Gain margin and phase margin explained
Gain margin and phase margin measure how close a feedback system is to instability. They are read from the open-loop frequency response and are among the most useful numbers in classical control design.
Phase margin
Phase margin is evaluated at the gain crossover frequency, where the open-loop magnitude equals 0 dB (gain of one). It is the amount of additional phase lag that would bring the phase to −180° and make the loop marginally stable, so phase margin = 180° + ∠H(jω) at that frequency. A common design target is 45° to 60°.
Gain margin
Gain margin is evaluated at the phase crossover frequency, where the phase equals −180°. It is how much the loop gain can increase before the magnitude reaches 0 dB and the system goes unstable, so gain margin = −20·log10|H(jω)| at that frequency, in decibels. A typical target is at least 6 dB.
Why they matter
Real systems have uncertainty: component values drift, loads change, and unmodelled delays add phase. Healthy margins ensure the loop stays stable despite these variations and that the transient response is well damped rather than ringing. If either margin is negative, the closed loop is unstable.