# Phased array

This article is about general theory and electromagnetic phased array. For the ultrasonic and medical imaging application, see phased array ultrasonics. For the optical application, see phased-array optics.
Principle of operation of phased array (PA). The PA probe consists of many small elements, each of which can be pulsed separately. In the figure the element on the right is pulsed first, and emits an energy wave that spreads out like a ripple on a pond (largest semicircle). The second to right element is pulsed next, and emits a ripple that is slightly smaller than the first because it was started later. The process continues down the line until all the elements have been pulsed. The multiple waves add up to one single wave front travelling at a set angle. In other words, the beam angle can be set just by programming the pulse timings.
Cobra Dane passive electronically scanned array
BMEWS & PAVE PAWS Radars
Mammut phased array radar World War II

In antenna theory, a phased array is an array 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]

An antenna array is a group of multiple active antennas coupled to a common source or load to produce a directive radiation pattern. Usually, the spatial relationship of the individual antennas also contributes to the directivity of the antenna array. 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. One common application of this is with a standard multiband television antenna, which has multiple elements coupled together.

## History

Phased array transmission was originally developed in 1905 by Nobel laureate Karl Ferdinand Braun who demonstrated enhanced transmission of radio waves in one direction.[2][3] During World War II, Nobel laureate Luis Alvarez used phased array transmission in a rapidly steerable radar system for "ground-controlled approach", a system to aid in the landing of aircraft. At the same time, the GEMA in Germany built the PESA Mammut 1.[4] It was later adapted for radio astronomy leading to Nobel Prizes for Physics for Antony Hewish and Martin Ryle after several large phased arrays were developed at the University of Cambridge. The design is also used in radar, and is generalized in interferometric radio antennas. In 2007, DARPA researchers announced a 16 element phased array integrated with all necessary circuits to send at 30–50 GHz on a single silicon chip for military purposes.[5]

## 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. Simultaneous electrical scanning in both azimuth and elevation was first demonstrated in a phased array antenna at Hughes Aircraft Company, Culver City, California in 1957.[6]

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

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

On VHF, phased arrays are used extensively for FM broadcasting. These greatly increase the antenna gain, magnifying the emitted RF energy toward the horizon, which in turn greatly increases a station's broadcast range. In these situations, the distance to each element from the transmitter is identical, or is one (or other integer) wavelength apart. Phasing the array such that the lower elements are slightly delayed (by making the distance to them longer) causes a downward beam tilt, which is very useful if the antenna is quite high on a radio tower.

Other phasing adjustments can increase the downward radiation in the far field without tilting the main lobe, creating null fill to compensate for extremely high mountaintop locations, or decrease it in the near field, to prevent excessive exposure to those workers or even nearby homeowners on the ground. The latter effect is also achieved by half-wave spacing – inserting additional elements halfway between existing elements with full-wave spacing. This phasing achieves roughly the same horizontal gain as the full-wave spacing; that is, a five-element full-wave-spaced array equals a nine- or ten-element half-wave-spaced array.

### Naval usage

Active Phased Array Radar mounted on top of Sachsen class frigate F220 Hamburg's superstructure of the German Navy.
See also: Active Electronically Scanned Array, Aegis combat system and AN/SPY-1

Phased arrays are used in naval sonar, in active (transmit and receive) and passive (receive only) and hull-mounted and towed array sonar.

### Space probe communication

The MESSENGER spacecraft is a mission to the planet Mercury (arrived 18 March 2011). This spacecraft is the first deep-space mission to use a phased-array antenna for communications. The radiating elements are linearly-polarized, slotted waveguides. The antenna, which uses the X band, uses 26 radiative elements but can gracefully downgrade.[9]

### Weather research usage

AN/SPY-1A radar installation at NSSL, Norman, Oklahoma. The round dome primarily provides weather protection.

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. Current 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, School of Electrical and Computer Engineering, and Atmospheric Radar Research Center, 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.[10]

### Optics

Within the visible or infrared spectrum of electromagnetic waves it is possible to construct optical phased arrays. They are used in wavelength multiplexers and filters for telecommunication purposes,[11] laser beam steering, and holography. Synthetic array heterodyne detection is an efficient method for multiplexing an entire phased array onto a single element photodetector.

### Radio-frequency identification (RFID)

Recently, phased array antennas have been included in RFID systems to significantly boost the reading capability of passive UHF tags passing from 9 m (30 ft) to 180 m (600 ft).[12]

### Human-machine interfaces (HMI)

A phased array of acoustic transducers, denominated airborne ultrasound tactile display (AUTD), was developed at the University of Tokyo's Shinoda Lab to induce tactile feedback.[13] This system was demonstrated to enable a user to interactively manipulate virtual holographic objects.[14]

## Mathematical perspective and formulas

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 formalism 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.

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

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

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

Thus as N gets large, the term will be dominated by the $\begin{matrix}\frac{2\phi}{\pi}\end{matrix}$ term. As sine 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 antennas. 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.

## Different types of phased arrays

Main article: Beamforming

There are two main types of beamformers. These are time domain beamformers and frequency domain beamformers.

A graduated attenuation window is sometimes applied across the face of the array to improve side-lobe suppression performance, in addition to the phase shift.

Time domain beamformer works by introducing time delays. 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. The most common kind of time domain beam former is serpentine waveguide. Active phase array uses individual delay lines that are switched on and off. Yttrium iron garnet phase shifters vary the phase delay using the strength of a magnetic field.

There are two different types of frequency domain beamformers.

The first type separates the different frequency components that are present in the received signal into multiple frequency bins (using either an Discrete Fourier transform (DFT) or a filterbank). When different delay and sum beamformers are applied to each frequency bin, the result is that the main lobe simultaneously points in multiple different directions at each of the different frequencies. This can be an advantage for communication links, and is used with the SPS-48 radar.

The other type of frequency domain beamformer makes use of Spatial Frequency. Discrete samples are taken from each of the individual array elements. The samples are processed using a Discrete Fourier Transform (DFT). The DFT introduces multiple different discrete phase shifts during processing. The outputs of the DFT are individual channels that correspond with evenly spaced beams formed simultaneously. A 1-dimensional DFT produces a fan of different beams. A 2-dimensional DFT produces beams with a pineapple configuration.

These techniques are used to create two kinds of phase array.

• Dynamic - an array of variable phase shifters are used to move the beam
• Fixed - the beam position is stationary with respect to the array face and the whole antenna is moved

There are two further sub-categories that modify the kind of dynamic array or fixed array.

• Active - amplifiers or processors in each phase shifter element
• Passive - large central amplifier with attenuating phase shifters

### Dynamic Phased Array

Each array element incorporates an adjustable phase shifter that are collectively used to move the beam with respect to the array face.

Dynamic phase array require no physical movement to aim the beam. The beam is moved electronically. This can produce antenna motion fast enough to use a small pencil-beam to simultaneously track multiple targets while searching for new targets using just one radar set (track while search).

As an example, an antenna with a 2 degree beam with a pulse rate of 1 kHz will require approximately 8 seconds to cover an entire a hemisphere consisting of 8,000 pointing positions. This configuration provides 12 opportunities to detect a 1,000 metres per second (2,200 mph) vehicle over a range of 100 km (62 mi), which is suitable for military applications.[citation needed]

The position of mechanically steered antennas can be predicted, which can be used to create electronic countermeasures that interfere with radar operation. The flexibility resulting from phase array operation allows beams to be aimed at random locations, which eliminates this vulnerability. This is also desirable for military applications.

### Fixed Phase Array

Fixed phase array antennas are typically used to create an antenna with a more desirable form factor than the conventional parabolic reflector or cassegrain reflector. Fixed phased array radar incorporate fixed phase shifters. This kind of phase array is physically moved during the track and scan process. There are two configurations.

• Multiple frequencies with a delay-line
• Multiple adjacent beams

The SPS-48 radar uses multiple transmit frequencies with a serpentine delay line along the left side of the array to produce vertical fan of stacked beams. Each frequency experiences a different phase shift as it propagates down the serpentine delay line, which forms different beams. A filter bank is used to split apart the individual receive beams. The antenna is mechanically rotated.

Semi-active radar homing uses monopulse radar that relies on a fixed phase array to produce multiple adjacent beams that measure angle errors. This form factor is suitable for gimbal mounting in missile seekers.

### Active Phase Array

Active phased arrays elements incorporate transmit amplification with phase shift in each antenna element (or group of elements). Each element also includes receive pre-amplification. The phase shifter setting is the same for transmit and receive.

Active phase array do not require phase reset after the end of the transmit pulse, which is compatible with Doppler radar and Pulse-Doppler radar.

### Passive Phase Array

Passive phased arrays typically use large amplifiers that produce all of the microwave transmit signal for the antenna. Phase shifters typically consist of waveguide elements that contain phase shifters controlled by magnetic field, voltage gradient, or equivalent technology.[15][16]

The phase shift process used with passive phase array typically puts the receive beam and transmit beam into diagonally opposite quadrants. The sign of the phase shift must be inverted after the transmit pulse is finished and before the receive period begins to place the receive beam into the same location as the transmit beam. That requires a phase impulse that degrades sub-clutter visibility performance on Doppler radar and Pulse-Doppler radar. As an example, Yttrium iron garnet phase shifters must be changed after transmit pulse quench and before receiver processing starts to align transmit and receive beams. That impulse introduces FM noise that degrades clutter performance.

Passive phase array is used with AEGIS.[17]

## References

1. ^  This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188). Definition of Phased Array. Accessed April 27, 2006.
2. ^ http://nobelprize.org/nobel_prizes/physics/laureates/1909/braun-lecture.pdf Braun's Nobel Prize lecture. The phased array section is on pages 239-240.
3. ^ "Die Strassburger Versuche über gerichtete drahtlose Telegraphie" (The Strassburg experiments on directed wireless telegraphy), Elektrotechnische und Polytechnische Rundschau (Electrical technology and polytechnic review [a weekly]), (1 November 1905). This article is summarized (in German) in: Adolf Prasch, ed., Die Fortschritte auf dem Gebiete der Drahtlosen Telegraphie [Progress in the field of wireless telegraphy] (Stuttgart, Germany: Ferdinand Enke, 1906), vol. 4, pages 184-185.
4. ^ http://www.100jahreradar.de/index.html?/gdr_5_deutschefunkmesstechnikim2wk.html Mamut1 first early warning PESA Radar
5. ^ World’s Most Complex Silicon Phased Array Chip Developed at UC San Diego in UCSD News (reviewed 02. November 2007)
6. ^ See Joseph Spradley, “A Volumetric Electrically Scanned Two-Dimensional Microwave Antenna Array,” IRE National Convention Record, Part I - Antennas and Propagation; Microwaves, New York: The Institute of Radio Engineers, 1958, 204-212.
7. ^ "AEGIS Weapon System MK-7". Jane's Information Group. 2001-04-25. Archived from the original on 2006-07-01. Retrieved 2006-08-10..
8. ^ Scott, Richard (April 2006). "Singapore Moves to Realise Its Formidable Ambitions". Jane's Navy International 111 (4): 42–49.
9. ^ Phased-Array Antenna for the MESSENGER Deep Space Mission
10. ^ National Oceanic and Atmospheric Administration. PAR Backgrounder. Accessed April 6, 2006.
11. ^ 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
12. ^
13. ^ SIGGRAPH 2008, Airborne Ultrasound Tactile Display
14. ^ [1] SIGGRAPH 2009, Touchable holography
15. ^
16. ^ "Ferroelectric Phase Shifters". Microwaves 101.
17. ^ "Total Ownership Cost Reduction Case Study: AEGIS Radar Phase Shifters". Naval Postgraduate School.