Computational Electromagnetics

合集下载

cst基本辐射单元

cst基本辐射单元
CST（Computational Electromagnetics Studio）是一种电磁场仿真软件，用于电磁场分析和设计。

在CST中，基本辐射单元（Basic Radiating Element）是指构成天线结构的最小单元。

基本辐射单元根据具体的天线类型和设计需求而不同。

例如，在微带天线中，基本辐射单元可以是微带贴片天线的金属补偿片；在偶极子天线中，基本辐射单元可以是偶极子的导线。

通过将多个基本辐射单元进行组合和布局，可以形成复杂的天线结构。

通过对基本辐射单元的电磁特性进行仿真和优化，能够实现对天线的性能进行分析和改进。

需要注意的是，选择合适的基本辐射单元对于天线的设计和性能至关重要。

合理的基本辐射单元选择能够提高天线的辐射效率、增益、频率响应等关键指标。

因此，在进行天线设计时，需要根据具体的应用需求和设计要求选择合适的基本辐射单元。

应用FDTD方法解决电磁辐射问题

应用FDTD方法解决电磁辐射问题自电磁场基本方程以来，电磁场理论和应用的发展已经有一百多年的历史。

目前，电磁波的研究已深入到各个领域，应用十分广泛，例如无线电波传波，光纤通信和移动通信，雷达技术，微波，天线，电磁成像，地下电磁探测，电磁兼容等等。

在各类复杂系统中的电磁问题，主要依靠各种电磁场数值计算方法加以解决。

随着电子计算机处理能力和存储容量的巨大发展，更促进了这些计算方法在实际问题中的应用。

目前在电磁场领域应用的数值算法也是种类繁多，各有其优缺点，常用的电磁场计算方法大致有：FDTD Finite difference time domain （时域有限差分法）TLM Transmission line method （传输线法）FEM Finite element method （有限元法）BEM Boundary element method （边界元法）MoM Method of moments （矩量法）其中时域有限差分法(FDTD)理论经过30多年的发展和完善，已经成为时域电磁场数值计算的主要方法之一，并广泛应用各类实际工程电磁场中。

一、 FDTD 法简介时域有限差分法以差分原理为基础，直接从概括电磁场普遍规律的麦克斯韦旋度方程出发，将其转换为差分方程组，在一定体积内和一段时间上对连续电磁场的数据采样。

因此，它是以电磁场问题的最原始、最本质、最完备的数值模拟。

以它为基础制作的计算程序，对广泛的电磁场问题具有通用性，因此得到了广泛的应用。

1. Yee 差分算法基本原理考虑空间一个无源区域，其煤质参数不随时间变化且各向同性，由Maxwell 方程组中的两个旋度方程在直角坐标系中可导出六个耦合公式：1(1.1)1(1.2)H E H t E H E t ρμμσεε∂=-∇⨯-∂∂=∇⨯-∂ ⇒1()(1.3)1()(1.4)1()(1.5)1()(1.6)1()(1.7)1()(1.8)y x z x y x z y y x z z y x z x y x z y y x z z E H E H t z y H E E H t x z E E H H t y x H E H E t y z E H H E t z x H H E E t x y ρμρμρμσεσεσε∂⎧∂∂=--⎪∂∂∂⎪⎪∂∂∂=--⎪∂∂∂⎪⎪∂∂∂⎪=--∂∂∂⎪⎨∂∂∂⎪=--⎪∂∂∂⎪∂∂⎪∂=--⎪∂∂∂⎪∂∂∂⎪=--⎪∂∂∂⎩其中ε为介电常数（F/m ）；μ为磁导率（H/m ）；σ为电导率（S/m ）；ρ为磁阻率（/m Ω）。

电磁场百科全书

电磁场百科全书在电磁学里，电磁场（electromagnetic field）是因带电粒子的运动而产生的一种物理场。

处于电磁场的带电粒子会感受到电磁场的作用力。

电磁场与带电粒子（电荷或电流）之间的相互作用可以用麦克斯韦方程组和洛伦兹力定律来描述。

电磁场可以被视为电场和磁场的连结。

追根究底，电场是由电荷产生的，磁场是由移动的电荷（电流）产生的。

对于耦合的电场和磁场，根据法拉第电磁感应定律，电场会随着含时磁场而改变；又根据麦克斯韦-安培方程，磁场会随着含时电场而改变。

这样，形成了传播于空间的电磁波，又称光波。

无线电波或红外线是较低频率的电磁波；紫外光或 X-射线是较高频率的电磁波。

电磁场涉及的基本相互作用是电磁相互作用。

这是大自然的四个基本作用之一。

其它三个是引力相互作用，弱相互作用和强相互作用。

电磁场倚靠电磁波传播于空间。

从经典角度，电磁场可以被视为一种连续平滑的场，以类波动的方式传播。

从量子力学角度，电磁场是量子化的，是由许多个单独粒子构成的。

目录 [隐藏]1 概念2 电磁场的结构2.1 连续结构2.2 离散结构3 电磁场动力学4 电磁场是一个反馈回路5 数学理论6 电磁场性质6.1 光波是一种电磁辐射7 健康与安全8 参阅9 参考文献10 外部链接[编辑] 概念静止的电荷会产生静电场；静止的磁偶极子会产生静磁场。

运动的电荷形成电流，会产生电场和磁场。

电场和磁场统称为电磁场。

电磁场对电荷产生力，以此可以检测电磁场的存在。

电荷、电流与电磁场的关系由麦克斯韦方程组决定。

麦克斯韦方程共有四条，是一组偏微分方程，其未知量是电场(E)、磁场(B)、位移电流(D)、辅助磁量(H)。

其中包括这些未知量对时间和空间的偏导数。

给定了源(电荷与电流)和边界条件(电场与磁场在边界上的值)，可以用数值方法求解麦克斯韦方程，从而得到电场和磁场在不同时刻和位置的值。

这一过程称为电磁场数值计算，或者计算电磁学（英语：computational electromagnetics），在电子工程尤其是微波与天线工程中有重要地位。

计算电磁学

计算电磁学计算电磁学是指对一定物质和环境中的电磁场相互作用的建模过程，通常包括麦克斯韦方程计算上的有效近似。

计算电磁学被用来计算天线性能，电磁兼容，雷达散射截面和非自由空间的电波传播等问题。

计算电磁学的主要思想有，基于积分方程的方法，基于微分（差分）方程的方法，及其他模拟方法。

1.基于积分方程的方法1.1 离散偶极子近似（discrete dipole approximation，DDA） DDA是一种计算电磁波在任意几何形状物体上散射和吸收的方法，其表达式基于麦克斯韦方程的积分形式。

DDA用有限阵列的可极化点来近似连续形式的物体。

每个点通过对局部电场的响应获得对应的偶极子矩量，然后这些偶极子通过各自的电场相互作用。

因此，DDA 有时也被认为是耦合偶极子近似。

这种线性方程的计算一般采用共轭梯度迭代法。

由于离散矩阵的对称性，就可能在迭代中使用FFT计算矩阵的向量乘法。

1.2 矩量法（Method of Moments，MoM ），边界元法（Boundary Element Method，BEM ）MoM和BEM是求解积分形式（边界积分形式）的线性偏微分方程的数值计算方法，已被应用于如流体力学，声学，电磁学等诸多科技领域。

自从上世纪八十年代以来，该方法越来越流行。

由于只计算边界值，而不是方程定义的整个空间的数值，该方法是计算小表面（体积）问题的有效办法。

从概念上讲，它们在建模后的表面建立网格。

然而对于很多问题，此方法的效率较基于体积离散的方法（FEM，FDTD）低很多。

原因是，稠密矩阵的生成将意味着存储需求和计算时间会以矩阵维数的平方律增长。

相反的，有限元矩阵的存储需求和计算时间只会按维数的大小线性增长。

即使可以采用矩阵压缩技术加以改善，计算成功率和因此增加的计算复杂性仍强烈依赖问题的本质。

BEM可用在能计算出格林函数的场合，如在线性均匀媒质中的场。

为了能使用BEM，需要对问题有很多限制，使用上不方便。

计算电磁学

计算电磁学摘要：作为一门交叉学科，计算电磁学结合了计算机技术、数值计算学和电磁学等相关学科的知识，正经历着日新月异的发展。

各种各样的计算方法层出不穷，由此诞生的各种商业DEA软件如HFSS、CST、FECO、ADS等在工程领域中得到了广泛的应用，为解决各种复杂的工程问题提供了有力的帮助，极大地缩短了研究周期，降低了成本和提高了稳定性。

计算电磁学是指对一定物质和环境中的电磁场相互作用的建模过程，通常包括麦克斯韦方程计算上的有效近似。

计算电磁学被用来计算天线性能，电磁兼容，雷达散射截面和非自由空间的电波传播等问题。

计算电磁学的主要思想有，基于积分方程的方法，基于微分（差分）方程的方法，及其他模拟方法。

关键词：计算电磁学，麦克斯韦方程，雷达散射截面Computational ElectromagneticsAbstract: As an interdisciplinary, computational electromagnetics combines the knowledge of computer technology, numerical calculus and electromagnetics and other related disciplines, is experiencing the ever-changing development. A variety of computing methods emerge in an endless stream, the birth of a variety of commercial DEA software such as HFSS, CST, FECO, ADS, etc. in the field of engineering has been widely used to solve a variety of complex engineering problems provide a strong help , Greatly shortening the research cycle, reducing costs and improving stability. Computational electromagnetism is the modeling process for the interaction of electromagnetic fields in a given substance and environment, usually including the effective approximation of the Maxwell equation. Computational electromagnetism is used to calculate antenna performance, electromagnetic compatibility, radar cross section and non-free space radio propagation problems. The main ideas of computational electromagnetics are based on the integral equation method, the method based on differential (differential) equation, and other simulation methods.Key word: computational electromagnetics, Maxwell equation, radar cross section第一章引言1864年Maxwell在前人的理论（高斯定律、安培定律、法拉第定律和自由磁极不存在）和实验的基础上建立了统一的电磁场理论，并用数学模型揭示了自然界一切宏观电磁现象所遵循的普遍规律，这就是著名的Maxwell方程。

mom课本

Chapter1Computational ElectromagneticsBefore the digital computer was developed,the analysis and design of electromag-netic devices and structures were largely experimental.Once the computer and nu-merical languages such as FORTRAN came along,people immediately began using them to tackle electromagnetic problems that could not be solved analytically.This led to aﬂurry of development in aﬁeld now referred to as computational electromag-netics(CEM).Many powerful numerical analysis techniques have been developed in this area in the last50years.As the power of the computer continues to grow, so do the nature of the algorithms applied as well as the complexity and size of the problems that can be solved.While the data gleaned from experimental measurements are invaluable,the entire process can be costly in terms of money and the manpower required to do the required machine work,assembly,and measurements at the range.One of the fundamental drives behind reliable computational electromagnetics algorithms is the ability to simulate the behavior of devices and systems before they are actually built. This allows the engineer to engage in levels of customization and optimization that would be painstaking or even impossible if done experimentally.CEM also helps to provide fundamental insights into electromagnetic problems through the power of computation and computer visualization,making it one of the most important areas of engineering today.1.1COMPUTATIONAL ELECTROMAGNETICS ALGORITHMSThe extremely wide range of electromagnetic problems has led to the development of many different CEM algorithms,each with its own beneﬁts and limitations. These algorithms are typically classiﬁed as so-called“exact”or“low-frequency”and “approximate”or“high-frequency”methods and further sub-classiﬁed into time-or frequency-domain methods.We will quickly summarize some of the most commonly used methods to provide some context in how the moment methodﬁts in the CEM environment.12The Method of Moments in Electromagnetics1.1.1Low-Frequency MethodsLow-frequency(LF)methods are so-named because they solve Maxwell’s Equations with no implicit approximations and are typically limited to problems of small electrical size due to limitations of computation time and system memory.Though computers continue to grow more powerful and solve problems of ever increasing size,this nomenclature will likely remain common in the literature.1.1.1.1Finite Difference Time Domain MethodTheﬁnite difference time-domain(FDTD)method[1,2]uses the method ofﬁnite differences to solve Maxwell’s Equations in the time domain.Application of the FDTD method is usually very straightforward:the solution domain is typically discretized into small rectangular or curvilinear elements,with a“leap frog”in time used to compute the electric and magneticﬁelds from one another.FDTD excels at analysis of inhomogeneous and nonlinear media,though its demands for system memory are high due to the discretization of the entire solution domain,and it suffers from dispersion issues as well and the need to artiﬁcially truncate the solution boundary.FDTDﬁnds applications in packaging and waveguide problems,as well as in the study of wave propagation in complex dielectrics.1.1.1.2Finite Element MethodTheﬁnite element method(FEM)[3,4]is a method used to solve frequency-domain boundary valued electromagnetic problems by using a variational form.It can be used with two-and three-dimensional canonical elements of differing shape, allowing for a highly accurate discretization of the solution domain.The FEM is often used in the frequency domain for computing the frequencyﬁeld distribution in complex,closed regions such as cavities and waveguides.As in the FDTD method, the solution domain must be truncated,making the FEM unsuitable for radiation or scattering problems unless combined with a boundary integral equation approach [3].1.1.1.3Method of MomentsThe method of moments(MOM)is a technique used to solve electromagnetic bound-ary or volume integral equations in the frequency domain.Because the electromag-netic sources are the quantities of interest,the MOM is very useful in solving ra-diation and scattering problems.In this book,we focus on the practical solution of boundary integral equations of radiation and scattering using this method.1.1.2High-Frequency MethodsElectromagnetic problems of large size have existed long before the computers that could solve mon examples of larger problems are those of radar crossComputational Electromagnetics3 section prediction and calculation of an antenna’s radiation pattern when mounted on a large structure.Many approximations have been made to the equations of radiation and scattering to make these problems tractable.Most of these treat theﬁelds in the asymptotic or high-frequency(HF)limit and employ ray-optics and edge diffraction. When the problem is electrically large,many asymptotic methods produce results that are accurate enough on their own or can be used as a“ﬁrst pass”before a more accurate though computationally demanding method is applied.1.1.2.1Geometrical Theory of DiffactionThe geometrical theory of diffraction(GTD)[5,6]uses ray-optics to determine electromagnetic wave propagation.The spreading,amplitude intensity and decay in a ray bundle are computed using from Fermat’s principle and the radius of curvature at reﬂection points.The GTD attempts to account for theﬁelds diffracted by edges, allowing for a calculation of theﬁelds in shadow regions.The GTD is fast but often yields poor accuracy for more complex geometries.1.1.2.2Physical OpticsPhysical optics(PO)[7]is a method for approximating the high-frequency surface currents,allowing a boundary integration to be performed to obtain theﬁelds.As we will see,the PO and the MOM are used to solve the same integral equation, though the MOM calculates the surface currents directly instead of approximating them.While robust,PO does not account for theﬁelds diffracted by edges or those from multiple reﬂections,so supplemental corrections are usually added to it.The PO method is used extensively in high-frequency reﬂector antenna analyses,as well as many radar cross section prediction codes.1.1.2.3Physical Theory of DiffractionThe physical theory of diffraction(PTD)[8,9]is a means for supplementing the PO solution by adding the effects of nonuniform currents at the diffracting edges of an object.PTD is commonly used in high-frequency radar cross section and scattering analyses.1.1.2.4Shooting and Bouncing RaysThe shooting and bouncing ray(SBR)method[10,11]was developed to predict the multiple-bounce backscatter from complex objects.It uses the ray-optics model to determine the path and amplitude of a ray bundle,but uses a PO-based scheme that integrates surface currents deposited by the ray at each bounce point.The SBR method is often used in scattering codes to account for multiple reﬂections on a surface or that encountered inside a cavity,and as such it supplements PO and the PTD.The SBR method is also used to predict wave propagation and scattering4The Method of Moments in Electromagneticsin complex urban environments to determine the coverage for cellular telephone service.REFERENCES[1]A.Taﬂove and S.C.Hagness,Computational Electrodynamics:The Finite-Difference Time-Domain Method.Artech House,3rd ed.,2005.[2]K.Kunz and R.Luebbers,The Finite Difference Time Domain Method forElectromagnetics.CRC Press,1993.[3]J.Jin,The Finite Element Method in Electromagnetics.John Wiley and Sons,1993.[4]J.L.V olakis,A.Chatterjee,and L.C.Kempel,Finite Element Method forElectromagnetics.IEEE Press,1998.[5]J.B.Keller,“Geometrical theory of diffraction,”J.Opt.Soc.Amer.,vol.52,116–130,February1962.[6]R.G.Kouyoumjian and P.H.Pathak,“A uniform geometrical theory of diffrac-tion for and edge in a perfectly conducting surface,”Proc.IEEE,vol.62, 1448–1461,November1974.[7]C.A.Balanis,Advanced Engineering Electromagnetics.John Wiley and Sons,1989.[8]P.Uﬁmtsev,“Approximate computation of the diffraction of plane electro-magnetic waves at certain metal bodies(i and ii),”Sov.Phys.Tech.,vol.27, 1708–1718,August1957.[9]A.Michaeli,“Equivalent edge currents for arbitrary aspects of observation,”IEEE Trans.Antennas Propagat.,vol.23,252–258,March1984.[10]S.L.H.Ling and R.Chou,“Shooting and bouncing rays:Calculating theRCS of an arbitrarily shaped cavity,”IEEE Trans.Antennas Propagat.,vol.37, 194–205,February1989.[11]S.L.H.Ling and R.Chou,“High-frequency RCS of open cavities withrectangular and circular cross sections,”IEEE Trans.Antennas Propagat., vol.37,648–652,May1989.。

计算电磁学目录

Numerical Techniques in ElectromagneticsSecond EditionMatthew N. O. Sadiku, Ph.D.Numerical Techniques inElectromagnetics Second EditionBoca Raton London New York Washington, D.C.CRC PressThis book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use.Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microﬁlming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher.The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Speciﬁc permission must be obtained in writing from CRC Press LLC for such copying.Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identiﬁcation and explanation, without intent to infringe.International Standard Book Number 0-8493-1395-3Library of Congress Card Number 00-026823Printed in the United States of America 1 2 3 4 5 6 7 8 9 0Printed on acid-free paperPrefaceThe art of computation of electromagnetic(EM)problems has grown exponentially for three decades due to the availability of powerful computer resources.In spite of this,the EM community has suffered without a suitable text on computational techniques commonly used in solving EM-related problems.Although there have been monographs on one particular technique or the other,the monographs are written for the experts rather than students.Only a few texts cover the major techniques and do that in a manner suitable for classroom use.It seems experts in this area are familiar with one or few techniques and not many experts seem to be familiar with all the common techniques.This text attempts toﬁll the gap.The text is intended for seniors or graduate students and may be used for a one-semester or two-semester course.The main requirements for students taking a course based on this text are introductory EM courses and a knowledge of a high-level computer language,preferably FORTRAN or C.Software packages such as Matlab and Mathcad may be helpful tools.Although familiarity with linear algebra and numerical analysis is useful,it is not required.In writing this book,three major objectives were borne in mind.First,the book is intended to teach students how to pose,numerically analyze,and solve EM problems. Second,it is designed to give them the ability to expand their problem solving skills using a variety of available numerical methods.Third,it is meant to prepare graduate students for research in EM.The aim throughout has been simplicity of presentation so that the text can be useful for both teaching and self-study.In striving after simplicity,however,the reader is referred to the references for more information. Toward the end of each chapter,the techniques covered in the chapter are applied to real life problems.Since the application of the technique is as vast as EM and author’s experience is limited,the choice of application is selective.Chapter1covers some fundamental concepts in EM.Chapter2is intended to put numerical methods in a proper perspective.Analytical methods such as separation of variables and series expansion are covered.Chapter3discusses theﬁnite differ-ence methods and begins with the derivation of difference equation from a partial differential equation(PDE)using forward,backward,and central differences.The ﬁnite-difference time-domain(FDTD)technique involving Yee’s algorithm is pre-vsented and applied to scattering problems.Numerical integration is covered using trapezoidal,Simpson’s,Newton-Cotes rules,and Gaussian quadratures.Chapter4on variational methods serves as a preparatory ground for the next two major topics:moment methods andﬁnite element methods.Basic concepts such as inner product,self-adjoint operator,functionals,and Euler equation are covered. Chapter5on moment methods focuses on the solution of integral equations.Chap-ter6onﬁnite element method covers the basic steps involved in using theﬁnite element method.Solutions of Laplace’s,Poisson’s,and wave equations using the ﬁnite element method are covered.Chapter7is devoted to transmission-line matrix or modeling(TLM).The method is applied to diffusion and scattering problems.Chapter8is on Monte Carlo methods, while Chapter9is on the method of lines.Since the publication of theﬁrst edition,there has been an increased awareness and utilization of numerical techniques.Many graduate curricula now include courses in numerical analysis of EM problems.However,not much has changed in compu-tational electromagnetics.A major noticeable change is in the FDTD method.The method seems to have attracted much attention and many improvements are being made to the standard algorithm.This edition adds the noticeable change in incorpo-rating absorbing boundary conditions in FDTD,FEM,and TLM.Chapter9is a new chapter on the method of lines.AcknowledgementsI am greatly indebted to Temple University for granting me a sabbatical in Fall1998 during which I was able to do most of the revision.I speciﬁcally would like to thank my dean,Dr.Keya Sadeghipour,and my chairman,Dr.John Helferty,for their support. Special thanks are due to Raymond Garcia of Georgia Tech for writing Appendices C and D in C++.I am deeply grateful to Dr.Arthur D.Snider of the University of South Florida and Mohammad R.Zunoubi of Mississippi State University for taking the time to send me the list of errors in theﬁrst edition.I thank Dr.Reinhold Pregla for helping in clarifying concepts in Chapter9on the method of lines.I express my deepest gratitude to my wife,Chris,and our daughters,Ann and Joyce,for their patience,sacriﬁces,and prayers.A Note to StudentsBefore you embark on writing your own computer program or using the ones in this text,you should try to understand all relevant theoretical backgrounds.A computeris no more than a tool used in the analysis of a program.For this reason,you should be as clear as possible what the machine is really being asked to do before setting it off on several hours of expensive computations.It has been well said by A.C.Doyle that“It is a capital mistake to theorize before you have all the evidence.It biases the judgment.”Therefore,you should never trust the results of a numerical computation unless they are validated,at least in part.You validate the results by comparing them with those obtained by previous investigators or with similar results obtained using a different approach which may be analytical or numerical.For this reason,it is advisable that you become familiar with as many numerical techniques as possible.The references provided at the end of each chapter are by no means exhaustive but are meant to serve as the starting point for further reading.Contents1 Fundamental Concepts1.1 Introduction1.2 Review of Electromagnetic Theory1.2.1 Electrostatic Fields1.2.2 Magnetostatic Fields1.2.3 Time-varying Fields1.2.4 Boundary Conditions1.2.5 Wave Equations1.2.6 Time-varying Potentials1.2.7 Time-harmonic Fields1.3 Classiﬁcation of EM Problems1.3.1 Classiﬁcation of Solution Regions1.3.2 Classiﬁcation of Differential Equations1.4 Some Important Theorems1.4.1 Superposition Principle1.4.2 Uniqueness TheoremReferencesProblems2 Analytical Methods2.1 Introduction2.2 Separation of Variables2.3 Separation of Variables in Rectangular Coordinates2.3.1 Laplace’s Equations2.3.2 Wave Equation2.4 Separation of Variables in Cylindrical Coordinates2.4.1 Laplace’s Equation2.4.2 Wave Equation2.5 Separation of Variables in Spherical Coordinates2.5.1 Laplace’s Equation2.5.2 Wave Equation2.6 Some Useful Orthogonal Functions2.7 Series Expansion2.7.1 Poisson’s Equation in a Cube2.7.2 Poisson’s Equation in a Cylinder2.7.3 Strip Transmission Line2.8 Practical Applications2.8.1 Scattering by Dielectric Sphere2.8.2 Scattering Cross Sections2.9 Attenuation Due to Raindrops2.10 Concluding RemarksReferencesProblems3 Finite Difference Methods3.1 Introduction3.2 Finite Difference Schemes3.3 Finite Differencing of Parabolic PDEs3.4 Finite Differencing of Hyperbolic PDEs3.5 Finite Differencing of Elliptic PDEs3.5.1 Band Matrix Method3.5.2 Iterative Methods3.6 Accuracy and Stability of FD Solutions3.7 Practical Applications I — Guided Structures3.7.1 Transmission Lines3.7.2 Waveguides3.8 Practical Applications II — Wave Scattering (FDTD)3.8.1 Yee’s Finite Difference Algorithm3.8.2 Accuracy and Stability3.8.3 Lattice Truncation Conditions3.8.4 Initial Fields3.8.5 Programming Aspects3.9 Absorbing Boundary Conditions for FDTD3.10 Finite Differencing for Nonrectangular Systems3.10.1 Cylindrical Coordinates3.10.2 Spherical Coordinates3.11 Numerical Integration3.11.1 Euler’s Rule3.11.2 Trapezoidal Rule3.11.3 Simpson’s Rule3.11.4 Newton-Cotes Rules3.11.5 Gaussian Rules3.11.6 Multiple Integration3.12 Concluding RemarksReferencesProblems4 Variational Methods4.1 Introduction4.2 Operators in Linear Spaces4.3 Calculus of Variations4.4 Construction of Functionals from PDEs4.5 Rayleigh-Ritz Method4.6 Weighted Residual Method4.6.1 Collocation Method4.6.2 Subdomain Method4.6.3 Galerkin Method4.6.4 Least Squares Method4.7 Eigenvalue Problems4.8 Practical Applications4.9 Concluding RemarksReferencesProblems5 Moment Methods5.1 Introduction5.2 Integral Equations5.2.1 Classiﬁcation of Integral Equations5.2.2 Connection Between Differential and Integral Equations5.3 Green’s Functions5.3.1 For Free Space5.3.2 For Domain with Conducting Boundaries5.4 Applications I — Quasi-Static Problems5.5 Applications II — Scattering Problems5.5.1 Scattering by Conducting Cylinder5.5.2 Scattering by an Arbitrary Array of Parallel Wires5.6 Applications III — Radiation Problems5.6.1 Hallen’s Integral Equation5.6.2 Pocklington’s Integral Equation5.6.3 Expansion and Weighting Functions5.7 Applications IV — EM Absorption in the Human Body5.7.1 Derivation of Integral Equations5.7.2 Transformation to Matrix Equation (Discretization)5.7.3 Evaluation of Matrix Elements5.7.4 Solution of the Matrix Equation5.8 Concluding RemarksReferencesProblems6 Finite Element Method6.1 Introduction6.2 Solution of Laplace’s Equation6.2.1 Finite Element Discretization6.2.2 Element Governing Equations6.2.3 Assembling of All Elements6.2.4 Solving the Resulting Equations6.3 Solution of Poisson’s Equation6.3.1 Deriving Element-governing Equations6.3.2 Solving the Resulting Equations6.4 Solution of the Wave Equation6.5 Automatic Mesh Generation I — Rectangular Domains6.6 Automatic Mesh Generation II — Arbitrary Domains6.6.1 Deﬁnition of Blocks6.6.2 Subdivision of Each Block6.6.3 Connection of Individual Blocks6.7 Bandwidth Reduction6.8 Higher Order Elements6.8.1 Pascal Triangle6.8.2 Local Coordinates6.8.3 Shape Functions6.8.4 Fundamental Matrices6.9 Three-Dimensional Elements6.10 Finite Element Methods for Exterior Problems6.10.1 Inﬁnite Element Method6.10.2 Boundary Element Method6.10.3 Absorbing Boundary Conditions6.11 Concluding RemarksReferencesProblems7 Transmission-line-matrix Method7.1 Introduction7.2 Transmission-line Equations7.3 Solution of Diffusion Equation7.4 Solution of Wave Equations7.4.1 Equivalence Between Network and Field Parameters7.4.2 Dispersion Relation of Propagation Velocity7.4.3 Scattering Matrix7.4.4 Boundary Representation7.4.5 Computation of Fields and Frequency Response7.4.6 Output Response and Accuracy of Results7.5 Inhomogeneous and Lossy Media in TLM7.5.1 General Two-Dimensional Shunt Node7.5.2 Scattering Matrix7.5.3 Representation of Lossy Boundaries7.6 Three-Dimensional TLM Mesh7.6.1 Series Nodes7.6.2 Three-Dimensional Node7.6.3 Boundary Conditions7.7 Error Sources and Correction7.7.1 Truncation Error7.7.2 Coarseness Error7.7.3 Velocity Error7.7.4 Misalignment Error7.8 Absorbing Boundary Conditions7.9 Concluding RemarksReferencesProblems8 Monte Carlo Methods8.1 Introduction8.2 Generation of Random Numbers and Variables8.3 Evaluation of Error8.4 Numerical Integration8.4.1 Crude Monte Carlo Integration8.4.2 Monte Carlo Integration with Antithetic Variates8.4.3 Improper Integrals8.5 Solution of Potential Problems8.5.1 Fixed Random Walk8.5.2 Floating Random Walk8.5.3 Exodus Method8.6 Regional Monte Carlo Methods8.7 Concluding RemarksReferencesProblems9 Method of Lines9.1 Introduction9.2 Solution of Laplace’s Equation9.2.1 Rectangular Coordinates9.2.2 Cylindrical Coordinates9.3 Solution of Wave Equation9.3.1 Planar Microstrip Structures9.3.2 Cylindrical Microstrip Structures9.4 Time-Domain Solution9.5 Concluding RemarksReferencesProblemsA Vector RelationsA.1 Vector IdentitiesA.2 Vector TheoremsA.3 Orthogonal CoordinatesB Solving Electromagnetic Problems Using C++B.1 IntroductionB.2 A Brief Description of C++B.3 Object-OrientationB.4 C++ Object-Oriented Language FeaturesB.5 A Final NoteReferencesC Numerical Techniques in C++D Solution of Simultaneous EquationsD.1 Elimination MethodsD.1.1 Gauss’s MethodD.1.2 Cholesky’s MethodD.2 Iterative MethodsD.2.1 Jacobi’s MethodD.2.2 Gauss-Seidel MethodD.2.3 Relaxation MethodD.2.4 Gradient Methods ....D.3 Matrix InversionD.4 Eigenvalue ProblemsD.4.1 Iteration (or Power) MethodD.4.2 Jacobi’s MethodE Answers to Odd-Numbered ProblemsTo my teacherCarl A.Ventriceandmy par entsAyisat andSolomon Sad iku。

HIE-FDTD方法的基本理论、运用和发展

Vol. 10 , No. 2Jun. 2019第10卷第2期2019年6月现代应用物理MODERN APPLIED PHYSICSHIE-FDTD 方法的基本理论、运用和发展陈娟12,3,马寒啸】，施宏宇廿(1.西安交通大学信息与通信工程学院，西安710049； 2.西安交通大学深圳研究院，深圳518057；3.广东顺德西安交通大学研究院，顺德528300)摘要：时域有限差分(finite-difference time-domain, FDTD)方法是一种应用广泛的时域电磁计算方法，但由于需满足Courant-Friedrich-Levy 时间稳定性条件，因此该方法的时间步长由模拟空间的最小网格尺寸所决定，导致在模拟具有精细结构的电磁问题时，计算效率非常低。

为了克服该缺点，研究者们提出了混合显-隐式时域有限差分(hybrid implicit-explicitfinite-difference time-domain ，HIE-FDTD)方法。

HIE-FDTD 方法在沿精细结构所在方向上采用混合显-隐式差分，可以避免精细网格对时间步长的限制，在模拟沿一个方向具有精细结构的电磁问题时，与FDTD 方法相比，具有更高的计算效率。

分析了 HIE-FDTD 方法的基本公式、时间稳定性条件和色散误差，阐述了 HIE-FDTD 方法的连接边界、吸收边界和周期边界等边界条件，介绍了 HIE-FDTD 方法的应用和发展状况。

关键词：计算电磁学；时域有限差分方法；混合显-隐式差分中图分类号：TN80文献标志码：A DOI ： 10. 12061/j. issn. 2095 - 6223. 2019. 020101Basic Theory, Application andDevelopment of HIE-FDTD MethodCHEN Juan^'3, MA Han-xiao 1 , SHI Hong-yU(1. School of Information andCommunicationEngineering, Xi'anjiaotong University, Xi'an 710049, China ；2. Shenzhen Research School , Xi'anjiaotong University , Shenzhen 518057 , China ；3 . Guangdong Xi !an Jiaotong University Academy , Shunde 528300 , China)Abstract : The finite-difference time-domain (FDTD) method is one of the mostwidely used methods in computational electromagnetic field. But this method takes a long time to simulate theelectromagnetic problems with fine structure. To improve the computational efficiency of theFDTD method, researchers proposed a hybrid implicit-explicit finite —difference time-domain (HIE-FDTD) method which uses the hybrid implicit-explicit difference inthe direction oftarget with fine structure to avoid the confinement of the fine spatialmesh on the time step size. Compared with the FDTD method, the efficiency of the HIE-FDTD method in simula ting electromagnetic target with fine structure along one direction is significantly improved.In this paper, the basic formulas, time stability conditions and dispersion errors of the HIE- FDTD method are analyzed. The boundary conditions such as connection boundary, absorption收稿日期：2019 - 05 - 31 ；修回日期：2019 - 06 - 04基金项目：深圳市科技计划资助项目(JCYJ20170816100722642； JCYJ20180508152233431)；广东省自然科学基金资助项目(2018A030313429)十通信作者：施宏宇(1987—)男，黑龙江哈尔滨人，副教授，博士，主要从事计算电磁学、超材料及涡旋电磁波技术研究。

计算电磁学

计算电磁学摘要：作为一门交叉学科，计算电磁学结合了计算机技术、数值计算学和电磁学等相关学科的知识，正经历着日新月异的发展。

计算电磁学是指对一定物质和环境中的电磁场相互作用的建模过程，通常包括麦克斯韦方程计算上的有效近似。

计算电磁学被用来计算天线性能，电磁兼容，雷达散射截面和非自由空间的电波传播等问题。

计算电磁学的主要思想有，基于积分方程的方法，基于微分（差分）方程的方法，及其他模拟方法。

mesh物理学释义

mesh物理学释义英文回答：Meshing Defined.Meshing is a process that divides a complex 3D model into smaller, simpler elements called meshes. These meshes are typically triangles or quadrilaterals and form the geometric foundation for computer simulations. Meshing is crucial for discretizing the model and enabling numerical analysis.Types of Meshes.There are various types of meshes, each with its advantages and applications:Structured Mesh: Elements are arranged in a regular pattern, such as a grid or lattice.Unstructured Mesh: Elements are distributed randomly, allowing for more complex shapes.Hybrid Mesh: Combines structured and unstructured elements to optimize efficiency.Adaptive Mesh: Refines or coarsens the mesh based on local conditions or error estimates.Mesh Quality.Mesh quality is critical for accurate simulations. Factors affecting quality include:Element Shape: Avoids elongated or distorted elements that can introduce errors.Element Size: Small elements provide higher accuracy but increase computational cost.Element Connectivity: Ensures that elements are properly connected to form a continuous mesh.Aspect Ratio: Ratio between the longest and shortest edges within an element should be minimized.Mesh Optimization.Optimizing meshes involves balancing accuracy, efficiency, and stability:Mesh Generation: Choose the appropriate mesh type and refine it to meet desired accuracy.Mesh Simplification: Reduces the number of elements without compromising accuracy.Mesh Smoothing: Improves mesh quality by reducing element distortions.Mesh Regularization: Reorganizes the mesh to create more uniform elements.Mesh Applications.Meshed models are used in a wide range of simulations, including:Computational Fluid Dynamics (CFD): Analyzes fluid flow and heat transfer.Finite Element Analysis (FEA): Studies the behavior of structures under applied loads.Computational Electromagnetics (CEM): Solves electromagnetic problems.Particle-Based Simulations: Models the motion of particles, such as in molecular dynamics.Computer Graphics: Enables realistic rendering and visualization.中文回答：网格物理解释。

计算电磁学

计算电磁学CEM（computational electromagnetics）是笔者在研发过程中认为最复杂的物理场，难度在CFD和计算材料学之上。

计算电磁学的复杂主要表现在物理场抽象，计算规模大，同时求解方法众多，涉及到大量的底层技术知识。

求解的偏微分方程是麦克斯韦方程组，麦克斯韦在奥斯特，法拉利等前人试验基础上通过数学推理得到了完整的方程组，在该方程组的理论支持下，有了后来的电磁学的飞速发展。

该方程组完整的描述了电，磁，材料，频率，时间之间的关系。

求解电磁学可分为三类：解析法，数值法，以及半解析半数值。

(1) 时域方法与谱域方法电磁学的数值计算方法可以分为时域方法(Time Domain或TD)和频域方法(Frequeney Domain或FD)两大类。

时域方法对Maxwell方程按时间步进后求解有关场量。

最著名的时域方法是时域有限差分法(Finite Difference Time Domain或FDTD)。

这种方法通常适用于求解在外界激励下场的瞬态变化过程。

若使用脉冲激励源，一次求解可以得到一个很宽频带范围内的响应。

时域方法具有可靠的精度，更快的计算速度，并能够真实地反应电磁现象的本质，特别是在诸如短脉冲雷达目标识别、时域测量、宽带无线电通讯等研究领域更是具有不可估量的作用。

频域方法是基于时谐微分、积分方程，通过对N个均匀频率采样值的傅立叶逆变换得到所需的脉冲响应，即研究时谐(Time Harmonic)激励条件下经过无限长时间后的稳态场分布的情况，使用这种方法，每次计算只能求得一个频率点上的响应。

过去这种方法被大量使用，多半是因为信号、雷达一般工作在窄带。

当要获取复杂结构时域超宽带响应时，如果采用频域方法，则需要在很大带宽内的不同频率点上的进行多次计算，然后利用傅立叶变换来获得时域响应数据，计算量较大；如果直接采用时域方法，则可以一次性获得时域超宽带响应数据，大大提高计算效率。

特别是时域方法还能直接处理非线性媒质和时变媒质问题，具有很大的优越性。

cst做波动光学器件

cst做波动光学器件
CST（Computational Electromagnetics）在波动光学器件方面发挥着重要作用。

波动光学器件是利用光的波动性质来实现特定功
能的光学元件，比如衍射光栅、透镜、偏振器等。

CST作为一种电
磁场仿真软件，可以用来模拟和分析这些器件的电磁场行为。

首先，CST可以用来模拟波动光学器件的电磁场分布。

通过求
解Maxwell方程组，CST可以计算出器件中光的传播、衍射、干涉
等现象，帮助工程师了解器件内部的电磁场分布情况。

其次，CST可以进行光学性能的优化。

通过对波动光学器件的
电磁场分布进行仿真分析，工程师可以根据仿真结果对器件的结构
参数进行优化设计，以达到特定的光学性能要求，比如提高透射率、减小衍射损耗等。

此外，CST还可以用于波动光学器件的材料参数优化。

通过模
拟不同材料在器件中的电磁响应，工程师可以选择最适合的材料，
以实现器件所需的光学性能。

最后，CST还可以用于分析波动光学器件与周围环境的相互作
用。

比如，器件与其他光学元件的耦合效应、器件在复杂环境中的性能表现等。

综上所述，CST在波动光学器件方面可以帮助工程师进行电磁场仿真分析、优化设计、材料参数选择和环境相互作用分析，从而提高波动光学器件的设计效率和性能。

对称法求解电场强度

对称法求解电场强度对称法求解电场强度：理解和实践引言：电场强度是描述电场在空间分布上的重要参数，对于解决复杂电磁问题具有重要意义。

本文将介绍对称法求解电场强度的基本原理和应用方法，并探讨其在电磁学领域的重要性。

一、对称法的基本原理1.1 电场强度的定义电场强度描述了单位正电荷在某点受到的电场力大小和方向，用矢量表示。

在物理学中，电场强度的计算一般基于库仑定律。

1.2 对称法的基本概念对称法是一种常用的解决电磁学问题的方法之一，其基本思想是通过利用电场的对称性，把复杂的电磁问题转化为更易处理和计算的简单问题。

对称法在求解电场强度时可以节省大量计算量和简化计算过程。

二、对称法的应用方法2.1 理论计算对称法的应用方法之一是进行理论计算。

根据问题的特点和所给条件，确定问题的对称性。

同时将问题加以简化，使其符合所选的对称形式，进而应用对称性进行计算。

通过对称法求解电场强度，可以得到问题的解析解或近似解。

2.2 数值模拟对称法还可以应用于数值模拟中。

通过建立问题的几何模型和物理模型，使用数值计算方法求解电场强度，得到问题的数值解。

对称法在减少计算量和提高计算效率方面有着显著的优势。

这种方法可以利用计算机软件对电磁问题进行较为准确的数值模拟和分析。

三、对称法的重要性和应用领域3.1 重要性对称法在解决电磁学问题中具有重要的地位。

通过对称法求解电场强度，可以提高计算效率，简化计算过程，并且能够获得问题的解析解或近似解。

在实际应用中，对称法在研究电场分布、电场的相互作用和电场中粒子的运动轨迹等方面起着重要的作用。

3.2 应用领域对称法广泛应用于电磁学领域的各个方面，包括电场的分布分析、静电场的设计和分析、电磁场的辐射特性研究等。

尤其在电场分布对称性明显的问题上，对称法更加具有优势和重要性。

结论与展望通过本文的介绍，我们了解了对称法求解电场强度的基本原理和应用方法。

对称法在解决电磁学问题中起着重要作用，通过利用电场的对称性，可以简化计算过程，提高计算效率，并且可以获得问题的解析解或近似解。

快速多极子方法的并行技术

得到C(n,l)或
，这也1(n可,l) (以y) 用于xi∈E3(n,l)
• Step2:对于l=L-1,…,2,从step1得到值进行递归得到。
同样适合xi∈E3(n,l)
结果：得到分层组聚集系数
20
MLFMM Algorithm
—Downward Pass
• Step1:l=2,..L递归进行E4
• Generates a Dense Method of Moments Matrix
ZnnIn1 Vn1 Z j,i f j , G r,r ' fi r ' ds S 6
线性系统：
Mx=s M是N×N矩阵，x、s是N矢量
●Direct solution (Gauss elimination,LU Decomposition,SVD,…) 空间复杂度为O(N2) ，需要O(N3)次运算；
23
Grouping
(n,l) 1
(y)
ui(y,
xi
),
( n,l ) 2
(y)
ui(y, xi ),
xiE1 (n,l )
xiE2 (n,l )
(n,l) 3
(y)
ui(y,
xi
),
( n,l ) 4
(y)
ui(y, xi )
xiE3 (n,l )
xiE4 (n,l )
由于E2(n,l)和E3(n,l) 是互补的，因此对任意的n,l
近场部分
n1
m'Gn(m) jGm'
远场部分
k 2 K
16 2
wpDip [
Tp ( A pj j j )]
p 1
m 'Gn ( m )

电磁场的参考文献

电磁场的参考文献电磁场是物质中电荷所产生的一种物理现象，广泛应用于电子技术、通信、电力系统等领域。

了解电磁场的基本原理和相关研究是深入掌握这一领域的必备知识。

本文旨在为读者提供一些重要的参考文献，帮助其进一步了解电磁场的研究进展以及实际应用。

一、经典电动力学参考文献1.《电磁场与电磁波》（作者：刘家琳）该书是电动力学领域的经典之作，深入浅出地介绍了电磁场的基本原理和电磁波的性质。

该书内容系统全面，适合作为电动力学学习的参考书。

2.《电磁学基础》（作者：David J. Griffiths）这本教材是电磁学领域的经典之作，被广泛应用于大学本科及研究生课程中。

该书语言通俗易懂，涵盖了电磁场的基本概念、电场与磁场的计算方法以及麦克斯韦方程组的应用等内容。

二、电磁场数值计算参考文献1.《电磁场模拟与仿真》（作者：刘吉全）该书详细介绍了电磁场的数值计算方法，包括有限差分法、有限元法、边界积分方程法等。

通过实例的应用，读者可以深入了解电磁场的数值计算原理和技术。

2.《Computational Electromagnetics for RF and Microwave Engineering》（作者：David B. Davidson）该书介绍了电磁场的数值计算在射频和微波工程领域的应用。

从理论到实践，该书系统地阐述了电磁场的数值计算方法，并给出了实际工程中的应用案例。

三、电磁场实验技术参考文献1.《电磁场与电磁波实验》（作者：张铭双）该书包含了多个电磁场实验的设计和实施方法，对实验室中的电磁场实践课程非常有帮助。

书中提供了详细的实验操作步骤和实验装置原理，读者可以通过实验深入理解电磁场的概念与现象。

2.《Introduction to Electromagnetic Compatibility》（作者：Clayton R. Paul）该书主要介绍了电磁兼容性（EMC）领域的相关知识，讲解了电磁场对电子系统产生的干扰和噪声问题以及解决方法。

计算电磁学综述

计算电磁学综述摘要：本文介绍了计算电磁学及其电磁学的发展历史，并对计算电磁学中的几种常见数值计算方法进做了简单的介绍，并比较了各类数值方法的优缺点，介绍了一些常用的计算电磁软件，最后对计算电磁学近年来的进展和未来研究热点进行了综述。

关键词：计算电磁学，数值计算方法，电磁软件一、引言计算电磁学（Computational Electromagnetics），顾名思义它是对电磁问题进行求解计算的方法技术，同时这也是一门具有巨大实用价值的学科。

随着当今世界计算机技术的突飞猛进，许多传统学科物理、化学、生物等都在计算机的辅助下，不断发展进步，因此计算电磁学可以说是数学理论、电磁理论和计算机的有机结合，它是一门计算的艺术。

计算机技术和电磁学相结合的学科。

计算电磁学这门交叉学科也在这样的时代背景下应运而生，并得到真正的普及和发展壮大。

电磁学作为物理学的一个子类，其研究历史悠久。

中外古人都有许多对于电磁现象发现和记载以及规律的总结。

在19世纪之前，人们还没有发现电学和磁学之间的联系，19世纪之后，人们才发现电和磁之间的内在联系。

1819年丹麦物理学家H.C.奥斯特（1777-1851年）发表了《关于磁针上电流碰撞的实验》的论文，第一次揭示了电流可以产生磁场。

1820年法国物理学家A.M.安培（1775-1836年）对这一物理现象做了进一步研究，并讨论了两平行导线有电流通过时的相互作用问题，提出了著名的安培定理，人们才开始认识到电和磁的关系。

1831年英国物理学家M.法拉第（1791-1867年）首次报道了电磁感应现象，即通过移动磁体可在导线上感应出电流，他最先提出了电场和磁场的观点，认为电力和磁力两者都是通过场起作用的，使人们对电和磁的关系有了更为深刻的认识。

奥斯特、安培和法拉第等人的工作为电磁学的建立奠定了实验基础。

电磁学真正上升为一门理论则应归功于伟大的苏格兰物理学家J.C.麦克斯韦（1831-1879年）。

电大尺寸电磁结构的时域仿真实践-周小侠041216

分类号密级UDC1注学位论文电大尺寸电磁结构的时域仿真实践（题名和副题名）周小侠（作者姓名）指导教师姓名喻志远教授电子科技大学成都张敏博士CST China 上海（职务、职称、学位、单位名称及地址）申请专业学位级别硕士专业名称无线电物理论文提交日期2004.12 论文答辩日期 2005.1学位授予单位和日期电子科技大学答辩委员会主席评阅人2004年月日注1：注明《国际十进分类法UDC》的类号。

独创性声明本人声明所呈交的学位论文是本人在导师指导下进行的研究工作及取得的研究成果。

据我所知，除了文中特别加以标注和致谢的地方外，论文中不包含其他人已经发表或撰写过的研究成果，也不包含为获得电子科技大学或其它教育机构的学位或证书而使用过的材料。

与我一同工作的同志对本研究所做的任何贡献均已在论文中作了明确的说明并表示谢意。

签名：日期：年月日关于论文使用授权的说明本学位论文作者完全了解电子科技大学有关保留、使用学位论文的规定，有权保留并向国家有关部门或机构送交论文的复印件和磁盘，允许论文被查阅和借阅。

本人授权电子科技大学可以将学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存、汇编学位论文。

（保密的学位论文在解密后应遵守此规定）签名：导师签名：日期：年月日摘要随着科学技术的快速发展，以前只需进行定量分析的电大和复杂结构现在也需要进行定性分析。

随着计算机的发展，计算机的速度越来越快，内存越来越便宜，使得能够仿真的问题越来越大。

但无论如何也赶不上需求的增长。

因为算法是根本性和决定性的，所以选择一种好的算法才是解决问题的关键。

在诸多算法中，时域算法是求解电大尺寸物体的最佳选择。

我们选择CST 微波工作室®（以下简称CST MWS）来完成下面的设计和仿真。

本文详细叙述了有限积分法（FIT－Finite Integration Technique）的算法原理和仿真电大尺寸电磁结构的理论基础，并详细阐述了两个电大实例的仿真过程。

微波毫米波技术基本知识

60GHz, 1W, PAE=20%, 60GHz，3.8W, 31dB，8个模块合成 95GHz, 480mW, PAE=20% TRW公司InP HEMT低噪声MMIC： 170－200GHz, G=15dB, Nf=4.8dB
毫米波低噪声放大器MMIC
毫米波低噪声放大器MMIC（芯片）产品性能
微波系统构成
传输线及不连续性
无源和有源器件 (半导体或电真空)
微波部件微波模块
微波系统
二、微波和毫米波传输线
TEM传输线
非色散传输线－传播速度等于填充媒质中的光速，且不随工作频率而变。
平行双导线同轴线带状线微带线
柱面波导
色散传输线－传播速度随频率而变。
矩形波导，圆形波导椭圆形波导脊波导－单脊和双脊波导
20km－ 3km－ 200m－ 10m－ 1m以下 3km 200m 10m 1m
微波频段划分(UHF)
名称频率
波长
P
L
225- 0.39390 1.55 MHz MHz
133.2- 76.976.9 19.3 cm cm
S
1.553.9 GHz 19.37.69 cm
C
X
3.9-6.9 6.9GHz 12.4
频率 (GHz) 噪声系数(dB) 增益 (dB) 厂家
26-40 2.5 13
UMS
26-40 36-40 55-60
2.5 2.5
3.5
17 18
10
Sanders Fujitsu UMS
毫米波功率放大器MMIC
毫米波功率放大器MMIC（芯片）产品性能
频率
33-36
(GHz)
增益(dB) 17