Gain Margin Calculator — Formula
## Gain Margin
Gain margin measures how much the open-loop gain can increase before the system becomes unstable. It is evaluated at the phase crossover frequency (where the open-loop phase equals -180°).
### Formula
**GM = 1 / |G(j*omega_pc)| = -20*log10(|G(j*omega_pc)|) dB**
where omega_pc is the phase crossover frequency. A positive gain margin (in dB) indicates stability. The larger the gain margin, the more robust the system is to gain variations.
Gain margin measures how much the open-loop gain can increase before the system becomes unstable. It is evaluated at the phase crossover frequency (where the open-loop phase equals -180°).
### Formula
**GM = 1 / |G(j*omega_pc)| = -20*log10(|G(j*omega_pc)|) dB**
where omega_pc is the phase crossover frequency. A positive gain margin (in dB) indicates stability. The larger the gain margin, the more robust the system is to gain variations.
Exemplo Resolvido
The open-loop gain magnitude at -180° phase is 0.5.
- GM = 1 / 0.5 = 2.0 (absolute)
- GM = -20 × log10(0.5) = -20 × (-0.301) = 6.02 dB
- The gain can be increased by 100% before instability