Bode Plot (2nd-Order System)

How does a circuit or control system respond across frequency? A Bode plot lays it bare — gain on top, phase below — revealing resonance and roll-off at a glance.

Bode Plot (2nd-Order System)Live

frequency response

Controls

Presets

Natural frequency (Hz)

Damping ratio ζ

A Bode plot shows how a system responds across frequency: gain in decibels on top, phase shift below. This second-order low-pass passes low frequencies and rolls off at −40 dB/decade above its natural frequency. Low damping produces a resonant peak; high damping smooths it away.

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Data Inspector

Natural freq1,000 Hz

Damping ζ0.30

Resonant peak+4.8 dB

Roll-off−40 dB/dec

Governing equation

H (s) = \frac{ω _{n}^{2}}{s ^{2} + 2 ζ ω _{n} s + ω _{n}^{2}} = \frac{6 , 28 3 ^{2}}{s ^{2} + 3770 s + 6 , 28 3 ^{2}}

Reading this result: Low damping ζ=0.30 produces a sharp +4.8 dB resonant peak just below fn — great for selectivity, but it rings in the time domain.

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How it works

A Bode plot shows a system's frequency response: magnitude in decibels and phase in degrees against a logarithmic frequency axis. This second-order low-pass rolls off at −40 dB per decade beyond its natural frequency, and a low damping ratio produces a resonant peak. The core diagnostic of control and analog design.

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