Array factor: Difference between revisions

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{{technical|date=January 2019}}

An '''array factor''' is a mathematical factor in the [[directivity]] equation of an [[array antenna]]. It is the factor by which the directivity function of an individual antenna must be multiplied to get the directivity of the entire array.<ref>{{cite web|title=Array factors|url=http://www.engr.uky.edu/~cclu/EE522/NTS522_f.pdf|accessdate=19 June 2015}}</ref><ref>{{cite web|title=Antennas and Propagation|url=http://www.faculty.jacobs-university.de/jwallace/xwallace/courses/ap/ch5.pdf|publisher=Jacobs university|accessdate=19 June 2015}}</ref>

An array is simply a group of objects, and the array factor is a measure of how much a specific characteristic changes because of the grouping. This phenomenon is observed when antennas are grouped together. The radiation (or reception) pattern of the antenna group is considerably different from that of a single antenna. This is due to the constructive and destructive interference properties of radio waves. A well designed antenna array, allows the broadcast power to be directed to where it is needed most.

These antenna arrays are typically one dimensional, as seen on collinear dipole arrays, or two dimensional as on military phased arrays.

An array antenna is a set of multiple identical [[antenna (radio)|antenna]]s which work together as a single antenna. The individual antenna elements are connected to a single receiver or transmitter by [[feedline]]s that feed the power to the elements in a specific phase relationship. The radio waves from the individual antennas combine and [[superpose]], enhancing radiation in certain directions while suppressing radiation in other directions. The purpose of using multiple antennas in this way is to produce a [[radiation pattern]] that could not be achieved by a single antenna. Usually the goal is higher [[antenna gain|gain]] (directivity), more of the power radiated in a specific direction.

In order to simplify the mathematics, a number of assumptions are typically made:

The [[radiation pattern]] of an individual antenna element is given by a function <math display="inline">D(\theta, \phi)\,</math> of the azimuth angle <math display="inline">\theta\,</math> and elevation angle <math display="inline">\phi\,</math> called the directivity, which gives the signal strength radiated at any given angle. The radiation pattern of the entire array is given by another directivity function <math display="inline">D_\text{array}(\theta, \phi)\,</math>. The array factor ''AF'' is the factor by which the individual antenna's directivity must be multiplied to get the array's directivity

1. all radiators are equal in every respect

:<math>D_\text{array}(\theta, \phi) = \mathit{AF}\times D(\theta, \phi)\,</math>

2. all radiators are uniformly spaced

3. the signal phase shift between radiators is constant.

The array factor <math> AF </math> is the complex-valued [[far-field]] [[radiation pattern]] obtained for an array of <math> N </math> isotropic radiators located at [[coordinates]] <math> \vec{r}_n </math>, as determined by:<ref>{{cite book |last1=Balanis |first1=C. A. |title=Antenna Theory, Analysis and Design |page=291 |edition=3}}</ref>

<math> AF(\hat{r}) = \sum_{n=1}^N a_n e^{jk\hat{r}\cdot\vec{r}_n},</math>

where <math> a_n </math> are the complex-valued excitation coefficients, and <math> \hat{r} </math> is the direction [[unit vector]]. The array factor is defined in the transmitting mode,<ref>{{cite journal |title=IEEE Standard for definitions of terms for antennas |journal=IEEE STD |date=2014}}</ref> with the time convention <math> e^{j\omega t}</math>. A corresponding expression can be derived for the receiving mode, where a negative sign appears in the exponential factors, as derived in reference.<ref>{{Cite book|last=Frid|first=Henrik|url=http://kth.diva-portal.org/smash/record.jsf?pid=diva2%3A1392934&dswid=5174|title=Analysis and Optimization of Installed Antenna Performance|publisher=KTH (PhD thesis)|year=2020|isbn=978-91-7873-447-4|___location=Stockholm, Sweden|pages=36–39}}</ref>

==References==

{{reflistReflist}}

==See also==

[[Category:Antennas (radio)]]

* [[Array antenna]]

{{DEFAULTSORT:Monopulse Radar}}

{{Telecomm-stub}}

[[Category:Radar]]

[[Category:Antennas (radio)]]

[[Category:Signal processing]]