Bode Magnitude⚠ unverified
Physics / Controls · Compute the Bode magnitude of a second-order system at a given frequency
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| wn | wn | rad/s | 1.0 | Undamped natural frequency |
| zeta | ζ | — | 1.0 | Damping ratio (dimensionless) |
| omega | ω | rad/s | 1.0 | Evaluation frequency |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | mag | dB | Magnitude, in decibels (dB) |
The science & history
Understanding the Parameters
- $\omega_n$, $\zeta$ — shape the resonance peak (near $\omega_n$ for small $\zeta$).
- $\omega$ — evaluate along the $j\omega$ axis.
- mag — at $\omega = 0$, $|G| = 1$ for this prototype (0 dB if converted).
Derivation (Approaching a Proof)
Substitute $s = j\omega$ into $G(s) = \omega_n^{2}/(s^{2}+2\zeta\omega_n s+\omega_n^{2})$ and take the complex modulus. The result is the displayed formula.
History
Bode plots (H. W. Bode) are the standard frequency-response tool in classical control and electronics.
Related Concepts: Bandwidth, Gain Crossover Frequency, Phase Margin, Gain Margin
Notes: Registry calculator bode-magnitude (unverified). Unit bug: output labelled dB but
formula is linear $|G|$.