| This thesis applies the finite element method to calculate the complicated transmission lines, which mainly studies the transmission characteristics of finlines with right-handed materials loaded and microshield lines with both right-handed materials and left-handed materials loaded. When calculate, finlines are represented by bilateral finlines, and microshield lines are represented by rectangle-shaped microshield lines and elliptic-shaped microshield lines. Transmission characteristics include the cutoff wavelength of dominant mode, the single-mode bandwidth, the field patterns of the dominant mode and the first higher-order mode, and the dispersion characteristics.Firstly, we study the theory of node finite element method of equations which involved in finlines and microshield lines, including the derivation of equivalent functional for differential equation, the discretization of node finite element method, the imposition of the boundary condition, and the solution of generalized eigenvalue problem. The calculation of v-shaped microshield lines reveals the fact that the spurious solutions are caused by node finite element method, and then the reasons are analyzed.Secondly, we formulate the edge-based finite element of equations which involved in finlines and microshield lines. It includes two parts, where the first part is that we derivation the formulas of edge-based finite element method to calculate the cutoff wavelength of the dominant mode, the single-mode bandwidth and the field patterns, in which the magnetic field is employed as the working variable, the other part is that we derivation the formulas of edge-based finite element method to calculate the dispersion characteristics, in which the electric field is employed as the working variable. And then, we introduce the calculation process of the matrix elements which belong to two above generalized eigenvalue problems.Thirdly, after we verify the accuracy of two edge-based finite element equations and the reliability of procedures, we calculate the transmission characteristics o(?) bilateral finlines using edge-based finite element method. For model structure, the influence of transmission characteristics with varied dimensions are discussed, for loaded materials, we calculated the changes of transmission characteristics with the increase of the relative permittivity. We can obtain the changes of other finlines models by bilateral finlines in general.Lastly, we use the rectangle-shaped microshield lines and elliptic-shaped microshield lines to represent the microshield lines, and discuss them with different focuses. For rectangle-shaped microshield lines, the dependence of the transmission characteristics upon the varied signal lines are studied, for elliptic-shaped microshield lines, the influence of the transmission characteristics which caused by the changes of the loaded area are calculated. For loaded materials, right-handed and left-handed are both used, and we make a comparative study of the effect on the transmission characteristics of the two kinds of materials. |
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