# pattern

Plot antenna or transducer element directivity and patterns

Since R2019a

## Syntax

``pattern(element,FREQ)``
``pattern(element,FREQ,AZ)``
``pattern(element,FREQ,AZ,EL)``
``pattern(___,Name,Value)``
``[PAT,AZ_ANG,EL_ANG] = pattern(___)``

## Description

````pattern(element,FREQ)` plots the 3-D array directivity pattern (in dBi) for the element specified in `element`. The operating frequency is specified in `FREQ`. You can use this function to display the patterns for antennas that support polarization.```
````pattern(element,FREQ,AZ)` plots the element directivity pattern at the specified azimuth angle.```
````pattern(element,FREQ,AZ,EL)` plots the element directivity pattern at specified azimuth and elevation angles.```
````pattern(___,Name,Value)` plots the element pattern with additional options specified by one or more `Name,Value` pair arguments.```
````[PAT,AZ_ANG,EL_ANG] = pattern(___)` returns the element pattern in `PAT`. The `AZ_ANG` output contains the coordinate values corresponding to the rows of `PAT`. The `EL_ANG` output contains the coordinate values corresponding to the columns of `PAT`. If the `'CoordinateSystem'` parameter is set to `'uv'`, then `AZ_ANG` contains the U coordinates of the pattern and `EL_ANG` contains the V coordinates of the pattern. Otherwise, they are in angular units in degrees. UV units are dimensionless.```

## Input Arguments

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Antenna or transducer element, specified as a Phased Array System Toolbox System object.

Frequencies for computing directivity and patterns, specified as a positive scalar or 1-by-L real-valued row vector. Frequency units are in hertz.

• For an antenna, microphone, or sonar hydrophone or projector element, `FREQ` must lie within the range of values specified by the `FrequencyRange` or `FrequencyVector` property of the element. Otherwise, the element produces no response and the directivity is returned as `–Inf`. Most elements use the `FrequencyRange` property except for `phased.CustomAntennaElement` and `phased.CustomMicrophoneElement`, which use the `FrequencyVector` property.

• For an array of elements, `FREQ` must lie within the frequency range of the elements that make up the array. Otherwise, the array produces no response and the directivity is returned as `–Inf`.

Example: `[1e8 2e6]`

Data Types: `double`

Azimuth angles for computing directivity and pattern, specified as a 1-by-N real-valued row vector where N is the number of azimuth angles. Angle units are in degrees. Azimuth angles must lie between –180° and 180°.

The azimuth angle is the angle between the x-axis and the projection of the direction vector onto the xy plane. When measured from the x-axis toward the y-axis, this angle is positive.

Example: `[-45:2:45]`

Data Types: `double`

Elevation angles for computing directivity and pattern, specified as a 1-by-M real-valued row vector where M is the number of desired elevation directions. Angle units are in degrees. The elevation angle must lie between –90° and 90°.

The elevation angle is the angle between the direction vector and xy-plane. The elevation angle is positive when measured towards the z-axis.

Example: `[-75:1:70]`

Data Types: `double`

### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

Example: `CoordinateSystem,'polar',Type,'directivity'`

Plotting coordinate system of the pattern, specified as the comma-separated pair consisting of `'CoordinateSystem'` and one of `'polar'`, `'rectangular'`, or `'uv'`. When `'CoordinateSystem'` is set to `'polar'` or `'rectangular'`, the `AZ` and `EL` arguments specify the pattern azimuth and elevation, respectively. `AZ` values must lie between –180° and 180°. `EL` values must lie between –90° and 90°. If `'CoordinateSystem'` is set to `'uv'`, `AZ` and `EL` then specify U and V coordinates, respectively. `AZ` and `EL` must lie between -1 and 1.

Example: `'uv'`

Data Types: `char`

Displayed pattern type, specified as the comma-separated pair consisting of `'Type'` and one of

• `'directivity'` — directivity pattern measured in dBi.

• `'efield'` — field pattern of the sensor or array. For acoustic sensors, the displayed pattern is for the scalar sound field.

• `'power'` — power pattern of the sensor or array defined as the square of the field pattern.

• `'powerdb'` — power pattern converted to dB.

Example: `'powerdb'`

Data Types: `char`

Display normalized pattern, specified as the comma-separated pair consisting of `'Normalize`' and a Boolean. Set this parameter to `true` to display a normalized pattern. This parameter does not apply when you set `'Type'` to `'directivity'`. Directivity patterns are already normalized.

Data Types: `logical`

Plotting style, specified as the comma-separated pair consisting of `'Plotstyle'` and either `'overlay'` or `'waterfall'`. This parameter applies when you specify multiple frequencies in `FREQ` in 2-D plots. You can draw 2-D plots by setting one of the arguments `AZ` or `EL` to a scalar.

Data Types: `char`

Polarization type, specified as the comma-separated pair consisting of `'Polarization'` and either `'combined'`, `'H'`, or `'V'`. If `Polarization` is `'combined'`, the horizontal and vertical polarization patterns are combined. If `Polarization` is `'H'`, only the horizontal polarization is displayed. If `Polarization` is `'V'`, only the vertical polarization is displayed.

#### Dependencies

To enable this property, set the `element` argument to an antenna that supports polarization: `phased.CrossedDipoleAntennaElement`, `phased.ShortDipoleAntennaElement`, or `phased.CustomAntennaElement`, and then set the `'Type'` name-value pair to `'efield'`, `'power'`, or `'powerdb'`.

Data Types: `char` | `string`

## Output Arguments

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Element pattern, returned as an N-by-M real-valued matrix. The pattern is a function of azimuth and elevation. The rows of `PAT` correspond to the azimuth angles in the vector specified by `EL_ANG`. The columns correspond to the elevation angles in the vector specified by `AZ_ANG`.

Azimuth angles for displaying directivity or response pattern, returned as a scalar or 1-by-N real-valued row vector corresponding to the dimension set in `AZ`. The columns of `PAT` correspond to the values in `AZ_ANG`. Units are in degrees.

Elevation angles for displaying directivity or response, returned as a scalar or 1-by-M real-valued row vector corresponding to the dimension set in `EL`. The rows of `PAT` correspond to the values in `EL_ANG`. Units are in degrees.

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### Directivity

Directivity describes the directionality of the radiation pattern of a sensor element or array of sensor elements.

Higher directivity is desired when you want to transmit more radiation in a specific direction. Directivity is the ratio of the transmitted radiant intensity in a specified direction to the radiant intensity transmitted by an isotropic radiator with the same total transmitted power

`$D=4\pi \frac{{U}_{\text{rad}}\left(\theta ,\phi \right)}{{P}_{\text{total}}}$`

where Urad(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and Ptotal is the total power transmitted by an isotropic radiator. For a receiving element or array, directivity measures the sensitivity toward radiation arriving from a specific direction. The principle of reciprocity shows that the directivity of an element or array used for reception equals the directivity of the same element or array used for transmission. When converted to decibels, the directivity is denoted as dBi. For information on directivity, read the notes on Element Directivity and Array Directivity.

### Azimuth and Elevation Angles

The azimuth angle of a vector is the angle between the x-axis and its orthogonal projection onto the xy-plane. The angle is positive when going from the x-axis toward the y-axis. Azimuth angles lie between –180° and 180° degrees, inclusive. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy-plane. Elevation angles lie between –90° and 90° degrees, inclusive. ## Algorithms

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### Convert plotResponse to Pattern

For antenna, transducer, and array System objects, the `pattern` function replaces the `plotResponse` function. In addition, two new simplified functions exist just to draw 2-D azimuth and elevation pattern plots. These functions are `patternAzimuth` and `patternElevation`.

The following table is a guide for converting your code from using `plotResponse` to `pattern`. Notice that some of the inputs have changed from input arguments to Name-Value pairs and conversely. The general `pattern` method syntax is

`pattern(H,FREQ,AZ,EL,'Name1','Value1',...,'NameN','ValueN')`

plotResponse InputsplotResponse Descriptionpattern Inputs
`H` argumentAntenna, microphone, or array System object.`H` argument (no change)
`FREQ` argumentOperating frequency.`FREQ` argument (no change)
`V` argumentPropagation speed. This argument is used only for arrays.`'PropagationSpeed'` name-value pair. This parameter is only used for arrays.
`'Format'` and `'RespCut'` name-value pairs

These options work together to let you create a plot in angle space (line or polar style) or UV space. They also determine whether the plot is 2-D or 3-D. This table shows you how to create different types of plots using `plotResponse`.

Display space
Angle space (2D)

Set `'RespCut' to 'Az' or 'El'`. Set `'Format'` to `'line'` or `'polar'`.

Set the display axis using either the `'AzimuthAngles'` or `'ElevationAngles'` name-value pairs.

Angle space (3D)

Set `'RespCut'` to `'3D'`. Set `'Format'` to `'line'` or `'polar'`.

Set the display axis using both the `'AzimuthAngles'` and`'ElevationAngles'` name-value pairs.

UV space (2D)Set `'RespCut'` to`'U'`. Set `'Format'` to `'UV'`. Set the display range using the `'UGrid'` name-value pair.
UV space (3D)Set `'RespCut'` to`'3D'`. Set `'Format'` to `'UV'`. Set the display range using both the `'UGrid'` and `'VGrid'` name-value pairs.

`'CoordinateSystem'` name-value pair used together with the `AZ` and `EL` input arguments.

`'CoordinateSystem'` has the same options as the `plotResponse` method `'Format'`name-value pair, except that `'line'` is now named `'rectangular'`. The table shows how to create different types of plots using `pattern`.

Display space
Angle space (2D)Set `'Coordinate System'` to `'rectangular'` or `'polar'`. Specify either `AZ` or `EL` as a scalar.
Angle space (3D)Set `'Coordinate System'` to `'rectangular'` or `'polar'`. Specify both `AZ` and `EL` as vectors.
UV space (2D)Set `'Coordinate System'` to `'uv'`. Use `AZ` to specify a U-space vector. Use `EL` to specify a V-space scalar.
UV space (3D)Set `'Coordinate System'` to `'uv'`. Use `AZ` to specify a U-space vector. Use `EL` to specify a V-space vector.

If you set `CoordinateSystem` to `'uv'`, enter the UV grid values using `AZ` and `EL`.

`'CutAngle'` name-value pairConstant angle at to take an azimuth or elevation cut. When producing a 2-D plot and when `'RespCut'` is set to `'Az'` or `'El'`, use `'CutAngle'` to set the slice across which to view the plot.No equivalent name-value pair. To create a cut, specify either `AZ` or `EL` as a scalar, not a vector.
`'NormalizeResponse'` name-value pairNormalizes the plot. When `'Unit'` is set to `'dbi'`, you cannot specify `'NormalizeResponse'`.

Use the `'Normalize'` name-value pair. When `'Type'` is set to `'directivity'` you cannot specify `'Normalize'`.

`'OverlayFreq'` name-value pairPlot multiple frequencies on the same 2-D plot. Available only when `'Format'` is set to `'line'` or `'uv'` and `'RespCut'` is not set to `'3D'`. The value `true` produces an overlay plot and the value `false` produces a waterfall plot.

`'PlotStyle'` name-value pair plots multiple frequencies on the same 2-D plot.

The values `'overlay'` and `'waterfall'` correspond to `'OverlayFreq'` values of `true` and `false`. The option `'waterfall'` is allowed only when `'CoordinateSystem'` is set to `'rectangular'` or `'uv'`.

`'Polarization'` name-value pairDetermines how to plot polarized fields. Options are `'None'`, `'Combined'`, `'H'`, or `'V'`.`'Polarization'` name-value pair determines how to plot polarized fields. The `'None'` option is removed. The options `'Combined'`, `'H'`, or `'V'` are unchanged.
`'Unit'` name-value pairDetermines the plot units. Choose `'db'`, `'mag'`, `'pow'`, or `'dbi'`, where the default is `'db'`.

`'Type'` name-value pair, uses equivalent options with different names

`plotResponse``pattern`
`'db'``'powerdb'`
`'mag'``'efield'`
`'pow'``'power'`
`'dbi'``'directivity'`

`'Weights'` name-value pairArray element tapers (or weights).`'Weights'` name-value pair (no change).
`'AzimuthAngles'` name-value pairAzimuth angles used to display the antenna or array response.

`AZ` argument

`'ElevationAngles'` name-value pairElevation angles used to display the antenna or array response.

`EL` argument

`'UGrid'` name-value pairContains U coordinates in UV-space.

`AZ` argument when `'CoordinateSystem'` name-value pair is set to `'uv'`

`'VGrid'` name-value pairContains V-coordinates in UV-space.

`EL` argument when `'CoordinateSystem'` name-value pair is set to `'uv'`

## Version History

Introduced in R2019a