The above circuit diagram illustrates a simple ‘RC’ differentiator. 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 responds to ‘quick’ sudden changes, but tends to slowly ‘forget’ a steady level.
Of course, the meaning of ‘quick’ is relative to the circuit's Time Constant which is normally represented by the Greek letter ‘tau’ and 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.
It takes a finite time to change the charge stored by the capacitor. As a result, when we quickly change the input voltage we, initially, leave the voltage across the capacitor unaltered. Hence sudden voltage changes appear across the output resistor. However, any voltage across the resistor will produce a current that tends to change the capacitor's charge. The result is that the capacitor voltage slowly changes to ‘soak up’ the applied voltage. For this reason a steady input seems to vanish from the output, and a slowly changing input mainly affects the capacitor voltage and charge rather than appearing at the output.
The experiment on this page shows what happens when we apply a square-wave. This keeps ‘changing its mind’ about the input voltage. Experiment with changing the frequency and the component values and see what happens to the size and shape of the output waveform. You should find that when the half-period of the square-wave is much longer than the time constant value, the output looks like a series of ‘spikes’ which happen when the input squarewave changes. In effect, these show the edges of the squarewave shape. They correspond to where the waveform's rate-of-change (i.e. differential) is greatest. The size of these output spikes depends on the size of the edges, hence the output approximates to a differential of the input.
Content and pages maintained by: Jim Lesurf (firstname.lastname@example.org)
using HTMLEdit3 on a StrongARM powered RISCOS machine.
University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.