The above circuit diagram illustrates a simple 'RC' integrator. This page provides a 'Java' experiment which you can use to explore its properties when the applied signal is a squarewave.

The red line shows the input waveform and the blue line shows the output.
Th is half the time-period of each square-wave cycle.

You can use the buttons provided in the above experiment to alter the values of the applied frequency and the circuit components. You should find that the circuit tends to 'smooth over' quick changes, but passes low-frequency waves almost unaffected.

Of course, the meanings of 'low' and 'high' frequencies are relative. In this case they depend upon the filter's Time Constant which is normally represented by the Greek letter 'tau' and has a value

The action of the circuit can also be described in terms of a related quantity, the Turn Over Frequency, f0, which has a value

The circuit's behaviour can be understood as arising due to the finite time taken to change the capacitor's charge when we alter the applied input voltage. This process is illustrated in the diagram below.

A quick change in input voltage initially leaves the capacitor voltage unaffected. Hence it produces a voltage difference across the resistor, and so a current flows. This current tends to charge up the capacitor, moving its voltage towards that at the input end of the resistor. As the two voltages move closer the current falls and the rate of change reduces. The overall effect is an output voltage which moves in an exponential curve towards the input level. The rate of change of voltage is determined by the exponential factor

The experiment on this page shows what happens when we apply a square-wave. This keeps 'changing its mind' about the input voltage and never gives the circuit a chance to reach a steady level and settle down. Experiment with changing the frequency and the component values and see what happens to the size and shape of the output waveform. Then choose values for the resistor and capacitor (i.e. fix on a value for the time constant) and plot a graph of how Vpk(out)/Vpk(in) varies with the half-cycle time, Th (i.e. with signal frequency since Th =1/(2f)). You should find that this follows the rule

If you examine the output waveform when Th is much smaller than the time constant you should be able to see why this circuit is often called an integrator. The output approaches looking like a 'triangle' wave which linearly moves towards the current input level. i.e. its value changes linearly with time when we apply a steady input. In effect the charge in the capacitor (and hence its voltage) 'remembers' the overall current level for a while and gives an output level proportional to the averaged or integrated input. This behaviour isn't perfect, but it can sometimes be quite useful in electronic circuits as it provides a way to get a measure of the short-term average level of an input. The value of the time constant determines the length of time over which the recent input is 'remembered' and has a significant effect on the putput.

Content and pages maintained by: Jim Lesurf (jcgl@st-and.ac.uk)
using HTMLEdit3 on a StrongARM powered RISCOS machine.
University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.