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

TEM波导不规则变形边界对场分布的影响

• 批准号: 438107418
• 负责人: Professor Dr.-Ing. Heyno Garbe
• 金额: --
• 依托单位: Institut für Grundlagen der Elektrotechnik und Messtechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/438107418?language=en
• 关键词: Influence; non; regular; deformed; boundary

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.

在所提出的DFG项目中，申请人希望对具有不规则变形横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仿真。重点将放在TEM波导（两个电导体），因为TEM波只能传播，如果有两个电导体。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缺陷，并且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。Schelkunoff通过将麦克斯韦方程组转化为一组常微分方程，提出了一种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正交基函数，导出了一个无限大的微分方程组，即广义电报员方程（GTEs）。本项目的主要目标是发展一种系统的方法来分析TEM波导在制造过程中由于公差而引起的几何尺寸。基于Schelkunoff的概念，将麦克斯韦方程组转化为广义等效电磁场方程组，从而可以分析不规则变形TEM波导的电磁场。特别注意的是放置在不规则变形的表面的同轴TEM波导的建模。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。除了推导不规则变形TEM波导的广义电报员方程和数值求解这些微分方程组之外，另一个主要焦点是验证同轴TEM波导的模拟。场传感器探头校准的目的是用可测量的量充分描述由于几何缺陷而引起的不确定性。由于制造工艺而引起的表面粗糙度对场分布的影响通常是未知的。到目前为止，由于制造过程中的电磁场分布的公差的影响是不考虑的，但测量过程中必须给出的测量不确定度。因此，本项目的目的是调查这一问题。