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Phase Margin

The phase margin states how much extra phase lag the closed loop can tolerate at the crossover frequency (where the gain is 0 dB) before the system becomes unstable. A typical target is 45-60°. The smaller the phase margin, the closer the system is to instability and the more it tends to oscillate before settling.

PM=180^\circ+\angle L(j\omega_c)

phase margin at the crossover frequency \omega_c

Symbols

$PM$	phase margin	°
$\omega_c$	crossover frequency (where \|L\|=1)	rad/s
$L$	the loop gain GH

Example

The phase at $\omega_c$ is $-120^\circ$ :

$PM=180^\circ-120^\circ=60^\circ$ .

The phase margin is read at 0 dB (the crossover frequency), not at

-180^\circ

Practise frequency analysis for free →

← Bode Plot · Dead Time and Phase →

Part of Control Engineering: Frequency analysis.