INVESTIGATION OF FRACTAL ANTENNAS BASED ON SIERPINSKI NAPKIN - Научное сообщество
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INVESTIGATION OF FRACTAL ANTENNAS BASED ON SIERPINSKI NAPKIN

05.09.2022 21:06

[3. Технические науки]

Автор: Magro Valeriy Ivanovich, PhD, associate professor, Oles Honchar Dnipro National University, Dnipro; Khandak Diana Oleksiyivna, magistr, Oles Honchar Dnipro National University, Dnipro


It is known that fractal antennas are very compact and multiband and have useful applications in cellular telephone and microwave communications. The most famous fractal antennas are Serpinski's napkin, Serpinski's carpet, Koch's snowflake, Minkowski's curve. The property of self-similarity of fractal structures caused the high repeatability of their electromagnetic parameters in different frequency ranges. It is about input impedance, current density distribution, radiation pattern and other parameters of antennas. All this significantly simplifies their computer calculation and design. 

A triangular patch antenna fed by a microstrip line is chosen as the base antenna at iteration zero. An equilateral triangle made of metal (Cu) located on a dielectric substrate with a thickness of h=1.6 mm and a relative dielectric constant of ɛ=4.4 was chosen as a mathematical model of the microstrip antenna (Fig.1). A metal layer is placed on the lower side of the dielectric substrate. Mathematical modeling of the antenna is performed by the method of finite difference time domain (FDTD).

A study was conducted to select the optimal method of powering the antenna according to the criterion of the minimum reflection coefficient at the antenna input (scattering matrix parameter S11). A triangular antenna is quite effective at a resonant frequency of 7 GHz, and if the microstrip line is connected to the middle of the side. 

A study was conducted to select the optimal method of powering the antenna according to the criterion of the minimum reflection coefficient at the antenna input (scattering matrix parameter S11). A triangular antenna is quite effective at a resonant frequency of 7 GHz, and if the microstrip line is connected to the middle of the side. A good agreement between the calculation results and the data of work [1] was obtained.

It is interesting to consider this antenna in the fractal antenna model. The geometric construction of Serpinski's fractal and the coordinates of the points are made in accordance with the work [2]. Fractal antennas based on the Sierpinski napkin of the first, second and third iterations were studied. Fig. 2 shows the fractal antenna of the third iteration. 





When comparing the obtained resonant frequencies with the initial frez=7 GHz, which we take as 100%, we obtained:

• At the first stage of iteration, one resonant frequency was obtained, which is 108.9% of the initial one;

• At the second stage of iteration, two resonance frequencies were obtained, the first is 91.43% of the initial one, the second is 112% of the initial one;

• At the third stage of iteration, three resonance frequencies were obtained, the first is 85.57% of the original, the second is 107.14% of the original, the third is 136.71% of the original.

Literature

1. Priya S. K. Design and research of rectangular, circular and triangular microstrip patch antenna / S. K. Priya, J. K. Bhandari, M. K. Chaitanya // International Journal of Innovative Technology and Exploring Engineering (IJITEE). – 2019. – Vol. 8. – P. 1-2. 

2. Kaka A. O. Modified hexagonal Sierpinski gasket-based antenna design with multiband and miniaturized characteristics for UWB wireless communication / A. O. Kaka, M. Toycan // Turkish Journal of Electrical Engineering & Computer Sciences. – 2016. – Vol. 24. – P. 464-473. 




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