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Fractal constructions of linear and planar arrays

Since the pioneering work of Mandelbrot (1977) and others, fractal applications have appeared in many branches of engineering and science. This paper focuses on the application of fractal geometric concepts to the analysis and design of thinned fractal linear as well as planar arrays. There are many applications where it is advantageous to apply thinning techniques to the design of antenna arrays (Lo, 1988). In this paper, we approach thinning with the sole purpose of arranging the elements in a fractal pattern to investigate the usefulness of fractal array designs. In particular, the multiscaling of the fractal makes them attractive for wideband applications. Another advantage of these fractal arrays is that the self-similarity in their geometrical structure may be exploited in order to develop algorithms for rapid computation of radiation patterns. These algorithms are based on convenient product representations for the array factors and are much quicker to calculate than the discrete Fourier transform approach. Results for both the Canter linear array and the Sierpinski carpet planar array are presented.