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Monday, April 4, 2011

APPLICATIONS OF OP-AMP - II (DIFFERENTIATOR AND INTEGRATOR)


APPLICATIONS OF OP-AMP - II
                                      (DIFFERENTIATOR AND INTEGRATOR)
                                                  
      2.  a.  DIFFERENTIATOR

Design a differentiator circuit to differentiate an input signal that varies in frequency from 10 Hz to about 1 KHz.  If a sine wave of 1 V peak at 1000Hz is applied to the differentiator, draw the output waveform. Repeat the same for   square wave of 1Vpeak at 1kHz.

AIM:
To design a Differentiator circuit for the given specifications using Op-Amp IC 741.

APPARATUS REQUIRED:

S.No
Name of the Apparatus
Range
Quantity
1.
Function Generator
3 MHz
1
2.
CRO
30 MHz
1
3.
Dual RPS
0 – 30 V
1
4.
Op-Amp
IC 741
1
5.
Bread Board

1
6.
Resistors


7.
Capacitors


8.
Connecting wires and probes
As required


THEORY:

The differentiator circuit performs the mathematical operation of differentiation; that is, the output waveform is the derivative of the input waveform.  The differentiator may be constructed from a basic inverting amplifier if an input resistor R1 is replaced by a capacitor C1.  The expression for the output voltage is given as,

Vo = - Rf C1 (dVi /dt)

Here the negative sign indicates that the output voltage is 180 0 out of phase with the input signal.  A resistor Rcomp = Rf is normally connected to the non-inverting input terminal of the op-amp to compensate for the input bias current.  A workable differentiator can be designed by implementing the following steps:

  1. Select fa equal to the highest frequency of the input signal to be differentiated.  Then, assuming a value of C1 < 1 µF, calculate the value of Rf.
  2. Choose fb  = 20 fa and calculate the values of  R1 and Cf so that R1C1 = Rf Cf.

The differentiator is most commonly used in waveshaping circuits to detect high frequency components in an input signal and also as a rate–of–change detector in FM modulators.

PIN DIAGRAM:


CIRCUIT DIAGRAM OF DIFFERENTIATOR:


DESIGN :

Given fa = ---------------  
We know the frequency at which the gain is 0 dB,  fa  = 1 / (2π Rf C1)
Let us assume C1 = 0.1 µF; then
Rf = _________
Since fb = 20 fa, fb = ---------------
We know that the gain limiting frequency fb = 1 / (2π R1 C1)
Hence R1 = _________
Also since R1C1 = Rf Cf   ; Cf = _________

PROCEDURE:

  1. Connections are given as per the circuit diagram.
  2. + Vcc and - Vcc supply is given to the power supply terminal of the Op-Amp IC.
  3. By adjusting the amplitude and frequency knobs of the function generator, appropriate input voltage is applied to the inverting input terminal of the Op-Amp.
  4. The output voltage is obtained in the CRO and the input and output voltage waveforms are plotted in a graph sheet.

OBSERVATIONS:

Input - Sine wave

S.No.
Amplitude
( No. of div x Volts per div )
Time period
( No. of div x Time per div )
Input


Output



Input – Square wave

S.No.
Amplitude
( No. of div x Volts per div )
Time period
( No. of div x Time per div )
Input


Output




MODEL GRAPH:




















RESULT:
The design of the Differentiator circuit was done and the input and output waveforms were obtained.

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