Degrees of Freedom and Synthetic Functions in the Analysis of Large Antennas
Abstract
The Synthetic Function Expansion (SFX) method reduces the complexity of the MoM analysis of antenna and scattering problems by dividing the overall structure into portions, recognizing that the degrees of freedom of the field coupling between the solution on these portions are limited, and building basis that exploit this property. THE AGGREGATE-FUNCTION PARADIGM This work belongs to a class of methods that end up in reducing the actual size of the final algebraic problem associated with the Method-of-Moment (MoM) analysis of antennas and scatterers. These methods can in turn be divided into two major classes: those employing basis of higher polynomial order and with larger spatial support, and those that group basis (typically of low polynomial order) into functions defined over portions of the structure that are significantly larger than one cell of the initial mesh. The present method belongs to the second class. A large part of the functions approaches can be traced back to the so-called diakoptic approach (1, and references therein), originally developed for structures that are naturally or artificially broken down in sub-structures interconnected by ports. One (or two) are introduced per each port, that are essentially the solution of the sub-structure in isolation, and these are used to compact the MoM matrix. In order to reach convergence and/or accuracy, one or more iterations are employed, in which the interactions between the various regions of definition of the macro-basis are included. Various versions exists of the technique, with improvements of the above basic idea, e.g. (1), (2). Finally, it is noted that a recent addition to this list is the powerful characteristic basis function (CBF) technique outlined in (3). Another starting point in generating aggregate for electrically large structures is based on asymp- totic (high-frequency) solutions; an example of this approach is described in (4) for large and finite periodic arrays; similar constructs have been employed in (5). In the past years these authors have likewise worked on a reduced-complexity strategy, employing a few, global unknowns defined on different portions of the structure, with different strategies in the generation and use of these global basis (6, 7, 8). It can be observed that the underlying question behind the aggregate-function quest is what is the number of degrees of freedom of the solution we are looking for on each portion, and the implicit assumption that this number should be much smaller than the number of basis involved in discretizing the problem in the conventional way. In the present paper, this question is addressed explicitly from the offstart, and the problem of representing the unknown field quantities is accordingly phrased.