Self-Similarity and the Geometric Requirements for Frequency Independence in Antennae

Self-similarity and origin symmetry are shown to be the key geometric constraints in the determination of frequency independent properties of antennae. Fractal antennae with origin symmetry meet these criteria of the extended version of Rumsey's principle. Frequency independence is not achieved by self-similarity alone. Self-complementarity plays no role in frequency independence, but does aid in smoothing out impedance variations for coarsely iterated frequency independent antennae. New families of practical designs arise from these geometric insights, which need not follow the usual constraints of angle-defined structure of the original Rumsey's principle.