A New Approach to Frequency Independent Radiating Systems: Conformal Edge Antennas

TL;DR

This paper introduces a conformal transformation-based method to improve the frequency-independent input impedance of antennas, especially at low frequencies, enabling more realistic ultra wide-band antenna designs with controlled impedance.

Contribution

It presents a novel application of conformal geometry to antenna design, enhancing the impedance properties of self-complementary structures and allowing for better truncation and realization of ultra wide-band antennas.

Findings

Conformal transformations improve low-frequency impedance stability.

The method enables realistic truncation of infinite structures.

Applicable to 3D antennas of arbitrary shape and size.

Abstract

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, specially in the low frequency domain, where it usually fails due to the large wavelength involved. The effect of the conformal transformation is to bring infinity up to a finite distance and, in a way, to imprison the otherwise infinite structure in a compact region. 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 width-band antennas with a more controlled value of the input impedance in the whole operation range. Due to the fact that the tools here developed find their roots in the differential geometry of curved manifolds, they are quite general and also suitable for dealing with 3D-antennas of arbitrary shape, curvature and size, as well as with other systems in which the effects of truncation play a crucial role in defining physical properties of them.