System object: phased.UCA
Directivity of uniform circular array
D = directivity(sArray,FREQ,ANGLE)
D = directivity(sArray,FREQ,ANGLE,Name,Value)
D = directivity( returns
the Directivity (dBi) of a uniform circular
array (UCA) of antenna or microphone elements,
at frequencies specified by
FREQ and in angles
of direction specified by
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.
sArray— Uniform circular array
Uniform circular array, specified as a
comma-separated pairs of
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
Compute the directivity of two uniform circular arrays (UCA) at zero degrees azimuth and elevation. The first array consists of isotropic antenna elements. The second array consists of cosine antenna elements. In addition, compute the directivity of the cosine element array steered to a 45 degrees elevation.
Array of isotropic antenna elements
First, create a 10-element UCA with a radius of one-half meter consisting of isotropic antenna elements. Set the signal frequency to 300 MHz.
c = physconst('LightSpeed'); fc = 300e6; sIso = phased.IsotropicAntennaElement; sArray = phased.UCA('Element',sIso,'NumElements',10,'Radius',0.5); ang = [0;0]; d = directivity(sArray,fc,ang,'PropagationSpeed',c)
d = -1.1423
Array of cosine antenna elements
Next, create a 10-element UCA of cosine antenna elements also with a 0.5 meter radius.
sCos = phased.CosineAntennaElement('CosinePower',[3,3]); sArray1 = phased.UCA('Element',sCos,'NumElements',10,'Radius',0.5); ang = [0;0]; d = directivity(sArray1,fc,ang,'PropagationSpeed',c)
d = 3.2550
The directivity is increased due to the added directivity of the cosine antenna elements
Steered array of cosine antenna elements
Finally, steer the cosine antenna array toward 45 degrees elevation, and then examine the directivity at 45 degrees.
ang = [0;45]; lambda = c/fc; w = steervec(getElementPosition(sArray1)/lambda,ang); d = directivity(sArray1,fc,ang,'PropagationSpeed',c,... 'Weights',w)
d = -3.1410
The directivity is decreased because of the combined reduction of directivity of the elements and the array.
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
where Urad(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and Ptotal 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.
Computing directivity requires integrating the far-field transmitted radiant intensity over all directions in space to obtain the total transmitted power. There is a difference between how that integration is performed when Antenna Toolbox™ antennas are used in a phased array and when Phased Array System Toolbox antennas are used. When an array contains Antenna Toolbox antennas, the directivity computation is performed using a triangular mesh created from 500 regularly spaced points over a sphere. For Phased Array System Toolbox antennas, the integration uses a uniform rectangular mesh of points spaced 1° apart in azimuth and elevation over a sphere. There may be significant differences in computed directivity, especially for large arrays.