This document discusses operational amplifiers used as integrators and differentiators. It describes the ideal and practical implementations of op-amp integrators and differentiators, including their circuit diagrams and frequency responses. It also provides examples of applications for each, such as ramp generators and analog-to-digital converters for integrators, and wave shaping and high-pass filtering for differentiators. The document is a presentation about op-amp integrators and differentiators delivered by Jatin Mahato and Supriya Nayak to the Department of Physics on February 28, 2020.

1. OPERATIONAL AMPLIFIERAS INTEGRATOR AND
DIFFERENTIATOR
DEPARTMENT OF PHYSICS
PRESENTED BY JATIN MAHATO (1801168007)
SUPRIYA NAYAK (1801168017)
28-02-2020 1

2. CONTENTS
1. OPERATIONAL AMPLIFIER
2. IC 741
3. OP-AMP INTEGRATOR
4. DRAWBACKS IN IDEAL INTEGRATOR
5. PRACTICAL INTEGRATOR
6. FREQUNCY RESPONSE
7. APPLICATION
8. IDEAL DIFFERENTIATOR
9. PRACTICAL DIFFERENTIATOR
10. FREQUENCY RESPONSE
11. APPLICATION
12. REFERENCES
28-02-2020 2

3.  An Operational Amplifier, or op-amp for short, is fundamentally a voltage
amplifying device designed to be used with external feedback components such as
resistors and capacitors between its output and input terminals.
 These feedback components determine the resulting function or “operation” of the
amplifier and by virtue of the different feedback configurations whether resistive,
capacitive or both, the amplifier can perform a variety of different operations,
giving rise to its name of “Operational Amplifier”.
WHAT IS OP AMP
28-02-2020 3

4.  The 741 Op Amp IC is a monolithic integrated circuit, comprising of a
general purpose Operational Amplifier. It was first manufactured by Fairchild
semiconductors in the year 1963. The number 741 indicates that this
operational amplifier IC has 7 functional pins, 4 pins capable of taking input
and 1 output pin.
 IC 741 Op Amp can provide high voltage gain and can be operated over a
wide range of voltages, which makes it the best choice for use in integrators,
summing amplifiers and general feedback applications.
IC-741
28-02-2020 4

5. 28-02-2020 5

6. OP-AMP INTEGRATOR
 Op-amp Integrator is an operational amplifier circuit that performs the
mathematical operation of Integration, that is we can cause the output to
respond to changes in the input voltage over time as the op-amp integrator
produces an output voltage which is proportional to the integral of the
input voltage.
28-02-2020 6

7. From fig , current through the resistor R,
Due to the virtual ground, i = ic
28-02-2020 7
Since the open loop gain and the input impedance of the are infinite A point may be
treated as virtual ground.
The current through the feedback capacitor C, Where q=C(0-Vo)

8. Drawbacks in ideal integrator
• For dc input (f = 0), reactance of capacitance, Xc is infinite. Because of this op-
amp goes into open loop configuration.In open loop configuration the gain is
infinite and hence the small input offset voltages are also amplified and appears
at output as error. This is referred as false triggering and must be avoided.
• Bandwidth is very small and used for only small range of input frequencies.
Due to all such limitations, an ideal integrator needs to be modified.

9. CIRCUITDIAGRAMOF PRACTICAL INTEGRATOR
28-02-2020 9
• The limitations of an ideal integrator can be
minimized in the practical circuit by adding
resistor Rf in parallel with capacitor C this
Rf avoids op-amp going into open loop
configuration at low frequencies.
• The addition of Rf will fix the low
frequency gain (A) of the circuit to a fixed
small value and so the input offset voltage
will have practically no effect on the output
offset voltage and variations in the output
voltage is prevented.

10. FREQUENCY RESPONSE OF INTEGRATOR
28-02-2020 10
fa
fb
Frequency(Hz)
|A|
in
db
• At f<fa ,opamp acts as inverting opamp.
• To use the opamp as integrator, input
signal should have freq. > fa
• the true integration is possible over the range fa < f < fb.
fa=1/(2πRf C) , cut off frequency
fb=1/2πRC , unit gain frequency
Where,

11. Square Wave Sine Wave
Step signal

12. APPLICATIONs OF INTEGRATOR
 analog-to-digital(A-D) converters
 ramp generators
 wave shaping applications.
 Digital voltmeters
 Op-amp integrating amplifiers are used to perform calculus operations in
analogue computers.
28-02-2020 12

13. OP-AMP DIFFERENTIATOR
 An op amp differentiator is basically an inverting amplifier with a
capacitor of suitable value at its input terminal, performs the
mathematical operation of Differentiation, that is it “produces a voltage
output which is directly proportional to the input voltage’s rate-of-
change with respect to time’’.
28-02-2020 13

14. 28-02-2020 14
CIRCUITAL ANALYSIS
As we can see from the figure that all the input current Ic flows through the feedback
resistor R i.e
Eq (I) shows that the output is the differentiation of the input with an iversion and a scale
multiplier of RC.

15. PRACTICAL DIFFERENTIATOR
 For an ideal differentiator, the gain increases
as frequency increases. Thus, at some higher
frequencies, the differentiator may become
unstable and cause oscillations which results
in noise.
 These problems can be avoided or corrected
in a practical differentiator circuit which uses
a resistor R1 in series with the input capacitor
and a capacitor Cf in parallel with the
feedback resistor.
28-02-2020 15

16. FREQUENCY RESPONSE OF PRACTICAL DIFFERENTIATOR
☻The gain of an op-amp differentiator is
directly dependent on the frequency of the
input signal. Hence, for DC inputs where f
= 0, the output is also zero. As the
frequency of the input signal increases, the
output also increases.
☻The frequency f1 is the frequency for
which the gain of the differentiator
becomes unity. It can be seen from the
figure that for frequency less than f1, the
gain is less than unity. For f1, the gain
becomes the unity (0 dB) and beyond f1,
the gain increases at 20dB per decade
28-02-2020 16

17.  The sine wave is converted to a cosine waveform
- giving 90° of phase shift of the signal
 A fast change to the input voltage signal, the
greater the output voltage change in response.
 The square wave input, only very short spikes
should be seen. The spikes will be limited by the
slope of the edges of the input waveform and also
the maximum output of the circuit and its slew
rate and bandwidth.
 The triangular wave input transforms to a square
wave in line with the rising and falling levels of
the input waveform.
28-02-2020 17

18. APPLICATIONOF DIFFERENTIATOR
⁎ to operate on triangular and rectangular signals.
⁎ wave shaping circuits, to detect high frequency components in the input
signal.
⁎ Differentiators have frequency limitations while operating on sine wave
inputs; the circuit attenuates all low frequency signal components and
allows only high frequency components at the output. In other words,
the circuit behaves like a high-pass filter.
28-02-2020 18

19. REFERENCES
• GOOGLE IMAGES
• ELECTRONICS 4U
• ELECTRONICSHUB
• ELECTRONICS TUTORIALS
• FUNDAMENTAL ELECTRONICS BY V.K MEHETA
• ELECTRINICS BOOK BY B.S GHOSH
28-02-2020 19

20. 28-02-2020 20