Novel Gaussian beam method for the rapid analysis of largereflector antennas

A relatively fast and simple method utilizing Gaussian beams (GBs) is developed which requires only a few seconds on a workstation to compute the near/far fields of electrically large reflector antennas when they are illuminated by a feed with a known radiation pattern. This GB technique is fast, because it completely avoids any numerical integration on the large reflector surface which is required in the conventional physical optics (PO) analysis of such antennas and which could take several hours on a workstation. Specifically, the known feed radiation field is represented by a set of relatively few, rotationally symmetric GBs that are launched radially out from the feed plane and with almost identical interbeam angular spacing. These GBs strike the reflector surface from where they are reflected, and also diffracted by the reflector edge; the expressions for the fields reflected and diffracted by the reflector illuminated with a general astigmatic incident GB from an arbitrary direction (but not close to grazing on the reflector) have been developed in Chou and Pathak (1997) and utilized in this work. Numerical results are presented to illustrate the versatility, accuracy, and efficiency of this GB method when it is used for analyzing general offset parabolic reflectors with a single feed or an array feed, as well as for analyzing nonparabolic reflectors such as those described by ellipsoidal and even general shaped surfaces     

A study of three techniques used in the diffraction analysis ofshaped dual-reflector antennas

An examination is presented of three techniques used for the efficient computation of fields diffracted by a subreflector that has been shaped by geometrical optics synthesis. It is found that these techniques, which are based on the geometrical theory of diffraction (GTD), produce errors in the computed fields that are specific to shaped reflectors. These errors are examined for a reflector system shaped to produce maximum gain from a tapered feed illumination. The discrepancies are directly related to the caustic being located near an observation point of the GTD calculations. The errors found are localized, and they increase in magnitude as the caustic approaches the main reflector. In a general offset geometry, the location of the caustic may be located arbitrarily close to the main reflector given a prescribed output aperture distribution. For the specific case considered here-the common situation of shaping to produce maximum gain-the caustic is located near the edge of the main reflector and on the reflection shadow boundary. A local correction is derived which creates a uniform solution through the caustic and across the reflection shadow boundary. Away from this point the calculation recedes to the standard GTD solution     

Cross polarizing effects of a water film on a parabolic reflector at microwave frequencies

The cross polarizing effects introduced by a uniform water film on the surface of a parabolic reflector are evaluated at 10 and 34 GHz. The reflector is considered to be illuminated by an isotropic linearly polarized source at the focus, but the analysis can be applied for any given primary feed aperture field distribution. The aperture cress polarized field is obtained, and a worst case diffraction field (when opposite quadrants of the reflector are wet) is then calculated. A relatively low level cross polarizing effect is predicted, dependent on diameter-to-focal-length ratio.     

Dual parabolic cylindrical reflectors employed as a compact range

Compact ranges using dual parabolic cylindrical reflectors are investigated, and the dependence of the aperture field on the feed pattern and system geometrical parameters is studied. A uniformity factor is defined to indicate the aperture field uniformity and the significance of the diffracted fields is explored. Offset configurations are also considered and studied. It is shown that their feed location and orientation can be optimized to minimize the geometrical-optics cross polarization. The effects of offset angle on the edge diffraction and aperture shape are also studied     

A generalized diffraction synthesis technique for high performancereflector antennas

Stringent requirements on reflector antenna performances in modern applications such as direct broadcast satellite (DBS) communications, radar systems, and radio astronomy have demanded the development of sophisticated synthesis techniques. Presented in the paper is a generalized diffraction synthesis technique for single- and dual-reflector antennas fed by either a single feed or an array feed. High versatility and accuracy are achieved by combining optimization procedures and diffraction analysis such as physical optics (PO) and physical theory of diffraction (PTD). With this technique, one may simultaneously shape the reflector surfaces and adjust the positions, orientations, and excitations of an arbitrarily configured array feed to produce the specified radiation characteristics such as high directivity, contoured patterns, and low sidelobe levels, etc. The shaped reflectors are represented by a set of orthogonal global expansion functions (the Jacobi-Fourier expansion), and are characterized by smooth surfaces, well-defined (superquadric) circumferences, and continuous surface derivatives. The sample applications of contoured beam antenna designs and reflector surface distortion compensation are given to illustrate the effectiveness of this diffraction synthesis technique     

Some important geometrical features of conic-section-generated offset refelector antennas

Geometrical characteristics of conic-section-generated offset reflectors are studied in a unified fashion. Some unique geometrical features of the reflector rim constructed from the intersection of the reflector surface and a cone or cylinder are explored in detail. It is found that the intersection curve (rim) of the rotationally generated conic-section reflector surface and a circular cone with its tip at the focal point is always a planar curve and has a circular projection on the focal plane only for the offset parabolic reflector. Furthermore, in this case, the line going through the center of the circle, parallel to the focal axis, and the central axis of the cone do not intersect the reflector surface at the same point. Numerical results are presented to demonstrate some unique features of offset parabolic reflectors.     

Experimental verification of the analysis of umbrella parabolic reflectors

Gored umbrella parabolic reflectors with symmetric aperture illumination have been treated analytically in a recent paper. This communication extends the analysis to the case where the primary feed illumination is not symmetric, because real primary feeds usually have unequalE- andH-plane beamwidths. The gore loss and the shift in the defocusing curve obtained using the modified gain expression are in excellent agreement with values measured for a smooth parabolic reflector and a gore parabolic reflector of the same diameter.     

A comparison between GO/aperture-field and physical-optics methods of offset reflectors

Both geometrical optics (GO)/aperture-field and physical-optics (PO) methods are used extensively in the diffraction analysis of offset parabolic and dual reflectors. An analytical/numerical comparative study is performed to demonstrate the limitations of the GO/aperture-field method for accurately predicting the sidelobe and null positions and levels. In particular, it is shown that for offset parabolic reflectors and for feeds located at the focal point, the predicted far-field patterns (amplitude) by the GO/aperture-field method will always be symmetric even in the offset plane. This, of course, is inaccurate fur the general case and it is shown that the physical-optics method can result in asymmetric patterns for cases in which the feed is located at the focal point. Representative numerical data are presented and a comparison is made with available measured data.     

Compact range reflector analysis using the plane wave spectrumapproach with an adjustable sampling rate

An improved method for determining the test zone field of compact range reflectors is presented. The plane wave spectrum (PWS) approach is used to obtain the test zone field from knowledge of the reflector aperture field distribution. The method is particularly well suited to the analysis of reflectors with a linearly serrated rim for reduced edge diffraction. Computation of the PWS of the reflector aperture field is facilitated by a closed-form expression for the Fourier transform of a polygonal window function. Inverse transformation in the test zone region is accomplished using a fast Fourier transform (FFT) algorithm with a properly adjusted sampling rate (which is a function of both the reflector size and the distance from the reflector). The method is validated by comparison with results obtained using surface current and aperture field integration techniques. The performance of several serrated reflectors is evaluated in order to observe the effects of edge diffraction on the test zone fields     

Accurate numerical modeling of the TARA reflector system

The radiation pattern of the large parabolic reflectors of the Transportable Atmospheric RAdar system (TARA), developed at Delft University of Technology, has been accurately simulated. The electric field integral equation (EFIE) formulation has been applied to a model of the reflectors including the feed housing and supporting struts, discretised using the method of moments. Because the problem is electrically large (the reflector has a diameter of 33/spl lambda/) and nonsymmetrical, this lead to a badly conditioned linear system of approximately half a million unknowns. In order to solve this system, an iterative solver (generalized minimum residual method) was used, in combination with the multilevel fast multipole method. Because of the bad conditioning, the system could only be solved by using a huge preconditioner. A new block-incomplete LU preconditioner (ILU) algorithm has been employed to allow for efficient out-of-computer core memory preconditioning.     

Reflector materials for two‐dimensional low‐concentrating photovoltaic systems: the effect of specular versus diffuse reflectance on the module efficiency

Photovoltaic modules in two‐dimensional low‐concentrating systems with specular parabolic reflectors often experience high local irradiance that causes high local currents and cell temperatures. This generally results in power losses. The use of low‐angle scattering reflectors gives a smoother irradiance distribution, which results in a higher fill factor. In order to study how the choice of reflector material influences system performance, two different reflector materials (anodised aluminium and lacquered rolled aluminium laminated on a plastic substrate) were compared. The total and diffuse reflectance spectra of the reflector materials were measured, the integrated hemispherical and specular solar reflectance values calculated, and the angular distributions of scattered light investigated. Two geometrically identical 3× concentrating photovoltaic systems with semi‐parabolic over edge reflectors of the different materials were tested outdoors. While the anodised aluminium reflector, which had higher hemispherical and specular solar reflectance, resulted in a higher short‐circuit current, the low‐angle scattering lacquered foil gave a higher fill factor, due to a smoother image of the sun on the module surface, and an equally high calculated annual electricity production. Given its low price, the latter reflector should thus be more cost‐effective in low‐concentrating photovoltaic systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Focal shifts in parabolic reflectors

Given a parabolic reflector, the maximum directivity is not always achieved by placing the feed at the focal point. Depending on the nature of the feed, the maximum directivity can be obtained by axially displacing the feed either toward or away from the reflector. For low-tapered feeds, the shift should be toward the reflector. This result is similar to an optical phenomenon called the focal shift. We find that this positive shift depends mainly on the Fresnel number of the reflector. For highly tapered feeds, the shift should be away from the reflector. This negative shift becomes significant when the reflector aperture is small, in units of wavelength. A unified view is presented to explain both the positive shift and the negative shift in terms of spillover, aperture illumination efficiency and phase asynchronism. For a system with optimum aperture edge taper, no focal shift can exist.     

Diffraction corrections to the cylindrical wave radiated by a linear array feed of a cylindrical reflector antenna

A phase-steered linear array feed for a parabolic cylindrical reflector antenna is considered. The nearly cylindrical wave radiated from this line feed in the Fresnel zone is expressed in terms of the isolated-element pattern. The correction to this wave due to diffraction from the endpoints of the line feed and from the grating formed by the array elements is also derived.     

Back-to-Back Reflector Antennas With Reduced Moment of Inertia for Spacecraft Spinning Platforms

A back-to-back reflector antenna system with reduced moment of inertia is proposed in order to address the demanding problem of supporting large reflector antennas on spinning platforms. The configuration provides additional potential advantages, such as reducing the spinning speed by half for a given sampling rate when both back-to-back reflectors are utilized. Geometrical parameters of the reflector are determined such that the moment of inertia of the rotating system is reduced. It is shown that these back-to-back reflectors suffer from a high cross-pol level in the asymmetrical plane due to the large feed offset angle. Two different methods are explored to alleviate the high cross-pol level problem. In the first method, a sub reflector is utilized to minimize the cross-pol level by satisfying the Mizugutchi condition. In the second method, a tri-mode matched feed horn is suggested to achieve a similar result. The suppressed cross-pol level puts forward the gravitationally balanced back-to-back reflector antenna systems as a potential candidate for future spacecraft antennas on spinning platforms.     

Parametric study of the crosspolarisation efficiency of parabolic reflectors

The crosspolarisation efficiency of a reflector antenna is the ratio between the peak crosspolarisation from the complete antenna to that from the feed. The results of a parametric study into this factor for parabolic reflectors fed by a mathematical model of a common class of feeds are presented, and it is concluded that the efficiency is typically ?4 to ?6 dB.     

Aperture efficiency and line feed phase center of parabolic cylindrical reflector antenna

Formulas for calculation of the aperture efficiency of a parabolic cylindrical reflector antenna fed by a line feed along the focal line are presented. The efficiency is factorized into a number of subefficiencies which include contributions from line feed end diffraction, and from blockage and reflections from line feed supports and from diffraction by gaps in the reflector surface. One of the subefficiencies is used to define a phase center for the line feed as well as to obtain a formula for calculating it.     

Optimum corner reflectors for calibration of imaging radars

Trihedral corner reflectors are widely used as calibration targets for imaging radars because of their large radar cross section (RCS) and extremely wide RCS pattern. An important source of uncertainty in the RCS of a trihedral sitting on a ground plane is the coherent interaction of the ground plane with the trihedral. At UHF and low microwave frequencies the large physical size of corner reflectors become a limiting factor in regard to difficulties in field deployment and deviation of their RCS from the expected values. In this paper, a general class of corner reflectors with high-aperture efficiency referred to as self-illuminating corner reflectors, is introduced whose coherent interaction with the surrounding terrain is minimized and their total surface area is two-thirds of that of a triangular corner reflector having the same maximum RCS. Analytical expressions based on geometrical optics and a new numerical solution based on near-field physical optics for the RCS of two simple self-illuminating corner reflectors are presented and compared with backscatter measurements. Also the panel geometry for an optimum corner reflector which has the shortest edge length among polygonal self-illuminating corner reflectors is obtained. High-aperture efficiency is achieved at the expense of azimuth and elevation beamwidth. It is shown that the 1-dB RCS beamwidths of the optimal corner reflectors, both in azimuth and elevation directions, are about 16°. RCS measurements of corner reflectors in the presence of a ground plane show that the RCS of self-illuminating corner reflectors are less affected by the coherent ground interaction     

Scanning properties of large dual-shaped offset and symmetricreflector antennas

The scanning properties of shaped reflectors, both offset and circularly symmetric, are examined and compared to conic section scanning characteristics. Scanning of the pencil beam is obtained by lateral and axial translation of a single point source feed. The feed is kept pointed toward the center of the subreflector. The effects of power spillover and aperture phase error as a function beam scanning are examined for several different types of large reflector design including dual-offset, circularly symmetric large f/D, and smaller f/D dual reflector antenna system. It is shown that the Abbe-sine condition for improved scanning of an optical system cannot, inherently, be satisfied in a dual-shaped reflector system that is shaped for high gain and low feed spillover. The gain loss, with scanning, of a high-gain shaped reflector pair is demonstrated to be due to both aperture phase error loss and power spillover loss