Practical Differentiator

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.

Practical Differentiator

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

Practical Differentiator

where Z1 = Ri in series with C1

So in Laplace domain we can write,

 Practical Differentiator

Now the current II is,

Practical Differentiator

In Laplace,

Practical Differentiator

Taking we get,

Practical Differentiator

Applying at node A,

Practical Differentiator

Practical Differentiator

The time constant R 1C1 is much greater than R1C1 or R fC f and hence the equation (20) reduces to,

Practical Differentiator

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.

Practical Differentiator

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.

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