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Phased array

A phased array is an array of antennas in which the relative phases of the signals feeding the individual antennas are controlled to produce a of radio that can be electronically steered in and shape without requiring physical movement of the antenna structure. This technology leverages the principle of constructive and destructive , where shifts applied to each direct the toward a target while suppressing it in other directions. Phased arrays are commonly used in , communications, and systems due to their ability to rapidly scan large areas and adapt to dynamic environments. The core operation of a phased array involves a network that adjusts the and of signals transmitted or received by each , typically using shifters and amplifiers integrated into the system. Key components include the elements (such as patches or dipoles), transmit/receive modules for , and a computer controller to calculate and apply phase shifts in . Advantages over traditional mechanically steered antennas include faster beam switching (milliseconds versus seconds), higher reliability without moving parts, and the capacity for multiple simultaneous beams, enabling applications like simultaneous tracking of multiple targets. Types of phased arrays include passive arrays, which use a central transmitter with distribution networks, and active arrays, which incorporate solid-state amplifiers at each for greater power and flexibility. The concept of phased arrays dates back to 1905, when German physicist Ferdinand Braun demonstrated the first beamforming antenna using three monopole antennas arranged in a triangle to direct radio waves. Significant advancements occurred in the mid-20th century, particularly during the 1950s and 1960s, when research at institutions like focused on phased-array radar for military applications, leading to the development of electronically scanned systems for air defense and missile tracking. Modern phased arrays, powered by (GaAs) and (GaN) semiconductors, support diverse applications such as 5G base stations for in mobile networks, satellite communications for low-Earth orbit constellations, sonar systems in underwater detection, and even medical imaging through phased array ultrasonics. These systems continue to evolve, with ongoing research emphasizing wideband performance, miniaturization, and integration with for enhanced efficiency.

Introduction

Definition and Principles

A phased array is an system composed of multiple individual elements, typically arranged in a linear or planar configuration, where the relative phases—and often the amplitudes—of the signals feeding each element are controlled to shape and direct the overall . This electronic control enables the array to reinforce the signal in a specific while suppressing it in others, without requiring physical of the structure. The fundamental principle of operation relies on the of electromagnetic emitted from the array elements. By introducing controlled phase shifts to the input signals, the waves align constructively at the desired angle, maximizing signal strength through superposition, while they cancel out destructively in unwanted directions, minimizing sidelobes and . Signal distribution to the elements occurs via a of power dividers or combiners, often implemented using lines, waveguides, or integrated circuits, ensuring precise and minimal losses across the array. Key components of a phased array include the radiating elements themselves, such as dipoles, monopoles, or patches, which convert electrical signals into electromagnetic waves; phase shifters, which adjust the timing of signals to each element for ; and power dividers/combiners, which split or merge the input/output signals to maintain uniform excitation. These elements work together to enable rapid, precise , with phase shifters often being the critical technology for electronic control. In a representative linear configuration, a diagram would illustrate antennas spaced along a line, with arrows indicating progressive delays from one element to the next, resulting in a tilted main beam lobe away from broadside, demonstrating how phase progression achieves directional steering.

Advantages over Conventional Arrays

Phased array antennas offer rapid electronic beam steering, typically achieving repositioning in milliseconds, in contrast to mechanical systems that require seconds due to physical movement and inertia. This speed enables agile tracking of multiple targets simultaneously, allowing surveillance of thousands of angular locations and guidance for hundreds of objects, capabilities unattainable with slower fixed or mechanically scanned arrays. Additionally, the absence of moving parts eliminates mechanical wear, vibration, and associated maintenance needs, enhancing overall reliability in harsh operational environments such as aerospace or military settings. Another key benefit is the ability to form multiple independent beams concurrently from the same , supporting diverse functions like simultaneous communication links or detection without reconfiguration. Phased arrays also exhibit graceful degradation; failure of individual elements reduces performance proportionally rather than causing total system outage, unlike single-point failure risks in conventional designs. In military applications, this technology facilitates full 360-degree scanning electronically at rates far exceeding those of gimbaled mechanical systems, which are limited by rotational speed and settling times. Despite these strengths, phased arrays face notable limitations compared to conventional antennas. The complex , including numerous shifters and amplifiers, result in significantly higher upfront costs, often prohibitive for non-critical uses. shifters introduce insertion losses that increase with steering angle and variation, degrading signal and overall . In large arrays, power inefficiency arises from heat-generating transmit-receive modules, necessitating robust cooling systems that consume additional energy. Furthermore, mutual between closely spaced elements reduces and can cause blindness or distortions, complicating and optimization. These trade-offs highlight the need for careful application-specific evaluation, where the versatility of phased arrays justifies the added complexity and expense.

Types

Active and Passive Phased Arrays

Phased arrays are classified as passive or active based on their signal amplification architecture, which fundamentally affects their performance, reliability, and applications in radar and communication systems. Passive phased arrays employ a single central transmitter and receiver, from which signals are distributed to individual antenna elements via a corporate feed network incorporating phase shifters and attenuators for beam steering and amplitude control. This architecture results in lower overall system cost due to fewer active components, making it suitable for applications where budget constraints are primary, such as certain naval or ground-based surveillance radars. However, the centralized amplification leads to higher insertion losses from the extensive distribution network—often exceeding 10-20 dB in large arrays—and limits power handling, as the central transmitter must manage the total array output without risking overload during high-power operations. Additionally, passive arrays are susceptible to single-point failures in the central unit or feed lines, reducing fault tolerance and complicating maintenance. In contrast, active phased arrays, also known as active electronically scanned arrays (AESA), integrate a dedicated transmit/receive (T/R) module at each element, incorporating low-noise amplifiers for reception and power amplifiers for transmission, alongside phase shifters for individual element control. This distributed amplification enables significantly higher —potentially scaling to kilowatts across the array—by allowing each element to contribute independently without the losses of a central feed, while achieving lower noise figures (typically under 3 dB) through proximity of amplifiers to the elements. The element-level control facilitates advanced capabilities like adaptive nulling to suppress interference, enhanced for simultaneous multiple beam formation, and graceful degradation, where the failure of individual modules minimally impacts overall performance. Although more complex and costly due to the proliferation of solid-state components, active arrays offer superior reliability and versatility, particularly in demanding environments. A key distinction arises in operational and : passive arrays rely on vulnerable corporate feeds that can introduce single-point failures and constrain peak power to avoid central saturation, whereas active arrays distribute risk and power, enabling robust operation under conditions. For instance, AESAs have become the dominant choice for modern fighter jet radars, such as those on the F-35 Lightning II, precisely because they handle high peak powers—often exceeding 10 kW—without central overload, supporting rapid multibeam scanning and low-probability-of-intercept modes essential for air superiority.

Fixed and Dynamic Phased Arrays

Fixed phased arrays employ fixed shifters to establish a predetermined gradient across the array elements, enabling within a limited angular range, typically up to ±45 degrees from broadside. This design simplifies the architecture by eliminating the need for real-time adjustments, resulting in lower cost and reduced complexity compared to more versatile systems. Such arrays are particularly suited for applications requiring stable pointing to stationary or slowly moving targets, such as consumer satellite TV systems that track geostationary satellites. In contrast, dynamic phased arrays, also known as scanning phased arrays, utilize programmable phase shifters or digital controls to achieve full hemispherical or volumetric scanning, allowing the to be directed across a wide angular field without mechanical movement. These systems demand more sophisticated control and higher power consumption but provide extensive coverage essential for multi-target environments. Dynamic arrays are critical in surveillance , where rapid electronic scanning enables real-time monitoring of large areas and tracking of multiple airborne threats. A key design trade-off in fixed phased arrays involves optimizing element spacing to minimize lobes within the constrained ; spacings larger than λ/2 can be tolerated for limited steering angles like ±45 degrees, reducing the number of elements and overall cost while avoiding unwanted secondary beams in the operational range. Dynamic phased arrays, however, often incorporate digital techniques, where signals from individual elements are digitized and processed in real-time to form and adjust multiple beams adaptively, enhancing flexibility for full-scan operations despite increased computational demands. This digital approach can be integrated with active or passive architectures to support the complex and control required for wide-area coverage.

Time-Domain and Frequency-Domain Phased Arrays

Time-domain phased arrays achieve by introducing precise time delays to the signals at each array element, typically using true time-delay (TTD) elements such as switched delay lines or photonic delay networks, which maintain constant delay independent of operating frequency. This approach is prevalent in RF and systems where operation is required, as it enables accurate beam control without the frequency-dependent distortions inherent in phase-based methods. For instance, in TTD implementations, discrete delay units are switched to approximate the required progressive delays across the array, ensuring coherent summation in the desired direction. In contrast, frequency-domain phased arrays rely on phase adjustments at a fixed carrier frequency or employ frequency translation and dispersive elements, such as waveforms or frequency-selective filters, to steer the beam. These systems signals in the , often via digital beamforming where transforms allow per-bin phase corrections, making them suitable for wideband applications by mitigating issues like phase shifter quantization errors through adaptive frequency-dependent weighting. Dispersive elements, for example, exploit varying group delays across frequencies to form beams, avoiding the need for mechanical or switched components in some designs. The trade-offs between these approaches highlight their complementary roles: time-domain methods using TTD offer simplicity in for scenarios but become sensitive to delay mismatches and errors in contexts, potentially leading to . Frequency-domain techniques, while more complex in signal due to the need for FFT-based or frequency offset generation, excel in handling signals by compensating for dispersion and quantization limitations inherent in discrete shifters. Overall, time-domain arrays prioritize straightforwardness at the cost of scalability, whereas frequency-domain arrays demand advanced digital or photonic integration for superior performance. Frequency-domain techniques are particularly emerging in and systems for ultra-wideband beamforming in the mmWave spectrum, where they enable frequency-invariant patterns across multi-GHz bandwidths to support high-data-rate communications without beam squint. For example, joint phase-time hybrid architectures in these networks combine dispersive processing with minimal TTD elements to optimize power efficiency and steering precision in massive setups.

Historical Development

Early Concepts and Era

The foundational concepts of arrays emerged in the early 20th century, predating electronic phased arrays. For instance, in 1905, German physicist Ferdinand Braun demonstrated a antenna using three antennas arranged in a triangle to direct radio waves through interference patterns. In the 1930s, Karl Jansky's experiments at Bell Laboratories advanced array theory. Jansky constructed a linear array of dipoles operating at 20.5 MHz to investigate radio noise sources, demonstrating how spaced elements could form directional beams through constructive interference, contributing to applications in and . Theoretical advancements in further shaped principles applicable to phased arrays. German engineer Karl Küpfmüller described via phase shifting in groups in 1937, providing one of the earliest conceptual frameworks for electronic control of radiation patterns without mechanical movement. This idea influenced subsequent designs by highlighting the potential for phase adjustments to direct beams electronically. During , initial practical explorations of technologies occurred amid development efforts. In , the system, operational by 1940, used a mechanically steered for precise tracking in fire control. The later Mammut radar, operational from 1944, incorporated a fixed phased array with electrical phase adjustments to enable three-dimensional scanning over long ranges, marking an early deployment of such technology in combat. In the United States, the contributed to development between 1943 and 1945, focusing on components for amid wartime constraints. At the Naval Research Laboratory, researchers advanced technologies in the 1940s, supporting progress toward electronic systems. Phased array ideas were actively explored for fire-control s during , but implementations were severely limited by technology, which produced bulky, power-hungry phase shifters incapable of electronic steering at scale. Mechanical alternatives dominated, as electronic components lacked the speed and precision needed for operational deployment.

Postwar Advancements and Modern Era

Following , phased array technology advanced rapidly during the , driven by military needs for enhanced surveillance and defense. In the late 1950s, the U.S. Navy developed the AN/SPS-32, a frequency-scanned phased array integrated into the system aboard ships like the USS Long Beach and , marking the first operational deployment of such technology for long-range air search and target acquisition. This system utilized a massive "billboard" to provide 3D tracking without mechanical movement, addressing limitations in traditional radars during naval operations. By the 1960s, ground-based applications expanded with the AN/FPS-85, the world's first large-scale phased array radar, constructed at in for space surveillance. Operational from 1969, it was later adapted in the 1970s to include warning, scanning vast sectors with electronic to detect threats over the horizon. These early systems demonstrated the scalability of phased arrays, paving the way for integration into broader defense networks. From the 1970s through the 2000s, the focus shifted toward active electronically scanned arrays (AESAs), which incorporated transmit/receive modules at each element for improved performance and reliability. A landmark example was the AN/APG-77 AESA radar, introduced on the F-22 Raptor fighter jet in 2005, enabling simultaneous air-to-air and air-to-ground modes with low-probability-of-intercept capabilities and rapid beam agility. This era also saw phased array principles applied to civilian sectors, including beamforming techniques in 4G LTE cellular base stations to enhance signal directionality and capacity in urban environments. In the 2010s and 2020s, phased arrays proliferated in commercial satellite systems, exemplified by SpaceX's constellation, which deployed user terminals featuring electronically steered phased array antennas starting in 2020 to maintain high-bandwidth connections with low-Earth orbit satellites. These flat-panel arrays enable dynamic beam tracking without moving parts, supporting global access for remote users. Military advancements continued, such as Lockheed Martin's multi-band, multi-mission phased array antenna tested in 2020 for airborne and space applications, allowing simultaneous operation across frequencies to connect multiple satellites efficiently. Recent innovations include C-COM Satellite Systems' 2025 U.S. patent for a Ka-band phased array antenna-in-package technology, which enables hybrid passive/active designs for compact, cost-effective communications in and settings. In weather monitoring, the (NOAA) is advancing phased array upgrades to replace aging systems by 2035, incorporating adaptive scanning for faster, higher-resolution storm detection to improve forecasts. By 2025, the market for satellite phased array antennas is projected to grow at a (CAGR) of 15.6% through 2035, fueled by demand for low-Earth orbit broadband constellations like that require compact, electronically steerable antennas for mass deployment.

Theoretical Foundations

Array Factor and

The array factor (AF) represents the far-field contributed by the of signals from multiple antenna elements in a phased array, assuming identical element patterns. It isolates the effects of element spacing, weights, and shifts on the overall shape. For a uniform linear array of N elements spaced by distance d along the z-axis, with uniform amplitude excitation, the array factor in the azimuthal plane is expressed as \text{AF}(\theta) = \sum_{n=-(N-1)/2}^{(N-1)/2} e^{j (k d n \sin \theta + \phi_n)}, where k = 2\pi / \lambda is the wavenumber, \lambda is the wavelength, \theta is the observation angle from broadside (array normal, with \theta = 0^\circ at broadside), and \phi_n is the progressive phase excitation of the nth element. This formulation arises from the superposition of spherical waves emanating from each element, adjusted for path length differences. Beam steering in phased arrays is achieved by introducing a linear phase progression across the elements, which shifts the direction of constructive interference without mechanical movement. Specifically, to direct the main beam toward an angle \theta_0 from broadside, the phase shifts are set as \phi_n = -k d n \sin \theta_0, ensuring that the wavefronts align in the desired direction. This electronic control enables rapid scanning, with the beam direction determined solely by the applied phases. However, if the inter-element spacing d exceeds \lambda/2, grating lobes—unwanted secondary maxima—emerge within the visible angular range, degrading pattern quality and introducing potential ambiguities in signal processing. Sidelobe levels in the array factor, which represent undesired radiation directions, are influenced by the amplitude distribution across the elements. A uniform amplitude excitation produces the narrowest main beam but results in relatively high sidelobes, typically around -13 dB for large N. To suppress these sidelobes, tapered amplitude distributions—such as cosine, Taylor, or Chebyshev windows—are applied, gradually reducing excitation toward the array edges; this trade-off widens the main beam slightly while lowering peak sidelobes to -20 dB or below, enhancing overall pattern purity. Phased arrays can be configured for broadside or end-fire radiation preferences based on the desired orientation relative to the array axis. Broadside arrays achieve maximum perpendicular to the linear axis (\theta = 0^\circ) with zero progressive phase shift (\beta = 0), optimizing for scanning coverage. In end-fire configurations, the is directed along the array axis (\theta = \pm 90^\circ) by setting \beta = -k d \sin(\pm 90^\circ) = \mp k d, which compensates for the increased path differences along the line, though this often results in narrower and higher to mutual .

Mathematical Formulation and Derivations

The total far-field electric field pattern of a phased array antenna in the far zone is expressed as the product of the individual element pattern and the array factor: E(\theta) = E_{\text{element}}(\theta) \cdot \text{AF}(\theta) where E_{\text{element}}(\theta) represents the radiation pattern of a single isolated element, and \text{AF}(\theta) is the array factor that accounts for the constructive and destructive interference among elements. This formulation assumes the far-field approximation, where the distance from the array is sufficiently large that the wavefronts from all elements appear planar. The array factor is derived from the applied to the spherical waves emanating from each . For a uniform linear of N isotropic point sources spaced d apart along the x-axis, with the nth at x_n = n d (n = 0 to N-1) and excited by a progressive phase shift \phi between adjacent , the contribution from the nth to the far-field at \theta from broadside is proportional to \exp[j (k x_n \sin \theta + \phi_n)], where k = 2\pi / \lambda is the and \phi_n = n \phi. The factor is then the normalized sum: \text{AF}(\theta) = \frac{1}{N} \sum_{n=0}^{N-1} \exp \left[ j n (k d \sin \theta + \phi) \right] This geometric series sums to a closed-form expression: \text{AF}(\theta) = \frac{\sin(N \psi / 2)}{N \sin(\psi / 2)} \exp \left[ j (N-1) \psi / 2 \right] where \psi = k d \sin \theta + \phi. The maximum value of |\text{AF}(\theta)| = 1 occurs when \psi = 0. To steer the main beam to a desired direction \theta_0, the phase shift is set as \phi = -k d \sin \theta_0, shifting the argument to \psi = k d (\sin \theta - \sin \theta_0), so the beam peaks at \theta = \theta_0. For large N in a uniform broadside array (\theta_0 = 0, \phi = 0), the half-power beamwidth (HPBW), defined as the angular width where |\text{AF}(\theta)|^2 drops to 0.5, is approximated by \theta_{\text{BW}} \approx 0.886 \lambda / (N d) radians, or about $50.8^\circ / (N d / \lambda) in degrees; this arises from solving \sin(N \psi / 2) / (N \sin(\psi / 2)) = 1/\sqrt{2} for small \psi, yielding \psi_{3\text{dB}} \approx 2.78 / N and thus \theta_{\text{BW}} \approx \psi_{3\text{dB}} / (k d). The directivity for such large uniform linear arrays with isotropic elements and spacing d \approx \lambda/2 (to suppress grating lobes) approximates D \approx N, reflecting the N-fold increase in effective aperture compared to a single element while maintaining pattern efficiency near unity. As a worked example, consider a 10-element uniform linear array operating at 10 GHz (\lambda = c/f = 3 \times 10^8 / 10 \times 10^9 = 0.03 m = 3 cm) with inter-element spacing d = 1.5 cm = \lambda/2. To steer the beam to \theta_0 = 30^\circ (\sin 30^\circ = 0.5), the phase shift for the nth element is \phi_n = -n k d \sin \theta_0 = -n (2\pi / \lambda) d (0.5) = -n \pi / 2 radians \approx -n \times 90^\circ, since k d = \pi rad for d = \lambda/2. With uniform amplitudes, the main beam directs precisely to $30^\circ, and the first sidelobe level is approximately -13.2 dB below the main lobe peak, as determined from the \text{sinc}-like envelope of the array factor. In practical implementations, digital phase shifters introduce quantization errors that perturb the ideal \phi_n. For instance, 4-bit phase shifters with 22.5° produce maximum phase errors of ±11.25° and errors of about 6.5°, resulting in beam pointing deviations typically less than 0.5° depending on array size and steering angle, along with quantization around -20 dB. These effects degrade by less than 0.1 dB and broaden the beamwidth slightly.

Applications

Radar and Sonar Systems

Phased array radars, particularly active electronically scanned arrays (AESAs), play a critical role in air defense systems for simultaneous detection, tracking, and engagement of multiple airborne and surface threats. The radar, integral to the U.S. Navy's , exemplifies this capability as a multi-function phased-array system that provides 360-degree coverage and can track over 100 targets at ranges up to 310 km. This enables threat assessment in naval operations, where electronic allows instantaneous repositioning without mechanical movement. In civilian applications, phased array technology enhances weather surveillance by dramatically reducing volume scan times compared to traditional mechanical radars. NOAA's National Severe Storms Laboratory has developed and tested phased array prototypes, such as the National Weather Radar Testbed, which achieve full atmospheric scans in under one minute—compared to 4-5 minutes for conventional WSR-88D systems—enabling earlier detection of severe storms like tornadoes. These upgrades support faster update rates, improving forecast accuracy and public safety through adaptive scanning modes. Underwater sonar systems leverage phased arrays for submarine detection and oceanographic monitoring, with towed arrays being a primary configuration for . These linear arrays, often exceeding 1 km in length, employ digital —akin to time-domain phasing—to form directional beams and suppress noise, achieving long-range passive detection of quiet targets at distances up to 38 miles or more. Conformal phased array sonars mounted on hulls provide complementary 360-degree azimuthal coverage by integrating curved elements that adapt to the vehicle's structure, minimizing while maintaining broad . Key performance advantages in both and phased arrays stem from advanced techniques. Pulse enhances range resolution to as fine as 150 meters by transmitting long-duration coded waveforms that are matched-filtered upon reception, boosting without sacrificing precision. Digital beamforming further enables Doppler processing for (MTI), where multiple pulses per beam integrate over time to filter clutter and detect velocity shifts, supporting simultaneous tracking of dynamic threats. Phased array systems achieve rates up to thousands of degrees per second, equivalent to effective rotations of 60 RPM or higher, far surpassing mechanical limits for real-time operations.

Communications and Satellite Technology

Phased arrays play a critical role in communications by enabling electronic to maintain high-data-rate links with fast-moving s, particularly in () constellations. Ground terminals, such as those developed for services, utilize compact phased array antennas to dynamically track s without mechanical movement, ensuring continuous connectivity. For instance, the user terminals employ phased array technology to steer beams across approximately 11 degrees of arc within 15-second slots, accommodating the rapid orbital motion of s traveling at speeds up to 27,000 km/h. In space-based applications, phased arrays support deep-space probes by providing reliable, high-gain communication links; NASA's Deep Space Network (DSN) has explored phased array upgrades to enhance capacity and flexibility for future missions, including studies on large-scale arrays to supplement traditional parabolic antennas. In terrestrial communications, phased arrays are integral to 5G and emerging 6G networks, where massive multiple-input multiple-output (MIMO) configurations at base stations facilitate beam tracking in millimeter-wave (mmWave) bands to overcome path loss and support multi-user data streams. These arrays, often comprising hundreds of elements, enable adaptive spatial multiplexing for high-capacity urban deployments. Additionally, in radio-frequency identification (RFID) systems, phased array readers improve multi-tag inventory management by directing beams to interrogate numerous tags simultaneously in warehouses or retail settings, enhancing read accuracy and speed over conventional single-antenna setups. Key features of phased arrays in these domains include adaptive , which adjusts array weights in real-time to null interference from adjacent signals or environmental sources, thereby maintaining in crowded spectra. Hybrid architectures further optimize large-scale s by combining analog phase shifters with , significantly reducing the number of required radio-frequency (RF) chains—often from hundreds to tens—while preserving for cost-effective implementations. The satellite phased market, driven by demands in LEO systems, is projected to grow at a 15.5% (CAGR) from 2025 to 2033, with innovations in Ka-band designs enabling more compact, high-efficiency antennas through recent patents on integrated phased modules.

Scientific Research and Other Uses

In radio astronomy, phased arrays enable high-resolution imaging through by combining signals from multiple antennas to simulate a much larger . The Atacama Large Millimeter/submillimeter Array (), consisting of 66 high-precision antennas, operates at wavelengths between 0.32 and 3.6 mm to capture detailed images of cosmic phenomena such as and protoplanetary disks. Precursors to the (), including the Australian SKA Pathfinder (ASKAP) and Murchison Widefield Array (MWA), incorporate phased array feeds to facilitate wide-field surveys in the 2020s, mapping vast sky areas for transient events and galaxy evolution studies. Optical phased arrays have advanced in systems, allowing precise control of beams without mechanical parts for applications in autonomous vehicles and . These arrays achieve steering ranges up to 56° × 15° with low power consumption under 1 mW, enabling compact integration on chips. In ultrasonics, a development introduces all-optical phased arrays using light-responsive analog phase shifters driven by a single power source, facilitating scalable for such as tissue characterization and . Beyond traditional domains, phased arrays support human-machine interfaces (HMI) through gesture-tracking systems, where millimeter-wave arrays detect hand movements for intuitive control in devices and vehicles. In , TV towers employ phased panel arrays to optimize coverage by electronically tilting beams, ensuring uniform signal distribution over urban terrains without physical adjustments. For weather research, phased array s profile atmospheric structures like and layers, providing volumetric data at high to improve models. Wideband phased arrays have been explored for high-power applications, including directed energy systems.

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