时域积分方程在分析金属/介质及场—路混合问题中的算法研究与应用
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摘要
研究电磁场数值计算理论和算法的最终目的是解决各种实际的复杂电磁场问题。在复杂目标雷达散射截面(RCS)计算、宽带天线设计、电磁兼容性分析等领域,经常需要对金属/介质混合结构的三维目标电磁建模并仿真。围绕这一背景,我们选择了电磁场时域积分方程(TDIE)理论作为理论基础,以时间递推法(MOT)作为数值求解方法,研究了金属/介质混合结构的辐射、散射以及场-路混合问题,开发了可用于解决工程中的一些电磁计算问题的通用计算程序。论文内容分为两部分,第一部分主要阐述了用于分析金属/介质混合体辐射、散射的时域积分方程理论及基于MOT的求解技术;第二部分阐述了用TDIE结合电路中的改进节点分析(MNA)法模拟场-路混合问题的方法。
第一部分基于等效原理和边界条件,推导了针对金属/均匀介质混合体的辐射和散射问题的各种时域电磁场积分方程,包括时域电场积分方程(TD-EFIE)、时域磁场积分方程(TD-MFIE)、时域混合场积分方程(TD-CFIE)和时域C-PMCHW(Poggio-Miller-Chang-Harrington-Wu)耦合积分方程四种形式,并比较了各类积分方程的适用范围和优缺点;在此基础上,阐述了基于RWG函数的MOT求解各种混合体时域积分方程的一般方法。研究了混合体的建模剖分和数据提取,以及算法实现过程中的数学推导、矩阵元素的计算、计算后参数的提取和处理等问题。
论文对各种类型的时间基函数进行了评估,比较了它们所包含的高频分量;提出了用于金属/介质混合问题的阻抗矩阵预存储的方法,并给出了所需存储空间的计算公式,该方法大大节省了阻抗元素重复计算的时间。在阻抗矩阵元素计算中,研究了一种基于Duffy变换的包含时间迟滞项的奇异积分的精确计算方法,提高了计算精度,改善了MOT求解积分方程中的晚时不稳定性。最后通过一些金属/介质混合结构的辐射和散射算例验证了算法的正确性,并得出采用时域E-PMCHW耦合积分方程计算金属/介质混合体比采用TD-EFIE更稳定的结论。
第二部分针对复杂电磁结构体与电路互连的混合问题,将场分析中的TDIE法与电路分析中的MNA法相结合,实现了一种可同时模拟复杂电磁结构与线性、非线性集总电路间耦合的方法。这种方法的基础是在电路和电磁结构体间引入“耦合电流”的思想,并将完善的电流连续性方程和广义基尔霍夫定律应用于电磁结构与电路的耦合分析中。
最后采用时域E-PMCHW算法分析了微带功分器和微带滤波器的性能;计算了一种小型介质谐振腔加载贴片天线和一种圆盘单极振子印刷超宽带天线的阻抗匹配性能和远场辐射特性,通过计算分析,得出了影响各天线谐振频率和反射损耗带宽的天线结构参数。对于非线性器件,计算了应用于混频器中的微波二极管的特性。这些例子展示了时域E-PMCHW算法具有比其他形式的积分方程法更优良的稳定性和在时域计算上的优势。
The objective of studying and developing modern computing electromagnetic theory and algorithm is to solve all kinds of engineering electromagnetic problems. In the areas of computing radar cross section(RCS) of complex objects and broadband antenna design and Electromagnetic Compatibility(EMC) analysis, we often have to simulate the electromagnetic characteristics of some objects with complex metallic/ dielectric structures. Under these backgrounds, this thesis choses time domain integral equation (TDIE) theory as the theoretical foundation, marching-on-in-time(MOT) scheme as numerical solver, and investigates the scattering, radiation of the complex metallic/dielectric structures and mixed electromagnetic(EM)-circuit Simulation, and develops general electromagnetic computing software to solve the electromagnetic computing problems in engineering. The content of this thesis is made up of two parts, the first part expounds TDIE theory for complex metallic/dielectric structures and its resolving technique based on MOT; the second part expounds a formulation for mixed EM-circuit simulation using TDIE.
In the first part of this thesis, the TDIE including time-domain electric field integral equation (TD-EFIE), time-domain magnetic field integral equation (TD-MFIE), time- domain combined field integral equation (TD-CFIE) and time-domain combining PMCHW(Poggio, Miller, Chang, Harrington, Wu) formulation for complex metallic/dielectric structures are elaborated uniformly based on the surface equivalence principle and boundary conditions firstly. For an attempt to choose optimal TDIE for different structures, the applicability and excellence as well as disadvantages of different TDIEs are compared. Then the solving procedures of these TDIEs based on the RWG function using MOT are elaborated, including the model building of complex objects, data extraction, some mathematical formulations in realizing the algorithm, calculating the matrix elements, the parameter extraction and the post processing after the simulation, etc.
Different temporal bases functions are evaluated and their high frequency components are compared for the cause of their impact on late-time stability in this thesis. In addition, the method of impedance matrix prestorage for composite structures is presented, which largely saves the time of repeatedly computing impedance elements, and the required memory is formulated. In the procedure of computing impedance matrix elements, an improved method of accurate evaluation of retarded time integrals with singularity in self-impedance elements in MOT scheme is presented, which improve the late-time stability of MOT scheme. Some numerical results of practical complex antenna and scattering problems are presented to illustrate the validity of the method and better stability of TD-E-PMCHW compared with TD-EFIE for complex metallic/dielectric structures.
In the second part, for the interconnection between complex metallic/dielectric EM structures and circuits, a simultaneous simulation scheme of EM section and linear/ nonlinear lumped circuit section is developed through combining TDIE used in EM simulation and MNA used in circuit simulation. The scheme is based on thought of "coupling current" serving as the bridge to connect the circuit section and EM section. Following the "coupling current", the "modified" continuity equation and "generalized" Kirchoff's Law are used to analyzing the coupling between the EM section and circuit section.
Finally, a microstrip power splitter and a microstrip filter are analyzed using TD-E-PMCHW algorithm. In addition, a miniature dielectric resonator loaded patch antenna and a printed circular disc monopole Antenna for UWB systems are computed, and the performance of impedance match and radiation of the two antennas is analyzed. Through analysis effect of the antennas' structure parameters on resonant frequency and return loss bandwith is gained. For nonlinear elements in circuits, a diode applied in a mixer is computed. All these examples demonstrate the better stability in analysis of complex structure of TD-E-PMCHW algorithm compared with other TDIEs and the advantages of computation in time domain.
第一部分基于等效原理和边界条件,推导了针对金属/均匀介质混合体的辐射和散射问题的各种时域电磁场积分方程,包括时域电场积分方程(TD-EFIE)、时域磁场积分方程(TD-MFIE)、时域混合场积分方程(TD-CFIE)和时域C-PMCHW(Poggio-Miller-Chang-Harrington-Wu)耦合积分方程四种形式,并比较了各类积分方程的适用范围和优缺点;在此基础上,阐述了基于RWG函数的MOT求解各种混合体时域积分方程的一般方法。研究了混合体的建模剖分和数据提取,以及算法实现过程中的数学推导、矩阵元素的计算、计算后参数的提取和处理等问题。
论文对各种类型的时间基函数进行了评估,比较了它们所包含的高频分量;提出了用于金属/介质混合问题的阻抗矩阵预存储的方法,并给出了所需存储空间的计算公式,该方法大大节省了阻抗元素重复计算的时间。在阻抗矩阵元素计算中,研究了一种基于Duffy变换的包含时间迟滞项的奇异积分的精确计算方法,提高了计算精度,改善了MOT求解积分方程中的晚时不稳定性。最后通过一些金属/介质混合结构的辐射和散射算例验证了算法的正确性,并得出采用时域E-PMCHW耦合积分方程计算金属/介质混合体比采用TD-EFIE更稳定的结论。
第二部分针对复杂电磁结构体与电路互连的混合问题,将场分析中的TDIE法与电路分析中的MNA法相结合,实现了一种可同时模拟复杂电磁结构与线性、非线性集总电路间耦合的方法。这种方法的基础是在电路和电磁结构体间引入“耦合电流”的思想,并将完善的电流连续性方程和广义基尔霍夫定律应用于电磁结构与电路的耦合分析中。
最后采用时域E-PMCHW算法分析了微带功分器和微带滤波器的性能;计算了一种小型介质谐振腔加载贴片天线和一种圆盘单极振子印刷超宽带天线的阻抗匹配性能和远场辐射特性,通过计算分析,得出了影响各天线谐振频率和反射损耗带宽的天线结构参数。对于非线性器件,计算了应用于混频器中的微波二极管的特性。这些例子展示了时域E-PMCHW算法具有比其他形式的积分方程法更优良的稳定性和在时域计算上的优势。
The objective of studying and developing modern computing electromagnetic theory and algorithm is to solve all kinds of engineering electromagnetic problems. In the areas of computing radar cross section(RCS) of complex objects and broadband antenna design and Electromagnetic Compatibility(EMC) analysis, we often have to simulate the electromagnetic characteristics of some objects with complex metallic/ dielectric structures. Under these backgrounds, this thesis choses time domain integral equation (TDIE) theory as the theoretical foundation, marching-on-in-time(MOT) scheme as numerical solver, and investigates the scattering, radiation of the complex metallic/dielectric structures and mixed electromagnetic(EM)-circuit Simulation, and develops general electromagnetic computing software to solve the electromagnetic computing problems in engineering. The content of this thesis is made up of two parts, the first part expounds TDIE theory for complex metallic/dielectric structures and its resolving technique based on MOT; the second part expounds a formulation for mixed EM-circuit simulation using TDIE.
In the first part of this thesis, the TDIE including time-domain electric field integral equation (TD-EFIE), time-domain magnetic field integral equation (TD-MFIE), time- domain combined field integral equation (TD-CFIE) and time-domain combining PMCHW(Poggio, Miller, Chang, Harrington, Wu) formulation for complex metallic/dielectric structures are elaborated uniformly based on the surface equivalence principle and boundary conditions firstly. For an attempt to choose optimal TDIE for different structures, the applicability and excellence as well as disadvantages of different TDIEs are compared. Then the solving procedures of these TDIEs based on the RWG function using MOT are elaborated, including the model building of complex objects, data extraction, some mathematical formulations in realizing the algorithm, calculating the matrix elements, the parameter extraction and the post processing after the simulation, etc.
Different temporal bases functions are evaluated and their high frequency components are compared for the cause of their impact on late-time stability in this thesis. In addition, the method of impedance matrix prestorage for composite structures is presented, which largely saves the time of repeatedly computing impedance elements, and the required memory is formulated. In the procedure of computing impedance matrix elements, an improved method of accurate evaluation of retarded time integrals with singularity in self-impedance elements in MOT scheme is presented, which improve the late-time stability of MOT scheme. Some numerical results of practical complex antenna and scattering problems are presented to illustrate the validity of the method and better stability of TD-E-PMCHW compared with TD-EFIE for complex metallic/dielectric structures.
In the second part, for the interconnection between complex metallic/dielectric EM structures and circuits, a simultaneous simulation scheme of EM section and linear/ nonlinear lumped circuit section is developed through combining TDIE used in EM simulation and MNA used in circuit simulation. The scheme is based on thought of "coupling current" serving as the bridge to connect the circuit section and EM section. Following the "coupling current", the "modified" continuity equation and "generalized" Kirchoff's Law are used to analyzing the coupling between the EM section and circuit section.
Finally, a microstrip power splitter and a microstrip filter are analyzed using TD-E-PMCHW algorithm. In addition, a miniature dielectric resonator loaded patch antenna and a printed circular disc monopole Antenna for UWB systems are computed, and the performance of impedance match and radiation of the two antennas is analyzed. Through analysis effect of the antennas' structure parameters on resonant frequency and return loss bandwith is gained. For nonlinear elements in circuits, a diode applied in a mixer is computed. All these examples demonstrate the better stability in analysis of complex structure of TD-E-PMCHW algorithm compared with other TDIEs and the advantages of computation in time domain.
引文
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