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,
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 :
- 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.