Influence of the non-regular deformed boundary of a TEM-waveguide to the field distribution

在提出的DFG项目中，申请人希望对具有不规则变形的截面和传播方向上的随机缺陷的圆柱形波导中的电磁波进行建模和模拟。由于瞬变电磁波只有在两个导体的情况下才能传播，所以我们将把重点放在瞬变电磁波(两个导体)上。由于制造工艺的原因，实际中的波导在横截面上通常是不均匀的。所有真实曲面都有随机缺陷，并与理想几何形状不同，例如表面粗糙度。分析了表面粗糙度和几何形状的变化对电磁场分布的直接影响。通过将麦克斯韦方程转化为一组常微分方程组，Schelkunoff提出了更一般的电磁波在波导中的传输理论。通过将横向电磁场分量展开为一个正交基函数级数，得到了一个无限的微分方程组，即所谓的广义电报方程(GTES)。该项目的主要目标是开发一种系统的方法来分析由于制造过程中的公差而导致的横电磁波导管的几何尺寸。基于Schelkunoff的概念，将Maxwell方程转化为GTE，从而可以分析不规则变形的瞬变电磁波导的电磁场。重点研究了同轴横电磁波导非规则变形表面的模拟。边界条件描述了曲面的缺陷，我们假设这些变形没有规则。因此，将边界条件解释为随机变量是有用的。除了推导出不规则变形的横电磁波导方程组和这些微分方程组的数值解外，另一个重点是验证同轴横电磁波导上的模拟结果。现场传感器探头校准的目的是用可测量的量来全面描述由于几何缺陷引起的不确定度。由于制造过程导致的表面粗糙度对场分布的影响一般不为人所知。到目前为止，没有考虑制造过程中的误差对电磁场分布的影响，但在测量过程中必须给出测量不确定度。因此，本项目的目的就是研究这一问题。

In the proposed DFG-project the applicant wants to model and simulate electromagnetic waves in cylindrical waveguides with irregularly deformed cross-sections and random imperfections in the direction of propagation. Great emphasis will be put on TEM-waveguides (two electric conductors), because TEM-waves can only propagate, if there are two electric conductors. Practical waveguides are usually not uniform in their cross-section due to the manufacturing process. All real surfaces have random imperfections and differ from the ideal geometry, e.g. surface roughness. The direct effect of the surface roughness and the changes of the geometry on the electromagnetic field distribution will be analyzed. Schelkunoff introduced a more general transmission theory of electromagnetic waves in waveguides by transforming Maxwell’s equations into a set of ordinary differential equations. By expanding the transvers electromagnetic field components into an orthogonal series of basis functions, an infinite system of differential equation is derived, the so-called generalized telegraphist’s equations (GTEs).The main objective of the project is to develop a systematic approach to analyze TEM-waveguides with regard to their geometrical dimension due to tolerances in the manufacturing process. Based on the concept of Schelkunoff, Maxwell’s equations will be converted into GTEs and the electromagnetic field of an irregularly deformed TEM-waveguide can be analyzed. Special attention is placed on the modelling of the irregularly deformed surface of the coaxial TEM-waveguide. The boundary conditions describe imperfections of the surface where we assume that there is no rule for these deformations. Consequently, it is useful to interpret the boundary conditions as random variables. Besides the derivation of the so-called generalized telegraphist’s equations for the irregularly deformed TEM-waveguide and numerical solution to these differential equation systems, another main focus is to verify the simulations on a coaxial TEM-waveguide. The purpose of the calibration of field sensor probes is to fully describe the uncertainties due to the imperfections of the geometry with measurable quantities. The effect of surfaces roughness due to the manufacturing process on the field distribution is not generally known. So far the effect of tolerances due to the manufacturing process on the electromagnetic field distribution is not considered, but the measurement uncertainty must be given during the measurement process. Thus, the aim of this projects is to investigate this problem.