Op Amp Integrator Circuit

The op amp analogue integrator circuit is easy to realise using a few components and it finds uses in a number of applications.

Op-amp Circuits Include:
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The operational amplifier forms the ideal basis for an analogue integrator circuit. Having virtually zero input current the output voltage forms an accurate integral of the input signal.

While it is possible to develop a simple integrator circuit using just a resistor and capacitor, the operational amplifier enables much better performance, i.e. a more true integration to be obtained.

Electronic integrator basics

In most op amp circuits, the feedback that is used is mainly resistive in nature with a direct resistive path forming at least part of the network. However for the integrator this is not the case - the component providing the feedback between the output and input of the op amp is a capacitor.

As the name of the op amp integrator implies, it performs a function that is an electronic equivalent to the mathematical integration function. In fact electronic integrator circuits can be used in analogue computers.

In terms of their operation, the circuit produces an output that is proportional to the integral of its input voltage with respect to time.

This means that the output voltage at any time is determined by the start output voltage, the length of time the input voltage has been present and the value of the input voltage.

The basic idea behind an integrator circuit is shown below. Although there are a few changes for the op amp integrator circuit, this concept is what is behind its operation.

Waveforms for an analogue integrator — Waveforms for an integrator circuit

From the diagram, it can be seen that while the input remains at zero, so does the output. However when a step input voltage is applied to the input, the output rises. When the step input returns to zero, the output remains at the voltage it last attained.

Operational amplifier integrator circuit

The basic operational amplifier integrator circuit consists of an op amp with a capacitor between the output and the inverting input, and a resistor from the inverting input to the overall circuit input as shown.

Basic op amp analogue integrator — Basic analogue op amp integrator circuit

One of the first points to note is that as the signal is applied to the inverting input, the output of the circuit is the inverse of a basic CR integrator network.

Waveforms for an op amp analogue integrator - note the inversion of the output because the input is applied tot he inverting input — Waveforms for an op amp integrator circuit
*Note: the inversion of the output because the input is applied to the op amp inverting input*

Op amp integrator design calculations

The primary calculation required for the circuit is to determine the output voltage for a given input voltage for a given time.

V_{out} = - \int_{0}^{t} \frac{V_{in}}{R C} d t + c

Where:
Vout = output voltage from op amp integrator
Vin = input voltage
T = time after start of application of voltage in seconds
R = resistor value in integrator in Ω
C = capacitance of integrator capacitor in Farads
c = constant of integration and in this case is the output starting voltage.

The negative sign in the equation reflects the inversion resulting from the use of the inverting input of the op amp.

Op amp saturation

It is obvious that the output of the integrator cannot rise indefinitely as the output will be limited.

The output of the op amp integrator will be limited by supply or rail voltage and the saturation of the op amp itself, i.e. how close to the rails the output can swing.

When designing one of these circuits, it may be necessary to limit the gain or increase the rail voltage to accommodate the likely output voltage swings.

While small input voltages and for short times may be acceptable, care must be taken when designing circuits where the input voltages are maintained over longer periods of time.

Op amp analogue integrator showing saturation point

Integrator reset capability

It is sometimes necessary to have a means whereby the op amp integrator can be reset to zero.

The addition of a reset facility or capability is very easy to achieve. It is accomplished by simply adding a switch across the integrator capacitor. This has the effect of discharging the capacitor and thereby resetting the overall integrator.

Op amp analogue integrator with reset switch shorting the capacitor — Analogue op amp integrator circuit with reset switch

The reset switch can be implemented in a variety of ways. Obviously a simple mechanical switch can be used, but it is also possible to use semiconductor switches. These are typically FET based switches because they have a very high off resistance and can be controlled as switches in this type of application more easily.

The op amp integrator circuit enables accurate integration of the input signal to be obtained. The circuit has been used in many analogue computers, and today the integration function is required in a number of analogue applications, where the op amp circuit is the ideal solution.