**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 R**

_{1 }is replaced by a capacitor C_{1. }The expression for the output voltage is given as,**V**

_{o }= - R_{f}C_{1 }(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:**Select f**_{a}equal to the highest frequency of the input signal to be differentiated. Then, assuming a value of C_{1}< 1 µF, calculate the value of R_{f}.**Choose f**_{b}_{ }= 20 f_{a}and calculate the values of R_{1}and C_{f}so that R_{1}C_{1 }= 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}C_{1})**Let us assume C**

_{1}= 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 R_{1}C_{1})**Hence R**

_{1}= _________**Also since R**

_{1}C_{1 }= R_{f}C_{f}; C_{f}= _________**PROCEDURE:**

**Connections are given as per the circuit diagram.****+ V**_{cc }and - V_{cc}supply is given to the power supply terminal of the Op-Amp IC.**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.****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.

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

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