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PhaseMargins
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PhaseMargins

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PhaseMargins[lsys]

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

Details and Options

  • The system lsys can be a TransferFunctionModel or a StateSpaceModel.
  • The phase margins are phase lags needed to make the phase at the gain crossover frequencies.
  • At the gain crossover frequencies, the gain of lsys is unity.
  • PhaseMargins returns {{ωg1,p1},{ωg2,p2},…}, where ωgi are the gain crossover frequencies, and pi are the phase margins in radians.
  • PhaseMargins has the same options as GainPhaseMargins.
  • PhaseMargins has the attribute Listable.

    • List of all options

Examples

open allclose all

Basic Examples  (4)Summary of the most common use cases

The phase margins of a continuous-time system:

In[1]:=1
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https://wolfram.com/xid/0dc04l93iffm-gc4yzv
Out[1]=1

The phase margin in degrees:

In[2]:=2
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https://wolfram.com/xid/0dc04l93iffm-b9jsz6
Out[2]=2

A discrete-time system:

In[1]:=1
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https://wolfram.com/xid/0dc04l93iffm-zinh5
Out[1]=1

A system specified as a transfer-function model:

In[1]:=1
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https://wolfram.com/xid/0dc04l93iffm-zx4gvc
Out[1]=1

A time-delay system:

In[1]:=1
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https://wolfram.com/xid/0dc04l93iffm-j0v9ji
Out[1]=1

Generalizations & Extensions  (1)Generalized and extended use cases

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

In[1]:=1
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https://wolfram.com/xid/0dc04l93iffm-4cdtg
In[2]:=2
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https://wolfram.com/xid/0dc04l93iffm-woh5og
Out[2]=2

Properties & Relations  (1)Properties of the function, and connections to other functions

The phase margin increases with damping:

In[1]:=1
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https://wolfram.com/xid/0dc04l93iffm-2uw35f
In[2]:=2
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https://wolfram.com/xid/0dc04l93iffm-kybn43
Out[2]=2
Wolfram Research (2010), PhaseMargins, Wolfram Language function, https://reference.wolfram.com/language/ref/PhaseMargins.html.
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Wolfram Research (2010), PhaseMargins, Wolfram Language function, https://reference.wolfram.com/language/ref/PhaseMargins.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_phasemargins, author="Wolfram Research", title="{PhaseMargins}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PhaseMargins.html}", note=[Accessed: 22-April-2025 ]}

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@misc{reference.wolfram_2025_phasemargins, author="Wolfram Research", title="{PhaseMargins}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PhaseMargins.html}", note=[Accessed: 22-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_phasemargins, organization={Wolfram Research}, title={PhaseMargins}, year={2010}, url={https://reference.wolfram.com/language/ref/PhaseMargins.html}, note=[Accessed: 22-April-2025 ]}

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@online{reference.wolfram_2025_phasemargins, organization={Wolfram Research}, title={PhaseMargins}, year={2010}, url={https://reference.wolfram.com/language/ref/PhaseMargins.html}, note=[Accessed: 22-April-2025 ]}