Title :
The Peano-Gosper fractal array
Author :
Werner, Douglas H. ; Kuhirun, Waroth ; Werner, Pingjuan L.
Author_Institution :
Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA, USA
Abstract :
This paper investigates the radiation characteristics of a new type of array that is based on the family of space-filling and self-avoiding fractals known as Peano-Gosper curves. The elements of the fractal array are uniformly distributed along a Peano-Gosper curve, which leads to a planar array configuration with parallelogram cells that is bounded by a closed Koch curve. These unique properties are exploited in order to develop a design methodology for deterministic arrays that have no grating lobes even when the minimum spacing between elements is increased to at least one wavelength. This leads to a class of arrays that are relatively broad-band when compared to more conventional periodic planar arrays with square or rectangular cells and regular boundary contours. An efficient iterative procedure for calculating the radiation patterns of these Peano-Gosper fractal arrays to arbitrary stage of growth P is also introduced in this paper.
Keywords :
antenna arrays; antenna radiation patterns; broadband antennas; fractals; iterative methods; Peano-Gosper curves; Peano-Gosper fractal array; broad-band; closed Koch curve; deterministic arrays; iterative procedure; minimum spacing; parallelogram cells; planar array configuration; radiation characteristics; self-avoiding fractals; space-filling fractals; Antenna radiation patterns; Antenna theory; Array signal processing; Design methodology; Fractals; Genetic algorithms; Gratings; Phased arrays; Planar arrays; Robustness;
Journal_Title :
Antennas and Propagation, IEEE Transactions on
DOI :
10.1109/TAP.2003.815411