Phased array

Phased arrays take multiple forms. However, the four most common are the passive phased array (PESA), active electronically scanned array (AESA), hybrid beam forming phased array, and digital beam forming (DBF) array.[10]

A passive phased array or passive electronically scanned array (PESA) is a phased array in which the antenna elements are connected to a single transmitter 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 (AESA) is a phased array in which each antenna element has an analog transmitter/receiver (T/R) module[11] which creates the phase shifting required to electronically steer the antenna beam. Active arrays are a more advanced, second-generation phased-array technology which 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 former(s) to approximately three simultaneous beams for an AESA. Each beam former has a receiver/exciter connected to it.

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 together to form the full array. Each subarray has its own digital receiver/exciter. This approach allows clusters of simultaneous beams to be created.

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.

One possible physical implementation of a phased array is called a conformal antenna.[12] It 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.

Ferdinand Braun's 1905 directional antenna which used the phased array principle, consisting of 3 monopole antennas in an equilateral triangle. A quarter-wave delay in the feedline of one antenna caused the array to radiate in a beam. The delay could be switched manually into any of the 3 feeds, rotating the antenna beam by 120°.

US PAVE PAWS active phased array ballistic missile detection radar in Alaska. Completed in 1979, it was one of the first active phased arrays.

Closeup of some of the 2677 crossed dipole antenna elements that make up the plane array. This antenna produced a narrow "pencil" beam only 2.2° wide.

BMEWS & PAVE PAWS Radars

Mammut phased array radar World War II

Phased array transmission was originally shown in 1905 by Nobel laureate Karl Ferdinand Braun who demonstrated enhanced transmission of radio waves in one direction.[13][14] During World War II, Nobel laureate Luis Alvarez used phased array transmission in a rapidly steerable radar system for "ground-controlled approach", a system to aid in the landing of aircraft. At the same time, the GEMA in Germany built the Mammut 1.[15] It was later adapted for radio astronomy leading to Nobel Prizes for Physics for Antony Hewish and Martin Ryle after several large phased arrays were developed at the University of Cambridge. This design is also used for radar, and is generalized in interferometric radio antennas.

In 2004, Caltech researchers demonstrated the first integrated silicon-based phased array receiver at 24 GHz with 8 elements.[16] This was followed by their demonstration of a CMOS 24 GHz phased array transmitter in 2005[17] and a fully integrated 77 GHz phased array transceiver with integrated antennas in 2006[18][19] by the Caltech team. In 2007, DARPA 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.[20]

The relative amplitudes of—and constructive and destructive interference effects among—the signals radiated by the individual antennas determine the effective radiation pattern of the array. A phased array may be used to point a fixed radiation pattern, or to scan rapidly in azimuth or elevation. Simultaneous electrical scanning in both azimuth and elevation was first demonstrated in a phased array antenna at Hughes Aircraft Company, California in 1957.[21]

The radiation pattern of a phased array in polar coordinate system.

Mathematically a phased array is an example of N-slit diffraction, in which the radiation field at the receiving point is the result of the coherent addition of N point sources in a line. Since each individual antenna acts as a slit, emitting radio waves, their diffraction pattern can be calculated by adding the phase shift φ to the fringing term.

We will begin from the N-slit diffraction pattern derived on the diffraction formalism page, with ${\displaystyle N}$ slits of equal size ${\displaystyle a}$ and spacing ${\displaystyle d}$.

${\displaystyle \psi =\psi _{0}\,{\frac {\sin \left({\frac {\pi a}{\lambda }}\sin \theta \right)}{{\frac {\pi a}{\lambda }}\sin \theta }}\,{\frac {\sin \left({\frac {N}{2}}kd\sin \theta \right)}{\sin \left({\frac {kd}{2}}\sin \theta \right)}}}$

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

${\displaystyle \psi =\psi _{0}\,{\frac {\sin \left({\frac {\pi a}{\lambda }}\sin \theta \right)}{{\frac {\pi a}{\lambda }}\sin \theta }}\,{\frac {\sin \left({\frac {N}{2}}\left({\frac {2\pi d}{\lambda }}\sin \theta +\phi \right)\right)}{\sin \left({\frac {\pi d}{\lambda }}\sin \theta +{\frac {\phi }{2}}\right)}}}$

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

${\displaystyle {\begin{aligned}I&=I_{0}\left({\frac {\sin \left({\frac {\pi a}{\lambda }}\sin \theta \right)}{{\frac {\pi a}{\lambda }}\sin \theta }}\right)^{2}\left({\frac {\sin \left({\frac {N}{2}}\left({\frac {2\pi d}{\lambda }}\sin \theta +\phi \right)\right)}{\sin \left({\frac {\pi d}{\lambda }}\sin \theta +{\frac {\phi }{2}}\right)}}\right)^{2}\\I&=I_{0}\left({\frac {\sin \left({\frac {\pi a}{\lambda }}\sin \theta \right)}{{\frac {\pi a}{\lambda }}\sin \theta }}\right)^{2}\left({\frac {\sin \left({\frac {\pi }{\lambda }}Nd\sin \theta +{\frac {N}{2}}\phi \right)}{\sin \left({\frac {\pi d}{\lambda }}\sin \theta +{\frac {\phi }{2}}\right)}}\right)^{2}\end{aligned}}}$

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

${\displaystyle I=I_{0}{{\left({\frac {\sin \left({\frac {\pi a}{\lambda }}\sin \theta \right)}{{\frac {\pi a}{\lambda }}\sin \theta }}\right)}^{2}}{{\left({\frac {\sin \left({\frac {\pi }{4}}N\sin \theta +{\frac {N}{2}}\phi \right)}{\sin \left({\frac {\pi }{4}}\sin \theta +{\frac {\phi }{2}}\right)}}\right)}^{2}}}$

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

${\displaystyle {\begin{aligned}{\frac {\pi }{4}}N\sin \theta +{\frac {N}{2}}\phi &={\frac {\pi }{2}}\\\sin \theta &=\left({\frac {\pi }{2}}-{\frac {N}{2}}\phi \right){\frac {4}{N\pi }}\\\sin \theta &={\frac {2}{N}}-{\frac {2\phi }{\pi }}\end{aligned}}}$

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

${\displaystyle \theta =\sin ^{-1}1={\frac {\pi }{2}}=90^{\circ }}$

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

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

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

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

Time domain beamformer works by introducing time delays. The basic operation is called "delay and sum". It delays the incoming signal from each array element by a certain amount of time, and then adds them together. 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 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 (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 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

Fixed phased array

An antenna tower consisting of a fixed phase collinear antenna array with four elements

Fixed phased array antennas are typically used to create an antenna with a more desirable form factor than the conventional parabolic reflector or cassegrain reflector. Fixed phased arrays incorporate fixed phase shifters. For example, most commercial FM Radio and TV antenna towers use a collinear antenna array, 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 uses monopulse radar that relies on a fixed phased array to produce multiple adjacent beams that measure angle errors. This form factor is suitable for gimbal mounting in missile seekers.

Wikimedia Commons has media related to Phased arrays.

• Radar Research and Development - Phased Array Radar—National Severe Storms Laboratory
• Shipboard Phased Array Radars
• NASA Report: MMICs For Multiple Scanning Beam Antennas for Space Applications
• Principle of Phased Array
• 'Phased Array' microphone system of Tony Faulkner
• Software tool to predict the radiation pattern of an antenna array