Analog Filters. Second Edition

Analog Filters. Second Edition

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English

Description

Analog Filters, Second Edition covers four major fundamental types of analog filters - passive, op amp-RC, switched-capacitor, and operational transconductance amplifier-capacitor (OTA-C). (The last of these types is the major addition in the Second Edition). The emphasis is on the fundamental principles and theory of analog filters. It is targeted toward readers in telecommunications, signal processing, electronics, controls, instrumentation, bioengineering, etc. It introduces the reader to the elegant theory in the development of analog filters. Although some of the mechanical steps for generating filters are covered, the book stresses the mathematical bases and the scholastic ingenuity of analog filter theory. It should be helpful to nonspecialist electrical engineers to gain a background perspective and some basic insight to the development of real-time filters. In many modern advances in signal processing, their concepts and procedures have close links to analog filters. The material in this book will provide engineers with a better perspective and more penetrating appreciation of many modern signal-processing techniques.

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Published by
Published 01 January 1983
Reads 31
EAN13 0306479532
License: All rights reserved
Language English

Legal information: rental price per page €. This information is given for information only in accordance with current legislation.

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Contents
Preface
1
2
INTRODUCTION 1.1Preliminary Remarks 1.2The Analog Filter 1.3Ideal and Approximate Filter Characteristics 1.4MATLAB 1.5Circuit Analysis 1.6Normalization and Denormalization  Scaling 1.6.1Frequency scaling 1.6.2Impedance scaling 1.6.3Normalization and denormalization 1.7Steps Involved in the Design of Filters Problems
THE APPROXIMATION 2.1The Butterworth Lowpass Characteristic 2.1.1The normalized Butterworth lowpass characteristic 2.1.2Using a normalized Butterworth lowpass characteristic for a filtering requirement 2.2The Chebyshev Lowpass Characteristic 2.2.1The Chebyshev polynomial 2.2.2The Chebyshev lowpass characteristic 2.3Other ChebyshevRelated Characteristics 2.4The EllipticFunction Filter Characteristic 2.5Comparison of Standard Lowpass Characteristics 2.6Summary Problems
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1 1 3 4 7 9 13 13 14 16 16 20
25 26
27
29 30 31 34 37 39 41 43 43
3
4
5
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NETWORK FUNCTIONS 3.1General Procedure 3.2Network Functions for Butterworth filters 3.3Network Functions for Chebyshev Filters 3.4Network Functions for EllipticFunction Filters 3.5BesselThomson Filter Functions 3.6Delay Equalization 3.7Summary Problems
FREQUENCY TRANSFORMATION 4.1LowpasstoHighpass Transformation 4.2LowpasstoBandpass Transformation 4.3LowpasstoBandreject transformation 4.4Summary Problems
Contents
PROPERTIES AND SYNTHESIS OF PASSIVE NETWORKS 5.1The DrivingPoint Function of a Passive Oneport  the Positive Real Function 5.2The DrivingPoint Function of a Lossless Oneport  the Lossless Function 5.2.1 Properties of a lossless function 5.2.2a lossless functionFoster’s expansion of 5.2.3 Foster’s realizations of a lossless function 5.2.4 Removal of poles at infinity 5.2.5 Removal of poles at the origin 5.2.6 Removal of finite nonzero poles 5.2.7 Mixed canonic realization 5.2.8 Noncanonic realization 5.3Properties of Lossless Twoports 5.4LC Ladder Twoport 5.5Foster’s Preamble 5.6Summary Problems
49 49 53 58 62 66 71 74 74
77 78 80 86 88 88
93
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94 94 96 99 100 104 106 107 108 110 112 115 118 118
Contents
6
7
8
9
SINGLYTERMINATED LC LADDERSs 6.1LC Ladder with a Current Source 6.1.1 Transmission zeros at the origin and infinity 6.1.2 Zero shifting 6.1.3 LC ladder with finite nonzero transmission zeros 6.2LC Ladder with a Voltage Source 6.3Other SinglyTerminated Orientations 6.4Summary Problems
DOUBLYTERMINATED LC LADDERS 7.1Basic Formulation 7.2LC Ladders with Equal Terminations 7.3LC Ladder with Unequal Terminations 7.4A DoublyTerminated Filter Used in Reverse 7.5Summary Problems
SENSITIVITY 8.1SensitivityDefinition of 8.2Properties of FirstOrder Sensitivity 8.3Sensitivities of Network Performance 8.4Sensitivity Calculation 8.5Unnormalized Sensitivity 8.6Multiparameter and Statistical Sensitivities 8.7A Case for Low Sensitivity of Passive Filters 8.8Summary Problems
BASICS OF OP AMPRC CIRCUITS 9.1Comparison of Passive and Active Filters 9.2The Operational Amplifier (Op Amp) 9.3Some Simple Op Amp Circuits 9.4FirstOrder Sections
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123 123 125 131
133 136 139 140 141
145 145 149 158 163 167 167
171 173 174 175 177 180 181 182 184 184
187 187 190 192 195
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10
11
9.5
9.6
9.7 9.8 9.9
Contents
RC SingleOp Amp Circuit Relationships 9.5.1Finitegain singleop amp configuration 9.5.2Infinitegain singleop amp configuration Gain Adjustments 9.6.1 Gain reduction 9.6.2Gain enhancement RCCR Transformation Types of Biquads Summary Problems
OP AMPRC BIQUAD CIRCUITS 10.1SallenKey Biquads 10.1.1Lowpass biquad 10.1.2Highpass biquad 10.1.3Bandpass biquad 10.1.4Bandreject biquad 10.2InfiniteGain MultipleFeedback (MFB) Biquads 10.2.1Lowpass biquad 10.2.2Highpass biquad 10.2.3Bandpass biquad 10.2.4Bandreject and allpass biquad 10.3TwoIntegrator Biquads 10.3.1The KerwinHuelsmanNewcomb (KHN) biquad 10.3.2The TowThomas biquad 10.3.3The FleischerTow biquad 10.4Summary Problems
HIGHORDER OP AMPRC FILTERS 11.1Cascaded Biquads 11.1.1Gain allocation 11.1.2Polezero pairing 11.1.3Biquad sequencing
197 197 200 200 201 201 204 206 207 207
217 217 218 223 225 228 230 230 233 233 237 238
239 243 245 247 247
253 253 258 263 264
Contents
12
13
11.2
11.3
11.4 11.5
The StateVariable Method of Realization 11.2.1Realization of allpole transfer functions 11.2.2Realization of general transfer functions 11.2.3Realization using lossy integrators LowpasstoBandpass Transformation 11.3.1Coupled biquads with infiniteQ 11.3.2Bandpass filters using the primary resonator blocks Internal Gain Change Summary Problems
OP AMPRC SIMULATION OF PASSIVE FILTERS 12.1Some Active Twoports 12.2The Generalized Impedance Converter (GIC) 12.3Simulation of Inductances in an LC Ladder 12.3.1grounded inductorsSimulation of 12.3.2 Simulation of floating inductors 12.3.3Simulation of groups of inductors 12.4Simulation Using FrequencyDependent Negative Resistances (FDNRs) 12.5Functional Simulation of Passive Filters 12.5.1The leapfrog simulation 12.5.2Leapfrog realization of lowpass LC ladder 12.5.3Leapfrog realization of bandpass filters using biquads 12.5.4Leapfrog realization of bandpass filters using integrators 12.5.5Simulation of a special bandpass filter 12.6Summary Problems
SWITCHEDCAPACITOR FILTERS 13.1An Introduction 13.2Simulation of Resistors by Switched Capacitors
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265 265 266 270 274 274
276 277 280 281
285 286 288 291 291 292 295
299 301 302
305
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307 309 314 314
321 322 323
14
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13.3
13.4 13.5 13.6
Simple Basic Circuits 13.3.1Allcapacitor op amp circuits 13.3.2The inverting integrator 13.3.3The inverting lossy integrator 13.3.4The inverting weighted summing integrator 13.3.5A noninverting integrator 13.3.6Inverting summerintegrator combination 13.3.7The differential integrator 13.3.8The differential lossy integrator 13.3.9The differential amplifier 13.3.10The firstorder section SwitchedCapacitor Biquads Functional Simulation of LC Ladders Summary Problems
Contents
OPERATIONAL TRANSCONDUCTANCE AMPLIFIER (OTA) FILTERS 14.1 An Introduction 14.2 The Operational Transconductance Amplifier (The OTA) and Simple Circuits 14.2.1Grounded resistor 14.2.2 Floating resistor 14.2.3 Integrator 14.2.4 Lossy integrator 14.2.5Amplifier 14.2.6 Weighted summer 14.2.7Positive impedance inverter 14.3 FirstOrder Sections 14.4 The OTAC Biquads 14.4.1A simple biquad 14.4.2 A lowpass notch filter 14.4.3A fourOTA biquad 14.4.4A fiveOTA general biquad
327 327 328 329
329 330
330 331 331 332 333 335 337 338 341
345 345
347 348 348 349 350 350 351 352 353 354 354 356 357 359
Contents
14.5
14.6
14.7
Element Simulation of Passive Filters 14.5.1a highpass filterRealization of 14.5.2Realization of a lowpass filters Functional Simulation of Passive Filters 14.6.1The leapfrog realization 14.6.2Leapfrog realization of a lowpass filter 14.6.3Simulation of a bandpass LC filter Summary Problems
Appendix A
Bibliography
Index
TABLES OF FILTER FUNCTIONS
360 360 362 362 363 366 368 371 374
377
395
399
xi