Plot antenna or transducer element directivity and patterns
pattern(element,FREQ)
pattern(element,FREQ,AZ)
pattern(element,FREQ,AZ,EL)
pattern(___,Name,Value)
[PAT,AZ_ANG,EL_ANG] = pattern(___)
pattern(___,
plots the
element pattern with additional options specified by one or more Name,Value
)Name,Value
pair arguments.
[
returns the element pattern in PAT
,AZ_ANG
,EL_ANG
] = pattern(___)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.
element
— Antenna or transducer elementAntenna or transducer element, specified as a Phased Array System Toolbox System object.
FREQ
— Frequency for computing directivity and patternsFrequencies for computing directivity and patterns, specified as a positive scalar or 1byL realvalued 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
AZ
— Azimuth angles[180:180]
(default)  1byN realvalued row vectorAzimuth angles for computing directivity and pattern, specified as a 1byN realvalued 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 xaxis and the projection of the direction vector onto the xy plane. When measured from the xaxis toward the yaxis, this angle is positive.
Example: [45:2:45]
Data Types: double
EL
— Elevation angles[90:90]
(default)  1byM realvalued row vectorElevation angles for computing directivity and pattern, specified as a 1byM realvalued 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 xyplane. The elevation angle is positive when measured towards the zaxis.
Example: [75:1:70]
Data Types: double
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
CoordinateSystem,'polar',Type,'directivity'
'CoordinateSystem'
— Plotting coordinate system'polar'
(default)  'rectangular'
 'uv'
Plotting coordinate system of the pattern, specified as the
commaseparated 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
'Type'
— Displayed pattern type'directivity'
(default)  'efield'
 'power'
 'powerdb'
Displayed pattern type, specified as the commaseparated 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
'Normalize'
— Display normalize patterntrue
(default)  false
Display normalized pattern, specified as the commaseparated 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
'PlotStyle'
— Plotting style'overlay'
(default)  'waterfall'
'Polarization'
— Polarization type'combined'
(default)  'H'
 'V'
Polarization type, specified as the commaseparated 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.
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'
namevalue pair to 'efield'
, 'power'
, or
'powerdb'
.
Data Types: char
 string
PAT
— Element patternDirectivity 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 U_{rad}(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and P_{total} 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.
Computing directivity requires integrating the farfield transmitted radiant intensity over all directions in space to obtain the total transmitted power. There is a difference between how that integration is performed when Antenna Toolbox™ antennas are used in a phased array and when Phased Array System Toolbox antennas are used. When an array contains Antenna Toolbox antennas, the directivity computation is performed using a triangular mesh created from 500 regularly spaced points over a sphere. For Phased Array System Toolbox antennas, the integration uses a uniform rectangular mesh of points spaced 1° apart in azimuth and elevation over a sphere. There may be significant differences in computed directivity, especially for large arrays.
The azimuth angle of a vector is the angle between the xaxis and its orthogonal projection onto the xyplane. The angle is positive when going from the xaxis toward the yaxis. Azimuth angles lie between –180° and 180° degrees, inclusive. The elevation angle is the angle between the vector and its orthogonal projection onto the xyplane. The angle is positive when going toward the positive zaxis from the xyplane. Elevation angles lie between –90° and 90° degrees, inclusive.
For antenna, transducer, and array System objects, the
pattern
function replaces the plotResponse
function.
In addition, two new simplified functions exist just to draw 2D 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 NameValue
pairs and conversely. The general pattern
method syntax
is
pattern(H,FREQ,AZ,EL,'Name1','Value1',...,'NameN','ValueN')
plotResponse Inputs  plotResponse Description  pattern Inputs  

H argument  Antenna, microphone, or array System object.  H argument (no change)  
FREQ argument  Operating frequency.  FREQ argument (no change)  
V argument  Propagation speed. This argument is used only for arrays.  'PropagationSpeed' namevalue pair. This
parameter is only used for arrays.  
'Format' and 'RespCut' namevalue
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 2D or 3D. This table shows
you how to create different types of plots using

If you set  
'CutAngle' namevalue pair  Constant angle at to take an azimuth or elevation cut. When
producing a 2D plot and when 'RespCut' is set
to 'Az' or 'El' , use 'CutAngle' to
set the slice across which to view the plot.  No equivalent namevalue pair. To create a cut, specify either AZ or EL as
a scalar, not a vector.  
'NormalizeResponse' namevalue pair  Normalizes the plot. When 'Unit' is set
to 'dbi' , you cannot specify 'NormalizeResponse' .  'Normalize' namevalue pair. When 'Type' is
set to 'directivity' , you cannot specify  
'OverlayFreq' namevalue pair  Plot multiple frequencies on the same 2D 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. 
The values  
'Polarization' namevalue pair  Determines how to plot polarized fields. Options are 'None' , 'Combined' , 'H' ,
or 'V' .  'Polarization' namevalue pair determines
how to plot polarized fields. The 'None' option
is removed. The options 'Combined' , 'H' ,
or 'V' are unchanged.  
'Unit' namevalue pair  Determines the plot units. Choose 'db' , 'mag' , 'pow' ,
or 'dbi' , where the default is 'db' .  'Type' namevalue pair, uses equivalent
options with different names
 
'Weights' namevalue pair  Array element tapers (or weights).  'Weights' namevalue pair (no change).  
'AzimuthAngles' namevalue pair  Azimuth angles used to display the antenna or array response. 
 
'ElevationAngles' namevalue pair  Elevation angles used to display the antenna or array response. 
 
'UGrid' namevalue pair  Contains U coordinates in UVspace. 
 
'VGrid' namevalue pair  Contains Vcoordinates in UVspace. 

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