微波管高频电路快速有限元理论与CAD技术研究
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摘要
微波管作为核心电子器件被广泛应用于多功能雷达、有源相阵控系统、电子对抗装备、空间卫星通信、等离子诊断和核反应堆加热等领域。高频电路是微波管最重要的部件，它是电子注与高频场相互作用进行能量交换以实现微波振荡或放大的场所。微波管高频电路的特性直接影响微波管的工作频率、频带宽度、换能效率和输出功率，以及其他一系列整管性能。随着对微波管性能越来越高的要求，微波管高频电路的效率和性能要求也随之提高。而设计出高效率和高性能的微波管高频电路则迫切需要更精确、更高效、更稳定的高频电路三维数值分析理论与CAD软件。
本论文围绕着微波管高频电路快速有限元理论与CAD技术开展研究工作，工作的主要内容和创新点可以概括为下述五个方面。
1、提出了一种适用于任意结构的微波管高频电路三维快速有限元分析方法，该方法主要包含了下述四种新技术：(1)在高频电路有限元分析中，提出了一种同时利用高频电路纵向和角向周期性的旋转周期边界条件的“强”强加技术用于大幅提高高频电路的有限元分析效率。(2)结合位移求逆预处理隐式重启Arnoldi法和多波前LU分解法，提出了一种改进的隐式重启Arnoldi本征求解器用于快速求解高频电路有限元分析所得的大型广义本征问题。(3)在高频电路有限元分析中，不仅采用了一阶边棱元基函数而且采用了一种二阶插值型矢量基函数。(4)推导了在采用二阶插值型矢量基函数和旋转周期边界条件下高频电路的色散特性、耦合阻抗以及衰减常数等高频参数的精确有限元后处理公式。
2、采用一种新型的二阶叠层型矢量基函数对微波管高频电路三维有限元分析中的若干关键技术进行了研究。(1)提出了一种方便高效的去除高频电路有限元分析中的伪直流模式的新方法。(2)利用二阶叠层型基函数的叠层性，提出了一种p型多重网格本征求解器用于高效率地求解高频电路有限元分析所得的大型广义本征问题。
3、对考虑损耗下的微波管高频电路三维快速有限元理论进行了研究。(1)提出了一种新的微波管高频电路指定频率本征分析方法。(2)在p型多重网格本征求解器的基础上，提出了一种改进的不精确隐式重启Arnoldi本征求解器用于高效率地求解有损耗高频电路有限元分析所得的大型复不对称线性广义本征问题。
4、对采用非匹配周期网格的微波管高频电路快速有限元理论进行了研究。这部分研究工作主要有下述三个创新点：(1)提出一种完全不需要周期匹配网格的三维有限元分析技术用于精确快速地求解任意结构的有损耗微波管高频电路的各种高频参数。(2)这种新的技术不仅能够处理一般周期边界条件而且能够处理旋转周期边界条件。(3)在该技术中提出了一种新的二阶transverse electric(TE)周期边界条件。比起以往文献中采用的一阶Robin周期边界条件，新的二阶TE周期边界条件能够大幅地提高采用非匹配周期网格的高频电路的有限元分析效率。
5、在上述微波管高频电路快速有限元理论的基础上，开发了我国第一套具有完全自主知识产权的全三维微波管高频电路电磁仿真设计软件－高频电路模拟器（HFCS）。HFCS有着非常友好的用户操作界面、快捷的微波管高频电路建模功能、高质量的网格生成器、精确快速的有限元分析和本征求解模块、精确丰富的后处理计算和显示模块。HFCS的计算性能在本征值求解问题上明显优于国际上本领域最好的两个商业软件：CST MWS和HFSS。HFCS已经在中电集团12所、中科院电子所、国营七七二厂等微波管研究和制管单位发布了多个版本并被用于微波管高频电路的研究和设计中。HFCS对我国高效率高性能微波管的设计起到了积极作用。
Microwave tubes are widely applied as the core electron devices in many militaryfields such as the multifunction radar, the electronic countermeasures equipment, thespace communication and so on. The high-frequency circuit (HFC) is one of the mostimportant parts in the microwave tubes, where the electron beam and theelectromagnetic wave interacts each other. The performance of the HFC in themicrowave tube directly affect the bandwidth, gain, output power, efficiency and anyother performance parameter of the microwave tubes. As the requirement of theperformance of the microwave tubes improves, the efficiency and performance of theHFC are also required to be improved. However, the design of high-efficient andhigh-performance HFC eagerly demands more accurate, more efficient and more robustthree dimensional numerical algorithm and CAD software for HFC.
The research works of this dissertation are focused on the fast finite-element theoryand CAD technique for the HFC in the microwave tubes. Several important andvaluable results are listed as below:
1. We propose a fast finite-element method (FEM) for the arbitrary HFC in themicrowave tube. This advanced method mainly contains four new techniques:(1) Anovel rotated periodic boundary condition which utilize the longitudinal and azimuthalperiodicity of the HFC is proposed to significantly improve the efficiency of simulatingthe HFC using the FEM.(2) By using the implicit restarted Arnoldi method based onshift-invert preconditioner and the fast multi-front LU factorization, an improvedmodified implicit restarted Arnoldi method is proposed to efficiently solve the finallarge generalized eigenvalue problem.(3) Both the lower and higher order tetrahedralbasis functions are applied in the finite-element analysis.(4) The post-processingparameters of the HFC can precisely be computed with the tangential-vector FEM.
2. We investigate many key techniques in the fast finite-element analysis of theHFC using a new second-order hierarchical basis.(1) A convenient and efficientapproach for removing the spurious dc modes in finite-element solutions for modelingmicrowave tubes is proposed.(2) By utilize the hierarchical property of the basis, an advanced p-type multigrid eigensolver is proposed and applied to quite efficiently solvethe finial large eigenvalue problem.
3. We make deeply investigation on the fast finite-element analysis of the lossyHFC in the microwave tubes.(1) A novel a new frequency-specified eigenmodeanalysis for SWSs is proposed and utilized.(2) To further significantly improve theefficiency of modeling lossy HFC, an improved inexact implicit restarted Arnoldimethod is proposed.
4. A novel three-dimensional finite-element modeling technique for arbitrary lossyHFCs of microwave tubes without matching meshes is presented. By employing thistechnique, the cold parameters of HFCs can be accurately and quickly obtained from theeigenmode analysis for SWSs with completely nonmatching meshes. Moreover, a newsecond order TE periodic boundary condition is proposed to improve the modelingefficiency of lossy HFCs with nonmatching meshes and this technique is very suitablefor application of the rotated periodic boundary condition.
5. Based on the fast finite-element theory, we developed an advancedthree-dimensional finite-element electromagnetic-simulation tool for the HFCs in themicrowave tubes－High Frequency Circuit Simulator (HFCS). The HFCS have auser-friendly interface module, a fast model constructor for the HFC, a high qualitymesh generator, accurate and fast finite-element analysis and eiegensolver modules, andaccurate and rich post-processing functions. The HFCS is more efficient than the twocommercial software CST MWS and HFSS in the eigenmode analysis of the HFCs inthe microwave tubes. The HFCS has been released in many institutes and factory forresearching and designing the microwave tubes. The HFCS has been benefitted theresearch and manufacture of microwave tubes in China.
本论文围绕着微波管高频电路快速有限元理论与CAD技术开展研究工作，工作的主要内容和创新点可以概括为下述五个方面。
1、提出了一种适用于任意结构的微波管高频电路三维快速有限元分析方法，该方法主要包含了下述四种新技术：(1)在高频电路有限元分析中，提出了一种同时利用高频电路纵向和角向周期性的旋转周期边界条件的“强”强加技术用于大幅提高高频电路的有限元分析效率。(2)结合位移求逆预处理隐式重启Arnoldi法和多波前LU分解法，提出了一种改进的隐式重启Arnoldi本征求解器用于快速求解高频电路有限元分析所得的大型广义本征问题。(3)在高频电路有限元分析中，不仅采用了一阶边棱元基函数而且采用了一种二阶插值型矢量基函数。(4)推导了在采用二阶插值型矢量基函数和旋转周期边界条件下高频电路的色散特性、耦合阻抗以及衰减常数等高频参数的精确有限元后处理公式。
2、采用一种新型的二阶叠层型矢量基函数对微波管高频电路三维有限元分析中的若干关键技术进行了研究。(1)提出了一种方便高效的去除高频电路有限元分析中的伪直流模式的新方法。(2)利用二阶叠层型基函数的叠层性，提出了一种p型多重网格本征求解器用于高效率地求解高频电路有限元分析所得的大型广义本征问题。
3、对考虑损耗下的微波管高频电路三维快速有限元理论进行了研究。(1)提出了一种新的微波管高频电路指定频率本征分析方法。(2)在p型多重网格本征求解器的基础上，提出了一种改进的不精确隐式重启Arnoldi本征求解器用于高效率地求解有损耗高频电路有限元分析所得的大型复不对称线性广义本征问题。
4、对采用非匹配周期网格的微波管高频电路快速有限元理论进行了研究。这部分研究工作主要有下述三个创新点：(1)提出一种完全不需要周期匹配网格的三维有限元分析技术用于精确快速地求解任意结构的有损耗微波管高频电路的各种高频参数。(2)这种新的技术不仅能够处理一般周期边界条件而且能够处理旋转周期边界条件。(3)在该技术中提出了一种新的二阶transverse electric(TE)周期边界条件。比起以往文献中采用的一阶Robin周期边界条件，新的二阶TE周期边界条件能够大幅地提高采用非匹配周期网格的高频电路的有限元分析效率。
5、在上述微波管高频电路快速有限元理论的基础上，开发了我国第一套具有完全自主知识产权的全三维微波管高频电路电磁仿真设计软件－高频电路模拟器（HFCS）。HFCS有着非常友好的用户操作界面、快捷的微波管高频电路建模功能、高质量的网格生成器、精确快速的有限元分析和本征求解模块、精确丰富的后处理计算和显示模块。HFCS的计算性能在本征值求解问题上明显优于国际上本领域最好的两个商业软件：CST MWS和HFSS。HFCS已经在中电集团12所、中科院电子所、国营七七二厂等微波管研究和制管单位发布了多个版本并被用于微波管高频电路的研究和设计中。HFCS对我国高效率高性能微波管的设计起到了积极作用。
Microwave tubes are widely applied as the core electron devices in many militaryfields such as the multifunction radar, the electronic countermeasures equipment, thespace communication and so on. The high-frequency circuit (HFC) is one of the mostimportant parts in the microwave tubes, where the electron beam and theelectromagnetic wave interacts each other. The performance of the HFC in themicrowave tube directly affect the bandwidth, gain, output power, efficiency and anyother performance parameter of the microwave tubes. As the requirement of theperformance of the microwave tubes improves, the efficiency and performance of theHFC are also required to be improved. However, the design of high-efficient andhigh-performance HFC eagerly demands more accurate, more efficient and more robustthree dimensional numerical algorithm and CAD software for HFC.
The research works of this dissertation are focused on the fast finite-element theoryand CAD technique for the HFC in the microwave tubes. Several important andvaluable results are listed as below:
1. We propose a fast finite-element method (FEM) for the arbitrary HFC in themicrowave tube. This advanced method mainly contains four new techniques:(1) Anovel rotated periodic boundary condition which utilize the longitudinal and azimuthalperiodicity of the HFC is proposed to significantly improve the efficiency of simulatingthe HFC using the FEM.(2) By using the implicit restarted Arnoldi method based onshift-invert preconditioner and the fast multi-front LU factorization, an improvedmodified implicit restarted Arnoldi method is proposed to efficiently solve the finallarge generalized eigenvalue problem.(3) Both the lower and higher order tetrahedralbasis functions are applied in the finite-element analysis.(4) The post-processingparameters of the HFC can precisely be computed with the tangential-vector FEM.
2. We investigate many key techniques in the fast finite-element analysis of theHFC using a new second-order hierarchical basis.(1) A convenient and efficientapproach for removing the spurious dc modes in finite-element solutions for modelingmicrowave tubes is proposed.(2) By utilize the hierarchical property of the basis, an advanced p-type multigrid eigensolver is proposed and applied to quite efficiently solvethe finial large eigenvalue problem.
3. We make deeply investigation on the fast finite-element analysis of the lossyHFC in the microwave tubes.(1) A novel a new frequency-specified eigenmodeanalysis for SWSs is proposed and utilized.(2) To further significantly improve theefficiency of modeling lossy HFC, an improved inexact implicit restarted Arnoldimethod is proposed.
4. A novel three-dimensional finite-element modeling technique for arbitrary lossyHFCs of microwave tubes without matching meshes is presented. By employing thistechnique, the cold parameters of HFCs can be accurately and quickly obtained from theeigenmode analysis for SWSs with completely nonmatching meshes. Moreover, a newsecond order TE periodic boundary condition is proposed to improve the modelingefficiency of lossy HFCs with nonmatching meshes and this technique is very suitablefor application of the rotated periodic boundary condition.
5. Based on the fast finite-element theory, we developed an advancedthree-dimensional finite-element electromagnetic-simulation tool for the HFCs in themicrowave tubes－High Frequency Circuit Simulator (HFCS). The HFCS have auser-friendly interface module, a fast model constructor for the HFC, a high qualitymesh generator, accurate and fast finite-element analysis and eiegensolver modules, andaccurate and rich post-processing functions. The HFCS is more efficient than the twocommercial software CST MWS and HFSS in the eigenmode analysis of the HFCs inthe microwave tubes. The HFCS has been released in many institutes and factory forresearching and designing the microwave tubes. The HFCS has been benefitted theresearch and manufacture of microwave tubes in China.
引文
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