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

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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.