1st and 2nd-order Filters Simulation

Circuit Configurator

Resistor (R)

150 Ω

Inductor (L)

50 mH

Capacitor (C)

10 μF

H(s) = ...

Roll-off: -40 dB/dec
Cutoff (fc): --

Damping & System Behavior

1. The Damping Ratio (ζ)

In an RLC circuit, damping is determined by the ratio of energy dissipated (R) to energy stored (L, C). The formula is: ζ = (R/2) * √(C/L)

• ζ < 1 (Underdamped): Occurs when R is small. You will see a "resonant peak" at the cutoff.
• ζ = 1 (Critically Damped): The fastest response without oscillation.
• ζ > 1 (Overdamped): High R values. The roll-off starts much earlier and is sluggish.

2. Order & Equations

RC Circuit (1st Order): Cutoff fc = 1 / (2πRC). Roll-off is -20dB/dec.

RL Circuit (1st Order): Cutoff fc = R / (2πL). Roll-off is -20dB/dec.

RLC Circuit (2nd Order): Natural Freq fn = 1 / (2π√LC). Roll-off is -40dB/dec.