circuit theorem
TRANSCRIPT
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)
8BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
SOURCE TRANSFORMATION
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.
10BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
Source Transformation
11BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
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
16BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
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)
21BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
NORTON’S 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
23BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
Norton’s Theorem
ThN RR
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Finding Norton current IN.
Norton’s Theorem
Th
ThN
scN
R
VI
iI
25BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
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)
28BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
MAXIMUM POWER
TRANSFER
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
30BEE1113 Chapter 4 : Circuit TheoremNH-credit to NHA
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