On the sharpness of a needle [electromagnetic propagation]

In a recent paper [Oct. 2003], Van Bladel discussed in detail the behavior of fields and surface charges near singularities of metallic structures, such as a hollow circular cylinder, a circular cone, a thin prolate spheroid, and a uniformly charged segment. At times, the reasoning in [Van Bladel, Oct. 2003] leads to conclusions not as definitive as one might wish because of the various approximations introduced, such as the electrostatic limit for the field or idealized singularities for the conductors (e.g., the tip of a cone). In this work, an example is provided that may assist in shedding some light on the questions raised in [Van Bladel, Oct. 2003], because it consists of an exact, closed-form, simple solution to a boundary-value problem that is valid at all frequencies. The problem consists of a plane wave propagating in free space and axially incident on the convex side of a paraboloid of revolution. This problem was solved by Schensted [1955] for a perfectly conducting (PEC) paraboloid, and by Roy and Uslenghi [Oct. 1997] for an isorefractive paraboloid, which comprises the PEC paraboloid as a particular case. A remarkable fact is that these exact solutions are also the geometrical optics solutions.     

GTD analysis of near-field and far-field patterns of a parabolic subreflector illuminated by a plane wave

A geometrical theory of diffraction (GTD) analysis of the principal plane far-field and near-field patterns of a near-field Cassegrainian subreflector is presented. The uniform geometrical theory of diffraction (UGTD) [1] that drastically reduces the computation time has been utilized to analyze the subreflector in the form of a paraboloid illuminated by a plane wave. The numerical computations of the far-field amplitude and phase patterns of a typical paraboloidal subreflector based on the above technique correlate well with the results obtained by physical optics current integration, justifying the validity of the analysis presented. The GTD near-field analysis presented here is an improvement over that published earlier [2] and removes some of its limitations.     

基于最小二乘法的天线变形反射面的拟合

面天线变形反射面表达式的确立是计算其电性能的重要基础 ,提出的拟合方法就是用来精确确定变形反射面的数学方程的。其基本原理是通过分析天线结构 ,根据反射面节点位移 ,最小化整个曲面上采样型值点的轴向误差的均方根 ,从而求出用来确定变形抛物面几何位置的 6个参数 ,同时也就得到了基于最小二乘法的变形反射面方程。该拟合方法简单实用 ,易于程序实现 ,能够对天线机械结构设计人员提供了理论指导与帮助。     

New grids for improved polarization diplexing of microwaves in reflector antennas

Grids of thin wires are mounted between a paraboloid and a microwave feed at its focus, so as to obtain linear polarization everywhere in the far-field of the paraboloid. Three types of grids are proposed: 1) a family of hyperbolae on an arbitrary planeS, 2) projections of these hyperbolae on an arbitrary surface, and 3) a set of straight lines that converge on a certain pointF'on a planeS. If in cases 1) and 2) a point source is placed at the focus, the resulting plane wave reflected by the paraboloid will be polarized in one direction. In ease 3), there will also he a small cross-polarized component reflected by the paraboloid; the optimum choice ofF'that minimizes this undesirable component is determined. Only for certain orientations of S will the optimum choice ofF'be at infinity (in which case the grid is an ordinary parallel wire grid). A simple technique for fabricating grids on curved surfaces is also described. Using the grids discussed here, perfect (or nearly perfect, in case 3)) polarization diplexing at microwave frequencies can be achieved.     

Synthesis of offset dual shaped subreflector antennas for control of Cassegrain aperture distributions

Many existing large ground reflector antennas have been designed as Cassegrain systems-i.e., paraboloid/hyperboloid combinations. Other large ground antennas are simply paraboloid designs. Upgrading the gain of these systems to a gain comparable to that obtainable with a dual shaped reflector antenna system has been an important and costly objective of many such ground stations. A potentially economic method for such an antenna upgrade is presented herein. It involves a redesign of only the subreflector portion of a Cassegrain antenna or the introduction of a subreflector feed system for a parabaloid. A pair of offset subreflectors are synthesized which will give a controllable high gain amplitude distribution in the aperture of the large paraboloid. The synthesis method that is used is based on an approximate formulation for an offset dual shaped high gain antenna that was first presented by Galindo-Israel and Mittra in 1977. In that approximate formulation, the geometrical optics (GO) energy was scattered from a subreflector and then from a second large reflector which reflected a uniform phase distribution. In the present offset dual shaped subreflector (DSS) antenna, the second reflection is from a smaller (sub) reflector and it scatters a spherical wave that feeds a hyperboloid or feeds a large paraboloid directly. Excellent results are shown for the approximate synthesis of the DSS.     

Surface accuracy of Cassegrain antennas

For a Cassegrain antenna system, a simple and general procedure is presented for computing the effective surface root mean square (rms) and beam deviations considering primary surface distortions and relative translations and rotations of the antenna components. It is shown that certain primary reflector distortions can be compensated for by an appropriate adjustment of the subreflector position. Different methods in use for calculating surface rms are reviewed. It is shown that the method in which the deformed configuration of the primary reflector is best fitted with another paraboloid yields a surface rms almost equal to that obtained by the optimal positioning of the antenna components. The actual deformation patterns of several large Cassegrain antenna systems with different structural concepts are reviewed. It is shown that for a class of antenna structures, the gain can be significantly improved by an optimal positioning of the subreflector.     

Derivation and application of the equivalent paraboloid forclassical offset Cassegrain and Gregorian antennas

The equivalent paraboloid is derived for classical offset Cassegrain and Gregorian antennas. The important practical case of systems with circular exit apertures is discussed in detail, and a condition for a symmetric equivalent paraboloid is derived. For such systems, diffraction effects are investigated using tapered and scanned feeds to illuminate the equivalent paraboloid and the two-reflector system     

An improved recursive LMS algorithm using a modified gradient filter

The purpose of this letter is to discuss the application of a modified gradient filtering technique proposed by Friedlander [1] to the modified recursive least mean square (RLMS) algorithm of Hsia [2].     

La synthèse d’antennes à deux réflecteurs conformés à alimentation décalée

A potentially economic method for upgrading the gain of the large earth reflector antenna Cassegrain system to a gain comparable to that obtainable with a dualshaped reflector antenna system is presented herein. It involves a redesign of only the subreflector portion of a Cassegrain antenna or the introduction of a subreflector feed system for a paraboloid. A pair of offset subreflectors are synthesized which will give a controllable high gain amplitude distribution in the aperture of the large paraboloid. The synthesis method that is used is based on an approximate formulation for an offset dual shaped high gain antenna where the geometrical optics energy was scattered from a subreflector and then from a second large reflector which reflected a uniform phase distribution. In the present offset dual shaped subreflector (DSS) antenna, the second reflection is from a smaller subreflector and it scatters a spherical wave that feeds a hyperboloid or feeds a large paraboloid directly. Excellent results are shown for the approximate synthesis of the DSS.     

GTD analysis of the radiation patterns of a prime focus paraboloid with shroud

The uniform geometrical theory of diffraction (UGTD) is employed to analyze the far-field radiation patterns of a prime focus paraboloid with a cylindrical shroud. The blockage of the aperture illumination of the dish by the gooseneck and the primary feed is also taken into account in the analysis. Far-field radiation patterns (for0degleqTheta leq 180deg), calculated for a typical prime focus paraboloid with 2 m aperture diameter, designed and fabricated, are compared with the experimentally derived patterns at 8.8 GHz in theE- andH-planes. There is a satisfactory agreement between the two results.     

圆锥和抛物面天线的风荷载及变形特征分析

简述了研究雷达天线风荷载和变形特性所用的测试仪器、测试方法及数据处理。给出了抛物面及圆锥形两种雷达天线的主要研究结果，结果表明对于所研究的构形圆锥天线的阻力和方位力矩系数分别的为圆抛物面天线的1.34倍和4.0倍，而最大弹性变形量却仅为圆抛物面天线的75%，文中对上述两种雷达天线全然不同的风荷载及变形特性作了初步分析。     

任意空间位置雷达天线反射面拟合与评定技术

为测定空间一任意放置的抛物面形状的天线反射面及其形变量，提出了基于天线表面离散点坐标进行抛物面拟合及其误差评定的方法。论述了运用Jacobi变换方法来处理系数相关性问题，并探讨了将通用系数形式转化为标准旋转抛物面方程的方法，从而求得抛物面在空间的位置、方向和大小。阐述了一种新颖的基于迭代思想的抛物面误差评定方法。实验结果表明该方法拟合精度可达0．1％，适用性广。     

An efficient technique for the computation of vector secondary patterns of offset paraboloid reflectors

A series approach for the rapid computation of the vector secondary pattern of offset paraboloid reflectors wherein the feed is displaced is presented. We show that the Jacobi polynomial series method, which has been demonstrated to provide an efficient means for evaluating the radiation integral of symmetric paraboloid reflectors, can be extended to the case of an offset paraboloid without compromising the ease or speed of computation. The analysis leading to the series formula is also useful for deriving an analytic expression for the optimum scan plane for the displacement of the feed. Representative numerical results illustrating the application of the method and the properties of the offset paraboloid are presented.     

Cross entropy, dissimilarity measures, and characterizations of quadratic entropy

A unified approach is given for constructing cross entropy and dissimilarity measures between probability distributions, based on a given entropy function or a diversity measure. Special properties of quadratic entropy introduced by Rao [7] are described. In particular it is shown that the square root of the Jensen difference (dissimilarity measure) arising out of a quadratic entropy provides a metric on a probability space. Several characterizations of quadratic entropy are obtained.     

Coaxial feeds for high aperture efficiency and low spillover of paraboloidal reflector antennas

Coaxial feeds produce an approximate sector-shaped pattern, an almost optimum pattern of a feed for high aperture efficiency and low spillover of paraboloid antennas. Such a coaxial feed consists of a central circular waveguide which is surrounded by one or more conductors with circular cross sections. Theoretical and experimental investigations on coaxial feeds excited by H11modes have shown that the first ring yields the highest increase in the aperture efficiency of paraboloid antennas illuminated by them. Measurements performed on paraboloid antennas illuminated by a coaxial feed with only one ring yielded aperture efficiencies of 68 to 75 percent for angular apertures of the paraboloidal reflector of100degto160deg. Circularly symmetric patterns in conjunction with almost linearly polarized aperture fields can be achieved by multimode coaxial feeds. The values for the aperture efficiency, which are calculated for paraboloid antennas illuminated by multimode coaxial feeds, nearly reach the theoretical optimum. The measured values are 68 to 80 percent. In addition, the multimode feeds produce very little cross polarization.     

Pattern analysis of paraboloids fed by rectangular waveguides employing multipole expansion techniques

A multipole expansion technqiue is developed for calculating the co-polar and cross-polar radiation patterns of a prime-focus paraboloid fed by a dominant-mode rectangular waveguide feed. Initially, the feed radiation pattern is expressed in terms of electric and magnetic multipoles of different orders which are subsequently used to obtain the secondary radiation patterns (co-polar and cross-polar) in explicit closed form in the form of a rapid by a converging algebraic series. The validity of the analysis is effectively demonstrated by calculating the co-polar and cross-polar patterns of a typical paraboloid and comparing and results with calculations based on the direct numerical integration of the physical optics currents induced on the reflector surface.     

破片损伤对天线方向图的影响

利用电磁场分析软件FEKO,研究了抛物面天线在破片穿孔时天线方向图的变化规律。通过对物理光学法（PO）和物理绕射理论（PTD）的混合使用,对战损后抛物面天线的电气性能进行了建模与分析,以比较反射面损坏前后对天线方向图的影响。着重研究了天线反射面毁伤后,毁伤孔数、孔径及其位置变化对方向图的影响。     

一种L波段背射模螺旋馈源

螺旋天线具有较好的宽频带圆极化特性,在L或S波段体积和增益都很适中,加工制造公差要求较低,因此在该频段螺旋天线得到了广泛的应用。由背射模螺旋构成的L波段宽带馈源具有结构简单,馈电、调试方便,口面遮挡小,频带宽(大于25%),可以承受大功率等优点,可以满足L或S波段测控系统对天线的要求。用该背射模螺旋馈源研制的前馈天线的口径效率超过了53%,第一副瓣小于-20 dB,在工程中得到了很好的应用。     

Remarks on the concept of equivalent parabolas for Cassegrain antennas

In Cassegrain antennas, the whole focusing system is usually replaced by an equivalent paraboloid of focal length mf, where f is the focal length of the paraboloid and m is the magnification of the Cassegrain system. Here, it is shown that this equivalent paraboloid is useful only for feeds near the Cassegrainian focus. The discussion of series expansions of the phase in the system aperture yields severe differences between the Cassegrain system and the prime focus-fed equivalent paraboloid for larger radial or axial defocusing.     

GTD analysis of the near-field patterns of a prime-focus symmetric paraboloidal reflector antenna

The uniform geometrical theory of diffraction (UGTD) has been applied successfully to analyze the near-field patterns of a prime-focus paraboloid. In order to establish the validity of the analysis, near-field amplitude and phase patterns have been computed over the principal planes at several observation distances for a typical prime-focus paraboloid. These calculations compare very favorably with the corresponding results obtained numerically with the aid of Silver's near-field aperture integration formula.