Simulation algorithms for fractal radiation

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This thesis presents a method to analyze a series of structures, referred to as fractals, that radiate electromagnetic waves. The fractal series are components of the so-called "Minkowski island", and the patterns are generated, through successive iterations, from a square patch, usually referred to as the initiator or pre-fractal. Simulation software was specifically developed for the characterization of these structures and also to create the specific geometries used in the study. Another computer tool was implemented to construct the same structures in such a way that they would meet the input format requirements of a commercially available simulation suite since it was not easy to create complex fractal geometries using the graphic interface of the commercial software. This is also an essential tool to efficiently study the impact of variations in geometrical parameters in the radiation properties. Previous analyses show that fractal structures can be employed as either stand alone radiators or elements of antenna arrays for any specific application. Results obtained through this research compare very well with those from the industry standard software, and thus the simulation tool that has been designed in his research project is validated as an accurate procedure to study fractal patch antennas. The results presented involve the return loss parameter obtained at frequencies ranging from DC to 20 GHz for a pre-fractal patch as well as for the first two iterations of the "Minkowski island" fractal derived from it. The patterns show some resonances that are shifted down in frequency (as well as a trend towards wideband operation) as the number of iterations increase, a fact that agrees with previous studies for fractal elements and allows for antenna miniaturization.