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

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%.