Damping ↔ Overshoot ↔ Phase Margin
Convert between damping ratio, overshoot, Q and phase margin for a second-order loop.
Four ways to say the same thing
Damping ratio, overshoot, Q factor and phase margin are four views of one number — how stable a second-order loop is. They're locked together:
The handy mental anchors: ζ = 0.5 → ~16 % overshoot, ~52° phase margin;
ζ = 0.707 → ~4 % overshoot, ~65° PM, and the flattest frequency response;
ζ ≥ 1 → no overshoot at all. The rule of thumb PM ≈ 100·ζ (degrees)
holds well below ζ ≈ 0.7. Frequency-domain folks live in phase margin and Q; time-domain folks
live in overshoot — this converter lets you jump between them, so a "50° phase margin" spec and
a "< 20 % overshoot" spec become the same target. See the actual curve in the
step-response tool.