Phased array

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This article is about general theory and electromagnetic phased array.
For the ultrasonic and medical imaging application, see phased array ultrasonics.

A giant phased-array radar in Alaska

In wave theory, 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.^[1] This technology was originally developed by future Nobel Laureate Luis Alvarez during World War II as a rapidly-steerable radar system for "ground-controlled approach", a system to aid in the landing of airplanes in England. (GEMA in Germany built at the same time the PESA Mamut1. ^[2]) It was later adapted 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.

An antenna array is a plurality of active antennas coupled to a common source or load to produce a directive radiation pattern. Usually the spatial relationship also contributes to the directivity of the antenna. Use of the term "active antennas" is intended to describe elements whose energy output is modified due to the presence of a source of energy in the element (other than the mere signal energy which passes through the circuit) or an element in which the energy output from a source of energy is controlled by the signal input.

1 Usage
2 Mathematical perspective and formulae
3 Different types of phased arrays
4 See also
5 References
6 External links

[edit] 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 nighttime 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.

For information about active as well as passive phased array radars, see also active electronically scanned array.

[edit] Naval usage

Port and starboard octagonal panels are the phased array radar, AN/SPY-1D, on the USS Mason (DDG-87).

Phased array radar systems are also used by warships of several navies including the Chinese, Japanese, Norwegian, 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 small 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 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. The AN/SPY-1 phased array radar, part of the Aegis combat system deployed on modern U.S. cruisers and destroyers, "is able to perform search, track and missile guidance functions simultaneously with a capability of over 100 targets."^[3]

See also: Active Phased Array Radar, Aegis combat system and AN/SPY-1

[edit] Space usage

The MESSENGER spacecraft is a mission to the planet Mercury (arrival 18 March 2011). This spacecraft is the first deep-space mission to use a phased-array antenna for communications. It communicates in the I band. The radiating elements are circularly-polarized, slotted waveguides. The antenna can operate with 4 or 8 radiating elements.

[edit] Research usage

AN/SPY-1A radar installation at NSSL, Norman, OK.

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.^[4]

Harris Corporation is a contributor to the technology.

[edit] Optics

Within the visible or infrared spectrum of electromagnetic waves it is also possible to construct optical phased arrays. They are used in wavelength multiplexers and filters for telecommunication purposes^[5], laser beam steering, and holography.

[edit] Mathematical perspective and formulae

A phased array is an example of N-slit diffraction. It may also be viewed as the coherent addition of N line sources. 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.

$\psi ={{\psi }_0}\left[\frac{\sin \left(\frac{{\pi a}}{\lambda }\sin\theta \right)}{\frac{{\pi a}}{\lambda }\sin\theta}\right]\left[\frac{\sin \left(\frac{N}{2}{kd}\sin\theta\right)}{\sin \left(\frac{{kd}}{2}\sin\theta \right)}\right]$

Now, adding a φ term to the $\begin{matrix}kd\sin\theta\,\end{matrix}$ fringe effect in the second term yields:

$\psi ={{\psi }_0}\left[\frac{\sin \left(\frac{{\pi a}}{\lambda }\sin \theta\right)}{\frac{{\pi a}}{\lambda }\sin\theta}\right]\left[\frac{\sin \left(\frac{N}{2}\big(\frac{{2\pi d}}{\lambda }\sin\theta + \phi \big)\right)}{\sin \left(\frac{{\pi d}}{\lambda }\sin\theta +\phi \right)}\right]$

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

$I = I_0{{\left[\frac{\sin \left(\frac{\pi a}{\lambda }\sin\theta\right)}{\frac{{\pi a}}{\lambda } \sin [\theta ]}\right]}^2}{{\left[\frac{\sin \left(\frac{N}{2}(\frac{2\pi d}{\lambda} \sin\theta+\phi )\right)}{\sin \left(\frac{{\pi d}}{\lambda } \sin\theta+\phi \right)}\right]}^2}$

$I =I_0{{\left[\frac{\sin \left(\frac{{\pi a}}{\lambda } \sin\theta\right)}{\frac{{\pi a}}{\lambda } \sin\theta}\right]}^2}{{\left[\frac{\sin \left(\frac{\pi }{\lambda } N d \sin\theta+\frac{N}{2} \phi \right)}{\sin \left(\frac{{\pi d}}{\lambda } \sin\theta+\phi \right)}\right]}^2}$

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

$I =I_0{{\left[\frac{\sin \left(\frac{\pi }{\lambda } a \theta \right)}{\frac{\pi }{\lambda } a \theta }\right]}^2}{{\left[\frac{\sin \left(\frac{\pi }{4} N \sin\theta+\frac{N}{2} \phi \right)}{\sin \left(\frac{\pi }{4} \sin\theta+ \phi \right)}\right]}^2}$

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

$\frac{\pi }{4} N \sin\theta+\frac{N}{2} \phi = \frac{\pi }{2}$

$\sin\theta=\Big(\frac{\pi }{2} - \frac{N}{2} \phi \Big)\frac{4}{N \pi }$

$\sin\theta=\frac{2}{N}-\frac{2\phi }{\pi }$

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

$\theta = \sin^{-1}(1) = \begin{matrix}\frac{\pi}{2}\end{matrix} = 90^{\circ}$

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.

[edit] Different types of phased arrays

There are two main different types of phased arrays, also called beamformers. There are time domain beamformers and frequency domain beamformers.

A time domain beamformer works, like the name says, by doing time-based operations. The basic operation is called "delay and sum". It delays the incoming signal from each array element by a certain amount of time, and then adds them together. Sometimes a multiplication with a window across the array is done to increase the mainlobe/sidelobe ratio, and to insert zeroes in the characteristic.

A frequency domain beamformer, also called broadband beamformer, calculates the spectrum of the incomming signals with a Fourier transform. Then for each frequency bin a delay and sum is performed. But doing a delay in the time domain is equal to performing a multiplication with a complex factor in frequency domain. In the case of a 128 points FFT, we will have 128 frequency bins, wich gives us 128 beamformers for 128 different frequencies. So we could point the characteristic for ie 1 kHz to the left, and the characteristic for 2 kHz to the right. This is a substantial advantage.