
In
antenna theory, a phased array usually means an electronically scanned array, a computer-controlled
array of antennas which creates a
beam of radio waves that can be electronically steered to point in different directions without moving the antennas.
In a phased array, the power from the transmitter is fed to the radiating elements through devices called ''
phase shifter
A phase shift module is a microwave network module which provides a controllable phase shift of the RF signal. Phase shifters are used in phased arrays.
Classification
Active versus passive
Active phase shifters provide gain, while passive ...
s'', controlled by a computer system, which can alter the phase or signal delay electronically, thus steering the beam of radio waves to a different direction. Since the size of an antenna array must extend many wavelengths to achieve the high gain needed for narrow beamwidth, phased arrays are mainly practical at the high
frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
end of the radio spectrum, in the
UHF
Ultra high frequency (UHF) is the ITU designation for radio frequencies in the range between 300 megahertz (MHz) and 3 gigahertz (GHz), also known as the decimetre band as the wavelengths range from one meter to one tenth of a meter ...
and
microwave
Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
bands, in which the operating wavelengths are conveniently small.
Phased arrays were originally invented for use in military
radar
Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
systems, to detect fast moving planes and missiles, but are now widely used and have spread to civilian applications such as
5G MIMO
In radio, multiple-input and multiple-output (MIMO) () is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. MIMO has become an essential element of wirel ...
for cell phones. The phased array principle is also used in
acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
is such applications as
phased array ultrasonics
A phaser is an electronic sound processor used to filter a signal by creating a series of peaks and troughs in the frequency spectrum. The position of the peaks and troughs of the waveform being affected is typically modulated by an intern ...
, and in optics.
The term "phased array" is also used to a lesser extent for unsteered
array antenna
An antenna array (or array antenna) is a set of multiple connected antenna (radio), antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas (called ''elements'') are usually connected to a s ...
s in which the radiation pattern of the antenna array is fixed,
For example, AM broadcast radio antennas consisting of multiple
mast radiator
A mast radiator (or radiating tower) is a radio mast or tower in which the metal structure itself is energized and functions as an antenna. This design, first used widely in the 1930s, is commonly used for transmitting antennas operating at l ...
s are also called "phased arrays".
Description

A phased array is an electronically scanned array, a computer-controlled
array of antennas which creates a
beam of radio waves that can be electronically steered to point in different directions without moving the antennas.
The general theory of an electromagnetic phased array also finds applications in ultrasonic and medical imaging application (''
phased array ultrasonics
A phaser is an electronic sound processor used to filter a signal by creating a series of peaks and troughs in the frequency spectrum. The position of the peaks and troughs of the waveform being affected is typically modulated by an intern ...
'') and in optics (''
optical phased array
Phased-array optics is the technology of controlling the phase and amplitude of light waves transmitting, reflecting, or captured (received) by a two-dimensional surface using adjustable surface elements. An optical phased array (OPA) is the optica ...
'').
In a simple
array antenna
An antenna array (or array antenna) is a set of multiple connected antenna (radio), antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas (called ''elements'') are usually connected to a s ...
, the
radio frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the u ...
current from the
transmitter
In electronics and telecommunications, a radio transmitter or just transmitter (often abbreviated as XMTR or TX in technical documents) is an electronic device which produces radio waves with an antenna (radio), antenna with the purpose of sig ...
is fed to multiple individual antenna elements with the proper
phase
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
*Phase space, a mathematica ...
relationship so that the radio waves from the separate elements combine (
superpose) to form beams, to increase power radiated in desired directions and suppress radiation in undesired directions.
In a phased array, the power from the transmitter is fed to the radiating elements through devices called ''
phase shifter
A phase shift module is a microwave network module which provides a controllable phase shift of the RF signal. Phase shifters are used in phased arrays.
Classification
Active versus passive
Active phase shifters provide gain, while passive ...
s'', controlled by a computer system. The computer can alter the phase or signal delay of each antenna element electronically, this results in steering the beam of radio waves to a different direction.
Phased arrays were originally conceived for use in military
radar
Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
systems, to steer a beam of radio waves quickly across the sky to detect planes and missiles. These systems are now widely used and have spread to civilian applications such as
5G MIMO
In radio, multiple-input and multiple-output (MIMO) () is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. MIMO has become an essential element of wirel ...
for cell phones. The phased array principle is also used in
acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
, and phased arrays of
acoustic transducers are used in medical
ultrasound imaging
Medical ultrasound includes diagnostic techniques (mainly imaging) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscles, join ...
scanners (
phased array ultrasonics
A phaser is an electronic sound processor used to filter a signal by creating a series of peaks and troughs in the frequency spectrum. The position of the peaks and troughs of the waveform being affected is typically modulated by an intern ...
),
oil and gas prospecting (
reflection seismology
Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflection (physics), reflected seismic waves. The method requir ...
), and military
sonar
Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances ( ranging), communicate with or detect objects o ...
systems.
The term "phased array" is also used to a lesser extent for non steerable
array antenna
An antenna array (or array antenna) is a set of multiple connected antenna (radio), antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas (called ''elements'') are usually connected to a s ...
s in which the phase of the feed power and thus the radiation pattern of the antenna array is fixed.
For example, AM broadcast radio antennas consisting of multiple
mast radiator
A mast radiator (or radiating tower) is a radio mast or tower in which the metal structure itself is energized and functions as an antenna. This design, first used widely in the 1930s, is commonly used for transmitting antennas operating at l ...
s fed so as to create a specific radiation pattern are also called "phased arrays".
Types
Phased arrays take multiple forms. However, the four most common are the passive electronically scanned array (PESA), active electronically scanned array (AESA), hybrid beam forming phased array, and digital beam forming (DBF) array.
A ''passive phased array'' or ''
passive electronically scanned array
A passive electronically scanned array (PESA), also known as passive phased array, is an antenna in which the beam of radio waves can be electronically steered to point in different directions (that is, a phased array antenna), in which all the ...
'' (PESA) is a phased array in which the antenna elements are connected to a single
transmitter
In electronics and telecommunications, a radio transmitter or just transmitter (often abbreviated as XMTR or TX in technical documents) is an electronic device which produces radio waves with an antenna (radio), antenna with the purpose of sig ...
and/or
receiver, as shown in the first animation at top. PESAs are the most common type of phased array. Generally speaking, a PESA uses one receiver/exciter for the entire array.
An ''active phased array'' or ''
active electronically scanned array
An active electronically scanned array (AESA) is a type of phased array antenna, which is a computer-controlled antenna array in which the beam of radio waves can be electronically steered to point in different directions without moving the a ...
'' (AESA) is a phased array in which each antenna element has an analog transmitter/receiver (T/R) module which creates the phase shifting required to electronically steer the antenna beam. Active arrays are a more advanced, second-generation phased-array technology that are used in military applications; unlike PESAs they can radiate several beams of radio waves at multiple frequencies in different directions simultaneously. However, the number of simultaneous beams is limited by practical reasons of electronic packaging of the beam formers to approximately three simultaneous beams for an AESA. Each beam former has a receiver/exciter connected to it.
A ''digital beam forming (DBF) phased array'' has a digital receiver/exciter at each element in the array. The signal at each element is digitized by the receiver/exciter. This means that antenna beams can be formed digitally in a field programmable gate array (FPGA) or the array computer. This approach allows for multiple simultaneous antenna beams to be formed.
A ''hybrid beam forming phased array'' can be thought of as a combination of an AESA and a digital beam forming phased array. It uses subarrays that are active phased arrays (for instance, a subarray may be 64, 128 or 256 elements and the number of elements depends upon system requirements). The subarrays are combined to form the full array. Each subarray has its own digital receiver/exciter. This approach allows clusters of simultaneous beams to be created.
A ''
conformal antenna In radio communication and avionics a conformal antenna or conformal array is a flat array antenna which is designed to conform or follow some prescribed shape, for example a flat curving antenna which is mounted on or embedded in a curved surface ...
''
is a phased array in which the individual antennas, instead of being arranged in a flat plane, are mounted on a curved surface. The phase shifters compensate for the different path lengths of the waves due to the antenna elements' varying position on the surface, allowing the array to radiate a plane wave. Conformal antennas are used in aircraft and missiles, to integrate the antenna into the curving surface of the aircraft to reduce aerodynamic drag.
Time and frequency domains
There are two main types of beamformers. These are
time domain
In mathematics and signal processing, the time domain is a representation of how a signal, function, or data set varies with time. It is used for the analysis of mathematical functions, physical signals or time series of economic or environmental ...
beamformers and
frequency domain
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time ser ...
beamformers. From a theoretical point of view, both are in principle the same operation, with just a
Fourier transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
allowing conversion from one to the other type.
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. A
Butler matrix allows several beams to be formed simultaneously, or one beam to be scanned through an arc. The most common kind of time domain beam former is serpentine waveguide. Active phased array designs use individual delay lines that are switched on and off.
Yttrium iron garnet
Yttrium iron garnet (YIG) is a kind of synthetic garnet, with chemical composition , or Y3Fe5O12. It is a ferrimagnetic material with a Curie temperature of 560 K. YIG may also be known as yttrium ferrite garnet, or as iron yttrium oxide or ...
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 a
Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced Sampling (signal processing), samples of a function (mathematics), function into a same-length sequence of equally-spaced samples of the discre ...
(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 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
The pineapple (''Ananas comosus'') is a Tropical vegetation, tropical plant with an edible fruit; it is the most economically significant plant in the family Bromeliaceae.
The pineapple is indigenous to South America, where it has been culti ...
configuration.
These techniques are used to create two kinds of phased 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 are in each phase shifter element
:* Passive large central amplifier with attenuating phase shifters
Dynamic phased array
Each array element incorporates an adjustable phase shifter. These are collectively used to move the beam with respect to the array face.
Dynamic phased arrays 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, a capability known as ''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 hemisphere consisting of 8,000 pointing positions. This configuration provides 12 opportunities to detect a vehicle over a range of , which is suitable for military applications.
The position of mechanically steered antennas can be predicted, which can be used to create
electronic countermeasures
An electronic countermeasure (ECM) is an electrical or electronic device designed to countermeasure, trick or deceive radar, sonar, or other detection systems, like infrared (IR) or lasers. It may be used both offensively and defensively to deny ...
that interfere with radar operation. The flexibility resulting from phased array operation allows beams to be aimed at random locations, which eliminates this vulnerability. This is also desirable for military applications.
Fixed phased array

Fixed phased array antennas are typically used to create an antenna with a more desirable form factor than the conventional
parabolic reflector
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a Mirror, reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface ge ...
or
cassegrain reflector
The Cassegrain reflector is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and Antenna (radio), radio antennas, the main characteristic being that the optical path folds back onto itself, ...
. Fixed phased arrays incorporate fixed phase shifters. For example, most commercial FM Radio and TV antenna towers use a
collinear antenna array
In telecommunications, a collinear antenna array (sometimes spelled colinear antenna array) is an array of dipole or quarter-wave antennas mounted in such a manner that the corresponding elements of each antenna are parallel and collinear; th ...
, which is a fixed phased array of dipole elements.
In radar applications, this kind of phased 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
Semi-active radar homing (SARH) is a common type of missile guidance system, perhaps the most common type for longer-range air-to-air and surface-to-air missile systems. The name refers to the fact that the missile itself is only a passive dete ...
uses
monopulse radar
Monopulse radar is a radar system that uses additional encoding of the radio signal to provide accurate directional information. The name refers to its ability to extract range and direction from a single signal pulse.
Monopulse radar avoids prob ...
that relies on a fixed phased array to produce multiple adjacent beams that measure angle errors. This form factor is suitable for
gimbal
A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of ...
mounting in missile seekers.
Active phased array
Active electronically-scanned arrays (AESA) elements incorporate transmit amplification with
phase shift
In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a s ...
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 phased arrays do not require phase reset after the end of the transmit pulse, which is compatible with
Doppler radar
A Doppler radar is a specialized radar that uses the Doppler effect to produce velocity data about objects at a distance. It does this by bouncing a microwave signal off a desired target and analyzing how the object's motion has altered the fre ...
and
pulse-Doppler radar
A pulse-Doppler radar is a radar system that determines the range to a target using pulse-timing techniques, and uses the Doppler effect of the returned signal to determine the target object's velocity. It combines the features of pulse radars and ...
.
Passive phased 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 controlled by magnetic field, voltage gradient, or equivalent technology.
The phase shift process used with passive phased arrays 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
Yttrium iron garnet (YIG) is a kind of synthetic garnet, with chemical composition , or Y3Fe5O12. It is a ferrimagnetic material with a Curie temperature of 560 K. YIG may also be known as yttrium ferrite garnet, or as iron yttrium oxide or ...
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 phased array design is used in the AEGIS Combat System for
direction-of-arrival estimation.
History
Phased array transmission was originally shown in 1905 by
Nobel laureate
Karl Ferdinand Braun
Karl Ferdinand Braun (; ; 6 June 1850 – 20 April 1918) was a German physicist, electrical engineer, and inventor. Braun contributed significantly to the development of radio with his 2 circuit system, which made long range radio transmiss ...
who demonstrated enhanced transmission of
radio
Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...
waves in one direction. During
World War II
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, Nobel laureate
Luis Alvarez used phased array transmission in a rapidly
steerable radar
Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
system for "
ground-controlled approach", a system to aid in the landing of aircraft. At the same time, the GEMA in Germany built the
Mammut
A mastodon, from Ancient Greek μαστός (''mastós''), meaning "breast", and ὀδούς (''odoús'') "tooth", is a member of the genus ''Mammut'' (German for 'mammoth'), which was endemic to North America and lived from the late Miocene to ...
1. It was later adapted for
radio astronomy
Radio astronomy is a subfield of astronomy that studies Astronomical object, celestial objects using radio waves. It started in 1933, when Karl Jansky at Bell Telephone Laboratories reported radiation coming from the Milky Way. Subsequent observat ...
leading to
Nobel Prizes for Physics for
Antony Hewish
Antony Hewish (11 May 1924 – 13 September 2021) was a British radio astronomer who won the Nobel Prize for Physics in 1974 (together with fellow radio-astronomer Martin Ryle) for his role in the discovery of pulsars. He was also awarded the ...
and
Martin Ryle after several large phased arrays were developed at the
University of Cambridge
The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
Interplanetary Scintillation Array. This design is also used for
radar
Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
, and is generalized in
interferometric
Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
radio antennas.
In 1966, most phased-array radars use ferrite phase shifters or traveling-wave tubes to dynamically adjust the phase.
The AN/SPS-33 -- installed on the nuclear-powered ships Long Beach and Enterprise around 1961 -- was claimed to be the only operational 3-D phased array in the world in 1966.
The AN/SPG-59 was designed to generate multiple tracking beams from the transmitting array and simultaneously program independent receiving arrays.
The first civilian 3D phased array was built in 1960 at the National Aviation Facilities Experimental Center; but was abandoned in 1961.
In 2004,
Caltech
The California Institute of Technology (branded as Caltech) is a private university, private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small g ...
researchers demonstrated the first integrated silicon-based phased array receiver at 24 GHz with 8 elements. This was followed by their demonstration of a CMOS 24 GHz phased array transmitter in 2005 and a fully integrated 77 GHz phased array transceiver with integrated antennas in 2006 by the Caltech team. In 2007,
DARPA
The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Adva ...
researchers announced a 16-element phased-array radar antenna which was also integrated with all the necessary circuits on a single silicon chip and operated at 30–50 GHz.
The relative
amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
s of—and constructive and destructive
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extra ...
effects among—the signals radiated by the individual antennas determine the effective
radiation pattern
In the field of antenna design the term radiation pattern (or antenna pattern or far-field pattern) refers to the ''directional'' (angular) dependence of the strength of the radio waves from the antenna or other source.Constantine A. Balanis: " ...
of the array. A phased array may be used to point a fixed radiation pattern, or to
scan rapidly in
azimuth
An azimuth (; from ) is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system.
Mathematically, the relative position vector from an observer ( origin) to a point ...
or elevation. Simultaneous electrical scanning in both azimuth and elevation was first demonstrated in a phased array antenna at
Hughes Aircraft Company
The Hughes Aircraft Company was a major American aerospace and defense contractor founded on February 14, 1934 by Howard Hughes in Glendale, California, as a division of the Hughes Tool Company. The company produced the Hughes H-4 Hercules air ...
, California in 1957.
Formulation
Array factor
The total
directivity
In electromagnetics, directivity is a parameter of an antenna or optical system which measures the degree to which the radiation emitted is concentrated in a single direction. It is the ratio of the radiation intensity in a given direction f ...
of a phased array will be a result of the gain of the individual array elements, and the directivity due their positioning in an array. This latter component is closely tied (but not equal to
) to the
array factor.
In a (rectangular) planar phased array, of dimensions
, with inter-element spacing
and
, respectively, the array factor can be calculated accordingly
:
Here,
and
are the directions which we are taking the array factor in, in the coordinate frame depicted to the right. The factors
and
are the ''progressive phase shift'' that is used to steer the beam electronically. The factors
and
are the excitation coefficients of the individual elements.
Beam steering is indicated in the same coordinate frame, however the direction of steering is indicated with
and
, which is used in calculation of progressive phase:
:
:
In all above equations, the value
describes the
wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of ...
of the frequency used in transmission.
These equations can be solved to predict the nulls, main lobe, and grating lobes of the array. Referring to the exponents in the array factor equation, we can say that major and grating lobes will occur at integer
solutions to the following equations:
:
:
Worked example
It is common in engineering to provide phased array
values in
decibels
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a ...
through
. Recalling the complex exponential in the array factor equation above, often, what is ''really'' meant by array factor is the magnitude of the summed
phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude and initial phase are time-invariant and whose angular frequency is fixed. It is related to a mor ...
produced at the end of array factor calculation. With this, we can produce the following equation:
For the ease of visualization, we will analyze array factor given an input ''azimuth and elevation'', which we will map to the array frame
and
through the following conversion:
:
:
This represents a coordinate frame whose
axis is aligned with the array
axis, and whose
axis is aligned with the array
axis.
If we consider a
phased array, this process provides the following values for
, when steering to bore-sight (
,
):
These values have been clipped to have a minimum
of -50 dB, however, in reality, null points in the array factor pattern will have values significantly smaller than this.
Applications
Radar
Phased arrays were invented for radar tracking of ballistic missiles, and because of their fast tracking abilities phased array radars are widely used in military applications. For example, because of the rapidity with which the
beam can be steered, phased array radars allow a warship to use one
radar
Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
system for surface detection and tracking (finding ships), air detection and tracking (finding aircraft and missiles) and missile uplink capabilities. Before using these systems, each
surface-to-air missile
A surface-to-air missile (SAM), also known as a ground-to-air missile (GTAM) or surface-to-air guided weapon (SAGW), is a missile designed to be launched from the ground or the sea to destroy aircraft or other missiles. It is one type of anti-ai ...
in flight required a dedicated
fire-control radar
A fire-control radar (FCR) is a radar that is designed specifically to provide information (mainly target azimuth, elevation, range and range rate) to a fire-control system in order to direct weapons such that they hit a target. They are someti ...
, which meant that radar-guided weapons 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
A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particle ...
fire control directors provide the final guidance to the target. Because the antenna pattern 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
In naval terminology, a destroyer is a fast, maneuverable, long-endurance warship intended to escort
larger vessels in a fleet, convoy, or carrier battle group and defend them against a wide range of general threats. They were conceived i ...
, "is able to perform search, track and missile guidance functions simultaneously with a capability of over 100 targets." Likewise, the
Thales Herakles phased array multi-function radar used in service with
France
France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...
and
Singapore
Singapore, officially the Republic of Singapore, is an island country and city-state in Southeast Asia. The country's territory comprises one main island, 63 satellite islands and islets, and one outlying islet. It is about one degree ...
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
The Aster 15 and Aster 30 are a Franco-Italian family of all-weather, Vertical launching system, vertical launch surface-to-air missiles.[German Navy
The German Navy (, ) is part of the unified (Federal Defense), the German Armed Forces. The German Navy was originally known as the ''Bundesmarine'' (Federal Navy) from 1956 to 1995, when ''Deutsche Marine'' (German Navy) became the official ...](_blank)
and the
Royal Dutch Navy have developed the
Active Phased Array Radar System (APAR). The
MIM-104 Patriot
The MIM-104 Patriot is a mobile interceptor missile surface-to-air missile (SAM) system, the primary such system used by the United States Army and several allied states. It is manufactured by the U.S. defense contractor Raytheon and derives it ...
and other ground-based antiaircraft systems use phased array radar for similar benefits.
Phased arrays are used in naval sonar, in active (transmit and receive) and passive (receive only) and hull-mounted and
towed array sonar
A towed array sonar is a system of hydrophones towed behind a submarine or a surface ship on a cable. Trailing the hydrophones behind the vessel, on a cable that can be kilometers long, keeps the array's sensors away from the ship's own noise sou ...
.
Space probe communication
The ''
MESSENGER
Messenger, Messengers, The Messenger or The Messengers may refer to:
People
* Courier, a person or company that delivers messages, packages, or mail
* Messenger (surname)
* Bicycle messenger, a bicyclist who transports packages through cities
* M ...
'' spacecraft was a
space probe
Uncrewed spacecraft or robotic spacecraft are spacecraft without people on board. Uncrewed spacecraft may have varying levels of autonomy from human input, such as remote control, or remote guidance. They may also be autonomous, in which th ...
mission to the planet
Mercury (2011–2015
). This was the first deep-space mission to use a phased-array antenna for
communications
Communication is commonly defined as the transmission of information. Its precise definition is disputed and there are disagreements about whether Intention, unintentional or failed transmissions are included and whether communication not onl ...
. The radiating elements are
circularly-polarized, slotted
waveguide
A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency w ...
s. The antenna, which uses the
X band
The X band is the designation for a band of frequencies in the microwave radio region of the electromagnetic spectrum. In some cases, such as in communication engineering, the frequency range of the X band is set at approximately 7.0–11.2&nbs ...
, used 26 radiative elements and can
gracefully degrade.
Weather research usage

The
National Severe Storms Laboratory
The National Severe Storms Laboratory (NSSL) is a National Oceanic and Atmospheric Administration (NOAA) weather research laboratory under the Office of Oceanic and Atmospheric Research. It is one of seven NOAA Research Laboratories (RLs).
NSS ...
has been using a SPY-1A phased array antenna, provided by the US Navy, for weather research at its
Norman, Oklahoma
Norman () is the List of municipalities in Oklahoma, 3rd most populous city in the U.S. state of Oklahoma, with a population of 128,026 as of the 2020 United States census, 2020 census. It is the most populous city and the county seat of Clevel ...
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
The Lockheed Martin Corporation is an American Arms industry, defense and aerospace manufacturer with worldwide interests. It was formed by the merger of Lockheed Corporation with Martin Marietta on March 15, 1995. It is headquartered in North ...
,
United States Navy
The United States Navy (USN) is the naval warfare, maritime military branch, service branch of the United States Department of Defense. It is the world's most powerful navy with the largest Displacement (ship), displacement, at 4.5 millio ...
,
University of Oklahoma
The University of Oklahoma (OU) is a Public university, public research university in Norman, Oklahoma, United States. Founded in 1890, it had existed in Oklahoma Territory near Indian Territory for 17 years before the two territories became the ...
School of Meteorology, School of Electrical and Computer Engineering, and
Atmospheric Radar Research Center, Oklahoma State Regents for Higher Education, the
Federal Aviation Administration
The Federal Aviation Administration (FAA) is a Federal government of the United States, U.S. federal government agency within the United States Department of Transportation, U.S. Department of Transportation that regulates civil aviation in t ...
, and Basic Commerce and Industries. The project includes
research and development
Research and development (R&D or R+D), known in some countries as OKB, experiment and design, is the set of innovative activities undertaken by corporations or governments in developing new services or products. R&D constitutes the first stage ...
, future
technology transfer
Technology transfer (TT), also called transfer of technology (TOT), is the process of transferring (disseminating) technology from the person or organization that owns or holds it to another person or organization, in an attempt to transform invent ...
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. A team from Japan's RIKEN Advanced Institute for Computational Science (AICS) has begun experimental work on using phased-array radar with a new algorithm for
instant weather forecasts.
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, laser
beam steering, and holography.
Synthetic array heterodyne detection is an efficient method for
multiplexing
In telecommunications and computer networking, multiplexing (sometimes contracted to muxing) is a method by which multiple analog or digital signals are combined into one signal over a shared medium. The aim is to share a scarce resource� ...
an entire phased array onto a single element
photodetector
Photodetectors, also called photosensors, are devices that detect light or other forms of electromagnetic radiation and convert it into an electrical signal. They are essential in a wide range of applications, from digital imaging and optical ...
. The dynamic beam forming in an optical phased array transmitter can be used to electronically raster or vector scan images without using lenses or mechanically moving parts in a lensless projector.
Optical phased array receivers have been demonstrated to be able to act as lensless cameras by selectively looking at different directions.
Satellite broadband internet transceivers
Starlink
Starlink is a satellite internet constellation operated by Starlink Services, LLC, an international telecommunications provider that is a wholly owned subsidiary of American aerospace company SpaceX, providing coverage to around 130 countries ...
is a
low Earth orbit
A low Earth orbit (LEO) is an geocentric orbit, orbit around Earth with a orbital period, period of 128 minutes or less (making at least 11.25 orbits per day) and an orbital eccentricity, eccentricity less than 0.25. Most of the artificial object ...
satellite constellation
A satellite constellation is a group of artificial satellites working together as a system. Unlike a single satellite, a constellation can provide permanent global or near-global pass (spaceflight), coverage, such that at any time everywhere on E ...
that is available in over a hundred countries. It provides broadband internet connectivity to consumers; the user terminals of the system use phased array antennas.
Radio-frequency identification (RFID)
By 2014, phased array antennas were integrated into
RFID
Radio-frequency identification (RFID) uses electromagnetic fields to automatically identify and track tags attached to objects. An RFID system consists of a tiny radio transponder called a tag, a radio receiver, and a transmitter. When tri ...
systems to increase the area of coverage of a single system by 100% to while still using traditional passive
UHF
Ultra high frequency (UHF) is the ITU designation for radio frequencies in the range between 300 megahertz (MHz) and 3 gigahertz (GHz), also known as the decimetre band as the wavelengths range from one meter to one tenth of a meter ...
tags.
Human-machine interfaces (HMI)
A phased array of acoustic transducers, denominated airborne ultrasound tactile display (AUTD), was developed in 2008 at the University of Tokyo's Shinoda Lab to induce tactile feedback. This system was demonstrated to enable a user to interactively manipulate virtual holographic objects.
Radio astronomy
Phased Array Feeds (PAF)
have recently been used at the focus of
radio telescope
A radio telescope is a specialized antenna (radio), antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the r ...
s to provide many beams, giving the radio telescope a very wide
field of view
The field of view (FOV) is the angle, angular extent of the observable world that is visual perception, seen at any given moment. In the case of optical instruments or sensors, it is a solid angle through which a detector is sensitive to elec ...
. Three examples are the
ASKAP telescope in
Australia
Australia, officially the Commonwealth of Australia, is a country comprising mainland Australia, the mainland of the Australia (continent), Australian continent, the island of Tasmania and list of islands of Australia, numerous smaller isl ...
, the Apertif upgrade to the
Westerbork Synthesis Radio Telescope
The Westerbork Synthesis Radio Telescope (WSRT) is an aperture synthesis interferometer built on the site of the former World War II Nazi detention and transit Westerbork transit camp, camp Westerbork, north of the village of Westerbork (villag ...
in The
Netherlands
, Terminology of the Low Countries, informally Holland, is a country in Northwestern Europe, with Caribbean Netherlands, overseas territories in the Caribbean. It is the largest of the four constituent countries of the Kingdom of the Nether ...
, and the Florida Space Institute in the United States .
Broadcasting
In
broadcast engineering
Broadcast engineering or radio engineering is the field of electrical engineering, and now to some extent computer engineering and information technology, which deals with radio and television broadcasting. Audio engineering and RF engineering a ...
, the term 'phased array' has a meaning different from its normal meaning, it means an ordinary
array antenna
An antenna array (or array antenna) is a set of multiple connected antenna (radio), antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas (called ''elements'') are usually connected to a s ...
, an array of multiple
mast radiator
A mast radiator (or radiating tower) is a radio mast or tower in which the metal structure itself is energized and functions as an antenna. This design, first used widely in the 1930s, is commonly used for transmitting antennas operating at l ...
s designed to radiate a
directional radiation pattern, as opposed to a single mast which radiates an
omnidirectional pattern. Broadcast phased arrays have fixed radiation patterns and are not 'steered' during operation as are other phased arrays.
Phased arrays are used by many
AM broadcast radio stations
Radio broadcasting is the broadcasting of audio signal, audio (sound), sometimes with related metadata, by radio waves to radio receivers belonging to a public audience. In terrestrial radio broadcasting the radio waves are broadcast by a lan ...
to enhance
signal strength
In telecommunications, particularly in radio frequency engineering, signal strength is the transmitter power output as received by a reference antenna at a distance from the transmitting antenna. High-powered transmissions, such as those used i ...
and therefore coverage in the
city of license
In U.S., Canadian, and Mexican broadcasting, a city of license or community of license is the community that a radio station or television station is officially licensed to serve by that country's broadcast regulator.
In North American broadcast ...
, while minimizing
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extra ...
to other areas. Due to the differences between daytime and nighttime
ionospheric
The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays ...
propagation at
mediumwave
Medium wave (MW) is a part of the medium frequency (MF) radio band used mainly for AM broadcasting, AM radio broadcasting. The spectrum provides about 120 channels with more limited sound quality than FM stations on the FM broadcast band. Duri ...
frequencies, it is common for AM broadcast stations to change between day (
groundwave
Ground wave is a mode of radio propagation that consists of currents traveling through the earth. Ground waves propagate parallel to and adjacent to the surface of the Earth, and are capable of covering long distances by diffracting around the ...
) and night (
skywave
In radio communication, skywave or skip refers to the propagation of radio waves reflected or refracted back toward Earth from the ionosphere, an electrically charged layer of the upper atmosphere. Since it is not limited by the curvatur ...
) radiation patterns by switching the
phase
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
*Phase space, a mathematica ...
and power levels supplied to the individual antenna elements (
mast radiator
A mast radiator (or radiating tower) is a radio mast or tower in which the metal structure itself is energized and functions as an antenna. This design, first used widely in the 1930s, is commonly used for transmitting antennas operating at l ...
s) daily at
sunrise
Sunrise (or sunup) is the moment when the upper rim of the Sun appears on the horizon in the morning, at the start of the Sun path. The term can also refer to the entire process of the solar disk crossing the horizon.
Terminology
Although the S ...
and
sunset
Sunset (or sundown) is the disappearance of the Sun at the end of the Sun path, below the horizon of the Earth (or any other astronomical object in the Solar System) due to its Earth's rotation, rotation. As viewed from everywhere on Earth, it ...
. For
shortwave
Shortwave radio is radio transmission using radio frequencies in the shortwave bands (SW). There is no official definition of the band range, but it always includes all of the high frequency band (HF), which extends from 3 to 30 MHz (app ...
broadcasts many stations use arrays of horizontal dipoles. A common arrangement uses 16 dipoles in a 4×4 array. Usually this is in front of a wire grid reflector. The phasing is often switchable to allow
beam steering in azimuth and sometimes elevation.
See also
*
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. At each separation and ...
*
Digital antenna array
Digital antenna array (DAA) is a smart antenna with multi channels digital beamforming, usually by using fast Fourier transform (FFT).
The development and practical realization of digital antenna arrays theory started in 1962 under the guidanc ...
*
History of smart antennas The first smart antennas were developed for military communications and intelligence gathering. The growth of cellular telephone in the 1980s attracted interest in commercial applications. The upgrade to digital radio technology in the mobile phone ...
*
Huygens–Fresnel principle
The Huygens–Fresnel principle (named after Netherlands, Dutch physicist Christiaan Huygens and France, French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary w ...
*
Interferometric synthetic-aperture radar
Interferometric synthetic aperture radar, abbreviated InSAR (or deprecated IfSAR), is a radar technique used in geodesy and remote sensing. This geodetic method uses two or more synthetic aperture radar (SAR) radar imaging, images to generate maps ...
*
Inverse synthetic-aperture radar
*
Multi-user MIMO
Multi-user MIMO (MU-MIMO) is a set of multiple-input and multiple-output (MIMO) technologies for multipath wireless communication, in which multiple users or terminals, each radioing over one or more antennas, communicate with one another. In co ...
*
Optical heterodyne detection
Optical heterodyne detection is a method of extracting information encoded as modulation of the phase, frequency or both of electromagnetic radiation in the wavelength band of visible or infrared light. The light signal is compared with standard o ...
*
Radar MASINT
*
Reconfigurable antenna
*
Sensor array
A sensor array is a group of sensors, usually deployed in a certain geometry pattern, used for collecting and processing electromagnetic or acoustic signals. The advantage of using a sensor array over using a single sensor lies in the fact that an ...
*
Side-scan sonar
*
Single-frequency network
A single-frequency network or SFN is a broadcast network where several transmitters simultaneously send the same signal over the same frequency channel.
Analog AM and FM radio broadcast networks as well as digital broadcast networks can operat ...
*
Smart antenna
Smart antennas (also known as adaptive array antennas, digital antenna arrays, multiple antennas and, recently, Multiple-input multiple-output communications, MIMO) are antenna arrays with smart signal processing algorithms used to identify spatial ...
*
Standard linear array
*
Synthetic-aperture radar
*
Synthetic aperture sonar
Synthetic-aperture sonar (SAS) is a form of sonar in which sophisticated post-processing of sonar data is used in ways closely analogous to synthetic-aperture radar.
Synthetic-aperture sonars combine a number of acoustic pings to form an image wi ...
*
Synthetically thinned aperture radar Synthetic thinned aperture radiometry (STAR) is a method of radar in which the coherent product (correlation) of the signal from pairs of antennas is measured at different antenna-pair spacings (baselines). These products yield sample points in the ...
*
Thinned-array curse
*
Wave field synthesis
References
External links
Radar Research and Development - Phased Array Radar��
National Severe Storms Laboratory
The National Severe Storms Laboratory (NSSL) is a National Oceanic and Atmospheric Administration (NOAA) weather research laboratory under the Office of Oceanic and Atmospheric Research. It is one of seven NOAA Research Laboratories (RLs).
NSS ...
Shipboard Phased Array Radars
NASA Report: MMICs For Multiple Scanning Beam Antennas for Space Applications Principles of Phased Array systems- Tutorial 1
{{DEFAULTSORT:Phased Array
Antennas (radio)
Broadcast engineering
Domes
Radar
Radio frequency antenna types
Wireless locating