Digital systems
Capacitor discharging

Similar process comes on during capacitor discharging, i.e. after zero voltage at the input. The behavior in time follows an exponential as well, this time the function is:

If a short pulse is actuated at the input, the transient does not finish and the capacitor is partly charged, only. The discharge then commences from the last reached value.

Exponential behavior is parameterized by a time constant τ. A line, tangential to exponential curve, intersecting it at zero time, crosses a time axis at the time τ. For the RC circuit, the time constant is equal to product of capacity and resistance, τ = RC.

The system described above is a first order static system, also called a one capacitor system. Circuit with an inductor and resistor (RL) behaves a similar way – the current passed through the inductor follows the exponential function and the output voltage on the resistor varies proportionally to it.

We assumed, that the input is actuated by a hard voltage source, i.e. there is a voltage equal to u1m or 0 for discharge. The capacitor is discharged by negative current, flowing back to the voltage source. However, in many situations (e.g. in case of tank filling), the input is being disconnected, rather than connected to zero value. In this case, no discharging current is present and a capacitor remains charged forever (if parasitic self-discharging is neglected).

Fig. 8.7: Response static system 1. order to step input and relation to time constant