Affiliated with the
Communication & Space
Sciences Laboratory

Fractal Antenna Engineering

Fractile Arrays: A New Class of Tiled Arrays with Fractal Boundaries

A new class of antenna arrays, called fractile arrays, have been recently introduced by members of CEARL. A fractile array is defined as any array with a fractal boundary contour that tiles the plane without gaps or overlaps. It has been shown that the unique geometrical features of fractiles may be exploited in order to make available a family of deterministic arrays that offer several highly desirable performance advantages over their conventional periodic planar array counterparts. Most notably, fractile arrays have no grating lobes even when the minimum spacing between elements is increased to at least one-wavelength. This has led to the development of a new design methodology for modular broadband arrays that is based on fractal tilings. Efficient iterative procedures for calculating the radiation patterns of these fractile arrays to arbitrary stage of growth have also been developed.

Three Fudgeflakes with Fractal Boundaries Tiled Together
(please click on the image to enlarge it)


..: References :..

1-) A New Design Methodology for Modular Broadband Arrays Based on Fractal Tilings
by D. H. Werner, W. Kuhirun, and P. L. Werner
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2-) The Peano–Gosper Fractal Array
by D. H. Werner, W. Kuhirun, and P. L. Werner

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 is also introduced in this paper.




3-) A New Design Methodology for Modular Broadband Arrays Based on Fractal Tilings
by D. H. Werner, W. Kuhirun, and P. L. Werner
2003 IEEE Topical Conference on Wireless Communication Technology, Honolulu, Hawaii, October 15-17, 2003




4-) Fractile Arrays: A New Class of Broadband Tiled Arrays with Fractal Boundaries
by D. H. Werner, W. Kuhirun, and P. L. Werner
2004 IEEE International Symposium on Antennas and Propagation, Monterey, California, June 20-26.

ABSTRACT: In this paper a new class of antenna arrays are introduced, which we call fractile arrays. A fractile array is defined as any array with a fractal boundary contour that tiles the plane without gaps or overlaps. It will be shown that the unique geometrical features of fractiles may be exploited in order to make available a family of deterministic arrays that offer several highly desirable performance advantages over their conventional periodic planar array counterparts. Most notably, fractile arrays have no grating lobes even when the minimum spacing between elements is increased to at least one-wavelength. This has led to the development of a new design methodology for modular broadband arrays that is based on fractal tilings. Several examples of fractile arrays will be considered including Peano-Gosper, terdragon, six-terdragon, and fudgeflake arrays. Efficient iterative procedures for calculating the radiation patterns of these fractile arrays to arbitrary stage of growth P are also introduced in this paper.




5 -) Fractile Arrays: A New Class of Broadband Tiled Arrays with Fractal Boundaries
by D. H. Werner, W. Kuhirun, and P. L. Werner
IEEE Transactions on Antennas and Propagation




6-) Comparison of the Peano-Gosper Fractile Array and the Regular Hexagonal Array
by J. N. Bogard, D. H. Werner, and P. L. Werner
Microwave and Optical Technology Letters, Vol. 43, No. 6, pp. 524-526, Dec. 2004.

ABSTRACT: A new class of modular broadband low-sidelobe arrays, based on the theory of fractile (fractal tile) geometry, has been recently introduced. In this paper, the radiation properties of the Peano–Gosper fractile array are compared to those of the conventional square and hexagonal arrays. It is demonstrated that the Peano–Gosper array has the same desirable grating-lobe conditions as the hexagonal array, while achieving a much lower overall sidelobe level.
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7 -) Design of Broadband Planar Arrays Based on the Optimization of Aperiodic Tilings
by Thomas G. Spence, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 56, No. 1, January 2008

ABSTRACT: Antenna arrays based on aperiodic tilings have been shown to exhibit low sidelobe levels and modest bandwidths over which grating lobes are suppressed. In addition, compared to conventional periodic arrays, these arrays are naturally thinned (i.e., mean interelement spacing is greater than λ / 2). The generation of these arrays involves placing array elements at the locations of the vertices of an aperiodic tiling. To obtain a realizable design, the entire array is then scaled and truncated to achieve a desired minimum element spacing and aperture size. This paper demonstrates that it is possible to greatly extend the bandwidth of these arrays by incorporating a simple perturbation scheme into the basic array generation process. The implementation of this perturbation scheme is straightforward and it lends itself well to being combined with an optimization technique such as the genetic algorithm. It is successfully used to generate arrays that have large bandwidths (peak sidelobe level < -10 dB with no grating lobes) of up to a minimum element spacing of 5 λ . Moreover, the flexibility of this technique will be further demonstrated by introducing a slight variation of the basic scheme that is capable of generating arrays with extremely wide bandwidths. An example will be presented for an array design that has a bandwidth corresponding to a minimum element spacing of up to 11 λ .




8 -) The Pareto Optimization of Ultrawideband Polyfractal Arrays
by Joshua S. Petko, and Douglas H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 56, No. 1, January 2008

ABSTRACT: The application of global optimization techniques, such as genetic algorithms, to antenna array layouts can provide versatile design methodologies for highly directive, thinned, frequency agile, and shaped-beam antenna systems. However, these methodologies have their limitations when applied to more demanding design scenarios. Global optimizations are not well equipped to handle the large number of parameters used to describe large-N antenna arrays. To overcome this difficulty, a new class of arrays was recently introduced called polyfractal arrays that possess properties well suited for the optimization of large-N arrays. Polyfractal arrays are uniformly excited with an underlying self-similar geometrical structure that leads to aperiodic element layouts. This paper expands on polyfractal array design methodologies by applying a robust Pareto optimization technique with the goal of reducing the peak sidelobe levels at several frequencies specified over a wide bandwidth. A recursive beamforming algorithm and an autopolyploidy based mutation native to polyfractal geometries are used to dramatically accelerate the genetic algorithm optimization process. This paper also demonstrates that the properties of polyfractal arrays can be exploited to create designs that possess no grating lobes and relatively low sidelobe levels over ultrawide bandwidths. The best example discussed in this paper maintains a -15.97 dB peak sidelobe level with no grating lobes from a 0.5 λ , to more than a 20 λ minimum spacing between elements, which corresponds to at least a 40:1 bandwidth for the array.




9 -) Modular Broadband Phased-Arrays Based on a Nonuniform Distribution of Elements Along the Peano-Gosper Space-Filling Curve
by T. G. Spence, D. H. Werner and J. N. Carvajal
IEEE Transactions on Antennas and Propagation, Vol. 58, No. 2, February 2010

ABSTRACT: The Peano-Gosper space-filling curve provides an excellent framework for designing broadband planar antenna arrays with highly modular architectures. Uniformly distributing elements along the curve leads to an element distribution with a triangular lattice that has an irregular fractal boundary contour. This boundary contour allows for a modular subarray configuration and better sidelobe suppression than conventional triangular lattice arrays with a regular boundary contour. While they have a greater bandwidth than square-lattice distributions, arrays based on a triangular lattice still possess a rather limited bandwidth for beam steering applications due to the formation of gratinglobes. In this communication it will be shown that the beam steering capabilities of the Peano-Gosper array can be enhanced by introducing perturbations into the basic recursive array generation scheme. With the proper implementation, the perturbed arrays retain the attractive features of modularity and recursive beamforming that are associated with the standard Peano-Gosper array. Examples will be presented for several stages of Peano-Gosper arrays that were designed for 2:1 broadband performance while scanning within a 30° conical volume. Full-wave simulations will be used to examine the effects of mutual coupling on these aperiodic array layouts.




10 -) Generalized Space-Filling Gosper Curves and Their Application to the Design of Wideband Modular Planar Antenna Arrays
by T. G. Spence and D. H. Werner
IEEE Transactions on Antennas and Propagation, Vol. 58, No. 12, December 2010

ABSTRACT: The Peano-Gosper space-filling curve provides an excellent framework for designing planar antenna array distributions with modular architectures and suppressed sidelobes over a relatively wide bandwidth. The curve consists of a self-avoiding path that intersects a triangular lattice and its construction is based on the iterative application of a generating curve. There exist a number of other recently discovered curves, coined generalized Gosper curves, that possess properties similar to those of the Peano-Gosper curve but are based on larger and more complex generating curves. In this paper these generalized curves will be examined as the framework for antenna array layouts. It will be shown that arrays based on these curves have a number of excellent characteristics while offering modular array configurations and sizes that are not inherent to Peano-Gosper arrays. Moreover, when combined with a simple recursive-perturbation technique, the element distributions of these arrays can be efficiently adjusted to generate designs with bandwidths that far exceed that of standard periodic- and triangular-lattice arrays. The efficacy of this technique will be demonstrated through design examples, including one that has more than a 10:1 bandwidth. Full-wave simulations of a wideband patch array will also be used to investigate the effects of mutual coupling on these array distributions.




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