Q.Explain how an operational amplifier can be used as a differentiator?

An op-amp differentiator gives an output proportional to the rate of change of its input — it performs the mathematical inverse of integration. It resembles an inverting amplifier but with the input resistor replaced by a capacitor: the input $V_i$ is applied to the inverting $(-)$ node through a capacitor $C$, the feedback element is a resistor $R_f$, and the $(+)$ terminal is grounded.

At the virtual-ground node the current through the input capacitor is $C\,\dfrac{dV_i}{dt}$; this current flows through the feedback resistor, so the output is

The negative sign indicates inversion, and the output magnitude follows how fast the input is changing. A steady (DC) input gives zero output; a fast-changing input gives a large output.

Its characteristic waveform transformations are:

• A square-wave input produces sharp spikes at each edge, because the output responds only at the instants when the input changes abruptly. …