Modern Analog Filter Analysis and Design E-Book

R. Raut

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 464

Veröffentlichungsjahr: 2011

Beschreibung

Starting from the fundamentals, the present book describes methods of designing analog electronic filters and illustrates these methods by providing numerical and circuit simulation programs. The subject matters comprise many concepts and techniques that are not available in other text books on the market. To name a few - principle of transposition and its application in directly realizing current mode filters from well known voltage mode filters; an insight into the technological aspect of integrated circuit components used to implement an integrated circuit filter; a careful blending of basic theory, numerical verification (using MATLAB) and illustration of the actual circuit behaviour using circuit simulation program (SPICE); illustration of few design cases using CMOS and BiCMOS technological processes.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Preface

Abbreviations

Chapter 1: Introduction

Chapter 2: A Review of Network Analysis Techniques

2.1 Transformed Impedances

2.2 Nodal Analysis

2.3 Loop (Mesh) Analysis

2.4 Network Functions

2.5 One-Port and Two-Port Networks

2.6 Indefinite Admittance Matrix

2.7 Analysis of Constrained Networks

2.8 Active Building Blocks for Implementing Analog Filters

Practice Problems

Chapter 3: Network Theorems and Approximation of Filter Functions

3.1 Impedance Scaling

3.2 Impedance Transformation

3.3 Dual and Inverse Networks

3.4 Reversed Networks

3.5 Transposed Network

3.6 Applications to Terminated Networks

3.7 Frequency Scaling

3.8 Types of Filters

3.9 Magnitude Approximation

3.10 Frequency Transformations

3.11 Phase Approximation

3.12 Delay Equalizers

Practice Problems

Chapter 4: Basics of Passive Filter Design

4.1 Singly Terminated Networks

4.2 Some Properties of Reactance Functions

4.3 Singly Terminated Ladder Filters

4.4 Doubly Terminated LC Ladder Realization

Practice Problems

Chapter 5: Second-Order Active-RC Filters

5.1 Some Basic Building Blocks using an OA

5.2 Standard Biquadratic Filters or Biquads

5.3 Realization of Single-Amplifier Biquadratic Filters

5.4 Positive Gain SAB Filters (Sallen and Key Structures)

5.5 Infinite-Gain Multiple Feedback SAB Filters

5.6 Infinite-Gain Multiple Voltage Amplifier Biquad Filters

5.7 Sensitivity

5.8 Effect of Frequency-Dependent Gain of the OA on the Filter Performance

5.9 Second-Order Filter Realization Using Operational Transconductance Amplifier (OTA)

5.10 Technological Implementation Considerations

Practice Problems

Chapter 6: Switched-Capacitor Filters

6.1 Switched C and R Equivalence

6.2 Discrete-Time and Frequency Domain Characterization

6.3 Bilinear s ↔ z Transformation

6.4 Parasitic-Insensitive Structures

6.5 Analysis of SC Networks Using PI-SC Integrators

6.6 Analysis of SC Networks Using Network Simulation Tools

6.7 Design of SC Biquadratic Filters

6.8 Modular Approach toward Implementation of Second-Order Filters

6.9 SC Filter Realization Using Unity-Gain Amplifiers

Practice Problems

Chapter 7: Higher-Order Active Filters

7.1 Component Simulation Technique

7.2 Operational Simulation Technique for High-Order Active RC Filters

7.3 Cascade Technique for High-Order Active Filter Implementation

7.4 Multiloop Feedback (and Feed-Forward) System

7.5 High-Order Filters Using Operational Transconductance Amplifiers

7.6 High-Order Filters Using Switched-Capacitor (SC) Networks

Practice Problems

Chapter 8: Current-Mode Filters

8.1 Basic Operations in Current-Mode

8.2 Current Conveyors in Current-Mode Signal Processing

8.3 Current-Mode Filters Derived from Voltage-Mode Structures

8.4 Transformation of a VM Circuit to a CM Circuit Using the Generalized Dual

8.5 Transformation of VM Circuits to CM Circuits Using Transposition

8.6 Derivation of CTF Structures Employing Infinite-Gain Single-Ended OAs

8.7 Switched-Current Techniques

8.8 Switched-Current Filters

Practice Problems

Chapter 9: Implementation of Analog Integrated Circuit Filters

9.1 Active Devices for Analog IC Filters

9.2 Passive Devices for IC Filters

9.3 Preferred Architecture for IC Filters

9.4 Examples of Integrated Circuit Filters

Practice Problems

Appendices

Appendix A

A.1 Denominator Polynomial D(s) for the Butterworth Filter Function of Order n, with Passband from 0 to 1 rad s−1

A.2 Denominator Polynomial D(s) for the Chebyshev Filter Function of Order n, with Passband from 0 to 1 rad s−1

A.3 Denominator Polynomial D(s) for the Bessel Thomson Filter Function of Order n

A.4 Transfer Functions for Several Second-, Third-, and Fourth-Order Elliptic Filters

Appendix B

B.1 Bessel Thomson Filter Magnitude Error Calculations (MATLAB Program)

B.2 Bessel Thomson Filter Delay Error Calculations (MATLAB Program)

Appendix C

C.1 Element Values for All-Pole Single-Resistance-Terminated Low-Pass Lossless Ladder Filters

C.2 Element Values for All-Pole Double-Resistance-Terminated Low-Pass Lossless Ladder Filters

C.3 Element Values for Elliptic Double-Resistance-Terminated Low-Pass Lossless Ladder Filters

References

Index

Rabin Raut and M. N. S. Swamy

Modern Analog Filter Analysis and Design

Related Titles

Shenoi, B. A.

Introduction to Digital Signal Processing and Filter Design

2005

ISBN: 978-0-471-46482-2

Madsen, C. K., Zhao, J. H.

Optical Filter Design and Analysis

A Signal Processing Approach

1999

ISBN: 978-0-471-18373-0

The Authors

Dr. Rabin RautConcordia UniversityElectrical and Computer EngineeringMontreal, [email protected]

Dr. M.N.S. SwamyConcordia UniversityElectrical and Computer EngineeringMontreal, [email protected]

CoverSpieszdesign, Neu-Ulm, Germany

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Print ISBN: 978-3-527-40766-8 ePdf ISBN: 978-3-527-63151-3 ePub ISBN: 978-3-527-63235-0 Mobi ISBN: 978-3-527-64048-5

A student acquires a quarter of knowledge from the teacher, a quarter from self study, a quarter from class mates, and the final quarter in course of time.

From Neeti Sara

To

Our parents, teachers, and our wives Sucheta & LeelaandLate Prof. B. B. Bhattacharyya(Ph.D. superv isor of R. Raut andFirst Ph.D. student of M. N. S Swa my)

Preface

Filters, especially analog filters, are employed in many different systems that electrical engineers embark upon to design. Even many signal processing systems that are apparently digital, often contain one or more analog continuous-time filters either internally or as interface with the real-time world, which is analog in nature. This book on analog filters is intended as an intermediate-level text for a senior undergraduate and/or an entry-level graduate class in an electrical/electronic engineering curriculum. The book principally covers the subject of analog active filters with brief introductions to passive filters and integrated circuit filters. In the class of active filters, both continuous-time and sampled-data filters are covered. Further, both voltage-mode and current-mode filters are considered. The book is targeted at students and engineers engaged in signal processing, communications, electronics, controls, and so on.

The book is not intended to be an extensive treatise on the subject of analog filters. The subject of (analog) electrical filters is very vast and numerous authors have written excellent books on this subject in the past. Therefore, the question that naturally arises pertains to the need for yet another book on analog filters.

The subject of analog filters is so fascinating that there is always room to introduce the subject with slightly different orientation, especially one that is directed toward certain class of practitioners in the field of electrical engineering. This book exploits the existing wealth of knowledge to illustrate practical ways to implement an analog filter, both for voltage and current signals. Use of currents for signal processing has been a popular subject during the last two decades, and in this respect the book touches on a modern viewpoint of signal processing, relevant to analog filters. In particular, the concept of transposition and its usefulness in obtaining in a very simple manner a current-mode filter from a voltage-mode filter, or vice versa, is presented for the first time in this book. Even though this concept was developed in 1971 itself, its practical use came only after the advent of IC technology, and hence this concept did not receive much attention in earlier books.

This book has been written with a young practicing engineer in mind. Most of the engineers now have to work between deadline dates and have very little time to plunge into the details of theoretical work to scoop up the practical outcome; namely, the usable device such as the needed filter. Thus, the subject of filters has been introduced in this book in a systematic manner with as much theoretical exposure as is essential to be able to build a filter in question. Ample references have been cited to aid the reader in further exploration of the detailed theoretical matter, if the reader is interested. Most of the theoretical material presented in the book has been immediately illustrated via practical examples of synthesis and design, using modern numerical and circuit simulation tools such as MATLAB and SPICE. These tools are now easily available to an electrical engineer (either a student or a practitioner), so the user of the book will feel very close to the practical world of building the filter at hand.

In the era of computers, building analog filters could involve simple use of several software programs downloaded from the Internet and obtaining the required hardware components for the filter to be designed. The authors, however, expect that there are some inquisitive minds who want to know the why and how behind the working and implementation of the filters. Thus, the book attempts to infuse some understanding of the elegant mathematical methods behind the synthesis of a filter, and ingenious applications of these methods toward the implementation of the filter. The expected background knowledge on the part of the reader of this book is some basics related to circuit theory, electronics, Laplace transform, and z-transform. These topics are covered in most of the modern electrical engineering curricula within the span of the first two years of study.

Although this book is more compact than many other books on analog filters in the market, we still feel that the material in this text book cannot be covered satisfactorily over the span of the usual three-and-a-half month-long session pursued by most academic institutions in the Western world. For a one-term undergraduate course, material in Chapters 2–6 can be taught at a reasonable pace. Similarly, for a graduate class over a similar term, Chapters 5–9 may be covered. It is expected that a graduate student would be able to learn the materials in Chapters 2–4 by himself/herself, or that he/she has the required background earned previously from an undergraduate course in analog filters. In those schools where a two-semester course is available at the undergraduate level, the material in the whole book can be easily covered in detail.

Plenty of exercise problems have been added at the end of each chapter. The problems are carefully coordinated with the subject matter dealt with in the body of the pertinent chapter. These could be used by the students to profitably enhance their understanding of the subject. Some of the more challenging problems could be assigned as projects, by the instructor. The authors strongly feel that a course given by using this text book must be accompanied by one or more projects, so that the student develops the practical skill involved in designing and implementing an analog filter.

The authors wish to gratefully acknowledge the contributions made by numerous students upon whom the material has been tested over the past several years of teaching at Concordia University. The authors would like to thank their respective wives, Sucheta and Leela, for their patience and understanding during the course of writing this book. They also sincerely extend their thanks to Anja Tschörtner for her patience and cooperation while waiting for the final manuscript.

Montreal, CanadaJanuary 2010

R. RautM. N. S. Swamy

Abbreviations

APall-passBDIbackward digital integratorBJTbipolar junction transistorBLIbilinear integratorBLTbilinear transformationBPband-passBRband-rejectBSband-stopBTBessel-ThomsonCAcurrent amplifierCCcurrent conveyorCCCII+controlled CCII+CCCScurrent controlled current sourceCCEcharge conservation equationCCIIcurrent-conveyor type 2CCII−negative CCIICCII+positive CCIICCVScurrent controlled voltage sourceCDAcomposite delay and addCDTAcurrent differencing TCACHEBChebyshevCMcurrent modeCMOScomplementary MOSCMRRcommon-mode rejection ratioCNICcurrent-inversion type NICCOAcurrent operational amplifierCTFcurrent transfer functionDA-1delay and add type 1DA-2delay and add type 2dBdeci-belDCdirect currentDDCCIIdual differential CCIIDIOTAdifferential-input OTADISOdual input single outputDISO-OTAdifferential-input single-output OTADOCCIIdual output CCIIDPAdriving point admittanceDPIdriving point impedanceDSPdigital signal processingELLIPellipticFDCCIIfully differential CCIIFDIforward digital integratorFDNRfrequency dependent negative resistanceFIRfinite impulse responseFLFfollow the leader feedbackGDgeneralized dualGDTgeneralized dual transposeGICgeneralized immittance converterGSMglobal system mobile (communication)HPhigh-passIAMindefinite admittance matrixICintegrated circuit(s)ICHEBinverse ChebyshevIFintermediate frequencyIFLFinverse FLFIGMFBinfinite gain multiple feedbackIIimpedance inverterKCLKirchoff’s current lawKHNKerwin, Huelsman, NewcombLDIlossless digital integratorLHleft-halfLHPleft-half planeLPlow-passLTIlinear time invariantMFMmaximally flat magnitudeMISOmulti-input single outputMLFmultiloop feedbackMOSmetal-oxide semiconductorMOSFETMOS field effect transistorMOS-RMOSFET resistorMSFmodified shifted companion feedbackNAMnodal admittance matrixNICnegative immittance converterNIInegative impedance inverterNMOSN-type MOSFETOAoperational amplifierOTAoperational transconductance amplifierOTA-COTA-capacitorOTRAoperational transresistance amplifierPBpass-bandPCMpulse code modulationPIparasitic insensitivePICpositive immittance converterPIIpositive impedance inverterPMOSP-type MOSFETPRBprimary resonator blockPSRRpower supply rejection ratioRHSright-hand sideSAAsystolic array architectureSABsingle amplifier biquadSBstop-bandSCswitched capacitorSCFshifted companion feedbackSFGsignal flow graphSIswitched currentSIDOsingle input dual outputSIMOsingle input multi outputSKSallen & KeyTAFtransadmittance functionTBtransition-bandTCAtransconductance amplifierTFtransfer functionTIFtransimpedanace functionTSCtoggle-SCTTTow-ThomasUCNICunity gain CNICUGAunity gain amplifierUVNICunity gain VNICVAvoltage amplifierVCCSvoltage controlled current sourceVCVSvoltage controlled voltage sourceVLSIvery large scale integrated circuit/systemVMvoltage modeVNICvoltage inversion-type NICVTFvoltage transfer function

Chapter 1

Introduction

Electrical filters permeate modern electronic systems so much that it is imperative for an electronic circuit or system designer to have at least some basic understanding of these filters. The electronic systems that employ filtering process are varied, such as communications, radar, consumer electronics, military, medical instrumentation, and space exploration. An electrical filter is a network that transforms an electrical signal applied to its input such that the signal at the output has specified characteristics, which may be stated in the frequency or the time domain, depending upon the application. Thus, in some cases the filter exhibits a frequency-selective property, such as passing some frequency components in the input signal, while rejecting (stopping) signals at other frequencies.

The developments of filters started around 1915 with the advent of the electric wave filter by Campbell and Wagner, in connection with telephone communication. The early design advanced by Campbell, Zobel, and others made use of passive lumped elements, namely, resistors, inductors, and capacitors, and was based on image parameters (see for example, Ruston and Bordogna, 1971). This is known as the classical filter theory and it yields reasonably good filters without very sophisticated mathematical techniques.

Modern filter theory owes its origin to Cauer, Darlington, and others, and the development of the theory started in the 1930s. Major advancements in filter theory took place in the 1930s and 1940s. However, the filters were still passive structures using R, L, and C elements. One of the most important applications of passive filters has been in the design of channel bank filters in frequency division multiplex telephone systems.

Introduction of silicon integrated circuit (IC) technology together with the development of operational amplifiers (OAs) shifted the focus of filter designers in the 1960s to realize inductorless filters for low-frequency (voice band 300–3400 Hz) applications. Thus ensued the era of active-RC filters, with OA being the active element. With computer-controlled laser trimming, the values of the resistances in thick and thin film technologies could be controlled accurately and this led to widespread use of such low-frequency (up to about 4 kHz) active-RC filters in the pulse code modulation (PCM) system in telephonic communication.

Owing to the difficulty in fabricating large-valued resistors in the same process as the OA, low-frequency filters could not be built as monolithic devices. However, the observation that certain configurations of capacitors and periodically operated switches could function approximately as resistors led to the introduction of completely monolithic low-frequency filters. The advent of complementary metal-oxide semiconductor (CMOS) transistors facilitated this alternative with monolithic capacitors, CMOS OAs, and CMOS transistor switches. The switched-capacitor (SC) filters were soon recognized as being in the class of sampled-data filters, since the switching introduced sampling of the signals. In contrast, the active-RC filters are in the category of continuous-time filters, since the signal processed could theoretically take on any possible value at a given time. In the SC technique, signal voltages sampled and held on capacitors are processed via voltage amplifiers and integrators. Following the SC filters, researchers soon invented the complementary technique where current signals sampled and transferred on to parasitic capacitances at the terminals of metal-oxide semiconductor (MOS) transistors could be processed further via current mirrors and dynamic memory storage (to produce the effect of integration). This led to switched-current (SI) filtering techniques, which have become popular in all-digital CMOS technology, where no capacitors are needed for the filtering process.

In recent times, several microelectronic technologies (such as Bipolar, CMOS, and BiCMOS), filter architectures, and design techniques have emerged leading to high-quality fully integrated active filters. Moreover, sophisticated digital and analog functions (including filtering) can coexist on the same very large-scale integrated (VLSI) circuit chip. An example of the existence of several integrated active filters in a VLSI chip is illustrated in Figure 1.1. This depicts the floor plan of a typical PCM codec chip (Laker and Sansen, 1994).

Figure 1.1 A typical VLSI analog/digital system floor plan.

Together with the progress in semiconductor technology, new types of semiconductor amplifiers, such as the operational transconductance amplifier (OTA), and current conveyor (CC) became realizable in the late 1970s and onwards. This opened up the possibility for implementation of high-frequency filters (50 kHz to ∼300 MHz) in monolithic IC technology. An OTA can be conveniently configured to produce the function of a resistor and an inductor, so that usual high-frequency passive LCR filters can be easily replaced by suitable combinations of monolithic OTAs and capacitors leading to operational transconductance amplifier capacitor (OTA-C) (or gm − C) filters. Introduction of CCs in the 1990s encouraged researchers to investigate signal processing in terms of signal currents rather than signal voltages. This initiated activities in the area of current-mode (CM) signal processing and hence CM filtering, even though the idea of realizing current transfer functions goes back to the late 1950s and the 1960s (Thomas, 1959; Hakim, 1965; Bobrow, 1965; Mitra, 1967; Daggett and Vlach, 1969). In fact, a very simple and direct method of obtaining a current transfer function realization from that of a voltage transfer function employing the concept of transposition was advanced as early as 1971 by Bhattacharyya and Swamy (1971). Since for CM signal processing, the impedances at the input and output ports are supposed to be very low, the attendant bandwidth can be very large. Modern CMOS devices can operate at very low voltages (around 1 V direct current (DC)) with small currents (0.1 mA or less). Thus, CM signal processing using CMOS technology entails low-voltage high-frequency operation. The intermediate frequency (IF) (fo±100 MHz) filter in a modern mobile communication (global system mobile, GSM) system has typical specifications as presented in Table 1.1. The required filters can be implemented as monolithic IC filters in the CM, using several CC building blocks and integrated capacitors.

Table 1.1 Magnitude Response Characteristics of an IF Filter.

Considering applications in ultra wideband (∼10–30 GHz) communication systems, monolithic inductors (∼1–10 nH) can be conveniently realized in modern submicron CMOS technology. Thus, passive LCR filter structures can be utilized for completely monolithic very wideband electronic filters. Advances in IC technology have also led to the introduction of several kinds of digital ICs. These could be used to process an analog signal after sampling and quantization. This has led to digital techniques for implementing an electronic filter (i.e., digital filters), and the area falls under the general category of digital signal processing (DSP).

As the subject of electrical/electronic filter is quite mature, there are a large number of books on this subject contributed by many eminent teachers and researchers. The current book is presented with a practical consideration, namely, that with the advent of computers and the abundance of computer-oriented courses in the electrical engineering curricula, there is insufficient time for a very exhaustive book on analog filters to be used for teaching over the span of one semester or two quarters. The present book is, therefore, relatively concise and is dedicated to current concepts and techniques that are basic and essential to acquire a good initial grasp of the subject of analog filters. Recognizing the popularity of courses that are amenable to the use of computer-aided tools, many circuit analysis (i.e., SPICE) and numerical simulation (i.e., MATLAB) program codes are provided in the body of the book to reinforce computer-aided design and analysis skills. The present book is very close to the practical need of a text book that can be covered over the limited span of time that present-day electrical engineering curricula in different academic institutions in the world can afford to the subject of analog filters. Toward this, the subject matter is presented through several chapters as follows.

Chapter 2 presents a review of several network analysis methods, such as the nodal, loop, and indefinite matrix techniques, as well as a method for analyzing constrained networks. One- and two-port networks are defined and various methods of representing a two-port and the interrelationships between the parameters representing a two-port are also detailed. The analysis methods are illustrated by considering several examples from known filter networks.

Chapter 3 introduces several concepts such as impedance and frequency scaling, impedance transformation, dual (and inverse) two-port networks, reversed two-ports, and transposed networks. Some useful network theorems concerning dual two-ports and transposed two-ports are established, and their applications to singly and doubly terminated networks are considered. Also, the transposes of commonly used active elements are given. Various approximation techniques for both the magnitude and phase of a filter transfer function, as well as frequency transformations to transform a low-pass filter to a high-pass, band-pass, or band-reject filter are also presented in this chapter. Several MATLAB simulation codes are presented.

Chapter 4 presents passive filter realization using singly terminated as well as doubly terminated LC ladder structures. Synthesis of all-pole transfer functions using such ladders is considered in detail.

Chapter 5 introduces the subject of designing second-order filters with active devices and RC elements. The active devices employed are the OAs and the OTAs. Both the single-amplifier and multiamplifier designs are presented. The sensitivity aspect is also discussed. The chapter concludes with a brief introduction to the devices and passive elements that are available in typical microelectronic manufacturing environments. The objective is to provide a modest orientation to the designers of active-RC filters toward IC filter implementation.

Chapter 6 deals with the subject of SC filters. The concept of the equivalence of R and the classical switched-C is refined by introducing the notion of sampled-data sequence and z-transformed equations. Parasitic-insensitive second-order filters are discussed. Filters based on unity-gain buffer amplifiers are also presented. Techniques to utilize the common continuous-time circuit elements (i.e., transmission lines) to simulate the operation of an SC network are introduced. The principles are illustrated using SPICE simulation.

High-order filter realization using active devices and RC elements is presented in Chapter 7. The knowledge base developed through Chapters 3–6 is now integrated to illustrate several well-known techniques for high-order active filter implementation. Inductance simulation, frequency-dependent negative resistance technique, operational simulation, cascade method, and multiloop feedback methods are discussed. Implementations of high-order continuous-time filters using OAs and OTAs, as well as SC high-order filters using OAs are illustrated.

Chapter 8 deals with the subject matter of CM filters. This technique of filtering has been of considerable interest to researchers in the past two decades. The basic difference between, voltage-mode (VM) and CM transfer functions is highlighted and several active devices that can process current signals introduced. Derivation of CM filter structures from a given VM filter structure using the principles of dual networks and network transposition, are illustrated. In particular, the usefulness of the transposition operation in obtaining, in a very simple manner, a CM realization for a given VM realization (or vice versa) is brought out through a number of examples. Implementations of CM transfer functions using OAs, OTAs, and CCs are presented. SI filtering technique is also introduced in this chapter.

Chapter 9 introduces the concepts and techniques relevant to implementation of IC continuous-time filters. The cases of linear resistance simulation using MOS transistors, and integrator implementation using differential architecture are illustrated. Second-order integrated filter implementations using OAs and OTAs are considered. The chapter ends with two design examples for IC implementation: (i) a low-voltage differential wideband OTA-C filter in CMOS technology and (ii) an approach toward an IF filter for a modern mobile communication (GSM) handset.

The book ends with three appendices that contain several tables for the approximation of filter functions, as well as for implementation of the filter functions using LCR elements. It is expected that once the filter transfer function is known, or the specific LCR values for a high-order filter are known, the designer can use the knowledge disseminated throughout the book to implement the required filter using either discrete RC elements and active devices, or using the devices available in a given IC technology. A MATLAB program for deriving the design curves for Bessel–Thomson (BT) filters up to order 15 is also included.