Second Edition
`| a ;
`
`CMOS Analog
`Circuit Design
`
`=e
`
`

`

`
`
`CMOS Analog Circuit Desian
`
`Second Edition
`
`Phillip E. Allen
`Georgia Institute of Technology
`
`Douglas R. Holberg
`Cygnal Integrated Products, Inc.
`
`{
`
`New York Oxford
`OXFORD UNIVERSITY PRESS
`2002
`
`Page 2
`
`

`

`
`
`Oxford University Press
`
`Oxford New York
`
`Athens Auckland Bangkok Bogota Buenos Aires Cape Town
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`Paris
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`
`and associated companies in
`Berlin
`Ibadan
`
`Copyright © 2002 by Oxford University Press, Inc.
`
`Published by Oxford University Press, Inc.
`198 Madison Avenue, New York, New York, 10016
`http://www.oup-usa.org
`
`Oxford is a registered trademark of Oxford University Press
`
`All rights reserved. No partof this publication may be reproduced,
`stored ina retrieval system, or transmitted, in any form or by any means,
`electronic, mechanical, photocopying, recording, or otherwise,
`without the prior permission or Oxford University Press.
`
`ISBN 0-19-511644-5
`
`Printing number: 9 87654321
`
`Printed in the United States of America
`
`on acid-free paper
`
`
`
`Page 3
`
`

`

`
`
`To our wives
`
`Margaret
`and
`
`Candy
`
`To our children
`
`Kurt, Cheryl, and Paul
`and
`
`Samuel
`
`Page 4
`
`

`

`Contents
`
`————————————
`———_—_—_——
`
`Preface
`xiii
`Introduction and Background
`Chapter]
`1]
`Analog Integrated-Circuit Design
`1
`1.2 Notation, Symbology, and Terminology
`1.3 Analog Signal Processing
`9
`14
`Example of Analog VLSI Mixed-Signal Circuit Design
`15
`Summary
`15
`
`6
`
`|
`
`10
`
`Problems
`
`16
`
`References
`
`17
`
`18
`CMOS Technology
`Chapter 2
`t.1 Basic MOS Semiconductor Fabrication Processes
`2.2 Thepn Junction
`29
`36
`0.3 The MOS Transistor
`43
`2.4
`Passive Components
`
`2.6
`Integrated Circuit Layout
`55
`ct.)
`Summary
`66
`
`05=©6Other Considerations of CMOS Technology 48
`
`19
`
`Problems
`
`68
`
`References
`
`70
`
`
`Page 5
`
`vii
`
`

`

`viii
`
`CONTENTS
`
`73
`
`72
`CMOS Device Modeling
`Chapter 3
`3]
`Simple MOS Large-Signal Model (SPICE LEVEL 1)
`3.2 Other MOS Large-Signal Model Parameters
`79
`A)
`Small-Signal Model for the MOSTransistor
`87
`34 Computer Simulation Models
`92
`3.5
`Subthreshold MOS Model
`97
`3.6
`SPICE Simulation of MOSCircuits
`3]
`Summary
`109
`Problems
`110
`
`99
`
`References
`
`112
`
`113
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Chapter 4 Analog CMOS Subcircuits
`41 MOS Switch
`113
`42 MOSDiode/Active Resistor
`43 Current Sinks and Sources
`44° Current Mirrors
`134
`45 Current and Voltage References
`46 Bandgap Reference
`153
`4]
`Summary
`159
`Problems
`159
`
`124
`126
`
`143
`
`
`
`166
`
`
`CMOS Amplifiers
`Chapter S
`
`
`168
`5.1
`Inverters
`180
`5.2 Differential Amplifiers
`
`
`5.3 Cascode Amplifiers
`199
`
`
`§4 Current Amplifiers
`211
`
`
`55 Output Amplifiers
`218
`
`
`5.6 High-Gain Amplifier Architectures
`229
`
`References
`
`167
`
`Page 6
`
`

`

`——_
`
`o7
`
`Summary
`
`232
`
`Problems
`
`233
`
`References
`
`242
`
`043
`
`CMOS Operational Amplifiers
`Chapter 6
`6.1 Design of CMOS Op Amps
`244
`§.2 Compensation of Op Amps
`253
`269
`6.3 Design of Two-Stage Op Amps
`6.4
`Power-Supply Rejection Ratio of Two-Stage Op Amps
`6.5 Cascode Op Amps
`293
`6.6
`Simulation and Measurement of Op Amps
`6.) Macromodels for Op Amps
`323
`6.8
`Summary
`341
`
`310
`
`Contents
`
`ix
`
`286
`
`Problems
`
`342
`
`References
`
`349
`
`4351
`
`Chapter 7 High-Performance CMOS Op Amps
`71 BufferedOp Amps
`352
`1.2 High-Speed/Frequency Op Amps
`1.3 Differential-Outpat Op Amps
`384
`74 Micropower Op Amps
`393
`15
` Low-Noise OpAmps
`402
`14 Low-Voltage OpAmps
`415
`7.1
`Summary
`432
`
`368
`
`Problems
`
`433
`
`References
`
`437
`
`439
`Chapter 8 Comparators
`439
`8.1 Characterization of a Comparator
`§.2 Two-Stage, Open-Loop Comparators
`445
`
`
`
`Page 7
`
`

`

`Xx
`
`CONTENTS
`
`
`
`
`
`
` Other Open-Loop Comparators
`83
`461
`84
`Improving the Performance of Open-Loop Comparators
`
`464
`
`B.S
`
`8.6
`
`§.]
`
`Discrete-Time Comparators
`
`475
`
`High-Speed Comparators
`
`483
`
`Summary
`
`488
`
`Problems
`
`488
`
`References
`
`491
`
`Chapter 9
`
`Switched Capacitor Circuits
`
`492
`
`Switched Capacitor Circuits
`
`493
`
`Switched Capacitor Amplifiers
`
`507
`
`Switched Capacitor Integrators
`
`520
`
`z-Domain Models of Two-Phase Switched Capacitor Circuits
`
`532
`
`First-Order Switched Capacitor Circuits
`
`544
`
`Second-Order Switched Capacitor Circuits
`
`550
`
`Switched Capacitor Filters
`
`561
`
`Summary
`Problems
`
`600
`600
`
`References
`
`611
`
`4 N
`
`e
`
`43
`
`4.4
`
`45
`
`4.6
`
`4]
`
`4.8
`
`Chapter 10 Digital—Analog and Analog—Digital Converters
`
`ble
`
`Introduction and Characterization of Digital-Analog Converters
`
`613
`
`Parallel Digital-Analog Converters
`
`623
`
`Extending the Resolution of Parallel Digital-Analog Converters
`
`635
`
`Serial Digital-Analog Converters
`
`647
`
`Introduction and Characterization of Analog—Digital Converters
`
`652
`
`Serial Analog—Digital Converters
`
`665
`
`Medium-Speed Analog—Digital Converters
`
`667
`
`High-Speed Analog—Digital Converters
`
`682
`
`Oversampling Converters
`
`698
`
`Page 8
`
`
`
`10.
`
`Wie
`
`10.3
`
`10.4
`
`10.5
`
`10.6
`
`10.7
`
`
`
`
`
`
`
`
`
`10.8
`
`10.8
`
`
`

`

`
`
`Contents
`
`xi
`
`oMparators
`
`464
`
`10.10 Summary
`Problems
`
`713
`715
`
`References
`
`729
`
`Appendix # Circuit Analysis for Analog Circuit Design
`Appendix 8
`CMOSDevice Characterization
`744
`Appendix €
`Time and Frequency Domain Relationships
`for Second-Order Systems
`768
`
`733
`
`Je
`
`Index
`
`777
`
`T Circuits
`
`530
`
`|
`
`MWerters
`1Verters
`613
`
`’€rters
`
`635
`
`-rters
`
`652
`
`Page 9
`
`

`

`PREFACE
`
`The objective of the secondedition of this book continues to be to teach the design ofCMOS
`analog circuits. The teaching of design reaches far beyond giving examplesof circuits and
`showing analysis methods.It includes the necessary fundamentals and background but must
`apply themin a hierarchical manner that the novice can understand. Probably of most impor-
`tance is to teach the concepts of designing analog integrated circuits in the context of CMOS
`technology. These concepts enable the reader to understandthe operationofan analog CMOS
`circuit and to know how to changeits performance. With today’s computer-oriented thinking,
`it
`is vital to maintain personal control of a design, to know what to expect, and to discern
`when simulation results may be misleading. As integrated circuits become more complex,it is
`crucial to know “how the circuit works.” Simulating a circuit without the understanding of
`how it works can lead to disastrousresults.
`How does the reader acquire the knowledge of how a circuit works? The answertothis
`question has been the driving motivation of the secondedition ofthis text. There are several
`importantsteps in this process. The first is to learn to analyze the circuit. This analysis should
`produce simple results that can be understood and reapplied in different circumstances. The
`second is to view analog integrated circuit design from a hierarchical viewpoint. This means
`that the designeris able to visualize how subcircuits are used to formcircuits, how simple cir-
`cuits are used to build complexcircuits, and so forth. The third step is to set forth procedures
`that will help the new designer come up with working designs. This has resulted in the inclu-
`sion of many “design recipes,” which became popular with the first edition andhave been ex-
`pandedin the second edition. It
`is important that the designer realize that there are simply
`three outputs ofthe electrical design of CMOSanalog circuits, They are (1) a schematic of the
`circuit, (2) de currents, and (3) W/L ratios. Most design flows or “recipes” can be organized
`around these three outputs very easily.
`Fifteen years ago, it was not clear what importance CMOStechnology would have on
`analog circuits. However, it has become very clear that CMOStechnology has become the
`technology of choice for analog circuit design in a mixed-signal environment. This “choice”
`is not necessarily that of the designer but of industry trends that want to use standard tech-
`nologies to implement analog circuits along with digital circuits. As a result, the first edition
`of CMOSAnalog Circuit Design fulfilled a need for a text in this area before there were any
`other texts on this subject. It has found extensive use in industry and has been usedin class-
`roomsall over the world. Like the first edition, the second edition has also chosen notto in-
`clude BJT technology. The wisdom of this choice will be seen as the years progress. The sec-
`ond edition has been developed with the goal of extending the strengths of thefirst edition,
`namely in the area of analog circuit design insight and concepts.
`
`Page 10
`
`xiii
`
`

`

`PREFACE
`
`xiv
`
`The secondedition has been a long time in coming but has resulted in a unique blending
`of industry and academia. This blending has occurred over the past 15 years in short courses
`taught by the first author. Over 50 short courses have been taught from the first edition to over
`1500 engineers all over the world. In these short courses, the engineers demandedto under-
`stand the concepts and insight to designing analog CMOScircuits, and much of the response
`to these demandshasbeenincludedin the secondedition. In addition to the industrial input to
`the secondedition, the authors have taught this material at Georgia Institute of Technology
`and the University of Texas at Austin over the past 10-15 years. This experience has provided
`insight that has been included in the second edition from the viewpoint of students and their
`questions, Also, the academic application of this material has resulted in a large body of prob-
`lems that have been given as tests and have now been included in the second edition. Thefirst
`edition had 335 problems. The second edition has over 500 problems, and most of those are
`new to the second edition.
`The audience for the second edition is essentially the same as for the first edition. The
`first edition was very useful to those beginning a career in CMOSanalog design—many of
`whom have communicated to the authors that the text has been a ready referencein their daily
`work. The second edition should continue to be of value to both new and experienced engi-
`neers in industry. The principles and concepts discussed should never become outdated even
`though technology changes.
`The second audienceis the classroom. The output of qualified students to enter the field
`of analog CMOSdesign has not met the demand from industry. Our hopeis that the second
`edition will provide both instructors and students with a tool that will help fulfill this de-
`mand, In order to help facilitate this objective, both authors maintain websites that permit the
`downloading of short course lecture slides, short course schedules and dates, class notes, and
`problems-and solutions in pdf format. More information can be found at www.aicdesign.org
`(P.E. Allen) and www.holberg.org (D.R. Holberg), These sites are continually updated, and
`the readeror instructor is invited to make use of the information and teaching aides contained
`on thesesites.
`The second edition has received extensive changes. These changes include the moving
`of Chapter 4 of the first edition to Appendix B of the second edition. The comparator chap-
`ter of the first edition was before the op amp chapters and has been movedto after the op
`amp chapters. In the 15 years since the first edition, the comparator has become morelike a
`sense amplifier and less like an op amp without compensation. A major change has been the
`incorporation of Chapter 9 on switched capacitor circuits. There are two reasons for this.
`Switched capacitors are very important in analog circuits and systems design, and this infor-
`mation is needed for many of the analog—digital and digital-analog converters of Chapter 10.
`Chapter 11 of the first edition has been dropped. There were plansto replace it with a chapter
`on analog systems including phase-locked loops and VCOs, but time did not allow this to be
`realized. The problems of the second edition are organized into sections and have been de-
`signed to reinforce and extend the concepts and principles associated with a particular topic.
`The hierachical organization of the second editionis illustrated in Table 1.1-2. Chapter 1
`presents the material necessary to introduce CMOSanalogcircuit design. This chapter gives
`an overview of the subject of CMOSanalog circuit design, defines notation and convention,
`makesa brief survey of analog signal processing, and gives an example of analog CMOSde-
`sign with emphasis on the hierarchial aspect of the design. Chapters 2 and 3 form thebasis for
`analog CMOSdesign by covering the subjects of CMOStechnology and modeling. Chapter 2
`reviews CMOStechnology as applied to MOS devices, pn junctions, passive components
`_
`Page 11
`
`

`

`
`
`Preface
`
`xv
`
`BJT and latchup. This chapter also includes a section on the impact of integrated circuit
`layout. This portion of the text shows that the physical design of the integrated circuit is as
`important as the electrical design, and many goodelectrical designs can be ruined by poor
`physical design or layout. Chapter3 introduces the key subject of modeling, which is used
`throughout the remainderofthe text to predict the performance of CMOS circuits. The focus
`ofthis chapteris to introduce a model that is good enoughto predict the performance of a
`CMOScircuit to within +10% to +20%andwill allow the designer insight and understand-
`ing. Computer simulation can be used to more exactly modelthe circuits but will not give any
`direct insight or understanding of the circuit, The models in this chapter include the MOSFET
`Jarge-signal and small-signal models, including frequency dependence. In addition, how to
`model the noise and temperature dependence of MOSFETs and compatible passive elements
`is shown. This chapter also discusses computer simulation models. This topic is far too com-
`plex for the scopeofthis book, but some of the basic ideas are presentedso that the readercan
`appreciate computer simulation models. Other models for the subthreshold operation are pre-
`sented along with how to use SPICE for computer simulation of MOSFETcircuits.
`Chapters 4 and 5 represent the topics of subcircuits and amplifiers that will be used to
`design more complex analog circuits, such as an op amp. Chapter 4 covers the use of the
`MOSEETas a switch followed by the MOSdiode oractive resistor. The key subcircuits of cur-
`rent sinks/sources and current mirrors are presented next. These subcircuits permit the illus-
`tration of important design concepts suchas negative feedback, design tradeoffs, and match-
`ing principles. Finally, this chapter presents independent voltage and current references and
`the bandgap voltage reference. These references attempt to provide a voltage or current thatis
`independentof powersupply and temperature. Chapter 5 develops various types of amplifiers.
`These amplifiers are characterized from their large-signal and small-signal performance, in-
`cluding noise and bandwidth where appropriate. The categories of amplifiers include the
`inverter, differential, cascode, current, and output amplifiers. The last section discusses how
`high-gain amplifiers could be implemented from the amplifier blocks of this chapter.
`Chapters 6, 7, and 8 represent examples of complex analog circuits. Chapter 6 introduces
`the design of a simple two-stage op amp. This op amp is used to develop the principles of
`compensation necessary for the op amp to be useful, The two-stage op ampis usedto for-
`mally present methodsof designing this type of analog circuit. This chapter also examines the
`design of the cascode op amps, particularly the folded-cascode op amp. This chapter con-
`cludes with a discussion of techniques to measure and/or simulate op amps and macromodels.
`Macromodels can be used to moreefficiently simulate op ampsat higher levels of abstraction.
`Chapter 7 presents the subject of high-performance op amps. In this chapter various perfor-
`mances of the simple op amp are optimized, quite often at the expense of other performance
`aspects. The topics include buffered output op amps, high-frequency op amps, differential-
`output op amps, low-powerop amps, low-noise op amps, and low-voltage op amps. Chapter8
`presents the open-loop comparator, which is an op amp without compensation. This is
`followed by methods of designing this type of comparator for linear or slewing responses.
`Methodsof improving the performance of open-loop comparators, including autozeroing and
`hysteresis, are presented. Finally, this chapter describes regenerative comparators and how
`they can be combined with low-gain, high-speed amplifiers to achieve comparators with a
`very short propagation time delay.
`Chapters 9 and 10 focus on analog systems. Chapter9 is completely new and presents
`the topic of switched capacitorcircuits. The concepts of a switched capacitor are presented
`along with suchcircuits as the switched capacitor amplifier and integrator. Methodsof ana-
`lyzing and simulating switched capacitor circuits are given, andfirst-order and second-order
`Page 12
`
`

`

`xvi
`
`PREFACE
`
`switched capacitor circuits are used to design variousfilters using cascade and ladder ap-
`proaches. Chapter 9 concludes with anti-aliasing filters, which are required by all switched
`capacitor circuits. Chapter 10 covers the topics of CMOS digital—-analog and analog—digital
`converters. Digital—analog converters are presented according to their means of scaling the
`reference and include voltage, current, and charge digital—analog converters. Next, methods
`of extending the resolution of digital—analog converters are given. The analog—digital con-
`verters are divided into Nyquist and oversampling converters, The Nyquist converters are pre-
`sented accordingto their speed of operation—slow, medium andfast. Finally, the subject of
`oversampled analog—digital and digital—analog converters is presented. These converters
`allow high resolution and are very compatible with CMOS technology.
`Three appendices coverthe topics of circuit analysis methods for CMOSanalogcircuits,
`CMOSdevice characterization (this is essentially chapter 4 ofthefirst edition), and time and
`frequency domainrelationships for second-order systems.
`The material ofthe second edition is more than sufficient for a 15-weekcourse. Depending
`upon the background of the students, a 3-hour-per-week, 15-week-semester course could in-
`clude parts of Chapters 2 and 3, Chapters 4 through6,parts of Chapter 7, and Chapter8. Chap-
`ter 9 and 10 could be used aspart of the material for a course on analog systems. At Georgia
`Tech,this text is used along with the fourth edition ofAnalysis andDesign ofAnalog Integrated
`Circuits in a two-semestercourse that covers both BJT and CMOS analog IC design. Chapters
`9 and 10 are used for about 70% of a semester course on analog IC systemsdesign.
`The background necessary for this text
`is a good understanding of basic electronics.
`Topics of importance include large-signal models, biasing, small-signal models, frequency
`response, feedback, and op amps. It would also be helpful
`to have a good background in
`semiconductor devices and how they operate, integrated circuit processing, simulation using
`SPICE,and modeling of MOSFETs.With this background,the reader couldstart at Chapter 4
`with little problem.
`The authors wouldlike to express their appreciation and gratitude to the many individu-
`als who have contributed to the development of the second edition. These include both un-
`dergraduate and graduate students who have used the first edition and offered comments,
`suggestions, and corrections. It also includes the over 1500 industrial participants who, over
`the last 15 years, have attended a one-week course on this topic. We thank them for their
`encouragement, patience, and suggestions. We also appreciate the feedback and corrections
`from many individuals in industry and academia worldwide. The input from those who have
`read andusedthepreliminary edition is greatly appreciated. In particular, the authors would
`like to thank Tom DiGiacomo, Babak Amini, and Michael Hacknerfor providing useful feed-
`back on the new edition. The authors gratefully acknowledge the patience and encouragement
`of Peter Gordon, Executive Editor of Engineering, Science and Computer Science of Oxford
`University Press during the developmentof the second edition and the firm but gentle shep-
`herding of the second edition through the production phase by the project editor, Justin
`Collins. Lastly, the assistance of Marge Boehmein helping with detail work associated with
`the preparation and teachingof the secondedition is greatly appreciated.
`
`Phillip E. Allen
`Atlanta, GA
`
`Douglas R. Holberg
`Austin, TX
`
`
`
`Page 13
`
`
`
`

`

`
`
`chapter |
`|troduction and Background
`
`The evolution of very large-scale integration (VLSI) technology has developed to the point
`where millions of transistors can be integrated on a single die or “chip.” Where integrated cir-
`cuits once filled the role of subsystem components,partitioned at analog—digital boundaries,
`they now integrate complete systems on a chip by combining both analog and digital func-
`tions [1]. Complementary metal-oxide semiconductor (CMOS)technology has been the main-
`stay in mixed-signal* implementations becauseit provides density and power savings on the
`digital side, and a good mix of components for analog design. By reason ofits widespread
`use, CMOStechnologyis the subject of this text.
`Due in part to the regularity and granularity of digital circuits, computer-aided design
`(CAD) methodologies have been very successful in automating the design of digital systems
`given a behavioral description of the function desired. Such is not the case for analog circuit
`design. Analogdesignstill requires a “hands on”design approach in general. Moreover, many
`of the design techniques used for discrete analog circuits are not applicable to the design of
`analog/mixed-signal VLSIcircuits. It is necessary to examine closely the design process of
`analog circuits and to identify those principles that will increase design productivity and the
`designer’s chances for success. Thus, this book provides a hierarchical organization of the
`subject of analog integrated-circuit design and identification ofits general principles.
`The objective of this chapter is to introducethe subject of analog integrated-circuit de-
`sign and to lay the groundworkfor the material that follows.It deals with the general subject
`of analog integrated-circuit design followed by a description of the notation, symbology, and
`terminology used in this book. The next section covers the general considerationsfor an ana-
`log signal-processing system, and thelast section gives an example of analog CMOScircuit
`design. The reader may wish to review other topics pertinentto this study before continuing to
`Chapter 2. Such topics include modeling of electronic components, computer simulation
`techniques, Laplace and z-transform theory, and semiconductordevicetheory.
`
`LL] ANALOG INTEGRATED-CIRCUIT DESIGN
`
`Integrated-circuit design is separated into two majorcategories: analog anddigital. To char-
`acterize these two design methods we must first define analog anddigital signals. A signal
`will be considered to be any detectable value of voltage, current, or charge. A signal should
`
`“The term “mixed-signal” is a widely accepted term describing circuits with both analog and digital
`circuitry on the samesilicon substrate.
`
`1
`
`(li
`
`Page 14
`
`

`

`2
`
`INTRODUCTION AND BACKGROUND
`
`
`
`
`convey information aboutthe state or behavior of a physical system. An analog signalis a sig-
`nal that is defined over a continuous range of time and a continuous range of amplitudes. An
`analog signalis illustrated in Fig. 1.1-1(a). A digital signalis a signal that is defined only at
`discrete values of amplitude, or said another way, a digital signal is quantized to discrete val-
`ues. Typically, the digital signal is a binary-weighted sum of signals having only two defined
`values of amplitude asillustrated in Fig. 1.1-1(b) and shownin Eq. (1.1-1). Figure 1.1-1(b) is
`a three-bit representation of the analog signal shown in Fig. 1.1-1(a).
`N
`
`
`
`
`
`
`D = by) 2" + byo2? + by323 4 +b dN = DS by, 27
`
`i=]
`
`(1.1-1)
`
`The individual binary numbers, b;, have a value ofeither zero orone. Consequently,it is
`possible to implement digital circuits using componentsthat operate with only two stable
`states. This leads to a great deal of regularity and to an algebra that can be usedto describe the
`function ofthe circuit. As a result, digital circuit designers have been able to adaptreadily to
`the design of more complexintegratedcircuits.
`Another type of signal encountered in analog integrated-circuit design is an analog
`sampled-data signal. An analog sampled-data signalis a signal that is defined over a continu-
`ous range of amplitudesbutonly at discrete points in time. Often the sampled analogsignal is
`held at the value presentat the end of the sample period, resulting in a sampled-and-held sig-
`nal. An analog sampled-and-held signalis illustrated in Fig. 1.1-1(c).
`
`
`
`
`
`
`
`
`
`
`
`oO
`FENwWUD~1w
`SeNwWROH~]ow
`
`
`
`meNwBMH~)wo
`
`Amplitude
`
`
`
`
`
`
`Amplitude
`
`o
`
`Amplitude
`
`Sampled and held
`analog value
`
`
`
`
`Sample times 4
`
`f+ 4
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`4 t
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`(©)
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`T
`Figure 1.1-1 Signals. (a) Analog or continuous time. (b) Digital. (c) Analog sampled data or discrete
`time. T is the period of the digital or sampledsignals.
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`Page 15
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