# Op Amp Differentiator Circuit

### - design details, equations and practical ideas for the operational amplifier or op amp differentiator circuit.

The differentiator circuit, is in many ways, the exact opposite of the integrator.

As op amps make ideal platforms for many analogue functions, this is true for the differentiator and op amp differentiator circuits are quick and easy to realise with a minimum number of components.

## Op amp differentiator basics

A differentiator circuit is one in which the voltage output is directly proportional to the rate of change of the input voltage with respect to time.

This means that a fast change to the input voltage signal, the greater the output voltage change in response.

As a differentiator circuit has an output that is proportional to the input change, some of the standard waveforms such as sine waves, square waves and triangular waves give very different waveforms at the output of the differentiator circuit.

Waveforms after differentiation

For these waveforms it can be seen that the greater the change, the higher the output. In fact for the square wave input, only very short spikes should be seen. The spikes will be limited by the slope of the edges f the input waveform and also the maximum output of the circuit. The spikes should also decay swiftly. Again this may be limited by the circuit. On the diagram, the decay is not infinitely fast.

The triangular wave input transforms to a square wave in line with the rising and falling levels of the input waveform.

The sine wave is converted to a cosine waveform - giving 90° of phase shift of the signal. This can be useful in some circumstances.

## Op amp differentiator circuit

The circuit of the op amp differentiator is very similar to the integrator, except that the capacitor and inductor are changed in their positions.

Op amp differentiator circuit

Unlike the integrator circuit, the op amp differentiator has a resistive element in the feedback from the output to the inverting input. This gives it DC stability - an important factor in some applications.

## Design equations

In order to develop the component values within the op amp differentiator circuit, it is necessary to be able to assess its performance.

The voltage output for the op amp differentiator can be determined from the relationship below:

Where:
Vout = output voltage from op amp differentiator
Vin = input voltage
t = time in seconds
R = resistor value in differentiator in Ω
C = capacitance of differentiator capacitor in Farads
dVin/dt = rate of change of voltage with time.

## Op amp differentiator design considerations

There are a number of design considerations that need to be taken into account when using an op amp differentiator circuit.

• Remember output rises with frequency:   One of the key facets of having a series capacitor is that it has an increased frequency response at higher frequencies. The differentiator output rises linearly with frequency, although at some stage the limitations of the op amp will mean this does not hold good. Accordingly precautions may need to be made to account for this. The circuit, for example will be very susceptible to high frequency noise, stray pick-up, etc.
• Component value limits:   It is always best to keep the values of the capacitor and particularly the resistor within sensible limits. Often values of less than 100kΩ for the resistor are best. In this way the input impedance of the op amp should have no effect on the operation of the circuit.

## Applications

The differentiator circuit has many applications in a number of areas of electronic design. The op amp differentiator is particularly easy to use and therefore is possibly one of the most widely used versions.

Obviously the circuit is used in analogue computers where it is able to provide a differentiation manipulation on the input analogue voltage.Possibly the differentiator circuit is used most widely in process instrumentation. Here it can be used to monitor the rate of change of various points. If the measurement device returns a rate of change greater than a certain value, this will give an output voltage above a certain threshold and this can be measured using a comparator and used to set an alarm or warning indication.

In fact there are many signal conditioning applications where a differentiator may be required. Of the various options open to the electronic circuit designer, often the op amp solution is often the most attractive, requiring few components while still giving an excellent level of performance.

By Ian Poole

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