Phased array

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Image:Phased array radar.jpg In telecommunication, a phased array is a group of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions. This technology was originally developed for radio astronomy, leading to Physics Nobel Prizes for Antony Hewish and Martin Ryle after several large phased arrays were developed at Cambridge University. The design is also used in radar, and is generalized in interferometric radio antennas.

1 Usage
2 Mathematical perspective and formulae
3 See also
4 References
5 External links

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Usage

The relative amplitudes of — and constructive and destructive interference effects among — the signals radiated by the individual antennas determine the effective radiation pattern of the array. A phased array may be used to point a fixed radiation pattern, or to scan rapidly in azimuth or elevation. When phased arrays are used in Sonar it is called beamforming.

The phased array is used for instance in optical communication as a wavelength selective splitter.

Phased arrays are required to be used by many AM broadcast stations to enhance signal coverage in the city of license, while minimizing interference to other areas. Due to the differences between daytime and nightime ionospheric propagation at AM broadcast frequencies, it is common for AM broadcast stations to change between day and night radiation patterns by switching the phase and power levels supplied to the individual antenna elements daily at sunrise and sunset.

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Naval usage

Phased array radar systems are also used by warships of several navies including the Japanese, Spanish and United States' navies in the Aegis combat system. Phased array radars allow a warship to use one radar system for surface detection and tracking (finding ships), air detection and tracking (finding aircraft and missiles) and missile uplink capabilities. Prior to using these systems each surface-to-air missile in flight required a dedicated fire-control radar, which meant that ships could only engage a limited number of simultaneous targets. Phased array systems can be used to control missiles during the mid-course phase of the missile's flight. During the terminal portion of the flight, continuous-wave fire control directors provide the final guidance to the target. Because of the radar beam is electronically steered, phased array systems can direct radar beams fast enough to maintain a fire control quality track on many targets simultaneously while also controlling several in-flight missiles. Modern U.S. guided missile cruisers are capable of controlling more missiles than could previous classes of warships.

See also: Active Phased Array Radar and AN/SPY-1

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Space usage

Recently, the MESSENGER spacecraft was launched. This is a mission to the planet Mercury (arrival 12 March 2011). This spacecraft is the first deep-space mission to use a phased-array antenna for communications. It communicates in the X-Band. The radiating elements are circularly-polarized, slotted waveguides. The antenna can operate with 4 or 8 radiating elements.

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Research usage

The National Severe Storms Laboratory has been using a SPY-1A phased array antenna, provided by the US Navy, for weather research at its Norman, Oklahoma facility since April 23, 2003. It is hoped that research will lead to a better understanding of thunderstorms and tornadoes, eventually leading to increased warning times and enhanced prediction of tornadoes. Project participants include the National Severe Storms Laboratory and National Weather Service Radar Operations Center, Lockheed Martin, United States Navy, University of Oklahoma School of Meteorology and School of Electrical and Computer Engineering, Oklahoma State Regents for Higher Education, the Federal Aviation Administration, and Basic Commerce and Industries. The project includes research and development, future technology transfer and potential deployment of the system throughout the United States. It is expected to take 10 to 15 years to complete and initial construction was approximately $25 million.[1]

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Optics

Within the visible or infrared spectrum of electromagnetic waves it is also possible to build phased arrays. They are used in wavelength multiplexers and filters for telecommunication purposes<ref>P. D. Trinh, S. Yegnanarayanan, F. Coppinger and B. Jalali Silicon-on-Insulator (SOI) Phased-Array Wavelength Multi/Demultiplexer with Extremely Low-Polarization Sensitivity IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 9, NO. 7, JULY 1997</ref>

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Mathematical perspective and formulae

A phased array is an example of N-slit diffraction. Since each individual antenna acts as a slit, emitting radio waves, their diffraction pattern can be calculated by adding the phase shift Φ to the fringing term.

We will begin from the N-slit diffraction pattern derived on the diffraction page.

<math>

\psi ={{\psi }_0}\left[\frac{\sin \left(\fracTemplate:\pi a{\lambda }\theta \right)}{\fracTemplate:\pi a{\lambda }\sin\theta}\right]\left[\frac{\sin \left(\frac{N}{2}{kd}\sin\theta\right)}{\sin \left(\fracTemplate:Kd{2}\sin\theta \right)}\right] </math>

Now, adding a Φ term to the <math>\begin{matrix}kd\sin\theta\,\end{matrix}</math> fringe effect in the second term yields:

<math>\psi ={{\psi }_0}\left[\frac{\sin \left(\fracTemplate:\pi a{\lambda }\sin \theta\right)}{\fracTemplate:\pi a{\lambda }\sin\theta}\right]\left[\frac{\sin

\left(\frac{N}{2}\big(\fracTemplate:2\pi d{\lambda }\sin\theta + \phi \big)\right)}{\sin \left(\fracTemplate:\pi d{\lambda }\sin\theta +\phi \right)}\right] </math>

Taking the square of the wave function gives us the intensity of the wave.

<math>I = I_0{{\left[\frac{\sin \left(\frac{\pi a}{\lambda }\sin\theta\right)}{\fracTemplate:\pi a{\lambda } \sin [\theta

]}\right]}^2}{{\left[\frac{\sin \left(\frac{N}{2}(\frac{2\pi d}{\lambda} \sin\theta+\phi )\right)}{\sin \left(\fracTemplate:\pi d{\lambda } \sin\theta+\phi \right)}\right]}^2} </math>

<math>

I =I_0{{\left[\frac{\sin \left(\fracTemplate:\pi a{\lambda } \sin\theta\right)}{\fracTemplate:\pi a{\lambda } \sin\theta}\right]}^2}{{\left[\frac{\sin \left(\frac{\pi }{\lambda } N d \sin\theta+\frac{N}{2} \phi \right)}{\sin \left(\fracTemplate:\pi d{\lambda } \sin\theta+\phi \right)}\right]}^2} </math>

Now space the emitters a distance <math> d=\begin{matrix}\frac{\lambda}{4}\end{matrix}</math> apart. This distance is chosen for simplicity of calculation but can be adjusted as any scalar fraction of the wavelength.

<math>I =I_0{{\left[\frac{\sin \left(\frac{\pi }{\lambda } a \theta \right)}{\frac{\pi }{\lambda } a

\theta }\right]}^2}{{\left[\frac{\sin \left(\frac{\pi }{4} N \sin\theta+\frac{N}{2} \phi \right)}{\sin \left(\frac{\pi }{4} \sin\theta+ \phi \right)}\right]}^2}</math>

Sin achieves its maximum at <math>\begin{matrix}\frac{\pi}{2}\end{matrix}</math> so we set the numerator of the second term = 1.

<math>

\frac{\pi }{4} N \sin\theta+\frac{N}{2} \phi = \frac{\pi }{2} </math>

<math>

\sin\theta=\Big(\frac{\pi }{2} - \frac{N}{2} \phi \Big)\frac{4}{N \pi } </math>

<math>

\sin\theta=\frac{2}{N}-\frac{2\phi }{\pi } </math>

Thus as N gets large, the term will be dominated by the <math>\begin{matrix}\frac{2\phi}{\pi}\end{matrix}</math> term. As sin can oscillate between −1 and 1, we can see that setting <math>\phi=-\begin{matrix}\frac{\pi}{2}\end{matrix}</math> will send the maximum energy on an angle given by

<math>\theta = \sin^{-1}(1) = \begin{matrix}\frac{\pi}{2}\end{matrix} = 90^{\circ}</math>

Additionally, we can see that if we wish to adjust the angle at which the maximum energy is emitted, we need only to adjust the phase shift φ between successive antennae. Indeed the phase shift corresponds to the negative angle of maximum signal.

A similar calculation will show that the denominator is minimized by the same factor.

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