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

在拟议的dfg项目中，申请人希望对具有不规则变形截面和传播方向随机缺陷的圆柱形波导中的电磁波进行建模和模拟。重点将放在tem波导（两个电导体）上，因为tem波只有在有两个电导体的情况下才能传播。由于制造工艺的原因，实际波导的横截面通常不均匀。所有真实的表面都有随机的缺陷，并且与理想的几何形状不同，例如表面粗糙度。分析了表面粗糙度和几何形状变化对电磁场分布的直接影响。舍尔库诺夫通过将麦克斯韦方程组转化为一组常微分方程，介绍了波导中电磁波的更一般的传输理论。通过将横向电磁场分量展开成基函数的正交级数，导出了一个无穷微分方程组，即所谓的广义电报方程（gte）。该项目的主要目标是开发一种系统的方法来分析tem波导在制造过程中由于公差而产生的几何尺寸。基于舍尔库诺夫的概念，将麦克斯韦方程组转化为gte，分析不规则变形tem波导的电磁场。特别注意的是对同轴tem波导的不规则变形表面的建模。边界条件描述了表面的缺陷，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tem波导的广义电报方程，并对这些微分方程系统进行数值求解外，另一个重点是在同轴tem波导上进行仿真验证。场传感器探头标定的目的是用可测量的量来充分描述由几何缺陷引起的不确定性。由于制造过程引起的表面粗糙度对场分布的影响通常不为人所知。目前还没有考虑制造过程公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，这个项目的目的是调查这个问题。

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.