Electromagnetic Field Computation by Network Methods

Electromagnetic field computations in either man-made or natural complex struc- tures pose challenging problems with respect to electromagnetic wave propagation modeling, microwave circuit and antenna design, electromagnetic compatibility issues, high bit rate and ultra-wide band communications, biological hazards and numerous other problems. Since different problems exhibit specific combi- nations of geometrical features and scales, material properties and frequency ranges no single method is best suited for handling all possible cases: instead, a combination of methods is needed to attain the greatest flexibility and efficiency. Naturally, with progress of computing facilities, the main focus has shifted from analytical computations to numerical ones. However, in many instances, the com- putations are performed in order to design a certain component, such as an an- tenna or a filter. Dealing with design and optimization problems requires not only the modeling of a given structure but also the evaluation of the sensitivities to parameter changes. In these cases it is worthwhile to attain the highest numerical efficiency in order to be competitive. The present scenario witnesses the use of several different methods that, apart for a few noticeable exceptions, are not merged together. Clearly, from the efficiency point of view it would be desirable to solve the problem at hand in the most efficient way, thus subdividing the computational space in various subregions and by employing in each subregion the most satisfactory approach. Moreover, while the above procedure has been followed in several specific contributions, it is also important that the sought approach can be systematically employed for all cases. Of particular relevance are the rigorous treatment of the field at boundaries and the appropriate field representations inside bounded or unbounded regions. The common ground which allows to achieve solutions that are rigorous, preserve energy conservation, and that can unify different methods, is the use of network theory, i.e. a rigorous translation of our field problem into an equivalent network problem. In particular the field at boundaries can be rigorously represented by using the Tellegen theorem for fields, which provides the generalized transformer network representation. In fact, a boundary can be seen as a region of zero volume in which no energy is stored neither dissipated, exactly as in a transformer. A region of finite volume, instead, when lossless can be seen as a resonator and its behavior may be described in terms of its resonances. Also, field propagation in an infinite region can be described in terms of spherical transmission lines, which provide an infinite, discrete, set of modes traveling along the radial direction. Such scenario, to our knowledge, has not been presented systematically in a bookand, in our humble opinion, deserve instead some considerations. The aim of this book is therefore to illustrate with some detail how it is possible to describe whatever realistic electromagnetic field problem in terms of network elements, i.e. generalized transformers, RLC elements and transmission lines.