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eng.bode-gain-margin Calculator
Calculates gain margin and phase margin from a transfer function's Bode plot and assesses closed-loop stability. Gain margin above 6 dB and phase margin above 45° are standard stability requirements — systems with less margin are theoretically stable but show poor transient response.
Inputs
Crossover Freq Rad S
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Gain At Crossover Db
Reference formula or conversion factor shown for context.
Phase Crossover Deg
Reference formula or conversion factor shown for context.
Results
gain margin GM (dB)
The improvement or increase over the baseline.
phase margin PM (°)
The current phase of the cycle or process.
stability
Measure of how robust the system, structure, or process is to perturbations. Low stability means small changes can cause large deviations.
GM = -G(jωpc) dB
Reference formula or conversion factor shown for context.
PM = 180° + ∠G(jωgc)
Reference formula or conversion factor shown for context.