兰州大学机构库 >数学与统计学院
有限元法在复杂传输线计算中的应用—加载右或左手材料的鳍线和微屏蔽线的特性研究
Alternative TitleApplication of the finite element method to computation of the complicated transmission line—a study of characteristics in finline and microshield line loaded with right-handed or left-handed materials
孙海
Thesis Advisor伍渝江
2013-06-02
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword有限元方法 右手材料 左手材料 鳍线 微屏蔽线 传输特性
Abstract本文将有限元方法应用到复杂传输线的计算中,主要研究了加载右手材料的鳍线与同时加载右手和左手材料的微屏蔽线的传输特性.其中,选用双侧鳍线作为鳍线的代表进行计算,而微屏蔽线则以矩形微屏蔽线和椭圆形微屏蔽线为代表进行计算.传输特性主要包括主模截止波长,单模带宽,主模和第一高次模的场结构以及色散特性. 首先,讨论了鳍线和微屏蔽线所涉及方程的节点有限元法的相关理论.这其中包括微分方程等价泛函的推导,节点有限元离散,边界条件的强加,以及广义特征值问题的求解.且通过v形微屏蔽线为例得出节点有限元法在计算过程中出现伪解的事实,并分析了原因. 其次,推导了鳍线和微屏蔽线所涉及方程的矢量有限元公式.这其中包括两大部分,第一是推导了以磁场为工作变量的求解主模截止波长,单模带宽和场结构的矢量有限元公式;第二是推导了以电场为工作变量的色散特性的矢量有限元公式.并给出了两个广义特征值方程中各矩阵元素的计算过程. 再次,在验证两个矢量有限元方程的正确性以及所编写程序的可靠性后,运用矢量有限元法求解了双侧鳍线的传输特性.在模型结构方面,主要讨论随尺寸的变化而引起传输特性的变化;而在加载材料方面,以加载右手材料为前提,计算随加载介质相对介电常数的增加而带来的传输特性的改变.通过以双侧鳍线为代表的研究可大致获得其他鳍线模型的特性变化. 最后,针对微屏蔽线,以矩形微屏蔽线和椭圆形微屏蔽线为代表进行了不同侧重点的讨论.其中,在矩形微屏蔽线的讨论中,主要讨论了信号线的变化所引起的传输特性的改变;而在椭圆形微屏蔽线中,主要计算了加载区域的变化对传输特性的影响.在加载材料方面,既考虑了右手材料,也考虑了左手材料,且进行了两种材料对传输特性影响的比较研究.
Other AbstractThis 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 of 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...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224378
Collection数学与统计学院
Recommended Citation
GB/T 7714
孙海. 有限元法在复杂传输线计算中的应用—加载右或左手材料的鳍线和微屏蔽线的特性研究[D]. 兰州. 兰州大学,2013.
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