2022年自动化专业英语第三版王宏文 .pdf

UNIT 1 Electrical Networks A 电路An electrical circuit or network is composed of elements such as resistors, inductors, and capacitors connected together in some manner. If the network contains no energy sources, such as batteries or electrical generators, it is known as a passive network. On the other hand, if one or more energy sources are present, the resultant combination is an active network. In studying the behavior of an electrical network, we are interested in determining the voltages and currents that exist within the circuit. Since a network is composed of passive circuit elements, we must first define the electrical characteristics of these elements. 电路或电网络由以某种方式连接的电阻器、电感器和电容器等元件组成。如果网络不包含能源，如电池或发电机，那么就被称作无源网络。换句话说，如果存在一个或多个能源，那么组合的结果为有源网络。在研究电网络的特性时，我们感兴趣的是确定电路中的电压和电流。因为网络由无源电路元件组成，所以必须首先定义这些元件的电特性. In the case of a resistor, the voltage-current relationship is given by Ohms law, which states that the voltage across the resistor is equal to the current through the resistor multiplied by the value of the resistance. Mathematically, this is expressed as 就电阻来说，电压-电流的关系由欧姆定律给出，欧姆定律指出：电阻两端的电压等于电阻上流过的电流乘以电阻值。在数学上表达为: u=iR (1-1A-1) 式中 u=电压，伏特； i =电流，安培；R = 电阻，欧姆。The voltage across a pure inductor is defined by Faradays law, which states that the voltage across the inductor is proportional to the rate of change with time of the current through the inductor. Thus we have 纯电感电压由法拉第定律定义，法拉第定律指出： 电感两端的电压正比于流过电感的电流随时间的变化率。因此可得到：U=Ldi/dt 式中 di/dt = 电流变化率，安培 /秒； L = 感应系数，享利。The voltage developed across a capacitor is proportional to the electric charge q accumulating on the plates of the capacitor. Since the accumulation of charge may be expressed as the summation, or integral, of the charge increments dq, we have the equation 电容两端建立的电压正比于电容两极板上积累的电荷q 。 因为电荷的积累可表示为电荷增量dq 的和或积分，因此得到的等式为 u= ，式中电容量C 是与电压和电荷相关的比例常数。由定义可知， 电流等于电荷随时间的变化率，可表示为i = dq/dt 。因此电荷增量dq 等于电流乘以相应的时间增量，或dq = i dt， 那么等式 (1-1A-3) 可写为式中 C = 电容量，法拉。名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 1 页，共 21 页 - - - - - - - - - 归纳式 (1-1A-1)、(1-1A-2) 和 (1-1A-4)描述的三种无源电路元件如图1-1A-1 所示。注意，图中电流的参考方向为惯用的参考方向，因此流过每一个元件的电流与电压降的方向一致。 Active electrical devices involve the conversion of energy to electrical form. For example, the electrical energy in a battery is derived from its stored chemical energy. The electrical energy of a generator is a result of the mechanical energy of the rotating armature. 有源电气元件涉及将其它能量转换为电能，例如，电池中的电能来自其储存的化学能，发电机的电能是旋转电枢机械能转换的结果。Active electrical elements occur in two basic forms: voltage sources and current sources. In their ideal form, voltage sources generate a constant voltage independent of the current drawn from the source. The aforementioned battery and generator are regarded as voltage sources since their voltage is essentially constant with load. On the other hand, current sources produce a current whose magnitude is independent of the load connected to the source. Although current sources are not as familiar in practice, the concept does find wide use representing an amplifying device, such as the transistor, by means of an equivalent electrical circuit. 有源电气元件存在两种基本形式：电压源和电流源。 其理想状态为： 电压源两端的电压恒定，与从电压源中流出的电流无关。因为负载变化时电压基本恒定，所以上述电池和发电机被认为是电压源。另一方面，电流源产生电流，电流的大小与电源连接的负载无关。虽然电流源在实际中不常见， 但其概念的确在表示借助于等值电路的放大器件，比如晶体管中具有广泛应用。电压源和电流源的符号表示如图1-1A-2 所示。 A common method of analyzing an electrical network is mesh or loop analysis. The fundamental law that is applied in this method is Kirchhoffs first law, which states that the algebraic sum of the voltages around a closed loop is 0, or, in any closed loop, the sum of the voltage rises must equal the sum of the voltage drops. Mesh analysis consists of assuming that currents-termed loop currents-flow in each loop of a network, algebraically summing the voltage drops around each loop, and setting each sum equal to 0. 分析电网络的一般方法是网孔分析法或回路分析法。应用于此方法的基本定律是基尔霍夫第一定律，基尔霍夫第一定律指出：一个闭合回路中的电压代数和为0，换句话说，任一闭合回路中的电压升等于电压降。网孔分析指的是： 假设有一个电流即所谓的回路电流流过电路中的每一个回路，求每一个回路电压降的代数和，并令其为零。考虑图 1-1A-3a 所示的电路，其由串联到电压源上的电感和电阻组成，假设回路电流i ，那么回路总的电压降为因为在假定的电流方向上，输入电压代表电压升的方向，所以输电压在 （1-1A-5）式中为负。 因为电流方向是电压下降的方向，所以每一个无源元件的压降为正。利用电阻和电感压降公式，可得等式(1-1A-6)是电路电流的微分方程式。或许在电路中，人们感兴趣的变量是电感电压而不是电感电流。正如图1-1A-1 指出的用积分代替式 (1-1A-6)中的 i，可得 1-1A-7 A 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 2 页，共 21 页 - - - - - - - - - A Operational Amplifier A 运算放大器One problem with electronic devices corresponding to the generalized amplifiers（ n. 放 大 器 ）is that the gains, Au of Ai, depend upon internet properties of the two port system (,iR,oR , etc.). This makes design difficult since these parameters usually vary from devise to devise, as well as with temperature. The operational amplifier, or Op-Amp, is designed to device to minimize this dependence and to maximize the ease of design .An Op-Amp is an integrated circuit that has many component parts such as resistors and transistor built into the device. At this point we will make no attempt to describe these inner workings. 运算放大器像广义放大器这样的电子器件存在的一个问题就是它们的增益AU或 AI取决于双端口系统 (m、b、RI、Ro等)的内部特性。 器件之间参数的分散性和温度漂移给设计工作增加了难度。设计运算放大器或Op-Amp 的目的就是使它尽可能的减少对其内部参数的依赖性、最大程度地简化设计工作。运算放大器是一个集成电路，在它内部有许多电阻、晶体管等元件。就此而言，我们不再描述这些元件的内部工作原理。 A totally general analysis of the Op-Amp is beyond the scope of some texts. We will instead study one example in detail, then present the two Op-Amp laws and show how they can be used for analysis in many practical circuit applications. These two principles allow one to design many circuits without a detailed understanding of the device physic. Hence, Op-Amp are quiet useful for a researcher in a variety of technical field who need to build simple amplifier but do not want to design at the transistor lever. In the text of electrical circuits and electronics they will also show how to built simple filter circuits using Op-Amps. The transistor amplifiers, which are building block（积木） from which Op-Amp integrated circuits are constructed, will be discussed. 运算放大器的全面综合分析超越了某些教科书的范围。在这里我们将详细研究一个例子，然后给出两个运算放大器定律并说明在许多实用电路中怎样使用这两个定律来进行分析。这两个定律可允许一个人在没有详细了解运算放大器物理特性的情况下设计各种电路。因此，运算放大器对于在不同技术领域中需要使用简单放大器而不是在晶体管级做设计的研究人员来说是非常有用的。在电路和电子学教科书中，也说明了如何用运算放大器建立简单的滤波电路。作为构建运算放大器集成电路的积木晶体管，将在下篇课文中进行讨论。The symbol used for an ideal Op-Amp is shown in Fig.1-2A-1. Only three connections are shown: the positive and negative inputs, and the output. Not shown are other connections necessary to run the Op-Amp such as its attachment to power supplies and to ground potential（n. 电势） . The latter connections are necessary to use the Op-Amp in a practical circuit but are not necessary when considering the ideal Op-Amp applications we study in this unit. The voltages at the two inputs and output will be represented by the symbols. Each is measured with respect to ground potential Operational amplifiers are differential devices. By this we mean that the output voltage with respect to ground is given by the expression. 理想运算放大器的符号如图1-2A-1 所示。图中只给出三个管脚：正输入、负输入和输出。名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 3 页，共 21 页 - - - - - - - - - 让运算放大器正常运行所必需的其它一些管脚，诸如电源管脚、 接零管脚等并未画出。在实际电路中使用运算放大器时，后者是必要的， 但在本文中讨论理想的运算放大器的应用时则不必考虑后者。两个输入电压和输出电压用符号U +、U -和 Uo 表示。每一个电压均指的是相对于接零管脚的电位。运算放大器是差分装置。差分的意思是： 相对于接零管脚的输出电压可由下式表示 (1-2A-1) Where A is the gain of the Op-Amp andandUUthe voltages at inputs. In other words, the output voltage is A times the difference in potential between the two inputs. 式中 A 是运算放大器的增益，U + 和 U - 是输入电压。换句话说，输出电压是A 乘以两输入间的电位差。Integrated circuit technology allows construction of many amplifier circuits on a single composite chip of semiconductor material. One key to the success of an operational amplifier is the cascading (n, v. 串联 adj 串联的 ) of a number of transistor amplifiers to create a very large total gain. That is, the number A in Eq.(1-2A-1)can be on the order of(属于同类的，约为 ) 100,000 or more. (For example, cascading of five transistor amplifiers, each with a gain of 10, would yield this value for A.) A second important factor is that these circuits can be built in such a way that the current flow into each of he inputs is very small. A third important design feature is that the output of the device acts like an ideal voltage source. 集成电路技术使得在非常小的一块半导体材料的复合“芯片”上可以安装许多放大器电路。运算放大器成功的一个关键就是许多晶体管放大器“串联” 以产生非常大的整体增益。也就是说，等式 (1-2A-1)中的数 A约为 100,000 或更多 (例如，五个晶体管放大器串联，每一个的增益为 10，那么将会得到此数值的A )。 第二个重要因素是这些电路是按照流入每一个输入的电流都很小这样的原则来设计制作的。第三个重要的设计特点就是运算放大器的输出阻抗(Ro )非常小。也就是说运算放大器的输出是一个理想的电压源。We now can analyze the particular amplifier circuit given in Fig.1-2A-2 using these characteristics. First we note that the voltage at the positive input，U+, is equal to the source voltage,_UU.Various currents are defined in part b lf the figure. Applying KVL around the outer loop in Fig.1-2A-2b and remembering tat the output voltage,oU, is measured with respect ground ,we have 我们现在利用这些特性就可以分析图1-2A-2 所示的特殊放大器电路了。首先，注意到在正极输入的电压U +等于电源电压，即U + =Us 。各个电流定义如图1-2A-2 中的 b 图所示。对图 1-2A-2b 的外回路应用基尔霍夫定律，注意输出电压Uo 指的是它与接零管脚之间的电位，我们就可得到因为运算放大器是按照没有电流流入正输入端和负输入端的原则制作的，即I - =0 。 那 么 对 负 输 入 端 利 用 基 尔 霍 夫 定 律 可 得 I1 = I2 ， 利 用 等 式 (1-2A-2) ， 并设 I1 =I2 =I ， U0 = (R1 +R2 ) I (1-2A-3) 根据电流参考方向和接零管脚电位为零伏特的事实，利用欧姆定律，可得负极输入电压U - ：因此 U - =IR1 ，并由式 (1-2A-3)可得：因为现在已有了 U+ 和 U-的表达式，所以式 (1-2A-1)可用于计算输出电压， 综合上述等式，可得：最后可得： This is the gain factor for the circuit. If A is a very large number, large enough that the denomina名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 4 页，共 21 页 - - - - - - - - - tor, by the AR term. The factor A, which is in both the numerator and denominator, then cancels out and the gain is given by the expression 这是电路的增益系数。如果A 是一个非常大的数，大到足够使AR1 (R1 +R2) ，那么分式的分母主要由AR1 项决定，存在于分子和分母的系数A 就可对消，增益可用下式表示这表明 (1-2A-5b)，This shows that if A is very large, then the gain of the circuit is independent of the exact value of A and can be controlled by the choice of 21andRR. This is one of the key feature of Op-Amp itself. Note that if A=100,000 the price we have paid for this advantage is that we have used a device with a voltage gain of 100,000 to produce an amplifier with a gain if 10. In some sense, by using an Op-Amp we trade off （换取） power for control . 如果 A 非常大，那么电路的增益与A 的精确值无关并能够通过R1 和 R2 的选择来控制。这是运算放大器设计的重要特征之一在信号作用下，电路的动作仅取决于能够容易被设计者改变的外部元件，而不取决于运算放大器本身的细节特性。注意，如果A=100,000， 而(R1 +R2) /R1=10，那么为此优点而付出的代价是用一个具有100,000 倍电压增益的器件产生一个具有 10 倍增益的放大器。从某种意义上说，使用运算放大器是以“能量”为代价来换取“控制”。A similar mathematical analysis can be made in any Op-Amp circuit, but this is cumbersome and there are some very useful shortcuts that involve application if the two laws of Op-Amps which we now present. 对各种运算放大器电路都可作类似的数学分析，但是这比较麻烦， 并且存在一些非常有用的捷径，其涉及目前我们提出的运算放大器两个定律应用。1) The first law states this in normal Op-Amp circuits we may assume that the voltage difference between the input terminals is zero, that is, 第一个定律指出：在一般运算放大器电路中，可以假设输入端间的电压为零，也就是说，2) The second law states that in normal Op-Amp circuits both is of the input currents may be assumed to be zero: 2) 第二个定律指出：在一般运算放大器电路中，两个输入电流可被假定为零：I+=I-=0 The first law is due to the large value of the intrinsic（adj. 内在的）gain A. for example, if the output if an Op-Amp is 1V and A=100,000, then510UUV. this is such a small number that it can often be ignored, and we setUU. The second law comes from the construction of the circuitry （n. 电路）inside the Op-Amp which is such that almost mo current flows into either of the two input. 第一个定律是因为内在增益A 的值很大。例，如果运算放大器的输出是1V ，并且A=100,000, 那么 这是一个非常小、可以忽略的数，因此可设 U+=U-。第二个定律来自于运算放大器的内部电路结构，此结构使得基本上没有电流流入任何一个输入端。AA 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 5 页，共 21 页 - - - - - - - - - The Transfer Function and the Laplace Transformation BB 传递函数和拉普拉斯变换传递函数的概念 If the input-output relationship of the linear system of Fig.1 is known , the characteristics of the system itself are also known . The inputoutput relationship in the Laplace domain is called the transfer function (TF or G Gain) . By definition , the transfer function or system is the ration of the transformed output to the transformed input: 如果像式2-1B-1 表示的线性系统的输入输出关系已知，则系统的特性也可以知道。在拉普拉斯域表示的输入输出关系被称做传递函数。由定义， 元件或系统的传递函数是经拉氏变换的输出与输入的比值：This definition of the transfer function requires the system to be linear and stationary , with continuous variables and with zero initial conditions . The transfer function is most useful when the system is lumped parameter and when transport lags are absent or neglected . Under these conditions the transfer function itself can be expressed as a ratio of two polynomials in the complex Laplace variables, or 此传递函数的定义要求系统是线性的和非时变的，具有连续变量和零起始条件。传递函数最适用于系统是集中参数和当传输延迟不存在或可忽略的情况。在这种条件下， 传递函数本身可表示为拉普拉斯复数变量s的两个多项式的比值： For physical systems , N(s) will be of lower order than D(s) since nature integrates rather than differentiates. It will be shown later that a frequency transfer function for use in the frequency domain can be obtained by replacing the Laplace variable s in the transfer function by jwt . For a closed-loop system, closedthe transfer function is: 对于物理系统，由于系统特性是积分而不是微分，所以N(s)的阶次比 D(s)要低。后面我们将看到用于频域的频率传递函数，它是通过把传递函数中拉普拉斯变量s 用 jt 代换得到的。在式 2-1B-2 中，传递函数分母D(s)由于包含系统中所有的物理特征值而被称做特征方程。令 D(s)等于 0 即得到特征方程。特征方程的解决定系统的稳定性和对任一输入下的暂态响应的一般特性。多项式 N(s)是表示输入如何进入系统的函数。因而N(s)并不影响绝对稳定性或者暂态模式的数目和特性。在特定的输入下， 它决定每一暂态模式的大小和符号，从而确定暂态响应的图形和输出的稳态值。对于一个闭环系统，其传递函数为：式中 W(s)为闭环传递函数，G(s)H(s)称为开环传递函数，1+G(s)H(s)是特征函数。传递函数可以通过多种方法求得。一种方法是纯数学的，先对描述元件或系统的微分方程取拉普拉斯变换，然后求解得出传递函数。当存在非零起始条件时将之看作外加输入对待。第二种方法是试验法。通过给系统加上已知的输入，测出输出值， 通过整理数据和曲线得出传递函数。 某子系统或整个系统的传递函数经常通过对已知的单个元件传递函数的正确合并而得到。这种合并或化简称做方块图代数。拉普拉斯变换The Laplace transformation comes from the area of operational mathematics and is extremely useful in the analysis and design of linear systems. Ordinary differential equations with constant 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 6 页，共 21 页 - - - - - - - - - coefficients transform into algebraic equations that can be used to implement the transfer function concept. The Laplace transform is an evolution from the unilateral Fourier integral and is defined as: 拉氏变换源于工程数学领域，广泛用于线性系统的分析和设计。常系数的常微分方程转变为代数方程可通过传递函数的概念实现。此外，拉氏域更适合于工作，传递函数容易处理、修改和分析。 设计人员很快就会熟练地把拉普拉斯域的变化与时域状态联系起来而不需真地解系统方程（时域） 。当需要时域解时拉氏变换法可直接使用。解是全解，包括通解和特解，初始条件被自动包含在内。最后，可以很容易从拉氏域转到频域中去。 Where F(s) is the Laplace transform of f(t) . Conversely, f(t) is the inverse transform of F(s) and can be represented by the relationship: 变换拉氏是从傅立叶积分演变而来，它定义为： The symbol s denotes the Laplace variable and is a complex variable ;Consequently, s is sometimes referred to as a complex frequency and the Laplace domain is called the complex frequency domain. 这里 F(s)是 f(t)的拉氏变换。相反，f(t)是 F(s)反变换，它们之间的关系可由下式表达，符号 s表明拉氏变量是一个复数变量(+j)。因此， s 有时表示复频，拉氏域称做复频域。由于式（ 2-1B-4）的积分是不定积分，因此不是所有函数都可以进行拉氏变换。幸运的是， 系统设计者感兴趣的函数通常都可以。拉氏变换的使用条件、理论证明和其他用途可见于工程数学的标准著作中。式（ 2-1B-4）的定义可用来找到我们最常见和用到的函数的拉氏变换。为了方便，我们过去常建一个变换对的表，用于简化拉氏域变换和反变换。这里有几条拉氏变换的定理和性质，它们既必需也很有帮助。 1.线性和叠加：式中 c 和 ci 都是常数。 2. 微分和积分定理：对时间导数的拉氏变换可写为式中 f(0)， df(0)， 等是初始条件。如果初始条件为零，正如控制系统分析和设计的一般情况，最后的方程可缩减为：积分的拉氏变换是初始条件为零，它也可缩减为F(s)/s。 3. 初值和终值定理：初值定理表述为在进行拉氏反变换时有用处。终值定理表述为这里 fs