Side-by-side comparison
| Parameter | Gain Margin | Phase Margin |
|---|---|---|
| Definition | Additional gain (in dB) system can tolerate before instability | Additional phase lag (in degrees) system can tolerate before instability |
| Read from Bode plot at | Phase crossover frequency ωpc (where ∠G(jω)H(jω) = −180°) | Gain crossover frequency ωgc (where |G(jω)H(jω)| = 0 dB) |
| Formula | GM = −20 log|GH(jωpc)| dB | PM = 180° + ∠GH(jωgc) |
| Stable system value | GM > 0 dB (typically 6–12 dB) | PM > 0° (typically 30°–60°) |
| Marginally stable | GM = 0 dB | PM = 0° |
| Unstable system | GM < 0 dB | PM < 0° |
| Indicates robustness to | Gain variations and component tolerances | Time delays and phase-introducing elements |
| Preferred design target | ≥ 6 dB | 45°–60° for good transient response |
| Relation to overshoot | Indirect | PM ≈ 100ζ for ζ < 0.6 (approximate) |
Key differences
Gain margin tells you how much you can increase open-loop gain before the −180° phase shift makes the loop oscillate; a GM of 6 dB means doubling the gain reaches instability. Phase margin tells you how much additional phase lag — from a delay, a filter, or a transport lag — can be tolerated before oscillation; a PM of 45° corresponds roughly to ζ = 0.45 and about 20% overshoot. A system can have a healthy GM but dangerously low PM (common in systems with pure time delay), so both must always be checked together.
When to use Gain Margin
Use gain margin as the primary robustness specification when component gain tolerances dominate — a voltage regulator IC with ±20% resistor divider variation needs at least 6 dB GM to stay stable across all units.
When to use Phase Margin
Use phase margin as the primary specification when time delays are the main concern — a process control loop with 200 ms transport delay must be designed with PM ≥ 45° measured after including the delay in the model.
Recommendation
For GATE and placements, always state both margins. Choose to design for PM = 45°–60° first because it directly controls transient overshoot; then verify that GM ≥ 6 dB as a secondary check. Never report only one margin.
Exam tip: GATE asks you to read GM and PM directly from a given Bode plot — practise locating ωpc (phase = −180°) and ωgc (magnitude = 0 dB) quickly, then computing GM in dB and PM in degrees.
Interview tip: Placement interviewers ask what happens physically when PM approaches 0° — expected answer: closed-loop step response becomes nearly sinusoidal with large overshoot and slow decay, approaching sustained oscillation.