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 C_1.  The expression for the output voltage is given as,

V_o = - R_f C₁ (dV_i /dt)

Here the negative sign indicates that the output voltage is 180 ⁰ out of phase with the input signal.  A resistor R_comp = R_f 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 f_a equal to the highest frequency of the input signal to be differentiated.  Then, assuming a value of C₁ < 1 µF, calculate the value of R_f.
2. Choose f_b  = 20 f_a and calculate the values of  R₁ and C_f so that R₁C₁ = R_f C_f.

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 f_a = ---------------  

We know the frequency at which the gain is 0 dB,  f_a  = 1 / (2π R_f C₁)

Let us assume C₁ = 0.1 µF; then

R_f = _________

Since f_b = 20 f_a, f_b = ---------------

We know that the gain limiting frequency f_b = 1 / (2π R₁ C₁)

Hence R₁ = _________

Also since R₁C₁ = R_f C_f   ; C_f = _________

PROCEDURE:

1. Connections are given as per the circuit diagram.
2. + V_cc and - V_cc 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.