Calculadora de Margen de Ganancia Gratis
Calcula el margen de ganancia de un sistema de control. Indica cuánto puede aumentar la ganancia antes de la inestabilidad.
Gain Margin (absolute)
2.000
Gain Margin (absolute) vs Open-Loop Gain at Phase = -180° (|G|)
Fórmula
## 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.
Ejemplo Resuelto
The open-loop gain magnitude at -180° phase is 0.5.
- 01GM = 1 / 0.5 = 2.0 (absolute)
- 02GM = -20 × log10(0.5) = -20 × (-0.301) = 6.02 dB
- 03The gain can be increased by 100% before instability
Preguntas Frecuentes
What is a good gain margin?
A gain margin of at least 6 dB (factor of 2) is commonly recommended. For safety-critical systems, 8-12 dB is preferred. Very high gain margins (>20 dB) may indicate an overly conservative (slow) design.
How do gain margin and phase margin relate?
Both are stability margins but measured differently. A system can have good phase margin but poor gain margin, or vice versa. Both should be adequate for robust stability. Typically, GM > 6 dB and PM > 30° are used together.
What if the system has no phase crossover?
If the open-loop phase never reaches -180° (as in a first-order system), the gain margin is infinite—the system is stable for any gain. This is a desirable property but uncommon in complex systems.
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