directivity

System object: phased.ReplicatedSubarray
Namespace: phased

Directivity of replicated subarray

Syntax

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


Description

D = directivity(H,FREQ,ANGLE) returns the Directivity (dBi) of a replicated array of antenna or microphone element, H, 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.

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

Input Arguments

H — Replicated subarray

System object™

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

Example: H = phased.ReplicatedSubarray;

FREQ — Frequency for computing directivity and patterns

positive scalar | 1-by-L real-valued row vector

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

ANGLE — Angles for computing directivity

1-by-M real-valued row vector | 2-by-M real-valued matrix

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 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.

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

1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued matrix

Subarray weights, specified as the comma-separated pair consisting of 'Weights' and an N-by-1 complex-valued column vector or N-by-M complex-valued matrix. The dimension N is the number of subarrays in the array. The dimension L is the number of frequencies specified by the FREQ argument.

Weights dimension	FREQ dimension	Purpose
N-by-1 complex-valued column vector	Scalar or 1-by-L row vector	Applies a set of weights for the single frequency or for all L frequencies.
N-by-L complex-valued matrix	1-by-L row vector	Applies each of the L columns of ‘Weights’ for the corresponding frequency in the FREQ argument.

Example: 'Weights',ones(N,M)

Data Types: double

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

Output Arguments

D — Directivity

M-by-L matrix

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.

Examples

Directivity of Replicated Subarray

Compute the directivity of an array built up from ULA subarrays. Determine the directivity of the replicated subarray when the array is steered to towards 30 degrees azimuth.

Set the signal propagation speed to the speed of light. Set the signal frequency to 300 MHz.

c = physconst('LightSpeed');
fc = 3e8;
lambda = c/fc;

Create a 4-element ULA of isotropic antenna elements spaced 0.4-wavelength apart.

myArray = phased.ULA;
myArray.NumElements = 4;
myArray.ElementSpacing = 0.4*lambda;

Construct a 2-by-1 replicated subarray.

myRepArray = phased.ReplicatedSubarray;
myRepArray.Subarray = myArray;
myRepArray.Layout = 'Rectangular';
myRepArray.GridSize = [2 1];
myRepArray.GridSpacing = 'Auto';
myRepArray.SubarraySteering = 'Time';

Steer the array to 30 degrees azimuth and zero degrees elevation.

ang = [30;0];
mySV = phased.SteeringVector;
mySV.SensorArray = myRepArray;
mySV.PropagationSpeed = c;

Find the directivity at 30 degrees azimuth.

d = directivity(myRepArray,fc,ang,...
    'PropagationSpeed',c,...
    'Weights',step(mySV,fc,ang),...
    'SteerAngle',ang)

d = 
7.4776

More About

Directivity (dBi)

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

$$D=4\pi \frac{U_{\text{rad}}\left(\theta ,\phi \right)}{P_{\text{total}}}$$

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.