## Practical Differentiator

The noise and stability at high. frequency can be corrected, in the practical differentiator circuit using the resistance R1 in series with Cl and the capacitor C f in parallel with resistance R f.

The circuit is shown in the Fig. 2.49. The resistance R comp is used for bias compensation. ## The Analysis of the Practical Differentiator

As the input current of op-amp is zero, there is no current input at node B. Hence it is at the ground potential. From the concept of the virtual ground, node A is also at the ground potential and hence VB = VA = 0 V.

For the current I, we can write where Z1 = Ri in series with C1

So in Laplace domain we can write,

Now the current II is, In Laplace, Taking we get, Applying at node A,  The time constant R 1C1 is much greater than R1C1 or R fC f and hence the equation (20) reduces to, Thus the output voltage is the RfCi times the differentiation of the input.

It may be noted that though R fel is much larger than R fCf or R1C1, it is less than or equal to the time period T of the input, for the true differentiation. ## Applications of Practical Differentiator

The practical differentiator circuits are most commonly used in :

1. In the wave shaping circuits to detect the high frequency components in the input signal.
2. As a rite-of-change detector in the FM demodulators.
3. The differentiator circuit is avoided in the analog computers.