Phased array

# Phased array

Overview

In wave theory, a phased array is an array of antennas
Antenna array (electromagnetic)
An antenna array is a group of isotropic radiators such that the currents running through them are of different amplitudes and phases. These are radiators of electromagnetic frequency and energy. Antenna arrays are the solution to the problem defined as the limitations of operating a single antenna...

in which the relative phases
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern
In the field of antenna design the term radiation pattern most commonly refers to the directional dependence of the strength of the radio waves from the antenna or other source ....

of the array is reinforced in a desired direction and suppressed in undesired directions.

An antenna array
Antenna array
Antenna array may refer to:*Antenna array a group of isotropic radiators such that the currents running through them are of different amplitudes and phases*Interferometric array of radio telescopes used in radio astronomy...

is a group of multiple active antennas coupled to a common source or load to produce a directive radiation pattern.
Discussion

Encyclopedia

In wave theory, a phased array is an array of antennas
Antenna array (electromagnetic)
An antenna array is a group of isotropic radiators such that the currents running through them are of different amplitudes and phases. These are radiators of electromagnetic frequency and energy. Antenna arrays are the solution to the problem defined as the limitations of operating a single antenna...

in which the relative phases
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern
In the field of antenna design the term radiation pattern most commonly refers to the directional dependence of the strength of the radio waves from the antenna or other source ....

of the array is reinforced in a desired direction and suppressed in undesired directions.

An antenna array
Antenna array
Antenna array may refer to:*Antenna array a group of isotropic radiators such that the currents running through them are of different amplitudes and phases*Interferometric array of radio telescopes used in radio astronomy...

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
Television antenna
A television antenna, or TV aerial, is an antenna specifically designed for the reception of over the air broadcast television signals, which are transmitted at frequencies from about 41 to 250 MHz in the VHF band, and 470 to 960 MHz in the UHF band in different countries...

, which has multiple elements coupled together.

## History

Phased array transmission was originally developed in 1905 by Nobel
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

Laureate Karl Ferdinand Braun
Karl Ferdinand Braun
Karl Ferdinand Braun was a German inventor, physicist and Nobel laureate in physics. Braun contributed significantly to the development of the radio and television technology: he shared with Guglielmo Marconi the 1909 Nobel Prize in Physics.-Biography:Braun was born in Fulda, Germany, and...

who demonstrated enhanced transmission of radio
Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...

waves in one direction. During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

, Nobel
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

Laureate Luis Alvarez
Luis Alvarez
Luis W. Alvarez was an American experimental physicist and inventor, who spent nearly all of his long professional career on the faculty of the University of California, Berkeley...

used phased array transmission in a rapidly-steerable radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

system for "ground-controlled approach
Ground-controlled approach
In aviation a ground-controlled approach , is a type of service provided by air-traffic controllers whereby they guide aircraft to a safe landing in adverse weather conditions based on radar images...

", a system to aid in the landing of aeroplanes in Britain. At the same time GEMA in Germany built the PESA Mammut 1. It was later adapted for radio astronomy
Radio astronomy is a subfield of astronomy that studies celestial objects at radio frequencies. The initial detection of radio waves from an astronomical object was made in the 1930s, when Karl Jansky observed radiation coming from the Milky Way. Subsequent observations have identified a number of...

leading to Nobel Prizes for Physics for Antony Hewish
Antony Hewish
Antony Hewish FRS is a British radio astronomer who won the Nobel Prize for Physics in 1974 for his work on the development of radio aperture synthesis and its role in the discovery of pulsars...

and Martin Ryle
Martin Ryle
Sir Martin Ryle was an English radio astronomer who developed revolutionary radio telescope systems and used them for accurate location and imaging of weak radio sources...

after several large phased arrays were developed at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

. The design is also used in radar, and is generalized in interferometric
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...

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.

## Usage

The relative amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

s of — and constructive and destructive interference effects among — the signals radiated by the individual antennas determine the effective radiation pattern
In the field of antenna design the term radiation pattern most commonly refers to the directional dependence of the strength of the radio waves from the antenna or other source ....

of the array. A phased array may be used to point a fixed radiation pattern, or to scan
Scan
Scan may refer to:Acronyms:*Schedules for Clinical Assessment in Neuropsychiatry , a psychiatric diagnostic tool developed by WHO*Shared Check Authorization Network , a database of bad check writers and collection agency for bad checks...

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, CA, in 1957 (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). When phased arrays are used in sonar, it is called beamforming
Beamforming
Beamforming is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in the array in a way where signals at particular angles experience constructive interference and while others experience destructive...

.

The phased array is used for instance in optical communication
Optical communication
Optical communication is any form of telecommunication that uses light as the transmission medium.An optical communication system consists of a transmitter, which encodes a message into an optical signal, a channel, which carries the signal to its destination, and a receiver, which reproduces the...

as a wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

-selective splitter.

Active Electronically Scanned Array
An Active Electronically Scanned Array , also known as active phased array radar is a type of phased array radar whose transmitter and receiver functions are composed of numerous small solid-state transmit/receive modules . AESAs aim their "beam" by broadcasting radio energy that interfere...

.

Broadcast engineering is the field of electrical engineering, and now to some extent computer engineering and information technology, which deals with radio and television broadcasting...

, phased arrays are required to be used by many AM broadcast
AM broadcasting is the process of radio broadcasting using amplitude modulation. AM was the first method of impressing sound on a radio signal and is still widely used today. Commercial and public AM broadcasting is carried out in the medium wave band world wide, and on long wave and short wave...

radio stations to enhance signal strength
Signal strength
In telecommunications, particularly in radio, signal strength refers to the magnitude of the electric field at a reference point that is a significant distance from the transmitting antenna. It may also be referred to as received signal level or field strength. Typically, it is expressed in...

and therefore coverage in the city of license, while minimizing interference
Interference (communication)
In communications and electronics, especially in telecommunications, interference is anything which alters, modifies, or disrupts a signal as it travels along a channel between a source and a receiver. The term typically refers to the addition of unwanted signals to a useful signal...

to other areas. Due to the differences between daytime and nighttime ionospheric
Ionosphere
The ionosphere is a part of the upper atmosphere, comprising portions of the mesosphere, thermosphere and exosphere, distinguished because it is ionized by solar radiation. It plays an important part in atmospheric electricity and forms the inner edge of the magnetosphere...

propagation
Radio propagation is the behavior of radio waves when they are transmitted, or propagated from one point on the Earth to another, or into various parts of the atmosphere...

at mediumwave
Mediumwave
Medium wave is the part of the medium frequency radio band used mainly for AM radio broadcasting. For Europe the MW band ranges from 526.5 kHz to 1606.5 kHz...

frequencies, it is common for AM broadcast stations to change between day (groundwave) and night (skywave
Skywave
Skywave is the propagation of electromagnetic waves bent back to the Earth's surface by the ionosphere. As a result of skywave propagation, a broadcast signal from a distant AM broadcasting station at night, or from a shortwave radio station can sometimes be heard as clearly as local...

) radiation patterns by switching the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

and power levels supplied to the individual antenna elements (mast radiator
A mast radiator is a radio mast or tower in which the whole structure itself functions as an antenna. This design is commonly used for transmitting antennas operating at low frequencies, in the VLF, LF and MF ranges, in particular those used for AM broadcasting. The metal mast is electrically...

s) daily at sunrise
Sunrise
Sunrise is the instant at which the upper edge of the Sun appears above the horizon in the east. Sunrise should not be confused with dawn, which is the point at which the sky begins to lighten, some time before the sun itself appears, ending twilight...

and sunset
Sunset
Sunset or sundown is the daily disappearance of the Sun below the horizon in the west as a result of Earth's rotation.The time of sunset is defined in astronomy as the moment the trailing edge of the Sun's disk disappears below the horizon in the west...

. More modest phased array longwire antenna systems may be employed by private radio enthusiasts to receive longwave, mediumwave (AM) and shortwave radio broadcasts from great distances.

On VHF, phased arrays are used extensively for FM broadcasting
FM broadcasting is a broadcasting technology pioneered by Edwin Howard Armstrong which uses frequency modulation to provide high-fidelity sound over broadcast radio. The term "FM band" describes the "frequency band in which FM is used for broadcasting"...

. These greatly increase the antenna gain
Antenna gain
In electromagnetics, an antenna's power gain or simply gain is a key performance figure which combines the antenna's directivity and electrical efficiency. As a transmitting antenna, the figure describes how well the antenna converts input power into radio waves headed in a specified direction...

, magnifying the emitted RF energy toward the horizon
Horizon
The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...

, 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
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

) 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
Beam tilt
Beam tilt is used in radio to aim the main lobe of the vertical plane radiation pattern of an antenna below the horizontal plane.The simplest way is mechanical beam tilt, where the antenna is physically mounted in such a manner as to lower the angle of the signal on one side...

, 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
Side lobe
In antenna engineering, side lobes or sidelobes are the lobes of the far field radiation pattern that are not the main lobe....

, creating null fill
Null fill
Null fill is used in radio antenna systems which are located on mountains or tall towers, to prevent too much of the signal from overshooting the nearest part of intended coverage area. Phasing is used between antenna elements to take power away from the main lobe and electrically direct more of...

to compensate for extremely high mountain
Mountain
Image:Himalaya_annotated.jpg|thumb|right|The Himalayan mountain range with Mount Everestrect 58 14 160 49 Chomo Lonzorect 200 28 335 52 Makalurect 378 24 566 45 Mount Everestrect 188 581 920 656 Tibetan Plateaurect 250 406 340 427 Rong River...

top locations, or decrease it in the near field
Near field
Near field may refer to:*Near-field , an algebraic structure*Near and far field, parts of an electromagnetic field*Near field communication, a set of short-range wireless technologies, typically requiring a distance of 4 cm or less...

, 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

Phased array radar systems are also used by warships of many navies. Phased array radars allow a warship to use one radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

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
Surface-to-air missile
A surface-to-air missile or ground-to-air missile is a missile designed to be launched from the ground to destroy aircraft or other missiles...

in flight required a dedicated fire-control radar
A fire-control radar is a radar which is designed specifically to provide information to a fire-control system in order to calculate a firing solution...

, 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
Fire-control system
A fire-control system is a number of components working together, usually a gun data computer, a director, and radar, which is designed to assist a weapon system in hitting its target. It performs the same task as a human gunner firing a weapon, but attempts to do so faster and more...

track on many targets simultaneously while also controlling several in-flight missiles. The AN/SPY-1
AN/SPY-1
The AN/SPY-1 is a US naval radar system manufactured by Lockheed Martin. The array is a passive electronically scanned system and is a key component of the Aegis Combat System. The system is computer controlled, using four complementary antennas to provide 360 degree coverage...

phased array radar, part of the Aegis combat system
Aegis combat system
The Aegis Combat System is an integrated naval weapons system developed by the Missile and Surface Radar Division of RCA, and now produced by Lockheed Martin...

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." Likewise, the Thales Herakles
Thales Group
The Thales Group is a French electronics company delivering information systems and services for the aerospace, defense, transportation and security markets...

phased array multi-function radar onboard the Formidable class frigate
Formidable class frigate
The Formidable class multi-role stealth frigates are the latest surface platforms to enter into service with the Republic of Singapore Navy, and are multi-mission derivatives of the French Navy’s La Fayette class frigate. The frigates are key information nodes and fighting units, and are described...

s of the Republic of Singapore Navy
Republic of Singapore Navy
The Republic of Singapore Navy is the naval component of the Singapore Armed Forces , responsible for the defence of Singapore against sea-borne threats and protection of its sea lines of communications. Operating within the crowded littoral waters of the Singapore Strait, the RSN is regarded as...

has a track capacity of 200 targets and is able to achieve automatic target detection, confirmation and track initiation in a single scan, while simultaneously providing mid-course guidance updates to the MBDA Aster
MBDA Aster
Aster is a family of surface-to-air missiles manufactured by Eurosam, a European consortium consisting of MBDA France, MBDA Italy and the Thales Group .-Overview:The Aster family was developed to perform three distinct missions:...

missiles launched from the ship.
The German Navy
German Navy
The German Navy is the navy of Germany and is part of the unified Bundeswehr .The German Navy traces its roots back to the Imperial Fleet of the revolutionary era of 1848 – 52 and more directly to the Prussian Navy, which later evolved into the Northern German Federal Navy...

and the Dutch Navy have developed the Active Phased Array Radar
APAR is a shipborne multifunction radar developed and manufactured by Thales Nederland. It is the first Active Electronically Scanned Array MFR employed on an operational warship.-Characteristics:...

System (APAR).
Phased arrays are also used in naval sonar, both in active (transmit and receive) and passive (receive only).
Active Electronically Scanned Array
An Active Electronically Scanned Array , also known as active phased array radar is a type of phased array radar whose transmitter and receiver functions are composed of numerous small solid-state transmit/receive modules . AESAs aim their "beam" by broadcasting radio energy that interfere...

, Aegis combat system
Aegis combat system
The Aegis Combat System is an integrated naval weapons system developed by the Missile and Surface Radar Division of RCA, and now produced by Lockheed Martin...

and AN/SPY-1
AN/SPY-1
The AN/SPY-1 is a US naval radar system manufactured by Lockheed Martin. The array is a passive electronically scanned system and is a key component of the Aegis Combat System. The system is computer controlled, using four complementary antennas to provide 360 degree coverage...

### Space probe communication

The MESSENGER
MESSENGER
The MErcury Surface, Space ENvironment, GEochemistry and Ranging space probe is a robotic NASA spacecraft in orbit around the planet Mercury. The spacecraft was launched aboard a Delta II rocket in August 2004 to study the chemical composition, geology, and magnetic field of Mercury...

spacecraft is a mission to the planet Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

(arrival 18 March 2011). This spacecraft is the first deep-space mission to use a phased-array antenna for communication
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...

s. The radiating elements are linearly-polarized
Linear polarization
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation...

, slotted waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...

s. The antenna, which uses the X band
X band
The X band is a segment of the microwave radio region of the electromagnetic spectrum. In some cases, such as in communication engineering, the frequency range of X band is rather indefinitely set at approximately 7.0 to 11.2 gigahertz . In radar engineering, the frequency range is specified...

### Weather research usage

The National Severe Storms Laboratory
National Severe Storms Laboratory
The National Severe Storms Laboratory is a National Oceanic and Atmospheric Administration weather research laboratory located at the National Weather Center in Norman, Oklahoma....

has been using a SPY-1A phased array antenna, provided by the US Navy, for weather research at its Norman, Oklahoma
Norman, Oklahoma
Norman is a city in Cleveland County, Oklahoma, United States, and is located south of downtown Oklahoma City. It is part of the Oklahoma City metropolitan area. As of the 2010 census, Norman was to have 110,925 full-time residents, making it the third-largest city in Oklahoma and the...

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
Lockheed Martin
Lockheed Martin is an American global aerospace, defense, security, and advanced technology company with worldwide interests. It was formed by the merger of Lockheed Corporation with Martin Marietta in March 1995. It is headquartered in Bethesda, Maryland, in the Washington Metropolitan Area....

, United States Navy
United States Navy
The United States Navy is the naval warfare service branch of the United States Armed Forces and one of the seven uniformed services of the United States. The U.S. Navy is the largest in the world; its battle fleet tonnage is greater than that of the next 13 largest navies combined. The U.S...

, University of Oklahoma
University of Oklahoma
The University of Oklahoma is a coeducational public research university located in Norman, Oklahoma. Founded in 1890, it existed in Oklahoma Territory near Indian Territory for 17 years before the two became the state of Oklahoma. the university had 29,931 students enrolled, most located at its...

School of Meteorology, School of Electrical and Computer Engineering, and Atmospheric Radar Research Center
The Atmospheric Radar Research Center is an interdisciplinary research center of the University of Oklahoma located at the National Weather Center in Norman, Oklahoma...

, Oklahoma State Regents for Higher Education, the Federal Aviation Administration
The Federal Aviation Administration is the national aviation authority of the United States. An agency of the United States Department of Transportation, it has authority to regulate and oversee all aspects of civil aviation in the U.S...

, and Basic Commerce and Industries. The project includes research and development
Research and development
The phrase research and development , according to the Organization for Economic Co-operation and Development, refers to "creative work undertaken on a systematic basis in order to increase the stock of knowledge, including knowledge of man, culture and society, and the use of this stock of...

, future technology transfer
Technology transfer
Technology Transfer, also called Transfer of Technology and Technology Commercialisation, is the process of skill transferring, knowledge, technologies, methods of manufacturing, samples of manufacturing and facilities among governments or universities and other institutions to ensure that...

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.

### Optics

Within the visible or infrared spectrum of electromagnetic waves it is also possible to construct optical phased arrays
Phased array optics
Phased array optics is the technology of controlling the phase of light waves transmitting or reflecting from a two-dimensional surface by means of adjustable surface elements. It is the optical analog of phased array radar...

. They are used in wavelength multiplexers and filters for telecommunication purposes, laser beam steering, and holography. Synthetic array heterodyne detection is an efficient method for multiplexing an entire phased array onto a single element photodetector.

Recently, phased array antennas have been included in RFID systems in order to significantly boost the reading capability of passive UHF tags passing from 30 feet to 600 feet.

### 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. This system was also demonstrated to enable a user to interactively manipulate virtual holographic objects.

## Mathematical perspective and formulas

A phased array is an example of N-slit diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

. It may also be viewed as the coherent addition of N line source
Line source
A line source is a source of air, noise, water contamination or electromagnetic radiation that emanates from a linear geometry...

s. 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
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

page.

Now, adding a φ term to the fringe effect in the second term yields:

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

Now space the emitters a distance apart. This distance is chosen for simplicity of calculation but can be adjusted as any scalar fraction of the wavelength.

As sine achieves its maximum at , we set the numerator of the second term = 1.

Thus as N gets large, the term will be dominated by the term. As sine can oscillate between −1 and 1, we can see that setting will send the maximum energy on an angle given by
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

There are two main different types of phased arrays, also called beamformers. There are time domain
Time domain
Time domain is a term used to describe the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various...

beamformers and frequency domain
Frequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....

beamformers.

A time domain beamformer works, as 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.

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 different frequency bins (using either an FFT or a filterbank). When different delay and sum beamformers are applied to each frequency bin, it is possible to point the main lobe to different directions for different frequencies. This can be an advantage for communication links.

The other type of frequency domain beamformers makes use of so called Spatial Frequency. This means that an FFT is taken across the different array elements, not in time. The output of the N point FFT are N channels, which are evenly divided in space. This approach makes a simple implementation of several beamformers at the same time possible, but this approach is not flexible, because the different directions are fixed.

Rajendra is a passive Phased Array Radar developed by the Indian DRDO. It is a multifunction radar, capable of surveillance, tracking and engaging low radar cross section targets...

, India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

• Active Electronically Scanned Array
Active Electronically Scanned Array
An Active Electronically Scanned Array , also known as active phased array radar is a type of phased array radar whose transmitter and receiver functions are composed of numerous small solid-state transmit/receive modules . AESAs aim their "beam" by broadcasting radio energy that interfere...

APAR is a shipborne multifunction radar developed and manufactured by Thales Nederland. It is the first Active Electronically Scanned Array MFR employed on an operational warship.-Characteristics:...

• Antenna array (electromagnetic)
Antenna array (electromagnetic)
An antenna array is a group of isotropic radiators such that the currents running through them are of different amplitudes and phases. These are radiators of electromagnetic frequency and energy. Antenna arrays are the solution to the problem defined as the limitations of operating a single antenna...

• Aperture synthesis
Aperture synthesis
Aperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...

• Beamforming
Beamforming
Beamforming is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in the array in a way where signals at particular angles experience constructive interference and while others experience destructive...

Interferometric synthetic aperture radar, also abbreviated InSAR or IfSAR, is a radar technique used in geodesy and remote sensing. This geodetic method uses two or more synthetic aperture radar images to generate maps of surface deformation or digital elevation, using differences in the phase of...

Inverse synthetic aperture radar is a technique to generate a two-dimensional high resolution image of a target.ISAR technology utilizes the movement of the target rather than the emitter to create the synthetic aperture...

(ISAR)
• Optical heterodyne detection
Optical heterodyne detection
Optical heterodyne detection is an important special case of heterodyne detection. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference "local oscillator" that is set at a close-by frequency...

• Phased array optics
Phased array optics
Phased array optics is the technology of controlling the phase of light waves transmitting or reflecting from a two-dimensional surface by means of adjustable surface elements. It is the optical analog of phased array radar...

• Phased array ultrasonics
Phased array ultrasonics
Phased Array ultrasonics is an advanced method of ultrasonic testing that has applications in medical imaging and industrial nondestructive testing. In medicine a common application of phased array is the imaging of the heart...

Radar MASINT is one of the subdisciplines of Measurement and Signature Intelligence and refers to intelligence gathering activities that bring together disparate elements that do not fit within the definitions of Signals Intelligence , Imagery Intelligence , or Human Intelligence...

• Side-scan sonar
Side-scan sonar
Side-scan sonar is a category of sonar system that is used to efficiently create an image of large areas of the sea floor...

• Smart antenna
Smart antenna
Smart antennas are antenna arrays with smart signal processing algorithms used to identify spatial signal signature such as the direction of arrival of the signal, and use it to calculate beamforming vectors, to track and locate the antenna beam on the mobile/target...

Synthetic-aperture radar is a form of radar whose defining characteristic is its use of relative motion between an antenna and its target region to provide distinctive long-term coherent-signal variations that are exploited to obtain finer spatial resolution than is possible with conventional...

• Synthetic aperture sonar
Synthetic aperture sonar
Synthetic aperture sonar is a form of sonar in which sophisticated post-processing of sonar data are used in ways closely analogous to synthetic aperture radar. Synthetic aperture sonars combine a number of acoustic pings to form an image with much higher resolution than conventional sonars,...

Synthetic Thinned Aperture Radiometry is a method of radar in which the coherent product of the signal from pairs of antennas is measured at different antenna-pair spacings . These products yield sample points in the Fourier transform of the brightness temperature map of the scene, and the scene...

• Thinned array curse
Thinned array curse
The thinned array curse is a theorem in electromagnetic theory of transmitters. It states that a transmitting aperture which is synthesized by a coherent phased array of smaller apertures that are spaced apart will have a smaller minimum beam spot size The thinned array curse (sometimes, sparse...

• Tikhomirov Scientific Research Institute of Instrument Design
Tikhomirov Scientific Research Institute of Instrument Design
JSC V.V. Tikhomirov Scientific Research Institute of Instrument Design is a joint stock company, one of the major Russian enterprises in the development of weaponry control systems for fighter planes and mobile medium range anti-aircraft SAM defense vehicles.The institute was created on March 1,...

(NIIP) and Phazotron
Phazotron
JSC Phazotron , is Russia's largest developer of military radars and avionics. Named after one of the major projects and the most important one it was involved in, the first cosmotron in the former-USSR, it was first formed in 1917 to produce aviation instruments...

(NIIR), Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

n developers of phased arrays
• Wave field synthesis
Wave field synthesis
Wave field synthesis is a spatial audio rendering technique, characterized by creation of virtual acoustic environments. It produces "artificial" wave fronts synthesized by a large number of individually driven speakers. Such wave fronts seem to originate from a virtual starting point, the virtual...