Calculator · Dynamics & Control
Bode Plot Calculator
Enter G(s) = N(s)/D(s) in descending powers of s. The magnitude and phase are evaluated exactly at every plotted frequency — no straight-line approximation is used for the curves.
Input
G(s) = (1) / (s + 1)
Frequency range
The automatic range is derived from the break frequencies of the system.
Bode plot
Plotted from 0.01 to 100 rad/s (automatic range).
Frequency-domain summary
| DC gain G(0) | 1 (0 dB) |
|---|---|
| Low-frequency slope | 0 dB/decade |
| High-frequency slope | -20 dB/decade |
| Resonant peak | The magnitude is largest at the lowest frequency evaluated and never rises above it, so the response has no resonant peak. |
| −3 dB bandwidth | 1 rad/s |
Break frequencies
| ω [rad/s] | From | Slope change | Note |
|---|---|---|---|
| 1 | Pole | -20 dB/dec | — |
Technical reference
|G(jω)|dB = 20·log10 |G(jω)|
∠G(jω) = phase of G(jω), unwrapped along ω
- ω
- angular frequency[rad/s]
- G(jω)
- transfer function evaluated on the imaginary axis
For each finite-frequency first-order pole or zero factor, the asymptotic magnitude slope changes by −20 or +20 dB per decade after its break frequency; a finite-frequency complex-conjugate pair changes it by −40 or +40 dB per decade. Poles and zeros at the origin contribute their slope from the start of the frequency axis.
A right-half-plane (non-minimum-phase) zero adds the same magnitude slope as its left-half-plane mirror image but the opposite phase contribution, which is why it is flagged separately rather than folded into the slope figure.
Assumptions
- · Magnitude and phase are the exact values of G(jω); the straight-line asymptotes are reported only as slopes.
- · Phase is unwrapped along the frequency axis so multiple −180° crossings stay distinguishable.
- · Bandwidth is only attributed to a system whose response settles; otherwise it is reported as not applicable.
- · Gain and phase margins belong to the loop transfer function and have their own dedicated calculator.
Continue
Transfer function and frequency range travel with you.