Project Title: Transition from Maxwell to Transmission Line Theory
The computation of the propagation of electromagnetic waves on transmission lines is based on electrostatic and magnetostatic computations and on additional formula describing dynamic effects (skin effect, proximity effect). Although this procedure is numerically powerful, it is theoretically not consistent for several reasons. For example, the static computations implicitly assume different propagation constants in different media. It seems to be reasonable to clarify this situation by a rigorous computation of transmission line modes based on an analytic solution of Maxwell's equations. We have studied transmission line modes by the MMP code for computational electromagnetics. This code is based on a method that is very close to the analytic solution, because it uses basis functions that are analytic solutions of the Maxwell equations. The code allows to compute the propagation constant of guided modes by solving a nonlinear eigenvalue problem and gives important information on the accuracy of the results. It has been found that one can accurately compute both the electromagnetic field and the propagation constant of any mode when the frequency is sufficiently high. At lower frequencies, i.e. in the domain of the transmission line theory, the computation of the propagation constant becomes completely inaccurate. Nonetheless one can accurately compute the field. Therefore, the initial (wrong) assumption of different propagation constants in different media does not cause inaccuracies in the field computations.
Contacts: Ch.Hafner, IFH, ETZG95, ETH Zentrum, CH-8092 Zurich
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Index Terms: Maxwell Theory, Transmission Line Theory