In this video, op-amp differentiator circuit has been discussed (with derivation) and few examples have been solved based on this op-amp differentiator circuit.

Op-Amp as Differentiator:

In Op-amp integrator circuit, if we interchange the position of resistor and capacitor then it can be used as a differentiator. The relation between the output and input has been derived in this video.

Application of differentiator circuit:

The differentiator circuit can be used to identify the rate at which the input signal is changing.
So, the differentiator circuit can be used to find the high-frequency component of the input signal and it can be used in the application of edge detection.
In early days, when digital computers were not evolved at that time for analog computation these op-amp based differentiator circuits were used.

Limitation of simple differentiator circuit:

In this simple differentiator circuit, as the input frequency increases, the gain of the differentiator will increase. So, the simple differentiator is very sensitive to the high-frequency noise. Also, in simple differentiator, the input impedance of the circuit is equal to the reactance of the capacitor. So at high frequency, the input impedance will reduce.
These problems can be overcome by using the practical differentiator circuit.

Practical Differentiator Circuit:

In practical differentiator, the series resistor is added to input capacitor. This resistor will ensure that at high frequencies, the input impedance of the circuit will be at least equal to the value of the resistor.
And because of this series resistor, the gain of the op-amp at high frequency will be restricted.
For better stability of the output signal at the high frequency and to prevent oscillations, feedback capacitor is also connected in parallel with the feedback resistor.

The condition for proper differentiation of input signal:

For proper differentiation of the input signal, the frequency of the input signal should be lesser than the cut-off frequency. (At least 10 times less than the cut-off frequency for the accurate differentiation)

The timestamps for the different topic covered in the video is given below:

0:15 Op-Amp as a Differentiator
1:35 Derivation of Op-Amp Differentiator Circuit
3:39 Output of differentiator for the different input signals
4:22 Limitations of the simple differentiator circuit
7:56 Practical Op-Amp differentiator
11:55 Example 1
14:02 Example 2
16:48 Example 3

The link to the related videos on the op-amp:

Introduction to Operational Amplifier:
[ Ссылка ]

Inverting Op-Amp:
[ Ссылка ]

Non-Inverting Op-Amp:
[ Ссылка ]

Op-Amp Integrator
[ Ссылка ]

This video will be helpful to all students of science and engineering in understanding the working of op-amp differentiator.

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