jamesbond 2007-9-7 15:57
Optimization Methods in Electromagnetic Radiation【T.S.Angell,A.Kirsch】
[Name] Optimization methods in electromagnetic radiation
[Author] Thomas S. Angell, Andreas Kirsch
[Publisher] Springer-Verlag New York, Inc.
[Key Words] Electromagnetic, Radiation
[Briefing]
It is impossible to make this single volume self-contained. Our choice is to present introductory material about antennas, together with some elementary examples in the introductory chapter. That discussion may then serve as a motivation for a more wide-ranging analysis. On the other hand, in order to continue with the flow of ideas, we have chosen to place a summary of the mathematical tools that we will use in the Appendix. That background material may be consulted from time to time as the reader may find necessary and convenient.
The chapter which follows gives some basic information about Maxwell’s equations and the asymptotic behavior of solutions which is then used in Chapter 3. There we formulate a general class of optimization problems with radiated fields generated by bounded sources. Most importantly, we give several different measures of antenna performance related to the desired behavior of the radiated fields far from the antenna itself. These cost functionals are related to various properties of this far field and we discuss, in particular, their continuity properties which are of central importance to the problems of optimization.
In the fourth chapter, we concentrate on one particular problem, the synthesis problem mentioned earlier, and on its resolution. Since the problem is ill-posed, we give there a brief discussion of the mathematical nature of this class of problems.
The following two chapters then discuss, respectively, the boundary value problems for the two-dimensional Helmholtz equation, particularly important for treating TE and TM modes, and for the three-dimensional time-harmonic Maxwell equations. Our discussion, in both instances, includes some background in the numerical treatment of those boundary value problems.
Chapter 7, which together with Chapter 8 forms the central part of our presentation, contains the analysis of various optimization problems for specific examples based on the general framework that we constructed in Chapter 3. It is our belief that, while the traditional antenna literature analyzes the various concrete antenna structures somewhat independently, emphasizing the specific properties of each, a more over-arching approach can guide our understanding of the entire class of problems. In any specific application it is inevitable that there will come a time when the very particular details of the physical nature of the antenna will need to addressed in order to complete the design. That being said, the general analytical techniques we study here are applicable to antennas whether they take the form of a planar array of patches or of a line source on the curvilinear surface of the wing of an aircraft. For some of the standard (and simplest) examples, we include a numerical treatment which, quite naturally, will depend on the specifics of the antenna; a curvilinear line source will demand numerical treatment different from an array of radiating dipoles.
In the final chapter, Chapter 8, we address optimization problems arising when (as is most often the case) there is a need to optimize antenna performance with respect to two or more, often conflicting, measures. To give a simple example, there is often a desire to produce both a focused main beam and to minimize the electromagnetic energy trapped close to the antenna itself e.g, to maximize both directivity and gain simultaneously. In such a situation, the end result of such an analysis is a “design curve” which concretely represents the trade-offs that a design engineer must make if the design is to be in some sense optimal.
