Part1-Unit2 A: The Operational Amplifier One problem with electronic devices corresponding to the generalized amplifiers is that the gains, Au or Ai, depend upon internal properties of the two-port system. This makes design difficult since these parameters usually vary from device to device, as well as with temperature. The operational amplifier, or Op-Amp, is designed 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 transistors built into the device. At this point we will make no attempt to describe this inner workings. 如广义放大器这样的电子装置，存在一个问题就是增益，取决于两输入端系统的内部特性。 这使得电路的设计变得困难， 因为通常每个设备的参数是不同的， 并且随着温度的变化而变 化。运算放大器设计的目的正是尽量降低这种依赖性，并使电路设计变得简单。一个运算放 大器是一个内置了很多元器件（如电阻和晶体管）的集成电路。但在这里我们并不打算描述 其内部工作原理。 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 physics. Hence, Op-Amps are quite useful for researchers in a variety of technical fields who need to build simple amplifiers but do not want to design at the transistor level. In the texts of electrical circuits and electronics they will also show how to build simple filter circuits using Op-Amps. The transistor amplifiers, which are the building blocks from which Op-Amp integrated circuits are constructed, will be discussed. 运算放大器一般特性的分析超出了课程的范围。 我们将详细的学习一个例子， 然后给出两个 运算放大器的定律， 并示范如何将它们运用于实际的电路应用分析。 这两个定律使得我们可 以设计很多电路，而不需要对设备的物理性质有细致的理解。因此，运算放大器对众多技术 领域中的这些研究者很有用， 他们需要设计简单的放大器但并不想深入到晶体管层次。 在电 子电路课程中， 还将示范如何应用运算放大器构建简单滤波电路。 我们还将讨论晶体管放大 器，它是运算放大器集成电路构成的基础。 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 attachments to power supplies and to ground potential. 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 chapter. The voltages at the two inputs and the output will be represent by the symbols UI1, UI2, and UO. 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 UO=A(UI1-UI
　　2) Where A is the gain of the Op-Amp and UI1 and UI2 the voltages at inputs. In other words, the output voltage is A times the difference in potential between the two inputs. 理想运算放大器的示意图如图 1-2a-1 所示。只显示了三个引脚：正负输入和输出。其他一 些引脚没有画出来， 如连接电源和地的引脚。 这些引脚对于实际电路中的运算放大器的工作
是必须的。但是，在这一章的研究中，它们可以被省略，因为我们考虑的是理想的运算放大 器应用。分别用符号 UI
　　1、UI2,、和 UO 表示两个输入端的电压和输出端的电压。每一个电 压的测量都相对于地电势。运算放大器是差分元件。因此我们得到输出电压的表达式 UO=A(UI1-UI
　　2) 这里，A 是运算放大器的增益，UI1 和 UI2 是输入端的电压。即，输出电压等于 A 乘以两 个输入端电压的差值。 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” of a number of transistor amplifiers to create a very large total gain. That is, the number of A in Eq. (1-2A-
　　1) can be on the order of 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 the inputs is very small. This in turn means that the output of the device acts like an ideal voltage source. 集成电路技术允许将许多放大电路构建在一个单独的半导体材料复合芯片上。 运算放大器成 功的一个关键因素是许多晶体管放大器串联产生一个很大的总增益。也就是说，数字 A 可 能为 100000 或更大。 （例如， 五个晶体管放大器串联， 每一个增益为
　　10， 将产生这个 A 值。 ） 一个次重要的因素是这些电路可能以某种方式构建， 使得流入每个输入端的电流很小。 这就 意味着运放的输出相当于一个理想的电压源。

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 R1 and R
　　2. This is one of the key features of Op-Amp design?the action of the circuit on signals depends only upon the external elements which can be easily varied by the designer and which do not depend upon the detailed character of the Op-Amp itself. Note that if A=100000 and (R1+R
　　2)/R1=10, the price we have paid for this advantage is that we have used a device with a voltage gain of 100000 to produce an amplifier with a gain of
　　10. In some sense, by using an Op-Amp we trade off “power” for “control”. 这表明，如果 A 很大，则电路的增益将与 A 的值无关，而可以通过选择 R1 和 R2 来控制。 这是运算放大器设计的重要特性之一： 电路对信号作用的反应只取决于外部元件， 设计者可 以方便的改变这些外部元件，并且它们与运算放大器本身的细节特征无关。注意到如果 A=100000 and (R1+R
　　2)/R1=
　　10，我们为此付出的代价将使用一个电压增益为 100000 的设备 去构建一个增益为 10 的放大器。从某种意义上讲，我们是通过使用运算放大器以能量换取 控制。