directivity

R2026b

Compute array manifold directivity

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Syntax

D = directivity(arraymanifold,FREQ,ANGLE)
directivity(___,Name=Value)

Description

D = directivity(arraymanifold,FREQ,ANGLE) returns the Directivity (dBi) of an array manifold, arraymanifold, at frequencies specified by FREQ and in angles of direction specified by ANGLE.

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.

directivity(___,Name=Value) plots the array pattern with additional options specified by one or more Name=Value pair arguments.

example

Examples

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Open Live Script

Create a phased.ArrayManifold System object™ and evaluate the manifold values in multiple directions.

First, set up the azimuth angle, elevation angle, and frequency grids.

az = -180:10:180;
el = -90:10:90;
fc = [0 1e9 2e9];
manval = complex(ones(numel(az),numel(el),numel(fc),8));

Create the array manifold.

man1 = phased.ArrayManifold(manval,az,el,fc);

Evaluate the manifold at two frequencies and two directions.

M1 = man1([0 1e9],[30 40; 0 10])
M1 = 
M1(:,:,1) =

     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1


M1(:,:,2) =

     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1

Create a second frequency-invariant manifold. 

man2 = phased.ArrayManifold( ...
    manval(:,:,1,:),az,el,[]);

Frequency query values are ignored for frequency-invariant data.

M2 = man2([0 1e9 2e9],[0;0]);

Use the directivity object function to compute the directivity of the second manifold at az=-90 degrees and el=10 degrees.

[az(10),el(11)]
ans = 1×2

   -90    10


directivity(man2,fc(2),[az(10);el(11)])
ans = 
1.1025e-04

Using the pattern object function, plot the directivity pattern of the array manifold.

pattern(man2,fc(2))

Figure contains an axes object. The hidden axes object with title 3D Directivity Pattern contains 13 objects of type surface, line, text, patch.

Input Arguments

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Array manifold, specified as a phased.ArrayManifold 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 Hz.

Example: [1e8 2e6]

Data Types: double

Angles for computing directivity, specified as a 1-by-M real-valued row vector or a 2-by-M real-valued matrix, where M is the number of angular directions. Angle units are in degrees. If ANGLE is a 2-by-M matrix, then each column specifies a direction in azimuth and elevation, [az;el]. The azimuth angle must lie between –180° and 180°. The elevation angle must lie between –90° and 90°.

If ANGLE is a 1-by-M vector, then each entry represents an azimuth angle, with the elevation angle assumed to be zero.

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. The elevation angle is the angle between the direction vector and xy plane. This angle is positive when measured towards the z-axis. See Azimuth and Elevation Angles.

Example: [45 60; 0 10]

Data Types: double

Name-Value Arguments

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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"

Array weights, specified as the equal sign separated pair consisting of "Weights" and an N-by-1 complex-valued column vector or N-by-L complex-valued matrix. Array weights are applied to the elements of the array to produce array steering, tapering, or both. The dimension N is the number of elements in the array. The dimension L is the number of frequencies specified by FREQ.

Weights DimensionFREQ DimensionPurpose
N-by-1 complex-valued column vectorScalar or 1-by-L row vectorApplies a set of weights for the single frequency or for all L frequencies.
N-by-L complex-valued matrix1-by-L row vectorApplies each of the L columns of "Weights" for the corresponding frequency in FREQ.

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(N,M)

Data Types: double
Complex Number Support: Yes

Output Arguments

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Directivity, returned as an M-by-L matrix. Each row corresponds to one of the M angles specified by ANGLE. Each column corresponds to one of the L frequency values specified in FREQ. Directivity units are in dBi where dBi is defined as the gain of an element relative to an isotropic radiator.

More About

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Extended Capabilities

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C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021a

See Also