# Relationship Between Base Frequency of the Koch-Type Wire Dipole and Various Dimensions

01 Sep 2020-pp 1-6

TL;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%.

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##### References

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TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.

Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.

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Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

24,199 citations

### "Relationship Between Base Frequency..." refers background in this paper

...Minkowski dimension Firstly, let us consider the Minkowski dimension DM [27]....

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TL;DR: The most up-to-date resource available on antenna theory and design as mentioned in this paper provides an extended 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 applicationsComputer 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

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### "Relationship Between Base Frequency..." refers background in this paper

...INTRODUCTION Wire antennas of various types are widely used in modern telecommunication systems [1]....

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TL;DR: In this article, the fractal dimension of the set of points (t, f(t)) forming the graph of a function f defined on the unit interval was measured using a self-similarity property.

1,825 citations

### Additional excerpts

...Higuchi dimension Now let us consider the Higuchi dimension DH [30]....

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