Theoretical analysis of a fractal surface radiation

We compare, in this paper, the far field radiated by two fractal distributions of current. The first one is obtained by a fractal cut following the Cantor arrangement, the second one keeps the length of each previous current element, but modifies the distance between the elements which is now taken as a constant. We establish the analytical formulations of the far field at any step n of the Cantor set. Then, we extract the array factor and we analyse and compare the following properties : convergence of the radiation pattern, wide of the main lobe, side lobes level and directivity.