EE 1270: Introduction to Electric Circuits
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Lecture 13:
Operational Amplifiers
Part 1
Chapter 5
The Operational Amplifiers
Sections 5.1,5.2, 5.3
EE 1270 Introduction to Electric Circuits
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Operational Amplifiers
1
Purpose
1) Amplify AC/DC voltage (or current).
2) Perform addition, subtraction, multiplication, division,
differentiation, and integration of signals
EE 1270 Introduction to Electric Circuits
Suketu Naik
Operational Amplifiers: Applications
2
1) Amplify audio signals
2) Filter unwanted signals (frequencies)
3) And many more...
Audio Preamplifier
Subwoofer
Filter
EE 1270 Introduction to Electric Circuits
Suketu Naik
Operational Amplifiers
3
Pin Diagram
Positive
Power
Supply
Negative
Power
Supply
EE 1270 Introduction to Electric Circuits
Suketu Naik
Operational Amplifiers
4
Symbol & Notation
ip
in
EE 1270 Introduction to Electric Circuits
io
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OpAmp: Circuit Model
vp
vn
5
Output voltage in linear region
vo  Av d  A(v p  vn )
vo
Open loop gain
(without feedback)
vp
Input Resistance
Output Resistance
+
vo
-
vn
EE 1270 Introduction to Electric Circuits
Suketu Naik
OpAmp Characteristics
6
vp
+
vn
vo
-
An Ideal Op amp has infinite open-loop gain, infinite input
resistance and zero output resistance
When Op amp is connected in the circuit...

vp ip
vn in
vo
For an ideal OpAmp
 vp = vn (voltages at positive input
terminal and negative input terminal are
equal to each other)
 ip = in =
0 (currents entering the
positive and negative input terminals are
zero)
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example 5.1 a)
7
a) Find vo if va=1 V, vb=0 V
EE 1270 Introduction to Electric Circuits
Suketu Naik
AP5.1 a)
8
a) Find vo if vs=0.4, 2.0, 3.5, -0.6, -1.6, -2.4
Q: Which values of vs will cause op amp to saturate?
EE 1270 Introduction to Electric Circuits
Suketu Naik
p5.4 a) & (b)
9
40
5
2
10
a) Find vo if va = 1.5 V and vb = 0 V
b) Find vo if va = -0.5 V and vb = 0 V
EE 1270 Introduction to Electric Circuits
Suketu Naik
10
Op-Amp Configurations
1) Inverting Amplifier
2) Non-inverting Amplifier
3) Voltage Follower (or buffer)
4) Summing Amplifier
5) Difference Amplifier
EE 1270 Introduction to Electric Circuits
Suketu Naik
Inverting Amplifier
11
vo  
Rf
Rs
vs
1) Output and Input signals have opposite polarity (180 ° phase
shift)
2) Inverting Amplifier provides negative voltage gain
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example 5.2: Design of an Inverting Amplifier
EE 1270 Introduction to Electric Circuits
12
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p5.8: Design of an Inverting Amplifier
EE 1270 Introduction to Electric Circuits
13
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