P.L. Werner

Fractal antenna engineering: the theory and design of fractal antenna arrays

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 approaches 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 so far are intriguing, and may have future practical applications.

Frequency-independent features of self-similar fractal antennas

A generalized approach to the study of frequency-independent antennas is presented which relies on the recently developed theory of fractal geometry. It is demonstrated that this fractal geometric interpretation allows for the ability to characterize a much wider class of frequency-independent antennas. This includes radiating structures which are self-similar in the discrete sense, the smooth sense, and even the “rough” sense. The antenna configurations in this paper are all self-similar and have been parameterized in terms of a common similarity factor of τ. Finally, it is shown how this new theory of self-similar fractal radiators may be employed to develop a multiband linear array design methodology for which the directive gain is a log-periodic function of frequency.

The design of miniature three-element stochastic Yagi-Uda arrays using particle swarm optimization

A fixed grid structure of reduced length is employed to generate three-element miniature stochastic Yagi-Uda arrays. Particle swarm optimization (PSO) is utilized to alter the shape and the element distances for optimum forward gain, good front-to-back ratio, and 2:1 or better voltage standing wave ratio (VSWR). Simulation results of PSO are compared with binary valued genetic algorithm (GA) optimized designs and with a conventional three-element Yagi-Uda array.

On the synthesis of fractal radiation patterns

The fundamental relationship between self-similar, that is, fractal, arrays and their ability to generate radiation patterns which possess fractal features is examined in this paper. The theoretical foundation and design procedures are developed for using fractal arrays to synthesize fractal radiation patterns having certain desired characteristics. A family of functions, known as generalized Weierstrass functions, are shown to play a pivotal role in the theory of fractal radiation pattern synthesis. These functions are everywhere continuous but nowhere differentiable and exhibit fractal behavior at all scales. It will be demonstrated that the array factor for a nonuniformly but symmetrically spaced linear array can be expressed in terms of a Weierstrass partial sum (band-limited Weierstrass function) for an appropriate choice of array element spacings and excitations. The resulting fractal radiation patterns from these arrays possess structure over a finite range of scales. This range of scales can be controlled by the number of elements in the array. For a fixed array geometry, the fractal dimension of the radiation pattern may be varied by changing the array current distribution. A general and highly flexible synthesis technique is introduced which is based on the theory of Fourier-Weierstrass expansions. One of the appealing attributes of this synthesis technique is that it provides the freedom to select an appropriate generating function, in addition to the dimension, for a desired fractal radiation pattern. It is shown that this synthesis procedure results in fractal arrays which are composed of a sequence of self-similar uniformly spaced linear subarrays. Finally, a synthesis technique for application to continuous line sources is presented which also makes use of Fourier-Weierstrass expansions.

Techniques for evaluating the uniform current vector potential at the isolated singularity of the cylindrical wire kernel

The cylindrical wire kernel possesses a singularity which must be properly treated in order to evaluate the uniform current vector potential. Traditionally, the singular part of the kernel is extracted resulting in a slowly varying function which is convenient for numerical integration. This paper provides some new accurate and computationally efficient methods for evaluating the remaining singular integral. It is shown that this double integral may be converted to a single integral which no longer possesses a singular integrand and consequently may be efficiently evaluated numerically. This form of the integral is independent of the restrictions involving wire length and radius which are inherent in various approximations. Also presented is a highly convergent exact series representation of the integral which is valid except in the immediate vicinity of the singularity. Finally, a new approximation is derived which is found to be an improvement over the classical thin wire approximation. It is demonstrated that each of these methods provides extremely accurate as well as efficient results for a wide range of wire radii and field point locations. >

A novel frequency agile beam scanning reconfigurable antenna

A new and novel design methodology is introduced for a frequency agile planar reconfigurable antenna capable of 360/spl deg/ beam scanning in the azimuthal plane. The versatility of the reconfigurable antenna is demonstrated through several design examples. A similar approach is then used to design a volumetric antenna which is capable of beam steering in three dimensions. Tuning of both 2D and 3D reconfigurable antenna designs is accomplished by means of variable capacitors, whose values are determined via a genetic algorithm optimization process.

Fractile arrays: a new class of tiled arrays with fractal boundaries

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 low-sidelobe arrays that is based on fractal tilings. Several examples of fractile arrays will be considered including Peano-Gosper, terdragon, 6-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.

Design synthesis of miniature multiband monopole antennas with application to ground-based and vehicular communication systems

In this letter, we present a novel design methodology for miniature multiband monopole and whip-type antennas. The miniaturization and multiband response are simultaneously achieved by placing a fixed number of thin stubs at strategic locations along the antenna. A robust genetic algorithm technique is introduced to determine the optimal lengths and locations of the stubs for a specified percent reduction in monopole length.

Genetically engineered dual-band fractal antennas

Fractal antenna engineering concepts have been successfully combined with genetic algorithms to develop a powerful design optimization tool. The genetic optimization approach developed can simultaneously optimize the geometry of a fractal antenna, locations of loads, component values of loads, and the projected length of the fractal antenna. The results suggest that a 30-55% size reduction can be achieved by optimizing the fractalization and loading of a given antenna. The knowledge gained as a result of this study is directly applicable to the design of miniature fractal antennas.

An exact formulation for the electromagnetic fields of a cylindrical antenna with a triangular current distribution

A mathematically exact formulation for the vector potential and corresponding electromagnetic fields of a triangular current cylindrical dipole are presented for the first time in this paper. These exact expressions converge rapidly in the near-field region of the antenna allowing them to be used for the efficient and accurate computational modeling of electrically short cylindrical antennas. The exact series expansion of the triangular current vector potential is shown to contain two fundamental exponential integrals and their higher-order associated integrals. Numerically stable forward recurrence relations have been derived which may be used for the efficient evaluation of these higher-order integrals in addition to the cylindrical wire kernel. These recursions may also be employed in the computation of the electric and magnetic fields. It is demonstrated that the classical thin wire forms of the vector potential and electromagnetic fields are actually special cases of the more general exact expansions. Finally, the exact formulation was used to investigate the near-field behavior of traditional thin wire as well as moderately thick wire dipoles. Several near-field plots are presented including a vector plot of the total electric field in the vicinity of a moderately thick quarter-wavelength dipole.