Gain Margin Calculator

Calculate the gain margin from the open-loop gain at the phase crossover frequency for stability assessment.

Gain Margin (absolute)

2.000

Gain Margin6.02 dB
Maximum Gain Increase Before Instability100.0 %

Gain Margin (absolute) vs Open-Loop Gain at Phase = -180° (|G|)

Vedi formula →

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.

Esempio Risolto

The open-loop gain magnitude at -180° phase is 0.5.

  1. 01GM = 1 / 0.5 = 2.0 (absolute)
  2. 02GM = -20 × log10(0.5) = -20 × (-0.301) = 6.02 dB
  3. 03The gain can be increased by 100% before instability