# Miniaturization of a Koch-Type Fractal Antenna for Wi-Fi Applications

04 Jun 2020-Vol. 4, Iss: 2, pp 25

TL;DR: In this article, the dependence of the base frequency and the reflection coefficient on the dipole wire length and scale is analyzed, and it is shown that it is possible to distinguish a family of antennas operating at a given (identical) base frequency.

Abstract: Koch-type wire dipole antennas are considered herein. In the case of a first-order prefractal, such antennas differ from a Koch-type dipole by the position of the central vertex of the dipole arm. Earlier, we investigated the dependence of the base frequency for different antenna scales for an arm in the form of a first-order prefractal. In this paper, dipoles for second-order prefractals are considered. The dependence of the base frequency and the reflection coefficient on the dipole wire length and scale is analyzed. It is shown that it is possible to distinguish a family of antennas operating at a given (identical) base frequency. The same length of a Koch-type curve can be obtained with different coordinates of the central vertex. This allows for obtaining numerous antennas with various scales and geometries of the arm. An algorithm for obtaining small antennas for Wi-Fi applications is proposed. Two antennas were obtained: an antenna with the smallest linear dimensions and a minimum antenna for a given reflection coefficient.

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01 Sep 2020TL;DR: The work’s goal is to establish the dependence of the base frequency on the dimension of the curve forming the antenna arm of the Koch type, and it is concluded that for the second and third iterations, the best correlation is a correlation between the base Frequency and the Higuchi dimension.

Abstract: A dipole wire antenna of the Koch type is considered. The antenna consists of a wire dipole with symmetrical arms with respect to the feed point with the geometry similar to the Koch prefractal. The curves forming the arms differ from the classical Koch fractal only by the position of the central vertex. The work’s goal is to establish the dependence of the base frequency on the dimension of the curve forming the antenna arm. Various dimensions as characteristics of the curve are considered. The dimensions are Minkowski dimension, information dimension, correlation dimension and Higuchi fractal dimension. The algorithm to calculate the Higuchi dimension for our curves is adapted. Also, algorithms for calculating the other dimensions are described. Relationships between the base frequency of the Koch-type wire dipole and the dimensions are explored. The correlation analysis for the first three Koch-type prefractals is carried out. The values of all correlation coefficients between the base frequency and the considered dimensions are given in the tables. It is concluded that for the second and third iterations, the best correlation is a correlation between the base frequency and the Higuchi dimension. The optimal one-parameter regression models for the base frequency in the case of the second and third iterations are constructed. The obtained regression model for the second iteration approximates the frequency values with an error of 1.17%. The model for the third iteration approximates the frequency values with an error of 1.46%.

4 citations

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01 Mar 2019TL;DR: In this paper, an optimal multiband compact modified crinkle fractal antenna is proposed on FR-4 substrate having dimension of $14.5\ \mathbf{mm} \times 1 \mathBF{mm]$, dielectric constant 4.4, and loss tangent of 0.02.

Abstract: An optimal multiband compact modified crinkle fractal antenna is proposed in this report which is designed on FR-4 substrate having dimension of $14\ \mathbf{mm} \times 12.5\ \mathbf{mm} \times 1 \mathbf{mm}$ , dielectric constant 4.4, and loss tangent of 0.02. Proposed fractal antenna is optimized using dragonfly optimization (DO) and resonates at 1.3584 GHz, 1.9925GHz, 2.5714 GHz, 4.3910 GHz, 5.1629 GHz, 5.6591 GHz, 6.2932 GHz, 7.6165 GHz, 8.3609 GHz, 9.2431 GHz, and 10.4010GHz. Proposed antenna is characterized on the basis of various performance parameters like return loss, VSWR, radiation pattern, gain and bandwidth.

2 citations

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27 Jul 2021TL;DR: In this paper, a new integral representation formula for inframonogenic functions was derived for multidimensional Ahlfors-Beurling transforms closely connected to the use of two different orthogonal basis.

Abstract: Solutions of the sandwich equation $${^\phi \!\underline{\partial }}[f]{^\psi \!\underline{\partial }}=0$$
, where $${^\phi \!\underline{\partial }}$$
stands for the Dirac operator with respect to a structural set $$\phi $$
, are referred to as $$(\phi ,\psi )$$
-inframonogenic functions and capture the standard inframonogenic ones as special case. We derive a new integral representation formula for such functions as well as for multidimensional Ahlfors–Beurling transforms closely connected to the use of two different orthogonal basis in $${{\mathbb {R}}}^m$$
. Moreover, we also establish sufficient conditions for the solvability of a jump problem for the system $${^\phi \!\underline{\partial }}[f]{^\psi \!\underline{\partial }}=0$$
in domains with fractal boundary.

2 citations

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TL;DR: In this article, a Cauchy integral formula for holomorphic and hyperholomorphic functions in domains bounded by a Koch snowflake in two-and three-dimensional setting is derived.

Abstract: In this paper we derive a Cauchy integral formula for holomorphic and hyperholomorphic functions in domains bounded by a Koch snowflake in two- and three-dimensional setting.

2 citations

### Cites background from "Miniaturization of a Koch-Type Frac..."

...This important structure is not only relevant from a mathematical point of view, but also has important applications in engineering and is widely used in modern telecommunication systems [7, 8, 9]....

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##### References

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16 Mar 1990

TL;DR: In this article, a mathematical background of Hausdorff measure and dimension alternative definitions of dimension techniques for calculating dimensions local structure of fractals projections of fractality products of fractal intersections of fractalities.

Abstract: Part I Foundations: mathematical background Hausdorff measure and dimension alternative definitions of dimension techniques for calculating dimensions local structure of fractals projections of fractals products of fractals intersections of fractals. Part II Applications and examples: fractals defined by transformations examples from number theory graphs of functions examples from pure mathematics dynamical systems iteration of complex functions-Julia sets random fractals Brownian motion and Brownian surfaces multifractal measures physical applications.

6,325 citations

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01 Jul 19845,335 citations

### "Miniaturization of a Koch-Type Frac..." refers background or methods in this paper

...Wire antennas are widely used in modern telecommunication systems [1]....

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...In practice, various forms of broken balanced dipoles are used [1,8,9]....

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01 Jan 2005

TL;DR: The most up-to-date resource available on antenna theory and design is the IEEE 802.11 as mentioned in this paper, which provides detailed coverage of ABET design procedures and equations, making meeting ABET requirements easy and preparing readers for authentic situations in industry.

Abstract: The most-up-to-date resource available on antenna theory and design. Expanded coverage of design procedures and equations makes meeting ABET design requirements easy and prepares readers for authentic situations in industry. New coverage of microstrip antennas exposes readers to information vital to a wide variety of practical applications.Computer programs at end of each chapter and the accompanying disk assist in problem solving, design projects and data plotting.-- Includes updated material on moment methods, radar cross section, mutual impedances, aperture and horn antennas, and antenna measurements.-- Outstanding 3-dimensional illustrations help readers visualize the entire antenna radiation pattern.

2,907 citations

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TL;DR: Fractal geometry involves a recursive generating methodology that results in contours with infinitely intricate fine structures, which can be used to miniaturize wire and patch antennas using fractals as mentioned in this paper.

Abstract: 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.

724 citations

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TL;DR: In this article, the behavior of the small fractal Koch monopole is numerically and experimentally analyzed, and it is shown that as the number of iterations on the small Koch monopoles are increased, the Q of the antenna approaches the fundamental limit for small antennas.

Abstract: Fractal objects have some unique geometrical properties. One of them is the possibility to enclose in a finite area an infinitely long curve. The resulting curve is highly convoluted being nowhere differentiable. One such curve is the Koch curve. In this paper, the behavior the Koch monopole is numerically and experimentally analyzed. The results show that as the number of iterations on the small fractal Koch monopole are increased, the Q of the antenna approaches the fundamental limit for small antennas.

457 citations

### "Miniaturization of a Koch-Type Frac..." refers background in this paper

...A sufficient number of works have been devoted to the study and analysis of the base characteristics of both the Koch dipole and monopole [17,18], as well as its various modifications [19–21]....

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