2.2 Analog and Digital Circuits Design

Modern circuit design is a “mixed signal” endeavor thanks to the availability of sophisticated process technologies that make available bipolar and CMOS(Complementary Metal-Oxide-Semiconductor), power and signal, passive and active components on the same circuit. It is then up to the circuit designer's creativity and inclination to assemble these components into the analog and/or logic building blocks necessary to develop the intended system on a chip.

1.Analog Circuits

Analog circuits are circuits dealing with signals free to vary from zero to full power supply voltage. This stands in contrast to digital circuits, which almost exclusively employ “all or nothing” signals: voltages restricted to values of zero and full supply voltage, with no valid state in between those extreme limits. Analog circuits are often referred to as linear circuits to emphasize the valid continuity of signal range forbidden in digital circuits, but this label is unfortunately misleading. Just because a voltage or current signal is allowed to vary smoothly between the extremes of zero and full power supply limits does not necessarily mean that all mathematical relationships between these signals are linear in the “straight-line” or “proportional” sense of the word. Many so-called “linear” circuits are quite nonlinear in their behavior, either by necessity of physics or by design.

NPN Transistors

The NPN transistor (see Fig. 2-11) is the king of the traditional bipolar analog integrated circuits world. In fact in the most basic and most cost effective analog IC processes, the chip designer has at its disposal just that; a good NPN transistor. The rest, PNPs, resistors and capacitors are just by-products. For intuitive, back-of-the-envelope type analysis, it is sufficient to model the transistor mostly in DC (Direct Current), keeping in mind that the bandwidth of such an element is finite.

When complexity, like small-signal AC (Alternate Current) behavior, is added to the model, computing simulations should be used since the math quickly becomes hopeless. In Fig. 2-11 the NPN transistor is shown with its symbol (a) and its DC model (b). In this component the current flow enters the collector and base and exits the emitter. Simply stated, the transistor conducts a collector current I _C which is a copy of the base current I _B amplified by a factor of β . It follows that the emitter current I _E is one plus beta times the base current. A typical value for the amplification factor is 100. NPNs have excellent dynamic performance, or bandwidth, measured by their cutoff frequency; easily above 1GHz.

PNP Transistors

The PNP transistor (see Fig. 2-12) is complemen-tary to the NPN, with the current flow entering the emitter and exiting the collector and base, the opposite of what happens in the NPN. Simplicity dictates that PNPs are a by-product of the NPN construction, hence they often have less beta current gain and are slower than NPNs. A typical value for their amplification factor β is 50 and their cutoff frequency ( f _T ) is generally above 1MHz.

Transistor Equations

The voltage to current relation in a bipolar transistor follows a logarithmic law given by

where V _T is the thermal voltage and I _o is a characteristic current that depends on the specific process. This has some pretty interesting implications; for example, if the transistor from eq. (2-7) carries a current A times higher, we can write

The increase in voltage from the factor of A increase in current will be

where K is the Boltzman constant, T is the temperature in degrees Kelvin, and q is equal to the elec-tron charge in Coulombs.

Naturally the opposite is true for the current variation as a function of voltage. In fact if we invert the previous equation we have

which shows that the current varies exponentially with the V _BE . For a quick estimate of variations in current due to small voltage variations, we can linearize the exponential law and find that the current will vary at roughly 2%/mV. This strong dependence of current on the V _BE explains why the transistor is normally driven with current, not voltage.

This also explains how difficult it is to deal with offsets, or small voltage variations between identical transistors. Two identical transistors biased at the same identical voltage will have their current mismatched with a 2% error if their V _BE differs by just 1mV.

MOS Transistors

The dual of bipolar NPN and PNP transistors in CMOS technology are the P-channel and N-channel MOS transistors in Fig.2-13. The general function of the transistors is the same independently as their implementation but there are pros and cons to using both technologies. Generally speaking, the base, the emitter, and the collector of the bipolar transistor are analogous to the gate, source and drain of the MOS transistor, respectively. The bipolar transistors' main problem, which is not present in CMOS, is their need for a base current in order to function. Such current is a net transfer loss from emitter to collector. While the base current is small in small signal operation, in power applications, where the transistor is used as a switch, the base current necessary to keep the transistor on can be very high.

This high base current can lead to implementations with very poor efficiency. With the popularity of portable electronics and the need to extend battery life, it is no wonder that CMOS often tends to have the upper hand over bipolar technologies. The advantage of bipolar over CMOS is that it has better trans-conductance gain and better matching, leading to better differential input gain stages. The best performance processes are mixed-mode BiCMOS (Bipolar and CMOS) or BCD (Bipolar CMOS and DMOS) processes in which the designer can use the best component for the task at hand.

2.Digital Circuits

Boolean Algebra Fundamentals

Unlike other algebras, Boolean algebra allows only two possible values:0 or 1. The two value representation is often referred to as a bit (binary digit). The bit can represent on or off, true or false, or yes or no. Input variables such as A , B , C are used in logic expressions to represent switches, relay contacts and sensor inputs. The input variables can represent push button switches, limit switches, temperature sensitive switches, pressure switches, level switches, proximity sensors, light sensors, and weight sensors. The results of the logical expression are to perform some action: turn on or off solenoids, relays, motors, lights, buzzers, alarms and other output devices.

The phrase “digital electronics” is used to describe those circuit systems which primarily operate with the use of only two different voltage levels or two other binary states. Analog devices and systems process time-varying signals that can take on any value across a continuous range of voltage, current or other metric. The difference is that we can pretend that they don't.

Boolean algebra has only three basic operations: NOT or Negation, AND(·), and OR(+).

The NOT operation changes the value to the complement of the value. It changes a 1 to a 0, and a 0 to a 1. It can be represented by a bar over the variable. This is also referred to as inversion or negation.

The AND operation is a Boolean multiply and is 1 only when all values are 1. This is represented in Boolean variables as A · B = Y or AB = Y . The AND is like the old string of Christmas lights. All the lights have to work to have the stringy light.

The OR operation results in a 1 if any of the values is 1. In Boolean algebra, 1+1=1 is valid. Logically the statement means if there are one or more true values, the result is true.

As in regular algebra there are mathematical rules that must be followed. There are properties of Boolean operations that are important in working with logic expressions. Using these properties, Shannon showed that logical expression can be expanded and simplified which in turn resulted in simpler logic and reduced the number or relays and switches.

Commutative Law: A + B = B + A

Associative Law of Addition: A + B + C = A +( B + C )

Associative Law of Multiplication: A ( BC )=( AB ) C

Distributive Law: A ( B + C )= AB + AC

Identity:1· A = A , 0+ A = A

Complement:

De Morgan's Theorem:

Logic Gates

The most basic digital devices are called gates. Gates serve as the building blocks to more complex electronic digital logic circuits. They are fundamental to the design of computers. In general, a gate has one or more inputs and produces an output that is a function of the current input value (s). With each logic element there is a “truth table” that explains how the unit works. And there is a sym bol to represent every gate.

The three important kinds of gates are:

1) AND gate—produces a 1 output if both of its inputs are 1. The logic expression is F = A · B.

2) OR gate—produces a 1 output if one or both of its inputs are 1, produces a 0 output only if both of its inputs are 0. The logic expression is F = A + B .

3) NOT gate—more commonly called an inverter, produces an output value that is the opposite of the input value. The logic expression is

Three common symbols for every gate are shown in Fig.2-14～Fig.2-16 that we can meet in all kinds of references.

The basic electronic digital operations are also NOT, AND, OR, but there are combinations of these that are also commonly used: NAND, NOR and EXCLUSIVE NOR(see Fig.2-17). This is an example of convenient packaging of NAND and AND gates in integrated circuit form.

Combinational Logic and Sequential Logic Circuis

Logic circuits are classified into two types: combinational and sequential. A combinational logic is one whose outputs depend only on its current input. A combinational logic circuit may contain an arbitrary number of logic gates and inverters but no feedback loops( a signal path of a circuit that allows the output of a gate to propagate back to the input of that same gate).

When the input is combined with the previous state of the logic circuits, it is referred to as sequential logic. The use of the previous state is called feedback. The outputs of sequential logic circuit depend not only on the current inputs but also on the past sequence of inputs, possibly arbitrarily far back in time. In this sense, a sequential logic circuit can have memory.

In the analysis, use logic diagram and proceed to a formal description of the function performed by that circuit, such as a truth table or a logic expression. In the synthesis, from a formal description and proceeding to a logic diagram. We have learned that there are five possible representations for a combinational logic function:

1)Truth table.

2)An algebraic sum of minterms, the canonical sum.

3)A minterm list using the ∑ notation.

4)An algebraic product of maxterms, the canonical product.

5)A maxterm list using the Π notation.

Karnaugh map, like Boolean algebra, is a simplification tool applicable to digital logic. Boolean simplification is actually faster than the Karnaugh map for a task involving two or fewer Boolean variables. It is still quite usable at three variables, but a bit slower. At four input variables, Boolean algebra becomes tedious. Karnaugh maps are both faster and easier. Karnaugh maps work well for up to six input variables, and are usable for up to eight variables. For more than six to eight variables, simplification should be by CAD(Computer Automated Design). It simplifies a logic function by combining pairs of adjacent 1 cells into a Sum-of-Products terms that covers all of the 1 cells. Form groups of 0s to cover all 0s. The Product-of-Sums simplified result is built.

Flip-Flops

“Flip-flop” (see Fig.2-18) is the common name given to two-state devices which offer basic memory for sequential logic operations. Flip-flops are heavily used for digital data storage and transfer and are commonly used in banks called “registers” for the storage of binary numerical data.

In an S-R latch, activation of the S input sets the circuit, while activation of the R input resets the circuit. If both S and R inputs are activated simultaneously, the circuit will be in an invalid condition.

The J-K flip-flop is a modified version of an S-R flip-flop with no “invalid” or “illegal” output state. So a J-K flip-flop is nothing more than an S-R flip-flop with an added layer of feedback. This feedback selectively enables one of the two set/reset inputs so that they cannot both carry active signal to the multivibrator circuit, thus eliminating the invalid condition.

The D flip-flop tracks the input, making transitions with match those of the input D. The D stands for “data”; this flip-flop stores the value that is on the data line. It can be thought of as a basic memory cell. A D flip-flop can be made from a S-R flip-flop by tying the set to the reset through an inverter. The result may be clocked.

The T or “toggle” flip-flop changes its output on each clock edge, giving an output which is half the frequency of the signal to the T input. It is useful for constructing binary counters, frequency dividers, and general binary addition devices. It can be made from a J-K flip-flop by tying both of its inputs high.

NEW WORDS AND PHRASES

bipolar adj . 双极型的

CMOS abbr . Complementary Metal-Oxide-Semi-conductor 互补型金属-氧化物-半导体

semiconducting material 半导体材料

integrated circuits 集成电路

transistor n . 晶体管

DC abbr . Direct Current，直流

AC abbr . Alternate Current，交流

digital adj . 数字的，计数的

binary adj . 具有两个的，二进制的，二变量的

Boolean algebra 布尔代数

positive adj . 确实的，积极的，肯定的，现实的，正的，阳性的

negative adj . 否定的，否认的，反面的，消极的，反对的，负的，阴极的

hexadecimal adj . 十六进制的

number system 计数制

Commutative Law 交换律

Associative Law 结合律

Distributive Law 分配律

inverter n . 变换器，倒相器，倒换器，反演器，逆变器，“非”门

truth table 真值表

combinational adj . 组合的

sequential adj . 时序的

flip-flop n . 触发器

NOTES

1)Many so-called “linear” circuits are quite nonlinear in their behavior, either by necessity of physics or by design.

许多线性电路在工作时呈非线性，或者是由于物理结构造成的，或者是由于电路设计的问题。

2)Simply stated, the transistor conducts a collector current I _C which is a copy of the base current I _B amplified by a factor of β .

简单地说，晶体管集电极电流 I _C 较基极电流 I _B 放大 β 倍。

3)AND gate——produces a 1 output if both of its inputs are 1.

与门——输入全1输出1。

4)A combinational logic circuit may contain an arbitrary number of logic gates and inverters but no feedback loops.

组合逻辑电路可能包括许多逻辑门和反向器，但不包含反馈电路。

5)It simplifies a logic function by combining pairs of adjacent 1 cells into a Sum-Of-Products terms that covers all of the 1 cells.

卡诺图通过合并相邻项简化逻辑函数，把所有的1项合并成积和式。

EXERCISES

1.Please translate the following words and phrases into Chinese.

a)semiconductor

b)number system

c)IC

d)Commutative Law

e)AC

f)Distributive Law

g)binary

h)inverter

i)negative

j)sequential

2.Please translate the following words and phrases into English.

a）双极型的

b）晶体管

c）N沟道

d）线性化

e）布尔代数

f）真值表

g）触发器

h）组合逻辑电路

i）相邻项

j）积和式

3.Fill in the blanks with the missing word(s).

a)__________circuits are circuits dealing with signals free to vary from zero to full power supply voltage. This stands in contrast to__________, which almost exclusively employ “all or nothing”signals.

b)The PNP transistor is complementary to the NPN, with the current flow__________the emitter and the collector and base, the opposite of what happens in the NPN.

c)While the base current is small in small signal operation, in power applications, where the transistor is used as a__________, the base current necessary to keep the transistor on can be very high.

d)Logic circuits are classified into two types: combinational and sequential. A__________is one whose out-puts depend only on its current input.

e)A combinational logic circuit may contain an arbitrary number of logic gates and inverters but no__________(a signal path of a circuit that allows the output of a gate to propagate back to the input of that same gate).

f)When the input is combined with the previous state of the logic circuits, it is referred to as__________.The use of the previous state is called feedback.

g)The outputs of sequential logic circuit depend not only on the current inputs but also on__________, possi-bly arbitrarily far back in time. A seal-in circuit is an example of a__________.

4.Answer the following questions according to the text.

a)How does a NPN transistor work?

b)What is the advantage of bipolar over CMOS?

c)What are the combinational circuit and the sequential circuit?

d)What is the output/input relationship of NAND gate?

READING Operational Amplifier

运算放大器

The term operational amplifier or “op-amp” refers to a class of high-gain DC coupled amplifiers with two inputs and a single output. The operational amplifier is arguably the most useful single device in analog electronic circuitry. With only a handful of external components, it can be made to perform a wide variety of analog signal processing tasks. Most existing operational amplifiers are produced on a single semiconductor substrate as an integrated circuit. These integrated circuits are used as building blocks in a wide variety of applications.

运算放大器或“运放”是指有两个输入端和一个输出端的高增益的直流放大器。实践证明，运算放大器是模拟电子线路中最为有用的器件。只增加一些外部元器件，运算放大器可以完成很多种类的模拟信号处理任务。大多数现存的运算放大器都是集成在单一半导体基底上的集成电路。这些集成电路作为标准模块广泛应用。

1.History

1.发展历史

The operational amplifier was originally designed to per-form mathematical operations by using voltage as an analogue of another quantity. This is the basis of the analog computer, where op-amps were used to model the basic mathematical operations (addition, subtraction, integration, differentiation, and so on) . However, an ideal operational amplifier is an extremely versatile circuit element, with a great many applications beyond mathematical operations. Practical opamps, based on transistors, tubes, or other amplifying components and implemented as discrete or integrated circuits, are good approximations to the ideal.

最初设计运算放大器是为了用电压模拟其他量进行数学运算。这是模拟计算机的基础，计算机采用运放对简单的数学运算（加法、减法、积分、微分等）建模。然而，理想运放是一种用途非常广泛的电路器件，除了数学运算之外，还有非常多的应用。实际的运放具有同理想运放相近的优良性能，它们常常基于晶体管、电子管或其他放大器件，作为分立或集成电路使用。

Op-amps were originally developed in the vacuum tube era, where they were used in analog computers. Op-amps are now normally implemented as integrated circuits (ICs), though versions with discrete components are used when performance beyond that attainable with ICs is required (see Fig.2-19).

运放起源于电子管时代，应用于模拟计算机中。如今，虽然有些分立元件组成的电路在性能上可能会超过集成电路，但运放一般还是以集成电路的形式存在（见图2-19）。

The first integrated op-amp to become widely available, in the late 1960s, was the bipolar Fairchild μA709, created by Bob Widlar in 1965; it was rapidly superseded by the 741, which has better performance and is more stable and easier to use. The μA741 is still in production, and has become ubiquitous in electronics—many manufacturers produce a version of this classic chip, recognizable by part numbers containing “741.” Better designs have since been introduced, some based on the FET(late 1970s)and MOSFET(early 1980s). Many of these more modern devices can be substituted into an older 741-based circuit and work with no other changes, to give better performance.

20世纪60年代末期，第一代集成运放双极型Fairchild μA709得到广泛应用，它是Bob Widlar于1965年发明的，但很快被性能更好、更稳定、更简单的μA741所取代。现在μA741仍然在生产，并且在电子产品中无处不在——许多厂家都在生产这个经典芯片的不同版本，并且可以通过部件上标识的“741”来识别。人们已经开发出更好的设计方法，如基于FET（20世纪70年代末）和MOSEFT（20世纪80年代初）的集成运放。许多现代化的元器件可以取代老式的基于电子线路的741型集成运放，它们在使用方面没有任何区别，但能够达到更好的性能。

Op-amps usually have parameters within tightly specified limits, with standardized packaging and power supply needs. Op-amps have many uses in electronics. In its ordinary usage, the output of the op-amp is controlled by negative feedback which, because of the amplifier's high gain, almost completely determines the output voltage for any given input. Many standard IC op-amps cost only a few cents in moderate production volume, but integrated or discrete amplifiers with non-standard specifications may cost over$100 in small quantities.

运放的参数通常都具有严格指定的极限值，有标准封装和供电电压。运放广泛用于电子产品中。在正常使用中，运放的输出由负反馈信号控制，因为运放的增益很高，所以无论输入信号如何，负反馈信号都几乎完全决定了输出电压值。由于现代工业批量生产，许多标准化的集成运放都非常便宜，但也有一些集成的或分立的非标准运放会由于产量少，可能花费超过100美元。

2.Basic Principle of Amplifiers

2.运放的基本原理

Electronic amplifiers are often symbolized by a simple triangle shape, where the internal components are not individually represented. As shown in Fig.2-20, the usual circuit symbol for an op-amp is

电子放大器一般都表示成三角形，内部器件并不分别表示出来。如图2-20所示，运放的电路符号一般表示为

V ₊ : non-inverting input

V ₊ ：同相输入端

V _- : inverting input

V _-： 反相输入端

V _out : output

V _out ：输出端

V _s+ : positive power supply (sometimes also VDD, VCC or VCC+)

V _s+ ：正电源端（有时也记作VDD、VCC或VCC+）

V _s- : negative power supply (sometimes also VSS, VEE or VCC-)

V _s- ：负电源端（有时也记作VSS、VEE或VCC-）

These amplifier types are called the differential amplifier. Differential amplifiers amplify the voltage difference between two input signals. Voltage output equation is

这种放大器称为差分放大器。差分放大器对两个输入端口之间的电压差值进行放大。电压输出为

Where A is the open-loop gain of the op-amp. The inputs are as-sumed to have very high impedance; negligible current will flow into or out of the inputs. Op-amp outputs have very low source impedance. The input (-) is commonly referred to as the in-verting input and the (+) as the noninverting input. An increas-ingly positive voltage on the input (+) tends to drive the output voltage more positive, and an increasingly positive voltage on the input (-) tends to drive the output voltage more negative. When the polarity of the differential voltage matches the mark-ings for inverting and noninverting inputs, the output will be positive. When the polarity of the differential voltage clashes with the input markings, the output will be negative.

式中， A 是运放的开环增益。假设运放具有非常高的输入阻抗，那么几乎没有电流由输入端流入或流出运放。运放的输出端具有非常低的电源阻抗。“-”输入称为反相输入端，“+”输入称为同相输入端。增大同相输入端的电压，会使输出电压增大；增大反相输入端的电压，会使输出电压减小。当差分电压的极性与反相输入端和同相输入端的标记一致时，输出端为正；当不一致时，输出端为负。

If the output is connected to the inverting input, after being scaled by a voltage divider K = R ₁ / ( R ₁ + R ₂ )(see Fig.2-21), then

如果将输出端通过一个分压器 K = R ₁ / （ R ₁ + R ₂ ）连接到输入端（见图2-21），得到

Solving for V _out /V _in , we see that the result is a linear amplifier with gain

通过求解 V _out /V _in ，可发现结果呈线性放大，其增益为

If G is very large, V _out /V _in comes close to 1 /K , which equals 1+ R ₂ /R ₁ .

如果 G 非常大，则 V _out / V _in 将接近1 /K ，且1 /K =1+ R ₂ /R ₁ 。

This negative feedback connection is the most typical use of an op-amp, but many different configurations are possible, making it one of the most versatile of all electronic building blocks.

运放的典型连接采用负反馈形式，但也有许多不同的用法，这就使得运放成为所有电子模块中最为万能的器件之一。

When connected in a negative feedback configuration, the op-amp will try to make V _out whatever voltage is necessary to make the input voltages equal. These, and the high input impedance, are sometimes called the two “golden rules” of op-amp design (for circuits that use feedback) ：

当连接成负反馈形式时，运放将尽量保持 V _out 同输入电压之间必要的平衡。这一点连同高输入阻抗，常常被看作运算放大器（采用反馈的）电路设计中的两个“金科玉律”：

1) No current will flow into the inputs.

2) The input voltages will be equal to each other.

1）输入端无电流流入。

The exception is if the voltage required is greater than the op-amp's supply, in which case the output signal stops near the power supply rails, V _s+ or V _s- .

2）两个输入端的电压相等。

但也有例外，如果所需要的电压大于运放所能提供的电压，输出信号就会停止变化并接近电源值 V _s+ 或 V _s- 。

If we connect the output of an op-amp to its inverting input and apply a voltage signal to the noninverting input, we find that the output voltage of the op-amp closely follows that input voltage.

如果将运算放大器的输出端连接在反相输入端并且给同相输入端加上电压信号，我们就会发现运放的输出电压将跟踪输入电压。

As V _in increases, V _out will increase in accordance with the differential gain. However, as V _out increases, that output voltage is fed back to the inverting input, thereby acting to decrease the voltage differential between inputs, which acts to bring the output down. What will happen for any given voltage input is that the op-amp will output a voltage very nearly equal to V _in , but just low enough so that there's enough voltage difference left between V _in and the input(-) to be amplified to generate the output voltage.

当 V _in 增大时， V _out 和差分增益一致也增大。而当 V _out 增大时，输出电压将反馈到反相输入端，从而两输入端口之间的差分电压减小，进而使得输出端电压减小。在任何情况下，对于给定的输入电压，运放的输出电压必将近似等于输入电压 V _in ，但其电压差足够小，使得 V _in 和反相输入端之间有足够的电压差，进而对差分电压放大产生输出。

The circuit will quickly reach a point of stability (known as equilibrium in physics), where the output voltage is just the right amount to maintain the right amount of differential, which in turn produces the right amount of output voltage. Taking the op-amp's output voltage and coupling it to the inverting input is a technique known as negative feedback, and it is the key to having a self-stabilizing system (this is true not only of op-amps, but of any dynamic system in general). This stability gives the op-amp the capacity to work in its linear (active) mode, as opposed to merely being saturated fully “on” or “off” as it was used as a comparator, with no feedback at all.

电流将很快达到稳定点（称为物理平衡），这时输出电压达到维持正确差分量的适当值，而这反过来又产生适当的输出电压。我们将运放的输出电压引出并连接在反相输入端的技术称为负反馈，这正是形成自稳定系统的关键所在（不仅在运放电路中，而且在任何常用的动态系统中都是如此）。稳定性使得运放工作在它的线性（有源）模式中，而当运放用于饱和状态下的“开”或“关”时就不同了，如在比较器中，根本不存在反馈。

One great advantage to using an op-amp with negative feedback is that the actual voltage gain of the op-amp doesn't matter, so long as it's very large. If the op-amp's differential gain were 250,000 instead of 200,000, all it would mean is that the output voltage would hold just a little closer to V _in (less differential voltage needed between inputs to generate the required output). In the circuit of Fig. 2-22, the output voltage would still be (for all practical purposes) equal to the non-inverting input voltage. Op-amp gains, therefore, do not have to be precisely set by the factory in order for the circuit designer to build an amplifier circuitwith precise gain. Negative feedback makes the system self-cor-recting. The circuit as a whole will simply follow the input volt-age with a stable gain of 1.

将负反馈用在运放中的一个非常重要的优点就是不考虑运放实际的放大增益，只要其增益非常大即可。如果运放增益为250000而不是200000，也仅仅使得输出电压更接近 V _in 一些（输入端的电压差只需要很小就可以产生所要求的输出）。在图2-22所示的电路中，输出电压将（事实上也是这样）始终等于同相输入端的电压。所以，不必要求生产运放的厂家将运放的增益设定得很精准，不必要求电路设计者设计具有精准增益的放大器电路。负反馈使得系统具有自修正的功能。从整体来看，图2-22中的电路仅仅使输出电压跟随输入电压，它的稳定增益为1。

If we add a voltage divider (see Fig.2-23) to the negative feedback wiring so that only a fraction of the output voltage is fed back to the inverting input instead of the full amount, the output voltage will be a multiple of the input voltage (please bear in mind that the power supply connections to the op-amp have been omitted once again).

如果我们在负反馈线上添加分压器（见图2-23），则这样只有输出的一部分而不是全部反馈到反相输入端，输出电压将是输入电压的倍数（为简单起见，此处省略了电源同运放之间的连接）。

If R ₁ and R ₂ are both equal and V _in is 6V, the op-amp will output whatever voltage is needed to drop 6V across R ₁ (to make the inverting input voltage equal to 6V, as well, keeping the voltage difference between the two inputs equal to zero). With the 2:1 voltage divider of R ₁ and R ₂ , this will take 12V at the output of the op-amp to accomplish.

如果 R ₁ 和 R ₂ 相等，并且 V _in 为6V，无论输出电压是多少，都将使 R ₁ 两端的压降为6V（使得反向输入电压等于6V，同时保持两个输入之间的电压差为0）。设分压器 R ₁ / R ₂ 为2∶1，运放输出端的电压值为12V。

Another way of analyzing this circuit is to start by calculating the magnitude and direction of current through R ₁ , knowing the voltage on either side (and therefore, by subtraction, the voltage across R ₁ ), and R ₁ 's resistance. Since the left-hand side of R ₁ is connected to ground (0V) and the right-hand side is at a potential of 6V (due to the negative feedback holding that point equal to V _in ), we can see that we have 6V across R ₁ . This gives us 1mA of current through R ₁ from left to right. Because we know that both inputs of the op-amp have extremely high impedance, we can safely assume they won't add or subtract any current through the divider. In other words, we can treat R ₁ and R ₂ as being in series with each other: all of the electrons flowing through R ₁ must flow through R ₂ . Knowing the current through R ₂ and the resistance of R ₂ , we can calculate the voltage across R ₂ (6V), and its polarity. Counting up voltages from ground (0V) to the right-hand side of R ₂ , we arrive at 12V on the output.

还有一种分析这个电路的方法，首先计算通过 R ₁ 的电流的大小和方向，得出其两端的电压值（用减法计算 R ₁ 的电压）及 R ₁ 的电阻值。然后将 R ₁ 的左侧接地（0V），右侧接到6V的电势端（因为反馈使得此处电势等于 V _in ），我们将看到 R ₁ 两端的电压差为6V。我们将得到从左到右流过 R ₁ 的1mA的电流。我们知道运放的两个输入端都有非常高的阻抗，所以可以大胆地假设并没有通过分压器增加或减少电流。换句话说，我们可以认为 R ₁ 和 R ₂ 彼此串联，即流过 R ₁ 的电流一定会流过 R ₂ 。知道了通过 R ₂ 的电流以及 R ₂ 的电阻，就可以计算 R ₂ 两端的电压（6V）及其极性。计算从地（0V）到 R ₂ 右侧的电压值，可得到输出端电压为12V。

3.Integrator and Differentiator

3.积分器和微分器

An integrator circuit is shown in Fig.2-24. Show that the output signal of the amplifier is

图2-24所示为积分器电路。运放输出端信号为

Build the circuit with R =10kΩ, C =0.1μF and use square and sinusoidal wave forms to test the predicted behavior. Also place a 100MΩ resistor in parallel with the capacitor. This resistor drains charge to avoid saturation due to very low frequency or DC signals.

令 R =10kΩ， C =0.1μF，用方波和正弦波来测试电路的预测功能。同时把100MΩ电阻与电容平行放置。由于频率太低或直流信号，电阻会耗尽电荷以避免饱和。

A differentiator circuit is shown in Fig.2-25. Show that the output signal of the amplifier is

图2-25所示为微分器电路。运放输出端信号为

Build the circuit with R =10kΩ, C =0.1μF and use triangle and sinusoidal wave forms to test the predicted behavior.

令 R =10kΩ， C =0.1μF，用三角波和正弦波来测试电路的预测功能。

4.Oscillator

4.振荡器

An oscillator (see Fig.2-26) is a device that produces an Alternating Current (AC), or at least pulsing, output voltage. Oscillators are very useful devices, and they are easily made with just an op-amp and a few external components.

振荡器（见图2-26）用来产生交流（AC）的输出电压，至少是脉冲信号。振荡器应用很广，它可以由运放和少量外围器件简单组成。

When the output is saturated positive, the V _ref will be positive, and the capacitor will charge up in a positive direction. When V _ramp exceeds V _ref by the tiniest margin, the output will saturate negative, and the capacitor will charge in the opposite direction (polarity). Oscillation occurs because the positive feedback is instantaneous and the negative feedback is delayed (by means of a RC time constant). The frequency of this oscillator may be adjusted by varying the size of any component.

当输入是正饱和状态时， V _ref 也是正的，并且电容器将正方向充电。当 V _ramp 通过不断累积超出 V _ref 时，输出就会变为负饱和状态，并且电容器将反向充电。因为正反馈是瞬间发生的且负反馈会发生延迟（以 RC 为时间常数），所以振荡会重复地进行。振荡器的频率可以通过变换元器件的尺寸进行调节。

5.Low Power Op-Amp-Audio Amp(50 milliwatt)

5.低功率放大器和音频放大器（50mW）

Fig.2-27 illustrates using an op-amp as an audio amplifier for a simple intercom. A small 8Ω speaker is used as a microphone which is coupled to the op-amp input through a 0.1μF capacitor. The speaker is sensitive to low frequencies and the small value capacitor serves to attenuate the lower tones and produce a better overall response. You can experiment with different value capacitors to improve the response for various speakers. The op-amp voltage gain is determined by the ratio of the feedback resistor to the series input resistor which is around one thousand in this case (1MΩ/1kΩ). The non-inverting input (pin 3) to the op-amp is biased at 50% of the supply voltage (4.5V) by a couple 1kΩ resistors connected across the supply. Since both inputs will be equal when the op-amp is operating within it's linear range, the voltage at the inverting input (pin 2) and the emitter of the buffer transistor (2N3053) will also be 4.5V. The voltage change at the emitter of the transistor will be around±2V for a 2mV change at the input (junction of 0.1μF cap and 1kΩ resistor) which produces a current change of about 2/33=60mA through the 33Ω emitter resistor and the speaker output. The peak output speaker power is about I ² R or 0.06 ² ×8=28mW. The 100Ω resistor and 47μF capacitor are used to isolate the op-amp from the power supply and reduce the possibility of oscillation. An additional 22μF cap is used at the non-inverting input to further stabilize operation. These parts may not be needed in such a low power circuit but it's a good idea to decouple the power supply to avoid unwanted feedback. The circuit draws about 1.2W from a 9V source and is not very efficient but fairly simple to put together. The circuit was tested using a couple of 4 inch speakers located a few feet apart (to reduce feedback) and a small pocket transistor radio placed on top of the speaker/microphone as an audio source.

图2-27所示的是由运放组成的音频放大器，用来做简单的对讲机。一个8Ω的扬声器用来做麦克风，通过一个0.1μF的电容器连接到运放的输入端。扬声器对低频信号很敏感，小的电容器用来降低低的声调，并且产生更好的综合响应。你可以通过试验使用不同的电容器来改善各种扬声器的响应。运放的增益由反馈电阻和串联输入电阻之比决定，比值为1000（1MΩ/1kΩ）。由于有两个1kΩ的电阻跨接在电源端，运放的同相输入端（引脚3）有一个50%电源电压（4.5V）的偏置。当运放工作在线性区时，由于两个输入端口的电压相等，因此反向输入端（引脚2）和缓冲晶体管（2N3053）发射器的电压也同样为4.5V。对于输入端（连接0.1μF电容和1kΩ的电阻）发生2mV的电压变化，晶体管发射器的电压变化大约在±2V左右，大约2/33=60mA的电流流过33Ω的射极电阻和扬声器，扬声器的峰值输出约为 I ² R 或者0.06 ² ×8=28mW。100Ω的电阻和47μF的电容将运放同电源隔离，并且降低可能产生的振荡。在同相输入端加一个22μF的电容可使其功能更加稳定。这部分在低功率电路中不是必需的，但它是一种解除电源耦合的好方式，以避免不需要的反馈。该电路有一个电压为9V、功率为1.2W的电源，虽然效率不高，但连接很简单。用两个4英寸的扬声器对这个电路进行测试，让几个引脚分开（以减少反馈），将一个小型的晶体管收音机安装在扬声器/传声器的顶部位置作为音频源。

Although an operational amplifier is actually a differential-input voltage amplifier with a very high gain, it is almost never used directly as an open-loop voltage amplifier in linear applications for several reasons. First, the gain variation from one operational amplifier to another is quite high and may vary by±50% or more from the value specified by the manufacturer. Second, other nonidealities such as the offset voltage make it impractical to stabilize the DC operating point. Finally, performance characteristics such as linearity and bandwidth of the open-loop operational amplifier are poor. In linear applications, the operational amplifier is almost always used in a feedback mode.

虽然运算放大器实际上是一个高增益的差分输入电压放大器，但由于几种原因，它很少在线性应用中直接用作开环电压放大器。首先，根据制造商的特别说明，运放之间的增益变化非常大，大约±50%，甚至更大。其次，一些不想要的参数会使其不能稳定地工作在直流平衡点上，如失调电压。最后，运放的一些性能特征参数（如开环运算放大器的线性度和带宽）很差。在线性应用中，运放几乎都采用反馈模式。

NEW WORDS AND PHRASES

operational amplifier n . 运算放大器

high-gain n . 高增益

amplifier n . 扩音器，放大器

integrated circuit 集成电路

versatile adj . 通用的，万能的，多才多艺的，多面手的

tube n . 管，管子，＜美＞电子管，显像管

discrete adj . 不连续的，离散的

approximation n . 接近，走近，[数]近似值

discrete component 分立元件

bipolar adj . 有两极的，双极的

be superseded by 被……取代

ubiquitous adj . 到处存在的，（同时）普遍存在的

negative feedback 负反馈

differential amplifier 差分放大器

configuration n . 构造，结构，配置，外形

self-stabilizing system 自稳定系统

wiring n . 配线

input impedance 输入阻抗

fraction n . 小部分，片断，分数

subtraction n . 减少

sinusoidal wave 正弦波

square wave 方波

triangle wave 三角波

oscillator n . 振荡器

pulsing n . 脉冲调制

exceed v . 超过

tinily adv . 极小地，微小地

instantaneous adj . 瞬间的，即刻的，即时的

milliwatt n . 毫瓦

intercom n . 对讲机

emitter n . 发射极

junction n . 结，连接点

decouple v . 分离，减弱

open-loop n . 开环

manufacturer n . 制造业者，厂商

offset vt . 抵消

bandwidth n . 带宽

NOTES

1)Electronic amplifiers are often symbolized by a simple triangle shape, where the internal components are not individually represented.

电子放大器一般都表示成三角形，内部器件并不分别表示出来。

2)An increasingly positive voltage on the input(+) tends to drive the output voltage more positive, and an increasingly positive voltage on the input(-) tends to drive the output voltage more negative.

增大同相输入端（+）的电压，会使输出电压增大；增大反相输入端（-）的电压，会使输出电压减小。

3)Because we know that both inputs of the op-amp have extremely high impedance, we can safely assume they won't add or subtract any current through the divider.

因为我们知道，运算放大器的两个输入端都有相当高的电阻，所以我们完全可以假设它们没有增加或减少任何电流。

4)In other words, we can treat R ₁ and R ₂ as being in series with each other: all of the electrons flowing through R ₁ must flow through R ₂ .

换句话说，我们可以认为 R ₁ 和 R ₂ 串联，即通过 R ₁ 的电流一定会通过 R ₂ 。 NwqpwJCDxBdc9RXO/2Y96U3exTKTjlJR/vNiJVKVE9EbBjEZLudSFC07xltv8LVJ