D.P. Tabakov – Ph. D. (Phys.-Math.), Associate Professor, Volga State University of Telecommunications and Informatics (Samara)
Fractal (lat. Fractus – crushed, broken) – geometric figure with the property of self-similarity, that is composed of several parts, each of which is similar to the whole figure is entirely. In mathematics, a set of fractals understand points in Euclidean space with a fractional metric dimension (in the sense of Minkowski or Hausdorff) or metric dimension different from topological. Many objects in nature have fractal properties, such as the coast, clouds, the trees, snowflakes, blood circulatory system and the system of alveoli in humans or animals.
Currently, developers of technical means, following the experience of nature, designing antenna systems using fractal self-similarity principle. An example is the Sierpinski fractal antenna synthesized through five iterations, its characteristics are logarithmic in five bands.
It is quite evident the fact that the complexity of the geometry of fractal antennas makes it nearly impossible to empirical analysis, because the presence of a large number of bends and closely spaced interacting elements significantly affect the current distribution, and it is difficult to approve which character it has. Also complicates the analysis of the secondary antenna characteristics such as directivity pattern and input impedance. Therefore, a correct analysis of such structures is only possible on the basis of rigorous electrodynamic methods.
This article describes a procedure for model constructing of two thin-wire dipoles: fractal vibrator based on the Sierpinski triangle and broadband vibrator with similar dimensions shoulders. Electrodynamic analysis of structures was done using the corresponding integral representations of the electromagnetic field. Calculated normalized directivity pattern vibrators at multiple frequencies. The results are compared with the same diagrams for models based on finite elements. It is shown that fractal vibrator has the property of repeatability directivity characteristics in contrast to the broadband vibrator. It is found that the type of original item, based on which the construction of the fractal dipole significantly affects the shape of the directivity characteristic. Largest difference for directivity characteristics of the developed models to the models based on finite elements is observed in the high frequency region.
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