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Henrik Frid (talk | contribs) Removed the redirect to the 'directivity' page. Array factor and directivity are two different things and should have separate pages. As an example, the a lens antenna has a directivity, but no meaningful definition for array factor. Tags: Removed redirect Visual edit |
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{{technical|date=January 2019}}
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.
In order to simplify the mathematics, a number of assumptions are typically made:
1. all radiators are equal in every respect
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==
{{Reflist}}
==See also==
* [[Array antenna]]
{{DEFAULTSORT:Monopulse Radar}}
[[Category:Radar]]
[[Category:Antennas]]
[[Category:Signal processing]]
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