Op-Amp Integrator (with Derivation and Solved Examples)

In this video, op-amp integrator circuit has been discussed (with derivation) and few examples have been solved based on this op-amp integrator circuit. Op-Amp as Integrator: In inverting op-amp configuration, by replacing the feedback resistor with a capacitor, it can be used as integrator circuit. The relation between the output and input has been derived in this video. Limitation of simple integrator circuit: In this simple integrator circuit, for DC input or for very low-frequency signal the capacitor will act as an open circuit and the input signal will see a very high gain (Open loop gain of the op-amp). So, even if very small DC signal is present at the input, it can lead the output into the saturation. So, even if your signal does not contain any DC signal, but because of the input offset voltage, the output of the op-amp may get either saturated or distorted. Practical Integrator Circuit: The problem of the simple integrator circuit can be overcome by connecting feedback resistor in parallel with the feedback capacitor. So, because of the feedback resistor, the gain of the circuit for DC signal will get restricted and saturation of the output voltage can be avoided.And the circuit will behave as a low-pass filter. The condition for proper integration of input signal: For proper integration of input signal, the frequency of the input signal should be higher than the cut-off frequency. (At least 10 times the cut-off frequency) The timestamps for the different topic covered in the video is given below: 0:48 Op-Amp as an integrator (Derivation) 4:32 Output of Integrator for the different input signals 5:54 Limitations of the simple integrator circuit 8:57 Practical Op-Amp integrator 12:08 Example 1 13:10 Example 2 14:51 Example 3 17:15 Example 4 (For Practice) The link to the related videos on the op-amp: Introduction to Operational Amplifier:    • Introduction to Operational Amplifier: Cha...   Inverting Op-Amp:    • Operational Amplifier: Inverting Op Amp an...   Non-Inverting Op-Amp:    • Operational Amplifier: Non-Inverting Op-Am...   This video will be helpful to all students of science and engineering in understanding the working of op-amp integrator. Follow me on YouTube:    / allaboutelectronics   Follow me on Facebook:   / allaboutelecronics   Follow me on Instagram:   / all_about.electronics   Music Credit: http://www.bensound.com/