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📐 Bode Plot: Frequency Response and Stability Margins

Interactive Bode magnitude and phase plot where users adjust a transfer function's poles and zeros with sliders and watch gain and phase margins update live to reveal system stability.

Engineering & Materials3DModerate60 FPS

A pair of magnitude and phase curves float as stacked 3D panels sharing one log-frequency axis, with live gain- and phase-margin brackets that reveal exactly how stable — or unstable — the modelled control loop is.

🔬 What It Demonstrates

How pole and zero break frequencies shape the magnitude roll-off and phase lag of a transfer function, and how the gain crossover and phase crossover frequencies determine the phase margin and gain margin that decide closed-loop stability.

🎮 How to Use

Adjust gain K and the two pole frequencies to reshape both curves at once. Enable the zero to push phase back up. Watch the cyan and orange crossover lines and the coloured margin brackets update, and read the stability verdict live.

💡 Did You Know?

Hendrik Bode devised this plot at Bell Labs in the 1930s to stabilise telephone feedback amplifiers. A rule of thumb still used today: keep phase margin above about 45° and gain margin above roughly 6 dB for a comfortably damped response.

⚙ Under the hood

Interactive Bode magnitude and phase plot where users adjust a transfer function's poles and zeros with sliders and watch gain and phase margins update live to reveal system stability.

bode-plotfrequency-responsestability-marginscontrol-systemstransfer-functionsengineering

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install