DocumentCode :
1038388
Title :
On the theory of the synthesis of single and dual offset shaped reflector antennas
Author :
Galindo-israel, Victor ; Imbriale, William A. ; Mittra, Raj
Author_Institution :
California Institute of Technology, Pasadena, CA, USA
Volume :
35
Issue :
8
fYear :
1987
fDate :
8/1/1987 12:00:00 AM
Firstpage :
887
Lastpage :
896
Abstract :
Since Kinber (Radio Technika and Engineering-1963) and Galindo (IEEE Trans. Antennas Propagat.-1963/1964) developed the solution to the circular symmetric dual shaped synthesis problem, the question of existence (and of uniqueness) for offset dual (or single) shaped synthesis has been a point of controversy. Many researchers thought that the exact offset solutions may not exist. Later, Galindo-Israel and Mittra (IEEE Trans. Antennas Propagat.-1979) and others formulated the problem exactly and obtained excellent and numerically efficient but approximate solutions. Using a technique similar to that first developed by Schruben for the single reflector problem (Journal of the Optical Society-1973), Brickell and Westcott (Proc. Institute of Electrical Engineering-1981) developed a Monge-Ampere (MA) second-order nonlinear partial differential equation for the dual reflector problem. They solved an elliptic form of this equation by a technique introduced by Rall (1979) which iterates, by a Newton method, a finite difference linearized MA equation. The elliptic character requires a set of finite difference equations to be developed and solved iteratively. Existence still remained in question. Although the second-order MA equation developed by Schruben is elliptic, the first-order equations from which the MA equation is derived can be integrated progressively (e.g., as for an initial condition problem such as for hyperbolic equations) a noniterative and usually more rapid type solution. In this paper, we have solved, numerically, the first-order equations. Exact solutions are thus obtained by progressive integration. Furthermore, we have concluded that not only does an exact solution exist, but an infinite set of such solutions exists. These conclusions are inferred, in part, from numerical results.
Keywords :
Nonlinear equations; Offset reflector antennas; Partial differential equations; Reflector antennas, offset; Antenna theory; Antennas and propagation; Difference equations; Finite difference methods; Newton method; Nonlinear equations; Nonlinear optics; Optical propagation; Partial differential equations; Reflector antennas;
fLanguage :
English
Journal_Title :
Antennas and Propagation, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-926X
Type :
jour
DOI :
10.1109/TAP.1987.1144200
Filename :
1144200
Link To Document :
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