Genetic optimization of sparse, frequency invariant arrays using the HCR principle

The Hohlfeld-Cohen-Rumsey (HCR) principle describes the necessary and sufficient conditions for all frequency independent antennas, in terms of the fractal scaling properties of a radiating configuration and the symmetries obeyed by the source currents required by Maxwell´s equations. By illustration, we explicitly apply the HCR principle to the design of a frequency independent planar array covering a frequency range of 2.5:1. A genetic algorithm was used to optimally place the array elements within the template subarray, minimizing the height of sidelobes relative to the main lobe. The symmetry constraints embodied in the HCR principle lead to an efficient genome in the genetic algorithm so that more efficient optimization is obtained. Beam patterns are seen to be invariant across the passband, showing the practical use of the HCR principle in a wideband array. This methodology constitutes a general approach to design of frequency independent phased arrays.