Microelectronic circuits analysis and design muhammad h rashid 2nd edition

Preface xiiiTeaching Plans and Suggested Course Outlines xviiAbout the Author xix 1.1 Introduction 21.2 History of Electronics 21.3 Electronic Systems 41.4 Electronic Signals and Notatio

Microelectronic Circuits: Analysis and Design, Second Edition

Muhammad H Rashid Publisher, Global Engineering Program:

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Preface xiiiTeaching Plans and Suggested Course Outlines xviiAbout the Author xix

1.1 Introduction 21.2 History of Electronics 21.3 Electronic Systems 41.4 Electronic Signals and Notation 61.5 Classifications of Electronic Systems 101.6 Specifications of Electronic Systems 121.7 Types of Amplifiers 15

1.8 Design of Electronic Systems 171.9 Design of Electronic Circuits 201.10 Electronic Devices 27

1.11 Emerging Electronics 32References 36

Problems 37

Response

2.1 Introduction 402.2 Amplifier Characteristics 402.3 Amplifier Types 50

2.4 Cascaded Amplifiers 592.5 Frequency Response of Amplifiers 622.6 Miller’s Theorem 71

2.7 Frequency Response Methods 722.8 PSpice/SPICE Amplifier Models 872.9 Amplifier Design 88

Summary 91References 92Review Questions 92Problems 93

and Applications

3.1 Introduction 1043.2 Characteristics of Ideal Op-Amps 104

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3.3 Op-Amp PSpice/SPICE Models 1113.4 Analysis of Ideal Op-Amp Circuits 1143.5 Op-Amp Applications 128

3.6 Op-Amp Circuit Design 164Summary 165

References 166Review Questions 166Problems 167

4.1 Introduction 1804.2 Ideal Diodes 1804.3 Transfer Characteristics of Diode Circuits 1834.4 Practical Diodes 185

4.5 Analysis of Practical Diode Circuits 1924.6 Modeling of Practical Diodes 1964.7 Zener Diodes 208

4.8 Light-Emitting Diodes 2204.9 Power Rating 220

4.10 Diode Data Sheets 222Summary 226

References 226Review Questions 226Problems 227

5.1 Introduction 2385.2 Diode Rectifier 2385.3 Output Filters for Rectifiers 2605.4 Diode Peak Detectors and Demodulators 2725.5 Diode Clippers 276

5.6 Diode Clamping Circuits 2795.7 Diode Voltage Multipliers 2845.8 Diode Function Generators 287Summary 290

References 291Review Questions 291Problems 291

Characteristics

6.1 Introduction 3006.2 Semiconductor Materials 300

Contents vii

6.3 Zero-Biased pn Junction 3076.4 Reverse-Biased pn Junction 3146.5 Forward-Biased pn Junction 3196.6 Junction Current Density 3236.7 Temperature Dependence 3256.8 High-Frequency AC Model 326Summary 329

References 330Review Questions 330Problems 331

Transistors

7.1 Introduction 3367.2 Metal Oxide Field-Effect Transistors 3367.3 Enhancement MOSFETs 337

7.4 Depletion MOSFETs 3467.5 MOSFET Models and Amplifier 3497.6 A MOSFET Switch 356

7.7 DC Biasing of MOSFETs 3577.8 Common-Source (CS) Amplifiers 3647.9 Common-Drain Amplifiers 3757.10 Common-Gate Amplifiers 3807.11 Multistage Amplifiers 3837.12 DC Level Shifting and Amplifier 3867.13 Frequency Response of MOSFET Amplifiers 3937.14 Design of MOSFET Amplifiers 408

Summary 413References 413Review Questions 414Problems 414

8.1 Introduction 4348.2 Bipolar Junction Transistors 4348.3 Principles of BJT Operation 4368.4 Input and Output Characteristics 4478.5 BJT Circuit Models 449

8.6 The BJT Switch 4558.7 DC Biasing of Bipolar Junction Transistors 4578.8 Common-Emitter Amplifiers 467

8.9 Emitter Followers 4768.10 Common-Base Amplifiers 4838.11 Multistage Amplifiers 488

8.12 The Darlington Pair Transistor 4918.13 DC Level Shifting and Amplifier 4958.14 Frequency Model and Response of Bipolar Junction Transistors 5018.15 Frequency Response of BJT Amplifiers 508

8.16 MOSFETs versus BJTs 5288.17 Design of Amplifiers 528Summary 533

References 533Review Questions 533Problems 534

9.1 Introduction 5549.2 Internal Structure of Differential Amplifiers 5549.3 MOSFET Current Sources 558

9.4 MOS Differential Amplifiers 5669.5 Depletion MOS Differential Amplifiers 5809.6 BJT Current Sources 586

9.7 BJT Differential Amplifiers 6029.8 BiCMOS Differential Amplifiers 6209.9 Frequency Response of Differential Amplifiers 6269.10 Design of Differential Amplifiers 628

Summary 629References 629Review Questions 629Problems 630

10.1 Introduction 64210.2 Feedback 64310.3 Characteristics of Feedback 64410.4 Feedback Topologies 65210.5 Analysis of Feedback Amplifiers 65610.6 Series-Shunt Feedback 657

10.7 Series-Series Feedback 66710.8 Shunt-Shunt Feedback 67710.9 Shunt-Series Feedback 68610.10 Feedback Circuit Design 69210.11 Stability Analysis 69810.12 Compensation Techniques 711Summary 721

References 721Review Questions 722Problems 722

Chapter 11 Power Amplifiers

11.1 Introduction 74011.2 Classification of Power Amplifiers 74011.3 Power Transistors 743

11.4 Class A Amplifiers 74511.5 Class B Push-Pull Amplifiers 75611.6 Complementary Class AB Push-Pull Amplifiers 76611.7 Class C Amplifiers 777

11.8 Class D Amplifiers 78111.9 Class E Amplifiers 78411.10 Short-Circuit and Thermal Protection 78611.11 Power Op-Amps 788

11.12 Thermal Considerations 79211.13 Design of Power Amplifiers 796Summary 797

References 797Review Questions 797Problems 798

12.1 Introduction 80412.2 Active versus Passive Filters 80412.3 Types of Active Filters 80512.4 First-Order Filters 80812.5 The Biquadratic Function 81012.6 Butterworth Filters 81412.7 Transfer Function Realization 81812.8 Low-Pass Filters 819

12.9 High-Pass Filters 82912.10 Band-Pass Filters 83712.11 Band-Reject Filters 84312.12 All-Pass Filters 84812.13 Switched-Capacitor Filters 84912.14 Filter Design Guidelines 854Summary 855

References 855Review Questions 855Problems 856

13.1 Introduction 86213.2 Principles of Oscillators 86213.3 Audio-Frequency Oscillators 867

Contents ix

13.4 Radio Frequency Oscillators 88113.5 Crystal Oscillators 895

13.6 Active-Filter Tuned Oscillators 89913.7 Design of Oscillators 902

Summary 903References 903Review Questions 903Problems 903

14.1 Introduction 91014.2 Internal Structure of Op-Amps 91014.3 Parameters and Characteristics of Practical Op-Amps 91114.4 CMOS Op-Amps 933

14.5 BJT Op-Amps 94014.6 Analysis of the LM741 Op-Amp 94414.7 BiCMOS Op-Amps 962

14.8 Design of Op-Amps 974Summary 975

References 976Review Questions 976Problems 977

15.1 Introduction 98215.2 Logic States 98215.3 Logic Gates 98315.4 Performance Parameters of Logic Gates 98515.5 NMOS Inverters 996

15.6 NMOS Logic Circuits 101415.7 CMOS Inverters 101615.8 CMOS Logic Circuits 102215.9 Comparison of CMOS and NMOS Gates 102615.10 BJT Inverters 1026

15.11 Transistor-Transistor Logic Gates 103315.12 Emitter-Coupled Logic OR/NOR Gates 104915.13 BiCMOS Inverters 1057

15.14 Interfacing of Logic Gates 106015.15 Comparison of Logic Gates 106315.16 Design of Logic Circuits 1064Summary 1068

References 1068Review Questions 1068Problems 1069

Chapter 16 Integrated Analog Circuits and Applications

16.1 Introduction 108016.2 Circuits with Op-Amps and Diodes 108016.3 Comparators 1097

16.4 Zero-Crossing Detectors 110016.5 Schmitt Triggers 110116.6 Square-Wave Generators 111016.7 Triangular-Wave Generators 111316.8 Sawtooth-Wave Generators 111716.9 Voltage-Controlled Oscillators 112016.10 The 555 Timer 1126

16.11 Phase-Lock Loops 113916.12 Voltage-to-Frequency and Frequency-to-Voltage

Converters 114716.13 Sample-and-Hold Circuits 115516.14 Digital-to-Analog Converters 115816.15 Analog-to-Digital Converters 116516.16 Circuit Design Using Analog Integrated Circuits 1169Summary 1170

References 1170Review Questions 1170Problems 1171

Appendix A Introduction to OrCAD 1177Appendix B Review of Basic Circuits 1213Appendix C Low-Frequency Hybrid BJT Model 1261Appendix D Ebers–Moll Model of Bipolar Junction Transistors 1267Appendix E Passive Components 1275

Appendix F Design Problems 1281Answer to Selected Problems A1Index I1

Contents xi

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Semiconductor devices and integrated circuits (ICs) are the backbone of modern technology, and thus thestudy of electronics—which deals with their characteristics and applications—is an integral part of the un-dergraduate curriculum for students majoring in electrical, electronics, or computer engineering Tradi-tionally, the basic course in electronics has been a one-year (two-semester) course at most universities andcolleges However, with the emergence of new technologies and university-wide general education re-quirements, electrical engineering departments are under pressure to reduce basic electronics to a one-semester course This book can be used for a one-semester course as well as a two-semester course Theonly prerequisite is a course in basic circuit analysis A one-semester course would cover Chapters 1through 8, in which the basic techniques for analyzing electronic circuits are introduced using ICs asexamples In a two-semester course, the second semester would focus on detailed analysis of devices andcircuits within the ICs and their applications

The objectives of this book are:

• To develop an understanding of the characteristics of semiconductor devices and commonly used ICs

• To develop skills in analysis and design of both analog and digital circuits

• To introduce students to the various elements of the engineering design process, including lation of specifications, analysis of alternative solutions, synthesis, decision-making, iterations,consideration of cost factors, simulation, and tolerance issues

formu-Approach

This book adopts a top-down approach to the study of electronics, rather than the traditional bottom-upapproach In the classical bottom-up approach, the characteristics of semiconductor devices and ICs arestudied first, and then the applications of ICs are introduced Such an approach generally requires a year

of instruction, as it is necessary to cover all the essential materials in order to give students an overallknowledge of electronic circuits and systems In the top-down approach used here, the ideal characteris-tics of IC packages are introduced to establish the design and analytical techniques, and then the charac-teristics and operation of devices and circuits within the ICs are studied to understand the imperfectionsand limitations of IC packages This approach has the advantage of allowing the instructor to cover onlythe basic techniques and circuits in the first semester, without going into detail on discrete devices If thecurriculum allows, the course can continue in the second semester with detailed analysis of discrete de-vices and their applications

In practice, the lectures and laboratory experiments run concurrently If students’ experimental resultsdiffer from the ideal characteristics because of the practical limitations of IC packages, students may be-come concerned This concern may be addressed by a brief explanation of the causes of discrepancies Theexperimental results, however, will not differ significantly from the theoretically obtained results

Current ABET (Accreditation Board of Engineering and Technology) criteria and other ing criteria under the Washington Accord (http://www.washingtonaccord.org/) require the integration ofdesign and computer usage throughout the curriculum After students have satisfied other ABET and

engineer-accreditation requirements in math, basic science, engineering science, general education electives, andfree electives, they find that not many courses are available to satisfy the design requirements The lack

of opportunities for design credits in engineering curricula is a common concern Electronics is ally the first electrical engineering course well suited to the integration of design components and com-puter usage This book is structured to permit design content to constitute at least 50% of the course,and it integrates computer usage through PSpice Many design examples use PSpice to verify the designrequirements, and the numerous computer-aided design examples illustrate the usefulness of personalcomputers as design tools, especially in cases in which design variables are subjected to componenttolerances and variations

gener-New to This Edition

The second edition offers a reorganized order of chapters with the required material augmented and thenonessential topics abridged The key changes to this edition are summarized below:

• All new chapter on MOSFETs and amplifiers

• All new chapter on semiconductors and pn junctions

• Fully revised chapter on BJTs

• More emphasis on MOSFETs and active biasing techniques to allow students to move easily on todifferential amplifiers and ICs

• Extensive revision of power amplifiers to include MOSFET circuits with class C, D, and E amplifiers

• Integrated PSpice/OrCAD examples for both analysis and design verifications

• Developed Mathcad files for calculations of worked-out examples so that students can try similarproblems and explore the effects of design parameters

Content and Organization

After an introduction to the design process in Chapter 1, the book may be divided into six parts:

I Chapters 2 and 3 on characteristics of amplifiers and their frequency responses

II Chapters 4 and 5 on diodes and applicationsIII Chapters 6 to 8 and 11 on semiconductor fundamentals, transistors, and amplifiers

IV Chapters 10, 12, and 13 on characteristics and analyses of electronic circuits

V Chapter 15 on digital logic gates

VI Chapters 9, 14, and 16 on integrated circuits and applications

A review of basic circuit analysis and an introduction to PSpice are included in the appendices

Modern semiconductor technology has evolved to such an extent that many analog and digital cuits are available in the form of integrated circuit (IC) packages Manufacturers of these packages pro-vide application notes that can be used to implement circuit functions Knowledge of the characteristicsand operation of devices within the IC packages is essential, however, to understand the limitations ofthese ICs when they are interfaced as building blocks in circuit designs Such knowledge also serves asthe basis for developing future generations of IC packages Although the trend in IC technology suggeststhat discrete circuit design may disappear entirely in the future, transistor amplifiers (in large-scale or

cir-Preface

xiv

very-large-scale integrated forms) will continue to be the building blocks of ICs Thus, semiconductorfundamentals and transistor amplifiers are covered in Chapters 6 to 8, after the general types and spec-ifications of amplifiers have been introduced in Chapter 2 Because diodes are the building blocks ofmany electronic circuits, and because the techniques for the analysis of diodes are similar to those fortransistor amplifiers, diodes and their applications are addressed in detail in Chapters 4 and 5.

Pedagogy and Supplements

The pedagogical approach of the first edition has been enhanced and augmented in this edition matical derivations are kept to a minimum by using approximate circuit models of operational amplifiers,transistors, and diodes The significance of these approximations is established by computer-aided analy-sis using PSpice Important circuits are analyzed in worked-out examples in order to introduce the basictechniques and emphasize the effects of parameter variations At the end of each chapter, review questionsand problems test students’ learning of the concepts developed in the chapter The student learning out-comes (SLOs) are listed at the beginning of each chapter Symbols and their meanings have been uniquelyidentified at the beginning of each chapter to serve as a quick reference to the students Every chapteropens with an introduction that puts the content of the chapter in perspective of the field of microelec-tronics Solved examples carry captions that identify the objective of the example Notes interspersedthrough the text provide a link to other chapters and serve to guide students against common misconcep-tions and mistakes Key points of most of the sections are summarized in a box in addition to an end-of-chapter summary A list of references is included at the end of each chapter for those interested in furtherreading End-of-chapter exercises are divided into Review Questions and Problems Design problems andPSpice problems are identified by relevant symbols

Mathe-Student support from Cengage Learning is available on the book’s student website www.cengage.com/

engineering/rashid This website contains tools that are designed to help the student learn about tronics more effectively It includes electronic copies of all the PSpice schematics printed in this book,and Mathcad files for all worked-out examples in the book, which can be downloaded and allow students

elec-to work their own problems

The student version PSpice schematics and/or OrCAD capture software can be obtained or loaded from:

down-Cadence Design Systems, Inc

2655 Seely AvenueSan Jose, CA 95134, USAWebsites: http://www.cadence.com

http://www.orcad.comhttp://www.ema-eda.com

Support for Instructors

A solutions manual (in both print and electronic forms) and slides of the figures in this book are available onrequest from Cengage Learning through the Global Engineering website www.cengage.com/engineering

Teaching plans and suggested course outlines for one- and two-semester courses using this book areincluded just after this preface

Thanks are due to the editorial team at Cengage Learning, Chris Carson, Chris Shortt, Hilda Gowans,

Swati Meherishi, and Yumnam Ojen Singh for their guidance and support.

I would also like to thank the following reviewers for their comments and suggestions on the firstand the second editions:

Finally, thanks to my family for their patience while I was occupied with this and other projects

Any comments and suggestions regarding this book are welcome They should be sent to the author

at mrashidfl@gmail.com

Muhammad H RashidWeb: http://uwf.edu/mrashid

TEACHING PLANS AND SUGGESTED COURSE OUTLINES

As with any comprehensive microelectronics textbook, this text has more material than can be covered in twosingle-semester courses Instructors are often lost on what topics to cover in two semesters of 16 weeks each.The book covers diodes after op-amp circuits so that the complete coverage of op-amp circuitsincluding nonlinear circuits cannot be included in the same chapter However, if nonlinear op-amp cir-cuits are not to be covered in the course, then the op-amp circuits can be covered at the beginning, afterChapter 2 Most of the materials in Chapter 2 on introduction to amplifiers and in Chapter 5 on applica-tions of diodes can, however, be skipped in a first course Some approaches to typical first and secondelectronics courses are delineated below

First Electronics Course

This course usually covers (a) characteristics and models of amplifiers and their frequency responses;(b) IC op-amps and their applications; (c) physical operation, characteristics, and modeling of diodes, whichform the basis for understanding small-signal operation and modeling of transistors; (d) the operation, char-acteristics, modeling, and biasing of transistors; (e) the fundamentals of active sources and differential am-plifiers, which are generally used in IC amplifiers; and (f) understanding of frequency responses of electroniccircuits These can be covered by one of the following two approaches The suggested sequences of coursetopics are shown in Tables 1 and 2, respectively

TABLE 1 Suggested topics for first electronics course—Approach A

1 Introduction to Amplifiers and

Teaching Plans and Suggested Course Outlines

xviii

TABLE 2 Suggested topics for first electronics course—Approach B

TABLE 3 Suggested topics for second electronics course

1 Frequency Response of Amplifiers 3, 7, 8 2.7, 7.13, 8.15

Approach A: Op-amps are covered before diodes in which the course is not expected to cover nonlinear

op-amp circuits (using diodes) Since op-amps are the building blocks of many electronic circuits, the ses of simple op-amp circuits are often covered in the first Basic Circuit Analysis course, which is gener-ally a prerequisite for the electronics course This approach has the advantage of continuity with the circuitscourse and is more of a systems-based approach This approach may be viewed as a top-down approach

analy-Approach B: Op-amps are covered after diodes, so that students can work on nonlinear op-amp circuits(using diodes) as design projects This has the advantage of logical progression from the devices (diodesand transistors) to op-amp amplifiers

Second Electronics Course

This course covers the characteristics and applications of amplifiers The course usually covers (a) the quency response of amplifiers; (b) introduction to active filters; (c) feedback amplifiers; (d) oscillators;(e) differential amplifiers with active current sources; (f) power amplifies; (g) op-amps; and (h) IC appli-cations The sequence of course topics is shown in Table 3

fre-www.elsolucionario.org

ABOUT THE AUTHOR

Muhammad H Rashid is currently Professor (and past Director from 1997 to 2007) of Electrical and

Computer Engineering at the University of West Florida Dr Rashid received his B.Sc degree in cal Engineering from Bangladesh University of Engineering and Technology, and M.Sc and Ph.D de-grees from the University of Birmingham in the UK Previously, he worked as Professor of Electrical En-gineering and the Chair of the Engineering Department at Indiana University-Purdue University at FortWayne He has also served as Visiting Assistant Professor of Electrical Engineering at the University ofConnecticut, Associate Professor of Electrical Engineering at Concordia University (Montreal, Canada),Professor of Electrical Engineering at Purdue University Calumet, Visiting Professor of Electrical Engi-neering at King Fahd University of Petroleum and Minerals (Saudi Arabia), design and developmentengineer with Brush Electrical Machines Ltd (England, UK), Research Engineer with Lucas GroupResearch Centre (England), and Lecturer and Head of Control Engineering Department at the HigherInstitute of Electronics (Malta)

Electri-Dr Rashid is actively involved in teaching, researching, and lecturing, especially in the area ofpower electronics He has published 16 books and more than 130 technical papers His books areadopted as textbooks all over the world His books have been translated into several world languages,including Spanish, Portuguese, Indonesian, Korean, and Persian

Dr Rashid was a registered Professional Engineer in the Province of Ontario (Canada), and a istered Chartered Engineer (UK) He is a Fellow of the Institution of Electrical Engineers (IEE, UK)and a Fellow of the Institute of Electrical and Electronics Engineers (IEEE, USA) He was elected as

reg-an IEEE Fellow with the citation “Leadership in power electronics education reg-and contributions to theanalysis and design methodologies of solid-state power converters.” Dr Rashid is the recipient of the

1991 Outstanding Engineer Award from the IEEE He received the 2002 IEEE Educational ActivityBoard (EAB) Meritorious Achievement Award in Continuing Education with the following citation “Forcontributions to the design and delivery of continuing education in power electronics and computer-aided simulation.” He is the recipient of the 2008 IEEE Undergraduate Teaching Award with the citation

“For his distinguished leadership and dedication to quality undergraduate electrical engineering tion, motivating students and publication of outstanding textbooks.”

educa-Dr Rashid was an ABET program evaluator for electrical engineering from 1995 to 2000 and anengineering evaluator for the Southern Association of Colleges and Schools (SACS, USA) He has beenelected as an IEEE Industry Applications Society (IAS) Distinguished Lecturer and Speaker He is the

Series Editors of Power Electronics and Applications and Nanotechnology and Applications with the CRC Press He serves as the Editorial Advisor of Electric Power and Energy with Elsevier Publishing.

He lectures and conducts workshops on outcome-based education (OBE) and its implementations includingassessments

Learning Outcomes

After completing this chapter, students should be able to dothe following:

• Describe the historical development of electronics

• List electronic systems and their classifications

• List the types of electronic amplifiers

• Describe what constitutes engineering design

• Describe the design process of electronic circuitsand systems

• List some electronic devices and describe their basic input and output characteristics

Symbols and Their Meanings

AV, Av DC and small-signal voltage gains

BW, APB Bandwidth and pass-band voltage gain

fH, fL High and low cutoff frequencies

td, tr, tf, ton, toff Delay, rise, fall, on, and off times

T, f Period and frequency of a signal

vI(t), vo(t) Instantaneous input and output voltages

Vi, Vo rms (root mean square) input and output

voltages

INTRODUCTION TO ELECTRONICS AND DESIGN

1.1 Introduction

We encounter electronics in our daily life in the form of telephones, radios, televisions, audio equipments,home appliances, computers, and equipments for industrial control and automation Electronics havebecome the stimuli for and an integral part of modern technological growth and development The field of

electronics deals with the design and applications of electronic devices This chapter serves as an

intro-duction to electronics

1.2 History of Electronics

The age of electronics began with the invention of the first amplifying device, the triode vacuum tube, by Fleming in 1904 This invention was followed by the development of the solid-state point-contact diode (silicon) by Pickard in 1906, the first radio circuits from diodes and triodes between 1907 and 1927, the super heterodyne receiver by Armstrong in 1920, demonstration of television in 1925, the field-effect device by Lilienfield in 1925, frequency modulation (FM) by Armstrong in 1933, and radar in 1940 The first electronics revolution began in 1947 with the invention of the silicon transistor by Bardeen,

Bratain, and Shockley at Bell Telephone Laboratories Most of today’s advanced electronic technologies

are traceable to that one invention This revolution was followed by the first demonstration of color vision in 1950 and the invention of the unipolar field-effect transistor by Shockley in 1952.

tele-The next breakthrough came in 1956, when Bell Laboratories developed the pnpn triggering sistor, also known as a thyristor or a silicon-controlled rectifier (SCR) The second electronics revolution

tran-began with the development of a commercial thyristor by General Electric Company in 1958 That wasthe beginning of a new era for applications of electronics in power processing or conditioning, called

power electronics Since then, many different types of power semiconductor devices and conversion

techniques have been developed

The first integrated circuit (IC) was developed in 1958 simultaneously by Kilby at Texas

Instru-ments and Noyce and Moore at Fairchild Semiconductor, marking the beginning of a new phase in themicroelectronics revolution This invention was followed by development of the first commercial IC

operational amplifier, the A709, by Fairchild Semiconductor in 1968; the 4004 microprocessor by Intel

in 1971; the 8-bit microprocessor by Intel in 1972; and the gigabit memory chip by Intel in 1995 Theprogression from vacuum tubes to microelectronics is shown in Fig 1.1 Integrated circuit development

FIGURE 1.1 Progression from vacuum tubes tomicroelectronics

continues today in an effort to achieve higher-density chips with lower power dissipation; historicallevels of integration in circuits are shown in Table 1.1.

The degree of device integration continues to follow Moore’s law, which is an observation made byGordon E Moore that the number of transistors inside an IC could be doubled every 24 months at a densitythat also minimizes the cost of a transistor [1] Figure 1.2(a) shows the growth in the number of transistors

on ICs over the years Figure 1.2(b) shows the generations of microelectronics technology [2]

Introduction to Electronics and Design 3

TABLE 1.1 Levels of integration

1975 Very-large-scale integration (VLSI) From 104to 1091990s Ultra-large-scale integration (ULSI) More than 109

Number of transistors doubling every 18 months

Number of transistors doubling every 24 months

Pentium III

Pentium 4 Itanium Itanium 2

Itanium 2 (9 MB cache)

Year

2000 2004

(a) Growth in number of transistors

FIGURE 1.2 Growth in the number of transistors in an integrated circuit (http://commons.wikimedia.org/wiki/File:Moore_Law_diagram_(2004).jpg) and generations of microelectronic

technology (Continued)

Beyond very large-scale integration

Very large-scale integrated circuits

Integrated circuits

Transistors

Vacuum tubes Early 1900s

1958

(b) Generations of microelectronics technology

FIGURE 1.2 (Continued)

KEY POINT OF SECTION 1.2

■ Since the invention of the first amplifying device, the vacuum tube, in 1904, the field of electronicshas evolved rapidly Today ultra-large-scale integrated (ULSI) circuits have more than 109compo-nents per chip

1.3 Electronic Systems

An electronic system is an arrangement of electronic devices and components with a defined set of inputsand outputs Using transistors (trans-resistors) as devices, it takes in information in the form of input sig-nals (or simply inputs), performs operations on them, and then produces output signals (or outputs) Elec-tronic systems may be categorized according to the type of application, such as communication system,medical electronics, instrumentation, control system, or computer system

A block diagram of an FM radio receiver is shown in Fig 1.3(a) The antenna acts as the sensor Theinput signal from the antenna is small, usually in the microvolt range; its amplitude and power level areamplified by the electronic system before the signal is fed into the speaker A block diagram of a temper-ature display instrument is shown in Fig 1.3(b) The output drives the display instrument The temperaturesensor produces a small voltage, usually in millivolts per unit temperature rise above 0°C (e.g., 1 mV/°C).

Both systems take an input from a sensor, process it, and produce an output to drive an actuator

An electronic system must communicate with input and output devices In general, the inputsand outputs are in the form of electrical signals The input signals may be derived from the mea-surement of physical qualities such as temperature or liquid level, and the outputs may be used tovary other physical qualities such as those of display and heating elements Electronic systems of-

ten use sensors to sense external input qualities and actuators to control external output qualities.

Sensors and actuators are often called transducers The loudspeaker is an example of a transducer

that converts an electronic signal into sound

1.3.1 Sensors

There are many types of sensors, including the following:

• Thermistors and thermocouples to measure temperature

• Phototransistors and photodiodes to measure light

• Strain gauges and piezoelectric materials to measure force

• Potentiometers, inductive sensors, and absolute position encoders to measure displacement

• Tachogenerators, accelerometers, and Doppler effect sensors to measure motion

• Microphones to measure sound

• Anemometer to measure the wind speed

1.3.2 Actuators

Actuators produce a nonelectrical output from an electrical signal There are many types of actuators,including the following:

• Resistive heaters to produce heat

• Light-emitting diodes (LEDs) and light dimmers to control the amount of light

• Solenoids to produce force

Introduction to Electronics and Design 5

Antenna

Speaker

(a) Radio receiver

(b) Temperature display instrument

Electronic system

Temperature sensor

Electronic system

0 100

FIGURE 1.3 Examples of electronic systemswww.elsolucionario.org

KEY POINTS OF SECTION 1.3

■ An electronic system consists of electronic devices and components It processes electronic signals,acting as an interface between sensors on the input side and as actuators on the output side

■ Sensors convert physical qualities to electrical signals, whereas actuators convert electrical signals to

physical qualities Sensors and actuators are often called transducers.

• Meters to indicate displacement

• Electric motors to produce motion or speed

• Speakers and ultrasonic transducers to produce sound

1.4 Electronic Signals and Notation

Electronic signals can be categorized into two types: analog and digital An analog signal has a continuousrange of amplitudes over time, as shown in Fig 1.4(a) Figure 1.4(b) is the sampled form of the input signal

in Fig 1.4(a) A digital signal assumes only discrete voltage values over time, as shown in Fig 1.4(c) Adigital signal has only two values, representing binary logic state 1 (for high level) and binary logic state

0 (for low level) To accommodate variations in component values, temperature, and noise (or extraneous

0

4 3 2 1

0

4 3 2 1

FIGURE 1.4 Types of electronic signals

signals), logic state 1 is usually assigned to any voltage between 2 V and 5 V Logic state 0 may be assigned

to any voltage between 0 and 0.8 V

The output signal of a sensor is usually of the analog type, and actuators often require analog input toproduce the desired output An analog signal can be converted to digital form and vice versa The elec-

tronic circuits that perform these conversions are called analog-to-digital (A/D) and digital-to-analog (D/A) converters.

1.4.1 Analog-to-Digital Converters

An A/D converter converts an analog signal to digital form and provides an interface between analogand digital signals Consider the analog input voltage shown in Fig 1.5(a) The input signal is sampled at

periodic intervals determined by the sampling time Ts, and an n-bit binary number (b1b2 b n) is

assigned to each sample, as shown in Fig 1.5(b) for n  3 The n-bit binary number is a binary fraction

Introduction to Electronics and Design 7

FIGURE 1.5 Analog-to-digital conversion

that represents the ratio between the unknown input voltage vIand the full-scale voltage VFSof the

con-verter For n  3, each binary fraction is VFS⁄2n  VFS⁄8 The output voltage of a 3-bit A/D converter

tive error and then a positive error, as shown in Fig 1.5(d) This error, called the quantization error, can

be reduced by increasing the number of bits n Thus, the quantization error may be defined as the

small-est voltage that can change the LSB of the binary output from 0 to 1 The quantization error is also called

the resolution of the converter, and it can be found from

(1.1)

where VFSis the full-scale voltage of the converter For example, VLSBfor an 8-bit converter of VFS 5 V is

1.4.2 Digital-to-Analog Converters

A D/A converter takes an input signal in binary form and produces an output voltage or current in an analog

(or continuous) form A block diagram of an n-bit D/A converter consisting of binary digits (b1b2 b n)

is shown in Fig 1.6 It is assumed that the converter generates the binary fraction, which is multiplied by

the full-scale voltage VFSto give the output voltage, expressed by

VO (b121 b222 b323  b n2n )V

where the ith binary digit is either b i  0 or b i  1 and b1is the most significant bit (MSB) For

exam-ple, for VFS 5 V, n  3, and a binary word b1b2b3 110, Eq (1.2) gives

VO (1  21 1  22 0  23) 5  3.75 V

1.4.3 Notation

An analog signal is normally represented by a symbol with a subscript The symbol and the subscript can

be either uppercase or lowercase, according to the conventions shown in Table 1.2 For example, consider

the circuit in Fig 1.7(a), whose input consists of a DC voltage VDC 5 V and an AC voltage vab 2 sin t.

The instantaneous voltages are shown in Fig 1.7(b) The definitions of voltage and current symbols are asfollows:

1 VDCand IDCare DC values: uppercase variables and uppercase subscripts

B

FIGURE 1.7 Notation for electronic signals

Total instantaneous value of the signal (DC and AC) Lowercase Uppercase vD

Complex variable, phasor, or rms value of the signal Uppercase Lowercase Vd

TABLE 1.2 Definition of symbols and subscripts

1.5 Classifications of Electronic Systems

The form of signal processing carried out by an electronic system depends on the nature of the input nals, the output requirements of the actuators, and the overall functional requirement However, certainfunctions are common to a large number of systems These include amplification, addition and subtraction

sig-of signals, integration and differentiation sig-of signals, and filtering Some systems require a sequence sig-ofoperations such as counting, timing, setting, resetting, and decision making Also, it may be necessary togenerate sinusoidal or other signals within a system

Electronic systems find applications in automobiles, home entertainment, office and cation equipments, and medicines, among other areas, and help us maintain our high-tech lifestyles.Electronic systems are often classified according to the type of application:

Analog electronics deals primarily with the operation and applications of transistors as amplifying

devices The input and output signals take on a continuous range of amplitude values over time Thefunction of analog electronics is to transport and process the information contained in an analog inputsignal with a minimum amount of distortion

Digital electronics deals primarily with the operation and applications of transistors as “on” and “off”

switching devices Both input and output signals are discontinuous pulse signals that occur at uniformlyspaced points in time The function of digital electronics is to transport and process the information contained

in a digital input signal with a minimum amount of error at the fastest speed

Power electronics deals with the operation and applications of power semiconductor devices,

includ-ing power transistors, as “on” and “off ” switches for the control and conversion of electric power Analogand/or digital electronics are used to generate control signals for the switching power devices in order toobtain the desired conversion strategies (AC/DC, AC/AC, DC/AC, or DC/DC) with the maximum con-version efficiency and the minimum amount of waveform distortion The input to a power electronicsystem is a DC or an AC power supply voltage (or current) Power electronics is primarily concerned withpower content and quality rather than the information contained in a signal For example, a power

KEY POINTS OF SECTION 1.4

■ There are two types of electronic signals: analog and digital An analog signal can be converted to ital form and vice versa

dig-■ A lowercase symbol is used to represent an instantaneous quantity, and an uppercase symbol is usedfor DC and rms values A lowercase subscript is used to represent instantaneous AC and rms quanti-ties, and an uppercase subscript is used for the total value, which includes both AC and DC quantities

electronic circuit can provide a stable DC power supply, say 12 V to an analog system and 5 V to a ital system, from an AC supply of 120 V at 60 Hz.

dig-Microelectronics has given us the ability to generate and process control signals at an incredible speed

Power electronics has given us the ability to shape and control large amounts of power with a high ciency—between 94% and 99% Many potential applications of power electronics are now arising fromthe marriage of power electronics—the muscle—with microelectronics—the brain Also, power electron-ics has emerged as a distinct discipline and is revolutionizing the concept of power processing and condi-tioning for industrial power control and automation

effi-Many electronic systems use both analog and digital techniques Each method of implementationhas advantages and disadvantages, summarized in the following list:

• Noise is usually present in electronic circuits It is defined as the extraneous signal that arises fromthe thermal agitation of electrons in a resistor, the inductive or capacitive coupling of signals fromother systems, or other sources Noise is added directly to analog signals and hence affects the sig-nals, as shown in Fig 1.8(a) Thus noise is amplified by the subsequent amplification stages Sincedigital signals have only two levels (high or low), noise will not affect the digital output, shown inFig 1.8(b), and can effectively be removed from digital signals

• An analog circuit requires fewer individual components than a digital circuit to perform a givenfunction However, an analog circuit often requires large capacitors or inductors that cannot be man-ufactured in ICs

• A digital circuit tends to be easier to implement than an analog circuit in ICs, although it can bemore complex than an analog circuit Digital circuits, however, generally offer much higher qualityand speed of signal processing

• Analog systems are designed to perform specific functions or operations, whereas digital systemsare adaptable to a variety of tasks or uses

• Signals from sensors and to actuators in electronic systems are generally analog If an input signalhas a low magnitude and must be processed at very high frequencies, then the analog technique isrequired For optimal performance and design, both analog and digital approaches are often used

Introduction to Electronics and Design 11

FIGURE 1.8 Effects of noise on analog and digital signals

KEY POINT OF SECTION 1.5

■ Electronics can be classified into three areas: analog, digital, and power electronics The classification

is based primarily on the type of signal processing Electronic systems are often classified according

to the type of application such as medical electronics and consumer electronics

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1.6 Specifications of Electronic Systems

An electronic system is normally designed to perform certain functions or operations The performance of

an electronic system is specified or evaluated in terms of voltage, current, impedance, power, time, and quency at the input and output of the system The performance parameters include transient specifications,distortion, frequency specifications, and DC and small-signal specifications

• Delay time tdis the time before the circuit can respond to any input signal

• Rise time tris the time required for the output to rise from 10% to 90% of its final (high) value

• On time tonis the time during which the circuit is fully turned on and is functioning in its normalmode

• Fall time tfis the time required for the output to decrease from 90% to 10% of its initial (high) value

• Off time toffis the time during which the circuit is completely off, not operating

Thus, the switching period T is

and the switching frequency is f 1⁄T These times limit the maximum switching speed fmaxof a circuit

For example, the maximum switching frequency of a circuit with td 1 s and tr tf 2 s is

fmax =

1

(td + tr + tf)

=1

0 0.1

FIGURE 1.9 Pulse response of a circuit

Introduction to Electronics and Design 13

fied as the total harmonic distortion (THD), which is the ratio of the rms value of the harmonic component

to the rms value of the fundamental component (at the frequency of the sinusoidal input) The THD should

be as low as possible

1.6.3 Frequency Specifications

The range of signal frequencies of electronic signals varies widely, depending on the application, as shown

in Table 1.3 The frequency specifications refer to the plot of the output signal as a function of the inputsignal frequency A typical plot for a system such as the one in Fig 1.11(a) is shown in Fig 1.11(b) For

frequencies less than fLand greater than fH, the output is attenuated But for frequencies between fLand

fH, the output remains almost constant The frequency range from fLto fHis called the bandwidth BW of

the circuit That is, BW fH fL A system with a bandwidth like the one shown in Fig 1.11(b) is said

to have a band-pass characteristic If fL 0, the system is said to have a low-pass characteristic If fH ,the system is said to have a high-pass characteristic

Harmonic

(b) Clipping (a) Sine wave

For an operating frequency within the bandwidth or pass-band range, the voltage gain is defined as

where Viand Voare the rms values of the input and output voltages, respectively The input impedance isdefined as

where Ii is the rms value of the input current of the circuit Zi is often referred to as the small-signal

input resistance Ri because the output is almost independent of the frequency in the midband range

Ideally, Ri should tend to infinity Thevenin’s equivalent resistance seen from the output side is

speci-fied as the output impedance Zo or the output resistance Ro, which should ideally be zero

1.6.4 DC and Small-Signal Specifications

The DC and small-signal specifications include the DC power supply VCC, DC biasing currents

(re-quired to activate and operate internal transistors), and power dissipation PD(power requirement from

the DC power supply) The voltage gain (the ratio of the output voltage vO to the input voltage vI) is

−

√+

−

(b) Frequency response (a) Circuit

f (in Hz)

Vo

Vi

FIGURE 1.11 Typical frequency characteristic

TABLE 1.3 Bandwidths of electronic signals

often specified If the vO–vI relationship is linear, as shown in Fig 1.12(a), and the circuit operates at

a quiescent point Q, the voltage gain is given by

AV is often called the large-signal voltage gain The characteristic plot of transistors is generally nonlinear, as shown in Fig 1.12(b), and the circuit is operated at a quiescent operating point, the Q- point The input signal is made to vary over a small range so that the vO–vI relation is essentially

linear The voltage gain is then referred to as the small-signal gain Av, expressed by

Electronic circuits, especially amplifiers, are normally operated over a practically linear range of the

char-acteristic For an operating frequency within the BW of the circuit, Av⬅ APB, where APBis the pass-band

or midfrequency gain of the amplifier

FIGURE 1.12 Large-signal and small-signal characteristics

KEY POINT OF SECTION 1.6

■ The parameters that describe the performance of electronic circuits and systems usually include sient specifications, distortion, frequency specifications, and large- and small-signal specifications

tran-1.7 Types of Amplifiers

There are many types of amplifiers, which can be classified according to the type of signal amplification,the function, the type of interstage coupling, the frequency range, and the type of load

Signal amplification types are classified by the types of input and output signals:

1 A voltage amplifier produces an amplified output voltage in response to an input voltage signal.

2 A transconductance amplifier produces an amplified output current in response to an input voltage

signal

3 A current amplifier produces an amplified output current in response to an input current signal.

4 An impedance amplifier produces an amplified output voltage in response to an input current

signal

5 A power amplifier produces an amplified output voltage and delivers power to a low resistance load

in response to an input voltage signal

Functional types are classified by their function or output characteristics:

1 A linear amplifier produces an output signal in response to an input signal without introducing

significant distortion on the output signal, whereas a nonlinear amplifier does introduce distortion

2 An audio amplifier is a power amplifier in the audio frequency (AF) range.

3 An operation amplifier performs some mathematical functions for instruments and for signal

processing

4 A wideband amplifier amplifies an input signal over a wide range of frequencies to boost signal

levels, whereas a narrowband amplifier amplifies a signal over a specific narrow range of frequencies

5 A radio frequency (RF) amplifier amplifies a signal for use over the RF range.

6 A servo amplifier uses a feedback loop to control the output at a desired level

Interstage coupling types are classified by the coupling method of the signal at the input, at the output, or

between stages:

1 An RC-coupled amplifier uses a network of resistors and capacitors to connect it to the following

and preceding amplifier stages

2 An LC-coupled amplifier uses a network of inductors and capacitors to connect it to the following

and preceding amplifier stages

3 A transformer-coupled amplifier uses transformers to match impedances to the load side and input

side

4 A direct-coupled amplifier uses no interstage elements, and each stage is connected directly to the

following and preceding amplifier stages

Frequency types are classified in accordance to the frequency range:

1 A DC amplifier is capable of amplifying signals from zero frequency (DC) and above.

2 An AF amplifier is capable of amplifying signals from 20 Hz to 20 kHz.

3 A video amplifier (VA) is capable of amplifying signals up to a few hundred megahertz (<10 MHz

for TV)

4 An ultra-high-frequency (UHF) amplifier is capable of amplifying signals up to a few gigahertz.

Load types are classified in accordance to the type of load:

1 An audio amplifier has an audio type of load

2 A video amplifier has a video type of load.

3 A tuned amplifier amplifies a single RF or band of frequencies

KEY POINT OF SECTION 1.7

■ Amplifiers can be classified according to the type of signal amplification, the function, the type ofinterstage coupling, the frequency range, and the type of load

1.8 Design of Electronic Systems

Engineering systems are becoming increasingly complex Thus, it is highly desirable that engineers havethe skills needed to analyze, synthesize, and design complex systems A design transforms specificationsinto circuits that satisfy those specifications Designing a system is a challenging task involving many vari-ables One can use different approaches to implement the same specifications, and hence many decisionsmust be made in implementing the specifications

In practical design work, the most challenging tasks are attacked first, and then the simple tasksare tackled That way, if an acceptable solution cannot be found to the difficult problems, time andmoney are not wasted on solving easier problems Thus, the engineering design process follows a hi-erarchy in which systems are designed first through functional block diagrams, after which circuitsand then devices are designed This approach is the opposite of what is normally taught in academiccourses The system-level design is conceptualized and expressed in terms of functional blocks andsystem integration [3] The major steps in the design process, shown in Fig 1.13, are as follows:

1 General product description

2 Definition of specifications/requirements

Introduction to Electronics and Design 17

Definition of specifications for circuit design

Product

Testing and verification

Simulation/

modeling

System integration

Comparison with specifications

Comparison with specifications

System design through block diagrams

Definition of specifications

General product description

FIGURE 1.13 System-level design process

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3 System design through functional block diagrams

4 Definition of specifications of functional blocks for circuit-level synthesis and implementation

5 System integration

6 Simulation or modeling

7 Testing and verification

The system-level solution to designing the radio receiver in Fig 1.3(a) is shown in Fig 1.14 Itincludes RF, intermediate frequency (IF), and AF amplifiers The local oscillator tunes the radio receiver

to receive the signal of a desired station

Only the broad outlines of the design process are given here The details depend on the type ofsystem being designed The design process may be viewed as a means to accomplish the following [4]:

1 Identify needs.

2 Generate ideas for meeting the needs.

3 Refine the ideas.

4 Analyze all possible solutions.

5 Decide on the action to be taken.

6 Implement the decision.

These steps are shown in Fig 1.15 The steps are repeated until the desired specifications have been fied Each of these six steps can be subdivided, as shown in Fig 1.16 As the figure suggests, engineering

satis-Input signal specifications

RF filter

RF amplifier

Local oscillator

amplifier

Audio amplifier

Peak detector

IF filter Radio receiver

Speaker Antenna

FIGURE 1.14 System-level block diagram of radio receiver

Analyze Refine

Generate

Decide

Implement Identify

Recycle design process

as needed

FIGURE 1.15 Recycling of the design process (John

Burkhardt, Lecture Notes on the Art of Design Fort Wayne, IN:

The Indiana University–Purdue University Fort Wayne, 1996)

Introduction to Electronics and Design 19

KEY POINT OF SECTION 1.8

■ In practical design work, the most challenging tasks are attacked before the simple tasks Thus theengineering design process follows a hierarchy in which systems are designed first through functionalblock diagrams, after which circuits, and then devices are designed

Working drawings

Scale drawings

6 Implementation

5 Decision

Continue Reject

Combine

Stop Restudy

Marketing Solution

Models

Details Specs

4 Analysis

3 Refinement of ideas

Shape/form Properties Development

Weight

Experience Engineering

Graphics

Logic

Science Mathematics

1 Identification of the problem 2 Generation of ideas

Effects Causes

Data

Needs

Economics Background

Problem identification

Try new approach

Brainstorm Ideate

Sketch

List ideas

Make notes

Preliminary ideas

University Fort Wayne, 1996)

design involves many disciplines, and a design engineer must be able to function in a multidisciplinaryteam and communicate effectively with other team members

1.9 Design of Electronic Circuits

A circuit-level design is implemented and expressed in terms of components, devices, and voltage–currentrelationships The lowest level is device-level design, which involves selecting types of devices Beforestarting this level of design, you must have some knowledge of electronic devices and their characteristics,parameters, and models

1.9.1 Analysis versus Design

Analysis is the process of finding the unique specifications or properties of a given circuit Design, on theother hand, is the creative process of developing a solution to a problem We start with a desired set of spec-ifications or properties and find a circuit that satisfies them The solution is not unique, and finding itrequires synthesis For example, the current flowing from a 12-V battery to a 5- load resistance is simply2.4 A However, if you were asked to arrange a load that would draw 2.4 A from a battery of 12 V, youcould use many possible combinations of series and parallel resistors Figure 1.17 shows a comparison ofanalysis and design

1.9.2 Definition of Engineering Design

What is engineering design? If you asked several different engineers, you would probably set with severaldifferent definitions The Accreditation Board for Engineering and Technology (ABET) provides the fol-lowing broad definition [5]:

Engineering design is the process of devising a system, component, or process to meet desiredneeds It is a decision-making process (often iterative), in which the basic sciences andmathematics and engineering sciences are applied to convert resources optimally to meet thesestated needs Among the fundamental elements of the design process are the establishment

of objectives and criteria, synthesis, analysis, construction if feasible, testing, and evaluation

The engineering design component of a curriculum must include most of the following features:

development of student creativity, use of open-ended problems, development and use of design theory and methodology, formulation of design problem statements and specifications,consideration of alternative solutions, feasibility considerations, production processes,concurrent engineering design, and detailed system descriptions Further, it is essential toincorporate appropriate engineering standards and include multiple realistic constraints such aseconomic, environmental, social, political, ethical, health and safety, manufacturability, andsustainability

1.9.3 The Circuit-Level Design Process

The major steps in the circuit-level design process, shown in Fig 1.18, are as follows:

Step 1. Study the design problem

Step 2. Define the design objectives—that is, establish the design’s performance requirements

Step 3. Establish the design strategy, and find the functional block diagram solution

Step 4. Select the circuit topology or configuration after evaluating alternative solutions

Step 5. Select the component values and devices Analysis and synthesis may be required to findthe component values Use simple device models to simplify the analytical derivations

Step 6. Evaluate your design, and predict its performance Modify your design values if necessary

Introduction to Electronics and Design 21

Test

Select the component values

Get cost estimate

Model/

simulate

Predict performance

Study the problem

Comparison with specifications

Comparison with specifications

Find the block diagram solution

Define the design objectives

Select the circuit topology

FIGURE 1.18 Circuit-level design process

Step 7. Model and simulate the circuit by using more realistic (or complex) device models Getthe worst-case results given the component and parameter variations Modify your design asneeded.

Step 8. Get a cost estimate for the project if cost is a prime constraint Plan component layout so thatthe project requires the minimum fabrication time and is as inexpensive as possible

Step 9. Build a prototype unit in the lab, and test it and take measurements to verify your design.Modify your design as needed

Carrying out the design process Design a circuit to measure DC voltage in the range from 0 to 20 V.For a full-scale deflection, the indicating meter draws 100 A at a voltage of 1 V across it The current drawnfrom the DC supply should not exceed 1 mA

con-The design statement expresses the objective in a single sentence with few or no numbers—for example,

Design of a DC indicating meter

The performance requirements must be specific and related to the required performance characteristics in

terms of voltage, current, impedance, power, time, frequency, and so on The values refer to the input and outputterminals of the circuit and are normally expressed in mathematical inequalities—for example,

The design criteria are the criteria for judging the quality of a design and may include factors such as

accu-racy, cost, reliability, efficiency, response time, bandwidth, and power dissipation—for example,

• The excess of IMover 100A should be a minimum, say 5%: