Figure 1.  Circuit Diagram for a Dual-Supply Op Amp Differentiator

Figure 2.  Circuit Diagram for a Single-Supply Op Amp Differentiator

The circuits shown in Figures 1 and 2 are differentiator circuits, which are also sometimes referred to as 'differentiation amplifiers'. The main component of these circuits is the operational amplifier, configured in such a way that its output voltage is proportional to the derivative of its input voltage.

The circuit in Fig. 1 operates on two supplies, while that in Fig. 2 is a single-supply differentiator.  However, what makes them both differentiators is the combination of the feedback resistor (R2 in both examples) and the capacitor at the inverting input of the op amp (C1 in both examples).

To illustrate how these circuits perform differentiation, consider the circuit in Figure 1.  Since the current going into the inverting input is ideally zero, then the current through capacitor C1 is practically equal to the current through R2.  The current through C1 is just C1 times the rate of change of the voltage across it, dVc/dt.  If R1 << R2, then this current is approximately C1(dVin/dt). 

The output voltage Vout of this circuit is equal to the negative of this current times the resistance of R2.  Thus, Vout = -R2C1(dVin/dt), which clearly shows that the circuit is indeed a differentiator. As a graphical example, the input voltage in both circuit examples is a triangle wave.  This emerges as a square wave at the output of the circuits (the derivative of a triangle wave is a square wave).

Differentiator circuits like this are commonly seen in wave-shaping and function-generating circuits.  

See also:  Operational Amplifiers

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