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嵌入式 DSP 开发实战:从需求到量产的全流程指南英文版 电子书-159页

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嵌入式 DSP 开发实战:从需求到量产的全流程指南(HOW THE PROS DEVELOP EMBEDDED SOFTWARE)英文版


摘要:

本书是嵌入式 DSP 软件开发的实战指南,以语音替换装置项目为完整案例,覆盖从需求分析到量产验证的全流程。书中系统讲解需求建模、面向对象架构设计、成本估算、硬件适配、模块设计、编码规范、调试排错、集成验证与安全设计等核心环节,结合 TMS320VC5416 DSP 平台与 C 语言、汇编实现,详解 DMA、音频 Codec、串口、滤波、基音检测、波形合成等关键模块开发。同时提供开发环境搭建、团队协作、项目管理与问题解决方法,兼顾工程实践与规范流程,适合嵌入式与 DSP 开发人员快速掌握量产级开发方法。


HOW THE PROS DEVELOP EMBEDDED SOFTWARE

 A no-nonsense guide for developers

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INTRODUCTION

Too many books on embedded software development deliver conceptually

elegant models of the development process, but lack the down-to-earth details of how to actually get the job done.

This no-nonsense guide fills in those details by showing an actual project from start to finish, and all of the methods and documents created along the way.  This information comes directly from the author's 20 years of experience. developing embedded software for electronic products made by top U.S. corporations

This guide walks the reader through the creation of a typical embedded application, a voice controlled synthesizer, from requirements an alysis through validation.

It is intended that a programmer with no previous embedded experience can read this book, and feel neither lost nor out of place in his first embedded project.  The new embedded developer may use the methods in this book as a starting point for his own collection of techniques.

The sample application is called a voice substitution device.  It measures the   fundamental frequency, if any, in an input signal; and substitutes a synthesized waveform of the same frequency in the output.  Hopefully, this example is challenging enough to illustrate most common embedded development practices.

SOME DEFINITIONS

An embedded system is an information appliance that is supplied with sensors  and effecters which permit it to interact with the external environment.  It uses a microprocessor to control the sensors and effecters, and software to guide its   interpretation of incoming signals, and its production of outgoing signals.

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The memory chips, processor, input and output peripherals, sensors and effecters comprise the hardware of the embedded system.  The bit sequence in the memory chip is called the software of the embedded system.

Embedded systems are collections of interacting components.  The definitions below provide a framework for discussing those collections further.

Every component of an embedded system which interacts with other components is called an object. Each object is distinct from other objects, has an internal state, and exhibits a repertoire of behavior.  Objects exhibit their behavior by exchanging messages with other objects.  A message is an influence that passes between objects.

Objects may be hardware or virtual.  A hardware object is made out of material parts.  A virtual object is simulated in software.

Objects may be composed of other objects.  A compound object is an object which is  composed of other objects.  A mixed object is a compound object composed of some hardware and some virtual objects.


THE CONCEPTUAL MAP

Software developers create bit sequences that go into memory chips.

The typical developer cannot listen to a description of desired system behavior, and then just dash off a bit sequence that does the trick.  Instead, he must create a conceptual map of the problem to be solved, and all of the elements that make up a solution.  This conceptual map has both a material and a mental form.



MATERIAL CONCEPTUAL MAP

The material form of the conceptual map is a collection of data sheets, an alysis and design documents, interviews, and meeting minutes which bear on the

project. These documents are usually kept organized and readily accessible to each member of the team.

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MENTAL CONCEPTUAL MAP

The mental form of the conceptual map is a representation in each team member's mind of the environment, goals, hardware, and software objects, and the ways in which they interact.

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The dreaded "learning curve" of an embedded project is the time necessary for a new team member to create, from conversations and from the project's material conceptual map,  a mental conceptual map for the project.

LAYERS OF THE CONCEPTUAL MAP

It can be helpful to subdivide the conceptual map into different layers of

concepts, each of which deals with different portions of the mapping between the real external world, and the embedded software which interacts with it.

The diagram below shows one such subdivision of an embedded project's conceptual map:

image.png

In this diagram, the subdivisions of the conceptual map relate to the flow of information in the embedded system.  Information flows in from the external process layer through the hardware layer, is transformed by the virtual machine layer, and processed by the application layer.  Response information is sent back out via the virtual machine layer, through the hardware layer, into the external process layer.

In the external process layer,  the embedded system is considered as a unit which exchanges influences with the external world.  The concepts in this layer describe in a general way each of those interactions.  They also describe in measurable detail every aspect of those interactions which motivated the building of the system.

The hardware layer of the conceptual map contains data sheets, schematics, and concepts related to the operation of the embedded system hardware.

Documentation is provided by hardware vendors and designers for the processor, peripherals, sensors, effecters, memory chips, comm chips, and power supplies.

The layer between the hardware and the application is called the virtual machine layer.  It describes the virtual (software-simulated) objects through which the application accesses the hardware, and organizes itself in time.  These virtual objects include the primitives of the programming language, the operating system (if any), and any I/O drivers supplied with the operating system or written separately.  Some of the concepts and documents for this layer are supplied by  language and operating system vendors, and some are created by the developers.

The application layer is a collection of virtual objects which interact to model the external process and/or exchange influences with it via the virtual machine and hardware layers.  This layer is mostly invented and documented by the developers.  It may also include virtual objects supplied in code libraries by the system sponsor, or by third party vendors.


The quality of the conceptual map, in both its physical and mental forms, figures prominently in the success orfailure of an embedded project.

If the team members have access to a well organized collection of system documents, and if they take the time to read and understand those documents; the project has a much higher prospect of success than if they do not.

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 A final word about the conceptual map. A belief persists among some  developers, typically the more hardware oriented, that real engineers don't write  documentation. There is some justification for this position. In a s mall system,  not too complex, it is possible to write code for the system without documenting 

the conceptual map.

Troubles arise only when the number of callable functions exceeds a couple of  hundred, and/or there is frequent turnover in the engineering staff, or safety and regulatory issues require full disclosure of the development process.

Throughout this book, various methods will be used to document the conceptual map, be it in requirements, architecture, or design documents. If the reader is convinced that documenting is gilding the lily, then he will surely ignore these methods.

Nikola Tesla, arguably the Earth's greatest engineer, kept most of his plans and notes (except for patent applications) in his head. Mr. Tesla was the acknowledged master of the mental conceptual map. Perhaps that is why some of his greatest inventions weren't rediscovered until many years after his death.

 Just as some engineers favor sparse documentation, others prefer rich documentation. These are persons who require more rigor than that supplied in the methods used here. Those readers will no doubt feel free to use their own methods of documenting the conceptual map, or adopt methods that may be found in abundance in the literature.


DEVELOPMENT PROCESSES

 The software developer's task is to complete the conceptual map of the embedded system, and to implement and test it's virtual objects on the target hardware. This requires her to discover and document the system's required interactions with the outer world, learn how the hardware works, understand the virtual machine, invent the interacting virtual objects of the application, and debug and test their operation. To these ends, the developer participates in the processes described below.

  •  AN ALYSIS

 Develop descriptions of the external process and the desired useful ways of interacting with it. Formulate a complete set of measurable goals for the embedded system to meet. Digest the vendor and hardware designer supplied documentation of the hardware and virtual machine. Understand any predecessor systems. If system safety is a concern, perform an initial study of the hazards created by the system, and possible ways of mitigating those hazards.

  •  ARCHITECTURE

 Describe in overview how the hardware and virtual objects work together 

to interact with the external process. Put the description into an 

architectural document. Revise ana lysis concepts where necessary to 

accommodate real-world facts revealed by the architecture.

  •  ESTIMATING

For planning purposes, break the remaining software development process into s mall chunks, and estimate how much effort of how many persons will be required to complete each chunk. Make some guesses 

about the number of lines of code, and function points required, and estimate total project resources from those estimates.

  •  HARDWARE SUPPORT

Support the persons developing the embedded system hardware by writing test code. Use the information gained from writing the test code to improve the architecture and assist with the design of the system. In some cases incorporate the test code directly into the final system code.

  •  DESIGN

Create an orderly description of a collection of virtual objects, which implement the system architecture. Document the collection in a design document. Review the design document with team members and third parties. Make sure the design will result in a system that meets its goals and operates safely. Revise an alysis and architectural concepts as necessary to accommodate changes motivated by the design process.


  • CODE

Implement in the chosen languages, all invented virtual objects, including those in the virtual machine. Revise ana lysis, architecture, and design as needed.

  •  DEBUG

Make all of the hardware and virtual objects work as intended. Revise an alysis, architecture, design and code as needed.

  •  INTEGRATION

Make all of the hardware and virtual objects interact in the way envisioned in the architecture and design. Revise ana lysis, architecture, design and code as needed.

  •  VERIFICATION

 Formally demonstrate that the virtual objects work properly. Revise all above as needed.

  •  VALIDATION

Formally demonstrate that the overall embedded system meets the goals it was intended to meet. Revise all above as needed.

 The processes described above will be considered in more detail in the next few sections of this book


ANA LYSIS

 A better heading for this chapter might be "Learning".

 Whether you come in at the beginning or some time during the middle of a project, your first task is to learn everything there is to know about the project. In no particular order, you need to know:

 1) Why is this project happening?

 2) What persons support the project?

 3) What persons oppose the project?

 4) Is this a new product, or a new version of an older product?

 5) What are the technical goals of the project?

 6) What is the technical environment of the project?

 7) Are project resources adequate to support your efforts?

 8) What is the expected schedule for the project? Is it realistic?

 9) What are the skills, strengths, and weaknesses of other team members?

 10) Which team members do you like? Which ones can you trust? What are their skill sets?

 11) Is product safety an issue? If so, does the resource provider support an emphasis on product safety?

 You won't answer all these questions immediately. In fact, you may never answer all of these questions; but these are things you should find out as soon as possible after coming into a new project.

Now you may say: "Look man, I'm just a programmer on this project. I do my work, they write my check. What do I care about all that political stuff?"That may be so, but you are also responsible for your own life, and a medium sized embedded project is going to account for a big chunk of the next couple of years of your life. It's going to affect your relationships, and your happiness for as long as you are involved. Better to know what you are walking into, than to stumble blindly into a disaster in the making.


 Project Motivation and Support

 Why is this project happening? Ask around. Normally, you will find someone who champions the project. Get to know that person. What is their motivation?  If they get a spark in their eye when they talk about the project, that is a good sign. If they are just occupying an organizational position and carrying out policy, that may still be OK. If they are looking to make a lot of money, that is probably a bad sign. There are much easier ways to make money.

It's can be tough at first to find out, but you need to know the primate power relationships within the organization, as they relate to the project champion. He may be on the way out, in which case you'll have to find another situation. Make sure the project champion has the support of the main monkeys within the 

organization.

Next feel out the network of technical personnel. Have they been with the organization a long time, or did they just arrive. If the latter, are they replacing people who just left? Why? How is the morale of the technical staff? If they spend more time talking about the organization than about the work, get out of  there fast.

Does your entry into the project ignite professional jealousy in anyone on the staff? If so, acquaint yourself with that person. Once you get to know each other, the problem will likely go away. You will have a new friend. If that doesn't happen, keep your eye on that person.

Once you are comfortable with the project motivation and personnel, you are ready to enjoy the first technical challenge: discovering the requirements.


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工程电磁场数值计算-电子书

目录前言第1篇工程电磁场数值分析的数理基础1第1章电磁场的特性及其数学模型11.1数学模型11.2电磁场正问题数值分析的任务和内容21.3电磁场逆问题数值分析的任务和内容41.4电磁场的基本规律——麦克斯韦方程组51.5场向量的微分方程81.6位函数的微分方程91.7定解条件111.8电介质极化场的分析131.9媒质磁化场的分析151.10物理场的相似性17参考文献17第2章离散方程组的计算机解法192.1概述192.2高斯消去法202.3列主元消去法232.4改进的平方根法252.5松弛因子作自适应估计的SOR迭代法262.6共轭梯度加速迭代法292.7广义代数特征值问题的求解31附录2.1高斯消去法求解线性代数方程组程序33附录2.2高斯消去法求解对称正定线性代数方程组程序34附录2.3列主元消去法求解线性代数方程组程序37附录2.4改进的平方根法求解对称正定线性代数方程组程序39附录2.5松弛因子作自适应估计的SOR迭代法求解大型稀疏线性代数方程组程序41附录2.6共轭梯度雅可比加速迭代法求解大型稀疏线性代数方程组程序44附录2.7广义代数特征值问题Ax=λBx的求解程序48参考文献56第2篇电磁场正问题的数值分析57第3章数值积分法573.1概述573.2梯形与辛普生求积公式583.3高斯求积公式603.4椭圆积分的数值计算623.5基于场量积分式的数值积分法633.6基于场源离散化的数值积分法693.7典型算例74附录3.1变步长辛普生积分法程序83附录3.2二重积分的变步长辛普生积分法程序86附录3.3一维高斯积分法程序88应用算题90参考文献92第4章有限差分法934.1概述934.2差分与差商934.3差分格式的构造954.4差分方程组的求解994.5场强与电、磁积分量的计算1014.6典型算例1024.7等值点的寻求与描绘1104.8时域有限差分法113应用算题120参考文献122第5章有限元法1235.1概述1235.2变分原理1245.3有限元法的基本原理1315.4有限元的前、后处理的基础技术1395.5平行平面和轴对称静态电、磁场的有限元方程1475.6非线性场中的有限元法1545.7时谐电磁场中的有限元法1615.8等参数有限元法167附录5.1一阶有限元法的通用计算程序171附录5.2规则平面域的自动剖分程序181附录5.3圆形域的自动剖分程序185附录5.4有限单元编号按媒质特性重行排序的程序189附录5.5磁化曲线数值逼近的程序190附录5.6等值线绘制的Matlab程序191应用算题198参考文献201第6章模拟电荷法2026.1概述2026.2模拟电荷法的基本原理与应用2036.3模拟电荷的类型及其电位、场强系数的计算式2086.4典型算例2116.5优化模拟电荷法219应用算题220参考文献221第7章矩量法2227.1概述2227.2矩量法的数学基础——加权余量法2227.3点匹配法与典型算例2287.4伽辽金有限元法233应用算题236参考文献236第8章边界元法2378.1概述2378.2基础知识2388.3边界积分方程2408.4边界元方程及方法实施2428.5典型算例248附录8.1线性单元边界元法的通用计算程序251应用算题258参考文献259第3篇电磁场逆问题的数值分析260第9章电磁场逆问题2609.1概述2609.2优化算法2619.3参数计算与模型接口问题2619.4其他相关向题2629.5计算实例262参考文献264第10章随机类全局优化算法26610.1概述26610.2模拟退火算法26610.3禁忌算法26710.4基因(遗传)算法26810.5表面响应模型27010.6矢量优化算法27110.7计算实例273参考文献276第4篇数值计算的实践基础277第11章上机指南7711.1上机环境27711.2Fortran77语言的应用27711.3标准C语言概述28511.4Matlab软件的应用28711.5上机算题的指导289附录11.1列主元消去法求解线性代数方程组程序290附录11.2二重积分的变步长辛普生积分法程序293附录11.3应用有限差分法求解长直接地金属槽中电场的计算程序297附录11.4电磁散射场(FDTD)的计算程序301附录11.5一阶有限元法的通用计算程序306参考文献317附录318附录A坐标系统318附录B矢量分析公式318应用算题解答与提示321第1篇工程电磁场数值分析的数理基础第1章电磁场的特性及其数学模型本章基于宏观电磁理论描述表征电磁场特性的数学方程和关系式,形成建立工程电磁场数学模型和实施数值计算方法的数学物理基础。为适应工程问题分析计算的需要,阐述中特别强调在数学和物理意义上静态、准静态和动态电磁场之间的场特性的区别,并讨论了媒质不连续性和不均匀性的特征描述。为进一步扩展本书分析内容的深广度,本章还概括地提出了物理场的相似性。1.1数学模型回顾自然科学发展的历史,早在伽利略年代,即已认为理解宇宙的原理是数理。其后,牛顿(I.Newton,1642~1727)将力学法则用单纯的数学式来表达,结合由他创始的微积分方法,通过数学分析地球上的潮汐降落、摆的周期和天体中行星运动等自然现象,创立了牛顿力学。此后在包含物理学在内的自然科学领域内,致力于应用数学来阐明自然界各种现象,成为科学史的发展趋势。也就是说,人们应用单纯的数学关系式来描述自然法则,求其解答,并在与实验和观测结果相比较的基础上,去理解和应用自然现象。近代,随着电子计算机技术的迅速发展,数学的应用在继续深人延拓到各工程、物理学科领域的同时,也进一步扩展到经济、生态、人口和社会等非物理学科领域。实践表明,许多以工程经验判断、定性分析为依据的工程设计,现正逐步发展为相关的计算机辅助工程(CAE)和计算机辅助设计(CAD)等定量的工程优化设计;同样,许多以定性方法为基础的学科正在转向定量化发展的道路,众多边缘学科应运而生。这就使数学在发展生产、经济管理,以及各自然与工程科学学科中的重要性日益为人们所理解和接受,促成了近代应用数学及其相关学科相辅相成的新发展。当应用数学方法解决上述各类物理或非物理问题时,首先必须建立数学模型,然后得以在此模型的基础上进行实际问题的理论分析和科学研究。显然,建立的数学模型必须精确地逼近实际问题,否则,在理论分析中即使采用最巧妙的数学处理,其结果也未必有用。因此,建立一个完善的数学模型乃是解决各类实际问题的关键。所谓数学模型,指的是对客观事物的一种抽象的模拟,它遵循事物固有的规律性,通过数学语言(数学符号、数学表达式、图形等)刻画出客观事物的本质属性及其与周围事物的内在联系。应当指出,通常与客观事物完全吻合的数学表述并不多见,因此实际的数学模型往往是在对实际问题进行理想化假设后所给出的数学描述。此外,数学模型的确立,还必须要求它的分析计算结果能为实验、测试所证实,或者它能被推广说明许多事实,乃至可以预测为人们所公认的结果。例如,牛顿创立的万有引力定律就经受了对哈雷彗星的研究、海王星的发现等大量事实的考验。同样,麦克斯韦(J.C.Maxwell,1831~1879)在1865年提出电磁场基本方程组,并预言了电磁波的存在。至今,一百多年来电磁学科领域科技发展的进程证明麦克斯韦方程组是宏观电磁现象与电磁过程普遍适用的数学模型,奠定了经典电磁理论的基础。既然数学模型是客观事物的一种数学描述,因而对于同一事物,基于不同的出发点,就可以有不同类型的数学模型的描述。根据构造数学模型的数学方法分类,模型可以分为微分方程模型、积分方程模型、优化模型和控制论模型等。根据问题中变量的特征分类,模型又可分为确定性模型与随机性模型。根据问题的变化情况又可分为连续型模型与离散型模型。此外,还有线性模型与非线性模型,静态模型与动态模型等分类方法。应指出,数学模型的分类并不具有特殊的意义,但概念的引人将便于理解,有助于综合使用各种数学工具,从各个不同侧面去揭示某一实际问题的本质属性。如上所述,宏观电磁理论最高度概括的数学模型就是麦克斯韦方程组。结合实际问题中千变万化的定解条件(边界条件与初始条件),在引用相应的数学方法后,常用的各类电磁场问题的数学模型可以归结为微分方程模型、积分方程模型和属于优化模型的变分方程模型三大类。1.2电磁场正问题数值分析的任务和内容鉴于工程电磁场问题的复杂性,即各类电磁装置在其结构、几何形状上的复杂性,以及在材料性质变化上的复杂性,致使应用于电磁场分析计算的各种解析方法,例如分离变量法、保角变换法、镜像法和格林函数法等,已经无法适应广泛工程问题分析求解的需要。因而,30余年来,随着计算机技术的飞速发展,属于近似计算方法范畴的各种电磁场数值许算方法得到了长足的进展,并最终已可满足科技和工程方面对于数学模型精确分析的实际需要。归属电磁场分析研究领域的各类电磁装置中的电磁场问题,其共同的基本点在于给定场的计算区域、各区域材料(媒质)组成和特性,以及激励源的特性,求其场域中场量随时间、空间分布的规律(场分布),即构成为电磁场的正问题。因面,对应于电磁场正问题的电磁场数值分析的任务是根据电磁场的基本特性,即基于麦克斯韦方程组,首先,建立逼近实际工程电磁场正问题的连续型的数学模型;然后,采用相应的数值计算方法,经离散化处理,把连续型数学模型转化为等价的离散型数学模型——由离散数值构成的联立代数方程组(离散方程组),应用有效的代数方程组解法,计算出待求离散数学模型的离散解(即场量的数值解);最后,在所得该电磁场正问题的场量(含位函数)离散解的基础上再经各种后处理过程,就可以求出所需的场域中任意点处的场强、任意区域的能量、损耗分布,以及力、力矩和各类电磁参数与性能指标等,以达到对给定的工程电磁场正问题进行理论分析、工程判断乃至优化设计等目的。综合电磁场正问题数值分析处理的全过程,其流程图如图1-1所示。由图可见,以各种数值计算方法为其核心,执行电磁场正问题数值分析不仅必须具备一定的数学、物理基础和有关电磁场的专门知识,而且建模过程在很大程度上还必须有赖于工程知识和经验的积累,使之有可能采用恰当的理想化假设,准确地给定问题的定解条件(初始条件和边界条件)。此外,对应于计算流程的前处理(如场域剖分、数据文件构成等)、数据处理和后处理(如等位线、通量线描绘,以及场强、电磁参数、能量和力的计算等),分析者在计算机编程和应用方面的能力,以及包括计算机软件支持条件等,均是实现数值计算的重要因素。前已指出,高速、大容量计算机的问世,为高精度、高效率的数值计算奠定了基础。经过30余年来的发展,电磁场正问题的数值分析已经取得大量应用研究和工程分析、设计的成果,各种电磁场CAD商品化软件也已进人相关的研究部门、生产企业,产生日益明显的经济效益。与此同时,电磁场数值计算的理论和方法日趋完善,业已成为电工理论学科中的一门新兴的应用学科分支。就电磁场正问题数值分析的核心内容——各种实用的数值计算方法而论,它们是将原连续型数学模型转化为等价的离散型数学模型的基础。取决于不同的数学内涵,目前在电磁场数值分析中常用的数值计算方法有:应用于微分方程型数学模型的有限差分法、有限元法和蒙特卡洛法;应用于积分方程型数学模型的模拟电荷法、矩量法和边界元法,以及基于直接积分运算关系式的数值积分法等。此外,各类数值计算方法的相互组合,例如微分和积分组合型数学模型的单标量磁位法、双标量磁位法等,进一步拓展了数值计算方法在工程实践中的应用。本书将分章阐述其中常用的主要方法及其工程应用。1.3电磁场逆问题数值分析的任务和内容当前,工程科学技术的发展已经在各类电磁装置的综合问题上,即电磁场逆问题的数值分析研究领域,提出了日益迫切的需求。与电磁场正问题相对应,电磁场逆问题就是给定电磁装置理想的性能指标或参数,然后通过装置的优化设计来实现这一目标。目前,对于电磁场逆问题的求解,都是将其分解为一系列的正问题,然后采用一定的优化方法通过迭代解算达到最终优化设计的目的。由于在每一步迭代计算中,需要进行若干次电磁场正问题的数值计算和其他一些辅助计算,因此,相对正问题而言,逆问题的求解、计算量大,占用计算机内存和CPU时间多。也正因如此,惟有随着计算机技术的发展,以及电磁场数值计算理论和方法的不断丰富和完善,才使电磁场逆问题从20世纪80年代中期以来成为电磁场学术与工程界关注的研究热点,并日益展现其令人瞩目的工程实用前景。综合电磁场逆问题数值分析处理的全过程,其流程图如图1-2所示。鉴于工程优化设计的实际需要,如后第3篇所述,本书以工程电磁场问题的全局优化为逆问题数值分析的论点,因此,与图1-2中所列各种优化算法对应的全局优化算法,目前应用的有模拟退火算法、基因算法、进化算法、禁忌算法和神经网络等随机类优化算法。本书将分节阐述其中常用的主要方法及其工程应用。1.4电磁场的基本规律-----麦克斯韦方程组宏观电磁现象的基本规律可以非常简洁地用一个方程组,即麦克斯韦方程组来表示。这一电磁场基本方程组的基本变量为四个场向量:电场强度E(V/m)、磁感应强度B(T)、电位移向量D(C/n²)和磁场强度H(A/m);以及两个源量:电流密度J(A/m²)和电荷密度p(C/m³)。在静止媒质中其徽分形式可以表示为为表征在电磁场作用下媒质的宏观电磁特性,尚应给出以下三个媒质的构成关系式:应当注意,式(1-5)~式(1-7)中分别引入的媒质宏观特征参数——介电常数ε、磁导率μ和电导率γ,只有在线性且各向同性媒质的情况下,才是简单的常数。工程上广泛应用的铁磁材料,其B—H关系呈现为含有磁滞效应和损耗的复杂的非线性规律,此时,μ=μ(H)为依赖于场量变化的某个函数表达式。此外,e和μ还可以描述各向异性材料,这时由于材料中通量密度方向与场强方向的不一致,它们应分别记作张量。在SI单位制中,对应于自由空间的介电常数Eo=8.854×10-¹²F/m;磁导率μo=4π×10-⁷H/m,满足在真空中光速c=(μoEo)-¹/2=2.998×10⁸m/s的基本关系。麦克斯韦方程组描述了场源(电荷、电流)激发电磁场的一般规律,而从全面分析电磁场问题的需要出发,还常引用另一基本方程,即电荷守恒定律这一表征时变电荷与全电流密度之间关系的连续性方程可由麦克斯韦方程组直接导出。此外,从另一侧面为描述电磁场对电荷与电流(运动电荷)的作用,其规律归结为洛仑兹力公式1.4.1动态电磁场对应于动态情况下的时变电磁场,其基本方程即为一般形式的麦克斯韦方程组[式(1-1)~式(1-4)]。此时,式中的场量(E、B、D、H)和源量(J、p)均为空间坐标(位矢r=1x,y,z})和时间坐标(t)的函数。例如,天线辐射和接收场、速调管和磁控管这类电子装置中的场均属动态电磁场。应指出,麦克斯韦方程组的四个方程并不都是独立的。如对式(1-1)取散度,并代人连续性方程[式(1-8)],即导得式(1-4);同理,如对式(1-2)取散度,即导得式(1-3)。因此,只有两个旋度方程[式(1-1)和式(1-2)]是独立方程。鉴于每一个旋度方程对应于三个标量方程,所以麦克斯韦方程组给出了六个独立的标量方程。这样,在给定场源与相应的定解条件下,求解时变电磁场时,面对待求场向量(E、B、D、H)共十二个独立的待求分量,麦克斯韦方程组必须与媒质的构成关系式[式(1-5)~式(1-7)]相结合,才能完成数学模型的构造。1.4.2时谐电磁场在电气工程、无线电工程和电子工程装置中,常涉及随时间按正弦规律变化的电磁场(若是线性媒质中按非正弦周期变化的电磁场,则可以通过分解为基波和各次谐波正弦激励的叠加,予以分析处理)。例如,电磁信息传输中的波导场,交流电机、电器中的电磁场等。这时,在线性媒质、正弦激励且稳态条件下,一般形式的麦克斯韦方程组可归结为不显含时间的复相量表示形式。这就是说,任何一个电、磁场量都可用一复相量表示,例如,电场强度可用一个与时间无关的复相量表示成E(r)=E(r)e₂(),它所对应的实际时变电场则可取√2E(r)e“的实部而得(w为正弦激励的角频率),即所论场点p处电场的实时描述为这样,正弦稳态情况下的时变电磁场(时谐电磁场),由麦克斯韦方程组可推得其对应的相量形式为式中,以相量形式表征的各场量和源量均仅为空间坐标的函数,其模为相应正弦量的有效值。1.4.3准静态场在分析研究导电媒质中的时变电磁场时,若场域中各处位移电流密度远小于传导电流密度,则可忽略位移电流效应。此时,该时变电磁场即称之为准静态情况下的电磁场(磁准静态场),其基本方程除麦克斯韦第一方程(1-1)可近似表述为之外,其余方程(1-2)、(1-3)和(1-4)保持有效。而且基于式(1-14),因任一向量旋度的散度恒等于零,故在准静态下电荷守恒定律归结为显然,若该磁准静态场处于正弦激励、稳态工况下,则如上述,式(1-14)将进而可由相量表示为而与其他相量形式的方程(1-11)、(1-12)和(1-13)共同组成时谐的磁准静态场基本方程组。同样,电荷守恒定律表示成值得指出,此时,就导电媒质而言,应满足所谓良导体条件,即该媒质的电导率γ>>uE。按这一条件可见,相应的磁准静态场的激励源频率将可扩展至X射线的频率段。电工技术中的涡流问题就是这类磁准静态场的典型应用实例,它广泛地伴随在电机、变压器、感应加热装置、磁悬浮系统、磁记录头和螺线管传动机构等工程问题之中。与磁准静态场相对应,还存在另一种可忽略电磁感应效应而导出的准静态情况下的时变电磁场(电准静态场)。这类场的基本方程除麦克斯韦第二方程(1-2)可近似表述为之外,其余方程(1-1)、(1-3)和(1-4)保持有效。电力传输系统和装置中的高压电场,各种电子器件、设备和天线近区的电场等,均属这类电准静态场的工程应用实例。应该指出,无论是忽略电磁感应效应的电准静态,还是忽略位移电流效应的磁准静态,它们都满足所谓准静态条件:L<<λ[或(L/c)<<T]。也就是说,电磁波以速度c传播通过所论电磁系统的最大线度尺寸L,其所需时间应远小于该电磁波变动一个周期所对应的时间T。显然,准静态下的源量和场量都是时间和空间的函数,但电磁波传播的推迟作用可以忽略不计,这表明给定某一瞬间的源,即决定了同一瞬间的场分布,而该场分布与稍早瞬间的源状态并无关联。同样,这也表明,对于给定瞬间准静态场的分析计算,完全等同于相应的静态场问题。详细内容请见附件免责声明:本页面/内容部分素材来源于互联网公开信息,旨在传递更多信息,不代表本平台立场。版权归原作者或机构所有,如涉及侵权,请通过平台联系我们,我们将在核实后第一时间处理。本平台对转载内容的真实性、准确性不作任何保证,用户需自行判断并承担使用风险。

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