Starting points

After a number of years at the University of Illinois, in 1994 Carles Puente Baliarda joined the Universitat Politècnica de Catalunya (UPC) as Assistant Professor to continue his research on fractal-shaped antennae. Puente Baliarda very quickly became aware of the potential of this technology from a commercial point of view, and in 1995, while still at the UPC, he decided to file a patent application with the Spanish Patent Office. This application led to the first patent for a fractal antenna worldwide (ES2112163B1). A second Spanish patent (ES2142280B1) followed in 1998.

Together with Rubén Bonet, in 1999 he co-founded Fractus, S.A. as a spin-off from the UPC. With a Master’s in business administration from IESE Business School, Bonet provided the ideal complement to Puente Baliarda’s research background. In the same year, Fractus filed a patent application (WO01/22528A1) for a multi-level antenna which led to several patents worldwide, including the USA and Europe. A patent application for space-filling antennae (WO01/54225A1) followed in 2000. These patents became a third-generation evolution of the original fractal-shaped antennae, overcoming certain technical limitations caused by the pure fractal shape, and making them ripe for commercial application.

Soon Fractus had its first contract to develop a dual-band fractal antenna capable of operating on a second-generation (2G) cellular network. The antenna was compact enough to be built into a phone’s body and operate within the two major digital systems used across Europe: the Global System for Mobile Communications (GSM) standard, developed by the European Telecommunications Standards Institute for use in the European Union, and the Digital Cellular Service (DCS) for use in the United Kingdom.

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Technical Background

The frequency range at which an antenna emits is proportional to its size, while the radiation properties of the antenna (e.g. the direction in which it emits) are determined by its geometrical shape.


  • GSM (2G) mobile phones  (approx. 00 MHz) → typical length: 7,5 cm
  • Radio FM antennae (approx. 90 MHz) → typical length: 0,75 m

For this reason, short and stubby antennae were a fixture on early mobile phones, visibly protruding several centimetres from the phones’ bodies – a limiting factor for slimming down the size and shape of the first generation of mobile phones.

A fractal is a mathematical concept which can be used to describe a structure which is self-similar, meaning that the structure is formed by repetitions of its geometrical shape at smaller scales. Thanks to this property, fractal structures allow multiple long paths to be compacted in a small and contained area.

Fig. 1: Repetition of triangle at smaller scales (Sierpinski triangle with 7 scales). []

Fig. 2 Long paths in a small and contained area (Sierpinski triangle). []

From the antenna theory point of view, repetition of its geometrical shape at different scales would imply the same radiation properties at different frequencies, and compacting long paths in a small and contained area would reduce the size of the antenna for a given frequency range. By using these two properties of fractals, Puente Baliarda found that it was possible to design antennae which could be used to operate at different frequency ranges and would be small enough to fit into the body of a mobile phone without sacrificing function.

Last modified: Monday, 31 July 2017, 3:20 PM