Bode Plot Generator
Magnitude & phase for H(s) · step-by-step analysis · gain & phase margin
Quick examples
Common transfer functions
| System | H(s) | Type |
|---|---|---|
Syntax help
Multiply:
2*s not 2s Powers: s^2 Imaginary: -5+8.66j
Enter a transfer function and click Generate
Generate Bode magnitude and phase plots with step-by-step analysis.
Generate a Bode plot to see the magnitude and phase diagrams.
What is a Bode Plot?
A Bode plot is a standard way to visualize the frequency response of a linear time-invariant (LTI) system. It consists of two graphs: a magnitude plot showing |H(jω)| in decibels (dB) and a phase plot showing ∠H(jω) in degrees, both plotted against frequency ω on a logarithmic scale.
Named after Hendrik Bode, these plots are fundamental in control engineering for analyzing system stability, designing compensators, and understanding how systems respond to different input frequencies.
Key Concepts
Gain Margin
The amount of gain (in dB) that can be added before the system becomes unstable. Measured at the phase crossover frequency where phase = −180°.
Phase Margin
The additional phase lag before instability, measured at the gain crossover frequency where |H| = 0 dB. Positive margins indicate stability.
Corner Frequency
The frequency at which the asymptotic approximation changes slope. For a pole at s = −a, the corner frequency is ω = a rad/s.
Asymptotic Approximation
Each pole adds −20 dB/decade and −90° phase. Each zero adds +20 dB/decade and +90°. Straight-line approximations simplify hand sketching.
Applications
Control Systems
Design PID controllers, analyze loop gain, and determine stability margins for feedback systems.
Filter Design
Visualize low-pass, high-pass, band-pass, and notch filter frequency responses.
Stability Analysis
Determine gain and phase margins to assess closed-loop stability of feedback systems.
Audio Engineering
Analyze equalizer response curves, amplifier frequency characteristics, and speaker crossover networks.