## Limitations of fractal antennae and Fractus’ breakthrough

When designing antennae which can emit at different frequency bands with similar radiation properties, it is crucial to be able to choose the frequency bands flexibly. For example, a dual-band mobile phone working in the mobile networks of two different countries might need to operate in two bands, e.g. 900 MHz and 1800 MHz. However, pure fractal structures do not provide sufficient flexibility for this.

Fractus’ first two patents (patent applications WO01/22528A1 and WO01/54225A1) are the basis of its technology and represent a third generation of antennae, which deviate from the ideal fractal shape to achieve flexibility in the choice of frequency ranges (multi-level antennae) and/or improve their miniaturisation properties (space-filling antennae).

In multi-level antennae (WO01/22528A1), the building elements can use the same type of polygon (or polyhedron in the case of a three-dimensional antenna) as in fractal-shaped antennae, but the aspect ratios of the elements can be different, and the antenna itself does not need to have the same shape as the building elements. As a result, these antennae allow much greater flexibility in the choice of the frequency bands in which they operate.

^{Fig. 3 a) Fractal-shaped vs. b) multi-level antenna [http://www.fractal-explorer.com/picture.php?pictitle=STri2] [WO01/22528A1]}

Space-filling antennae (WO01/54225A1) are based on the second property of fractal geometry mentioned above: compacting long paths in a small and contained area. As shown in Figure 2, fractal shapes contain or define long curves which are confined in a small area. These kinds of curves do not, however, need to underlie a self-similar fractal shape. The idea behind the concept of space-filling antennae is that at least part of the antenna has the form of a space-filling curve, said space-filling curve not necessarily having to be strictly self-similar (see Figure 4). Eliminating the requirement of the fractal shape provides much more flexibility in the design of the antenna geometry, which allows a greater reduction in the size of the antenna for a given emission frequency.

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^{Fig. 4 a) Fractal shape and underlying space-filling curve vs. b) space-filling curve not part of a fractal shape. [https://en.wikipedia.org/wiki/Sierpinski_triangle] [WO01/54225A1]}

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