Op amp differentiator circuit design and working


Op amp is known as Operational Amplifier. We can design an Op amp differentiator circuit using a resistor and a capacitor. We connect capacitor at the input and a resistor at the feedback. So, lets discuss how an Op amp differentiator circuit works.

As the name implies this circuit performs the mathematical operation of differentiator. Therefore the output voltage is proportional to the rate of change of the input voltage with respect to time.

Circuit Diagram:

Opamp Differentiator
Opamp Differentiator
  • The above circuit is performed on NI Multisim Simulation. Check out the video below for the complete simulation.
  • Current flowing through capacitor= Input current In.
  • Current flowing through resistor= feedback current I1.
  • Now using virtual ground concept, voltage at negative terminal will be zero. Therefore no current flows through the op amp.
  • In=I1
  • I1= -Vout/R1
  • Capacitor Charge Q= Vin*C1
  • Differentating( Rate of Change)= dQ/dt= C1*(dVin/dt).
  • But dQ/dt= In= Capacitor current
  • In= I1C*(dVin/dt)
  • From above equations -Vout/R1C1*(dVin/dt).
  • Therefore Vout= -R1*C1*(dVin/dt).

The above equation represents the working of the Op amp as a differentiator. The output voltage is also proportional to the values of capacitor and resistor.

Output: Op Amp as a differentiator

Opamp Differentiator Output
Opamp Differentiator Output

Red graph is the input voltage and Dark Blue graph represents the output voltage.

The differential of sine wave is cos wave which we can see as an output.




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