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45-599: The EL/M-2032 is an advanced pulse Doppler, multimode planar array radar fire-control radar intended for multi-role fighter aircraft originated from the Lavi project. It is suitable for air-to-air and air-to-surface modes. As of 2009, Elta has integrated this radar system into the Sea Harrier , A-4 , F-4 , F-5 , F-16 , FA-50 , Mirage , Tejas Mk 1 and MiG-21 fighters. Planar array radar An antenna array can achieve higher gain ( directivity ), that

90-608: A traveling plane wave , whose evolution in time can be described as simple translation of the field at a constant wave speed c {\displaystyle c} along the direction perpendicular to the wavefronts. Such a field can be written as F ( x → , t ) = G ( x → ⋅ n → − c t ) {\displaystyle F({\vec {x}},t)=G\left({\vec {x}}\cdot {\vec {n}}-ct\right)\,} where G ( u ) {\displaystyle G(u)}

135-426: A complex exponential plane wave . When the values of F {\displaystyle F} are vectors, the wave is said to be a longitudinal wave if the vectors are always collinear with the vector n → {\displaystyle {\vec {n}}} , and a transverse wave if they are always orthogonal (perpendicular) to it. Often the term "plane wave" refers specifically to

180-423: A beam. This type is called an aperture antenna . A parabolic dish is an example of this type of antenna. A second technique is to use multiple antennas which are fed from the same transmitter or receiver; this is called an array antenna, or antenna array. For a transmitting antenna the electromagnetic wave received at any point is the vector sum of the electromagnetic waves from each of the antenna elements. If

225-402: A fixed radiation pattern, we may consider that the feed network is a part of the antenna array. Thus, the antenna array has a single port. Narrow beams can be formed, provided the phasing of each element of the array is appropriate. If, in addition, the amplitude of the excitation received by each element (during emission) is also well chosen, it is possible to synthesize a single-port array having

270-617: A function of one scalar parameter (the displacement d = x → ⋅ n → {\displaystyle d={\vec {x}}\cdot {\vec {n}}} ) with scalar or vector values, and S {\displaystyle S} is a scalar function of time. This representation is not unique, since the same field values are obtained if S {\displaystyle S} and G {\displaystyle G} are scaled by reciprocal factors. If | S ( t ) | {\displaystyle \left|S(t)\right|}

315-411: A large homogeneous region of space can be well approximated by plane waves when viewed over any part of that region that is sufficiently small compared to its distance from the source. That is the case, for example, of the light waves from a distant star that arrive at a telescope. A standing wave is a field whose value can be expressed as the product of two functions, one depending only on position,

360-402: A radiation pattern that closely approximates a specified pattern. Many methods have been developed for array pattern synthesis. Additional issues to be considered are matching, radiation efficiency and bandwidth. The design of an electronically steerable antenna array is different, because the phasing of each element can be varied, and possibly also the relative amplitude for each element. Here,

405-476: A scalar or a vector, is called the amplitude of the wave; the scalar coefficient f {\displaystyle f} is its "spatial frequency"; and the scalar φ {\displaystyle \varphi } is its " phase shift ". A true plane wave cannot physically exist, because it would have to fill all space. Nevertheless, the plane wave model is important and widely used in physics. The waves emitted by any source with finite extent into

450-405: A source of disadvantages in both transmission and reception. In fact, in transmission, they can lead to radiation in unwanted directions, while, in reception, they can be a source of ambiguity since the desired signal entering the mainlobe region could be strongly disturbed by other signals (unwanted interfering signals) entering the regions of the various grating lobes. Therefore, in periodic arrays,

495-935: A wave in a one-dimensional medium. Any local operator , linear or not, applied to a plane wave yields a plane wave. Any linear combination of plane waves with the same normal vector n → {\displaystyle {\vec {n}}} is also a plane wave. For a scalar plane wave in two or three dimensions, the gradient of the field is always collinear with the direction n → {\displaystyle {\vec {n}}} ; specifically, ∇ F ( x → , t ) = n → ∂ 1 G ( x → ⋅ n → , t ) {\displaystyle \nabla F({\vec {x}},t)={\vec {n}}\partial _{1}G({\vec {x}}\cdot {\vec {n}},t)} , where ∂ 1 G {\displaystyle \partial _{1}G}

SECTION 10

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540-402: A wide angle. To create a directional antenna ( high gain antenna ), which radiates radio waves in a narrow beam, two general techniques can be used: One technique is to use reflection by large metal surfaces such as parabolic reflectors or horns , or refraction by dielectric lenses to change the direction of the radio waves, to focus the radio waves from a single low gain antenna into

585-429: Is a function that gives the field's value as dependent on only two real parameters: the time t {\displaystyle t} , and the scalar-valued displacement d = x → ⋅ n → {\displaystyle d={\vec {x}}\cdot {\vec {n}}} of the point x → {\displaystyle {\vec {x}}} along

630-503: Is a narrower beam of radio waves, than could be achieved by a single element. In general, the larger the number of individual antenna elements used, the higher the gain and the narrower the beam. Some antenna arrays (such as military phased array radars) are composed of thousands of individual antennas. Arrays can be used to achieve higher gain, to give path diversity (also called MIMO ) which increases communication reliability, to cancel interference from specific directions, to steer

675-426: Is assumed that radiators have the same orientation and the same polarization of the electric field. Based on this, the array factor can be written as follows F ( u ) = ∑ n = 1 N I n e j k x n u {\displaystyle F(u)=\sum _{n=1}^{N}I_{n}\,e^{jk\,x_{n}u}} where N {\displaystyle N}

720-535: Is bounded in the time interval of interest (which is usually the case in physical contexts), S {\displaystyle S} and G {\displaystyle G} can be scaled so that the maximum value of | S ( t ) | {\displaystyle \left|S(t)\right|} is 1. Then | G ( x → ⋅ n → ) | {\displaystyle \left|G({\vec {x}}\cdot {\vec {n}})\right|} will be

765-546: Is called the direction of propagation . For each displacement d {\displaystyle d} , the moving plane perpendicular to n → {\displaystyle {\vec {n}}} at distance d + c t {\displaystyle d+ct} from the origin is called a " wavefront ". This plane travels along the direction of propagation n → {\displaystyle {\vec {n}}} with velocity c {\displaystyle c} ; and

810-456: Is intended to receive independent excitations during emission, and to deliver more or less independent signals during reception. Here also, the subject matters of matching and efficiency are involved, especially in the case of an antenna array of a mobile device (see chapter 10 of ), since, in this case, the surroundings of the antenna array influence its behavior, and vary over time. Suitable matching metrics and efficiency metrics take into account

855-529: Is now a function of a single real parameter u = d − c t {\displaystyle u=d-ct} , that describes the "profile" of the wave, namely the value of the field at time t = 0 {\displaystyle t=0} , for each displacement d = x → ⋅ n → {\displaystyle d={\vec {x}}\cdot {\vec {n}}} . In that case, n → {\displaystyle {\vec {n}}}

900-607: Is the number of antenna elements, k {\displaystyle k} is the wavenumber, I n {\displaystyle I_{n}} and x n {\displaystyle x_{n}} (in meters) are the complex excitation coefficient and the position of the n-th radiator, respectively, u = sin ⁡ θ cos ⁡ ϕ {\displaystyle u=\sin \theta \cos \phi } , with θ {\displaystyle \theta } and ϕ {\displaystyle \phi } being

945-831: Is the partial derivative of G {\displaystyle G} with respect to the first argument. The divergence of a vector-valued plane wave depends only on the projection of the vector G ( d , t ) {\displaystyle G(d,t)} in the direction n → {\displaystyle {\vec {n}}} . Specifically, ∇ ⋅ F → ( x → , t ) = n → ⋅ ∂ 1 G ( x → ⋅ n → , t ) {\displaystyle \nabla \cdot {\vec {F}}({\vec {x}},t)\;=\;{\vec {n}}\cdot \partial _{1}G({\vec {x}}\cdot {\vec {n}},t)} In particular,

SECTION 20

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990-419: Is usually another name for a Yagi–Uda antenna . A phased array usually means an electronically scanned array ; a driven array antenna in which each individual element is connected to the transmitter or receiver through a phase shifter controlled by a computer. The beam of radio waves can be steered electronically to point instantly in any direction over a wide angle, without moving the antennas. However

1035-427: The antenna array has multiple ports, so that the subject matters of matching and efficiency are more involved than in the single-port case. Moreover, matching and efficiency depend on the excitation, except when the interactions between the antennas can be ignored. An antenna array used for spatial diversity and/or spatial multiplexing (which are different types of MIMO radio communication) always has multiple ports. It

1080-454: The component antennas' axis relates to the radiation direction. There are also arrays (such as phased arrays ) which don't belong to either of these categories, in which the direction of radiation is at some other angle to the antenna axis. Array antennas can also be categorized by how the element antennas are arranged: Let us consider a linear array whose elements are arranged along the x-axis of an orthogonal Cartesian reference system. It

1125-420: The currents are fed to the antennas with the proper phase , due to the phenomenon of interference the spherical waves from the individual antennas combine (superpose) in front of the array to create plane waves , a beam of radio waves traveling in a specific direction. In directions in which the waves from the individual antennas arrive in phase , the waves add together ( constructive interference ) to enhance

1170-420: The direction n → {\displaystyle {\vec {n}}} . The displacement is constant over each plane perpendicular to n → {\displaystyle {\vec {n}}} . The values of the field F {\displaystyle F} may be scalars, vectors, or any other physical or mathematical quantity. They can be complex numbers , as in

1215-494: The extent of the visible space also changes accordingly. Now, suppose that the excitation coefficients are positive real variables. In this case, always in the domain of u {\displaystyle u} , the array factor magnitude has a main lobe with maximum value at u = 0 {\displaystyle u=0} , called mainlobe , several secondary lobes lower than the mainlobe, called sidelobes and mainlobe replicas called grating-lobes . Grating lobes are

1260-580: The field of radio astronomy , in which multiple radio telescopes consisting of large parabolic antennas are linked together into an antenna array, to achieve higher resolution. Using the technique called aperture synthesis such an array can have the resolution of an antenna with a diameter equal to the distance between the antennas. In the technique called Very Long Baseline Interferometry (VLBI) dishes on separate continents have been linked, creating "array antennas" thousands of miles in size. Most array antennas can be divided into two classes based on how

1305-538: The grating lobes are outside the interval [-1,1]. As seen above, when the spacing is constant between adjacent radiators, the array factor is characterized by the presence of grating lobes. In the literature, it has been amply demonstrated that to destroy the array factor's periodicity, the same array's geometry must also be made aperiodic. It is possible to act on the positions of the radiators so that these positions are not commensurable with each other. Several methods have been developed to synthesize arrays in which also

1350-428: The interval [ − 1 , 1 ] {\displaystyle [-1,1]} , which is associated with the values of θ {\displaystyle \theta } and ϕ {\displaystyle \phi } . In this case, the interval [-1,1] is called visible space . As shown further, if the definition of the variable u {\displaystyle u} changes,

1395-500: The maximum field magnitude seen at the point x → {\displaystyle {\vec {x}}} . A plane wave can be studied by ignoring the directions perpendicular to the direction vector n → {\displaystyle {\vec {n}}} ; that is, by considering the function G ( z , t ) = F ( z n → , t ) {\displaystyle G(z,t)=F(z{\vec {n}},t)} as

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1440-399: The other only on time. A plane standing wave , in particular, can be expressed as F ( x → , t ) = G ( x → ⋅ n → ) S ( t ) {\displaystyle F({\vec {x}},t)=G({\vec {x}}\cdot {\vec {n}})\,S(t)} where G {\displaystyle G} is

1485-572: The positions represent further degrees of freedom (unknowns). There are both deterministic and probabilistic methodologies. Since the probabilistic theory of aperiodic arrays is a sufficiently systematised theory, with a strong general methodological basis, let us first concentrate on describing its peculiarities. Suppose that the radiators positions, { x n } n = 1 N {\displaystyle \{x_{n}\}_{n=1}^{N}} , are independent and identically distributed random variables whose support coincides with

1530-416: The power radiated. In directions in which the individual waves arrive out of phase , with the peak of one wave coinciding with the valley of another, the waves cancel ( destructive interference ) reducing the power radiated in that direction. Similarly, when receiving, the oscillating currents received by the separate antennas from radio waves received from desired directions are in phase and when combined in

1575-416: The radio beam electronically to point in different directions, and for radio direction finding (RDF). The term antenna array most commonly means a driven array consisting of multiple identical driven elements all connected to the receiver or transmitter. A parasitic array consists of a single driven element connected to the feedline, and other elements which are not, called parasitic elements . It

1620-419: The receiver reinforce each other, while currents from radio waves received from other directions are out of phase and when combined in the receiver cancel each other. The radiation pattern of such an antenna consists of a strong beam in one direction, the main lobe , plus a series of weaker beams at different angles called sidelobes , usually representing residual radiation in unwanted directions. The larger

1665-529: The spacing between adjacent radiators must not exceed a specific value to prevent the appearance of grating lobes (in the visible space) in the visible space ), the spacing between adjacent radiators must not exceed a specific value. For example, as seen previously, the first grating lobes for d = λ / 2 {\displaystyle d=\lambda /2} occur in u = ± 2 {\displaystyle u=\pm 2} . So, in this case, there are no problems since, in this way,

1710-554: The term "phased array" is sometimes used to mean an ordinary array antenna. From the Rayleigh criterion , the directivity of an antenna, the angular width of the beam of radio waves it emits, is proportional to the wavelength of the radio waves divided by the width of the antenna. Small antennas around one wavelength in size, such as quarter-wave monopoles and half-wave dipoles , don't have much directivity ( gain ); they are omnidirectional antennas which radiate radio waves over

1755-478: The value of such a field can be written as F ( x → , t ) = G ( x → ⋅ n → , t ) , {\displaystyle F({\vec {x}},t)=G({\vec {x}}\cdot {\vec {n}},t),} where n → {\displaystyle {\vec {n}}} is a unit-length vector , and G ( d , t ) {\displaystyle G(d,t)}

1800-778: The value of the field is then the same, and constant in time, at every one of its points. The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave : a travelling plane wave whose profile G ( u ) {\displaystyle G(u)} is a sinusoidal function. That is, F ( x → , t ) = A sin ⁡ ( 2 π f ( x → ⋅ n → − c t ) + φ ) {\displaystyle F({\vec {x}},t)=A\sin \left(2\pi f({\vec {x}}\cdot {\vec {n}}-ct)+\varphi \right)} The parameter A {\displaystyle A} , which may be

1845-441: The wavelength, then the magnitude of the array factor has a period, in the domain of u {\displaystyle u} , equal to 2 {\displaystyle 2} . It is worth emphasising that u {\displaystyle u} is an auxiliary variable. In fact, from a physical point of view, the values of u {\displaystyle u} that are of interest for radiative purposes fall in

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1890-457: The whole array aperture. Consequently, the array factor is a stochastic process, whose mean is as follows E [ F ( u ) ] = ∫ − L / 2 L / 2 f ( x ) e j k x u d x {\displaystyle E\left[F(u)\right]=\textstyle \int \limits _{-L/2}^{L/2}f(x)\,e^{jkxu}\,dx} In an antenna array providing

1935-408: The width of the antenna and the greater the number of component antenna elements, the narrower the main lobe, and the higher the gain which can be achieved, and the smaller the sidelobes will be. Arrays in which the antenna elements are fed in phase are broadside arrays; the main lobe is emitted perpendicular to the plane of the elements. The largest array antennas are radio interferometers used in

1980-429: The worst possible excitations. Plane wave In physics , a plane wave is a special case of a wave or field : a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position x → {\displaystyle {\vec {x}}} in space and any time t {\displaystyle t} ,

2025-589: The zenith angle and azimuth angle, respectively. If the spacing between adjacent elements is constant, then it can be written that x n + 1 − x n = d {\displaystyle x_{n+1}-x_{n}=d} , and the array is said to be periodic. The array is periodic both spatially (physically) and in the variable u {\displaystyle u} . For example, if d = λ / 2 {\displaystyle d=\lambda /2} , with λ {\displaystyle \lambda } being

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