The Theoretical Precision with which an Arbitrary Radiation-Pattern may be Obtained from a Source of Finite Size
01 Sep 1948-Journal of the Institution of Electrical Engineers - Part III: Radio and Communication Engineering (IET)-Vol. 95, Iss: 37, pp 363-370
TL;DR: In this paper, it was shown that the broadside power gain is not a maximum when the amplitudes and phases of the elements are equal, unless the elements were ideal isotropic point-sources.
Abstract: It appears that it is possible to approximate as closely as desired to a specified radiation-pattern by a suitable distribution of field over an aperture of given size, though the necessary currents in the conducting elements of the source would in general be prohibitively large in comparison with the power radiated. The difficulty of obtaining a high degree of approximation, and in particular a power gain very much greater than that of a uniformly illuminated aperture, is thus a practical rather than a theoretical one. The same is true for the linear array of given length as for the continuous aperture if no limit is set to the number of elements. Even when this number is limited by the adoption of half-wavelength spacing, the broadside power gain is not a maximum when the amplitudes and phases of the elements are equal, unless the elements are ideal isotropic point-sources.
Citations
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TL;DR: In this paper, the authors apply the theory developed in the preceding paper to a number of questions about timelimited and bandlimited signals, and find the signals which do the best job of simultaneous time and frequency concentration.
Abstract: The theory developed in the preceding paper1 is applied to a number of questions about timelimited and bandlimited signals. In particular, if a finite-energy signal is given, the possible proportions of its energy in a finite time interval and a finite frequency band are found, as well as the signals which do the best job of simultaneous time and frequency concentration.
2,498 citations
Book•
30 Nov 1993
TL;DR: Details of Element Pattern and Mutual Impedance Effects for Phased Arrays and Special Array Feeds for Limited Field of View and Wideband Arrays are presented.
Abstract: Phased Arrays in Radar and Communication Systems. Pattern Characteristics and Synthesis of Linear and Planar Arrays. Patterns of Nonplanar Arrays. Elements, Transmission Lines, and Feed Architectures for Phased Arrays. Summary of Element Pattern and Mutual Impedance Effects. Array Error Effects. Special Array Feeds for Limited Field of View and Wideband Arrays.
2,233 citations
Cites background or methods from "The Theoretical Precision with whic..."
...The uniform pattern has another feature that makes it an ideal tool for synthesis: it is a member of an orthogonal set of beams, and therefore one can devise lossless networks to superimpose groups of beams and synthesize desired patterns [8, 9]....
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...Kirkpatrick [9] is attributed with introducing the measure of difference pattern slope km by which various antenna systems are compared....
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...7(b) [9] shows the patterns of a continuous line source of length 32l , an array of 64 elements spaced l /2 apart, and an array of 8 elements spaced 4l apart....
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...7(a) [9] shows radiation patterns for a continuous line source of length 4l and an eightelement array of l /2-spaced elements with uniform illumination....
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01 Jan 1955
TL;DR: In this article, the mathematical relationships involved in the radiation calculation are studied from the point of view of function theory, and the problem of constructing a line source with an optimum compromise between beamwidth and side-lobe level is considered.
Abstract: It is well known that the phenomenon of radiation from line-source antennas is very similar to that of the diffraction of light from narrow apertures. Unlike the optical situation, however, antenna design technique permits the use of other-than-uniform distributions of field across the antenna aperture. Line source synthesis is the science of choosing this distribution function to give a radiation pattern with prescribed properties such as, for example, narrow angular width of the main lobe and low side lobes. In the present article the mathematical relationships involved in the radiation calculation are studied from the point of view of function theory. Some conclusions are drawn which outline the major aspects of synthesis technique very clearly. In particular, the problem of constructing a line source with an optimum compromise between beamwidth and side-lobe level (analogous to the Dolph - Tchebycheff problem in linear array theory) is considered. The ideal pattern is cos π √ {u /sup 2/ - A/sup 2/} , where u = (2a/λ) cos θ, a is the half-length of the source, and cosh π A is the side-lobe ratio. Because of theoretical limitations, this pattern cannot be obtained from a physically realizable antenna; nevertheless its ideal characteristics can be approached arbitrarily closely. The procedure for doing this is given in detail.
518 citations
Journal Article•
TL;DR: In this article, the mathematical relationships involved in the radiation calculation are studied from the point of view of function theory, and the problem of constructing a line source with an optimum compromise between beamwidth and side-lobe level is considered.
Abstract: It is well known that the phenomenon of radiation from line-source antennas is very similar to that of the diffraction of light from narrow apertures. Unlike the optical situation, however, antenna design technique permits the use of other-than-uniform distributions of field across the antenna aperture. Line source synthesis is the science of choosing this distribution function to give a radiation pattern with prescribed properties such as, for example, narrow angular width of the main lobe and low side lobes. In the present article the mathematical relationships involved in the radiation calculation are studied from the point of view of function theory. Some conclusions are drawn which outline the major aspects of synthesis technique very clearly. In particular, the problem of constructing a line source with an optimum compromise between beamwidth and side-lobe level (analogous to the Dolph - Tchebycheff problem in linear array theory) is considered. The ideal pattern is cos π √ {u /sup 2/ - A/sup 2/} , where u = (2a/λ) cos θ, a is the half-length of the source, and cosh π A is the side-lobe ratio. Because of theoretical limitations, this pattern cannot be obtained from a physically realizable antenna; nevertheless its ideal characteristics can be approached arbitrarily closely. The procedure for doing this is given in detail.
502 citations
TL;DR: It is demonstrated that an optical mask designed that creates constructive interference of waves known as superoscillation, leading to a subwavelength focus of prescribed size and shape in a field of view beyond the evanescent fields, when illuminated by a monochromatic wave.
Abstract: The past decade has seen numerous efforts to achieve imaging resolution beyond that of the Abbe-Rayleigh diffraction limit. The main direction of research aiming to break this limit seeks to exploit the evanescent components containing fine detail of the electromagnetic field distribution at the immediate proximity of the object. Here, we propose a solution that removes the need for evanescent fields. The object being imaged or stimulated with subwavelength accuracy does not need to be in the immediate proximity of the superlens or field concentrator: an optical mask can be designed that creates constructive interference of waves known as superoscillation, leading to a subwavelength focus of prescribed size and shape in a field of view beyond the evanescent fields, when illuminated by a monochromatic wave. Moreover, we demonstrate that such a mask may be used not only as a focusing device but also as a super-resolution imaging device.
278 citations
Cites background from "The Theoretical Precision with whic..."
...Beginning from the pioneering work of Shelkunoff [23], the microwave community contemplated the idea of achieving antennae that beat the diffraction limit for directivity: several authors were able to prove that for a linear array of properly adjusted radiating antenna dipoles, there were no theoretical limits to directivity whatsoever [24, 25]....
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References
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TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Abstract: Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.
4,525 citations
01 Jun 1946
TL;DR: In this article, a one-parameter family of current distributions for symmetric broadside arrays of equally spaced point sources energized in phase was derived, and design curves relating the value of the parameter to side-lobe level as well as the relative current values expressed as a function of side lobe level were given for the cases of 8-, 12-, 16-, 20-, and 24-element linear arrays.
Abstract: A one-parameter family of current distributions is derived for symmetric broadside arrays of equally spaced point sources energized in phase. For each value of the parameter, the corresponding current distribution gives rise to a pattern in which (1) all the side lobes are at the same level; and (2) the beam width to the first null is a minimum for all patterns arising from symmetric distributions of in-phase currents none of whose side lobes exceeds that level. Design curves relating the value of the parameter to side-lobe level as well as the relative current values expressed as a function of side-lobe level are given for the cases of 8-, 12-, 16-, 20-, and 24-element linear arrays.
1,096 citations
TL;DR: In this article, a simple modification of the usual expression for the radiation intensity of a system of radiating sources was proposed, similar to the passage from the representation of instantaneous values of harmonically varying quantities by real numbers to a symbolic representation of these quantities by complex numbers.
Abstract: A MATHEMATICAL theory, suitable for appraising and controlling directive properties of linear antenna arrays, can be based upon a simple modification of the usual expression for the radiation intensity of a system of radiating sources. The first step in this modification is closely analogous to the passage from the representation of instantaneous values of harmonically varying quantities by real numbers to a symbolic representation of these quantities by complex numbers. The second step consists in a substitution which identifies the radiation intensity with the norm1 of a polynomial in a complex variable. The complex variable itself represents a typical direction in space. This mathematical device permits tapping the resources of algebra and leads to a pictorial representation of the radiation intensity.
526 citations
TL;DR: In this article, a summation method for finding the magnitude and phase of the field distribution over a plane aperture which will yield an approximation to a specified polar diagram on one side of the aperture plane is described.
Abstract: A summation method, especially adapted for numerical computation, is evolved for finding the magnitude and phase of the field distribution over a plane aperture which will yield an approximation to a specified polar diagram on one side of the aperture plane. The method is illustrated with a detailed example. A concise statement of numerical procedure is given.
171 citations