Analog Signal Processing [1 ed.] 0471125288

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ANALOG SIGNAL PROCESSING ___________________________________________________________

RAMÓN PALLÁS-ARENY Universitat Politécnica de Catalunya

JOHN G. WEBSTER University of Wisconsin-Madison

A Wiley-Interscience Publication

JOHN WILEY & SONS, INC. New York

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Chichester

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Weinheim

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Toronto

This book is printed on acid-free paper.

Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data: Pallás-Areny, Ramón Analog Signal Proocessing / Ramón Pallás-Areny and John G. Webster. p. cm. “A Wiley-Interscience Publication.” Includes index. ISBN 0-471-12528-8 (alk. paper) 1. Linear integrated circuits. 2. Signal processing. I. Webster, John G., 1932- . II. Title. TK7874.P345 1999 621.382'2–dc21 98-7295 CIP

Printed in the United States of America. 10 9 8 7 6 5 4 3 2

CONTENTS Preface 1 Signals and Sigual Processing

xiii 1

1.1 Signals, Information, Interference, and Noise, 1.2 Signal Classification, 2 1.2.1 Analog and Digital Signals, 2 1.2.2 Single-Ended, Differential, and Floating Signals, 4 1.2.3 Low-Impedance and High-Impedance Signals, 12 1.3 Dynamic Range and Signal-to-Noise Ratio, 14 1.4 Functions in Analog Signal Processing, 16 1.4.1 Linear and Nonlinear Functions, 16 1.4.2 Amplitude and Level Matching, 19 1.4.3 Impedance Adaptation. Buffering, 20 1.4.4 Domain Conversions, 23 1.4.5 Filtering, 25 1.4.6 Linearization, 26 1.4.7 Interference Compensation, 26 1.4.8 Level Comparison and Threshold Detection, 26 1.4.9 Terminal Matching, 27 1.5 Errors in Analog Signal Processing, 29 1.5.1 Errors and Their Classification, 29 1.5.2 Systematic Errors, 32 1.5.3 Random Errors, 32 1.5.4 Static Errors, 33 1.5.5 Dynamic Errors, 33 1.6 Problems, 39 References, 40 2 Voltage Amplification

42'

2.1 Ideal Voltage Amplifiers, 42 2.2 Practical Voltage Amplifiers, 45 2.2.1 Figures of Merit of Fully Differential Amplifiers, 45 2.2.2 Effects of Finite Input Impedances, 47 2.2.3 Error Modeling for Voltage Amplifiers, 53 2.2.4 Differential Versus Single-Ended Amplifiers, 57 v

vi

CONTENTS

2.3 Building Blocks for Voltage Amplifiers, 57 2.3.1 Voltage-Feedback Operational Amplifiers, 57 2.3.2 Current-Feedback Operational Amplifiers, 65 2.3.3 Difference Amplifiers, 68 2.3.4 Instrumentation Amplifiers, 69 2.3.5 Switched Capacitors, 72 2.3.6 Voltage Buffers, 73 2.4 de Amplifiers, 74 2.4.1 Single-Ended de Amplifiers, 74 2.4.2 Differential-Input de Amplifiers, 87 2.4.3 Fully Differential de Amplifiers, 93 2.5 ac Amplifiers, 97 2.5.1 Single-Ended ac Amplifiers, 100 2.5.2 Differential-Input ac Amplifiers, 104 2.5.3 Fully Differential ac Amplifiers, 107 2.6 Composite Amplifiers, 109 2.6.1 Cascaded Amplifiers, 109 2.6.2 Feedback Composite Amplifiers, III 2.6.3 Paralleled Amplifiers, 113 2.7 Programmable-Gain Amplifiers, 113 2.8 Problems, 117 References, 121 3 Current-to-Voltage and Voltage-to-Current Conversion

122

3.1 Ideal Current-to-Voltgage Converters, 122 3.2 Practical Current-to-Voltage Converters, 124 3.2.1 Figures of Merit of Fully Differential Current. to-Voltage Converters, 124 3.2.2 Error Modeling for Current-to-Voltage Converters, 126 3.3 Building Blocks for Current-to-Voltage Converters, 128 3.3.1 Current Integrators, 128 3.3.2 Integrated Transimpedance Amplifiers, 130 3.4 Current-to-Voltage Converter Amplifiers, 130 3.4.1 Transimpedance Amplifiers, 130 3.4.2 Charge Amplifiers, 142 3.5 Ideal Voltage-to-Current Converters, 148 3.6 Practical Voltage-to-Current Converters, 150 3.6.1 Figures of Merit of Fully Differential Voltage-to-Current Converters, 150 3.6.2 Error Modeling for Voltage-to-Current Converters, 150 3.7 Operational Transconductance Amplifiers, 152

CONTENTS

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3.8 Voltage-to-Current Converter Circuits, 154 3.8.1 de Current Sources and Sinks, 154 3.8.2 Transconductance Amplifiers, 159 3.8.3 Voltage-to-(4 rnA to 20mA) Converters, 165 3.9 Other Components and Circuits for Processing Currents, 167 3.9.1 Current Mirrors, 167 3.9.2 Current Amplifiers, 168 3.9.3 Current Conveyors, 172 3.9.4 Bidirectional Current Sources, 173 3.10 Problems, 174 References, 179 4 Linear Analog Functions

181

4.1 Addition, 181 4.1.1 Single-Ended Voltage Addition, 181 4.1.2 Differential Voltage Addition, 187 4.1.3 Level Shifting, 190 4.2 Subtraction, 193 4.2.1 Single-Ended Voltage Subtraction, 193 4.2.2 Differential Voltage Subtraction, 194 4.3 Differentiation, 195 4.3.1 Single-Ended Differentiator, 196 4.3.2 Difference Differentiator, 201 4.4 Integration, 203 4.4.1 Single-Ended Integrator, 203 4.4.2 Difference Integrator, 210 4.5 Impedance Transformation and Conversion, 214 4.5.1 Negative Impedance Conversion, 214 4.5.2 Impedance Gyration, 219 4.5.3 Capacitance Multiplication, 222 4.6 Problems, 225 References, 228 5 aelde Signal Conversion 5.1 Description of ac Signals, 229 5.2 Signal Rectification, 231 5.2.1 Half-Wave Rectification, 231 5.2.2 Full-Wave Rectification: Absolute-Value Circuits, 234 5.3 Peak and Valley Detection, 245 5.3.1 Peak Detection, 245

229

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CONTENTS

5.3.2 Valley Detection, 248 5.4 rms-to-dc Conversion, 249 5.4.1 Thermal rms-to-dc Conversion, 249 5.4.2 Direct Computation rms-to-dc Conversion, 251 5.4.3 Implicit Computation rms-to-dc Conversion, 253 5.5 Amplitude Demodulation, 255 5.5.1 Envelope Detection, 257 5.5.2 Coherent Demodulation, 259 5.6 Problems, 270 References, 273 6 Other NonUnear Analog Functions

274

6.1 Voltage Comparison, 274 6.1.1 Voltage Comparators, 274 6.1.2 Schmitt Triggers, 285 6.1.3 Window Comparators, 287 6.2 Voltage Limiting (Clipping), 288 6.3 Logarithmic Amplifiers, 293 6.3.1 Transdiode Logarithmic Amplifiers, 296 6.3.2 Log Ratio Amplifiers, 301 6.4 Exponential (Antilog) Amplifiers, 302 6.5 Analog Multipliers, 304 6.5.1 Multiplier Error Specifications, 304 6.5.2 Transconductance Multipliers, 304 6.5.3 Log-Antilog Multiplier, 311 6.5.4 Additional Multiplier Circuits, 312 6.6 Analog Dividers, 315 6.6.1 Analog Division by Feedback, 315 6.6.2 Log-Antilog Dividers, 317 6.7 Problems, 318 References, 321 7 Analog Signal Filtering 7.1 Introduction to Filtering and Filter Design, 322 7.1.1 Filter Specification, 322 7.1.2 Frequency Response, 326 7.1.3 Transformation Rules, 330 7.1.4 Normalization and Scaling Laws, 331 7.1.5 Transient Response, 331 7.1.6 Differential Filters, 333 7.1.7 Filter Sensitivity, 338

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CONTENTS

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7.2 Components for Filter Implementation, 338 7.2.1 Passive Components, 339 7.2.2 Operational Amplifiers, 342 7.2.3 Switched Capacitors, 343 7.3 Low-Pass Filters, 345 7.3.1 RC Low-Pass Filters, 345 7.3.2 LC Low-Pass Filters, 347 7.3.3 Active Low-Pass Filters, 348 7.4 High-Pass Filters, 352 7.4.1 RC High-Pass Filters, 352 7.4.2 LC High-Pass Filters, 352 7.4.3 Active High-Pass Filters, 354 7.5 Bandpass Filters, 357 7.5.1 Passive Bandpass Filters, 357 7.5.2 Active Bandpass Filters, 359 7.6 Band-Reject (Notch) Filters, 361 7.6.1 Passive Band-Reject Filters, 361 7.6.2 Active Band-Reject Filters, 362 7.7 All-Pass Filters, 365 7.8 Nonlinear Analog Filters, 369 7.9 Input Filters and Circuit Protection, 372 7.9.1 Single-Ended Inputs, 372 7.9.2 Differential Inputs, 374 7.10 Problems, 376 References, 377

8 Analog Signal Switching, Multiplexing, and Sampling

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8.1 Introduction to Signal Acquisition, 379 8.2 Analog Switches, 382 8.2.1 The Ideal Analog Switch, 382 8.2.2 Practical Analog Switches, 383 8.2.3 dc Model and Errors for Analog Switches, 385 8.2.4 ac Model and Errors for Analog Switches, 389 8.2.5 Switching and Control Models for Analog Switches, 393 8.3 Analog Multiplexers, 393 8.3.1 Basic Structure and Models, 393 8.3.2 dc Model and Errors for Analog Multiplexers, 396 8.3.3 ac Model and Errors for Analog Multiplexers, 400 8.3.4 Switching and Control Models for Analog Multiplexers, 405 8.3.5 Input Channel Extension, 406 8.4 Crosspoint Switch Arrays, 411

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CONTENTS

8.5 Sample-and-Hold Amplifiers, 412 8.5.1 The Need for Sample-and-Hold Amplifiers, 412 8.5.2 The Basic Sample-and-Hold Circuit, 414 8.5.3 Errors in Sample-and-Hold Amplifiers, 415 8.6 Problems, 422 References, 424 9

Error Analysis and Reduction

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9.1 Error Sources in Analog Signal Processing, 425 9.1.1 Sources of Systematic Errors, 426 9.1.2 Sources of Random Errors, 431 9.2 Error Budget and Calculation, 432 9.3 Error Reduction by Internal Calibration, 439 9.3.1 Single-Point Calibration, 439 9.3.2 Two-Point Calibration, 441 9.3.3 Three-Point Calibration, 444 9.3.4 n-Point Calibration, 448 9.4 Offset Reduction Techniques, 450 9.4.1 Autozero Techniques, 451 9.4.2 The Recirculation Method, 452 9.5 Gain-Error Reduction Techniques, 453 9.6 Problems, 455 References, 456 10 Interference and its Reduction 10.1 Interference Coupling in Electronic Circuits, 457 10.1.1 Conductive Coupling, 458 10.1.2 Capacitive Coupling, 463 10.1.3 Inductive Coupling, 472 10.2 Grounding for Interference Reduction, 476 10.2.1 Safety Ground, 476 10.2.2 Signal Grounding, 477 10.2.3 Partition Grounding, 479 10.3 Shielding of Conductors and Circuits, 480 10.3.1 The Electric Shield Concept, 481 10.3.2 Circuit Guards, 482 10.3.3 Electric Shield Grounding, 484 10.3.4 Magnetic Shielding, 489 10.4 Signal Isolation. Isolation Amplifiers, 493

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CONTENTS

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10.5 Problems, 496 References, 497 11 Noise, Drift, and Their Reduction

499

11.1 Noise Fundamentals, 499 11.1.1 Noise Description, 499 11.1.2 Thermal Noise, 503 11.1.3 Shot Noise, 505 11.1.4 Low-Frequency Noise, 507 11.1.5 Noise Bandwidth, 509 11.1.6 Noise Calculations, 513 11.2 Noise in Electronic Components and Circuits, 519 11.2.1 Equivalent Input Noise, 520 11.2.2 Optimal Source Resistance and Noise Matching, 525 11.2.3 Noise in Operational Amplifiers, 527 11.2.4 Noise in Instrumentation Amplifiers, 544 11.2.5 Noise in Resistors, 546 11.2.6 Noise in Transimpedance Amplifiers, 549 11.2.7 Noise in Charge Amplifiers, 551 11.2.8 Noise in DifTerentiators, 554 11.2.9 Noise in Integrators, 556 11.3 Drift in Electronic Components, 558 11.4 Environmental Noise (Pseudonoise), 559 11.4.1 Thermal Pseudonoise, 560 11.4.2 Chemical Pseudonoise, 562 11.4.3 Mechanical Pseudonoise, 562 11.5 Problems, 563 References, 564 APPENDIX A: Web Sites of Interest in Analog Signal Processing

566

APPENDIX 8: Standard EIA Resistor and Capacitor Values

570

INDEX

573

ANALOG SIGNAL PROCESSING

1 SIGNALS AND SIGNAL PROCESSING

In the first years of microelectronics, analog integrated circuits were mainly considered an alternative to electronic tubes to perform calculations in the socalled analog computers. Nowadays, analog computers are but a forgotten curiosity in a few specialized museums. Price reduction for digital computing and storage has resulted in an ever-increasing number of applications where electronic circuits process information from sensors probir a process or system. Analog circuits, however, have anything but disappeared. Power circuits for example have analog circuits present wherever there is an active electronic component. Analog signal processing circuits are present in most applications using sensors because most sensors yield analog signals. The design of these circuits cannot be automated like that of some digital circuits. Nevertheless a systematic approach to design is still possible by first considering the nature of the signals to be processed and the process to be performed. fT

1.1 SIGNALS, INFORMATION, INTERFERENCE, AND NOISE A signal is a detectable (or measurable) physical quantity whose magnitude varies with time and conveys information about a process or event. Signals from natural processes depend on one or more quantities such as temperature, humidity, level, distance, velocity, pressure, or fluid flow rate. Signals must be processed in order to extract the information embedded in them. An electric signal is a time-varying voltage or current. Electric signals are obtained from processes by means of sensors or transducers and their I

1.2 SIGNAL CLASSIFICA nON

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and the common-mode voltage (1.2)

The information is in the differential voltage. The common-mode voltage is a nuisance and should not degrade the information when processing the differential voltage. As in the case for single-ended signals, the reference point of differential signals can be independent of ground-diffe~entialand floating signal. Figure 1.4a, ground itself-differential and grounded signal, Figure 1.4b, or have a finite impedance to ground. The common-mode voltage (with respect to the respective reference point) for a floating signal· or a grounded signal, may be zero. When Vd « vc ' in order to simplify circuit analysis it is common to use the equivalent circuit in Figure lAc. Here, the potential at terminal L does not change in direction opposite of that for the potential in terminal H; rather, it is V c which may be constant. Signal sources whose equivalent circuit is like that in Figure 1.4c provide pseudo-differential signals. However, no distinction is usually made in their processing as compared to that of differential signals. Sometimes, the signal of interest is the difference in electric potential between two points whose respective potential with respect to a reference point changes, but not in a symmetrical mode. We have then a difference signal, though it is also considered "differential." The electrocardiogram taken between two limbs is an example of difference signal. Real-world floating signals will have a finite impedance between their reference point and ground. Any drop in voltage across this impedance constitutes a common-mode signal with respect to ground. It is sometimes called an isolated mode signal in order to distinguish it from the common-mode voltage with respect to the reference (ungrounded) point. The signa] is then differential and driven off ground, Figure 1.4d. If the equivalent output impedances for each terminal of a differential signal are equal, the signal is said to be differential and balanced, otherwise it is differential and unbalanced. Example 1.2 Draw the equivalent circuit for the output signal of the de bridge in Figure E 1.2a and classify that signal. Repeat the analysis when there is only one resistive sensor and the other three arms are fixed resistors Ro, Figure E1.2c. x is a relative change of resistance produced by a timevarying quantity. The voltage from the high-output terminal to ground will be VH

1 +x V X = V - - = - + v222

8

SIGNALS AND SIGNAL PROCESSING

z,

(a)

(b)

H

L

(e)

REFERENCES

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[6] A. V. Oppenheim and A. S. Willsky. Signals and Systems, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1997. [7] J. Dostal. Operational Amplifiers, 2nd ed. Boston: Butterworth-Heinemann. 1993. [8] B. J. Kuo. Automatic Control Systems, 7th ed. Englewood Cliffs, NJ: PrenticeHall, 1995.