## 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.