Designing Embedded Hardware, 2nd Edition

RC Circuits

Combining resistors and capacitors can yield some interesting and useful effects. A resistor-capacitor combination is known as an RC circuit, and it can take one of three forms. The first form is where the resistor and capacitor are in parallel (Figure 4-31).

Figure 4-31. Resistor and capacitor in parallel

Now, what does this do? A voltage (V) applied across the pair will charge the capacitor (as well as some current flowing down through the resistor). When the applied voltage is removed, the capacitor will discharge through the resistor. The resistor will limit the rate of discharge, since it limits current flow. From Ohm's Law, we have:

   I = - V / R

(The negative voltage is because we're discharging the capacitor.) Now, the current flow out of a capacitor is given by:

   I = C * dV/dt

So, we have:

   dV/dt = - V / RC

Integrating this with respect to time, with zero initial conditions, gives us:

   V = e-t/RC

This gives us the discharge waveform shown in Figure 4-32, which represents the voltage across the capacitor.

A parallel RC circuit will provide an exponential decay in the output voltage. The value for t when the output voltage is at 37% of the maximum is known as the time constant for the circuit and is simply the product of R and C:

   t = R * C

For example, a parallel RC circuit where the resistor is 100 kΩ and the capacitor is 10 uF gives a time constant of 1 second.

The second ...