Introduction

Operational amplifiers (op-amps) are versatile components widely used in analog electronics. They can perform various mathematical operations, including amplification, differentiation, and integration. This document outlines the configurations and applications of op-amps in amplifier, differentiator, and integrator circuits.

1. Op-Amp as an Amplifier

Inverting Amplifier

Circuit Configuration:

  • The input signal is applied to the inverting terminal (-) through a resistor (R1).
  • A feedback resistor (R2) is connected from the output to the inverting terminal.
  • The non-inverting terminal (+) is grounded.

Transfer Function: [ V_{out} = -\left(\frac{R2}{R1}\right) V_{in} ]

  • The output voltage is inverted and scaled by the ratio of the resistors.

Applications:

  • Signal conditioning
  • Audio amplifiers
  • Data acquisition systems

Non-Inverting Amplifier

Circuit Configuration:

  • The input signal is applied to the non-inverting terminal (+).
  • A feedback resistor (R2) is connected from the output to the inverting terminal (-), with another resistor (R1) connected from the inverting terminal to ground.

Transfer Function: [ V_{out} = \left(1 + \frac{R2}{R1}\right) V_{in} ]

  • The output voltage is in phase with the input and scaled by the resistor ratio.

Applications:

  • Buffering signals
  • Voltage followers
  • Signal amplification without inversion

2. Op-Amp as a Differentiator

Differentiator Circuit

Circuit Configuration:

  • The input signal is applied to the inverting terminal (-) through a capacitor (C).
  • A resistor (R) is connected from the inverting terminal to the output.
  • The non-inverting terminal (+) is grounded.

Transfer Function: [ V_{out} = -RC \frac{dV_{in}}{dt} ]

  • The output voltage is proportional to the rate of change of the input voltage.

Applications:

  • Edge detection in signal processing
  • High-frequency signal detection
  • Analog computation of derivatives

3. Op-Amp as an Integrator

Integrator Circuit

Circuit Configuration:

  • The input signal is applied to the inverting terminal (-) through a resistor (R).
  • A capacitor (C) is connected from the inverting terminal to the output.
  • The non-inverting terminal (+) is grounded.

Transfer Function: [ V_{out} = -\frac{1}{RC} \int V_{in} dt ]

  • The output voltage is proportional to the integral of the input voltage over time.

Applications:

  • Signal integration in analog computers
  • Low-pass filters
  • Accumulating data in control systems

Conclusion

Operational amplifiers are fundamental components in analog electronics, providing essential functions such as amplification, differentiation, and integration. Understanding these configurations allows engineers and technicians to design and implement a wide range of electronic circuits for various applications.