Bode Plot

A Bode plot is a control engineer's stethoscope: magnitude and phase across frequency, with margins that predict whether the loop will hold.

Bode PlotLive

magnitude & phase vs frequency

Controls

Presets

Gain K

Pole 1 (rad/s)

Pole 2 (rad/s)

A Bode plot shows how a system responds across frequencies: magnitude in decibels above, phase below. The gain and phase margins — how far the curves sit from instability at the crossover — predict whether closing the loop stays stable. Educational tool.

▶ Run in Python

Data Inspector

Gain crossover0.01 rad/s

Phase margin179°

Stabilitystable ✓

Governing equation

H (j ω) = \frac{1}{( 1 + j \frac{ω}{1} ) ( 1 + j \frac{ω}{10} )} \Rightarrow ∣ H ∣ = - 0.0 dB, ∠ H = - 1^{\circ}

Reading this result: A healthy 179° phase margin means the loop closes with plenty of stability and little overshoot.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

★ Sign in to save this setup

Save your tuned setup, or drop this simulation into your own site, docs, or course page.

How it works

The Bode plot shows a system's magnitude (dB) and phase (degrees) versus frequency on a log scale. The phase margin — how much phase remains above −180° at the gain crossover — measures how close the closed loop is to instability. Educational tool.

✦

Ask the AI about this model

The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

More Robotics simulations

Forward Kinematics Inverse Kinematics Differential Drive Cart-Pole Balance Quadcopter Control RRT Path Planning DC Motor Kalman Filter

Frequently asked questions

Is this bode plot simulator tool really free?▾

Yes. Bode Plot runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

Can I save or share my simulation?▾

Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.

How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.