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Operational Amplifiers: Basics and Design Aspects







A tutorial by Jonathan Ames

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Table of Contents


1. Operational Amplifi er (Op-Amp) Basics................................................................ 4
1.1. Symbols and Schematic ..................................................................................... 4
1.2. Kirchhoff’s Current Law applied to Op-amps .................................................... 6
1.3. Input/Output Impedance ..................................................................................... 8
1.4. Supply voltages................................................................................................. 10
1.5. Open/Closed Loop Gain, Positive/Negative Feedback..................................... 11
1.6. Frequency Response ......................................................................................... 12
1.7. Basic Op-Amp Circuits..................................................................................... 13

1.7.1. Inverting amplifier .................................................................................... 13
1.7.2. Non-inverting amplifier ............................................................................ 14
1.7.3. Comparator ............................................................................................... 15
1.7.4. Voltage follower ....................................................................................... 16

2. Op-amp Circuits ..................................................................................................... 18
2.1. Derived Op-Amp Circuits................................................................................. 18

2.1.1. Summation amplifier ................................................................................ 18
2.1.2. Integration ................................................................................................. 19
2.1.3. Differentiation........................................................................................... 20
2.1.4. Differential amplifier ................................................................................ 21

2.2. Applied Op-Amp Circuits................................................................................. 22
2.2.1. Audio amplifier......................................................................................... 22
2.2.2. Instrumentation amplifier.......................................................................... 24
2.2.3. Precision full-wave rectifier...................................................................... 26
2.2.4. Voltage-to-Current converter.................................................................... 27

3. Op-Amp Practical Considerations ........................................................................ 29
3.1. Input/Output Offset Voltage ............................................................................. 29
3.2. Input Bias Current / Input Offset Current ......................................................... 29
3.3. Common Mode Rejection Ratio (CMRR) ........................................................ 29
3.4. Output Short-Circuit Current ............................................................................ 30

4. Op-amp Circuit Design .......................................................................................... 31
5. Conclusions.............................................................................................................. 39
6. References................................................................................................................ 41

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KCL analysis for the integrator can be accomplished by introducing the following

formula for the current through the capacitor:









=
dt

dV
Ci cc

The current flowing through the capacitor fluctuates as time passes, so the above formula

is necessary to describe it. The KCL analysis looks like this:

0=+ cr ii

0=+
−−

dt
dV

C
R
VV cs

Vc is the voltage across the capacitor, so Vc = Vout – V- , and

( )

0=
−−

+
−−

dt
VVd

C
R
VV outs

V- = 0, so

0=+
dt

dV
C

R
V outs

s
out V

RCdt
dV 1

−= ∫−=
2

1

1 t

t
sout dtVRC

V



2.1.3. Differentiation


Differentiation is the counterpart to integration and by simply switching the

location of the resistor (R) and capacitor (C), a differentiator circuit can be formed.

Since a capacitor does not allow dc current to pass through it, the voltage sources

associated with the integrator and differentiator circuits are ac sources. See the circuit

below.

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Figure 16 Differentiator circuit


The KCL analysis for a differentiator is naturally similar to the analysis of the integrator.

Once again, ⎟







=
dt

dV
Ci cc

0=+ cr ii

0=+
−−

dt
dV

C
R

VV cout

V- = 0 and Vc = Vs – V-, so

0=+
dt

dV
C

R
V sout

dt
dV

RCV sout −=



2.1.4. Differential amplifier



Figure 17 Differential amplifier [6]



Vout
+

-

R

C

Vs

ir

ic

-

+

-

+

-
+ Vout

+

-

Rf

Rb

Ra

Vb -
+ Va

Rc

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inverting or non-inverting amplifier, comparator, or voltage follower, and if a capacitor is

included, then integration and differentiation is possible. Three op-amps grouped into two

stages form an instrumentation amplifier, while an op-amp working with a couple diodes

produces a rectifier. However, certain practical considerations should be realized when

dealing with op-amps including offset voltages and output short-circuit current. Finally,

op-amp circuit design is the same as for any other project when it comes to simulation

and breadboarding. Multisim8 makes the simulation of a project, like the siren circuit,

possible without having to purchase components or be concerned with cost factors.

Breadboarding the siren circuit confirms its functionality, and oscilloscope prints

illustrate the various waveforms. Sometimes it is best to work with the individual op-

amps, especially if problems are encountered. Many other projects and designs are

possible with operational amplifiers, and hopefully a tutorial such as this will enhance the

understanding needed to make such projects succeed.

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6. References


[1] Cox, James, Fundamentals of Linear Electronics: Delmar (2002)

[2] Paynter, Robert, Introductory Electronic Devices and Circuits, Upper Saddle River,
New Jersey: Prentice Hall (2003)

[3] Hambley, Allan R., Electronics, Upper Saddle River, New Jersey: Prentice Hall
(2000)

[4] Grob, Bernard; Schultz, Mitchel E, Basic Electronics: Glencoe/McGraw-Hill (2003)

[5] Gayakwad, Ramakant A., Op-amps and Linear Integrated Circuits, Upper Saddle
River, New Jersey: Prentice Hall (2000)

[6] DeCarlo, Raymond A.; Lin, Pen-Min, Linear Circuit Analysis, New York, New York:
Oxford University Press (2001)

[7] Multisim8

[8] Datasheet for MC1458, by ON Semiconductor™ http://onsemi.com March 2001

[9] Datasheet for LM741, by National Semiconductor www.national.com August 2000

[10] Datasheet for LM380, by National Semiconductor, December 1972

[11] Datasheet for LM386, by National Semiconductor www.national.com January 2000

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