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

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

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

The circuit in Fig. 1 operates on two supplies, while that in Fig. 2 is a single-supply integrator.  However, what makes them both integrators is the combination of the feedback capacitor (C1 in both examples) and the input resistor at the inverting input of the op amp (R1 in both examples).

To illustrate how these circuits perform integration, consider the circuit in Figure 1.  Given the properties of an op-amp, the voltages at the op amp inputs are equal and practically zero.  Since the currents going into the op amp inputs are ideally zero, then the current through R1 is equal to the sum of the currents through C1 and R2. Making R2>>R1 will make the R1 current practically the same as the C1 current, ic.  The current through R1 is Vin/R1, so ic is very close to Vin/R1 if R2>>R1.

Vout is equal to the voltage across C1, so Vout = -1/C ∫ ic dt. Thus Vout = -1/C ∫ Vin/R1 dt, which clearly shows that the circuit is indeed a integrator.

As a graphical example, the input voltage in both circuit examples is a square wave.  This emerges as a triangle wave at the output of the circuits (the integral of a square wave is a triangle wave).

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

See also:  Operational Amplifiers

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