# Antenna array An **antenna array** is a set of two or more connected antennas that work together as a single radiating or receiving system, fed so that the waves each element sends out combine by interference into one shaped beam rather than the broad, fixed pattern any one element would produce alone. On transmit, the elements' waves add constructively in the directions the array is meant to serve and cancel in most others; on receive, the same phase relationship lets a receiver combine several weak signals into one strong one while rejecting interference arriving from elsewhere. The primary microsim on this page builds that beam element by element: the reader sets how many radiators the array has, how far apart they sit, and what phase steers the beam, and watches a single sharp lobe form, swing off broadside, and eventually sprout an unwanted twin. An array earns its keep wherever a single antenna's pattern is too broad, too fixed, or too weak. A large reflector dish can be pointed only by moving the whole structure; an array of many small elements can be pointed, reshaped, or split into several simultaneous beams entirely by changing the phase and amplitude fed to each element, with no motor and no moving part at all. That flexibility is bought with a real cost in feed hardware, calibration and processing, a trade this article follows from the basic interference principle through the periodic and aperiodic layouts arrays commonly take, to the practical work of designing one. ## Principle Every element of an array radiates the same signal, but a listener at a given angle, far enough away that the wavefront reaching the array is effectively a [[Plane_wave|plane wave]], receives each element's contribution after a slightly different path length, so the waves arrive with a phase offset that depends on that angle, the element spacing, and any phase the feed network adds deliberately. Summing N such contributions, each a phasor advanced by an electrical angle ψ from its neighbour, gives the array factor `AF(ψ) = Σ a_n·e^(jnψ)`, which for equal-amplitude elements reduces to a closed form that peaks sharply where ψ is zero and falls away on either side. That peak is the main lobe, and steering it is simply a matter of choosing the feed phase between neighbouring elements so that ψ, not the elements' physical aim, equals zero in whatever direction the array should point; the array factor is standard antenna theory and is the same relation the primary microsim evaluates directly, summing the individual element phasors rather than relying on the closed form, so it also handles the tapered case the closed form cannot. The array's overall pattern is this array factor multiplied by the pattern of a single element, such as a [[Dipole_antenna|dipole]], so an array can only steer and sharpen what one element already radiates somewhere, never fill in a direction the element itself is blind to. ## Types Arrays are classified first by geometry: a linear array lines its elements along one axis and steers in a plane, a planar array arranges them over a surface and steers a beam in two angles at once, and a conformal array follows the curved surface of a vehicle or a structure, trading a simple feed geometry for one that must correct the extra phase each element's position on the curve introduces. They are classified again by how the beam is set: a fixed-beam array, such as the vertical towers of a directional AM [[Broadcast_engineering|broadcast]] station, is wired once for a pattern that never changes, while a phased array retunes its feed phases electronically to steer the beam pulse to pulse, the arrangement behind most modern [[Radar|radar]] and [[Sonar|sonar]] systems. A further distinction separates an array that forms one shared beam from a [[MIMO|MIMO]] system, which instead treats each element as an independent transmitter or receiver carrying its own data stream, trading a single strong beam for several parallel ones through the same cluttered channel, an arrangement now standard equipment in cellular base stations.[^mimo-cellular] A retrodirective array goes a step further still, wiring each element so the array automatically re-radiates a signal straight back toward whatever direction it arrived from, with no steering calculation and no knowledge of that direction needed at all.[^vanatta] ## Periodic arrays The common case, and the one the primary microsim models, spaces identical elements at equal intervals along a line or a grid. Spacing them at exactly half a wavelength keeps the array factor's main lobe unique across the entire range of possible steering angles; this half-wavelength rule is the antenna equivalent of the [[Nyquist_frequency|Nyquist]] sampling limit, since the array factor is, mathematically, a spatial [[Discrete_Fourier_transform|Fourier transform]] of the element spacing and its excitation into the [[Frequency_domain|spatial-frequency domain]], and grating lobes are simply the spatial aliases that appear once the elements are spaced too far apart to represent the wavefront uniquely. Push the spacing toward one full wavelength or beyond, and a second, equally strong lobe appears at another angle entirely, radiating or receiving power the designer never intended to send or accept there. ## Aperiodic arrays An array whose elements are spaced irregularly, deliberately thinned, or placed at effectively random intervals trades the clean, single grating lobe a periodic array produces once its spacing is too wide for a diffuse scatter of much weaker sidelobes instead, since there is no longer one repeating spacing for stray energy to collect behind. This lets a designer cover a large aperture, and so achieve a narrow main lobe, using far fewer elements than a fully populated periodic array of the same size would need, at the cost of a higher general sidelobe floor and a pattern that is harder to predict in closed form than the uniform case's Dirichlet formula. Large radio-astronomy interferometers commonly place their dishes at deliberately non-uniform spacings for exactly this reason, favouring image quality over the coherent grating lobes a neat grid would introduce, since a telescope array's job is forming a clean image over a wide field rather than pointing one narrow beam.[^interferometry] A thinned array can also be grown or shrunk incrementally, adding elements where budget allows without redesigning the spacing of the ones already in place, a practical convenience a strict periodic grid does not offer once it is built. ## Design of antenna arrays Real arrays depart from the idealised sum of independent elements in several practical ways. Elements placed close enough to steer without grating lobes also sit close enough to load each other electromagnetically, a mutual coupling that shifts each element's effective impedance and pattern away from what it would show in isolation and that a careful design must measure or model rather than assume away. The feed network that splits the transmitter's power, or combines the receiver's signals, among every element adds its own loss and, in a phase shifter built for every element, its own cost, which is usually the practical ceiling on how large an electronically steered array can grow; the [[Semiconductor_device|semiconductor devices]] used for those phase shifters, not the antenna elements themselves, are often what an [[Radio-frequency_engineering|RF engineer]] spends the design budget on, and the falling cost of one phase shifter per element over the past few decades is a large part of why active electronically scanned arrays have spread from a handful of high-end military radars to a much wider range of fielded systems.[^aesa] Tapering the amplitude fed to the outer elements, the same idea as a window function applied in [[Signal_processing|signal processing]], trades a wider main lobe for markedly lower sidelobes than the roughly −13 dB an unwindowed, uniformly fed array is stuck with. On receive, a large array's sensitivity is ultimately limited the same way any single antenna's is, by the [[Johnson–Nyquist_noise|thermal noise]] of the receiver and by the sky or ground brightness temperature the array's combined beam collects, a budget in which a bigger array buys gain but not a lower noise floor by itself.[^ell105array] Spreading the work over many elements also buys a measure of [[Fault_tolerance|fault tolerance]] a single dish cannot offer: losing a handful of elements out of hundreds degrades the sidelobes and trims the gain slightly, rather than blinding the array outright. ## Microsims The primary microsim builds a linear array on screen and updates its beam pattern as fast as the controls move. Element count sets how many radiators feed the array and, directly, how narrow and how deep the main lobe becomes. Spacing, given in wavelengths, is the periodic-array control above: near half a wavelength keeps a single clean lobe, and pushing it past about one wavelength brings a full-strength grating lobe into view on the polar plot. A steering control sets the phase between neighbouring elements and swings the whole beam off broadside without moving a single element. A taper toggle switches between uniform feed, whose first sidelobe sits at the standard −13.2 dB the sketch itself marks on its polar plot, and a tapered feed that trades a wider main lobe for a much quieter sidelobe floor. The sketch is illustrative: it models identical, lossless elements in free space, without the mutual coupling or feed-network loss described above. A three.js companion elsewhere on the site renders the same array factor as a full three-dimensional lobe, showing element count, spacing, steering phase and grating lobes together on one surface. *Try:* Push the spacing control out past one wavelength and watch a second, equally strong lobe appear on the polar plot at another angle, the grating lobe a periodic array produces once its elements sit too far apart to keep the wavefront unambiguous. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Antenna_array) : [Wikitube](https://en.wikitube.io/wiki/Antenna_array) Skeleton mirrored at revision 1350560217. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Radar]] - [[Sonar]] - [[MIMO]] - [[Dipole_antenna]] - [[Doppler_effect]] - [[Discrete_Fourier_transform]] ## References The array factor, its closed-form Dirichlet reduction, the half-wavelength spacing rule and the resulting grating-lobe condition are standard antenna theory used throughout radio engineering and are not separately footnoted here, per the Wikitube style guide's §6.1. Page numbers below are PDF pages of the open edition linked in Further reading. [^interferometry]: Citation needed: a named radio-astronomy facility's array-configuration record would confirm the specific non-uniform spacing scheme and its stated imaging rationale. [^ell105array]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 104-105 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^vanatta]: Citation needed: the original patent or paper describing the retrodirective (Van Atta) array, commonly dated to 1959, would confirm the inventor, assignee and priority date. [^aesa]: Citation needed: a specific active electronically scanned array radar's published element count and fielding date would support a concrete example here. [^mimo-cellular]: Citation needed: the cellular standard and release that made multi-element MIMO antenna arrays a mandatory base-station feature would confirm the date claimed for this trend. **Further reading** — the open textbooks this article draws on, since the pair carries no separate Further reading heading of its own: - Steven Ellingson. *Radio Systems Engineering, Revised First Edition*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory - Don Johnson. *Fundamentals of Electrical Engineering I*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 - Michael Stiber; Bilin Stiber; Eric Larson. *Signal Computing: Digital Signals in the Software Domain*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain - Allen Downey. *Think DSP: Digital Signal Processing in Python*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python - John Dyer; Chad Davis. *Measurement and Instrumentation: An Introduction to Concepts and Methods, 1st Edition*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/measurement-and-instrumentation-an-introduction-to-concepts-and-methods **External links** — the live sketch, since the pair carries no separate External links heading of its own: - Live sketch: https://editor.p5js.org/sciencenibber/full/aYSDWi7st - Editor source: https://editor.p5js.org/sciencenibber/sketches/aYSDWi7st <!-- Hubs: Signal_processing. Portals: PORTAL_Signal_Processing. Signal Processing portal wave 1 · 2026-09-17 · drafted. -->