**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 Z_{1} = Ri in series with C1

So in Laplace domain we can write,

Now the current I_{I} 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 R_{1}C_{1}, 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 :

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