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Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of...
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Transcript of Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of...
![Page 1: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/1.jpg)
![Page 2: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/2.jpg)
Objective of LectureState Thévenin’s and Norton Theorems.
Chapter 4.5 and 4.6 Fundamentals of Electric Circuits
Demonstrate how Thévenin’s and Norton theorems can be used to simplify a circuit to one that contains three components: a power source, equivalent resistor, and load.
![Page 3: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/3.jpg)
Thévenin’s TheoremA linear two-terminal circuit can be replaced
with an equivalent circuit of an ideal voltage source, VTh, in series with a resistor, RTh.VTh is equal to the open-circuit voltage at the
terminals.RTh is the equivalent or input resistance when
the independent sources in the linear circuit are turned off.
![Page 4: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/4.jpg)
Circuit Schematic:Thévenin’s Theorem
![Page 5: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/5.jpg)
Definitions for Thévenin’s Theorem
Linear circuit is a circuit where the voltage is directly proportional to the current (i.e., Ohm’s Law is followed).
Two terminals are the 2 nodes/2 wires that can make a connection between the circuit to the load.
![Page 6: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/6.jpg)
Definitions for Thévenin’s Theorem
Open-circuit voltage Voc is the voltage, V, when the load is an open circuit (i.e., RL = ∞).
+Voc
_
ThOC VV
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Definitions for Thévenin’s TheoremInput resistance is the resistance seen by
the load when VTh = 0V.
It is also the resistance of the linear circuit when the load is a short circuit (RL = 0).
SCThThin iVRR
![Page 8: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/8.jpg)
Steps to Determine VTh and RTh1. Identify the load, which may be a resistor or a
part of the circuit.2. Replace the load with an open circuit .3. Calculate VOC. This is VTh.4. Turn off all independent voltage and currents
sources in the linear 2-terminal circuit.5. Calculate the equivalent resistance of the
circuit. This is RTh. The current through and voltage across the load
in series with VTh and RTh is the load’s actual current and voltage in the original circuit.
![Page 9: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/9.jpg)
Norton’s TheoremA linear two-terminal circuit can be replaced
with an equivalent circuit of an ideal current source, IN, in parallel with a resistor, RN.IN is equal to the short-circuit current at the
terminals.RN is the equivalent or input resistance when
the independent sources in the linear circuit are turned off.
![Page 10: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/10.jpg)
Circuit Schematic:Norton’s Theorem
![Page 11: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/11.jpg)
Definitions for Norton’s Theorem
Short-circuit current Isc is the current, i, when the load is a short circuit (i.e., RL = 0).
NSC II
![Page 12: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/12.jpg)
Definitions for Norton’s TheoremInput resistance is the resistance seen by
the load when IN = 0A.
It is also the resistance of the linear circuit when the load is an open circuit (RL = ∞).
NOCNin IVRR
![Page 13: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/13.jpg)
Steps to Determine IN and RN1. Identify the load, which may be a resistor or a
part of the circuit.2. Replace the load with a short circuit .3. Calculate ISC. This is IN.4. Turn off all independent voltage and currents
sources in the linear 2-terminal circuit.5. Calculate the equivalent resistance of the
circuit. This is RN. The current through and voltage across the load
in parallel with IN and RN is the load’s actual current and voltage in the original circuit.
![Page 14: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/14.jpg)
Source ConversionA Thévenin equivalent circuit can easily be
transformed to a Norton equivalent circuit (or visa versa).If RTh = RN, then VTh = RNIN and IN = VTh/RTh
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Voltage Polarity and Current Flow
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Value of TheoremsSimplification of complex circuits.
Used to predict the current through and voltage across any load attached to the two terminals.
Provides information to users of the circuit.
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Example #1
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Example #1 (con’t)Find IN and RN
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Example #1 (con’t)Calculation for IN
Look at current divider equation:
If RTh = RN= 1k, then IN = 6mA
NN
N
NloadNload
NloadN
load
eqload
IRk
RmA
IRRR
RRI
R
RI
22
1
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Why chose RTh = RN?Suppose VTh = 0V and IN = 0mA
Replace the voltage source with a short circuit.Replace the current source with an open
circuit.
Looking towards the source, both circuits have the identical resistance (1k).
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Source TransformationEquations for Thévenin/Norton
Transformations
VTh = IN RTh
IN = VTh/RTh
RTh= RN
![Page 23: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/23.jpg)
Example #1: Norton’s Theorem IN is the current that flows when a short circuit
is used as the load with a voltage source
IN = VTh/RTh = 6mA
![Page 24: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/24.jpg)
Example #1: Norton’s TheoremRN is the resistance of the linear circuit when the power sources in the original circuit are turned off (VTh is replaced with a short circuit).
![Page 25: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/25.jpg)
Example #1: Norton’s TheoremThe Norton equivalent circuit is:
![Page 26: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/26.jpg)
Check: Thévenin Theorem VTh is the voltage across the load when an open
short circuit is used as the load with a current source
VTh = IN RTh = 6V
![Page 27: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/27.jpg)
Check: Iload and Vload
VV
kmAV
mAI
mAkk
kI
load
load
load
load
4
)2(2
2
621
1
![Page 28: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/28.jpg)
Example #2Simplification through Transformation
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Example #2 (con’t)
![Page 30: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/30.jpg)
Example #2 (con’t)Find Req to obtain a Norton equivalent circuit
![Page 31: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/31.jpg)
Example #2 (con’t)
RTh = 3
VTh = 0.1A (3) = 0.3V
0.3V
Current Source to Voltage Source
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Example #2 (con’t)
0.3V
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Example #2 (con’t)
RTh = 2
IN = 3V/2 = 1.5A
Voltage Source to Current Source
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0.3V
Example #2 - Solution 1Simplify to Minimum Number of Current
Sources
![Page 35: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/35.jpg)
RTh = 6
IN = 0.3V/6 = 50.0mA
0.3V
Voltage Source to Current Source
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Example #2 (con’t)
![Page 37: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/37.jpg)
Current Sources in Parallel Add
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Example #2 - Solution 2Simplify to Minimum Number of Voltage
Sources
0.3V
![Page 39: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/39.jpg)
Example #2 (con’t)Transform solution for Norton circuit to Thévenin circuit to obtain single voltage source/single equivalent resistor in series with load.
![Page 40: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/40.jpg)
PSpice
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Example #2 - Solution 1
![Page 42: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/42.jpg)
Example #2 – Solution 2
![Page 43: Objective of Lecture State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits Demonstrate how Thévenin’s and Norton.](https://reader037.fdocuments.us/reader037/viewer/2022110400/56649dbd5503460f94aafd77/html5/thumbnails/43.jpg)
SummaryThévenin and Norton transfomrations are
performed to simplify a circuit for analysis and design. Two techniques were described.
Examples using the source transformation technique were given.