The differentiation or differentiator circuit performs the mathematical operation of differentiation; that is, the output waveform is the derivative of the input waveform. A circuit in which the output voltage waveform is the differentiation of input voltage is called differentiator as shown in Figure 1.
Figure 1
The expression for the output voltage can be obtained from the Kirchoff's current equation written at node V2.
Thus the output Vo is equal to the RC times the negative instantaneous rate of change of the input voltage Vin with time. A cosine wave input produces sine output. Figure 1 also shows the output waveform for different input voltages.
The input signal will be differentiated properly if the time period T of the input signal is larger than or equal to RfC.
T ≥ RfC
As the frequency changes, the gain changes. Also at higher frequencies the circuit is highly susceptible at high frequency noise and noise gets amplified. Both the high frequency noise and problem can be corrected by adding few components. as shown in figure 2.
Figure 2
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