Fractal Array Antenna Research

The origin of fractal can be traced back to the famous Wierestrass function and 3-part Cantor set, etc. in the late nineteenth century. The word fractal is created by French American mathematician B.B.Mandelbrot in 1975. Fractal geometry, which studies the content of the self-similarity on the graphics and the fractional dimension on the number. Fractal geometry, combining with classic electromagnetic theory, has produced the fractal antenna system theory. The so-called fractal antenna is the antenna with geometric properties of the self-similarity and fractal dimension. Fractal antenna includes two aspects:fractal element antennas and fractal antenna array. Fractal antenna array also includes two aspects:one is fractal unit arranged in regular arrays and the other is common antenna arranged in fractal arrays. Fractal antenna has preserved the original characteristics of the fractal images, and it has a strong space-filling nature. Some fractal antennas are also adapt to the development and the application of the miniature antenna technology. Compared with common antenna, fractal antenna has more advantages. It has characteristics of multi-band and broadband, especially similar radiation characteristics when working in multiple frequency bands. Some of the fractal antennas have a strong capacity of space-filling to make the antenna radiation characteristics remain basically unchanged as well as a shorter size, which can also minimize the equipment size. Fractal antenna also has a certain visual effect in appearance, and it has played a role in both the antenna and decoration, generally applied in indoor coverage.Firstly, the basic knowledge of fractal geometry theory is briefly introduced in this paper, and then it describes the characteristics of fractal geometry, the generation method of classification and fractal graph as well as the dimension calculation of a simple fractal graph. The common fractal antennas are summarized:Koch fractal antenna, Sierpinski fractal antenna, Hilbert fractal antenna, Peano fractal antenna, Minkowski fractal antenna, Sierpinski fractal carpet, Crown fractal antenna, Koch Island, the Mandelbrot fractal tree antenna and equiangular spiral antenna. This paper focuses on the fractal array antenna. This paper focuses on the concentric ring fractal array of the low side lobe characteristics in fractal antenna arrays. According to different generators, the concentric ring fractal array can be divided into the linear array, the plane triangular array, the flat square array and the hexagonal array. Meanwhile, the array distribution and radiation properties are studied and the array pattern is given. In addition, the paper also describes the linear Cantor array, planar Sierpinski array, Weierstrass fractal array and Peano-Gosper fractal array. Finally, the fractal array antennas are designed. With the helical antenna and a V-shaped plate antenna as a unit antenna and the second-order hexagon as the array, the antennas are integrated and simulated and get the low side-lobe characteristics.