RLC Circuit & Damping Ratio Simulator

System Analyzer

Resistance (R) 100 Ω

Inductance (L) 10 mH

Capacitance (C) 10 μF

Damping Ratio (ζ) 0.7

Natural Freq (ωn) 1000 rad/s

H(s) =

ω_n² s² + 2ζω_ns + ω_n²

ROLL-OFF -40 dB/dec

CUTOFF (f_c) 159 Hz

PEAK GAIN 0 dB

MAGNITUDE RESPONSE (BODE)

PHASE RESPONSE (DEGREES)

Damping and Circuit Response

1. Understanding the Damping Ratio (ζ)

In an RLC circuit, the damping ratio describes how quickly oscillations die out. It depends on the balance between energy lost through resistance (R) and energy stored in the inductor (L) and capacitor (C). The damping ratio is given by: ζ = (R/2) * √(C/L)

• ζ < 1 (Underdamped): Low resistance allows oscillations to occur, producing a noticeable resonant peak near the cutoff frequency.
• ζ = 1 (Critically Damped): The system reaches its steady state as quickly as possible without overshooting or oscillating.
• ζ > 1 (Overdamped): Excessive resistance suppresses oscillations, resulting in a slower and more gradual response.

2. Circuit Order and Key Relationships

RC Circuit (First Order): The cutoff frequency is fc = 1 / (2πRC), with an attenuation rate of -20 dB per decade beyond the cutoff.

RL Circuit (First Order): The cutoff frequency is fc = R / (2πL), also exhibiting a -20 dB/decade roll-off.

RLC Circuit (Second Order): The natural frequency is fn = 1 / (2π√LC), and the response decreases more steeply at -40 dB/decade.