The effect of different weighting functions when using the method of moments in linear antenna analysis : a different approach

Nasr, Nagwa Hamed Mohamed (1979) The effect of different weighting functions when using the method of moments in linear antenna analysis : a different approach. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (27MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

It is the purpose of the present investigation to obtain and study mathematical expressions for the currents of a center-fed linear antenna subjected to a known incident electrical field. In the analysis process the direct solution of an integral equation for the current expression is replaced by the solution of an integral equation for a certain intermediate function. This method which is discussed by Walsh²⁷⁻³⁰ eliminates the need for applying boundary conditions to an integral operator. The proposed method has been examined using the moment method in conjunction with three different weighting functions for solving the integral equation and a comparative study of the results is made. A set of Walsh functions is used for the basis functions. The use of Walsh functions for weighting functions allows efficient calculations of the matrix elements, and yields accurate results for certain antenna lengths. However, for other lengths the use of cosine functions for weighting functions is found to be more efficient. The third set of weighting functions used ispiece-wise sinusoidal functions, which yields the most complicated calculations. Several examples are given to illustrate the application of the proposed method, when the moment method is used in conjunction with three different weighting functions. The method has a rate of convergence which is in general much faster than the methods used by Srivastava²⁴ and Thiele²⁵. The results obtained by Srivastava are based on the same method of analysis, with the same basis functions used in this thesis, but in conjunction with point-matching, while Thiele's results are based on solving Pocklington's equation using point-matching in conjunction with different basis functions. It is of interest to note that, the proposed method has the same flexibility as Pocklington's equation, but is better behaved numerically. Furthermore, the use of the moment method in conjunction with different weighting functions rather than using the point-matching technique, yields a smaller matrix to be inverted. In general, the results are in good agreement with the results obtained by other researchers.

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