**Practical Differentiator:**

The noise and stability at high frequency can be corrected, in the practical differentiator circuit using the resistance R_{1} in series with C_{1} 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.

**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 V_{B} = V_{A} = 0V.

For the current I, we can write

where Z_{1} = R_{1} in series with C_{1}

So in Laplace domain we can write,

Now the current I_{1} is,

In Laplace,

Taking we get,

Applying at node A,

If R_{f}C_{f} = R_{1}C_{1} then

The time constant R_{f}C_{1} is much greater than R_{1}C_{1} or R_{f}C_{f} and hence the equation (20) reduces to,

Thus the output voltage is the R_{f}C_{1} times the differentiation of the input.

It may be noted that though R_{f}C_{1} is much larger than R_{f}C_{f} 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.