To Angelina and Jahan, for their love and patience v

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About the Author Behzad Razavi received the BSEE degree from Sharif University of Technology in 1 985 and the MSEE and PhDEE degrees from Stanford University in 1988 and 1992, re spectively. He was with AT&T Bell Laboratories and Hewlett-Packard Laboratories until 1996. Since 1996, he has been Associate Professor and subsequently Profess or of electrical engineering at University of California, Los Angeles. His curre nt research includes wireless transceivers, frequency synthesizers, phase-lockin g and clock recovery for high-speed data communications, and data converters. Pr ofessor Razavi was an Adjunct Professor at Princeton University from 1992 to 199 4, and at Stanford University in 1995. He served on the Technical Program Commit tees of the International Solid-State Circuits Conference (ISSCC) from 1993 to 2 002 and VLSI Circuits Symposium from 1998 to 2002. He has also served as Guest E ditor and Associate Editor of the IEEE Journal of Solid-State Circuits, IEEE Tra nsactions on Circuits and Systems, and International Journal of High Speed Elect ronics. Professor Razavi received the Beatrice Winner Award for Editorial Excell ence at the 1994 ISSCC, the best paper award at the 1994 European Solid-State Ci rcuits Conference, the best panel award at the 1995 and 1997 ISSCC, the TRW Inno vative Teaching Award in 1997, and the best paper award at the IEEE Custom Integ rated Circuits Conference in 1998. He was the co-recipient of both the Jack Kilb y Outstanding Student Paper Award and the Beatrice Winner Award for Editorial Ex cellence at the 2001 ISSCC. He was also recognized as one of the top 10 authors in the 50-year history of ISSCC. Professor Razavi is an IEEE Distinguished Lectu rer, a Fellow of IEEE, and the author of Principles of Data Conversion System De sign (IEEE Press, 1995), RF Microelectronics (Prentice Hall, 1998) (translated t o Chinese), Design of Analog CMOS Integrated Circuits (McGraw-Hill, 2001) (trans lated to Chinese and Japanese), and Design of Integrated Circuits for Optical Co mmunications (McGraw-Hill, 2003), and the editor of Monolithic Phase-Locked Loop s and Clock Recovery Circuits (IEEE Press, 1996), and Phase-Locking in High-Perf ormance Systems (IEEE Press, 2003). vii

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Preface With the advances in the semiconductor and communication industries, it has beco me increasingly important for electrical engineers to develop a good understandi ng of microelectronics. This book addresses the need for a text that teaches mic roelectronics from a modern and intuitive perspective. Guided by my industrial, research, and academic experience, I have chosen the topics, the order, and the depth and breadth so as to ef ciently impart analysis and design principles that t he students will nd useful as they enter the industry or graduate school. One sal ient feature of this book is its synthesis- or design-oriented approach. Rather than pulling a circuit out of a bag and trying to analyze it, I set the stage by stating a problem that we face in real life (e.g., how to design a cellphone ch arger). I then attempt to arrive at a solution using basic principles, thus pres enting both failures and successes in the process. When we do arrive at the nal s olution, the student has seen the exact role of each device as well as the logic al thought sequence behind synthesizing the circuit. Another essential component of this book is analysis by inspection. This mentality is created in two steps. Fir st, the behavior of elementary building blocks is formulated using a verbal descri ption of each analytical result (e.g., looking into the emitter, we see 1=g m .). Second, larger circuits are decomposed and mapped to the elementary blocks to avoi d the need for writing KVLs and KCLs. This approach both imparts a great deal of intuition and simpli es the analysis of large circuits. The two articles followin g this preface provide helpful suggestions for students and instructors. I hope these suggestions make the task of learning or teaching microelectronics more en joyable. This preview edition is introduced as a test vehicle so as to collect fee dback from students and instructors and polish the book for the rst edition. A se t of Powerpoint slides and a solutions manual are available for instructors. Beh zad Razavi April 2006 ix

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xi Acknowledgments This book has taken three years to write and bene ted from contributions of many i ndividuals. I wish to thank the following for their input at various stages of t his books development: David Allstot (University of Washington), Joel Berlinghier i, Sr. (The Citadel), Bernhard Boser (University of California, Berkeley), Charl es Bray (University of Memphis), Marc Cahay (University of Cincinnati), Norman C ox (University of Missouri, Rolla), Tranjan Farid (University of North Carolina at Charlotte), Paul Furth (New Mexico State University), Roman Genov (University of Toronto), Maysam Ghovanloo (North Carolina State University), Gennady Gilden blat (Pennsylvania State University), Ashok Goel (Michigan Technological Univers ity), Michael Gouzman (SUNY, Stony Brook), Michael Green (University of Californ ia, Irvine), Sotoudeh Hamedi-Hagh (San Jose State University), Reid Harrison (Un iversity of Utah), Payam Heidari (University of California, Irvine), Feng Hua (C larkson University), Marian Kazmierchuk (Wright State University), Roger King (U niversity of Toledo), Edward Kolesar (Texas Christian University), Ying-Cheng La i (Arizona State University), Daniel Lau (University of Kentucky, Lexington), St anislaw Legowski (University of Wyoming), Philip Lopresti (University of Pennsyl vania), Mani Mina (Iowa State University), James Morris (Portland State Universi ty), Khalil Naja (University of Michigan), Homer Nazeran (University of Texas, El Paso), Tamara Papalias (San Jose State University), Matthew Radmanesh (Californ ia State University, Northridge), Angela Rasmussen (University of Utah), Sal R. Riggio, Jr. (Pennsylvania State University), Ali Sheikholeslami (University of T oronto), Yannis Tsividis (Columbia University), Thomas Wu (University of Central Florida), Darrin Young (Case Western Reserve University). I am grateful to Nare sh Shanbhag (University of Illinois, Urbana-Champaign) for test driving a draft of the book in a course and providing valuable feedback. I also thank my publish ers, Catherine Schultz and Bill Zobrist, for their dedication and exuberance. My wife, Angelina, typed the entire book and kept her humor as this project dragge d on. My deepest thanks go to her. Behzad Razavi April 2006

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Suggestions for Students You are about to embark upon a journey through the fascinating world of microele ctronics. Fortunately, microelectronics appears in so many facets of our lives t hat we can readily gather enough motivation to study it. The reading, however, i s not as easy as that of a story book; we must deal with analysis and design, ap plying mathematical rigor as well as engineering intuition every step of the way . This article provides some suggestions that students may nd helpful in studying microelectronics. Rigor and Intuition Before reading this book, you have taken one or two courses on basic circuit theory, mastering Kirchoffs Laws and the anal ysis of RLC circuits. While quite abstract and bearing no apparent connection wi th real life, the concepts studied in these courses form the foundation for micr oelectronicsjust as calculus does for engineering. Our treatment of microelectron ics also requires rigor but entails two additional components. First, we identif y many applications for the concepts that we study. Second, we must develop intu ition, i.e., a feel for the operation of microelectronic devices and circuits. Wit hout an intuitive understanding, the analysis of circuits becomes increasingly m ore dif cult as we add more devices to perform more complex functions. Analysis by Inspection We will expend a considerable effort toward establishing the mentali ty and the skills necessary for analysis by inspection. That is, looking at a comp lex circuit, we wish to decompose or map it to simpler topologies, thus formulatin g the behavior with a few lines of algebra. As a simple example, suppose we have encountered the resistive divider shown in Fig. (a) and derived its Thevenin eq uivalent. Now, if given the circuit in Fig. (b), we can R1 V in (a) R2 Vout V in R1 C1 (b) R2 L1 Vout readily replace Vin , R1 , and R2 with a Thevenin equivalent, thereby simplifyin g the calculations. 40 Pages per Week While taking courses on microelectronics, you will need to read about 40 pages of this book every week, with each page con taining many new concepts, derivations, and examples. The lectures given by the instructor create a skeleton of each chapter, but it rests upon you to connect the dots by reading the book carefully and understanding each paragraph before procee ding to the next. Reading and understanding 40 pages of the book each week requi res concentration and discipline. You will face new material and detailed deriva tions on each page and should set aside two- or three-hour distraction-free bloc ks of time (no phone calls, TV, email, etc.) so that you xiii

xiv can follow the evolution of the concepts while honing your analytical skills. I also suggest that you attempt each example before reading its solution. 40 Probl ems per Week After reading each section and going through its examples, you are encouraged to evaluate and improve your understanding by trying the correspondin g endof-chapter problems. The problems begin at a relatively easy level and grad ually become more challenging. Some problems may require that you return to the section and study the subtle points more carefully. The educational value provid ed by each problem depends on your persistence. The initial glance at the proble m may be discouraging. But, as you think about it from different angles and, mor e importantly, re-examine the concepts in the chapter, you begin to form a path in your mind that may lead to the solution. In fact, if you have thought about a problem extensively and still have not solved it, you need but a brief hint fro m the instructor or the teaching assistant. Also, the more you struggle with a p roblem, the more appealing and memorable the answer will be. Attending the lectu re and reading the book are examples of passive learning: you simply receive (and, hopefully, absorb) a stream of information provided by the instructor and the t ext. While necessary, passive learning does not exercise your understanding, thu s lacking depth. You may highlight many lines of the text as important. You may even summarize the important concepts on a separate sheet of paper (and you are encouraged to do so). But, to master the material, you need practice (active lear ning). The problem sets at the end of each chapter serve this purpose. Homeworks and Exams Solving the problems at the end of each chapter also prepares you for homeworks and exams. Homeworks, too, demand distraction-free periods during whic h you put your knowledge to work and polish your understanding. An important pie ce of advice that I can offer here is that doing homeworks with your fellow stud ents is a bad idea! Unlike other subject matters that bene t from discussions, arg uments, and rebuttals, learning microelectronics requires quiet concentration. ( After all, you will be on your own during the exam!) To gain more con dence in you r answers, you can discuss the results with your fellow students, the instructor , or the teaching assistants after you have completed the homework by yourself. Time Management Reading the text, going through the problem sets, and doing the homeworks require a time commitment of at least 10 hours per week. Due to the fa st pace of the course, the material accumulates rapidly, making it dif cult to kee p up with the lectures if you do not spend the required time from the very rst we ek. In fact, the more you fall behind, the less interesting and useful the lectu res become, thus forcing you to simply write down everything that the instructor says while not understanding much. With your other courses demanding similar ti me commitments, you can soon become overwhelmed if you do not manage your time c arefully. Time management consists of two steps: (1) partitioning your waking ho urs into solid blocks, and (2) using each block ef ciently. To improve the ef ciency , you can take the following measures: (a) work in a quiet environment to minimi ze distractions; (b) spread the work on a given subject over the week, e.g., 3 h ours every other day, to avoid saturation and to allow your subconscious to proc ess the concepts in the meantime. Prerequisites Many of the concepts that you ha ve learned in the circuit theory courses prove essential to the study of microel ectronics. Chapter 1 gives a brief overview to refresh your memory. With the lim ited lecture time, the instructor may not cover this material in the class, leav ing it for you to read at home. You can rst glance through the chapter and see wh ich concepts bother you before sitting down to concentrate.

Suggestions for Instructors Teaching undergraduate courses proves quite challengingespecially if the emphasis is on thinking and deduction rather than on memorization. With todays young mind s used to playing fast-paced video games and clicking on the Internet toward their destination, it has become increasingly more dif cult to encourage them to concen trate for long periods of time and deal with abstract concepts. Based on one dec ade of teaching, this article provides suggestions that instructors of microelec tronics may nd helpful. Therapy The students taking the rst microelectronics cours e have typically completed one or two courses on basic circuit theory. To many, that experience has not been particularly memorable. After all, the circuit theo ry textbook is most likely written by a person not in the eld of circuits. Simila rly, the courses are most likely taught by an instructor having little involveme nt in circuit design. For example, the students are rarely told that node analys is is much more frequently used in hand calculations than mesh analysis is. Or, they are given little intuition with respect to Thevenin and Norton theorems. Wi th the foregoing issues in mind, I begin the rst course with a ve-minute therapy se ssion. I ask how many came out of the circuit theory courses with a practical under standing. Very few raise their hands. I then ask, But how about your calculus cou rses? How many of you came out of these courses with a practical understanding? Sub sequently, I explain that circuit theory builds the foundation for microelectron ics just as calculus does for engineering. I further point out that some abstrac tness should also be expected in microelectronics as we complete the foundation for more advanced topics in circuit analysis and design. I then point out that ( 1) microelectronics is very heavily based on intuitive understanding, requiring that we go beyond simply writing KVLs and KCLs and interpret the mathematical ex pressions intuitively, and (2) this course offers many applications of microelec tronic devices and circuits in our daily lives. In other words, microelectronics is not as dry as arbitrary RLC circuits consisting of 1- resistors, 1-H inducto rs, and 1-F capacitors. First Quiz Since different students enter each course wi th different levels of preparation, I have found it useful to give a 10-minute q uiz in the very rst lecture. Pointing out that the quiz does not count towards th eir grade but serves as a gauge of their understanding, I emphasize that the obj ective is to test their knowledge rather than their intelligence. After collecti ng the quizzes, I ask one of the teaching assistants to assign a binary grade to each: those who would receive less than 50% are marked with a red star. At the end of the lecture, I return the quizzes and mention that those with a red star need to work harder and interact with the teaching assistants and myself more ex tensively. The Big Picture A powerful motivational tool in teaching is the big pi cture, i.e., the practical application of the concept under study. The two examples of microelectronic systems described in Chapter 1 serve as the rst step toward c reating the context for the material covered xv

xvi in the book. But, the big picture cannot stop here. Each new concept may merit a n application however brief the mention of the application may beand most of this burden falls on the lecture rather than on the book. The choice of the applicati on must be carefully considered. If the description is too long or the result to o abstract, the students miss the connection between the concept and the applica tion. My general approach is as follows. Suppose we are to begin Chapter 2 (Basi c Semiconductor Physics). I ask either What would our world look like without sem iconductors? or Is there a semiconductor device in your watch? In your cellphone? In your laptop? In your digital camera? In the ensuing discussion, I quickly go o ver examples of semiconductor devices and where they are used. Following the big picture, I provide additional motivation by asking, Well, but isnt this stuff old ? Why do we need to learn these things? I then brie y talk about the challenges in todays designs and the competition among manufacturers to lower both the power co nsumption and the cost of portable devices. Analysis versus Synthesis Let us con sider the background of the students entering a microelectronics course. They ca n write KVLs and KCLs ef ciently. They have also seen numerous random RLC circuits; i.e., to these students, all RLC circuits look the same, and it is unclear how t hey came about. On the other hand, an essential objective in teaching microelect ronics is to develop speci c circuit topologies that provide certain characteristi cs. We must therefore change the students mentality from Heres a circuit that you m ay never see again in your life. Analyze it! to We face the following problem and we must create (synthesize) a circuit that solves the problem. We can then begin with the simplest topology, identify its shortcomings, and continue to modify it until we arrive at an acceptable solution. This step-by-step synthesis approach (a) illustrates the role of each device in the circuit, (b) establishes a design -oriented mentality, and (c) engages the students intellect and interest. Analysis by Inspection In their journey through microelectronics, students face increasi ngly more complex circuits, eventually reaching a point where blindly writing KV Ls and KCLs becomes extremely inef cient and even prohibitive. In one of my rst few lectures, I show the internal circuit of a complex op amp and ask, Can we analyz e the behavior of this circuit by simply writing node or mesh equations? It is th erefore important to instill in them the concept of analysis by inspection. My app roach consists of two steps. (1) For each simple circuit, formulate the properti es in an intuitive language; e.g., the voltage gain of a common-source stage is g iven by the load resistance divided by 1=g m plus the resistance tied from the s ource to ground. (2) Map complex circuits to one or more topologies studied in st ep (1). In addition to ef ciency, analysis by inspection also provides great intui tion. As we cover various examples, I emphasize to the students that the results thus obtained reveal the circuits dependencies much more clearly than if we simp ly write KVLs and KCLs without mapping. What If? Adventures An interesting method of reinforcing a circuits properties is to ask a question like, What if we tie thi s device between nodes C and D rather than between nodes A and B ? In fact, stude nts themselves often raise similar questions. My answer to them is Dont be afraid! The circuit doesnt bite if you change it like this. So go ahead and analyze it i n its new form. For simple circuits, the students can be encouraged to consider s everal possible modi cations and determine the resulting behavior. Consequently, t he students feel much more comfortable with the original topology and understand why it is the only acceptable solution (if that is the case). Numeric versus Sy mbolic Calculations In the design of examples, homeworks, and exams, the instruc tor must decide between numeric and symbolic calculations. The students may,

xvii of course, prefer the former type as it simply requires nding the corresponding e quation and plugging in the numbers. What is the value in numeric calculations? In my opinion, they may serve one of two purposes: (1) make the students comfort able with the results recently obtained, or (2) give the students a feel for the typical values encountered in practice. As such, numeric calculations play a li mited role in teaching and reinforcing concepts. Symbolic calculations, on the o ther hand, can offer insight into the behavior of the circuit by revealing depen dencies, trends, and limits. Also, the results thus obtained can be utilized in more complex examples. Blackboard versus Powerpoint This book comes with a compl ete set of Powerpoint slides. However, I suggest that the instructors carefully consider the pros and cons of blackboard and Powerpoint presentations. I can off er the following observations. (1) Many students fall asleep (at least mentally) in the classroom if they are not writing. (2) Many others feel they are missing something if they are not writing. (3) For most people, the act of writing some thing on paper helps carve it in their mind. (4) The use of slides leads to a fast pace (if we are not writing, we should move on!), leaving little time for the stu dents to digest the concepts. For these reasons, even if the students have a har dcopy of the slides, this type of presentation proves quite ineffective. To impr ove the situation, one can leave blank spaces in each slide and ll them with crit ical and interesting results in real time. I have tried this method using transp arencies and, more recently, tablet laptops. The approach works well for graduat e courses but leaves undergraduate students bored or bewildered. My conclusion i s that the good old blackboard is still the best medium for teaching undergradua te microelectronics. The instructor may nonetheless utilize a hardcopy of the Po werpoint slides as his/her own guide for the ow of the lecture. Discrete versus I ntegrated How much emphasis should a microelectronics course place on discrete c ircuits and integrated circuits? To most of us, the term microelectronics remains synonymous with integrated circuits, and, in fact, some university curricula have gradually reduced the discrete design avor of the course to nearly zero. However, only a small fraction of the students taking such courses eventually become act ive in IC products, while many go into board-level design. My approach in this b ook is to begin with general concepts that apply to both paradigms and gradually concentrate on integrated circuits. I also believe that even board-level design ers must have a basic understanding of the integrated circuits that they use. Bi polar Transistor versus MOSFET At present, some controversy surrounds the inclus ion of bipolar transistors and circuits in undergraduate microelectronics. With the MOSFET dominating the semiconductor market, it appears that bipolar devices are of little value. While this view may apply to graduate courses to some exten t, it should be borne in mind that (1) as mentioned above, many undergraduate st udents go into board-level and discrete design and are likely to encounter bipol ar devices, and (2) the contrasts and similarities between bipolar and MOS devic es prove extremely useful in understanding the properties of each. The order in which the two species are presented is also debatable. (Extensive surveys conduc ted by Wiley indicate a 50-50 split between instructors on this matter.) Some in structors begin with MOS devices to ensure enough time is spent on their coverag e. On the other hand, the natural ow of the course calls for bipolar devices as a n extension of pn junctions. In fact, if diodes are immediately followed by MOS devices, the students see little relevance between the two. (The pn junctions in MOSFETs do not come into the picture until the device capacitances are introduc ed.)

xviii My approach in this book is to rst cover bipolar devices and circuits while build ing the foundation such that the MOS counterparts are subsequently taught with g reater ease. As explained below, the material can comfortably be taught even in one quarter with no sacri ce of details of either device type. Course Syllabi This book can be used in a two-quarter or two-semester sequence. Depending on the in structors preference, the courses can follow various combinations of the chapters . Figure 0.1 illustrates some possibilities. I have followed Syllabus I for the quarter system at UCLA for a number of years. 1 Syllabus II sacri ces op amp circu its for an introductory treatment of digital CMOS circuits. In a semester system , Syllabus I extends the rst course to current mirrors and cascode stages and the second course to output stages and analog lters. Syllabus II, on the other hand, includes digital circuits in the rst course, moving current mirrors and cascodes to the second course and sacri cing the chapter on output stages. Figure 0.2 show s the approximate length of time spent on the chapters as practiced at UCLA. In a semester system, the allotted times are more exible. Coverage of Chapters The m aterial in each chapter can be decomposed into three categories: (1) essential c oncepts that the instructor should cover in the lecture, (2) essential skills th at the students must develop but cannot be covered in the lecture due to the lim ited time, and (3) topics that prove useful but may be skipped according to the instructors preference. 2 Summarized below are overviews of the chapters showing which topics should be covered in the classroom. Chapter 1: Introduction to Micr oelectronics The objective of this chapter is to provide the big picture and make the students comfortable with analog and digital signals. I spend about 30 to 45 minutes on Sections 1.1 and 1.2 , leaving the remainder of the chapter (Basic C oncepts) for the teaching assistants to cover in a special evening session in th e rst week. Chapter 2: Basic Semiconductor Physics Providing the basics of semico nductor device physics, this chapter deliberately proceeds at a slow pace, exami ning concepts from different angles and allowing the students to digest the mate rial as they read on. A terse language would shorten the chapter but require tha t the students reread the material multiple times in their attempt to decipher t he prose. It is important to note, however, that the instructors pace in the clas sroom need not be as slow as that of the chapter. The students are expected to r ead the details and the examples on their own so as to strengthen their grasp of the material. The principal point in this chapter is that we must study the phy sics of devices so as to construct circuit models for them. In a quarter system, I cover the following concepts in the lecture: electrons and holes; doping; dri ft and diffusion; pn junction in equilibrium and under forward and reverse bias. Chapter 3: Diode Models and Circuits This chapter serves four purposes: (1) mak e the students comfortable with the pn junction as a nonlinear device; (2) intro duce the concept of linearizing a nonlinear model to simplify the analysis; (3) cover basic circuits with which any electrical engineer must be familiar, e.g., recti ers and limiters; and (4) develop the skills necessary to analyze heavily-no nlinear circuits, e.g., where it is dif cult to predict which diode turns on at wh at input voltage. Of these, the rst three are essential and should be covered in the lecture, whereas the last depends on the instructors preference. (I cover it in my lectures.) In the 1 We offer a separate undergraduate course on digital circuit design, which the students can take only after our rst microelectronics course. 2 Such topics are identi ed in the book by a footnote.

xix Quarter System, Syllabus I First Quarter: Introduction to Microelectronics (Chap ter 1) MOS Devices (Chapter 6) Physics of Semiconductors (Chapter 2) MOS Circuit s (Chapter 7) Diode Models and Circuits (Chapter 3) Op Amp as Black Box (Chapter 8) Differential Pairs (Chapter 10) Frequency Response (Chapter 11) Feedback and Stability (Chapter 12) Bipolar Transistors (Chapter 4) Bipolar Circuits (Chapte r 5) Second Quarter: Current Mirrors and Cascodes (Chapter 9) Quarter System, Syllabus II First Quarter: Introduction to Microelectronics (Cha pter 1) MOS Devices (Chapter 6) Physics of Semiconductors (Chapter 2) MOS Circui ts (Chapter 7) Diode Models and Circuits (Chapter 3) Bipolar Transistors (Chapte r 4) Bipolar Circuits (Chapter 5) Digital CMOS Circuits (Chapter 15) Differential Pairs (Chapter 10) Frequency Res ponse (Chapter 11) Feedback and Stability (Chapter 12) Second Quarter: Current Mirrors and Cascodes (Chapter 9) Semester System, Syllabus I First Semester: Introduction to Microelectronics (Ch apter 1) MOS Devices (Chapter 6) Second Semester: Differential Pairs (Chapter 10 ) Physics of Semiconductors (Chapter 2) MOS Circuits (Chapter 7) Frequency Respo nse (Chapter 11) Diode Models and Circuits (Chapter 3) Op Amp as Black Box (Chap ter 8) Bipolar Transistors (Chapter 4) Bipolar Circuits (Chapter 5) Current Mirrors and Cascodes (Chapter 9) Output Stages (Chapter 13) Analog Filte rs (Chapter 14) Feedback and Stability (Chapter 12) Semester System, Syllabus II First Semester: Introduction to Microelectronics (C hapter 1) MOS Devices (Chapter 6) Second Semester: Current Mirrors and Cascodes (Chapter 9) Physics of Semiconductors (Chapter 2) MOS Circuits (Chapter 7) Diffe rential Pairs (Chapter 10) Diode Models and Circuits (Chapter 3) Op Amp as Black Box (Chapter 8) Frequency Response (Chapter 11) Bipolar Transistors (Chapter 4) Bipolar Circuits (Chapter 5) Digital CMOS Circuits (Chapter 15) Feedback and Stability (Chapter 12) Analog Fi lters (Chapter 14) Figure 0.1 Different course structures for quarter and semester systems. interest of time, I skip a number of sections in a quarter system, e.g., voltage doublers and level shifters. Chapter 4: Physics of Bipolar Transistors Beginnin g with the use of a voltagecontrolled current source in an ampli er, this chapter introduces the bipolar transistor as an extension of pn junctions and derives it s small-signal model. As with Chapter 2, the pace is rela-

xx Quarter System, Syllabus I First Quarter: 1.5 Weeks Introduction to Microelectro nics (Chapter 1) 1 Week MOS Devices (Chapter 6) Second Quarter: 2 Weeks Current Mirrors and Cascodes (Chapter 9) 3 Weeks Differential Pairs (Chapter 10) 2 Weeks Frequency Response (Chapter 11) 3 Weeks Feedback and Stability (Chapter 12) Phy sics of Semiconductors (Chapter 2) 2 Weeks MOS Circuits (Chapter 7) 1.5 Weeks Di ode Models and Circuits (Chapter 3) 1 Week Op Amp as Black Box (Chapter 8) 1 Wee k Bipolar Transistors (Chapter 4) 2 Weeks Bipolar Circuits (Chapter 5) Figure 0.2 Timetable for the two courses. tively slow, but the lectures need not be. I cover structure and operation of th e bipolar transistor, a very simpli ed derivation of the exponential characteristi c, and transistor models, mentioning only brie y that saturation is undesirable. S ince the T-model of limited use in analysis and carries little intuition (especi ally for MOS devices), I have excluded it in this book. Chapter 5: Bipolar Circu its This is the longest chapter in the book, building the foundation necessary f or all subsequent work in electronics. Following a bottom-up approach, this chap ter establishes critical concepts such as input and output impedances, biasing, and small-signal analysis. While writing the book, I contemplated decomposing Ch apter 5 into two chapters, one on the above concepts and another on bipolar ampl i er topologies, so that the latter could be skipped by instructors who prefer to continue with MOS circuits instead. However, teaching the general concepts does require the use of transistors, making such a decomposition dif cult. Chapter 5 pr oceeds slowly, reinforcing, step-by-step, the concept of synthesis and exploring circuit topologies with the aid of What if? examples. As with Chapters 2 and 4, t he instructor can move at a faster pace and leave much of the text for the stude nts to read on their own. In a quarter system, I cover all of the chapter, frequ ently emphasizing the concepts illustrated in Figure 5.7 (the impedance seen loo king into the base, emitter, or collector). With about two (perhaps two and half ) weeks allotted to this chapter, the lectures must be precisely designed to ens ure the main concepts are imparted in the classroom. Chapter 6: Physics of MOS D evices This chapter parallels Chapter 4, introducing the MOSFET as a voltage-con trolled current source and deriving its characteristics. Given the limited time that we generally face in covering topics, I have included only a brief discussi on of the body effect and velocity saturation and neglected these phenomena for the remainder of the book. I cover all of this chapter in our rst course. Chapter 7: MOS Circuits Drawing extensively upon the foundation established in Chapter 5, this chapter deals with MOS ampli ers but at a faster pace. I cover all of this chapter in our rst course. Chapter 8: Operational Ampli er as a Black Box Dealing with op-amp-based circuits, this chapter is written such that it can be taught i n almost any order with respect to other chapters. My own preference is to cover this chapter after ampli er topologies have been studied, so that the students ha ve some bare understanding of the internal circuitry of op amps and its gain lim itations. Teaching this chapter near the end of the rst course also places op amp s closer

xxi to differential ampli ers (Chapter 10), thus allowing the students to appreciate t he relevance of each. I cover all of this chapter in our rst course. Chapter 9: C ascodes and Current Mirrors This chapter serves as an important step toward inte grated circuit design. The study of cascodes and current mirrors here also provi des the necessary background for constructing differential pairs with active loa ds or cascodes in Chapter 10. From this chapter on, bipolar and MOS circuits are covered together and various similarities and contrasts between them are pointe d out. In our second microelectronics course, I cover all of the topics in this chapter in approximately two weeks. Chapter 10: Differential Ampli ers This chapte r deals with large-signal and small-signal behavior of differential ampli ers. The students may wonder why we did not study the largesignal behavior of various am pli ers in Chapters 5 and 7; so I explain that the differential pair is a versatil e circuit and is utilized in both regimes. I cover all of this chapter in our se cond course. Chapter 11: Frequency Response Beginning with a review of basic con cepts such as Bodes rules, this chapter introduces the high-frequency model of tr ansistors and analyzes the frequency response of basic ampli ers. I cover all of t his chapter in our second course. Chapter 12: Feedback and Stability Most instru ctors agree that the students nd feedback to be the most dif cult topic in undergra duate microelectronics. For this reason, I have made great effort to create a st ep-by-step procedure for analyzing feedback circuits, especially where input and output loading effects must be taken into account. As with Chapters 2 and 5, th is chapter proceeds at a deliberately slow pace, allowing the students to become comfortable with each concept and appreciate the points taught by each example. I cover all of this chapter in our second course. Chapter 13: Output Stages and Power Ampli ers This chapter studies circuits that deliver higher power levels th an those considered in previous chapters. Topologies such as pushpull stages and their limitations are analyzed. This chapter can be comfortably covered in a se mester system. Chapter 14: Analog Filters This chapter provides a basic understa nding of passive and active lters, preparing the student for more advanced texts on the subject. This chapter can also be comfortably covered in a semester syste m. Chapter 15: Digital CMOS Circuits This chapter is written for microelectronic s courses that include an introduction to digital circuits as a preparation for subsequent courses on the subject. Given the time constraints in quarter and sem ester systems, I have excluded TTL and ECL circuits here. Problem Sets In additi on to numerous examples, each chapter offers a relatively large problem set at t he end. For each concept covered in the chapter, I begin with simple, con dencebui lding problems and gradually raise the level of dif culty. Except for the device p hysics chapters, all chapters also provide a set of design problems that encoura ge students to work in reverse and select the bias and/or component values to sati sfy certain requirements. SPICE Some basic circuit theory courses may provide ex posure to SPICE, but it is in the rst microelectronics course that the students c an appreciate the importance of simulation tools. Appendix A of this book introd uces SPICE and teaches circuit simulation with the aid of numerous examples. The objective is to master only a subset of SPICE commands that allow simulation of most circuits at this level. Due to the limited lecture time, I ask the teachin g assistants to cover SPICE in a special evening session around the middle of th e quarterjust before I begin to assign SPICE problems.

xxii Most chapters contain SPICE problems, but I prefer to introduce SPICE only in th e second half of the rst course (toward the end of Chapter 5). This is for two re asons: (1) the students must rst develop their basic understanding and analytical skills, i.e., the homeworks must exercise the fundamental concepts; and (2) the students appreciate the utility of SPICE much better if the circuit contains a relatively large number of devices (e.g., 5-10). Homeworks and Exams In a quarte r system, I assign four homeworks before the midterm and four after. Mostly base d on the problem sets in the book, the homeworks contain moderate to dif cult prob lems, thereby requiring that the students rst go over the easier problems in the book on their own. The exam questions are typically twisted version of the problem s in the book. To encourage the students to solve all of the problems at the end of each chapter, I tell them that one of the problems in the book is given in t he exam verbatim. The exams are open-book, but I suggest to the students to summ arize the important equations on one sheet of paper.

Contents 1 Introduction to Microelectronics 1.1 Electronics versus Microelectronics 1.2 E xamples of Electronic Systems . . 1.2.1 Cellular Telephone . . . . . 1.2.2 Digit al Camera . . . . . . . 1.2.3 Analog versus Digital . . . 1.3 Basic Concepts . . . . . . . . . . . 1.3.1 Analog and Digital Signals . 1.3.2 Analog Circuits . . . . . . . 1.3.3 Digital Circuits . . . . . . . 1.3.4 Basic Circuit Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . 2 . 2 . 4 . 6 . 7 . 7 . 9 . 10 . 11 19 19 20 22 25 32 33 38 42 45 49 49 50 56 56 56 57 62 65 67 73 81 82 93 96 98 103 116 xxiii 2 Basic Physics of Semiconductors 2.1 Semiconductor Materials and Their Properti es 2.1.1 Charge Carriers in Solids . . . . . . . 2.1.2 Modi cation of Carrier Dens ities . . 2.1.3 Transport of Carriers . . . . . . . . . 2.2 PN Junction . . . . . . . . . . . . . . . . . 2.2.1 PN Junction in Equilibrium . . . . . 2.2.2 PN Ju nction Under Reverse Bias . . 2.2.3 PN Junction Under Forward Bias . . 2.2.4 I/V Characteristics . . . . . . . . . . 2.3 Reverse Breakdown . . . . . . . . . . . . . 2.3.1 Zener Breakdown . . . . . . . . . . . 2.3.2 Avalanche Breakdown . . . . . . . . 3 Diode Models and Circuits 3.1 Ideal Diode . . . . . . . . . . . . . . . . . . 3.1.1 Initial Thoughts . . . . . . . . . . . . 3.1.2 Ideal Diode . . . . . . . . . . . . . . 3.1.3 Application Examples . . . . . . . . 3.2 PN Juncti on as a Diode . . . . . . . . . . . . 3.3 Additional Examples . . . . . . . . . . . . . 3.4 Large-Signal and Small-Signal Operation . . 3.5 Applications of Diod es . . . . . . . . . . . . 3.5.1 Half-Wave and Full-Wave Recti ers . 3.5.2 Voltage Regulation . . . . . . . . . 3.5.3 Limiting Circuits . . . . . . . . . . . 3.5. 4 Voltage Doublers . . . . . . . . . . 3.5.5 Diodes as Level Shifters and Switch es 4 Physics of Bipolar Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xxiv 4.1 4.2 4.3 4.4 4.5 4.6 General Considerations . . . . . . . . . . . . . . . Structure of Bipolar Transi stor . . . . . . . . . . . Operation of Bipolar Transistor in Active Mode . . 4. 3.1 Collector Current . . . . . . . . . . . . . . 4.3.2 Base and Emitter Current s . . . . . . . . . Bipolar Transistor Models and Characteristics . . . 4.4.1 La rge-Signal Model . . . . . . . . . . . . 4.4.2 I/V Characteristics . . . . . . . . . . . . . 4.4.3 Concept of Transconductance . . . . . . . 4.4.4 Small-Signal Model . . . . . . . . . . . . 4.4.5 Early Effect . . . . . . . . . . . . . . . . . Operation of Bipolar Transistor in Saturation Mode The PNP Transistor . . . . . . . . . . . . . . . . . 4.6.1 Structure and Operation . . . . . . . . . . 4.6 .2 Large-Signal Model . . . . . . . . . . . . 4.6.3 Small-Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 118 119 121 125 127 127 129 131 133 137 142 145 145 146 149 165 165 166 170 170 172 173 175 179 182 185 189 189 215 230 238 266 266 268 269 274 283 284 286 286 287 288 289 290 292 293 304 5 Bipolar Ampli ers 5.1 General Considerations . . . . . . . . . . . 5.1.1 Input a nd Output Impedances . . . 5.1.2 Biasing . . . . . . . . . . . . . . . 5.1.3 DC and Small-Signal Analysis . . . 5.2 Operating Point Analysis and Design . . . . 5.2.1 Simple Biasing . . . . . . . . . . . 5.2.2 Resistive Divider Biasing . . .

. . . 5.2.3 Biasing with Emitter Degeneration . 5.2.4 Self-Biased Stage . . . . . . . . . . 5.2.5 Biasing of PNP Transistors . . . . . 5.3 Bipolar Ampli er Topol ogies . . . . . . . . 5.3.1 Common-Emitter Topology . . . . 5.3.2 Common-Base To pology . . . . . . 5.3.3 Emitter Follower . . . . . . . . . . 5.4 Summary and Ad ditional Examples . . . . 6 Physics of MOS Transistors 6.1 Structure of MOSFET . . . . . . . . . . . 6.2 Operation of MOSFET . . . . . . . . . . 6.2.1 Qualitati ve Analysis . . . . . . . 6.2.2 Derivation of I/V Characteristics . 6.2.3 Channe l-Length Modulation . . . 6.2.4 MOS Transconductance . . . . . 6.2.5 Velocity Sa turation . . . . . . . 6.2.6 Other Second-Order Effects . . . 6.3 MOS Device Mod els . . . . . . . . . . . 6.3.1 Large-Signal Model . . . . . . . 6.3.2 Small-Sig nal Model . . . . . . . 6.4 PMOS Transistor . . . . . . . . . . . . . 6.5 CMOS T echnology . . . . . . . . . . . . 6.6 Comparison of Bipolar and MOS Devices 7 CM OS Ampli ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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xxv 7.1 7.2 7.3 7.4 7.5 General Considerations . . . . . . . . . . . . 7.1.1 MOS Ampli er Topologies . . . . . . 7.1.2 Biasing . . . . . . . . . . . . . . . . 7.1.3 Realization of Curren t Sources . . . . Common-Source Stage . . . . . . . . . . . . 7.2.1 CS Core . . . . . . . . . . . . . . . . 7.2.2 CS stage With Current-Source Load . 7.2.3 CS s tage With Diode-Connected Load 7.2.4 CS Stage With Degeneration . . . . . 7.2.5 CS Core With Biasing . . . . . . . . Common-Gate Stage . . . . . . . . . . . . . 7.3.1 CG Stage With Biasing . . . . . . . . Source Follower . . . . . . . . . . . . . . . . 7.4.1 Source Follower Core . . . . . . . . 7.4.2 Source Follower Wi th Biasing . . . . Summary and Additional Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 304 304 308 309 309 312 313 314 318 320 324 326 326 328 330 353 353 355 355 358 360 366 368 368 369 370 370 370 373 377 381 382 394 394 394 401 408 408 410

418 438 438 438 440 442 443 443 8 Operational Ampli er As A Black Box 8.1 General Considerations . . . . . . . . . . . 8.2 Op-Amp-Based Circuits . . . . . . . . . . 8.2.1 Noninverting Ampli er . . . . . . . 8.2.2 Inverting Ampli er . . . . . . . . . 8.2.3 Integrator and Differe ntiator . . . . 8.2.4 Voltage Adder . . . . . . . . . . . 8.3 Nonlinear Function s . . . . . . . . . . . . . 8.3.1 Precision Recti er . . . . . . . . . 8.3.2 Logar ithmic Ampli er . . . . . . . 8.3.3 Square-Root Ampli er . . . . . . . 8.4 Op Amp No nidealities . . . . . . . . . . . 8.4.1 DC Offsets . . . . . . . . . . . . . 8.4 .2 Input Bias Current . . . . . . . . . 8.4.3 Speed Limitations . . . . . . . . . 8.4.4 Finite Input and Output Impedances 8.5 Design Examples . . . . . . . . . . . . . . 9 Cascode Stages and Current Mirrors 9.1 Cascode Stage . . . . . . . . . . . . 9.1.1 Cascode as a Current Source 9.1.2 Cascode as an Ampli er . . 9.2 C urrent Mirrors . . . . . . . . . . . 9.2.1 Initial Thoughts . . . . . . . 9.2.2 Bipolar Current Mirror . . . 9.2.3 MOS Current Mirror . . . . 10 Differential Am pli ers 10.1 General Considerations . . . 10.1.1 Initial Thoughts . . . 10.1.2 Dif ferential Signals . 10.1.3 Differential Pair . . . 10.2 Bipolar Differential Pai r . . 10.2.1 Qualitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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xxvi 10.3 10.4 10.5 10.6 10.2.2 Large-Signal Analysis . . 10.2.3 Small-Signal Analysis . . MOS Differenti al Pair . . . . . . . 10.3.1 Qualitative Analysis . . . 10.3.2 Large-Signal Anal ysis . . 10.3.3 Small-Signal Analysis . . Cascode Differential Ampli ers . CommonMode Rejection . . . . Differential Pair with Active Load 10.6.1 Qualitative Ana lysis . . . 10.6.2 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . 449 453 459 459 463 468 471 475 479 479 481 504 504 506 507 508 509 512 512 514 516 516 517 519 521 521 523 525 529 532 532 547 547 550 551 551 553 554 558 558 559 560 562 565 567 567 571 574 578 11 Frequency Response 11.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Relationship Between Transfer Function and Freque ncy Response 11.1.2 Bode Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3 Association of Poles with Nodes . . . . . . . . . . . . . . . . . . 11.1.4 Millers Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 11 .2 High-Frequency Models of Transistors . . . . . . . . . . . . . . . . . . . 11 .2.1 High-Frequency Model of Bipolar Transistor . . . . . . . . . . . 11.2.2 Hig h-Frequency Model of MOSFET . . . . . . . . . . . . . . . . 11.2.3 Transit Frequ ency . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Frequency Response o f CE and CS Stages . . . . . . . . . . . . . . . . . 11.3.1 Use of Millers Theore m . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Direct Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.3 Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Frequency Response of CB and CG Stage s . . . . . . . . . . . . . . . . . 11.5 Frequency Response of Followers . . . . . . . . . . . . . . . . . . . . . 11.5.1 Input and Output Impedances . . . . . . . . . . . . . . . . . . . 11.6 Frequency Response of Cascode Stage . . . . . . . . . . . . . . . . . . . 11.6.1 Input and Output Impedances . . . . . . . . . . . . . . . . . . . 11.7 Frequency Response of Differential Pairs . . . . . . . . . . . . . . . . . 12 Feedback 12.1 General Considerations . . . . . . . . . 12 .1.1 Loop Gain . . . . . . . . . . . 12.2 Properties of Negative Feedback . . . . 12.2.1 Gain Desensitization . . . . . . 12.2.2 Bandwidth Extension . . . . . . 12.2.3 Modi cation of I/O Impedances 12.2.4 Linearity Improvement . . . . . 12.3 Types of Ampli ers . . . . . . . . . . . 12.3.1 Simple Ampli er Models . . . . 12.3. 2 Examples of Ampli er Types . 12.4 Sense and Return Techniques . . . . . . 12.5 P olarity of Feedback . . . . . . . . . . 12.6 Feedback Topologies . . . . . . . . . . 12.6.1 Voltage-Voltage Feedback . . . 12.6.2 Voltage-Current Feedback . . . 12.6.3 Current-Voltage Feedback . . . 12.6.4 Current-Current Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xxvii 12.7 Effect of Finite I/O Impedances . . 12.7.1 Inclusion of I/O Effects . . 12. 8 Stability in Feedback Systems . . 12.8.1 Review of Bodes Rules . 12.8.2 Problem of Instability . . 12.8.3 Stability Condition . . . . 12.8.4 Phase Margin . . . . . . . 12.8.5 Frequency Compensation . 12.8.6 Miller Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 582 593 593 595 598 601 602 606 623 623 624 626 629 629 632 636 636 637 640 640 641 641 642 644 645 645 646 647 656 656 657 658 661 664 665 667 668 671 676 676 681 685 690 690 695

13 Output Stages and Power Ampli ers 13.1 General Considerations . . . . . . . . . . . 13.2 Emitter Follower as Power Ampli er . . . . 13.3 Push-Pull Stage . . . . . . . . . . . . . . . 13.4 Improved Push-Pull Stage . . . . . . . . . 13.4.1 Red uction of Crossover Distortion . 13.4.2 Addition of CE Stage . . . . . . . . 13. 5 Large-Signal Considerations . . . . . . . . 13.5.1 Biasing Issues . . . . . . . . . . . 13.5.2 Omission of PNP Power Transistor 13.5.3 High-Fidelity Design . . . . . . . . 13.6 Short-Circuit Protection . . . . . . . . . . . 13.7 Heat Diss ipation . . . . . . . . . . . . . . . 13.7.1 Emitter Follower Power Rating . . 1 3.7.2 Push-Pull Stage Power Rating . . . 13.7.3 Thermal Runaway . . . . . . . . . 13.8 Ef ciency . . . . . . . . . . . . . . . . . . 13.8.1 Ef ciency of Emitter Fol lower . . . 13.8.2 Ef ciency of Push-Pull Stage . . . 13.9 Power Ampli er Classes . . . . . . . . . . 14 Analog Filters 14.1 General Considerations . . . . . . . . . . . 14.1.1 Filter Characteristics . . . . . . . . 14.1.2 Classi cation of Filter s . . . . . . . 14.1.3 Filter Transfer Function . . . . . . 14.1.4 Problem of Se nsitivity . . . . . . . 14.2 First-Order Filters . . . . . . . . . . . . . . 14. 3 Second-Order Filters . . . . . . . . . . . . 14.3.1 Special Cases . . . . . . . . . . . . 14.3.2 RLC Realizations . . . . . . . . . . 14.4 Active Filters . . . . . . . . . . . . . . . . 14.4.1 Sallen and Key Filter . . . . . . . . 14.4.2 Integrator-Based Biquads . . . . . . 14.4.3 Biquads Using Simulated Inductors 14 .5 Approximation of Filter Response . . . . . 14.5.1 Butterworth Response . . . . . . . 14.5.2 Chebyshev Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Digital CMOS Circuits 707 15.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707

xxviii 15.1.1 Static Characterization of Gates . . 15.1.2 Dynamic Characterization of G ates 15.1.3 Power-Speed Trade-Off . . . . . . 15.2 CMOS Inverter . . . . . . . . . . . . . . . 15.2.1 Initial Thoughts . . . . . . . . . . . 15.2.2 Voltage Tran sfer Characteristic . . . 15.2.3 Dynamic Characteristics . . . . . . 15.2.4 Powe r Dissipation . . . . . . . . . 15.3 CMOS NOR and NAND Gates . . . . . . . 15.3. 1 NOR Gate . . . . . . . . . . . . . . 15.3.2 NAND Gate . . . . . . . . . . . . . A Introduction to SPICE A.1 Simulation Procedure . . . . . . A.2 Types of Anal ysis . . . . . . . . A.2.1 Operating Point Analysis A.2.2 Transient Analysis . . . A.2.3 DC Analysis . . . . . . A.3 Element Descriptions . . . . . . A.3.1 Curr ent Sources . . . . . A.3.2 Diodes . . . . . . . . . A.3.3 Bipolar Transistors . . . A.3.4 MOSFETs . . . . . . . A.4 Other Elements and Commands A.4.1 Dependent Sources . . . A.4.2 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708 714 717 719 719 721 726 731 734 734 737 746 746 748 749 749 752 753 753 754 756 758 761 761 762

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 1 (1) 1 Introduction to Microelectronics Over the past ve decades, microelectronics has revolutionized our lives. While be yond the realm of possibility a few decades ago, cellphones, digital cameras, la ptop computers, and many other electronic products have now become an integral p art of our daily affairs. Learning microelectronics can be fun. As we learn how each device operates, how devices comprise circuits that perform interesting and useful functions, and how circuits form sophisticated systems, we begin to see the beauty of microelectronics and appreciate the reasons for its explosive grow th. This chapter gives an overview of microelectronics so as to provide a contex t for the material presented in this book. We introduce examples of microelectro nic systems and identify important circuit functions that they employ. We also pro vide a review of basic circuit theory to refresh the readers memory. 1.1 Electronics versus Microelectronics The general area of electronics began about a century ago and proved instrumenta l in the radio and radar communications used during the two world wars. Early sy stems incorporated vacuum tubes, amplifying devices that operated with the ow of el ectrons between plates in a vacuum chamber. However, the nite lifetime and the la rge size of vacuum tubes motivated researchers to seek an electronic device with better properties. The rst transistor was invented in the 1940s and rapidly disp laced vacuum tubes. It exhibited a very long (in principle, in nite) lifetime and occupied a much smaller volume (e.g., less than 1 cm3 in packaged form) than vac uum tubes did. But it was not until 1960s that the eld of microelectronics, i.e., the science of integrating many transistors on one chip, began. Early integrated circuits (ICs) contained only a handful of devices, but advances in the technolo gy soon made it possible to dramatically increase the complexity of microchips. Example 1.1 Todays microprocessors contain about 100 million transistors in a chip area of ap proximately 3 cm 3 cm. (The chip is a few hundred microns thick.) Suppose integr ated circuits were not invented and we attempted to build a processor using 100 million discrete transistors. If each device occupies a volume of 3 mm 3 mm 3 mm, de termine the minimum volume for the processor. What other issues would arise in s uch an implementation? The minimum volume is given by 27 mm3 108 , i.e., a cube 1.4 m on each side! Of course, the 1 Solution

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 2 (1) 2 Chap. 1 Introduction to Microelectronics wires connecting the transistors would increase the volume substantially. In add ition to occupying a large volume, this discrete processor would be extremely sl ow; the signals would need to travel on wires as long as 1.4 m! Furthermore, if each discrete transistor costs 1 cent and weighs 1 g, each processor unit would be priced at one million dollars and weigh 100 tons! Exercise How much power would such a system consume if each transistor dissipates 10 W? This book deals with mostly microelectronics while providing suf cient foundation for general (perhaps discrete) electronic systems as well. 1.2 Examples of Electronic Systems At this point, we introduce two examples of microelectronic systems and identify some of the important building blocks that we should study in basic electronics . 1.2.1 Cellular Telephone Cellular telephones were developed in the 1980s and r apidly became popular in the 1990s. Todays cellphones contain a great deal of sop histicated analog and digital electronics that lie well beyond the scope of this book. But our objective here is to see how the concepts described in this book prove relevant to the operation of a cellphone. Suppose you are speaking with a friend on your cellphone. Your voice is converted to an electric signal by a mic rophone and, after some processing, transmitted by the antenna. The signal produ ced by your antenna is picked up by the your friends receiver and, after some pro cessing, applied to the speaker [Fig. 1.1(a)]. What goes on in these black boxes ? Why are they needed? Transmitter (TX) Microphone ? ? (a) (b) Figure 1.1 (a) Simpli ed view of a cellpho ne, (b) further simpli cation of transmit and receive paths. Receiver (RX) Speaker Let us attempt to omit the black boxes and construct the simple system shown in Fig. 1.1(b). How well does this system work? We make two observations. First, ou r voice contains frequencies from 20 Hz to 20 kHz (called the voice band). Second, for an antenna to operate ef ciently, i.e., to convert most of the electrical sig nal to electromagnetic radiation, its dimension must be a signi cant fraction (e.g ., 25) of the wavelength. Unfortunately, a frequency range of 20 Hz to 20 kHz tra nslates to a wavelength1 of 1:5 107 m to 1:5 104 m, requiring gigantic antennas for each cellphone. Conversely, to obtain a reasonable antenna length, e.g., 5 c m, the wavelength must be around 20 cm and the frequency around 1.5 GHz. 1 Recall that the wavelength is equal to the (light) velocity divided by the fre quency.

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 3 (1) Sec. 1.2 Examples of Electronic Systems 3 How do we convert the voice band to a gigahertz center frequency? One possible app roach is to multiply the voice signal, xt, by a sinusoid, A cos2fc t [Fig. 1.2(a)]. S ince multiplication in the time domain corresponds to convolution in the frequen cy domain, and since the spectrum x (t ) Voice Signal A cos( 2 f C t ) Out ut Waveform t (a) t t X (f ) Voice S ectrum 20 kHz +20 kHz 0 S ectrum of Cosine Out ut S ectrum f fC 0 +fC f fC 0 +fC f (b)

Figure 1.2 (a) Multi lication of a voice signal by a sinusoid, (b) equivalent o

eration in the frequency domain. of the sinusoid consists of two im ulses at fc , the voice s ectrum is sim ly shi fted (translated) to fc [Fig. 1.2(b)]. Thus, if fc = 1 GHz, the out ut occu ies a bandwidth of 40 kHz centered at 1 GHz. This o eration is an exam le of am litude modulation.2 We therefore ostulate that the black box in the transmitter of Fig . 1.1(a) contains a multi lier,3 as de icted in Fig. 1.3(a). But two other issue s arise. First, the cell hone must deliver Power Am lifier A cos( 2 f C t ) (a) Oscillator (b) Figure 1.3 (a) Sim le transmitter, (b) more com lete transmitter. a relatively large voltage swing (e.g., 20 V ) to the antenna so that the radi ated ower can reach across distances of several kilometers, thereby requiring a ower am li er between the multi lier and the antenna. Second, the sinusoid, A cos 2fc t, must be roduced by an oscillator. We thus arrive at the transmitter archite cture shown in Fig. 1.3(b). Let us now turn our attention to the receive ath of the cell hone, beginning with the sim le realization illustrated in Fig. 1.1(b) . Unfortunately, This to ology fails to o erate with the rinci le of modulation : if the signal received by the antenna resides around a gigahertz center freque ncy, the audio s eaker cannot roduce meaningful information. In other words, a means of 2 Cell hones in fact use other ty es of modulation to translate the voice band t o higher frequencies. 3 Also called a mixer in high frequency electronics.

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 4 (1) 4 Cha . 1 Introduction to Microelectronics translating the s ectrum back to zero center frequency is necessary. For exam le , as de icted in Fig. 1.4(a), multi lication by a sinusoid, A cos2fc t, translates the s ectrum to left and right by Out ut S ectrum Received S ectrum S ectrum of Cosine fC 0 +fC f fC 0 +fC f (a) 2 f C 0 +2 f C f LowNoise Am lifier LowPass Filter LowPass Filter Am lifier oscillator (b) oscillator (c) Figure 1.4 (a) Translation of modulated signal to zero center frequency, (b) sim le receiver, (b) more com lete receiver. fc , restoring the original voice band. The newly generated com onents at 2fc can be removed by a low ass lter. We thus arrive at the receiver to ology shown in Fig. 1.4(b). Our receiver design is still incom lete. The signal received by the antenna can be as low as a few tens of microvolts whereas the s eaker may require swings of

several tens or hundreds of millivolts. That is, the receiver must rovide a gr eat deal of am li cation (gain) between the antenna and the s eaker. Furthermore, si nce multi liers ty ically suffer from a high noise and hence corru t the received signal, a low noise am li er must recede the multi lier. The overall architecture i s de icted in Fig. 1.4(c). Todays cell hones are much more so histicated than the to ologies develo ed above. For exam le, the voice signal in the transmitter an d the receiver is a lied to a digital signal rocessor (DSP) to im rove the qua lity and ef ciency of the communication. Nonetheless, our study reveals some of th e fundamental building blocks of cell hones, e.g., am li ers, oscillators, and lter s, with the last two also utilizing am li cation. We therefore devote a great deal of effort to the analysis and design of am li ers. Having seen the necessity of a m li ers, oscillators, and multi liers in both transmit and receive aths of a cel l hone, the reader may wonder if this is old stuff and rather trivial com ared to the state of the art. Interestingly, these building blocks still remain among th e most challenging circuits in communication systems. This is because the design entails critical trade offs between s eed (gigahertz center frequencies), noise , ower dissi ation (i.e., battery lifetime), weight, cost (i.e., rice of a cel l hone), and many other arameters. In the com etitive world of cell hone manufa cturing, a given design is never good enough and the engineers are forced to furth er ush the above trade offs in each new generation of the roduct. 1.2.2 Digita l Camera Another consumer roduct that, by virtue of going electronic, has dramati cally changed our habits and routines is the digital camera. With traditional ca meras, we received no immediate

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 5 (1) Sec. 1.2 Exam les of Electronic Systems 5 feedback on the quality of the icture that was taken, we were very careful in s electing and shooting scenes to avoid wasting frames, we needed to carry bulky r olls of lm, and we would obtain the nal result only in rinted form. With digital cameras, on the other hand, we have resolved these issues and enjoy many other f eatures that only electronic rocessing can rovide, e.g., transmission of ictu res through cell hones or ability to retouch or alter ictures by com uters. In this section, we study the o eration of the digital camera. The front end of the c amera must convert light to electricity, a task erformed by an array (matrix) o f ixels.4 Each ixel consists of an electronic device (a hotodiode that roduces a current ro ortional to the intensity of the light that it receives. As illustr ated in Fig. 1.5(a), this current ows through a ca acitance, CL , for a certain eriod of time, thereby develo ing a 25 Am lifier 00 C ol um ns Light I Diode CL Photodiode (a) (b) V out 2500 Rows Signal Processing (c) Figure 1.5 (a) O eration of a hotodiode, (b) array of ixels in a digital camer a, (c) one column of the array. ro ortional voltage across it. Each ixel thus rovides a voltage ro ortional to the local light density. Now consider a camera with, say, 6.25 million ixels a rranged in a 2500 2500 array [Fig. 1.5(b)]. How is the out ut voltage of each i xel sensed and rocessed? If each ixel contains its own electronic circuitry, t he overall array occu ies a very large area, raising the cost and the ower diss i ation considerably. We must therefore time share the signal rocessing circuits among ixels. To this end, we follow the circuit of Fig. 1.5(a) with a sim le, c om act am li er and a switch (within the ixel) [Fig. 1.5(c)]. Now, we connect a w ire to the out uts of all 2500 ixels in a column, turn on only one switch at a ti

me, and a ly the corres onding voltage to the signal rocessing block outside the column. The overall array consists of 2500 of such columns, with each column em loying a dedicated signal rocessing block.

Exam le 1.2 A digital camera is focused on a chess board. Sketch the voltage column as a function of time. 4 The term ixel is an abbreviation of icture cell.

roduced by one

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 6 (1) 6 Cha . 1 Introduction to Microelectronics Solution The ixels in each column receive light only from the white squares [Fig. 1.6(a) ]. Thus, the V column V column t (a) (b) (c) Figure 1.6 (a) Chess board ca tured by a digital camera, (b) voltage waveform of one column. column voltage alternates between a maximum for such ixels and zero for those r eceiving no light. The resulting waveform is shown in Fig. 1.6(b). Exercise Plot the voltage if the rst and second squares in each row have the same color.

What does each signal rocessing block do? Since the voltage roduced by each i xel is an analog signal and can assume all values within a range, we must rst digi tize it by means of an analog to digital converter (ADC). A 6.25 mega ixel array mu st thus incor orate 2500 ADCs. Since ADCs are relatively com lex circuits, we ma y time share one ADC between every two columns (Fig. 1.7), but requiring that th e ADC o erate twice as fast (why?). In the extreme case, ADC Figure 1.7 Sharing one ADC between two columns of a ixel array. we may em loy a single, very fast ADC for all 2500 columns. In ractice, the o t imum choice lies between these two extremes. Once in the digital domain, the vide o signal collected by the camera can be mani ulated extensively. For exam le, to z oom in, the digital signal rocessor (DSP) sim ly considers only

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 7 (1) Sec. 1.3 Basic Conce ts 7 a section of the array, discarding the information from the remaining ixels. Al so, to reduce the required memory size, the rocessor com resses the video signal. The digital camera exem li es the extensive use of both analog and digital microe lectronics. The analog functions include am li cation, switching o erations, and a nalog to digital conversion, and the digital functions consist of subsequent sig nal rocessing and storage. 1.2.3 Analog versus Digital Am li ers and ADCs are exa m les of analog functions, circuits that must rocess each oint on a waveform (e. g., a voice signal) with great care to avoid effects such as noise and distortion . By contrast, digital circuits deal with binary levels (ONEs and ZEROs) and, evide ntly, contain no analog functions. The reader may then say, I have no intention o f working for a cell hone or camera manufacturer and, therefore, need not learn about analog circuits. In fact, with digital communications, digital signal roce ssors, and every other function becoming digital, is there any future for analog design? Well, some of the assum tions in the above statements are incorrect. Fi rst, not every function can be realized digitally. The architectures of Figs. 1. 3 and 1.4 must em loy low noise and ower am li ers, oscillators, and multi liers regardless of whether the actual communication is in analog or digital form. For exam le, a 20 V signal (analog or digital) received by the antenna cannot be dir ectly a lied to a digital gate. Similarly, the video signal collectively ca tur ed by the ixels in a digital camera must be rocessed with low noise and distor tion before it a ears in the digital domain. Second, digital circuits require a nalog ex ertise as the s eed increases. Figure 1.8 exem li es this oint by illust rating two binary data waveforms, one at 100 Mb/s and another at 1 Gb/s. The nite risetime and falltime of the latter raises many issues in the o eration of gate s, i o s, and other digital circuits, necessitating great attention to each oint on the waveform. 10 ns x 1 (t ) 1 ns t x 2 (t ) t Figure 1.8 Data waveforms at 100 Mb/s and 1 Gb/s. 1.3 Basic Conce ts Analysis of microelectronic circuits draws u on many conce ts that are taught in basic courses on signals and systems and circuit theory. This section rovides a brief review of these conce ts so as to refresh the readers memory and establis h the terminology used throughout this book. The reader may rst glance through th is section to determine which to ics need a review or sim ly return to this mate

rial as it becomes necessary later. 1.3.1 Analog and Digital Signals An electric signal is a waveform that carries information. Signals that occur in nature can assume all values in a given range. Called analog, such signals include voice, vi deo, seismic, and music This section serves as a review and can be ski ed in classroom teaching.

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 8 (1) 8 Cha . 1 Introduction to Microelectronics waveforms. Shown in Fig. 1.9(a), an analog voltage waveform swings through a cont inuum of V (t ( V ( t ( + Noise t t (a) (b) Figure 1.9 (a) Analog signal , (b) effect of noise on analog signal. values and rovides information at each instant of time. While occurring all aro und us, analog signals are dif cult to rocess due to sensitivities to such circuit im erfections as noise and distortion.5 As an exam le, Figure 1.9(b) illustrates the effect of noise. Furthermore, analog signals are dif cult to store because they req uire analog memories (e.g., ca acitors). By contrast, a digital signal assumes onl y a nite number of values at only certain oints in time. De icted in Fig. 1.10(a ) is a binary waveform, which remains at only one of two levels for V (t ( ZERO ONE V ( t ( + Noise T T (a) t (b) t Figure 1.10 (a) Digital signal, (b) effect of noise on digital signal.

each eriod, T . So long as the two voltages corres onding to ONEs and ZEROs dif fer suf ciently, logical circuits sensing such a signal rocess it correctlyeven if noise or distortion create some corru tion [Fig. 1.10(b)]. We therefore conside r digital signals more robust than their analog counter arts. The storage of binar y signals (in a digital memory) is also much sim ler. The foregoing observations favor rocessing of signals in the digital domain, suggesting that inherently a nalog information must be converted to digital form as early as ossible. Indeed , com lex microelectronic systems such as digital cameras, camcorders, and com a ct disk (CD) recorders erform some analog rocessing, analog to digital conversi on, and digital rocessing (Fig. 1.11), with the rst two functions laying a criti cal role in the quality of the signal. Digital Processing and Storage Analog Signal Analog Processing AnalogtoDigital Conversion

It is worth noting that many digital binary signals must be viewed and rocessed as analog waveforms. Consider, for exam le, the information stored on a hard di sk in a com uter. U on retrieval, the digital data a ears as a distorted waveform with only a few millivolts of am litude 5 Distortion arises if the out ut is not a linear function of in ut.

Figure 1.11 Signal

rocessing in a ty ical system.

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 9 (1) Sec. 1.3 Basic Conce ts 9

t Figure 1.12 Signal icked u from a hard disk in a com uter. is to drive a logical gate, demanding a great deal of am li cation and other analo g rocessing before the data reaches a robust digital form. 1.3.2 Analog Circuit s Todays microelectronic systems incor orate many analog functions. As exem li ed b y the cell hone and the digital camera studied above, analog circuits often limi t the erformance of the overall system. The most commonly used analog function is am li cation. The signal received by a cell hone or icked u by a micro hone roves too small to be rocessed further. An am li er is therefore necessary to rai se the signal swing to acce table levels. The erformance of an am li er is charac terized by a number of arameters, e.g., gain, s eed, and ower dissi ation. We study these as ects of am li cation in great detail later in this book, but it is instructive to brie y review some of these conce ts here. A voltage am li er roduce s an out ut swing greater than the in ut swing. The voltage gain, Av , is de ned a s Av = vvout : in (1.1) In some cases, we refer to ex ress the gain in decibels (dB): Av jdB = 20 log vvout : in (1.2) For exam le, a voltage gain of 10 translates to 20 dB. The gain of ty ical am li e rs falls in the range of 101 to 105 . A cell hone receives a signal level of 20 V , but it must deliver a swing of 50 mV to the s eaker that re roduces the voice. Calculate the required voltage gain in decibels. Exam le 1.3 Solution We have

(Fig. 1.12). Such a small se aration between ONEs and ZEROs this signal ~3 mV Hard Disk

roves inadequate if

Av = 20 log 50 mV 20 V 68 dB: (1.3) (1.4) Exercise What is the out ut swing if the gain is 50 dB?

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 10 (1) 10 Cha . 1 Introduction to Microelectronics In order to o erate ro erly and rovide gain, an am li er must draw ower from a voltage source, e.g., a battery or a charger. Called the ower su ly, this source is ty ically denoted by VCC or VDD [Fig. 1.13(a)]. In com lex circuits, we may sim lify the notation to that shown in Am lifier VCC V in Vout V CC V in Vout Ground (a) (b) (c) Figure 1.13 (a) General am li er symbol along with its ower su ly, (b) sim li ed diagram of (a), (b) am li er with su ly rails omitted. V in Vout Fig. 1.13(b), where the ground terminal signi es a reference oint with zero otenti al. If the am li er is sim ly denoted by a triangle, we may even omit the su ly t erminals [Fig. 1.13(c)], with the understanding that they are resent. Ty ical a m li ers o erate with su ly voltages in the range of 1 V to 10 V. What limits the s eed of am li ers? We ex ect that various ca acitances in the circuit begin to m anifest themselves at high frequencies, thereby lowering the gain. In other word s, as de icted in Fig. 1.14, the gain rolls off at suf ciently high frequencies, l imiting the (usable) bandwidth Am lifier Gain HighFrequency Rolloff Frequency Figure 1.14 Roll off an am li ers gain at high frequencies. of the circuit. Am li ers (and other analog circuits) suffer from trade offs betwe en gain, s eed and ower dissi ation. Todays microelectronic am li ers achieve band widths as large as tens of gigahertz. What other analog functions are frequently used? A critical o eration is ltering. For exam le, an electrocardiogra h measurin g a atients heart activities also icks u the 60 Hz (or 50 Hz) electrical line voltage because the atients body acts as an antenna. Thus, a lter must su ress t his interferer to allow meaningful measurement of the heart. 1.3.3 Digital Circuit s More than 80 of the microelectronics industry deals with digital circuits. Exam les include micro rocessors, static and dynamic memories, and digital signal r ocessors. Recall from basic logic design that gates form combinational circuits, a nd latches and i o s constitute sequential machines. The com lexity, s eed, and owe r dissi ation of these building blocks lay a central role in the overall system erformance. In digital microelectronics, we study the design of the internal c

ircuits of gates, i o s, and other com onents. For exam le, we construct a circuit using devices such as transistors to

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 11 (1) Sec. 1.3 Basic Conce ts 11 realize the NOT and NOR functions shown in Fig. 1.15. Based on these im lementat ions, we NOT Gate NOR Gate A Y =A A B Y =A +B Figure 1.15 NOT and NOR gates. then determine various ro erties of each circuit. For exam le, what limits the s eed of a gate? How much ower does a gate consume while running at a certain s eed? How robustly does a gate o erate in the resence of nonidealities such as noise (Fig. 1.16)? ? Figure 1.16 Res onse of a gate to a noisy in ut. Consider the circuit shown in Fig. 1.17, where switch S1 is controlled by the di gital in ut. That RL A S1 V DD Vout Exam le 1.4 Figure 1.17 is, if A is high, S1 is on and vice versa. Prove that the circuit rovides the N OT function. If A is high, S1 is on, forcing Vout to zero. On the other hand, if A is low, S1 remains off, drawing no current from RL . As a result, the voltage dro across RL is zero and hence Vout = VDD ; i.e., the out ut is high. We thus observe that, for both logical states at the in ut, the out ut assumes the o o site state. Solution Exercise Determine the logical function if S1 and RL are swa ed and Vout is sensed acros s RL .

The above exam le indicates that switches can erform logical o erations. In fac t, early digital circuits did em loy mechanical switches (relays), but suffered from a very limited s eed (a few kilohertz). It was only after transistors were in vented and their ability to act as switches was recognized that digital circuits consisting of millions of gates and o erating at high s eeds (several gigahertz ) became ossible. 1.3.4 Basic Circuit Theorems Of the numerous analysis techniq ues taught in circuit theory courses, some rove articularly im ortant to our s tudy of microelectronics. This section rovides a review of such conce ts.

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 12 (1) 12 Cha . 1 Introduction to Microelectronics I1 I2 In Ij Figure 1.18 Illustration of KCL. Kirchoffs Laws The Kirchoff Current Law (KCL) states that the sum of all currents owing into a node is zero (Fig. 1.18): X j Ij = 0: (1.5) KCL in fact results from conservation of charge: a nonzero sum would mean that e ither some of the charge owing into node X vanishes or this node roduces charge. The Kirchoff Voltage Law (KVL) states that the sum of voltage dro s around any closed loo in a circuit is zero [Fig. 1.19(a)]: 2 V2 1 V2 V3 3 1 2 3 V1 V1 V3 V4 4 V4 4 (a)

(b) Figure 1.19 (a) Illustration of KVL, (b) slightly different view of the circuit . X j Vj = 0; (1.6) where Vj denotes the voltage dro across element number j . KVL arises from the conservation of the electromotive force. In the exam le illustrated in Fig. 1.19(a ), we may sum the voltages in the loo to zero: V1 + V2 + V3 + V4 = 0. Alternati vely, ado ting the modi ed view shown in Fig. 1.19(b), we can say V1 is equal to t he sum of the voltages across elements 2, 3, and 4: V1 = V2 + V3 + V4 . Note tha t the olarities assigned to V2 , V3 , and V4 in Fig. 1.19(b) are different from those in Fig. 1.19(a). In solving circuits, we may not know a riori the correc t olarities of the currents and voltages. Nonetheless, we can sim ly assign arb itrary olarities, write KCLs and KVLs, and solve the equations to obtain the ac tual olarities and values.

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 13 (1) Sec. 1.3 Basic Conce ts 13 Exam le 1.5 The to ology de icted in Fig. 1.20 re resents the equivalent circuit of an am li e r. The de endent current source i1 is equal to a constant, gm ,6 multi lied by t he voltage dro across v in v out RL r v i 1 g v R L m v out Figure 1.20 r . Determine the voltage gain of the am li er, vout =vin . We must com ute vout in terms of vin , i.e., we must eliminate v from the equatio ns. Writing a KVL in the in ut loo , we have Solution vin = v ; and hence gm v (1.7) = gmvin . A KCL at the out ut node yields gm v + vout = 0: R L It follows that (1.8) vout = ,g R : m L vin Note that the circuit am li es the in ut if gm RL sign sim ly means the circuit inv erts the signal. (1.9) 1. Unim ortant in most cases, the negative Exercise

Re eat the above exam le if r ! infty. Exam le 1.6 Figure 1.21 shows another am li er to ology. Com ute the gain. r v i 1 g v R L m v out v in Figure 1.21 6 What is the dimension of gm ?

BR Wiley/Razavi/Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 14 (1) 14 Cha . 1 Introduction to Microelectronics Noting that r in fact a ears in arallel with vin , we write a KVL across these two com onents: Solution vin = ,v : The KCL at the out ut node is similar to (1.8). Thus, (1.10) vout = g R : vin m L Interestingly, this