Thevenin’s Theorem

ThLTh

LLLL

LTh

ThL V

RR

RIRV

RR

VI

Page 19: Circuit Theorem

19BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine the Thevenin equivalent at terminals a-b

Example 3

(RTh=6Ω, VTh=20 V)

Page 20: Circuit Theorem

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)

Page 21: Circuit Theorem

21BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

NORTON’S THEOREM

Page 22: Circuit Theorem

22BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

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

Page 23: Circuit Theorem

23BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Norton’s Theorem

ThN RR

Page 24: Circuit Theorem

24BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Finding Norton current IN.

Norton’s Theorem

Th

ThN

scN

R

VI

iI

Page 25: Circuit Theorem

25BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Thevenin and Norton Equivalent

NN

Th

sc

ocTh

scN

ocTh

RI

V

i

vR

iI

vV

Page 26: Circuit Theorem

26BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine the Norton equivalent at terminals a-b

Example 4

(RN=5Ω, IN=7 A)

Page 27: Circuit Theorem

27BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Determine the Norton equivalent at terminals a-b

Exercise 4

(RN=1Ω, IN=10 A)

Page 28: Circuit Theorem

28BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

MAXIMUM POWER

TRANSFER

Page 29: Circuit Theorem

29BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

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

Maximum Power Transfer

Page 30: Circuit Theorem

30BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA

Maximum Power Transfer

Th

ThThL R

VpRR

4

2

max

Page 31: Circuit Theorem

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)

Page 32: Circuit Theorem

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)

Page 33: Circuit Theorem

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