Advanced antenna analysis and design by tailored Eigenmode decompositions

用于天线电磁分析和设计的软件工具通常使用全波方法，以数值方式解决麦克斯韦方程组。它们允许对复杂问题进行精确建模，并使数值建模成为设计和分析电磁系统的基本部分。虽然整个电磁场或电流密度是这个问题的通用解决方案，但它们有时无法直观地了解天线的潜在物理行为。整个电流密度的模态分解，如所谓的特征模态（CM），旨在通过允许识别与辐射最相关的结构的特征模态，进一步阐明电磁行为。同时，一些商业软件工具在基本层面上包含了特征模式分析，允许受过教育的用户从这种高级洞察力中受益。在过去的10年里，CM在天线分析和设计中的应用显示出快速和持续的增长，从而产生了创新的天线设计。然而，特征模态是一个特定的模态分解集中在一个结构的辐射特性。依赖于存储能量的参数，例如天线阻抗，不太容易被这个特征值问题访问。最近，研究开始着眼于不同的模态分解，以便设计定制的特征值问题，更好地解决天线的其他方面。虽然电流密度的所有特征值问题都是基于底层问题的公共阻抗矩阵，但每个模态分解都代表自己，并且与特定特征值问题派生的不同特征模态相关联。因此，必须推导出不同分解之间的数学关系，以便将它们结合起来计算某一天线的有意义的参数。该项目的总体目标是探索突出天线不同方面的阻抗算子的各种模态分解，并有目的地将它们结合起来进行整体天线分析和设计。为了实现这一总体目标，首先将生成一个模态分解的结构化目录。该目录应能够在应用层面、形式层面和解释层面识别模态分解的异同。在此基础上，建立基于阻抗算子的模态分解数学框架，实现有目的地设计模态分解和模态分解之间的转换。模态分解的计算和数值方面以及它们的转换和关联将在接下来处理。这将允许对某一天线问题进行混合模态分析，并根据目标参数对天线进行直观的设计和调谐。

Software tools for the electromagnetic analysis and design of antennas typically utilize full-wave methods that solve Maxwell’s equations numerically. They allow for accurate modelling of even complex problems and enable numerical modelling being a fundamental part in design and analysis electromagnetic systems. While the entire electromagnetic field or current density are the universal solution to the problem, they offer sometimes less intuitive insight into the underlying physical behavior of the antenna. Modal decompositions of the entire current density, such as the so-called Characteristic Modes (CM) are designed to illuminate the electromagnetic behavior a little further by allowing to identify Eigenmodes of the structure that are most relevant for radiation. Meanwhile, Characteristic Mode analysis is included in some commercial software tools on a basic level allowing the educated user to benefit from this advanced insight. Within the last 10 years application of CM for the analysis and design of antennas has shown a rapid and continuous growth resulting in innovative antenna designs. However, Characteristic Modes is a specific modal decomposition focussing on the radiation properties of a structure. Parameters that rely on the stored energy, e.g. antenna impedance, are less accessible by this Eigenvalue problem. Recently, research started looking at different modal decompositions in order to design tailored Eigenvalue problems that address better other aspects of antennas. Although all Eigenvalue problems of the current density are based on the common impedance matrix of the underlying problem, each modal decomposition stands for its own and is associated with different Eigenmodes derived from the specific Eigenvalue problem. Consequently, mathematical relations between the different decompositions have to be derived in order to combine them to calculate meaningful parameters for a certain antenna. The overall objective of the project is to explore various modal decompositions of the impedance operator that highlight different antenna aspects and combine them purposefully for holistic antenna analysis and design. In order to achieve this overall goal a structured catalogue of modal decompositions will be generated first. The catalogue shall enable to identify similarities and differences of modal decompositions on the application level, formal level and interpretation level. Based thereon, a mathematical framework of modal decompositions based on the impedance operator will be developed that enables to purposefully design modal decomposition and convert between them. Computational and numerical aspects of modal decompositions and their conversion and correlation will be dealt with next. This shall allow for mixed modal analysis of a certain antenna problem and intuitive design and tuning of antennas with respect to target parameters.