Synthesis of Offset Dual Reflector Antennas Transforming a Given Feed Illumination Pattern Into a Specified Aperture Distribution
Hyjazie, Fayez Mohamed
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https://hdl.handle.net/2142/66231
Description
Title
Synthesis of Offset Dual Reflector Antennas Transforming a Given Feed Illumination Pattern Into a Specified Aperture Distribution
Author(s)
Hyjazie, Fayez Mohamed
Issue Date
1980
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
The problem of transforming a given primary feed pattern into a desired aperture field distribution through two reflections by an offset dual reflector system is investigated using the concepts of geometrical optics. A numerically rigorous solution for the reflector surfaces is developed. The solution gives an exact aperture phase distribution and an aperture amplitude distribution accurate to within some numerical tolerance. In a previous work, Galindo, Mittra and Cha {7} have addressed the same problem and have developed an approximate solution which is constructed via a two-step process. The first step consists of generating a solution on the basis of an ad hoc assumption on the mapping function which relates the two reflector surfaces. Next, the solution, thus obtained was corrected by keeping only the subreflector and synthesizing a new main reflector which exactly satisfies the requirement for the aperture phase distribution (but not the amplitude condition). In our synthesis method, we derive the solution for both of the reflector surfaces in a one-step process. However, this procedure does not always yield a smooth solution; i.e., the reflector surfaces may not be continuous or their slopes may vary too rapidly. In the event of nonexistence of a numerically rigorous smooth solution, an approximate solution that enforces the smoothness of the reflector surfaces can be obtained. In the approximate solution, the requirement for the aperture amplitude distribution is relaxed and the condition on the aperture phase distribution is continued to be exactly satisfied.
In both the numerically rigorous solution and the approximate solution, the reflector surfaces are simultaneously built up point-by-point from an initial starting curve which lies on the subreflector surface. This is accomplished without requiring the reflector surfaces to have any prespecified perimeter boundaries. At this time, there is no systematic way available for choosing the starting curve such that the existence of a solution can be guaranteed. The solution thus derived is verified by performing an analysis of the secondary pattern.
Numerical results are presented illustrating the advantages of this synthesis method.
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