This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


gives the gain and phase margins of the linear time-invariant system sys.
  • GainPhaseMargins returns an expression of the form , where the are the phase crossover frequencies, the are the gain margins, the are the gain crossover frequencies, and the are the phase margins.
  • The frequencies and are in radians per time unit, the gain margins are the absolute values, and the phase margins are in radians.
  • The following options can be given:
FeedbackType"Negative"the feedback type
MethodAutomaticmethod to use
SamplingPeriodNonethe sampling period
  • Explicit settings for the Method option include and . In each case the methods of Solve or NSolve can be specified as suboptions. The default setting of Automatic switches between these methods depending on whether sys is exact or inexact.
The gain and phase margins of a system:
The gain and phase margins of a system:
Click for copyable input
The gain and phase margins of a system:
This can be visualized on all the frequency response plots:
The gain margins in decibels:
The phase margins in degrees:
If the crossover frequencies are in radians/second, they can be converted to hertz as follows:
A system with multiple crossover frequencies:
The number of gain crossover frequencies:
By default the system is assumed to be the loop transfer function of a negative-feedback system:
Specify the system as part of a positive-feedback system:
Specify the system as a closed-loop system:
A positive-feedback system:
Transfer functions specified as expressions are assumed to be continuous-time systems:
A discrete-time system specified as an expression:
The setting StabilityMargins->True computes and draws the gain and phase margins:
New in 8