This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# BodePlot

 BodePlot[g]gives the Bode plot of a rational function g in one complex variable. BodePlot[sys]gives the Bode plot of a TransferFunctionModel or StateSpaceModel object sys. BodePlotgives the plot for frequencies from to .
• BodePlot consists of a magnitude plot and a phase plot of the sinusoidal transfer function of the model. The frequency is plotted along the horizontal axis.
• Frequencies are given in radians per time unit.
• If the frequency range is not specified, an appropriate range is computed automatically.
• BodePlot has the same options as Plot, with the following changes and additions:
 Exclusions None frequencies to exclude FeedbackType "Negative" the feedback type Frame True whether to draw a frame around each plot MeshFunctions {{#1&},{#1&}} how to determine the placement of mesh divisions PlotLayout "VerticalGrid" the layout to be used PlotRange {{Full,Automatic},{Full,Automatic}} range of values to include SamplingPeriod None the sampling period ScalingFunctions {{"Log10","dB"},{"Log10","Degree"}} the scaling functions StabilityMargins False whether to show the stability margins StabilityMarginsStyle Automatic graphics directives to specify the style of the stability margins
• The other options of BodePlot can be specified as a list of two elements, with the first element corresponding to the magnitude plot and the second to the phase plot.
• Option specifications include:
 opt->val use val for both the magnitude and the phase plot opt->{val} use val for the magnitude plot and the default for the phase plot opt->{val1,val2} use for the magnitude plot and for the phase plot opt->{Automatic,val} use the default for the magnitude plot and val for the phase plot
• The frequency scales magfreqscale and phasefreqscale can be or , which correspond to the base 10 logarithmic scale and linear scale, respectively.
• The magnitude scale magscale can be or , which correspond to the decibel and absolute values of the magnitude, respectively.
• The phase scale phasescale can be or .
The Bode plot of a system:
Specify the system as a transfer-function object:
Plot over a wider frequency range:
Bode plot of a state-space model:
The Bode plot of a system:
 Out[1]=

Specify the system as a transfer-function object:
 Out[2]=
Plot over a wider frequency range:
 Out[3]=

Bode plot of a state-space model:
 Out[1]=
 Scope   (12)
Bode plot of a constant-gain system:
Bode plot of an integrator:
Bode plot of a differentiator:
Bode plot of a first-order lag:
Bode plot of a first-order lead:
Bode plot of a second-order system:
Specify a system as a transfer-function object:
A discrete-time system:
A discrete-time system given as a transfer-function object:
Specify the frequency range:
The Bode plot of a state-space model:
The Bode plot of a multiple-input, multiple-output system:
 Options   (20)
To obtain coordinates, select the graphics and press the period key:
Obtain frequency values in Hertz by dividing it by :
Frequency values for each plot in different units:
Frequency values in Hertz, magnitude in absolute units, and phase in radians:
Specify radians as both the displayed and copied value of phase:
Show grid lines:
Show grid lines only on the magnitude plot:
Show specific grid lines:
Specify grid lines style:
Specify different grid lines styles:
By default, the magnitude plot is placed vertically above the phase plot:
Obtain the result in a list:
Specify the sampling period in the system description:
Specify the sampling period in the BodePlot function:
A smaller sampling period results in a higher bandwidth:
Show absolute values of magnitude and phase in radians:
Plot frequency in the linear scale:
Show stability margins:
Show the phase margin only:
Specify the stability margins style:
Specify frequency ticks in Hertz:
Show ticks on the plot:
Obtain the ticks:
Change the frequency ticks to Hertz:
Change the magnitude ticks to absolute values:
Change the phase ticks to radians:
The modified plots:
 Applications   (4)
The static position error constant of a type 0 system is the magnitude at steady state:
Discrete-time type 0 system:
The static velocity error constant of a type 1 system is approximately the intersection of the initial -20 dB/decade segment (or its extension) with the 0 dB line:
Discrete-time type 1 system:
The square root of the static acceleration error constant of a type 2 system is approximately the intersection of the initial -40 dB/decade segment (or its extension) with the 0 dB line:
Discrete-time type 2 system:
Visualize the improvement in phase margin by using a proportional-integral (PI) compensator:
SingularValuePlot generalizes the Bode magnitude plot to MIMO systems:
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