What is a good phase margin?

For most practical systems, a phase margin between 30° and 60° is desirable. Above 60° the transient response can be sluggish; below 30° the closed loop tends to overshoot or oscillate. 45° is a common design target.

What does negative phase margin mean?

A negative phase margin means the phase of G(jω) has already crossed −180° before the gain drops to 0 dB. The closed-loop system is unstable. You need to add a lead compensator or reduce the loop gain.

What transfer function form does this tool support?

This tool models G(s) = K / [(1 + s·T1)(1 + s·T2)(1 + s·T3)] — a DC gain with up to three real poles expressed as time constants. Add integrators (1/s poles) via the integrator count field.

How is gain crossover frequency found?

The tool numerically sweeps log-spaced frequencies from 0.001 to 10000 rad/s and bisection-searches for the frequency where the magnitude equals 1 (0 dB). It then evaluates the phase angle at that exact frequency.

What is the difference between phase margin and gain margin?

Phase margin is extra phase at the gain crossover frequency. Gain margin is the additional gain (in dB) at the phase crossover frequency (where phase = −180°). Both must be positive for a stable system. This tool focuses on phase margin.

Phase Margin Calculator

Name: Phase Margin Calculator
Availability: InStock
Author: Nham Vu

Enter your open-loop transfer function parameters to calculate phase margin and determine closed-loop stability.

Transfer Function Parameters

Model: G(s) = K · s^-n / [(1+sT₁)(1+sT₂)(1+sT₃)]

DC Gain (K)

Integrators (pure 1/s poles)

Real Poles (time constants, seconds)

Leave 0 to omit that pole.

T₁ (s)

T₂ (s)

T₃ (s)

Bode Plot Preview

Gain (top) and Phase (bottom) vs. frequency. Red dashed line marks the gain crossover.

Summary