Fasmarginalen

Fasmarginalen (the phase margin) is a measure used in control theory and electronic feedback design to quantify how close a system is to oscillation or instability. It is defined for an open-loop transfer function as the amount of additional phase lag required at the gain crossover frequency (where the loop magnitude equals unity or 0 dB) to bring the total phase to −180°. Numerically, phase margin = 180° + ∠L(jω_gc).

Phase margin is typically determined from a Bode plot or Nyquist plot. On a Bode plot, one reads the phase at the frequency where the magnitude crosses 0 dB and computes the difference to −180°. On a Nyquist plot, it corresponds to the angular separation between the plot and the −1 point when scaled to the unity-gain condition.

The metric is important because it correlates with closed-loop stability and transient behavior: positive phase margin generally indicates a stable closed-loop system, larger margins give more damping and less overshoot, while small margins lead to oscillatory responses and possible instability. Designers often aim for a phase margin in the range of about 30°–60°, with ~45° a common compromise between responsiveness and robustness.

Limitations include sensitivity to model inaccuracies, unmodeled dynamics, and time delays, which reduce phase margin. Phase margin is used alongside gain margin and bandwidth to assess robustness and performance of feedback systems.