A new measure of lacunarity for generalized fractals and its impact in the electromagnetic behavior of Koch dipole antennas
A new measure of lacunarity for generalized fractals and its impact in the electromagnetic behavior of Koch dipole antennas
复制标题
广义分形空隙性的新度量及其对科赫偶极子天线电磁行为的影响
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
K. Vinoy
中科院分区：
文献类型：
--
作者：
K. Sengupta;K. Vinoy
近年来，分形几何在科学和工程的各个分支中得到了探索。在天线工程中，由于据称具有实现多谐振天线的潜力，因此对其中一些几何形状进行了研究。尽管由于分形的复杂性，以前的大多数研究都是实验性的，但对使用分形的天线的性能进行了一些分析研究。一种这样的分析尝试旨在定量地将分形维数与单个分形集中的天线特性相关联。然而，希望将所有分形几何形状涵盖在天线设计和其他类似应用的一个框架下。以此为最终目标，我们在本文中力求通过将分形几何的缺陷纳入其空间分布的度量，将早期的方法扩展到更普遍的情况。由于发现可用的空隙度度量不一致，因此在本文中我们建议使用一种新的度量来量化分形空隙度。我们还展示了这种新方法的使用，以独特地解释由广义科赫曲线组成的偶极子天线的行为，并继续展示基本的空隙性如何影响分形天线的电磁行为。预计这种平均的空隙度测量可能会在天线以外的领域得到应用。
In recent years, fractal geometries have been explored in various branches of science and engineering. In antenna engineering several of these geometries have been studied due to their purported potential of realizing multi-resonant antennas. Although due to the complex nature of fractals most of these previous studies were experimental, there have been some analytical investigations on the performance of the antennas using them. One such analytical attempt was aimed at quantitatively relating fractal dimension with antenna characteristics within a single fractal set. It is however desirable to have all fractal geometries covered under one framework for antenna design and other similar applications. With this objective as the final goal, we strive in this paper to extend an earlier approach to more generalized situations, by incorporating the lacunarity of fractal geometries as a measure of its spatial distribution. Since the available measure of lacunarity was found to be inconsistent, in this paper we propose to use a new measure to quantize the fractal lacunarity. We also demonstrate the use of this new measure in uniquely explaining the behavior of dipole antennas made of generalized Koch curves and go on to show how fundamental lacunarity is in influencing electromagnetic behavior of fractal antennas. It is expected that this averaged measure of lacunarity may find applications in areas beyond antennas.