A new approach to nearly constant input impedance of self-complementary antennas

Conformal techniques, based on the covariance of Maxwell's electrodynamics under the full conformal group in four spacetime dimensions, are discussed in relation with the constant input impedance properties of frequency-independent antennas. In particular, we show that by applying suitable conformal transformations to existing self-complementary planar structures like logarithmic spirals, the constant input impedance property is considerably improved, especially in the low-frequency domain, where it usually fails due to the large wavelength involved. This procedure enables to perform a more intelligent truncation with the aim to capture some of the properties left behind in the cutting and to design realistic ultra wideband antennas with a more controlled value of the input impedance in the whole operation range.