patternElevation

System object: phased.ConformalArray
Namespace: phased

Plot conformal array 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` — Conformal array
System object™

Conformal array, specified as a phased.ConformalArray System object.

Example: sArray= phased.ConformalArray;

`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 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.

`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` — Array weights
M-by-1 complex-valued column vector

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

Note

Use complex weights to steer the array response toward different directions. You can create weights using the phased.SteeringVector System object or you can compute your own weights. In general, you apply Hermitian conjugation before using weights in any Phased Array System Toolbox™ function or System object such as phased.Radiator or phased.Collector. However, for the directivity, pattern, patternAzimuth, and patternElevation methods of any array System object use the steering vector without conjugation.

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

Data Types: double
Complex Number Support: Yes

`Elevation` — Elevation angles
`[-180:180]` (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',[-180:2:180]

Data Types: double

`Parent` — Handle to axis
scalar

Handle to the axes along which the array geometry is displayed specified as a scalar.

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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Plot Elevation Pattern of 5-Element Cross Sonar Array

Open Live Script

Construct a 5-element acoustic cross array (UCA) using the ConformalArray System object™. Assume the operating frequency is 4 kHz. A typical value for the speed of sound in seawater is 1500.0 m/s. Plot the array patterns at two different azimuth angles.

Construct and view array

N = 5;
fc = 4000;
c = 1500.0;
lam = c/fc;
x = zeros(1,N);
y = [-1,0,1,0,0]*lam/2;
z = [0,0,0,-1,1]*lam/2;
sMic = phased.OmnidirectionalMicrophoneElement(...
    'FrequencyRange',[0,10000],'BackBaffled',true);
sArray = phased.ConformalArray('Element',sMic,...
    'ElementPosition',[x;y;z],...
    'ElementNormal',[zeros(1,N);zeros(1,N)]);
viewArray(sArray)

Figure contains an axes object. The hidden axes object with xlabel x axis (Az 0 El 0) -->, ylabel y axis --> contains 7 objects of type scatter, line, text.

Plot magnitude elevation pattern

fc = 4000;
c = 1500.0;
patternElevation(sArray,fc,[0,90],...
    'PropagationSpeed',c,...
    'Type','efield')

Figure contains an axes object. The hidden axes object contains 4 objects of type line, text. These objects represent 0.0 deg azimuth Ⓐ , 90.0 deg azimuth .

Plot directivity elevation pattern

Plot the pattern for elevation angles between -60 and 6- degrees at 0.1 degree resolution.

patternElevation(sArray,fc,[0,90],...
    'PropagationSpeed',c,...
    'Type','directivity',...
    'Elevation',[-60:0.1:60])

Figure contains an axes object. The hidden axes object contains 4 objects of type line, text. These objects represent 0.0 deg azimuth Ⓐ , 90.0 deg azimuth .

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.

Version History

Introduced in R2015a

patternElevation

Syntax

Description

Input Arguments

sArray — Conformal array 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 Arguments

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

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

Weights — Array weights M-by-1 complex-valued column vector

Elevation — Elevation angles [-180:180] (default) | 1-by-P real-valued row vector

Parent — Handle to axis scalar

Output Arguments

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

Examples

Plot Elevation Pattern of 5-Element Cross Sonar Array

More About

Directivity

Version History

See Also

`sArray` — Conformal array
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` — Array weights
M-by-1 complex-valued column vector

`Elevation` — Elevation angles
`[-180:180]` (default) | 1-by-P real-valued row vector

`Parent` — Handle to axis
scalar

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