Phase Margin Calculator

Calculate the phase margin of a second-order open-loop system from damping ratio as a quick stability check.

Approximate Phase Margin

51.83 °

Simplified Phase Margin (100×zeta)50.0 °

Approximate Phase Margin vs Damping Ratio (zeta)

Vedi formula →

Formula

## Phase Margin Phase margin is the additional phase lag that would bring the system to the verge of instability. It is measured at the gain crossover frequency (where the open-loop gain equals 1). ### Approximation for Second-Order Systems For a standard second-order system, the phase margin can be approximated from the damping ratio. A useful rule of thumb is PM ≈ 100 × zeta (in degrees) for zeta between 0.1 and 0.7. Adequate phase margin (typically 30-60°) ensures robustness against modeling errors and parameter variations.

Esempio Risolto

A system with damping ratio zeta = 0.5.

  1. 014*zeta^4 = 4 × 0.0625 = 0.25
  2. 02sqrt(1 + 0.25) = sqrt(1.25) = 1.1180
  3. 03-2 × 0.25 + 1.1180 = 0.6180
  4. 042 × 0.5 / sqrt(0.6180) = 1.0 / 0.7861 = 1.2721
  5. 05PM = atan(1.2721) × 180/pi = 51.8°
  6. 06Simple approximation: 100 × 0.5 = 50°