Download Slides - ECE 2040

5/23/2013
Linear Circuits
Dr. Bonnie H. Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
An introduction to electric circuit elements and a study of circuits
containing such devices.
School of Electrical and Computer Engineering
Concept Map: Module 2
1
Background
2
Resistive
Circuits
5
Power
3
Reactive
Circuits
4
Frequency
Analysis
2
1
5/23/2013
Concept Map
Background
current,
voltage,
sources,
resistance,
circuits
Resistive Circuits
•
•
•
•
Resistors
Ohm’s Law
Kirchoff’s
Laws
Resistive
Series and
Circuits
parallel resistors
•
•
•
•
•
Superposition
Solution methods
Max Power
Configurations
Sensors
Power
Reactive
Circuits
Frequency
Analysis
3
2
8/13/2013
Resistivity and
Ohm’s Law
Nathan V. Parrish
PhD Candidate & Graduate
Research Assistant
School of Electrical and
Computer Engineering
•Learn how materials resist the flow of current
•Learn about Ohm’s law – a law relating current and voltage
through materials
•Find resistance of materials from their dimensions and electric
properties
School of Electrical and Computer Engineering
Lesson Objectives
Define resistance
Calculate conductance from resistance
Apply Ohm’s Law to find currents, voltages,
or resistances
Calculate the resistance of a material using
its dimensions and electrical properties
5
1
8/13/2013
Ohm’s Law
6
Resistance and Conductance
7
2
8/13/2013
Reason for Resistance
hydrogen
helium
1
2
H
He
1.0079
4.0026
lithium
beryllium
boron
carbon
nitrogen
oxygen
neon
3
4
5
6
7
8
9
10
Li
Be
B
C
N
O
F
Ne
6.941
9.0122
10.811
12.011
14.007
15.999
18.998
20.180
sodium
magnesium
aluminium
silicon
phosphorus
sulfur
chlorine
11
12
Na Mg
22.990
potassium
19
K
24.305
calcium
scandium
titanium
20
21
22
Ca Sc Ti
vanadium
23
V
argon
13
14
15
16
17
18
Al
Si
P
S
Cl
Ar
26.982
28.086
30.974
32.065
35.453
39.948
krypton
chromium
manganese
iron
cobalt
nickel
copper
zinc
gallium
germanium
arsenic
selenium
bromine
24
25
26
27
28
29
30
31
32
33
34
35
Kr
83.798
39.098
40.078
44.956
47.867
50.942
51.996
54.938
55.845
58.933
58.693
63.546
65.38
69.723
72.64
74.922
78.96
79.904
rubidium
strontium
yttrium
zirconium
niobium
molybdenum
technetium
ruthenium
rhodium
palladium
silver
cadmium
indium
tin
antimony
tellurium
iodine
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
I
Xe
Rb Sr
85.468
87.62
caesium
barium
55
56
Cs Ba
Y
88.906
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
92.906
95.96
[98]
101.07
102.91
106.42
107.87
112.41
114.82
118.71
121.76
127.60
126.90
131.29
hafnium
tantalum
tungsten
rhenium
osmium
iridium
platinum
gold
mercury
thallium
lead
bismuth
polonium
astatine
radon
72
73
74
75
76
77
78
79
80
81
82
83
84
85
Pt Au Hg Tl Pb Bi Po At Rn
195.08
137.33
178.49
180.95
183.84
186.21
190.23
192.22
francium
radium
rutherfordium
dubnium
seaborgium
bohrium
hassium
meitnerium
87
88
104
105
106
107
108
109
Fr Ra
[223]
[226]
196.97
Cl
86
W Re Os Ir
132.91
Cu
Si
xenon
91.224
Hf Ta
Li
36
Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br
200.59
204.38
207.2
208.98
[209]
[210]
[222]
lutetium
darmstadtium roentgenium
110
111
Rf Db Sg Bh Hs Mt Ds Rg
[261]
[262]
lanthanum
cerium
57
58
[266]
[264]
praseodymium neodymium
59
60
[277]
[268]
[271]
[272]
promethium
samarium
europium
gadolinium
terbium
dysprosium
holmium
erbium
thulium
ytterbium
61
62
63
64
65
66
67
68
69
70
71
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
138.91
140.12
140.91
144.24
[145]
150.36
151.96
157.25
158.93
162.50
164.93
167.26
168.93
173.05
174.97
actinium
thorium
protactinium
uranium
neptunium
plutonium
americium
curium
berkelium
californium
einsteinium
fermium
mendelevium
nobelium
lawrencium
99
100
101
102
103
89
90
91
Ac Th Pa
[227]
232.04
231.04
92
93
94
95
96
97
98
U Np Pu Am Cm Bk Cf
238.03
[237]
[244]
[243]
[247]
[247]
[251]
Es Fm Md No Lr
[252]
[257]
[258]
[259]
[262]
9
The Electron Bucket Brigade
10
3
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Example: Electron Drift Rate
Pause
11
Resistivity
Pause
12
4
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Finding Resistance
13
Summary
Used background to see how voltage and current
relate moving through materials
Introduced Ohm’s Law and its application
Discussed the physical cause for resistance
Described electron drift rate and calculated this
value in a case study
Calculated resistance using the dimensions and
resistivity of a material
15
5
8/13/2013
Kirchhoff’s Laws
Nathan V. Parrish
PhD Candidate & Graduate
Research Assistant
School of Electrical and
Computer Engineering
•Introduce Kirchhoff’s Voltage Law (KVL) and apply to parallel
circuits
•Introduce Kirchhoff’s Current Law (KCL) and apply to series
circuits
•Use Kirchhoff’s Laws to solve a simple circuit
School of Electrical and Computer Engineering
Lesson Objectives
Describe KVL and KCL
Describe the voltage relationship of parallel
elements
Describe the current relationship of series
elements
Use Kirchhoff’s Laws to find unknown values in a
simple circuit
5
1
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Kirchhoff’s Voltage Law (KVL)
6
KVL and Parallel Circuits
7
2
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Kirchhoff’s Current Law (KCL)
8
What if?
9
3
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KCL and Series Circuits
10
Solving Values in Circuits
11
4
8/13/2013
Summary
Introduced KVL and KCL
Applied KVL to parallel elements
Applied KCL to series elements
Gave a justification for KCL
Solved a simple circuit using
Kirchhoff’s Laws
13
5
8/13/2013
Resistors
Nathan V. Parrish
PhD Candidate & Graduate
Research Assistant
School of Electrical and
Computer Engineering
•Introduce resistors as a circuit element
•Consider resistors in series and parallel
•Calculate equivalent resistance by combining parallel/series
resistors
School of Electrical and Computer Engineering
Learning Objectives
Apply Ohm’s Law and Kirchhoff’s Laws to simple
resistive circuits
Calculate an equivalent resistance of resistors in
parallel/series
Find equivalent resistance through successive
application of combining parallel and series
resistors
5
1
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Resistors
8
Review
Ohm’s Law
Kirchhoff’s Current Law
Kirchhoff’s Voltage Law
9
2
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Resistors in Series
Pause
10
Voltage Divider
11
3
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Resistors in Parallel
Pause
12
Current Divider
13
4
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Example
14
Summary
Introduced to resistors as a circuit element
Combine series/parallel resistors
Found an equivalent resistance using
successive application of series/parallel
resistance
16
5
8/13/2013
Dr. Bonnie Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
Lab Demo:
Introduction to
Electrical
Components
Demonstrate basic instruments and components.
School of Electrical and Computer Engineering
Lab Demo: Introduction to
Electrical Components
4
1
8/13/2013
Summary
Physical resistors
Color codes
Tolerances
Digital Multimeter (DMM)
Measure voltage, current, resistance
Protoboard (breadboard)
Ease of building circuits
5
Credits
Thanks to Marion Crowder (School of Electrical and Computer Engineering at
Georgia Tech) for video-taping the experiment
DMM used in experiment is manufactured by Fluke Corporation
7
2
8/13/2013
Lab Demo:
Resistors and
Connections
Dr. Bonnie Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
Resistors in series and parallel, measuring voltage and current in
circuits.
School of Electrical and Computer Engineering
Lesson Objectives
Demonstrate
Series and parallel resistance
Measure voltage and current
using the voltage divider law
and Ohm’s Law
4
1
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Review
R=R1+R2
R1
R2
R=
R1 R2
R1 + R2
R1
Resistors in Parallel
Protoboard
Resistors in Series
5
Lab Demo: Resistors and Connections
6
2
8/13/2013
Summary
Connect physical resistors in
parallel and in series
Measure voltages and currents in
a circuit, applying the voltage
divider law and Ohm’s Law
7
Credits
Thanks to Marion Crowder (School of Electrical and Computer Engineering
at Georgia Tech) for video-taping the experiment
DMM used in experiment is manufactured by Fluke Corporation
9
3
8/13/2013
Linearity
Nathan V. Parrish
PhD Candidate & Graduate
Research Assistant
School of Electrical and
Computer Engineering
•Describe linearity, superposition, and homogeneity
School of Electrical and Computer Engineering
Lesson Objectives
Define linearity, superposition, and
homogeneity
Identify if a given function exhibits
superposition or homogeneity
5
1
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Linear Circuits
Why is this course called linear circuits?
What does the linear mean?
6
Linearity Defined
If both properties hold,
the system is linear.
7
2
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Ohm’s Law: Linear
8
Examples and Counterexamples
9
3
8/13/2013
Summary
Introduced linear operators (superposition
and homogeneity)
Identified if an operator is linear
Used linear operators to generate new linear
operators
10
4
8/13/2013
Superposition
Nathan V. Parrish
PhD Candidate & Graduate
Research Assistant
School of Electrical and
Computer Engineering
•Use linearity (particularly superposition) to solve circuits
•Identify superposition as an important part of many analysis
techniques
School of Electrical and Computer Engineering
Lesson Objectives
Given a complex system, generate a set of
simple systems, each with a single
independent source
Using solution of simple systems, find the
complete behavior of the system
5
1
8/13/2013
Isolating Independent Sources
6
Steps For Superposition
Zero-out all independent sources
Return sources one at a time and solve for
value of interest in simplified system
Take the arithmetic sum of these values to
find the final quantity
7
2
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Example 1
8
Example 1 (a)
9
3
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Example 1 (b)
v(a) = 1V
10
Example 1 (c)
v(a) = 1V
v(b) = 3V
11
4
8/13/2013
Working with Dependent Sources
Dependent sources must be analyzed in each
solution
Must be linear
12
Example 2
13
5
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Example 2 (a)
14
Example 2 (b)
15
6
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Summary
Used superposition to solve circuits
Independent sources only
With dependent sources
16
7
8/13/2013
Dr. Bonnie Ferri
Systematic
Solution Methods:
Part 1
Professor and Associate Chair
School of Electrical and
Computer Engineering
Introduce several ways of obtaining circuit equations.
School of Electrical and Computer Engineering
Lesson Objective
Introduce
Mesh analysis
Node analysis
Thévenin equivalent circuit
Norton equivalent circuit
5
1
8/13/2013
Physical Behavior
Ohm’s Law
KVL
V = iR
sum of all voltages around any loop = 0
KCL
sum of all currents out of any node = 0
6
Systematic Ways to Solve Circuit Problems
Method
Mesh Analysis
Summary
Systematic KVL to obtain simultaneous
equations for currents
Node Analysis
Systematic KCL to obtain simultaneous
equations for voltages
Thévenin and
Norton Equivalent
Circuits
• Reduce circuit to smaller equivalent
• Source transformations using graphical
method
7
2
8/13/2013
Mesh Analysis
Define mesh currents, one for
each non-inclusive loop
Do KVL around each loop
is
I2
1.
2.
v1
+
-
R1
I1
R3
R2
Ro
I3
+
-
+
vo
-
v2
8
Node Analysis
Select a ground node
Define node voltages for every node
connected to 3 or more elements
Do KCL at every node
is
1.
2.
3.
v1
+
-
R1
R3
R2
Ro
+
-
+
vo
-
v2
9
3
8/13/2013
Summary
Method
Mesh Analysis
Summary
When to Apply
Systematic KVL,
• Multiple currents are needed
simultaneous equations for • Current sources are present
currents
Node Analysis
Systematic KCL,
• Multiple voltages are needed
simultaneous equations for • Voltage sources are present
voltages
Thévenin and Norton
Equivalent Circuits
Simple equivalent circuits,
source transformations
• Intermediate values not
important; only output voltage
or current
10
4
8/13/2013
Dr. Bonnie Ferri
Systematic
Solution Methods:
Part 2
Professor and Associate Chair
School of Electrical and
Computer Engineering
Introduce several ways of obtaining circuit equations.
School of Electrical and Computer Engineering
Lesson Objective
Demonstrate
Thévenin equivalent and Norton equivalent circuits
Source transformations
4
1
8/13/2013
Systematic solution Methods
Method
Summary
Node Analysis
KCL to obtain simultaneous • Multiple voltages are needed
equations for voltages
• Voltage sources are present
Thévenin and Norton
Equivalent Circuits
Simple equivalent circuits,
source transformations
Mesh Analysis
When to Apply
KVL to obtain simultaneous • Multiple currents are needed
equations for currents
• Current sources are present
• Intermediate values not
important; only output voltage
or current
5
Thévenin Equivalent
isc
a
Circuit
vTh
≈
vTh +
a
RTh
-
b
b
Replace circuit with equivalent
resistance and voltage source
6
2
8/13/2013
Thévenin Equivalent Circuit
vTh : open circuit across a-b and find vab= vTh
isc : short circuit across a-b and find isc
isc a
a
Circuit
Circuit
vTh
b
v Th = R Th i sc
b
RTh : circuit resistance with voltage sources
shorted and current sources open circuited
(when no dependent sources are present)
7
Thévenin Equivalent Example
0.2A
1v
+
-
10Ω
2Ω
4Ω
Ro
+
vo
-
+
-
2v
8
3
8/13/2013
Norton Equivalent Circuit
isc
a
RTh
vTh +
a
≈
-
isc
RTh
b
Thévenin equivalent circuit
Norton equivalent
circuit
b
Source Transformation: these configurations
are interchangeable in a circuit
9
Source Transformation Example
0.2A
1v
+
-
10Ω
2Ω
4Ω
Ro
+
vo
-
+
-
2v
10
4
8/13/2013
Summary
Mesh and node analysis
Systematic ways to find independent
simultaneous equations
Thévenin and Norton methods
Replace most of the circuit with a simple
equivalent circuit
Source transformations
Extra worked problems are given on
these methods
11
5
8/13/2013
Maximum Power
Transfer
Nathan V. Parrish
PhD Candidate & Graduate
Research Assistant
School of Electrical and
Computer Engineering
An introduction to linear electric circuit elements and a study of
circuits containing such devices.
School of Electrical and Computer Engineering
Lesson Objectives
Find the load resistance that gives maximum
power transfer to the load
Calculate this power consumed by the load
resistor giving maximum power transfer
5
1
8/13/2013
Two-Terminal Linear Circuits
6
Power Equations for Resistors
7
2
8/13/2013
Load Resistance
8
Maximum Power Transfer
9
3
8/13/2013
Summary
Specified power equations for resistors
Matched load resistance to system resistance
for maximum power transfer
Specified equation for maximum power
transfer
10
4
8/13/2013
Nathan V. Parrish
PhD Candidate & Graduate
Research Assistant
School of Electrical and
Computer Engineering
Wye-Delta
Transforms and
the Wheatstone
Bridge
•Transform resistors from a wye configuration to a delta
configuration and vice-versa
•How to use a wheatstone bridge to measure a resistance
School of Electrical and Computer Engineering
Learning Objectives
Transform resistor circuits between wye and
delta configurations
Specify a test resistor which balances a
Wheatstone bridge
Identify whether the resistor under test in a
Wheatstone bridge is below or above the target
resistance
5
1
8/13/2013
Wye-Delta Transformation
6
Summary
7
2
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Example
8
Wheatstone Bridge
9
3
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Summary
Used Y-∆ transform to simplify circuits
Balanced a Wheatstone bridge
Identified whether the resistor under test was
above or below balanced resistance based on
current across the bridge
10
4
8/13/2013
Dr. Bonnie Ferri
Application:
Resistors in
Sensors
Professor and Associate Chair
School of Electrical and
Computer Engineering
Show sensors that depend on variable resistance.
School of Electrical and Computer Engineering
Resistors in Sensors
Sensor: device that converts a physical
quantity to an electrical signal
Variable Resistors:
R ↓ as pressure ↑
R ↓ as temperature ↑
R ↑ as strain gauge elongates
R varies with position
4
1
8/13/2013
Lab Demo: Variable Resistors in Sensors
5
Summary
Resistance often varies with physical
properties
Sensors utilize this property to convert
physical quantities to voltage
6
2
8/13/2013
Credits
Thanks to Marion Crowder (School of Electrical and Computer Engineering at
Georgia Tech) for video-taping the experiment
Thanks for James Steinberg and Kevin Pham for technical assistance
Flexforce sensor manufactured by Tekscan
8
3
8/13/2013
Application:
Wheatstone
Bridge
Dr. Bonnie Ferri
Professor and Associate Chair
School of Electrical and
Computer Engineering
An Wheatstone Bridge used in a sensor.
School of Electrical and Computer Engineering
Wheatstone Bridge
R1
vs
+
-
R2
a
b
R3
Rx
Balance R2 and R3 so va =vb and apply the
voltage divider law
R3
Rx
vs =
vs
R1 + R3
R2 + R x
Cancel the vs . Similarly
R1
R2
=
R1 + R3 R2 + R x
Divide both sides of these last equations to get
Measure va - vb
R3 R x
=
R1 R2
4
1
8/13/2013
Lab Demo: Wheatstone Bridge
5
Summary
Wheatstone bridge is used to detect small changes in
resistance
Four strain gauges in a Wheatstone configuration
removes thermal effect
6
2
8/13/2013
Credits
Thanks to Sterling Skinner for building the flexible beam experimental platform
and Dr. Aldo Ferri for expertise on that system (both of the George W.
Woodruff School of Mechanical Engineering at Georgia Tech).
Thanks to Marion Crowder (School of Electrical and Computer Engineering at
Georgia Tech) for video-taping the experiment
DMM used in experiment is manufactured by Fluke Corporation
7
3
8/13/2013
Dr. Bonnie Ferri
Module 2
Resistive Circuits
Wrap Up
Professor and Associate Chair
School of Electrical and
Computer Engineering
Summary of Resistive Circuits Module
School of Electrical and Computer Engineering
Concept Map
Background
current,
voltage,
sources,
resistance,
circuits
Resistive Circuits
•
•
•
•
Resistors
Ohm’s Law
Kirchoff’s
Laws
Resistive
Series and
Circuits
parallel resistors
• Superposition
• Circuit
equations
• Max Power
• Configurations
• Applications
Power
Reactive
Circuits
Frequency
Analysis
3
1
8/13/2013
Important Concepts and Skills
Be able to reduce resistive networks to a single
equivalent resistance using parallel and series
connections
Understand Kirchoff’s Voltage Law (KVL) and
Kirchoff’s Current Law (KCL)
Be able to apply KVL and KCL to circuits to obtain
equations
Be able to compute voltages and currents from the
voltage divider law and the current divider laws
Understand superposition and its application in
circuits to find specific voltages and currents
4
Important Concepts and Skills
Given a color chart, be able to identify physical resistor values and
tolerances
Understand the purpose of a protoboard (breadboard) and its basic
operation
Understand how current can be measured in a circuit using the voltage
divider law
Given a circuit with multiple sources, be able
to use the Superposition Principle to solve for
circuit voltages and currents
5
2
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Important Concepts and Skills
Have a basic understanding of mesh analysis, node analysis, Thévenin
equivalent and Norton equivalent circuits and when to use one versus
another
Be able to solve for specific voltages and currents in a given circuit
Be able to compute the load resistance that
maximizes the power
6
Important Concepts and Skills
Know the transformation
Understand that these configurations may be used
in different applications, such as 3 phase circuits
Know examples of resistors that vary with physical
quantities
Understand how a potentiometer is used to measure
position or angle
Know when a Wheatstone Bridge is used in a
practical application
Be able to write equations for a Wheatstone Bridge
7
3
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Concept Map
1
Background
2
Resistive
Circuits
5
Power
3
Reactive
Circuits
4
Frequency
Analysis
8
4