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Relationship between lacunarity and bandwidth of a koch-type wire antenna

31 Aug 2018-Vol. 7, Iss: 15, pp 88-98
TL;DR: In this article, a dipole wire antenna of the Koch type is considered and a correlation analysis is provided with a correlation of bandwidth as well as relative bandwidth with lacunarity.
Abstract: A dipole wire antenna of the Koch type is considered. The antenna represents a wire dipole symmetrical with respect to the point of feeding. Arms of the dipole have a geometry similar to Koch's pre-fractal. The curves forming the arms differ from the classical Koch fractal only by the position of the central vertex. A family of antennas is singled out, in which the antennas differ from each other by coordinates of the central vertices. An algorithm for calculating lacunarity is described. A correlation analysis is provided with a correlation of bandwidth as well as relative bandwidth with lacunarity. Antennas having the geometry of the first three iterations of a Koch-type curve are chosen for the analysis. The calculated correlation coefficients are given in the tables. It is shown that increasing the iteration leads to a decrease in the correlation between the selected parameters. It is obtained that the correlation coefficients for the relative bandwidth are smaller than those for the bandwidth. Single-parameter regression models for the bandwidth and the relative bandwidth are constructed. The root-mean-square errors for the models are calculated. The proposed regression formulas can be used to design broadband wire antennas.
Citations
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Journal ArticleDOI
04 Jun 2020
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.

14 citations


Cites background from "Relationship between lacunarity and..."

  • ...It can be noted that if the goal is to simulate a broadband antenna, then in the present study it is necessary to add a model for the bandwidth [40]....

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References
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Journal ArticleDOI
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


"Relationship between lacunarity and..." refers background in this paper

  • ...But the most common way to minimize or improve the given properties of antennas is their fractalization (Gianvittorio and Rahmat-Samii, 2002; Baker and Iskander, 2015; Karpukov et al, 2002; Wagh, 2015; Krzysztofik, 2013; Beigi and Mohammadi, 2016)....

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Journal ArticleDOI
TL;DR: Lacunarity analysis is broadly applicable to many data sets used in the natural sciences; it is illustrated its application to both geological and ecological data.
Abstract: Lacunarity analysis is a multiscaled method for describing patterns of spatial dispersion. It can be used with both binary and quantitative data in one, two, and three dimensions. Although originally developed for fractal objects, the method is more general and can be readily used to describe nonfractal and multifractal patterns. Lacunarity analysis is broadly applicable to many data sets used in the natural sciences; we illustrate its application to both geological and ecological data. {copyright} {ital 1996 The American Physical Society.}

522 citations


"Relationship between lacunarity and..." refers methods in this paper

  • ...The computer algorithm Gliding Box usually relies on the representation of a given set in the form of a matrix of pixels (Plotnick et al, 1996)....

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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: The calculus of deterministic fractal functions is introduced in this article, which can be explicitly indefinitely integrated any number of times, yielding a hierarchy of successively smoother interpolation functions which generalize splines and which are attractors for iterated function systems.

237 citations


"Relationship between lacunarity and..." refers methods in this paper

  • ...As is known, the fractal Koch curve can be constructed using the following iterative scheme (Barnsley and Harrington, 1989): 𝑲𝟎 = [𝟎, 𝟏], 𝑲𝒏 = ⋃ 𝑨𝒊(𝑲𝒏−𝟏) 𝟒 𝒊=𝟏 , 𝑲 = 𝐥𝐢𝐦 𝒏→∞ 𝑲𝒏, (1) where 𝐴𝑖, 𝑖 = 1....

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  • ...As is known, the fractal Koch curve can be constructed using the following iterative scheme (Barnsley and Harrington, 1989):...

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Journal ArticleDOI
TL;DR: In this paper, the design of Log Periodic Fractal Koch Antennas (LPFKA) is proposed for UHF band applications, and the procedure to design the LPFKA with three different numbers of iterations to reduce the antenna size is discussed.
Abstract: In this paper, the design of Log Periodic Fractal Koch Antennas (LPFKA) is proposed for Ultra High Frequency (UHF) band applications. The procedure to design the LPFKA with three different numbers of iterations in order to reduce the antenna size is discussed. The Computer Simulation Technology (CST) software has been used to analyze the performances of the designed antennas such as return loss, radiation patterns, current distribution and gain. The antennas have been fabricated using FR4 laminate board with wet etching technique. Using fractal Koch technique, the size of the antenna can be reduced up to 27% when the series iteration is applied to the antennas without degrading the overall performances. Both simulated and measured results are compared, analyzed and presented in this paper.

92 citations