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GainMargins
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GainMargins

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GainMargins[lsys]

gives the gain margins of the linear time-invariant system lsys.

Details and Options

  • The system lsys can be a TransferFunctionModel or a StateSpaceModel.
  • The gain margins are the reciprocals of the magnitude of lsys at the phase crossover frequencies.
  • At the phase crossover frequencies lsys has phase .
  • GainMargins returns {{ωp1,g1},{ωp2,g2},…}, where ωpi are the phase crossover frequencies, and gi are the absolute values of the gain margins.
  • GainMargins has the same options as GainPhaseMargins.
  • GainMargins has the attribute Listable.

    • List of all options

Examples

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Basic Examples  (3)Summary of the most common use cases

The gain margins of a continuous-time system:

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In[1]:=1
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https://wolfram.com/xid/05fwqrhe26-7eoh8b
Direct link to example
Out[1]=1

The gain margins in decibels:

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In[2]:=2
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https://wolfram.com/xid/05fwqrhe26-3ldc00
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Out[2]=2

A discrete-time system:

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In[1]:=1
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https://wolfram.com/xid/05fwqrhe26-rwlchs
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Out[1]=1

A time-delay system:

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In[1]:=1
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https://wolfram.com/xid/05fwqrhe26-j0v9ji
Direct link to example
Out[1]=1

Generalizations & Extensions  (1)Generalized and extended use cases

GainMargins[TransferFunctionModel[g,var]] is equivalent to GainMargins[g]:

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In[1]:=1
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https://wolfram.com/xid/05fwqrhe26-4cdtg
Direct link to example
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In[2]:=2
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https://wolfram.com/xid/05fwqrhe26-woh5og
Direct link to example
Out[2]=2
Wolfram Research (2010), GainMargins, Wolfram Language function, https://reference.wolfram.com/language/ref/GainMargins.html.
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Wolfram Research (2010), GainMargins, Wolfram Language function, https://reference.wolfram.com/language/ref/GainMargins.html.

Text

Wolfram Research (2010), GainMargins, Wolfram Language function, https://reference.wolfram.com/language/ref/GainMargins.html.

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Wolfram Research (2010), GainMargins, Wolfram Language function, https://reference.wolfram.com/language/ref/GainMargins.html.

CMS

Wolfram Language. 2010. "GainMargins." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GainMargins.html.

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Wolfram Language. 2010. "GainMargins." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GainMargins.html.

APA

Wolfram Language. (2010). GainMargins. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GainMargins.html

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Wolfram Language. (2010). GainMargins. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GainMargins.html

BibTeX

@misc{reference.wolfram_2025_gainmargins, author="Wolfram Research", title="{GainMargins}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GainMargins.html}", note=[Accessed: 06-April-2025 ]}

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@misc{reference.wolfram_2025_gainmargins, author="Wolfram Research", title="{GainMargins}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GainMargins.html}", note=[Accessed: 06-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_gainmargins, organization={Wolfram Research}, title={GainMargins}, year={2010}, url={https://reference.wolfram.com/language/ref/GainMargins.html}, note=[Accessed: 06-April-2025 ]}

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@online{reference.wolfram_2025_gainmargins, organization={Wolfram Research}, title={GainMargins}, year={2010}, url={https://reference.wolfram.com/language/ref/GainMargins.html}, note=[Accessed: 06-April-2025 ]}