Generation, Application and Analysis of a Novel Family of M-Segment Quadratic Fractal Curves to Antennas

Abstract

Abstract-A novel family of fractal curves is proposed which provides the designer a systematic way of miniaturizing the microwave components with the freedom of choosing among form factor, design complexity and achieved miniaturization. The proposed fractal curve is characterized by two integer values m and n. The m value determines the form factor of the fractal while n value governs the iteration number. The equations governing the geometry of fractals are also presented. The proposed fractal is characterized for miniaturization by designing a printed monopole antenna for various values of m and n. The results from the full wave simulations and experiments are analysed and explained. The effect of fractal on reducing the resonant frequency is quantified by an equation based on its physical interpretation. Based on this analysis, saturation point for miniaturization is established. The curves being symmetric around a straight line, distortionless radiation patterns are seen.

Design and analysis of m‐segment fractal boundary antennas

“…The m-segment quadratic fractal curve has an interesting property, that different geometries could be generated at the same iteration. 5 The fractal is generated by dividing a straight line into m number of segments and then drawing two new lines at an angle of 45 such that they form a right-angled triangle with the original segment. The lines are drawn alternately around the line segments of the previous iteration.…”

“…When the total wire length is adjusted such that antennas of differing geometry are resonant at the same frequency, the antennas essentially exhibit identical electromagnetic behavior. A similar study has been done on a novel family of fractal curves characterized by two integer values, the form factor of the fractal and the iteration . The effect of fractal on reducing the resonant frequency has been quantified by an equation.…”

“…A similar study has been done on a novel family of fractal curves characterized by two integer values, the form factor of the fractal and the iteration. 5 The effect of fractal on reducing the resonant frequency has been quantified by an equation.…”