WOLFRAM

BodePlot[lsys]

generates a Bode plot of a linear time-invariant system lsys.

BodePlot[lsys,{ωmin,ωmax}]

plots for the frequency range ωmin to ωmax.

BodePlot[expr,{ω,ωmin,ωmax}]

plots expr using the variable ω.

Details and Options

Examples

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

The Bode plot of a system:

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A second-order system:

Plot over an explicit frequency range:

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Bode plot of a state-space model:

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Scope  (13)Survey of the scope of standard use cases

Bode plot of a constant-gain system:

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Bode plot of an integrator:

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Bode plot of a differentiator:

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Bode plot of a first-order lag:

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Bode plot of a first-order lead:

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Bode plot of a second-order system:

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A higher-order TransferFunctionModel:

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Bode plot of a time-delay system:

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A discrete-time system:

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Specify the frequency range:

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The Bode plot of a state-space model:

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A system specified using its sinusoidal transfer function:

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The Bode plot of a multiple-input, multiple-output system:

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Generalizations & Extensions  (1)Generalized and extended use cases

A Bode plot can be obtained from a transfer-function model or directly from its expression:

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Options  (21)Common values & functionality for each option

CoordinatesToolOptions  (5)

To obtain coordinates, select the graphics and press the period key:

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If frequency is in rad/s, obtain coordinate frequency values in hertz by dividing it by :

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Coordinate frequency values in different units for each plot:

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Frequency values in original units, magnitude in absolute units, and phase in radians:

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Specify radians as both the displayed and copied value of phase:

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GridLines  (3)

Show grid lines:

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Show grid lines only on the magnitude plot:

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Show specific grid lines:

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GridLinesStyle  (2)

Specify grid lines style:

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Specify different grid lines styles:

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PhaseRange  (1)

The phase is typically plotted as a continuous function:

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Specify a phase range:

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PlotLayout  (1)

By default, the magnitude plot is placed vertically above the phase plot:

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Obtain the result in a list:

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Only the magnitude plot:

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Only the phase plot:

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PlotTheme  (2)

Use a theme with simple ticks and grid lines in a bright color scheme:

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Change the color scheme:

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SamplingPeriod  (2)

Specify the sampling period in the system description:

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Specify the sampling period in the BodePlot function:

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A smaller sampling period results in a higher bandwidth:

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ScalingFunctions  (2)

Show absolute values of magnitude and phase in radians:

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Plot frequency in the linear scale:

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StabilityMargins  (2)

Show stability margins:

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Show the phase margin only:

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StabilityMarginsStyle  (1)

Specify the stability margins style:

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Applications  (7)Sample problems that can be solved with this function

The static position error constant of a type 0 system is the magnitude at steady state:

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Discrete-time type 0 system:

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The static velocity error constant of a type 1 system is approximately the intersection of the initial dB/decade segment (or its extension) with the 0 dB line:

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Discrete-time type 1 system:

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The square root of the static acceleration error constant of a type 2 system is approximately the intersection of the initial dB/decade segment (or its extension) with the 0 dB line:

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Discrete-time type 2 system:

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Visualize the improvement in phase margin by using a proportional-integral (PI) compensator:

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Visualize the frequency response of a zero-order hold with sampling period 1:

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Obtain the Bode plot with frequency in Hertz, when the Laplace variable is in radians/second:

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For continuous-time systems, the same result can be obtained by scaling the Laplace variable:

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The plot in Hertz for a discrete-time system with the Z-transform variable in radians/second:

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

SingularValuePlot generalizes the Bode magnitude plot to MIMO systems:

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Wolfram Research (2010), BodePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/BodePlot.html (updated 2014).
Wolfram Research (2010), BodePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/BodePlot.html (updated 2014).

Text

Wolfram Research (2010), BodePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/BodePlot.html (updated 2014).

Wolfram Research (2010), BodePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/BodePlot.html (updated 2014).

CMS

Wolfram Language. 2010. "BodePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/BodePlot.html.

Wolfram Language. 2010. "BodePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/BodePlot.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_bodeplot, author="Wolfram Research", title="{BodePlot}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/BodePlot.html}", note=[Accessed: 15-April-2025 ]}

@misc{reference.wolfram_2025_bodeplot, author="Wolfram Research", title="{BodePlot}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/BodePlot.html}", note=[Accessed: 15-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_bodeplot, organization={Wolfram Research}, title={BodePlot}, year={2014}, url={https://reference.wolfram.com/language/ref/BodePlot.html}, note=[Accessed: 15-April-2025 ]}

@online{reference.wolfram_2025_bodeplot, organization={Wolfram Research}, title={BodePlot}, year={2014}, url={https://reference.wolfram.com/language/ref/BodePlot.html}, note=[Accessed: 15-April-2025 ]}