Conformal techniques, based on the covariance of Maxwell's electrodynamicsunder the full conformal group in four spacetime dimensions, are discussed inrelation with the constant input impedance properties of frequency-independentantennas. In particular we show that by applying suitable conformaltransformations to existing self-complementary planar structures likelogarithmic spirals, the constant input impedance property is considerablyimproved, specially in the low frequency domain, where it usually fails due tothe large wavelength involved. The effect of the conformal transformation is tobring infinity up to a finite distance and, in a way, to imprison the otherwiseinfinite structure in a compact region. This procedure enables to perform amore intelligent truncation with the aim to capture some of the properties leftbehind in the cutting, and to design realistic ultra width-band antennas with amore controlled value of the input impedance in the whole operation range. Dueto the fact that the tools here developed find their roots in the differentialgeometry of curved manifolds, they are quite general and also suitable fordealing with 3D-antennas of arbitrary shape, curvature and size, as well aswith other systems in which the effects of truncation play a crucial role indefining physical properties of them.
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