Analysis of passive microwave devices by using three‐dimensional tangential vector finite elements

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Abstract
There are two major difficulties in applying the finite element method to the analysis of microwave devices in three dimensions. One is to obtain a stable vector finite element which does not generate spurious modes, or non‐physical solutions, in the numerical analysis. The other is to model efficiently the coupling of port regions and the discontinuity region. In this paper, we describe the application of two new finite element techniques, the tangential vector finite element method and the transfinite element method, for modelling three‐dimensional microwave devices. The tangential vector finite element method, unlike the conventional nodal finite element methods, imposes only the tangential continuity of the vector unknown across elements' boundaries. As a result, there would be no spurious modes, and reliable solutions are obtained. The transfinite element method, which combines the modal basis functions and the finite element basis functions through the variational technique, provides an efficient way to model the open boundary nature of the device. To validate the current analysis, a low VSWR waveguide connector and two microstrip low‐pass filters are analysed. Numerical results agree very well with the measurements or those obtained by other methods.

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