How to use the Bode Plot Generator
- 1. Type the numeratorFor example 100, 10(s+1) or a coefficient list.
- 2. Type the denominatorFor example s(s+2)(s+10) or s^2+4s+100.
- 3. Draw the plotSee both plots, margins, a decade table and the working.
How a Bode plot is built
Put s = jω in G(s) and plot 20 log₁₀|G(jω)| in dB and ∠G(jω) in degrees against log ω. Each real pole bends the magnitude down by 20 dB/decade at its corner frequency and adds −90° of phase; each real zero does the opposite. A complex pair with natural frequency ωn and damping ζ adds ±40 dB/decade and ±180°, with a resonant peak when ζ is small. A pole at the origin gives a −20 dB/decade slope from the start and a constant −90°.
Worked example: G(s) = 100 / (s(s + 2)(s + 10)). Corners at 2 and 10 rad/s. The phase reaches −180° at ωpc = √20 = 4.47 rad/s, where |G| = 0.417 (−7.6 dB), so the gain margin is 7.6 dB. The gain crosses 0 dB at about 2.80 rad/s, where the phase is −160.1°, so the phase margin is 19.9°.
Gain margin, phase margin and exam questions
Gain margin = −|G| in dB at the phase crossover; phase margin = 180° + ∠G at the gain crossover. For a minimum-phase open-loop system, both positive means the unity-feedback closed loop is stable. Larger PM means less overshoot.
- Sketch the asymptotic Bode plot of 10/(s(s+1)(s+5)) and find GM and PM (9.54 dB, 25.4°).
- Find K for a gain margin of 6 dB.
- Find the resonant peak for a second-order system with ζ = 0.2.
The tool draws exact curves, which you can compare with your hand-drawn straight-line asymptotes.
Frequently asked questions
How do I enter my transfer function?
Write the numerator and denominator as polynomials in s, such as 10(s+1) and s(s+2)(s+10). You can also give coefficients from the highest power, such as 1 12 20 0.
Why is my phase margin infinite?
If the magnitude never crosses 0 dB, there is no gain crossover, so PM is reported as infinite. Likewise, no −180° crossing gives an infinite GM.
Can I use Bode margins for unstable open-loop systems?
Not reliably. With right half-plane poles or zeros, use the Nyquist criterion. The tool warns you when G(s) has them.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.