Digital systems
Capacitor charging

Let us consider modified circuit as shown in picture. Capacitor in series with a resistor is being supplied from a constant voltage source. The response of this system to two input pulses of magnitude u1m and two different lengths (longer and shorter pulse) is plotted on the figure. The output value is a capacitor voltage uc.

After step of input voltage u1m, the capacitor is being charged (accumulates electric charge) and a its voltage follows an exponential function

At the beginning, the capacitor voltage is zero and charging current is maximal (limited by a resistance of resistor R). As the capacitor charges, its voltage increases and difference between it and a voltage at the input (u1m – uc), leading to decrease of charging current, and, as a consequence, the increase of capacitor voltage slows down. In steady state, the capacitor voltage (uc) is equal to the input voltage (u1m) and no current flows through the resistor.

Fig. 8.6: Simple electric circuit