Analysis of Bipolar and CMOS Amplifiers

415 Pages·2007·3.41 MB·English

by  Amir M. Sodagar

A
NALYSIS OF
B CMOS
IPOLAR AND
A
MPLIFIERS
A
NALYSIS OF
B CMOS
IPOLAR AND
A
MPLIFIERS
A M. S
MIR ODAGAR
K.N. T U T
OOSI NIVERSITYOF ECHNOLOGY
T ,I
EHRAN RAN
AND
U M
NIVERSITYOF ICHIGAN
ANN ARBOR, MI, U.S.A.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2007 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20130916
International Standard Book Number-13: 978-1-4200-4645-8 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
To the fruits of my life:
Ali and Shokoufeh
Table of Contents
Preface ....................................................................................................................xi
1 Basics of Amplifiers........................................................................1
1.1 Introduction ...................................................................................................1
1.2 Basic Concepts................................................................................................1
1.3 A Signal and Its DC and AC Components...............................................2
1.3.1 A Convention to Name a Signal and Its Components...............3
1.4 Basic Types of Amplifiers.............................................................................3
1.4.1 Voltage Amplifier..............................................................................4
1.4.2 Current Amplifier..............................................................................8
1.4.3 Transconductance Amplifier..........................................................12
1.4.4 Transresistance Amplifier...............................................................13
1.5 Cascaded Amplifiers...................................................................................15
1.6 Small-Signal and Large-Signal Amplifiers..............................................15
1.7 A Fundamental Question...........................................................................16
1.8 Simulation Examples...................................................................................17
1.9 Problems........................................................................................................24
2 Transistors......................................................................................27
2.1 Introduction .................................................................................................27
2.2 Basic Concepts..............................................................................................27
2.3 Metal-Oxide Semiconductor Field-Effect Transistor..............................29
2.3.1 NMOS Transistor.............................................................................30
2.3.2 PMOS Transistor..............................................................................35
2.4 Bipolar Junction Transistor.........................................................................37
2.4.1 NPN Transistor................................................................................38
2.4.2 PNP Transistor.................................................................................44
2.5 Simulation Examples...................................................................................45
2.6 Problems........................................................................................................48
3 Biasing............................................................................................51
3.1 Introduction..................................................................................................51
3.2 Biasing Bipolar Transistors.........................................................................51
3.2.1 Operating Point...............................................................................52
3.2.2 Biasing a Transistor.........................................................................52
3.2.3 A Circuit Drawing Convention.....................................................56
3.2.4 Approximation in the Analysis of Electronic Circuits..............58
3.2.5 A Brief Review.................................................................................61
3.2.6 Bipolar Transistor in Saturation....................................................64
3.3 Voltage-Divider Biasing..............................................................................64
3.3.1 Voltage-Divider Biasing Circuit: A Different View....................70
3.4 Biasing PNP Transistors.............................................................................73
3.5 Biasing MOS Transistors.............................................................................77
3.5.1 Operating Point...............................................................................78
3.6 Simulation Examples...................................................................................84
3.7 Problems........................................................................................................96
4 Single-Stage Amplifiers..............................................................103
4.1 Introduction................................................................................................103
4.2 The Transistor as an Amplifier................................................................103
4.2.1 Small-Signal Model for a Transistor..........................................106
4.3 Two-Step Analysis of a Small-Signal Amplifier...................................108
4.4 Coupling the Input/Output Signal to/from an Amplifier.................111
4.5 Basic Single-Stage Amplifier Configurations........................................115
4.5.1 Common-Source Configuration..................................................116
4.5.1.1 Bypass Capacitor.............................................................120
4.5.2 Common-Gate Configuration.....................................................126
4.5.3 Common-Drain or Source-Follower Configuration................130
4.5.3.1 Source Follower as a Voltage Buffer............................132
4.6 Analysis by Inspection..............................................................................134
4.6.1 Virtual Resistances Seen into a Transistor................................135
4.6.1.1 The Virtual Resistance Seen into the Gate..................135
4.6.1.2 The Virtual Resistance Seen into the Source..............136
4.6.1.3 The Virtual Resistance Seen into the Drain................138
4.6.2 AC Analysis of Amplifiers by Inspection.................................140
4.7 Other Basic Types of Amplifiers.............................................................142
4.8 Bipolar Amplifiers.....................................................................................146
4.8.1 Bipolar Transistor as an Amplifier.............................................147
4.8.1.1 Virtual Resistances Seen into a Bipolar Transistor....150
4.8.2 Single-Stage Bipolar Configurations..........................................155

4.8.2.1 Common-Emitter Configuration..................................155
4.8.2.2 Common-Base Configuration.......................................158
4.8.2.3 Common-Collector or Emitter Follower
Configuration...................................................................160
4.8.3 Other Basic Types of Bipolar Amplifiers...................................161
4.9 An Important Note....................................................................................164
4.10 Simulation Examples.................................................................................166
4.11 Problems......................................................................................................173
5 MultiStage Amplifiers................................................................181
5.1 Introduction................................................................................................181
5.2 Biasing/Coupling......................................................................................181
5.3 AC Analysis................................................................................................188
5.4 Useful Compound Configurations.........................................................195
5.4.1 Darlington Pair..............................................................................195
5.4.1.1 Varieties of the Darlington Configuration..................200
5.4.2 Cascode Amplifier.........................................................................202
5.4.2.1 Folded-Cascode Amplifier.............................................205
5.4.3 Differential Amplifier...................................................................206
5.4.3.1 The Basic Differential Amplifier...................................214
5.4.3.2 Differential Amplifier with Ideal Current Source.....217
5.4.3.3 Differential Amplifier with Real Current Source......223
5.4.3.4 Bipolar Differential Amplifier.......................................229
5.4.3.5 Differential Amplifiers in General...............................231
5.5 Simulation Examples.................................................................................233
5.6 Problems......................................................................................................239
6 Current Sources/Mirrors.............................................................245
6.1 Introduction................................................................................................245
6.2 Simple Current Source/Mirror................................................................245
6.3 Cascode Current Source/Mirror.............................................................256
6.4 Current Scaling..........................................................................................260
6.5 Multi-Output Current Sources/Mirrors................................................260
6.6 Bipolar Current Sources/Mirrors............................................................260
6.7 Current Sources for Biasing and as Active Loads...............................265
6.7.1 Differential Amplifier with Active Load...................................270
6.8 Simulation Examples.................................................................................276
6.9 Problems......................................................................................................281
7 Analysis of Amplifiers at Low Frequencies.............................285
7.1 Introduction................................................................................................285
7.2 Basic Concepts in Frequency Domain....................................................285
7.3 Plotting an Amplifier’s Response at Low Frequencies.......................287
7.3.1 Bode Plots for Low-Frequency Transfer Functions.................291
7.4 Low-Frequency Analysis by AC Analysis Methods............................296
7.5 Low-Frequency Analysis by Inspection.................................................301
7.5.1 Amplifiers with a Coupling Capacitor......................................302
7.5.2 Amplifiers with a Bypass Capacitor..........................................306
7.6 Time Response...........................................................................................311
7.6.1 Step Response................................................................................314
7.6.2 Response to a Square Wave.........................................................314
7.6.2.1 2(cid:85)f << p...........................................................................315
S
7.6.2.2 2(cid:85)f >> p...........................................................................317
S
7.6.3 Response to a Sine Wave.............................................................318
7.6.4 The Bypass Capacitor Case.........................................................319
7.7 More Than One External Capacitor.......................................................321
7.7.1 Transfer Function..........................................................................321
7.7.2 Low Cutoff Frequency..................................................................325
7.8 Simulation Examples.................................................................................326
7.9 Problems......................................................................................................342
8 Analysis of Amplifiers at High Frequencies............................349
8.1 Introduction................................................................................................349
8.2 Basic Concepts at High Frequencies......................................................349
8.3 Amplifiers at High Frequencies..............................................................350
8.4 Plotting an Amplifier’s Response at High Frequencies......................351
8.4.1 Bode Plots for High-Frequency Transfer Functions................354
8.5 High-Frequency Analysis.........................................................................356
8.5.1 High-Frequency Analysis by Inspection...................................360
8.5.1.1 The First Equivalent High-Frequency Pole, (cid:92) ........361
1H
8.5.1.2 Boosting the Time Constant..........................................368
8.5.1.3 The Second Equivalent High-Frequency Pole, (cid:92) ...372
2H
8.6 Time Response...........................................................................................374
8.6.1 Step Response................................................................................375
8.6.1.1 Contribution of the Nondominant Pole......................377
8.6.2 Response to a Square Wave.........................................................377
8.6.2.1 2(cid:85)f << (cid:92) ........................................................................377
S 1H
8.6.2.2 2(cid:85)f >> (cid:92) ........................................................................380
S 1H
8.7 High Cutoff Frequency.............................................................................380
8.8 Complete Response over the Entire Frequency Range.......................382
8.8.1 Transfer Function and Frequency Response.............................383
8.8.2 Time Response...............................................................................385
8.9 Case Studies for High-Frequency Analysis of Multistage
Amplifiers...................................................................................................386
8.9.1 Case Study 1: The Common-Source/Common-Emitter
Amplifier.........................................................................................386
8.9.2 Case Study 2: The Cascode Amplifier.......................................387
8.9.3 Case Study 3: A Multistage Amplifier.......................................388
8.10 Simulation Examples.................................................................................390
8.11 Problems......................................................................................................396
References............................................................................................403

Index.....................................................................................................405
Preface
Several invaluable reference books have been published, which generally
introduce the basics of analog circuit analysis and design, and specifically
apply these concepts to amplifiers. These books usually describe the classic
approach to evaluating small-signal amplifiers, which includes all the
contributing factors and precise calculations of the quantities of desired
parameters. This technique involves a tedious and sometimes difficult pro-
cess, however, especially when the number of components increases. Even
if a circuit is precisely designed or analyzed using hand analysis, the circuit
variables will likely deviate from the expected values in practice. Thus, it is
sometimes preferred to roughly determine the quantities of interest with a
straightforward method and not bother with spending too much time and
effort to precisely analyze the circuit by solving several equations.
After more than 14 years of research and teaching experience in analog and
mixed-signal circuits, I decided that aside from the voluminous wide-scope
reference books, there should be a book mainly focused on the introduction
of a much simpler technique, known as “analysis by inspection,” for bipolar
and complementary metal-oxide semiconductor (CMOS) small-signal amplifiers.
This allows a straightforward approach to analyzing a wide variety of small-
signal analog circuits quickly, yet within an acceptable accuracy range while
still based upon scientific fundamentals. This includes both AC analysis at
midband frequencies, as well as analysis at low and high frequencies, for
both bipolar and CMOS circuits.
The target audience of this book includes senior undergraduate and first-
year graduate students in electrical engineering and related disciplines. It is
assumed that the reader has a basic background in the analysis of electric
circuits and the theory of signals and systems.
Chapters 4, 5, 7, and 8 discuss the main concepts presented in this book.
Chapters 1 through 3 and 6 provide only the minimum basic concepts
required to support the flow of the discussion. For example, transistors in
Chapter 2 are introduced with their electrical function and not their physical
behavior. Moreover, no body or short-channel effects are discussed for MOS
transistors, allowing for the simplest possible small-signal model for tran-
sistors to be utilized in practice.
I am grateful to the following for their help during the development of
this text: Professors A. Ashrafi (University of Alabama), P. Bhatti (Georgia
Institute of Technology), M. Ghovanloo (North Carolina State University),
R. Lofti (Ferdowsi University of Mashhad), also Dr. Y. Yao (University of
Michigan), and University of Michigan graduate students: A. Borna, R.M.
Haque, G.E. Perlin, and S. Naraghi. I would also like to express my appre-
ciation to all the indivdiuals who have contributed to the production of this
book at Taylor and Francis/CRC Press, especially Nora Konopka, the Editor
of Engineering and Environmental Sciences, Marsha Pronin, the Project
Coordinator, and Jennifer Smith, the Project Editor.
I also want to take this opportunity to thank Professor G. Roientan Lahiji,
who opened my eyes to the exciting world of advanced electronics.
Finally, I thank, from the bottom of my heart, my parents who were my
first and best teachers and with my most sincere gratitude I acknowledge
my wife’s patience, support, and help, without which this work would not
have been possible.
Amir M. Sodagar
University of Michigan
Ann Arbor, Michigan