An underdamped 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 in parallel. The term "underdamped" refers to the circuit's response to changes in its input voltage or current.
To understand the underdamped behavior, let's briefly review the components of the RLC circuit:
Resistor (R): A passive component that dissipates electrical energy in the form of heat. It opposes the flow of current and is characterized by its resistance, measured in ohms (Ξ©).
Inductor (L): Another passive component that stores energy in a magnetic field when current flows through it. It opposes any sudden changes in current and is characterized by its inductance, measured in henries (H).
Capacitor (C): A passive component that stores electrical energy in an electric field when voltage is applied across its terminals. It opposes any sudden changes in voltage and is characterized by its capacitance, measured in farads (F).
When the RLC circuit is excited with a voltage or current source, it exhibits transient behavior before settling into a steady-state response. The type of damping (underdamped, overdamped, or critically damped) depends on the values of R, L, and C.
An underdamped RLC circuit occurs when the damping factor is less than 1. The damping factor is given by the formula:
Damping factor (ΞΆ) = R / (2 * β(L / C))
In an underdamped RLC circuit, the energy oscillates back and forth between the inductor and the capacitor, causing damped oscillations in the circuit's response. The current or voltage may overshoot or undershoot the steady-state value before settling down. These oscillations gradually decrease in amplitude over time until the circuit reaches its steady-state condition.
Underdamped RLC circuits are commonly encountered in many electronic and electrical systems, and their analysis is important in various engineering applications, such as signal processing, control systems, and telecommunications. Engineers must consider the underdamped behavior when designing circuits to ensure proper performance and stability.