The operational amplifier differentiator is similar to the basic inverting amplifier circuit except that the input component is a capacitor rather than a resistor (see Figure 2-22)
The output voltage of the differentiator circuit can be determined by the following equation:
In this equation AVIIAt is the change in input voltage divided by a specified time interval. A problem with the basic differentiator circuit is that the reactance of input capacitor CI (l/21rfCI) varies inversely with frequency. This causes the output voltage to increase with frequency and makes the circuit susceptible to high-frequency noise. To compensate for this problem, a resistor is connected in series with the capacitor on the inverting input (see Figure 2-23).
However, this circuit functions as a differentiator only on input frequencies which are less than those which can be determined by the following equation:
The time constant (RICl) should be approximately equal to the period of the input signal to be differentiated. In practice, series resistor RS is approximately 50 Ohm to 100 Ohm