# A new technique of synthesis of the near- or far-field patterns of arrays

TL;DR: In this paper, a unified approach for synthesizing the near or far-field radiation patterns of an array of uniformly or non-uniformly spaced point sources or directive elements located on a planar contour of arbitrary shape is presented.

Abstract: A unified approach for synthesizing the near- or far-field radiation patterns of an array of uniformly or nonuniformly spaced point sources or directive elements located on a planar contour of arbitrary shape is presented. The synthesis problem is formulated employing the free-space Green's dyadic as well as the translational and rotational addition theorems for spherical vector wave functions. A similar unified approach for synthesizing the near- or far-field radiation patterns of a uniformly or nonuniformly spaced linear array of point dipoles is also presented. The validity of the technique presented is established with several typical numerical illustrations.

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TL;DR: In this paper, the basic working principles and applications of the NF-focused (NFF) microwave antennas as well as the synthesis procedures suggested for the NF shaping around the focal point and the technologies currently used for their implementation are discussed.

Abstract: Focusing the electromagnetic field radiated by an antenna at a point in the antenna near-field (NF) region is a wellknown technique to increase the electromagnetic power density in a size-limited spot region close to the antenna aperture. This article encompasses the basic working principles and the applications of the NF-focused (NFF) microwave antennas as well as the synthesis procedures suggested for the NF shaping around the focal point and the technologies currently used for their implementation.

128 citations

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TL;DR: In this article, a technique of synthesizing or reconstructing the excitation currents of a planar array of aperture-type antennas from the known near-field patterns of the radiating source is presented.

Abstract: A technique of synthesizing or reconstructing the excitation currents of a planar array of aperture-type antennas from the known near-field patterns of the radiating source is presented. This technique uses an exact solution to the fields radiated by the aperture antenna without disregarding the source currents. Typical numerical computations have been carried out to validate the analytical technique developed. Sensitivity and stability of the numerical computations performed have been studied. The available iterative bandlimited signal extrapolation technique is used to reconstruct the aperture excitation currents only if the far-field patterns of the radiating source are known. Far-field patterns of aperture antennas measured in the laboratory were also used to reconstruct the aperture electric field distribution in the principal plane. >

18 citations

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TL;DR: In this article, a new technique of synthesis of near-field amplitude and phase patterns of linear, planar, of volume arrays of finite size or arrays located on a planar contour of a finite size is presented.

Abstract: A new technique of synthesis of near-field (NF) amplitude and phase patterns of linear, planar, of volume arrays of finite size or arrays located on a planar contour of finite size is presented The array could consist of point dipoles or directive elements The criterion for prescribing the NF (amplitude and phase) pattern information in the synthesis problem for unique determination of array excitation currents is also stated The proposed near-field synthesis technique is based on the potential integral solution of source currents, Nyquist sampling of the near-field data and the technique of linear least square approximation (LLSA) The NF pattern synthesis technique is illustrated to synthesize a variety of NF patterns with a number of array configurations Application of the proposed NF pattern synthesis technique to minimize distortion in far-field patterns of arrays mounted on a conducting platform and to realize array antennas with low sidelobes in the near and far field is also presented

17 citations

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TL;DR: In this paper, an analytical method to synthesize shaped-beam patterns with planar arrays, based on the handling of spherical waves, is proposed, which only requires the a priori knowledge of the Generalized Scattering Matrix of each array element considered as isolated from the rest of the array elements.

Abstract: An analytical method to synthesize shaped-beam patterns with planar arrays, based on the handling of spherical waves, is proposed. Translational Addition Theorems will be used here for two different purposes: (1) relating the spherical modes produced by each element in the array to calculate the mutual coupling effects, and (2) expressing the field radiated by each element in terms of spherical modes corresponding to the whole array, to carry out a spherical-wave synthesis procedure based on the orthogonal properties of spherical modes. This field synthesis method is based on the fact that any antenna radiated field can be expressed as a discrete series of weighted spherical vector wave functions and it only requires the a priori knowledge of the Generalized Scattering Matrix of each array element considered as isolated from the rest of the array elements.

13 citations

### Cites methods from "A new technique of synthesis of the..."

...In [27], a spherical-mode-based method for pattern synthesis was proposed for planar arrays whose elements are placed on an arbitrary contour, although antennas were assumed to be uncoupled point dipoles....

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TL;DR: In this paper, a technique of synthesis of near-field patterns of a nonuniformly spaced linear array of point dipoles with identical direction of current flow for each array element, or a uniformly spaced array of points with variation in direction for each dipole is presented.

Abstract: A technique of synthesis of near-field patterns of a nonuniformly spaced linear array of point dipoles with identical direction of current flow for each array element, or a uniformly spaced array of point dipoles with variation in direction of current flow for each dipole is presented. Further, it is described how one should prescribe the near-field (NF) pattern and how one should sample the same, while performing the NF pattern synthesis. Also discussed is how NF pattern synthesis should be performed so that the synthesized NF amplitude pattern closely follows a prescribed far-field amplitude pattern of the same array. Numerical computations are performed to demonstrate the validity of the physical concepts made use of in the technique proposed for performing the NF pattern synthesis successfully.

10 citations

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TL;DR: In this article, the authors derived translation theorems for spherical vector wave functions in a reduced form by the use of formulas relating the coefficients that arise in expansion of the product of two associated Legendre functions.

Abstract: : Translational addition theorems for spherical vector wave functions are derived in a reduced form. The reduction is accomplished by the use of formulas relating the coefficients that arise in expansion of the product of two associated Legendre functions. These addition theorems should be useful in those cases in which spherical vector wave functions are used where the distances of bodies and sources are separated by the order of a few wavelengths.

413 citations

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TL;DR: In this paper, the vector wave function addition theorems are based on corresponding theorem for the spherical scalar wave functions, which are the characteristic solutions in spherical coordinates of vector wave equation, such as occurs in electromagnetic problems.

Abstract: Addition theorems are described for spherical vector wave functions, under both rotations and translations of the coordinate system. These functions are the characteristic solutions in spherical coordinates of the vector wave equation, such as occurs in electromagnetic problems. The vector wave function addition theorems are based on corresponding theorems for the spherical scalar wave functions. The latter are reviewed and discussed. (auth)

363 citations

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TL;DR: In this article, a new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as 10 λ in radius at a spacing as small as two spheres in contact becomes feasible.

Abstract: Solution to the multiple scattering of electromagnetic (EM) waves by two arbitrary spheres has been pursued first by the multipole expansion method. Previous attempts at numerical solution have been thwarted by the complexity of the translational addition theorem. A new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as 10\lambda in radius at a spacing as small as two spheres in contact becomes feasible. Simplification and approximation for various cases are also given. With the availability of exact solution, the usefulness of various approximate solutions can be determined quantitatively. For high frequencies, the ray-optical solution is given for two conducting spheres. In addition to the geometric and creeping wave rays pertaining to each sphere alone, there are rays that undergo multiple reflections, multiple creeps, and combinations of both, called the hybrid rays. Numerical results show that the ray-optical solution can be accurate for spheres as small as \lambda/4 in radius is some cases. Despite some shortcomings, this approach provides much physical insight into the multiple scattering phenomena.

306 citations

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TL;DR: In this article, a perturbational procedure for reducing the sidelobe level of discrete linear arrays with uniform amplitude excitation by using nonuniform element spacing is presented, and the calculation of the required element spacings is quite simple.

Abstract: A perturbational procedure for reducing the sidelobe level of discrete linear arrays with uniform amplitude excitation by using nonuniform element spacing is presented. The calculation of the required element spacings is quite simple. The method can reduce the sidelobe level to about 2/N times the field intensity of the main lobe, where N is the total number of elements, without increasing the beamwidth of the main lobe. Several examples are given.

245 citations

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TL;DR: In this article, the authors used spherical-wave expansions as a numerical technique for expressing arbitrary fields specified by analytical, experimental, or numerical data, and found that the generally accepted wave order cutoff value corresponds to 99.9 percent or more of the power in the input pattern.

Abstract: Spherical-wave expansions are a well-known technique of expressing electromagnetic field data. However, most previous work has been restricted to idealized cases in which the expansion coefficients are obtained analytically. In this paper spherical-wave expansions are used as a numerical technique for expressing arbitrary fields specified by analytical, experimental, or numerical data. Numerical results on the maximum wave order needed to expand fields arising from a source of a given size are given for two practical cases, and it is found that the generally accepted wave order cutoff value corresponds to 99.9 percent or more of the power in the input pattern. Near-field patterns computed from far-field data are compared to measured data for the two cases, demonstrating the excellent numerical accuracy of the technique.

116 citations