patternElevation

System object: phased.ReplicatedSubarray
Package: phased

Plot replicated subarray directivity or pattern versus elevation

Syntax

patternElevation(sArray,FREQ) patternElevation(sArray,FREQ,AZ) patternElevation(sArray,FREQ,AZ,Name,Value) PAT = patternElevation(___)

Description

patternElevation(sArray,FREQ) plots the 2-D array directivity pattern versus elevation (in dBi) for the array sArray at zero degrees azimuth angle. When AZ is a vector, multiple overlaid plots are created. The argument FREQ specifies the operating frequency.

The integration used when computing array directivity has a minimum sampling grid of 0.1 degrees. If an array pattern has a beamwidth smaller than this, the directivity value will be inaccurate.

patternElevation(sArray,FREQ,AZ), in addition, plots the 2-D element directivity pattern versus elevation (in dBi) at the azimuth angle specified by AZ. When AZ is a vector, multiple overlaid plots are created.

patternElevation(sArray,FREQ,AZ,Name,Value) plots the array pattern with additional options specified by one or more Name,Value pair arguments.

PAT = patternElevation(___) returns the array pattern. PAT is a matrix whose entries represent the pattern at corresponding sampling points specified by the 'Elevation' parameter and the AZ input argument.

Input Arguments

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`sArray` — Replicated subarray
System object™

Replicated subarray, specified as a phased.ReplicatedSubarray System object.

Example: sArray= phased.ReplicatedSubarray;

`FREQ` — Frequency for computing directivity and pattern
positive scalar

Frequency for computing directivity and pattern, specified as a positive scalar. Frequency units are in hertz.

For an antenna or microphone element, FREQ must lie within the range of values specified by the FrequencyRange or the 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

Data Types: double

`AZ` — Azimuth angles for computing directivity and pattern
1-by-N real-valued row vector

Azimuth angles for computing sensor or array directivities and patterns, specified as a 1-by-N real-valued row vector where N is the number of desired azimuth directions. Angle units are in degrees. The azimuth angle 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. This angle is positive when measured from the x-axis toward the y-axis.

Example: [0,10,20]

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated 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.

`'Type'` — Displayed pattern type
`'directivity'` (default) | `'efield'` | `'power'` | `'powerdb'`

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

`'PropagationSpeed'` — Signal propagation speed
speed of light (default) | positive scalar

Signal propagation speed, specified as the comma-separated pair consisting of 'PropagationSpeed' and a positive scalar in meters per second.

Example: 'PropagationSpeed',physconst('LightSpeed')

Data Types: double

`'Weights'` — Subarray weights
M-by-1 complex-valued column vector

Subarray weights, specified as the comma-separated pair consisting of 'Weights' and an M-by-1 complex-valued column vector. Subarray weights are applied to the subarrays of the array to produce array steering, tapering, or both. The dimension M is the number of subarrays in the array.

Example: 'Weights',ones(10,1)

Data Types: double
Complex Number Support: Yes

`'SteerAngle'` — Subarray steering angle
`[0;0]` (default) | scalar | 2-element column vector

Subarray steering angle, specified as the comma-separated pair consisting of 'SteerAngle' and a scalar or a 2-by-1 column vector.

If 'SteerAngle' is a 2-by-1 column vector, it has the form [azimuth; elevation]. The azimuth angle must be between –180° and 180°, inclusive. The elevation angle must be between –90° and 90°, inclusive.

If 'SteerAngle' is a scalar, it specifies the azimuth angle only. In this case, the elevation angle is assumed to be 0.

This option applies only when the 'SubarraySteering' property of the System object is set to 'Phase' or 'Time'.

Example: 'SteerAngle',[20;30]

Data Types: double

`'ElementWeights'` — Weights applied to elements within subarray
`1` (default) | complex-valued N_SE-by-N matrix

Subarray element weights, specified as complex-valued N_SE-by-N matrix. Weights are applied to the individual elements within a subarray. All subarrays have the same dimensions and sizes. N_SE is the number of elements in each subarray and N is the number of subarrays. Each column of the matrix specifies the weights for the corresponding subarray.

Dependencies

To enable this name-value pair, set the SubarraySteering property of the array to 'Custom'.

Data Types: double
Complex Number Support: Yes

`'Elevation'` — Elevation angles
`[-90:90]` (default) | 1-by-P real-valued row vector

Elevation angles, specified as the comma-separated pair consisting of 'Elevation' and a 1-by-P real-valued row vector. Elevation angles define where the array pattern is calculated.

Example: 'Elevation',[-90:2:90]

Data Types: double

Output Arguments

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`PAT` — Array directivity or pattern
L-by-N real-valued matrix

Array directivity or pattern, returned as an L-by-N real-valued matrix. The dimension L is the number of elevation angles determined by the 'Elevation' name-value pair argument. The dimension N is the number of azimuth angles determined by the AZ argument.

Examples

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Elevation Pattern of Array with Subarrays

Open Live Script

Create a 2-by-2-element URA of isotropic antenna elements, and arrange four copies to form a 16-element URA. Plot the elevation directivity pattern within a restricted range of elevation angles from -45 to 45 degrees in 0.1 degree increments. Plot directivity for 0 degrees and 15 degrees azimuth.

Create the array

fmin = 1e9;
fmax = 6e9;
c = physconst('LightSpeed');
lam = c/fmax;
sIso = phased.IsotropicAntennaElement(...
    'FrequencyRange',[fmin,fmax],...
    'BackBaffled',false);
sURA = phased.URA('Element',sIso,...
    'Size',[2 2],...
    'ElementSpacing',lam/2);
sRS = phased.ReplicatedSubarray('Subarray',sURA,...
    'Layout','Rectangular','GridSize',[2 2],...
    'GridSpacing','Auto');

Plot elevation directivity pattern

fc = 1e9;
wts = [0.862,1.23,1.23,0.862]';
patternElevation(sRS,fc,[0,15],...
    'PropagationSpeed',physconst('LightSpeed'),...
    'Elevation',[-45:0.1:45],...
    'Type','directivity',...
    'Weights',wts);

More About

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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

$D = 4 π \frac{U_{rad} (θ, φ)}{P_{total}}$

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.

Documentation

patternElevation

Syntax

Description

Input Arguments

`sArray` — Replicated subarray
System object™

`FREQ` — Frequency for computing directivity and pattern
positive scalar

`AZ` — Azimuth angles for computing directivity and pattern
1-by-N real-valued row vector

Name-Value Pair Arguments

`'Type'` — Displayed pattern type
`'directivity'` (default) | `'efield'` | `'power'` | `'powerdb'`

`'PropagationSpeed'` — Signal propagation speed
speed of light (default) | positive scalar

`'Weights'` — Subarray weights
M-by-1 complex-valued column vector

`'SteerAngle'` — Subarray steering angle
`[0;0]` (default) | scalar | 2-element column vector

`'ElementWeights'` — Weights applied to elements within subarray
`1` (default) | complex-valued N_SE-by-N matrix

Dependencies

`'Elevation'` — Elevation angles
`[-90:90]` (default) | 1-by-P real-valued row vector

Output Arguments

`PAT` — Array directivity or pattern
L-by-N real-valued matrix

Examples

Elevation Pattern of Array with Subarrays

More About

Directivity

See Also

Phased Array System Toolbox Documentation

Support

Documentation

patternElevation

Syntax

Description

Input Arguments

sArray — Replicated subarray System object™

FREQ — Frequency for computing directivity and pattern positive scalar

AZ — Azimuth angles for computing directivity and pattern 1-by-N real-valued row vector

Name-Value Pair Arguments

'Type' — Displayed pattern type 'directivity' (default) | 'efield' | 'power' | 'powerdb'

'PropagationSpeed' — Signal propagation speed speed of light (default) | positive scalar

'Weights' — Subarray weights M-by-1 complex-valued column vector

'SteerAngle' — Subarray steering angle [0;0] (default) | scalar | 2-element column vector

'ElementWeights' — Weights applied to elements within subarray 1 (default) | complex-valued NSE-by-N matrix

Dependencies

'Elevation' — Elevation angles [-90:90] (default) | 1-by-P real-valued row vector

Output Arguments

PAT — Array directivity or pattern L-by-N real-valued matrix

Examples

Elevation Pattern of Array with Subarrays

More About

Directivity

See Also

Phased Array System Toolbox Documentation

Support

`sArray` — Replicated subarray
System object™

`FREQ` — Frequency for computing directivity and pattern
positive scalar

`AZ` — Azimuth angles for computing directivity and pattern
1-by-N real-valued row vector

`'Type'` — Displayed pattern type
`'directivity'` (default) | `'efield'` | `'power'` | `'powerdb'`

`'PropagationSpeed'` — Signal propagation speed
speed of light (default) | positive scalar

`'Weights'` — Subarray weights
M-by-1 complex-valued column vector

`'SteerAngle'` — Subarray steering angle
`[0;0]` (default) | scalar | 2-element column vector

`'ElementWeights'` — Weights applied to elements within subarray
`1` (default) | complex-valued N_SE-by-N matrix

`'Elevation'` — Elevation angles
`[-90:90]` (default) | 1-by-P real-valued row vector

`PAT` — Array directivity or pattern
L-by-N real-valued matrix