What is a critically damped RLC circuit?

In an RLC circuit, the inductor and capacitor store energy in the form of a magnetic field and an electric field, respectively. When there is a change in the input voltage or current, the energy stored in these elements starts to transfer between them. The rate of energy transfer and dissipation depends on the values of R, L, and C.

A critically damped RLC circuit is characterized by a damping factor equal to the square root of (4 times the inductance L divided by the resistance R). Mathematically, the damping factor (ζ) for a critically damped RLC circuit is given by:

ζ = √(4L/R)

When an RLC circuit is critically damped, it achieves the fastest response to a step change in the input without any oscillations or overshoot. This means the circuit returns to its steady-state condition in the shortest time without any ringing or transient behavior. Critically damped RLC circuits are often used in applications where a fast and stable response is desired, such as in some control systems or power supply circuits.

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.