Frequency independent features of self-similar fractal antennas

One of the fundamental properties of classical frequency independent antennas is their ability to retain the same shape under certain scaling transformations. More recently, it has been demonstrated that this self-similar property is also shared by many fractals. The framework for a more general theoretical treatment of frequency-independent antennas is established in this paper. This generalization of frequency-independent antenna theory is accomplished by removing the restrictions imposed by a past reliance on classical Euclidean geometry in favor of adopting a more modern fractal geometric interpretation. Of particular interest in this paper is the application of this new theory of self-similar fractal radiators to the development of a multiband linear array design methodology for which the directive gain is a log-periodic function of frequency.