A critically damped RLC circuit is a type of electrical circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series or parallel. The circuit is called "critically damped" when the damping factor is equal to the critical damping value.
Damping refers to the process of reducing or controlling oscillations in a circuit. In an RLC circuit, when energy is initially stored in the inductor and capacitor, it creates an oscillating current. The circuit can be classified into three damping conditions based on the value of the damping factor (ζ):
Overdamped (ζ > 1): In an overdamped RLC circuit, the damping factor is greater than one, which means the circuit dissipates energy rapidly, causing the oscillations to die out without any overshooting.
Underdamped (0 < ζ < 1): An underdamped RLC circuit has a damping factor between zero and one. In this case, the circuit's energy oscillates back and forth, causing overshooting before finally settling down to a stable state.
Critically damped (ζ = 1): In a critically damped RLC circuit, the damping factor is exactly equal to one. This means that the circuit dissipates energy as quickly as possible without any oscillations or overshooting. The response reaches a stable state in the shortest possible time.
The damping factor (ζ) can be calculated using the following formula:
ζ = R / (2 * sqrt(L / C))
Where:
R = Resistance in ohms
L = Inductance in henries
C = Capacitance in farads
When ζ = 1, the circuit is critically damped. This specific condition is desirable in certain applications, especially in cases where quick and stable response without overshooting is required, such as in certain control systems or voltage regulators.