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The performance properties of several electrically small, self-resonant fractal antennas (ESFA) are compared as a function of their total wire length, geometry, and effective volume. The radiation properties considered include resonant frequency, radiation resistance, and quality factor. It is shown that the resonant properties of these antennas are directly a function of the antenna's effective height and effective volume, which are established by both total fractal length and fractal geometry. To estimate the a-forms, possible algorithms are formulated, permitting the Hausdorff measure to be evaluated through application of fractional derivatives and integrals. It is shown, that these properties of ESFA are practically realized due to use structured artificial conducting fractal material elements.

antenna theory; Hausdorff measure; a -forms; antenna quality factor; differintegral volume; fractal antenna; fractal material; small antennas