Rigorous analysis of electrically large reflector antennas. - Page 50 |
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33
2.4 Analysis of Three-Dimensional EFIE Using an
Electrically Large B asis Function
The work in this chapter has demonstrated the viability of using the electrically
large basis function to solve a two-dimensional EFIE. As stated in Chap. 1, three
rigorous solution techniques for electrically large reflector antennas are considered
in this dissertation, the work of this chapter being the first. Due to the success of
the third method, which is an iterative solution of the EFIE (developed in Chap. 4),
the electrically large basis function was not implemented to solve the three-dimensional
EFIE. However, issues relating to the three-dimensional
implementation of the electrically large basis function have been identified and are
now discussed.
The first issue is the non-linear equation solver. The Newton-Raphson method
was very successful in two-dimensions. This is largely in part due to the accuracy
of the starting guess via the physical optics approximation. However, the intent of
this work is to solve electrically large reflector-antenna geometries that cannot be
accurately handled using physical optics. With a poor starting guess, the Newton-
Raphson method (as well as any non-linear equation solution algorithm) can have
difficulties [25]. These difficulties stem from the fact that a system of non-linear
equations might have more than one solution. In contrast, systems of linear
equations have only one solution, allowing robust usage of iterative solution
techniques, as is done in Chap. 4. In order to successfully implement the
electrically large basis function in three-dimensions, a robust non-linear equation
solver would be required.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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| Title | Rigorous analysis of electrically large reflector antennas. - Page 50 |
| Repository email | cisadmin@lib.usc.edu |
| Full text | 33 2.4 Analysis of Three-Dimensional EFIE Using an Electrically Large B asis Function The work in this chapter has demonstrated the viability of using the electrically large basis function to solve a two-dimensional EFIE. As stated in Chap. 1, three rigorous solution techniques for electrically large reflector antennas are considered in this dissertation, the work of this chapter being the first. Due to the success of the third method, which is an iterative solution of the EFIE (developed in Chap. 4), the electrically large basis function was not implemented to solve the three-dimensional EFIE. However, issues relating to the three-dimensional implementation of the electrically large basis function have been identified and are now discussed. The first issue is the non-linear equation solver. The Newton-Raphson method was very successful in two-dimensions. This is largely in part due to the accuracy of the starting guess via the physical optics approximation. However, the intent of this work is to solve electrically large reflector-antenna geometries that cannot be accurately handled using physical optics. With a poor starting guess, the Newton- Raphson method (as well as any non-linear equation solution algorithm) can have difficulties [25]. These difficulties stem from the fact that a system of non-linear equations might have more than one solution. In contrast, systems of linear equations have only one solution, allowing robust usage of iterative solution techniques, as is done in Chap. 4. In order to successfully implement the electrically large basis function in three-dimensions, a robust non-linear equation solver would be required. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. |
