Numerical analysis of small parabolic antennas using the method of current and change integral equations

The method of current and charge integral equations [1] is applied to numerical electrodynamic analysis of radiation and impedance matching characteristics of parabolic antennas with reflector diameter from 0.5 to 10λ. As a result as opposed to the current method relying on physical optics approximation the influence of feed on reflector’s radiation pattern, the influence of reflector on feed’s impedance matching and the contribution of feed’s rear radiation into reflector’s radiation pattern are all accounted for. A new model of representing a parabolic surface in the form of its square approximation is suggested, which provides almost uniform partitioning grid and has at least 2.5 times less boundary elements that the common revolution surface representation while having the same sampling coefficient. Dependences of antenna’s directivity on reflector dimensions (0.5–10λ) are calculated for six different focus distance to reflector’s diameter ratios using the developed by the authors crystal_U software package. The calculated results are confirmed by good matching with well-known experimental results.     

On the accuracy of physical optics

The first-order correction to the physical optics (PO) solution for the axial radiation field from parabolic reflector antennas is found. The correction is of orderk^{-1}and is in quadrature with the PO solution. By means of the correction term the accuracy of the PO surface integral is round to be better than0.22(lambda/D)^{2}dB on axis, whereDis the diameter of the reflector. Thus, the PO solution for the directivity is extremely accurate for commun reflector sizes of several wavelengthslambda.     

Théorie asymptotique de la diffraction en optique physique appliquée aux antennes à réflecteur

In physical optics approximation, the high frequency asymptotic analysis is used to obtain the scattered field from a given reflector. The results for a circular flat reflector are compared with numerical exact solution. The derived physical optics diffraction coefficientsare found to be numerically in good agreement with those of the geometrical theory of diffraction (GID).Transition functions are introduced in those coefficients to remove the singularities at stradow and reflection boundaries. This asymptotic analysis is generalized for reflectors of arbitrary shape. The derived formal expression of diffraction dyadic is shown to be similar to the one of GTD only for axially symmetric reflectors. In this case, the diffracted field has a simple practical formula. Results for a paraboloid reflector fed by a short dipole are compared to physical optics solution.     

Focal region fields of distorted reflectors

The problem of the focal region fields scattered by an arbitrary surface reflector under uniform plane wave illumination is solved. The physical-optics (PO) approximation is used to calculate the current induced on the reflector. The surface of the reflector is described by a number of triangular domain-wise fifth-degree bivariate polynomials. A two-dimensional Gaussian quadrature is employed to numerically evaluate the integral expressions of the scattered fields. No Fresnel or Fraunhofer approximations are made. The relation of the focal fields problem to surface compensation techniques and other applications are mentioned. Several examples of distorted parabolic reflectors are presented and discussed     

A resistive sheet approximation for mesh reflector antennas

A simplified method of estimating the equivalent surface resistance of a reflecting mesh is presented. The equivalent resistance is obtained from the approximate mesh reflection coefficients, which are based on averaged boundary conditions. This resistance approximation allows an integral equation solution for the mesh reflector that is a simple extension of that for the perfectly conducting reflector. Paraboloid radiation patterns using physical optics in conjunction with the reflection coefficients are compared to an E-field integral equation solution for a resistive surface. The agreement is excellent for low to moderate resistance values, even in the sidelobe regions     

Equivalence of surface current and aperture field integrations for reflector antennas

The "extinction theorem" is used to prove that the fields of reflector antennas determined by integration of the current on the illuminated surface of the reflector are identical to the fields determined by aperture field integration with the Kottler-Franz formulas over any surfaceS_{a}that caps the reflector. As a corollary to this equivalence theorem, the fields predicted by integration of the physical optics (PO) surface currents and the Kottler-Franz integration of the geometrical optics (GO) aperture fields onS_{a}agree to within the locally plane-wave approximation inherent in PO and GO. Moreover, within the region of accuracy of the fields predicted by PO current or GO aperture field integration, the far fields predicted by the Kottler-Franz aperture integration are closely approximated by the far fields obtained from aperture integration of the tangential electric or magnetic field alone. In particular, discrepancies in symmetry between the far fields of offset reflector antennas obtained from PO current and GO aperture field integrations disappear when the aperture of integration is chosen to cap (or nearly cap) the reflector.     

Offset parabolic reflector antennas

The paper provides a tutorial review of a number of offset parabolic reflector configurations including both single and double-reflector geometries. The author commences by describing some basic techniques which can be applied to predict the vector radiation fields and provides some indication of the validity of these methods. The formulation of a relatively simple analytical model for the offset reflector antenna is described based upon the physical-optics approximation. The electrical performance of the single-offset reflector is examined by comparison of predicted and measured data. The particular problems arising from the choice of polarisation and reflector dimensions are highlighted, and some practical applications involving multiplebeams, shaped and contoured beams, monopulse tracking and low sidelobes are briefly reviewed. Practical primary-feeds for offset-reflector antennas are discussed and the matched-feed concept is outlined, the matching of the electric fields in the primary-feed aperture to the reflector focal fields being illustrated. The advantages and disadvantages of dual-reflector antennas are then examined, with particular emphasis upon the open Cassegrainian configuration and the optimised doubleoffset configuration which offers, in principle, both freedom from blockage and low levels of cross-polarised radiation.     

Analysis and characterization of multilayered reflector antennas:rain/snow accumulation and deployable membrane

There are important engineering issues in designing reflector antennas that cannot be addressed by simply assuming a perfect electric conductor (PEC) reflector surface. For example, coatings may exist on antenna surfaces for protection, rain or snow can accumulate on outdoor reflectors, and the deployable mesh or inflatable membrane antennas usually do not have solid PEC reflector surfaces. Physical optics (PO) analysis remains the most popular method of reflector analysis owing to its inherent simplicity, accuracy, and efficiency. The conventional PO analysis is performed under the assumption of perfectly conducting reflector surface. To generalize the PO analysis to arbitrary reflector surfaces, a modified PO analysis is presented. Under the assumptions of locally planar reflector surface and locally planewave characteristic of the waves incident upon the reflector surface, the reflection and transmission coefficients at every point of the reflector surface are determined by the transmission-line analogy to the multilayered surface structure. The modified PO currents, taking into account by the finite transmissions of the incident waves, are derived from the reflection and transmission coefficients. Applications on the analyses of the rain and snow accumulation effects on the direct-broadcast TV antennas and the effects of finite thickness and finite conductivity of the metal coating on a 15-m inflatable antenna are described and results are presented     

Time-domain physical-optics

The authors extend the concept of the frequency-domain physical-optics approximation to the time domain, and use it to determine some significant properties of large reflector antennas. When this method is used to determine the equivalent surface-current density on the reflector, the effects of time-delayed mutual coupling between points on the surface are ignored. Consequently, many of the numerical limitations found in other conventional time-domain techniques are avoided, e.g. boundary-truncation error, interpolation error, numerical dispersion error, numerical instability, error accumulation with time marching, etc. More significantly, this method requires relatively small amounts of computer memory and CPU time. Several applications to the transient analysis of pulsed radar systems are given     

Finite difference analysis of electrically large parabolicreflector antennas

A reflector antenna is analyzed using the finite-difference method (FD). The induced current densities on an axially symmetric parabolic reflector are rigorously calculated. The measured equation of invariance (MEI) is used to terminate the FD mesh very close to the reflector surface. To take advantage of the axial symmetry, the theory of coupled-azimuthal potentials (CAPs) is employed. Illustrative results are obtained for reflector antennas with different aperture dimensions. Results by physical optics (PO) approximation are also included for comparison. The purpose of this paper is not to replace ray optics (RO) and PO in the design of reflector antennas, but to demonstrate the advancement in the FD method, which hitherto was limited to low-frequency and closed-boundary regime. The calculated surface current densities of a reflector antenna do show that the normal component of the current densities at the edges exhibits high standing waves which are missing in PO, and which we know should be there. The standing wave of current densities may not affect the main beam, but certainly will have an effect on side lobes and have a major impact in estimating the loss of the antenna     

A fast hybrid asymptotic and numerical physical optics analysis of very large scanning cylindrical reflectors with stacked linear array feeds

A novel hybrid combination of an analytical asymptotic high-frequency method with a numerical physical optics (PO) procedure is developed to efficiently and accurately predict the far zone fields of extremely long, scanning, very high gain, offset cylindrical reflectors of arbitrary cross-section, with large stacked finite periodic linear phased array feeds, for spaceborne applications. In this method, the field generated by each finite length linear feed array is represented as a spectral integral and the induced current on the cylindrical reflector surface due to this illumination is obtained via the PO approximation. The reflector surface is divided into thin, long, piecewise planar strips along the generator of the cylindrical reflector, and the radiation integral over each strip is evaluated asymptotically in closed form, yielding an eight-term ray solution for the radiated fields. What remains is simply the superposition of the contributions of each strip and linear array in the feed stack. The proposed approach is shown to be extremely efficient and accurate as compared to the conventional PO integration technique. In addition, the method is sufficiently versatile to account for the reflector edge treatments (e.g., using resistive cards), as well as to account for a twist in the reflector surface due to thermal distortions in space.     

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。     

长条形空间反射镜组件轻量化结构设计

针对某700 mm×249 mm长条形空间反射镜组件结构设计要求,对反射镜及其支撑结构进行了详细的光机结构设计。首先,从反射镜材料选择、径厚比、支撑方案及轻量化形式等角度出发,对反射镜进行结构设计。通过理论计算得到长条形反射镜的支撑点数。对支撑点位进行了优化,并探索了支撑孔位对反射镜自重变形的影响规律。其次,为满足反射镜组件的力、热环境适应性要求,设计了一种新型柔性支撑结构,并给出了柔性铰链薄弱环节对反射镜面形精度的影响;对支撑结构安装位置深度进行优化,给出反射镜面形精度关于支撑结构安装位置的变化曲线。然后,对反射镜组件进行了有限元分析,自重和5 ℃温升载荷工况下,反射镜面形精度峰谷（Peak Valley,PV）值和均方根（Root Mean Square,RMS）值最大分别达到58.2 nm和12.3 nm;反射镜组件一阶固有频率为259 Hz,低频正弦扫描振动条件下柔性支撑最大应力响应为138 MPa。最后,进行了动力学试验测试。测试结果表明,反射镜组件一阶固有频率为255 Hz,有限元分析误差为1.7%。分析和试验结果表明,反射镜组件结构设计合理,满足设计指标要求。     

Characterization of effects of periodic and aperiodic surface distortions on membrane reflector antennas

The focus of this paper is to characterize the effects of periodic and aperiodic surface distortions on the performance of membrane reflector antennas. Since the surface of this class of reflector antennas is very thin, it is susceptible to various types of periodic and aperiodic distortions. The particular antenna dimensions used for this study are similar to the specifications for the JPL/UCLA half scale model of second generation precipitation radar (PR-2) mission reflector. Analytical expressions are introduced to model periodic and aperiodic surfaces and based on these models the effects of distortions on the radiation performance of the antenna are simulated. Aperiodic distortions are more realistic cases of distortions due to the fact that the period of the distortions is not constant through out the reflector surface. For each case, far-field patterns of the reflector are simulated and it is shown that closed-form expressions can then be derived which result in a very efficient computational method to predict some of the unique features of these patterns including location and level of observed grating lobes. Furthermore, based on spatial Fourier analysis of the surface distortion, it is shown that deviation from periodicity in the distortions of reflector surface results in lowering these grating lobes. Parametric studies have been performed to provide design guidelines for acceptable surface behavior for large deployable membrane reflector antennas for future space borne missions.     

An imaging beam waveguide feed

A pseudo-frequency-independent beam waveguide feed has been designed and built to accommodate a new liquid-helium-cooled millimeter wave radio astronomy receiver in the side cab of the Crawford Hill 7-m antenna. This enables the antenna to be tilted without tilting the liquid-filled receiver. Comparison with the old vertex-cab feed indicates very little measured transmission loss through the beam waveguide. The frequency independence is based upon the Fresnel zone imaging principle. Design procedures and practical bandwidth limitations are explained. An explicit expression for the third-order term of an offset reflector surface clarifies the approximation of a lens by an offset reflector.     

On the theory of the synthesis of offset dual-shapedreflectors-case examples

In an earlier paper by V. Galindo-Israel et al. (see ibid., vol.AP-35, p.887-96, August 1987) the geometrical optics (GO) principles, constraints, and requirements of the dual- and single-offset-shaped reflector synthesis problem were collected and developed into a set of nonlinear first-order partial differential equations (PDEs). Methods of solving these PDEs numerically were illustrated, as were certain problems that may arise. An extension of the methods by which solutions to the PDEs can be obtained is presented, together with several case examples. These examples are independently analyzed by GO and physical optics diffraction methods. The starting point for the integration over each reflector can be taken on the outer rim, at the center, or at an intermediate point-the intermediate starting point being the more general case. The utility of the speed of this synthesis method is demonstrated. This makes practical the incorporation of the synthesis into a search algorithm that can optimize one or more parameters of the reflector system. As an example, the optimization of the mapping equations for low cross polarization is discussed     

Modeling of the Bistatic Electromagnetic Scattering From Sea Surfaces Covered in Oil for Microwave Applications

This paper describes the influence of oil pollution over sea surfaces on the height spectrum and the height autocorrelation function of rough surfaces. An oil slick damps the capillarity waves of the surface height spectrum and reduces the root mean square slope of the surface. These modified functions then have an influence on the radar cross section (RCS) from contaminated sea surfaces. The bistatic RCS of the contaminated sea surface is then presented by comparison with a clean sea: results from a benchmark numerical model are presented and compared with a new semiempirical model using the geometric optics approximation and then the first-order smallslope approximation.     

Nonlinear operation of a planar circular-grating DBR laser

An approximate method for the analysis of the nonlinear operation of a planar circular-grating distributed Bragg reflector laser is presented. The analysis is based upon vector-wave self-consistent coupled-mode equations modified to take into account gain saturation effects. With the help of an energy theorem and threshold field approximation, an approximate formula relating small-signal gain to the output power and laser parameters is derived. The laser characteristics obtained reveal behavior of the optimal coupling strength of the Bragg reflector, which provides maximal power efficiency as a function of the laser parameters. It is also shown that the gain saturation effect provides mode selectivity in the laser structure     

Optimum beam scanning in offset single and dual reflector antennas

Optimum beam scanning in offset single reflector (paraboloid) and dual reflector (Cassegrain and Gregorian) antennas is considered. Analytical, computationally efficient solutions and results are presented for the optimum feed position, the constant beam direction feed loci, and the optimum feed position locus. Examples are presented to verify that the analysis technique yields the optimum feed position, which exhibits better gain, pattern symmetry, and sidelobe levels when compared with other feed positions producing beams scanned to the same direction. The solutions described were obtained under the ray optics approximation and a "receive mode" analysis. Although the developed method was applied to the antennas listed above, it can be easily extended to othern-reflector systems, shaped reflector antennas, lenses, and other similar systems.