patternAzimuth

System object: phased.HeterogeneousConformalArray
Namespace: phased

Plot heterogeneous conformal array directivity or pattern versus azimuth

Syntax

patternAzimuth(sArray,FREQ) patternAzimuth(sArray,FREQ,EL) patternAzimuth(sArray,FREQ,EL,Name,Value) PAT = patternAzimuth(___)

Description

patternAzimuth(sArray,FREQ) plots the 2-D array directivity pattern versus azimuth (in dBi) for the array sArray at zero degrees elevation angle. 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.

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

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

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

Input Arguments

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`sArray` — Heterogeneous conformal array
System object™

Heterogeneous conformal array, specified as a phased.HeterogeneousConformalArray System object.

Example: sArray= phased.HeterogeneousConformalArray;

`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

`EL` — Elevation angles
1-by-N real-valued row vector

Elevation angles for computing sensor or array directivities and patterns, specified as a 1-by-N real-valued row vector. The quantity N is the number of requested 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 the xy plane. When measured toward the z-axis, this angle is positive.

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

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

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

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

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 azimuth values determined by the 'Azimuth' name-value pair argument. The dimension N is the number of elevation angles, as determined by the EL input argument.

Examples

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Plot Azimuthal Directivity Pattern of Disk Array

Open Live Script

Construct a 24-element disk array using elements with two different types of cosine antennas. Then, plot the array azimuthal directivity pattern.

Create the array

The array consists of cosine antenna elements with different power exponents.

sElement1 = phased.CosineAntennaElement('CosinePower',1.5);
sElement2 = phased.CosineAntennaElement('CosinePower',1.8);
N = 8;
azang = (0:N-1)*360/N-180;
p0 = [zeros(1,N);cosd(azang);sind(azang)];
posn = [0.6*p0, 0.4*p0, 0.2*p0];
sArray = phased.HeterogeneousConformalArray(...
    'ElementPosition',posn,...
    'ElementNormal', zeros(2,3*N),...
    'ElementSet',{sElement1,sElement2},...
    'ElementIndices',[1 1 1 1 1 1 1 1,...
    1 1 1 1 1 1 1 1,...
    2 2 2 2 2 2 2 2]);

View the disk array

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 the power pattern

Plot the azimuthal power pattern of this array for three different elevation angles: 0, 10 and 25 degrees. Apply radial tapering to the array. Assume the operating frequency is 1 GHz and the wave propagation speed is the speed of light.

c = physconst('LightSpeed');
fc = 1e9;
wts = [0.5*ones(N,1); 0.7*ones(N,1); 1.0*ones(N,1)];
wts = wts/sum(abs(wts));
patternAzimuth(sArray,fc,[0,10,25],'PropagationSpeed',c,...
    'Type','directivity','Weights',wts)

Figure contains an axes object. The hidden axes object contains 5 objects of type line, text. These objects represent 0.0 deg elevation Ⓐ , 10.0 deg elevation , 25.0 deg elevation .

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

patternAzimuth

Syntax

Description

Input Arguments

sArray — Heterogeneous conformal array System object™

FREQ — Frequency for computing directivity and pattern positive scalar

EL — Elevation angles 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

Azimuth — Azimuth 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 Azimuthal Directivity Pattern of Disk Array

More About

Directivity

Version History

See Also

`sArray` — Heterogeneous conformal array
System object™

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

`EL` — Elevation angles
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

`Azimuth` — Azimuth 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