Performance Characteristics of the Minkowski Curve Fractal Antenna

Abstract
The performance properties of the Minkowski curve fractal antenna have been investigated and compared with the performance properties of the traditional straight-wire dipole. Numerical simulations were done using NEC4 which is moment-method based software. Results of radiation pattern, voltage standing wave ratio, input impedance, gain, and half power beamwidth are provided. The results show that the self similarity properties of the fractal shapes are translated into its multiband behavior. It is concluded that the Minkowski curve fractal can be used to achieve miniaturization in antenna systems while maintening the radiation properties of the traditional straight-wire dipole. Thus this fractal antenna is likely to have a very promising future in portable device applications.
Key words: fractal antennas; Minkowski curves; small antennas; iterated function system.

I. Introduction
One of the prevailing trends in modern wireless mobile devices is a continuing decrease in physical size. In addition, as integration of multiple wireless technologies becomes possible, the wireless device will operate at multiple frequency bands. A reduction in physical size and multiband capability are thus important design requirements for antennas in future wireless devices. The geometry of the fractal antenna encourages its study both as a multiband solution [1-5] and also as a small physical size antenna [6-10]. First, because one should expect a self-similar antenna, which contains many copies of itself at several scales, to operate in a similar way at several wavelengths. That is, the antenna should keep similar radiation parameters through several bands. Second, because fractals are space filling contours, meaning electrically large features can be efficiently packed into small areas.
The first application of fractals to antenna design was thinned fractal linear and planar arrays [11-15], i.e, arranging the elements in a fractal pattern to reduce the number of elements in the array and obtain wideband arrays or multiband performance. Cohen [6] was the first to develop an antenna element using the concept of fractals. He demonstrated that the concept of fractal could be used to significantly reduce the antenna size without degenerating the performance. Puente et al. [4] demonstrated the multiband capability of fractals by studying the behavior of the Sierpinski monopole and dipole. The Sierpinski monopole displayed a similar behavior at several bands for both the input return loss and radiation pattern. Other fractals have also been explored to obtain small size and multiband antennas such as the Hilbert curve fractal [16], the Minkowski island fractal [9], and the Koch fractal [17]. The majority of this paper will be focused upon the Minkowski curve fractal antenna and comparing its performance characteristics with those of the half-waveleng