创建一个高效的仿真模型外文翻译

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1、毕业论文外文翻译原文题目：Creating an Efficient Simulation Model译文题目：创建一个高效的仿真模型在本章中，我们描述的数值模拟软件的总体结构实现一个高效的仿真模型，在不同的步骤。5.1数值模拟软件的总体结构数值模拟软件由三个主要部件预处理，求解和后处理，如图所示。 5.1。图5.1。数值模拟软件的主要组成部分前和后处理被纳入了一个交互式图形用户界面（GUI）。求解器启动，并从这个接口控制。虽然今天的用户可能会觉得只有一个软件，该司825创建一个高效的仿真模型软件分为三个主要部分组成，从逻辑和说教感观点。5.1.1预处理预处理器用于建立仿真模型，如图。 5.2

2、。图5.2。基本的仿真模型，包括天线的几何尺寸，材料性能，港口，边界条件，为近场录音盒我们在下面的列表给出一个简短的概述，在处理的任务在模型生成的过程。每个项目的解释在随后的章节中更多的细节。一般定义：在这个阶段，不同层次或组件定义组织的数据。此外，物理量的单位被选中，例如，长度以毫米为单位，在主频。几何对象的几何形状的定义。中有一般三种不同的方法，可以结合几何进入交互图形用户界面（GUI），几何导入数据从一个CAD文件，或描述的对象是由一个宏语言。材料性能：介电性能被分配到几何已在第一步为蓝本的对象。材料选择从数据库中预定义的常用材料或新材料是指通过指定的介质和磁学性质。激励：端口都定义为了

3、激发结构和评估基于电路。5.1一般结构的数值模拟软件边界条件：在不同的模拟量的外部边界各种边界条件适用于以代表自由空间，电场和磁场的墙壁或对称平面。啮合：离散成小分子结构与均匀材料的性能。该模型的离散化是至关重要的一步，因为它会影响所需的数值的努力和解决方案的准确性。仿真参数：定义额外的参数控制解决方案的过程中，例如，要使用一种求解，定义一个endcriterion时间步进算法，所需的精度，AR滤波，多激励，端口模式。5.1.2求解求解计算电磁问题的近似解预处理过程中产生的数据的基础上。该解决方案的过程是通常在一个所谓的日志文件记录，列出了重要的细节，并模拟的统计信息，例如：解决方案需要时间，

4、数量遇到未知数，内存的要求，以及警告和错误在解决方案的过程中。5.1.3后处理后处理器是用来评估的求解结果。结果可表中显示，一维，二维和三维图。端口的相关参数：输入阻抗等参数，散射从外地求解结果中提取参数，电压和电流。这些参数需要指定结构的行为当连接到电路或其他RF元件。可视化：不同的场分布（等高线和箭头图）近场数量显示。场分布的可视化到结构的工作方式，给用户的见解。这种理解可以帮助改善结构的性能，或帮助确定在该模型的错误。天线参数：天线参数，如辐射方向图，增益，方向性，半功率波束宽度，旁瓣抑制和辐射效率计算。其他参数：例如，评价特定吸收率（SAR）和EMC领域的优势，在一个指定的距离的相关数

5、据，如在比较EMC限制。5创建一个高效的仿真模型。5.2几何在建立仿真模型的第一步是一代三维结构，如天线或一个过滤器的形状。在最新的电磁建模软件中，通常有三种方式存在实现这一目标：通过图形用户界面（GUI）的互动建设，进口的CAD（计算机辅助设计）数据和通过宏语言对象的定义。5.2.1互动建设，通过图形用户界面（GUI）图形用户界面（GUI），可帮助用户创建交互式的他的模型几何。 GUI施工能力非常相似那些提供基本的电脑辅助设计（CAD）软件撤消修改图5.3。简单三维物体一般建设开始与简单对象的定义。更多结合和操作简单的对象，可以产生复杂的对象。简单的对象，可分为一，二，三维形状。简单的一维对

6、象包括直线，多边形和样条段。简单的两维对象包括三角形，长方形，圆形，椭圆形和封闭的多边形。简单的三维对象包括盒，圆筒，锥体和球体（见图5.3）。根据软件更复杂的基本如环形，螺旋，螺旋，椭圆形，与债券线的形状。可以修改这些简单的对象，即，旋转，移动，镜像，复制，缩放或拉伸。此外，布尔运算，可应用于重叠的元素。图。 5.4影响减法，加法和路口显示。如果我们绘制两个重叠的像一个盒子和一个3D对象球体（图5.4A），我们从包装盒中减去球体形状是一个球形，作为在图中切出框。 54亿。布尔操作另外结合两图所示的对象。 5.4c。如果我们相交两个对象，我们得到一个对象框的共同部分组成和球体图所示。 5.4d

7、。图5.4。不同的布尔运算修改的对象：（一）重叠的方块和领域，（二）减法球体从框，（三）除了和（d）路口框和球旋转二维实体。图5.5显示了基本的概念。图。 5.5A12D脸是沿着一个矢量方向的挤压。图。 5.5（二）一个二维的脸被扭曲沿曲线图。 5.5c二维面是围绕一个轴旋转。这些操作都非常在强大的创建复杂的几何形状。一般可以控制输出其他选项，例如对象可以是锥形，即大小二维面有所不同，因为它沿传播的挤压载体（图5.5d）。有时GUI包括先进的功能，如对象的描述复杂的数学公式或边缘平滑（四舍五入）。虽然已经变得非常的几何形状的图形强大的几何应保持尽可能的简单。只有细节影响电磁行为应列入。圆边的结

8、果865创建一个高效的仿真模型。图5.5。从二维轮廓3D对象的创建在一个有吸引力的模型，但导致的细离散结构和从而增加了计算负担。5.2.2通过宏语言的对象定义在初期的EM模拟一个基于文本的模型的定义输入文件是共同使用。今天，这种模型的创建仍然是有用的如果许多类似的几何结构进行了分析。几何特征可以定义变量和被轻易改变。因此，基于文本输入文件是适合的参数研究和优化程序。最EM建模软件包，提供基于文本的宏语言模型的定义。5.2.3导入CAD（计算机辅助设计）数据在EM建模，设计和微波分析，我们可以区分组件。在后一种情况下，它可能会使用CAD数据的实际从生产过程中的微波元件。图5.6显示了作为一个5.

9、2几何87例如，一个天线模块组成一个具有三维载体复杂形状的天线板。机械CAD软件ProEngineer，SolidWorks或CATIA拥有许多更强大的功能，形状复杂的机械设计对象比基本的CAD纳入EM仿真工具软件。为了从机械CAD软件导入模型可以使用标准化的数据交换格式，如STEP（产品模型数据交换标准）的IGES（初始图形交换规范）DXF（图形交换格式）。图5.6。CAD模型的天线模块虽然进口的CAD数据可能看起来造型非常优雅的方式也有一些缺点。与CAD数据的第一个问题是，许多包括机械重要的，但电无关的细节。这些CAD细节导致更细的网格中，并因此增加模拟时间没有显着提高结果的准确性。另一个

10、问题与CAD数据可能出现的几何精度（精度）。如果CAD系统和EM建模软件的图形用户界面，适用于不同程度几何精度的意外可能会发生错误。例如，小学连接对象显示重叠区域是分开的。由此，我们得出这样的结论：CAD导入很少是一个“任务。 “随后的模型简化和数据愈合的繁琐的任务。作为一个例子图。 5.7A给出了一个天线模块，包括小孔和差距。这些细节都包含在原有的机械CAD文件原因（紧固），但电无关。图5.7b所示删除不必要的细节后的天线模块。图5.7c-F显示如何的小细节，在精细网格的结果，导致较长的模拟倍。另一个例子是薄的金属结构。这些薄薄结构，例如，图微带线带导体。 5.8，可以看作一个二维（平面）对

11、象。这种建模方法模拟。图5.7。从CAD模型的详细信息：（一）含有原始的CAD数据的去除无关紧要的小细节，（二）简化模型（细节），（CF）的影响正交和三角网格少未知数和增加细胞大小的机型相比，体积建模。5.2.4综述当设立一个仿真模型，意图应的几何不从视觉角度来看，最准确的结构但最简单的一个代表的电磁现象正在审议的结构。此外，过多的细节可以放大计算的努力，一方面，导致容易出错，很难验证仿真模型。撤消修改图5.8。 FDTD离散化微带线的截面。简化模型一个两维板薄带导体的代表性有时又何尝不是如此明确，以决定是否有一定的几何初步细节重大与否。在这种情况下，建议开始与简单的模型，并验证这个细节的具体

12、影响，在一个单独的仿真模型。5.3材料特性几何结构定义后，被分配到材料性能不同的对象。例如，在微带结构中，我们有一个金属地平面和金属的痕迹，基材是介质和体积顶层上面是空气。技术上重要的和广泛使用的材料往往是预定在该软件。他们可以直接从数据库中选取。最重要的预定义的材料是真空和PEC（理想导体）。如果列表中没有提供一种特殊材料，它可以通过指定定义其相对介电常数介电常数，电导率，和相对渗透率R。代替的电导率的损耗角正切tan的可能定义。表5.1列出了一些通用材料的介电性能。不同的技术上有趣的介电性能的典型值从1 GHz至10 GHz频率范围内的基板材料选项卡。 5.2。表5.1。不同材料的介电性能

13、材料介电常数/ S / MR真空1.00.01.0空气1.0060.01.0特氟隆（无损）2.20.0 1.0铜1.05.81071.0PEC的1.01.0表5.2。不同的基板材料的介电性能的典型值在1-10千兆赫的频率范围材料介电常数的tanR氧化铝9.5 - 10.50.0002 - 0.00031.0FR4的3.9 - 4.30.01 - 0.0251.0聚四氟乙烯2.0 - 2.20.001 - 0.0031.0撤消修改频率相关的介电性能，可以进入软件在选定的频率定义的属性和使用分段线性在选定的频率之间的频率间隔的近似。有时频率的依赖关系可以定义为封闭形式的功能或身体放松模型（Debe

14、ye材料）。各向异性审议确定各向异性张量。此外，非电参数是必要的具体计算在后加工的数量必须指定。例如，质量密度需要以特定吸收率的计算（SAR）的生物组织。高导电性的结构，应仿照完美电导体（PEC），如果在材料的损失是微不足道的。它的优点一个PEC，努力减少计算：领域内PEC等于零，因此字段值也不需要计算基于卷的算法。虽然FDTD和FEM是基于对三维量元素，持平或一维的PEC的对象可以是创建。这是特别有用的薄金属板或电线。5.4端口端口用于激发的被动结构和计算电路有关像散射参数，输入阻抗，电压和电流的数量。以下类型的端口，在大多数软件包可供选择：波导港口，平面波激励和集中或集中的港口。结构可以有

15、多个端口。在一个多模型软件可以自动计算出的散射矩阵的所有元素描述了不同的端口之间的相互作用。根据数值方法的应用，这是由一系列的模拟只一个端口兴奋的时间和所有其他模式相匹配的港口阻抗（例如，FDTD法）。其他方法（例如，MOM）计算散射在一个单一的模拟矩阵。另一种方式来使用多个端口同时更激发多个端口。这可以用来激发没有明确的天线阵列造型喂食网络。在计算的同时激发的情况下散射参数是不可能执行的方法一系列的模拟来确定散射参数。5.4.1波导端口撤消修改高频元件通常是由波导馈，如微带同轴或共面线。在仿真模型的进料线延长计算空间的边界，如图。 5.9A-B。在边界波导端口被定义，模拟半无限传输行向前行波

16、送入。在时域的情况下解决方案的过程（例如，时域有限差分法）来波进入计算空间，互动的结构与入射功率的一小部分旅行通过端口备份。从传入和传出的信号散射参数可以计算。为了激发结构，领域向前传播模式上料线的波待定。由于总是比较一个模式，可以沿直线传播，端口模式是由用户指定。在大多数技术应用的基本模式使用，例如，上同轴线TEM波在矩形TE10模式波导。在该行的横截面的二维场模式计算之前，通过一个特殊的二维求解全三维分析。作为一个二维的例子准TEM微带线的基本模式是港口领域的格局描绘图。 5.9c。入射波进入结构是二维平面的大小一个关键点。如果只有基本模式感兴趣的是，2D平面入射波进入结构没有大到足以让在

17、港口区的边缘被扭曲。另一方面，如果2D平面上升，高阶模式可以传播。港口区的大小取决于线的几何形状，以及基板的介电常数作为频率。对于许多实际问题，一个合理的起点港区是：五至十倍的基板的高度和五至十倍宽度跟踪。在MOM代码，定义没有计算量，微带线可兴奋的跟踪边缘。在不连续的高阶模式出现。如果是高阶模式非传播模式，他们迅速腐烂，因为他们沿直线传播。港口和连续性之间的距离应该足以允许非蔓延（逝）模式衰减。如果高阶模式设备的操作是必不可少的，必须考虑到这些模式在与这些模式相关的分析和S参数必须计算。5.4.2平面波激励激发入射平面波的结构图所示。 5.10在各种应用中非常有用。一个例子是计算雷达图5.9

18、。波导微带端口：（一）顶视图，（二）透视图（三）二维场模式（端口模式）入射波在侧视图截面（RCS）的散射对象。另一个例子是分析排入中的电磁兼容性（EMC）领域。入射平面波的振幅通常描述电场矢量，极化矢量和传播方向。内部结构，电流，电压和当地的电力观测点和磁场值可以被定义。此外，散射场进行采样，以计算对象的雷达截面。撤消修改图5.10。平面波令人兴奋的一个被动的平面结构。坡印廷矢量S指示方向的传播和E和H的电场和磁场领域的组成部分，分别。5.4.3集总端口集中或集中的端口，可用于计算空间内激励结构。他们通常都放在两个导电部件如电压或电流源模型和行为与定义的特征阻抗。图5.11显示了一个集中的港口

19、，激发中心馈电偶极。图5.11。集总端口激动人心的一个中心馈电偶极子天线集中可以计算空间内使用的端口是多灵活的比通常是在边界定义的端口波导问题域。此外，他们并不需要加强离散饲养结构。因此，他们提供的通常是一个很好的起点为简单的仿真模型，并可以取代波导端口，如果有更多的精确的模型或模式的分离是必需的。集中的港口限于相比是很小的喂养结构波长。他们可以通过评估散射参数计算在港口的电压和电流。撤消修改Creating an Efficient Simulation ModelIn this chapter we describe the general structure of numerical m

20、odeling softwareand the different steps towards an efficient simulation model.5.1 General Structure of Numerical Modeling SoftwareNumerical simulation software consists of three main components preprocessor,solver, and postprocessor as shown in Fig. 5.1.Fig. 5.1. Main components of numerical simulat

21、ion softwareThe pre- and postprocessor are incorporated into an interactive GraphicalUser Interface (GUI). The solver is started and controlled from this interface.Although today the user may feel only one software, the division of thesoftware into three main components makes sense from a logical an

22、d didacticpoint of view.5.1.1 PreprocessorThe preprocessor is used to set up the simulation model as shown in Fig. 5.2.Fig. 5.2. Basic simulation model including antenna geometry, material properties,ports, boundary conditions, box for nearfield recordingIn the following list we give a short overvie

23、w over the tasks that are addressedwithin the process of model generation. Each item is explained inmore detail in the subsequent sections.General definitions: At this stage different layers or components are definedto organize the data. Furthermore, the units of physical quantitiesare selected, e.g

24、., length in millimeters, frequency in GHz.Geometry: The geometrical shapes of the objects are defined. There are ingeneral three different approaches that can be combined: The geometry isentered interactively by a graphical user interface (GUI), the geometricaldata is imported from a CAD file, or t

25、he objects are described by a macrolanguage.Material properties: Dielectric properties are assigned to the geometricalobjects that have been modeled in the first step. Materials are selectedfrom a database of predefined commonly used materials or new materialsare defined by specifying dielectric and

26、 magnetic properties.Excitation: Ports are defined in order to excite the structure and to evaluatecircuit-based quantities like scattering parameters, impedances, voltagesand currents.Boundary conditions: At the outer boundary of the simulation volume differentkinds of boundary conditions are appli

27、ed in order to represent freespace, electric and magnetic walls or planes of symmetry.Meshing: The structure is discretized into small elements with homogeneousmaterial properties. The discretization of the model is a crucial step sinceit affects the required numerical effort and the accuracy of the

28、 solution.Simulation parameters: Additional parameters are defined to control thesolution process, e.g., the kind of solver to be used, definition of an endcriterionfor time-stepping algorithms, desired accuracy, AR filtering, multiportexcitation, number of port modes.5.1.2 SolverThe solver calculat

29、es the approximate solution of the electromagnetic problembased on the data generated during preprocessing. The solution process istypically documented in a so-called log-file that lists important details andstatistics of the simulation, for example: time need for the solution, number ofunknowns, me

30、mory requirements, as well as warnings and errors encounteredduring the solution process.5.1.3 PostprocessorThe postprocessor is used to evaluate the results of the solver. The results canbe displayed in tables, 1D-, 2D- and 3D-plots.Port-related parameters: Parameters like input impedances, scatter

31、ingparameters, voltages and currents are extracted from the field solver results.These parameters are needed to specify the behavior of the structurewhen connected to a circuit or other RF components.Visualization: Field distributions (contour and arrow plots) of differentnearfield quantities are di

32、splayed. The visualization of field distributionsgives the user insights into the way the structure works. This understandingcan help to improve the performance of the structure or help to identifyerrors in the model.Antenna parameters: Antenna parameters like radiation pattern, gain, directivity,ha

33、lf-power beam width, side lobe suppression and radiation efficiencyare calculated.Additional parameters: For example, evaluation of specific absorption rate(SAR) and EMC related data like field strengths in a specified distancein comparison to EMC limits.84 5 Creating an Efficient Simulation Model5.

34、2 GeometryThe first step in setting up the simulation model is the generation of thethree-dimensional structure, e.g., the shape of an antenna or of a filter.In up-to-date electromagnetic modeling software usually three ways existto accomplish this goal: interactive construction via Graphical User I

35、nterface (GUI), import of CAD (Computer Aided Design) data and object definition via macro language.5.2.1 Interactive Construction via Graphical User Interface (GUI)A Graphical User Interface (GUI) helps the user to create interactively thegeometry of his model. The GUI construction capabilities are

36、 very similar tothose that are available in basic Computer Aided Design (CAD) software.Fig. 5.3. Simple three-dimensional objectsUsually the construction starts with the definition of simple objects. Morecomplex objects can be generated by combining and manipulating simple objects.Simple objects can

37、 be classified into one-, two- and three-dimensionalshapes. Simple one-dimensional objects include line, polygon and spline segment.Simple two-dimensional objects include triangle, rectangle, circle, ellipseand closed polygon. Simple three-dimensional objects include box, cylinder,cone and sphere (s

38、ee Fig. 5.3). Depending on the software more complex basicshapes like toroid, spiral, helix, ellipsoid, and bond-wires are available.These simple objects can be modified, i.e., rotated, moved, mirrored,copied, scaled or stretched. Furthermore, boolean operations can be appliedon overlapping elements

39、. In Fig. 5.4 the effects of subtraction, addition andintersection are shown. If we draw two overlapping 3D objects like a box and asphere (Fig. 5.4a) and we subtract the sphere from the box the resulting shapeis a box with a spherical cut-out in it as shown in Fig. 5.4b. The boolean operationadditi

40、on combines the two objects as shown in Fig. 5.4c. If we intersectthe two objects we get an object that consists of the common parts of the boxand sphere as shown in Fig. 5.4d.Fig. 5.4. Objects modified by different boolean operations: (a) overlapping boxand sphere, (b) subtraction of sphere from bo

41、x, (c) addition and (d) intersectionof box and sphere、Another way to create more complex 3D objects is to extrude, twist, orrotate 2D entities. Figure 5.5 shows the basic concepts. In Fig. 5.5a a 2D faceis extruded along a vector. In Fig. 5.5b a 2D face is twisted along a curve andin Fig. 5.5c a 2D

42、face is rotated around an axis. These operations are verypowerful in creating complex geometries. Usually the output can be controlledby additional options, for example the object can be tapered, i.e., the size ofthe 2D face varies as it propagates along the extrusion vector (Fig. 5.5d).Sometimes th

43、e GUI includes advanced features like the description of objectsby complex mathematical formulas or the smoothening (rounding) of edges.Although the graphical generation of geometrical shapes has become verypowerful, the geometry should be kept as simple as possible. Only details thataffect the elec

44、tromagnetic behavior should be included. Rounded edges resultFig. 5.5. Creation of 3D objects from 2D contoursin an appealing model but lead to a finer discretization of the structure andthus increase the computational burden.5.2.2 Object Definition via Macro LanguageIn the early days of EM modeling

45、 the definition of a model by a text-basedinput file was common use. Today this kind of model creation is still usefulif many structures with similar geometry are analyzed. Geometrical featurescan be defined by variables and are easily changed. Therefore, text-basedinput files are suited for paramet

46、er studies and optimization routines. MostEM modeling software packages provide a macro language for the text-baseddefinition of models.5.2.3 Import of CAD (Computer Aided Design) DataIn EM modeling we can distinguish between design and analysis of microwavecomponents. In the latter case it may be p

47、ossible to use CAD data of actualmicrowave components from the production process. Figure 5.6 shows as an5.2 Geometry 87example an antenna module consisting of a three-dimensional carrier with acomplex-shaped antenna plate.Mechanical CAD software like ProEngineer, SolidWorks or Catia possessmany mor

48、e powerful features for the design of complex-shaped mechanicalobjects than the basic CAD tools that are incorporated in EM simulationsoftware. In order to import models originating from mechanical CAD softwareone can use standardized exchange data formats like STEP (STandard for the Exchange of Pro

49、duct model data) IGES (Initial Graphics Exchange Specification) DXF (Drawing eXchange Format).Fig. 5.6. CAD model of an antenna moduleAlthough import of CAD data may seem a very elegant way of modelingthere are some drawbacks. The first problem with CAD data is that manymechanically important but el

50、ectrically irrelevant details are included. TheseCAD details result in a finer mesh and therefore increase the simulation timewithout significantly improving the accuracy of the results. Another problemwith CAD data may arise from geometrical accuracy (precision). If the CADsystem and the GUI of the

51、 EM modeling software apply different degreesof geometrical precision unexpected errors may occur. For example, primaryconnected objects show overlapping areas or are separated.From this we conclude that CAD import is seldom a one-click task. Thesubsequent model simplification and data healing are c

52、umbersome tasks.As an example Fig. 5.7a shows an antenna module that includes smallholes and gaps. These details are included in the original CAD file for mechanicalreasons (fastening) but are electrically irrelevant. Figure 5.7b showsthe antenna module after the unnecessary details are removed. Fig

53、ures 5.7cfshow how the small details result in finer meshes that lead to longer simulationtimes.Another example concerns thin metallic structures. These thin structures,e.g., a strip conductor of a microstrip line shown in Fig. 5.8, can be modeled asa two-dimensional (flat) object. This modeling app

54、roach leads to simulationFig. 5.7. Removal of details from a CAD model: (a) Original CAD data containingsmall irrelevant details, (b) simplified model (details removed), (c-f) Effects onorthogonal and triangular meshingmodels with less unknowns and increased cell sizes compared to volumetricModeling

55、.5.2.4 SummaryWhen setting up the geometry of a simulation model the intention shouldnot be to draw the most accurate structure from the visual point of viewbut the simplest one that represents the electromagnetic phenomena of thestructure under consideration. Moreover, too many details can enlarge

56、thecomputational effort, on the one hand, and result in an error-prone, difficultto validate simulation model.Fig. 5.8. FDTD discretization of cross-section of a microstrip line. Simplified modelby representation of the thin strip conductor by a two-dimensional plateSometimes is it not so clear to d

57、ecide initially if a certain geometricaldetail is significant or not. In this case it is recommended to start with thesimple model and to validate the specific influence of this detail in a separatesimulation model.5.3 Material PropertiesAfter a geometrical structure is defined, material properties

58、are assigned todifferent objects. For example, in a microstrip structure we have a metallicground plane and metallic traces, the substrate is dielectric and the volumeabove the top layer is air.Technically important and widely used materials are often predefined inthe software. They can be selected

59、directly from a database. The most importantpredefined materials are vacuum and PEC (perfect electric conductor).If a special material is not available in the list, it can be defined by specifyingits relative permittivity r, electrical conductivity , and relative permeabilityr. Instead of defining t

60、he conductivity the loss tangent tan may bedefined. Table 5.1 lists the dielectric properties of some generic materials.Typical values for the dielectric properties of different technically interestingsubstrate materials in the frequency range from 1 GHz to 10 GHz are givenin Tab. 5.2.Table 5.1. Die

61、lectric properties of different materialsMaterial r / S/m rVacuum 1.0 0.0 1.0Air 1.006 0.0 1.0Teflon (lossless) 2.2 0.0 1.0Copper 1.0 5.8 107 1.0PEC 1.0 1.090 5 Creating an Efficient Simulation ModelTable 5.2. Typical values for the dielectric properties of different substrate materialsin the freque

62、ncy range 110 GHzMaterial r tan rAlumina 9.5 10.5 0.0002 0.0003 1.0FR4 3.9 4.3 0.01 0.025 1.0PTFE 2.0 2.2 0.001 0.003 1.0Frequency dependent dielectric properties can be entered into the softwareby defining the properties at selected frequencies and using piecewise linearapproximations in the freque

63、ncy intervals between the selected frequencies.Sometimes frequency dependence can be defined by closed-form functions orphysical relaxation models (Debeye materials). Anisotropic properties can beconsidered by defining an anisotropy tensor.Furthermore, non-electric parameters that are necessary to calculate specificquantities in the post processing have to be specified. For example, themass density is needed in order to calculate the specific absorption rate(SAR) in biological tissue.Structures with high conductivity should be modeled as Perfectly ElectricConduc