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Lecture 4: Operational
Amplifiers
What can you do with infinite gain?
23 May 2017
Introduction to Engineering Electronics
K. A. Connor
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Some History
Fairchild
0.60 Inches
1964: The First Linear IC
1965: A Best-Seller
The µA702 Op-Amp
The µA709 Op-Amp
12 Transistors
14 Transistors
Designer: Bob Widlar
Designer: Bob Widlar
23 May 2017
Introduction to Engineering Electronics
K. A. Connor
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2 Minute Quiz
Name_____________
• What is the voltage
measured by the
blue probe?
• What is the voltage
measured by the
green probe?
• What is the voltage
measured by the red
probe?
23 May 2017
Section _____
R1
V
90k
V1
V
R2
10V
10k
Introduction to Engineering Electronics
K. A. Connor
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V
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Answers
• The green probe:
10V
• The red probe: 1V
• The blue probe: 0V
• Voltage Divider:
R2
V 
10V
R1  R2
R1
V
90k
V1
V
R2
10V
10k
0
23 May 2017
Introduction to Engineering Electronics
K. A. Connor
V
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What can you do with infinite gain?
• The goal of amplifier designers: huge gain.
• What are the problems and opportunities
associated with infinite gain?
• First, we need a model.
23 May 2017
Introduction to Engineering Electronics
K. A. Connor
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Op-Amp
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Introduction to Engineering Electronics
K. A. Connor
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Ideal Op-Amp Model
• Gain is infinite
VOUT
VOUT
A


V  V
V IN
• Input resistance is infinite
RIN  
• Output resistance is zero
ROUT  0
• Input voltage is zero
V IN  0
• Input current is zero
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I  0
Introduction to Engineering Electronics
K. A. Connor
I  0
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Ideal Op-Amp Continued
• Bandwidth is also infinite. Thus, an ideal
op-amp works the same at all
frequencies.
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Introduction to Engineering Electronics
K. A. Connor
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Feedback
• Like most engineered systems, the opamp uses feedback to realize its
potential value.
• Feedback comes in two forms
 Positive Feedback
 Negative Feedback
• It seems like positive feedback might be
best, but negative feedback makes the
op-amp work
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Introduction to Engineering Electronics
K. A. Connor
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Feedback Examples
From a Zoology Course
• You just ate a Krispy Kreme donut and your
blood glucose levels are on the rise. In
response to this rise, the pancreas is
releasing insulin into the blood stream
stimulating storage of glucose. As a result,
blood glucose levels begin to drop. Is this an
example of positive or negative feedback?
• A woman is in labor, pressure receptors in
the birth canal send messages to her brain
that result in increased contraction of the
uterus and increased pressure in the birth
canal. Is this positive or negative feedback?
23 May 2017
Introduction to Engineering Electronics
K. A. Connor
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Feedback: Valve Example
• As the water nears the specified level, the
valve is closed.
• Negative feedback is most commonly used to
control systems.
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Introduction to Engineering Electronics
K. A. Connor
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Golden Rules for Op-Amps
• The output attempts to do whatever is
necessary to make the voltage
difference between the two inputs zero.
(Negative Feedback is Required)
• The inputs draw no current.
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Introduction to Engineering Electronics
K. A. Connor
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Positive and Negative
Feedback
• Connecting the output to the positive
input is positive feedback
• Connecting the output to the negative
input is negative feedback
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Introduction to Engineering Electronics
K. A. Connor
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Op-Amp Configurations
• Buffer or Voltage Follower
 No voltage difference between the output
and the input
 Draws no current, so it puts no load on the
source
 Used to isolate sources from loads
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Introduction to Engineering Electronics
K. A. Connor
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Op-Amp Configurations
V2
• Non-Inverting Amplifier
 No voltage difference between inputs
V1  V2
 Resistors act like voltage divider
R2
V2 
VO
R1  R2
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Introduction to Engineering Electronics
K. A. Connor
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Op-Amp Configurations
• Non-Inverting Amplifier Continued
 Combining the two equations for the
voltages gives us the relationship between
input and output
VOUT

R1 
 VIN 1  
R2 

Note that this formula is different in the lab write up
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Introduction to Engineering Electronics
K. A. Connor
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Op-Amp Configurations
V2
• Inverting Op-Amp
 Current through R1 equals the current
through Rf
 No current in the inputs
 The voltage at both inputs is zero
V2  0
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Introduction to Engineering Electronics
K. A. Connor
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Op-Amp Configurations
• Inverting Op-Amp Continued
 Current through R1
 Current through Rf
23 May 2017
V1  0 V1
I1 

R1
R1
VO  0
VO
I2  

Rf
Rf
Introduction to Engineering Electronics
K. A. Connor
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Op-Amp Configurations
• Why the minus sign for the current
through Rf?
 The convention for Ohm’s Law is that the
current flows from the high voltage to the
low voltage for a resistor
 Here the current flows from the low voltage
(ground) to the high voltage (VO)
23 May 2017
Introduction to Engineering Electronics
K. A. Connor
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Op-Amp Configurations
• Inverting Op-Amp Continued
 The current through R1 must equal the
current through R2 since there is no current
in the inputs.
 Combining the two equations for the
currents
VOUT  VIN
23 May 2017
Introduction to Engineering Electronics
K. A. Connor
Rf
R1
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Op-Amp Configurations
• Inverting Summing Amplifier
 Each input resistor contributes to the
current.
R
R
R
VOUT  V1
23 May 2017
f
R1
 V2
Introduction to Engineering Electronics
K. A. Connor
f
R2
 V3
f
R3
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Op-Amps: Practical Issues
• Op-Amps require power
 741 requires plus and minus 15V
 Others may require only positive or both
positive and negative voltages
 Output voltage is limited to  VCC  VOUT  VCC
 Usually filter capacitors are connected to
power to reduce noise
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Introduction to Engineering Electronics
K. A. Connor
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Op-Amps: Practical Issues
Note: Literally a
Black Box
• We use real op-amps: 741
• Note the pin connections for the IC
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Introduction to Engineering Electronics
K. A. Connor
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Op-Amps: Practical Issues
+ 15 V
7
1
+
1.0 uF
+
2
-
6
Vout
LM741
4
5
R1
3
U1
Rstability
V1
1.0 uF
+
-15 V
R2
• Note the pins (not all are used)
• Extra resistor corrects offset problem
Rstability 
23 May 2017
R1 R2
R1  R2
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K. A. Connor
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• ICs come in many
types of packages.
We will use the 8pin, dual-in-line or
DIP package
• Note the other offset
nulling circuit
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Introduction to Engineering Electronics
K. A. Connor
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Where Will You See This
Information Next?
• Op-amps: Many Courses Including
 ECSE-2010 Electric Circuits
 ECSE-2050 Analog Electronics
• Feedback and Control
 ENGR-2350 Embedded Control
 ECSE-4440 Control Systems Engineering
 ECSE-496x Control Systems Design
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Introduction to Engineering Electronics
K. A. Connor
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Embedded Control
• Studio Classroom
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Introduction to Engineering Electronics
K. A. Connor
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http://litec.rpi.edu
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Introduction to Engineering Electronics
K. A. Connor
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Feedback and Control Example
• The inverted pendulum is like balancing
a baseball bat
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Introduction to Engineering Electronics
K. A. Connor
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Inverted Pendulum Experiment
http://www.univ-valenciennes.fr/LAMIH/pendule/english/index.html
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Introduction to Engineering Electronics
K. A. Connor
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Magnetic Levitation
• Trains can magnetically fly over a
roadbed with position sustained by
some kind of control system
• Our Lab 10 is on maglev
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Introduction to Engineering Electronics
K. A. Connor
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More Magnetic Levitation
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Introduction to Engineering Electronics
K. A. Connor
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Engineering Ethics
• Electrical and Computer Engineers do not
usually face immediate ethical issues
involving public health and safety
• System control is one of many exceptions
• From the IEEE Code of Ethics
 We agree to accept responsibility in making
engineering decisions consistent with the safety,
health and welfare of the public, and to disclose
promptly factors that might endanger the public or
the environment;
• http://www.iit.edu/departments/csep/eac/post
_workshop.html
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Introduction to Engineering Electronics
K. A. Connor
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