# bode

Bode plot of frequency response, or magnitude and phase data

## Syntax

## Description

`bode(`

creates
a Bode plot of the frequency response of a dynamic
system model `sys`

)`sys`

. The plot displays
the magnitude (in dB) and phase (in degrees) of the system response
as a function of frequency. `bode`

automatically
determines frequencies to plot based on system dynamics.

If `sys`

is a multi-input, multi-output (MIMO)
model, then `bode`

produces an array of Bode plots,
each plot showing the frequency response of one I/O pair.

If `sys`

is a model with complex coefficients, then
in:

Log frequency scale, the plot shows two branches, one for positive frequencies and one for negative frequencies. The plot also shows arrows to indicate the direction of increasing frequency values for each branch. See Bode Plot of Model with Complex Coefficients.

Linear frequency scale, the plot shows a single branch with a symmetric frequency range centered at a frequency value of zero.

`bode(sys1,sys2,...,sysN)`

plots the frequency
response of multiple dynamic systems on the same plot. All systems
must have the same number of inputs and outputs.

`bode(sys1,`

specifies a
color, line style, and marker for each system in the plot.`LineSpec`

1,...,sysN,LineSpecN)

`bode(___,`

plots
system responses for frequencies specified by `w`

)`w`

.

If

`w`

is a cell array of the form`{wmin,wmax}`

, then`bode`

plots the response at frequencies ranging between`wmin`

and`wmax`

.If

`w`

is a vector of frequencies, then`bode`

plots the response at each specified frequency. The vector`w`

can contain both negative and positive frequencies.

You can use `w`

with any of the input-argument
combinations in previous syntaxes.

## Examples

## Input Arguments

## Output Arguments

## Tips

When you need additional plot customization options, use

`bodeplot`

(Control System Toolbox) instead.

## Algorithms

`bode`

computes the frequency response as
follows:

Compute the zero-pole-gain (

`zpk`

(Control System Toolbox)) representation of the dynamic system.Evaluate the gain and phase of the frequency response based on the zero, pole, and gain data for each input/output channel of the system.

For continuous-time systems,

`bode`

evaluates the frequency response on the imaginary axis*s*=*jω*and considers only positive frequencies.For discrete-time systems,

`bode`

evaluates the frequency response on the unit circle. To facilitate interpretation, the command parameterizes the upper half of the unit circle as:$$z={e}^{j\omega {T}_{s}},\text{\hspace{1em}}0\le \omega \le {\omega}_{N}=\frac{\pi}{{T}_{s}},$$

where

*T*is the sample time and_{s}*ω*is the Nyquist frequency. The equivalent continuous-time frequency_{N}*ω*is then used as the*x*-axis variable. Because $$H\left({e}^{j\omega {T}_{s}}\right)$$ is periodic with period 2*ω*,_{N}`bode`

plots the response only up to the Nyquist frequency*ω*. If_{N}`sys`

is a discrete-time model with unspecified sample time,`bode`

uses*T*= 1._{s}

## Version History

**Introduced before R2006a**