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.

中文翻译：

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自互补天线几乎恒定输入阻抗的新方法

与频率无关天线的恒定输入阻抗特性相关地讨论了基于四个时空全共形群下麦克斯韦电动力学协方差的共形技术。特别是我们表明，通过对现有的自互补平面结构（如对数螺旋）应用适当的共形变换，恒定输入阻抗特性得到了显着改善，特别是在低频域中，由于涉及大波长，它通常会失败。共形变换的效果是将无穷大带到有限距离，并在某种程度上将原本无穷大的结构禁锢在一个紧凑的区域中。该程序能够执行更智能的截断，目的是捕捉切割过程中留下的一些特性，并设计真实的超宽带天线，在整个操作范围内输入阻抗值更可控。由于这里开发的工具在弯曲流形的微分几何中找到它们的根源，它们非常通用，也适用于处理任意形状、曲率和尺寸的 3D 天线，以及其他系统截断效应在定义它们的物理特性方面起着至关重要的作用。