Design Example: Underdamped Parallel RLC Circuit

Underdamped parallel RLC circuits can sustain oscillations at a resonant frequency, making them suitable for use in oscillators.

An electrical engineer is tasked with designing a model oscillator circuit with a damped natural frequency of 4 kilohertz and a damping factor of 4 radians per second.

With a set resistance of 200 ohms, the precise values for capacitance and inductance can be determined.

Since the damping factor for the circuit is the reciprocal of twice the product of the resistance and capacitance, the required capacitance value for the circuit design is obtained.

The mathematical expression correlating the resonant frequency, damping factor, and damped natural frequency is used to obtain the resonant frequency.

The resonant frequency is inversely proportional to the square root of the product of inductance and capacitance.

The known values are substituted into this equation to obtain the required inductance.

The damped natural frequency is lower than the resonant frequency, and the inductance value is less than four times the square of resistance multiplied by capacitance. Both these conditions confirm underdamped oscillation.