Affiliated with the
Communication & Space
Sciences Laboratory

Fractal Antenna Engineering

Generalized Self-Scalable/Similar Fractal Arrays

A schematic representation for a recursively generated thinned hexagonal array. The first four stages of growth are indicated by the blue (Stage 1), red (Stage 2), green (Stage 3), and orange (Stage 4) arrays respectively. The six-element generating sub-array is shown in the upper-right-hand corner, where the elements are located at the vertices of the hexagon.
Contour plots of the radiation patterns for Stage 1 through Stage 4 of the recursively
generated thinned hexagonal arrays shown in the previous figure.

..: References :..

1-) Generalized Self-Scalable and Self-Similar Fractal Arrays
by D.H. Werner and P.L. Werner

2-) Fractal Antenna Engineering: Theory and Design of Fractal Antenna Arrays
by D.H. Werner, R. L. Haupt and P.L. Werner

ABSTRACT: A fractal is a recursively generated object having a fractional dimension. Many objects, including antennas, can be designed using the recursive nature of a fractal. In this article, we provide a comprehensive overview of recent developments in the field of fractal antenna engineering, with particular emphasis placed on the theory and design of fractal arrays. We introduce some important properties of fractal arrays, including the frequency-independent multi-band characteristics, schemes for realizing low-sidelobe designs, systematic approach to thinning, and the ability to develop rapid beam-forming algorithms by exploiting the recursive nature of fractals. These arrays have fractional dimensions that are found from the generating subarray used to recursively create the fractal array. Our research is in its infancy, but the results do far are intriguing, and may have future practical applications.

3-) A General Class of Self-Scalable and Self-Similar Arrays
by D. H. Werner and P. L. Werner
1999 IEEE International Symposium on Antennas and Propagation. Orlando, Florida, July 11-16.

ABSTRACT: A rich class of fractal and related arrays exist which can be formed recursively through the repetitive application of a generating array. A generating array is a small array at scale one P=1) used to recursively construct larger arrays at higher scales (i.e., P>1). In many cases the generating array has elements that are turned on and off in a certain pattern. A set formula for copying, scaling, and translating of the generating array is then followed in order to produce a family of higher order arrays. Hence, arrays which are created in this manner will be composed of a sequence of self-scalable or, in some cases, self-similar arrays.

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