There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Recent efforts by several researchers around the world to combine fractal geometry with electromagnetic theory have led to a plethora of new and innovative antenna designs. In this report, we provide a comprehensive overview of recent developments in the rapidly growing field of fractal antenna engineering. Fractal antenna engineering research has been primarily focused in two areas: the first deals with the analysis and design of fractal antenna elements, and the second concerns the application of fractal concepts to the design of antenna arrays. Fractals have no characteristic size, and are generally composed of many copies of themselves at different scales. These unique properties of fractals have been exploited in order to develop a new class of antenna-element designs that are multi-band and/or compact in size. On the other hand, fractal arrays are a subset of thinned arrays, and have been shown to possess several highly desirable properties, including multi-band performance, low sidelobe levels, and the ability to develop rapid beamforming algorithms based on the recursive nature of fractals. Fractal elements and arrays are also ideal candidates for use in reconfigurable systems. Finally, we provide a brief summary of recent work in the related area of fractal frequency-selective surfaces.

An overview of fractal antenna engineering research

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

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Fractal design concepts for stretchable electronics

The multiband behavior of the fractal Sierpinski (1915) antenna is described. Due to its mainly triangular shape, the antenna is compared to the well-known single-band bow-tie antenna. Both experimental and numerical results show that the self-similarity properties of the fractal shape are translated into its electromagnetic behavior. A deeper physical insight on such a behavior is achieved by means of the computed current densities over the antenna surface, which also display some similarity properties through the bands.

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On the behavior of the Sierpinski multiband fractal antenna

Fractal geometry involves a recursive generating methodology that results in contours with infinitely intricate fine structures. This geometry, which has been used to model complex objects found in nature such as clouds and coastlines, has space-filling properties that can be utilized to miniaturize antennas. These contours are able to add more electrical length in less volume. In this article, we look at miniaturizing wire and patch antennas using fractals. Fractals are profoundly intricate shapes that are easy to define. It is seen that even though the mathematical foundations call for an infinitely complex structure, the complexity that is not discernible for the particular application can be truncated. For antennas, this means that we can reap the rewards of miniaturizing an antenna using fractals without paying the price of having to manufacture an infinitely complex radiator. In fact, it is shown that the required number of generating iterations, each of which adds a layer of intricacy, is only a few. A primer on the mathematical bases of fractal geometry is also given, focusing especially on the mathematical properties that apply to the analysis of antennas. Also presented is an application of these miniaturized antennas to phased arrays. It is shown how these fractal antennas can be used in tightly packed linear arrays, resulting in phased arrays that can scan to wider angles while avoiding grating lobes.

Fractal antennas: a novel antenna miniaturization technique, and applications

Experimental and computed results show a multiband behaviour over five bands for the new fractal Sierpinski antenna. Such a behaviour is based on the self-similarity properties of the antenna's fractal shape, which might open an alternative way for designing new multiband and frequency independent antennas.

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Fractal multiband antenna based on the Sierpinski gasket

A small but long wire fractal antenna based on the Koch curve is presented. Experimental and numerical results show that the antenna improves the features of a common linear monopole. The radiation resistance is increased and the Q is reduced at each fractal iteration, approaching the fundamental limit on small antennas.

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Small but long Koch fractal monopole

A multiband handset antenna combining a PIFA and multiple slots on a ground plane is presented. It is shown by means of simulations that the slots on the ground plane have a double function: to tune the ground plane resonance at low frequencies (f ? 900 MHz) and to act as parasitic radiators at high frequencies (f ? 1800 MHz). A prototype is designed and built featuring a behavior suitable for low frequencies (GSM850 and GSM900) and for high frequencies spanning from DCS1800 to Bluetooth, and including, for instance, PCS1900, UMTS2000, and other possible systems. Reflection coefficient, efficiency, and radiation patterns are measured and compared with a design without slots to prove the advantages of the slotted ground plane. The component effect is investigated to determine critical areas where the placement is not recommended. Besides, the effect of the slot of the ground plane on SAR is investigated, by discussing the effect of the ground plane and slot modes for two phone positions. The total antenna volume of the proposed design is 40 × 15 × 6 mm3.

Multiband Handset Antenna Combining a PIFA, Slots, and Ground Plane Modes

The combination of fractal geometry with electromagnetic theory opens an interesting window for research to find new antenna designs and applications Fractal technology applications can be divided into six main groups: (1) multifrequency antenna elements, frequency-selective surfaces, and arrays; (2) electrically small antennas; (3) high-directivity radiating elements; (4) low-sidelobe arrays; (5) undersampled arrays; and (6) fast computational methods This article reviews most of the work done in the fractal technology field covering the last six fields


Keywords:

fractal;
antennas;
multifrequency;
arrays;
small antennas;
arrays;
microstrip antennas;
broadband;
high-directivity

Fractal Shaped Antennas: A Review

The constant evolution of wireless handheld devices together with the apparition of multiple wireless communication systems fosters the antenna community to design new radiating and measurements systems capable of satisfying the market demands. It is an object of the present paper to provide an overview of the evolution that wireless handheld technology has experienced in the last years. In this sense, a description of the evolution of wireless handheld devices, regulations, challenges in today’s smartphones, and handset characterization is reviewed. Finally, recent advances in antenna technology for wireless handheld or portable devices are presented.

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Carles Puente

Papers

Fractal multiband antenna based on the Sierpinski gasket

Small but long Koch fractal monopole

Multiband Handset Antenna Combining a PIFA, Slots, and Ground Plane Modes

Fractal Shaped Antennas: A Review

Advances in Antenna Technology for Wireless Handheld Devices