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

  • Garnik Abgaryan Kazan Federal University
  • Dmitrii Tumakov Kazan Federal University
Keywords: Koch-type antenna, bandwidth, fraction bandwidth, lacunarity, regression analysis.


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.


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Author Biographies

Garnik Abgaryan, Kazan Federal University

Kazan Federal University

Dmitrii Tumakov, Kazan Federal University

Kazan Federal University


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How to Cite
Abgaryan, G., & Tumakov, D. (2018). Relationship between lacunarity and bandwidth of a koch-type wire antenna. Amazonia Investiga, 7(15), 88-98. Retrieved from