# pattern

Plot antenna or transducer element directivity and patterns

## 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 azimuthPattern and elevationPattern.

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

plotResponsepattern
'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