Fractal’ term was first coined by Benoit Mandelbrot in 1983 to classify the structure whose dimensions were not whole numbers. One of the properties of fractals geometry is that it can have an infinite length while fitting in a finite volume. The radiation characteristic of any electromagnetic radiator depends on electrical length of the structure. Using the property of fractal geometry, we may increase the electrical length of an antenna, keeping the volume of antenna same. There are an infinite number of possible geometries that are available to try as a design of fractal antenna.
One of the important benefits of fractal antenna is that we get more than one resonant band. The fractal concept can be used to reduce antenna size, such as the Koch dipole, Koch monopole, Koch loop, and Minkowski loop. Or, it can be used to achieve multiple bandwidth and increase bandwidth of each single band due to the self-similarity in the geometry, such as the Sierpinski dipole, Cantor slot patch, and fractal tree dipole.
The Simplest example of antenna using fractal geometry is given by the Von Koch, researcher. The method of creating this shape is to repeatedly replace each line segment with the following 4 line segments. The process starts with a single line segment and continues for ever. The first few iterations of this procedure are shown in below figure. Fractal dimension contains information about the self-similarity and the space-filling properties.
There are many ongoing efforts to develop low profile and wideband antennas such as frequency independent antennas using Fractal. One fundamental property of classical frequency independent antennas is their ability to retain the same shape under certain scaling transformations, which is the self-similar property shared by many fractals.
Hilbert Curves Fractal Antenna
I design Hilbert Curves Fractal Antenna that use the co-planar wave guide feed. The first few iterations of Hilbert curves are shown below fig. This geometry is a space-Filling curve.
Simulation Result ( FDTD Solver)