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System object: phased.URA
Package: phased

Directivity of uniform rectangular array


D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)


D = directivity(H,FREQ,ANGLE) computes the Directivity of a uniform rectangular array (URA) of antenna or microphone elements, H, at frequencies specified by the FREQ and in angles of direction specified by the 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.

D = directivity(H,FREQ,ANGLE,Name,Value) computes the directivity with additional options specified by one or more Name,Value pair arguments.

Input Arguments

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Uniform rectangular array specified as a phased.URA System object.

Example: H = phased.URA

Frequencies for computing directivity and patterns, specified as a positive scalar or 1-by-L real-valued 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

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

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.

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

Array weights, specified as the comma-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.


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.


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Compute the directivity of two uniform rectangular arrays (URA). The first array consists of isotropic antenna elements. The second array consists of cosine antenna elements. In addition, compute the directivity of the first array steered to a specific direction.

Array of isotropic antenna elements

First, create a 10-by-10-element URA of isotropic antenna elements spaced one-quarter wavelength apart. Set the signal frequency to 800 MHz.

c = physconst('LightSpeed');
fc = 3e8;
lambda = c/fc;
myAntIso = phased.IsotropicAntennaElement;
myArray1 = phased.URA;
myArray1.Element = myAntIso;
myArray1.Size = [10,10];
myArray1.ElementSpacing = [lambda*0.25,lambda*0.25];
ang = [0;0];
d = directivity(myArray1,fc,ang,'PropagationSpeed',c)
d = 15.7753

Array of cosine antenna elements

Next, create a 10-by-10-element URA of cosine antenna elements also spaced one-quarter wavelength apart.

myAntCos = phased.CosineAntennaElement('CosinePower',[1.8,1.8]);
myArray2 = phased.URA;
myArray2.Element = myAntCos;
myArray2.Size = [10,10];
myArray2.ElementSpacing = [lambda*0.25,lambda*0.25];
ang = [0;0];
d = directivity(myArray2,fc,ang,'PropagationSpeed',c)
d = 19.7295

The directivity is increased due to the directivity of the cosine antenna elements.

Steered array of isotropic antenna elements

Finally, steer the isotropic antenna array to 30 degrees in azimuth and examine the directivity at the steered angle.

ang = [30;0];
w = steervec(getElementPosition(myArray1)/lambda,ang);
d = directivity(myArray1,fc,ang,'PropagationSpeed',c,...
d = 15.3309

The directivity is maximum in the steered direction and equals the directivity of the unsteered array at boresight.

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