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The art of_electronics The art of_electronics Document Transcript

  • The Art Of Electronics - 2nd EditionPaul Horowitz UNlvERSITyWinfield Hill ROWLANDINSTITUTEFOR SCIENCE. CAMBRIDGE, MASSACHUSETTSCAMBRIDGEUNIVERSITY PRESS
  • Published by the Press Syndicate of the Universityof CambridgeThe Pitt Building, Trumpington Street, Cambridge CB2 IRP40 West 20th Street, New York, NY 10011-4211, USA10 Stanlford Road, Oakleigh, Melbourne3166, AustraliaO Cambridge University Press 1980, 1989First published1980Second edition 1989Reprinted 1990 (twice), 1991, 1993, 1994Printed in the United States of AmericaLibrary of Cotlgress C(lrn1oguit~g-111-PublicationData is available.A ccltc[loguerecord for this book is ailabl ablefrom the Britislr Librcln~.ISBN 0-521-37095-7 hardback
  • ContentsList of tables xviPreface xixPreface to first edition xxiCHAPTER 1FOUNDATIONS 1lntroduction 1Voltage, current, and resistance 21.O1 Voltage and current 21.02 Relationship between voltage andcurrent: resistors 41.03 Voltage dividers 81.04 Voltage and current sources 91.05 Thevenins equivalent circuit 111.06 Small-signal resistance 13Signals 151.07 Sinusoidal signals 151.08 Signal amplitudes anddecibels 161.09 Other signals 171.10 Logic levels 191.11 Signal sources 19Capacitors and ac circuits 201.12 Capacitors 201.13 RC circuits: V and I versustime 231.14 Differentiators 251.15 Integrators 26Inductors and transformers 281.16 Inductors 281.17 Transformers 28Impedance and reactance 291.18 Frequency analysis of reactivecircuits 301.19 Refilters 351.20 Phasor diagrams 391.21 "Poles" and decibels peroctave 401.22 Resonant circuits and activefilters 411.23 Other capacitor applications 421.24 ThCvenins theoremgeneralized 44Diodes and diode circuits 441.25 Diodes 441.26 Rectification 441.27 Power-supply filtering 451.28 Rectifier configurations for powersupplies 461.29 Regulators 481.30 Circuit applications of diodes 481.31 Inductive loads and diodeprotection 52Other passive components 531.32 Electromechanical devices 531.33 Indicators 571.34 Variable components 57Additional exercises 58CHAPTER 2TRANSISTORS 61Introduction 612.01 First transistor model: currentamplifier 62Some basic transistor circuits 632.02 Transistor switch 632.03 Emitter follower 65vii
  • viii CONTENTS2.04 Emitter followers as voltageregulators 682.05 Emitter follower biasing 692.06 Transistor current source 722.07 Common-emitter amplifier 762.08 Unity-gain phase splitter 772.09 Transconductance 78Ebers-Moll model applied to basictransistor circuits 7910 Improved transistor model:transconductance amplifier 7911 The emitter follower revisited 812.12 The common-emitter amplifierrevisited 822.13 Biasing the common-emitteramplifier 842.14 Current mirrors 88Some amplifier building blocks 912.15 Push-pull output stages 912.16 Darlington connection 942.17 Bootstrapping 962.18 Differential amplifiers 982.19 Capacitance and Miller effect 1022.20 Field-effect transistors 104Some typical transistor circuits 1042.21 Regulated power supply 1042.22 Temperature controller 1052.23 Simple logic with transistors anddiodes 107Self-explanatory circuits 1072.24 Good circuits 1072.25 Bad circuits 107Additional exercises 107CHAPTER 3FIELD-EFFECT TRANSISTORS 113lntroduction 1133.01 FET characteristics 1143.02 FET types 1173.03 Universal FET characteristics 1193.04 FET drain characteristics 1213.05 Manufacturing spread of FETcharacteristics 122Basic FET circuits 1243.06 JFET current sources 1253.07 FET amplifiers 1293.08 Source followers 1333.09 FET gate current 1353.10 FETs as variable resistors 138FET switches 1403.11 FET analog switches 1413.12 Limitations of FET switches 1443.13 Some FET analog switchexamples 1513.14 MOSFET logic and powerswitches 1533.15 MOSFET handlingprecautions 169Self-explanatory circuits 1713.16 Circuit ideas 1713.17 Bad circuits 171 vskip6ptCHAPTER 4FEEDBACK AND OPERATIONALAMPLIFIERS 175lntroduction 1754.01 Introduction to feedback 1754.02 Operational amplifiers 1764.03 The golden rules 177Basic op-amp circuits 1774.04 Inverting amplifier 1774.05 Noninverting amplifier 1784.06 Follower 1794.07 Current sources 1804.08 Basic cautions for op-ampcircuits 182An op-amp smorgasbord 1834.09 Linear circuits 1834.10 Nonlinear circuits 187A detailed look at op-amp behavior 1884.11 Departure from ideal op-ampperformance 1894.12 Effects of op-amp limitations oncircuit behavior 1934.13 Low-power and programmableop-amps 210
  • CONTENTS ixA detailed look at selected op-ampcircuits 2134.14 Logarithmic amplifier 2134.15 Active peak detector 2174.16 Sample-and-hold 2204.17 Active clamp 2214.18 Absolute-value circuit 2214.19 Integrators 2224.20 Differentiators 224Op-amp operation with a single powersupply 2244.2 1 Biasing single-supply acamplifiers 2254.22 Single-supply op-amps 225Comparators and Schmitt trigger 2294.23 Comparators 2294.24 Schmitt trigger 231Feedback with finite-gain amplifiers2324.25 Gain equation 2324.26 Effects of feedback on amplifiercircuits 2334.27 Two examples of transistoramplifiers with feedback 236Some typical op-amp circuits 2384.28 General-purpose lab amplifier 2384.29 Voltage-controlled oscillator 2404.30 JFET linear switch with RoNcompensation 2414.31 TTL zero-crossing detector 2424.32 Load-current-sensing circuit 242Feedback amplifier frequencycompensation 2424.33 Gain and phase shift versusfrequency 2434.34 Amplifier compensationmethods 2454.35 Frequency response of the feedbacknetwork 2474.37 Bad circuits 250Additional exercises 251CHAPTER 5ACTIVE FILTERS ANDOSCILLATORS 263Active filters 2635.01 Frequency response with RCfilters 2635.02 Ideal performance with LCfilters 2655.03 Enter active filters: anoverview 2665.04 Key filter performancecriteria 2675.05 Filter types 268Active filter circuits 2725.06 VCVS circuits 2735.07 VCVS filter design using oursimplified table 2745.08 State-variable filters 2765.09 Twin-T notch filters 2795.10 Gyrator filter realizations 2815.1 1 Switched-capacitor filters 281Oscillators 2845.12 Introduction to oscillators 2845.13 Relaxation oscillators 2845.14 The classic timer chip:the 555 2865.15 Voltage-controlled oscillators 2915.16 Quadrature oscillators 2915.17 Wien bridge and LCoscillators 2965.18 LC oscillators 2975.19 Quartz-crystal oscillators 300Self-explanatory circuits 3035.20 Circuit ideas 303Additional exercises 303CHAPTER 6VOLTAGE REGULATORS AND POWERCIRCUITS 307Self-explanatory circuits 250 Basic regulator circuits with the4.36 Circuit ideas 250 classic 723 307
  • x CONTENTS6.01 The 723 regulator 307 CHAPTER 76.02 Positive regulator 309 PRECISION CIRCUITS AND LOW-NOISE6.03 High-current regulator 311 TECHNIQUES 391Heat and power design 3126.04 Power transistors and heatsinking 3126.05 Foldback current limiting 3166.06 Overvoltage crowbars 3176.07 Further considerations in high-current power-supply design 3206.08 Programmable supplies 3216.09 Power-supply circuit example 3236.10 Other regulator ICs 325Precision op-amp design techniques391Precision versus dynamicrange 391Error budget 392Example circuit: precisionwith automatic null offsetA precision-design errorbudget 394Component errors 395amplifier392The unregulated supply 325 7.06 Amplifier input errors 3966.11 ac line components 3267.07 Amplifier output errors 4036.12 Transformer 328 7.08 Auto-zeroing(chopper-stabilized)6.13 dc components 329 amplifiers 415Voltage references 3316.14 Zener diodes 3326.15 Bandgap (VBE)reference 335Three-terminal and four-terminalregulators 3416.16 Three-terminal regulators 3416.17 Three-terminal adjustableregulators 3446.18 Additional comments about3-terminal regulators 3456.19 Switching regulators and dc-dcconverters 355Special-purpose power-supplycircuits 3686.20 High-voltage regulators 3686.21 Low-noise, low-drift supplies 3746.22 Micropower regulators 3766.23 Flying-capacitor (charge pump)voltage converters 3776.24 Constant-current supplies 3796.25 Commercial power-supplymodules 382Self-explanatory circuits 3846.26 Circuit ideas 3846.27 Bad circuits 384Additional exercises 384Differentialand instrumentationamplifiers 4217.09 Differencing amplifier 4217.10 Standard three-op-ampinstrumentation amplifier 425Amplifier noise 4287.11 Origins and kinds of noise 4307.12 Signal-to-noise ratio and noisefigure 4337.13 Transistor amplifier voltage andcurrent noise 4367.14 Low-noise design withtransistors 4387.15 FET noise 4437.16 Selecting low-noise transistors 4457.17 Noise in differential and feedbackamplifiers 445Noise measurements and noisesources 4497.18 Measurement without a noisesource 4497.19 Measurement with noisesource 4507.20 Noise and signal sources 4527.21 Bandwidth limiting and rms voltagemeasurement 4537.22 Noise potpourri 454
  • CONTENTS xiInterference: shielding andgrounding 4557.23 Interference 4557.24 Signal grounds 4577.25 Grounding betweeninstruments 457Self-explanatory circuits 4667.26 Circuit ideas 466Additional exercises 466CHAPTER 8DIGITAL ELECTRONICS 471Basic logic concepts 4718.01 Digital versus analog 4718.02 Logic states 4728.03 Number codes 4738.04 Gates and truth tables 4788.05 Discrete circuits for gates 4808.06 Gate circuit example 4818.07 Assertion-levellogic notation 482TTL and CMOS 4848.08 Catalog of common gates 4848.09 IC gate circuits 4858.10 TTL and CMOScharacteristics 4868.11 Three-state and open-collectordevices 487Combinational logic 4908.12 Logic identities 4918.13 Minimization and Karnaughmaps 4928.14 Combinational functions availableas ICs 4938.15 Implementing arbitrary truthtables 500Sequential logic 5048.16 Devices with memory: flip-flops 5048.17 Clocked flip-flops 5078.18 Combining memory and gates:sequential logic 5128.19 Synchronizer 515Monostable multivibrators 5178.20 One-shot characteristics 5178.21 Monostable circuit example 5198.22 Cautionary notes aboutmonostables 5198.23 Timing with counters 522Sequential functions available asICs 5238.24 Latches and registers 5238.25 Counters 5248.26 Shift registers 5258.27 Sequential PALS 5278.28 Miscellaneous sequentialfunctions 541Some typical digital circuits 5448.29 Modulo-n counter: a timingexample 5448.30 Multiplexed LED digitaldisplay 5468.31 Sidereal telescope drive 5488.32 An n-pulse generator 548Logic pathology 5518.33 dc problems 5518.34 Switching problems 5528.35 Congenital weaknesses of TTL andCMOS 554Self-explanatorycircuits 5568.36 Circuit ideas 5568.37 Bad circuits 556Additional exercises 556CHAPTER 9DIGITAL MEETS ANALOG 565CMOS and TTL logic interfacing 5659.01 Logic family chronology 5659.02 Input and outputcharacteristics 5709.03 Interfacing between logicfamilies 5729.04 Driving CMOS amd TTLinputs 5759.05 Driving digital logic fromcomparators and op-amps 577
  • xii CONTENTS9.06 Some comments about logicinputs 5799.07 Comparators 5809.08 Driving external digital loads fromCMOS and TTL 5829.09 NMOS LSI interfacing 5889.10 Opto-electronics 590Digital signals and long wires 5999.1 1 On-board interconnections 5999.12 Intercard connections 6019.13 Data buses 6029.14 Driving cables 603Analogldigital conversion 6129.15 Introduction to A/Dconversion 6129.16 Digital-to-analog converters(DACs) 6149.17 Time-domain (averaging)DACs 6189.18 Multiplying DACs 6199.19 Choosing a DAC 6199.20 Analog-to-digitalconverters 6219.21 Charge-balancing techniques 6269.22 Some unusual AID and DIAconverters 6309.23 Choosing an ADC 631Some AID conversion examples 6369.24 16-Channel AID data-acquisitionsystem 6369.25 3 + - ~ i ~ i tvoltmeter 6389.26 Coulomb meter 640Phase-locked loops 6419.27 Introduction to phase-lockedloops 6419.28 PLL design 6469.29 Design example: frequencymultiplier 6479.30 PLL capture and lock 6519.31 Some PLL applications 652Pseudo-random bit sequences and noisegeneration 6559.32 Digital noise generation 6559.33 Feedback shift registersequences 6559.34 Analog noise generation frommaximal-length sequences 6589.35 Power spectrum of shift registersequences 6589.36 Low-pass filtering 6609.37 Wrap-up 6619.38 Digital filters 664Self-explanatorycircuits 6679.39 Circuit ideas 6679.40 Bad circuits 668Additional exercises 668CHAPTER 10MICROCOMPUTERS 673Minicomputers, microcomputers, andmicroprocessors 67310.01 Computer architecture 674A computer instruction set 67810.02 Assembly language and machinelanguage 67810.03 Simplified 808618 instructionset 67910.04 A programming example 683Bus signals and interfacing 68410.05 Fundamental bus signals: data,address, strobe 68410.06 Programmed 110: data out 68510.07 Programmed I/O: data in 68910.08 Programmed 110: statusregisters 69010.09 Interrupts 69310.10 Interrupt handling 69510.11 Interrupts in general 69710.12 Direct memory access 70110.13 Summary of the IBM PCs bussignals 70410.14 Synchronous versus asynchronousbus communication 70710.15 Other microcomputer buses 70810.16 Connecting peripherals to thecomputer 711
  • CONTENTS xiiiSoftware system concepts 71410.17 Programming 71410.18 Operating systems, files, and use ofmemory 716Data communications concepts 71910.19 Serial communication andASCII 72010.20 Parallel communication:Centronics, SCSI, IPI,GPIB (488) 73010.21 Local area networks 73410.22 Interface example: hardware datapacking 73610.23 Number formats 738CHAPTER 11MICROPROCESSORS 743A detailed look at the 68008 74411.O1 Registers, memory, and I/O 74411.02 Instruction set andaddressing 74511.03 Machine-languagerepresentation 75011.04 Bus signals 753A complete design example: analogsignal averager 76011.05 Circuit design 76011.06 Programming: defining thetask 77411.07 Programming: details 77711.08 Performance 79611.09 Some afterthoughts 797Microprocessor support chips 79911.10 Medium-scale integration 80011.11 Peripheral LSI chips 80211.12 Memory 81211.13 Other microprocessors 820CHAPTER 12ELECTRONIC CONSTRUCTIONTECHNIQUES 827Prototyping methods 82712.01 Breadboards 82712.02 PC prototyping boards 82812.03 Wire-Wrap panels 828Printed circuits 83012.04 PC board fabrication 83012.05 PCboarddesign 83512.06 StuffingPC boards 83812.07 Some further thoughts on PCboards 84012.08 Advanced techniques 841Instrument construction 85212.09 Housing circuit boards in aninstrument 85212.10 Cabinets 85412.11 Construction hints 85512.12 Cooling 85512.13 Some electrical hints 85812.14 Where to get components 860CHAPTER 13HIGH-FREQUENCY AND HIGH-SPEEDTECHNIQUES 863High-frequency amplifiers 86313.01 Transistor amplifiers at highfrequencies: first look 86313.02 High-frequency amplifiers: the acmodel 86413.03 A high-frequency calculationexample 86613.04 High-frequency amplifierconfigurations 86813.05 A wideband design example 86913.06 Some refinements to the acmodel 87213.07 The shunt-series pair 87213.08 Modular amplifiers 873systems, Radiofrequencycircuit elements 879logic analyzers, and evaluationboards 821 13.09 Transmission lines 879
  • xiv CONTENTS13.10 Stubs, baluns, andtransformers 88113.11 Tuned amplifiers 88213.12 Radiofrequency circuitelements 88413.13 Measuring amplitude orpower 888Radiofrequency communications:AM 89213.14 Some communicationsconcepts 89213.15 Amplitude modulation 89413.16 Superheterodyne receiver 895Advanced modulation methods 89713.17 Single sideband 89713.18 Frequency modulation 89813.19 Frequency-shift keying 90013.20 Pulse-modulation schemes 900Radiofrequency circuit tricks 90213.21 Special constructiontechniques 90213.22 Exotic RF amplifiers anddevices 903High-speed switching 90413.23 Transistor model andequations 90513.24 Analog modeling tools 908Some switching-speed examples 90913.25 High-voltage driver 90913.26 Open-collector bus driver 91013.27 Example: photomultiplierpreamp 911Self-explanatory circuits 91313.28 Circuit ideas 913Additional exercises 913CHAPTER 14LOW-POWER DESIGN 917Introduction 91714.01 Low-power applications 918Power sources 92014.02 Battery types 92014.03 Wall-plug-in units 93114.04 Solar cells 93214.05 Signal currents 933Power switching and micropowerregulators 93814.06 Power switching 93814.07 Micropower regulators 94114.08 Ground reference 94414.09 Micropower voltage references andtemperature sensors 948Linear micropower designtechniques 94814.10 Problems of micropower lineardesign 95014.11 Discrete linear designexample 95014.12 Micropower operationalamplifiers 95114.13 Micropower comparators 96514.14 Micropower timers andoscillators 965Micropower digital design 96914.15 CMOS families 96914.16 Keeping CMOS low power 97014.17 Micropower microprocessors andperipherals 97414.18 Microprocessor design example:degree-day logger 978Self-explanatory circuits 98514.19 Circuit ideas 985CHAPTER 15MEASUREMENTS AND SIGNALPROCESSING 987Overview 987Measurement transducers 98815.01 Temperature 98815.02 Light level 99615.03 Strain and displacement 1001
  • CONTENTS xv15.04 Acceleration, pressure, force,velocity 100415.05 Magnetic field 100715.06 Vacuum gauges 100715.07 Particle detectors 100815.08 Biological and chemical voltageprobes 1012Precision standards and precisionmeasurements 101615.09 Frequency standards 101615.10 Frequency, period, and time-interval measurements 101915.1 1 Voltage and resistance standardsand measurements 1025Bandwidth-narrowing techniques 102615.12 The problem of signal-to-noiseratio 102615.13 Signal averaging and multichannelaveraging 102615.14 Making a signal periodic 103015.15 Lock-in detection 103115.16 Pulse-height analysis 103415.17 Time-to-amplitude converters1035Spectrum analysis and Fouriertransforms 103515.18 Spectrum analyzers 103515.19 Off-line spectrum analysis 1038Self-explanatory circuits 103815.20 Circuit ideas 1038APPENDIXES 1043Appendix AThe oscilloscope 1045Appendix BMath review 1050Appendix CThe 5%resistor color code 1053Appendix D1%Precision resistors 1054Appendix EHow to draw schematic diagrams 1056Appendix FLoad lines 1059Appendix GTransistor saturation 1062Appendix HLC Butterworth filters 1064Appendix IElectronics magazines and journals1068Appendix JIC prefixes 1069Appendix KData sheets 10722N4400-1NPN transistor 1073LF41 1-12 JFET operationalamplifier 1078LM317 3-terminal adjustableregulator 1086Bibliography 1095Index 1101
  • Tables7.47.58.18.28.38.4xviDiodes 43Small-signal transistors 109JFETs 125MOSFETs 126Dual matched JFETs 128Current regulator diodes 129Power MOSFETs 164BJT-MOSFET comparison 166Electrostatic voltages 170Operational amplifiers 196Recommended op-amps 208High-voltage op-amps 213Power op-amps 214Time-domain filter comparison273VCVS low-pass filters 274555-type oscillators 289Selected VCOs 293Power transistors 314Transient suppressors 326Power-line filters 327Rectifiers 331Zener and reference diodes 334500mW zeners 334IC voltage references 336Fixed voltage regulators 342Adjustable voltage regulators346Dual-tracking regulators 352Seven precision op-amps 401Precision op-amps 404High-speed precision op-amps412Fast buffers 418Instrumentation amplifiers 4294-bit integers 477TTL and CMOS gates 484Logic identities 491Buffers 560Transceivers 560Decoders 561Magnitude comparators 561Monostable multivibrators 562D-registers and latches 562Counters 563Shift registers 564Logic family characteristics 570Allowed connections between logicfamilies 574Comparators 584DIA converters 620AID converters 632Integrating AID converters 634IBM PC bus 704Computer buses 709ASCII codes 721RS-232 signals 724Serial data standards 727Centronics (printer) signals 7306800018 instruction set 746Allowable addressing modes 7486800018 addressing modes 74968008 bus signals 7536800018 vectors 788Zilog 8530 registers 804Zilog 8530 serial port initialization806Microprocessors 822PC graphic patterns 839Venturi fans 858RF transistors 877Wideband op-amps 878Primary batteries 922Battery characteristics 923Primary-battery attributes 930
  • TABLES xvii14.4 Low-power regulators 942 14.9 Microprocessor controllers 97614.5 Micropower voltage references 14.10 Temperature logger current drain949 98314.6 Micropower op-amps 956 15.1 Thermocouples 99014.7 Programmable op-amps 958 D.1 Selected resistor types 105514.8 Low-power comparators 966 H.1 Butterworth low-pass filters 1064
  • Ch2: TransistorsINTRODUCTIONThe transistor is our most important ex-ample of an "active" component, a devicethat can amplify, producing an output sig-nal with more power in it than the inputsignal. The additional power comes froman external source of power (the powersupply, to be exact). Note that voltage am-plification isnt what matters, since, for ex-ample, a step-up transformer, a "passive"component just like a resistor or capaci-tor, has voltage gain but no power gain.Devices with power gain are distinguish-able by their ability to make oscillators, byfeeding some output signal back into theinput.It is interesting to note that the prop-erty of power amplification seemed veryimportant to the inventors of the transis-tor. Almost the first thing they did toconvince themselves that they had reallyinvented something was to power a loud-speaker from a transistor, observing thatthe output signal sounded louder than theinput signal.The transistor is the essential ingredi-ent of every electronic circuit, from thesimplest amplifier or oscillator to the mostelaborate digital computer. Integrated cir-cuits (ICs), which have largely replaced cir-cuits constructed from discrete transistors,are themselves merely arrays of transistorsand other components built from a singlechip of semiconductor material.A good understanding of transistors isvery important, even if most of yourcircuits are made from ICs, because youneed to understand the input and outputproperties of the IC in order to connectit to the rest of your circuit and to theoutside world. In addition, the transistoris the single most powerful resource forinterfacing, whether between ICs and othercircuitry or between one subcircuit andanother. Finally, there are frequent (somemight say too frequent) situations wherethe right IC just doesnt exist, and youhave to rely on discrete transistor circuitryto do the job. As you will see, transistorshave an excitement all their own. Learninghow they work can be great fun.Our treatment of transistors is goingto be quite different from that of manyother books. It is common practice touse the h-parameter model and equivalentt
  • TRANSISTORSi2 Chapter 2circuit. In our opinion that is unnecessar-ily complicated and unintuitive. Not onlydoes circuit behavior tend to be revealed toyou as something that drops out of elabo-rate equations, rather than deriving from aclear understanding in your own mind asto how the circuit functions; you also havethe tendency to lose sight of which param-eters of transistor behavior you can counton and, more important, which ones canvary over large ranges.In this chapter we will build up instead avery simple introductory transistor modeland immediately work out some circuitswith it. Soon its limitations will becomeapparent; then we will expand the modelto include the respected Ebers-Moll con-ventions. With the Ebers-Moll equationsand a simple 3-terminal model, you willhave a good understanding of transistors;you wont need to do a lot of calculations,and your designs will be first-rate. In par-ticular, they will be largely independent ofthe poorly controlled transistor parameterssuch as current gain.Some important engineering notationshould be mentioned. Voltage at a tran-sistor terminal (relative to ground) is in-dicated by a single subscript (C, B, orE): Vc is the collector voltage, for in-stance. Voltage between two terminals isindicated by a double subscript: VBE isthe base-to-emitter voltage drop, for in-stance. If the same letter is repeated, thatmeans a power-supply voltage: Vcc is the(positive) power-supply voltage associatedwith the collector, and VEE is the (neg-ative) supply voltage associated with theemitter.2.01 First transistor model: currentamplifierLets begin. A transistor is a 3-terminaldevice (Fig. 2.1) available in 2 flavors (npnand pnp), with properties that meet thefollowing rules for npn transistors (for pnpsimply reverse all polarities):1. The collector must be more positivethan the emitter.2. The base-emitter and base-collectorcircuits behave like diodes (Fig. 2.2).Normally the base-emitter diode is con-ducting and the base-collector diode is re-verse-biased, i.e., the applied voltage isin the opposite direction to easy currentflow.Figure 2.1. Transistor symbols, and smalltransistor packages.Figure 2.2. An ohmmeters view of a transis-tors terminals.3. Any given transistor has maximumvalues of Ic, IB, and VCE that cannotbe exceeded without costing the exceederthe price of a new transistor (for typicalvalues, see Table 2.1). There are also otherlimits, such as power dissipation (revCE),temperature, VBE, etc., that you must keepin mind.4. When rules 1-3 are obeyed, Icis rough-ly proportional to IBand can be written aswhere hFE, the current gain (also calledbeta), is typically about 100. Both Icand IEflow to the emitter. Note: Thecollector current is not due to forwardconduction of the base-collector diode;
  • SOME BASIC TRANSISTOR CIRCUITS2.02 Transistor switch 6:that diode is reverse-biased. Just think ofit as "transistor action."Property 4 gives the transistor its useful-ness: A small current flowing into the basecontrols a much larger current flowing intothe collector.Warning: hFE is not a "good"transistorparameter; for instance, its value can varyfrom 50 to 250 for different specimens of agiven transistor type. It also depends uponthe collector current, collector-to-emittervoltage, and temperature. A circuit thatdepends on a particular value for hFE isa bad circuit.Note particularly the effect of property 2.This means you cant go sticking a voltageacross the base-emitter terminals, becausean enormous current will flow if the baseis more positive than the emitter by morethan about 0.6 to 0.8 volt (forward diodedrop). This rule also implies that an op-erating transistor has VB % VE +0.6 volt(VB = VE + VBE). Again, polarities arenormally given for npn transistors; reversethem for pnp.Let us emphasize again that you shouldnot try to think of the collector currentas diode conduction. It isnt, because thecollector-base diode normally has voltagesapplied across it in the reverse direction.Furthermore, collector current varies verylittle with collector voltage (it behaves likea not-too-great current source), unlike for-ward diode conduction, where the currentrises very rapidly with applied voltage.SOME BASIC TRANSISTOR CIRCUITS2.02 Transistor switchLook at the circuit in Figure 2.3. This ap-plication, in which a small control currentenables a much larger current to flow in an-other circuit, is called a transistor switch.From the preceding rules it is easy to un-derstand. When the mechanical switch isopen, there is no base current. So, from10V 0.1AmechanicalswitchFigure 2.3. Transistor switch example.rule 4, there is no collector current. Thelamp is off.When the switch is closed, the baserises to 0.6 volt (base-emitter diode is inforward conduction). The drop acrossthe base resistor is 9.4 volts, so the basecurrent is 9.4mA. Blind application of rule4 gives Ic = 940mA (for a typical betaof 100). That is wrong. Why? Becauserule 4 holds only if rule 1 is obeyed; at acollector current of lOOmA the lamp has10 volts across it. To get a higher currentyou would have to pull the collector belowground. A transistor cant do this, andthe result is whats called saturation - thecollector goes as close to ground as it can(typical saturation voltagesare about 0.05-0.2V, see Appendix G) and stays there. Inthis case, the lamp goes on, with its rated10 volts across it.Overdriving the base (we used 9.4mAwhen 1.OmA would have barely sufficed)makes the circuit conservative; in thisparticular case it is a good idea, sincea lamp draws more current when cold(the resistance of a lamp when cold is 5to 10 times lower than its resistance atoperating current). Also transistor betadrops at low collector-to-base voltages, sosome extra base current is necessary tobring a transistor into full saturation (seeAppendix G). Incidentally, in a real circuityou would probably put a resistor frombase to ground (perhaps 10k in this case)to make sure the base is at ground withthe switch open. It wouldnt affect the
  • TRANSISTORS64 Chapter 2"on" operation, because it would sink only0.06mA from the base circuit.There are certain cautions to be ob-served when designing transistor switches:1. Choose the base resistor conservativelyto get plenty of excess base current, es-pecially when driving lamps, because ofthe reduced beta at low VCE. This isalso a good idea for high-speed switching,because of capacitive effects and reducedbeta at very high frequencies (many mega-hertz). A small "speedup" capacitor is of-ten connected across the base resistor toimprove high-speed performance.2. If the load swings below ground forsome reason (e.g., it is driven from ac,or it is inductive), use a diode in serieswith the collector (or a diode in the reversedirection to ground) to prevent collector-base conduction on negative swings.3. For inductive loads, protect the transis-tor with a diode across the load, as shownin Figure 2.4. Without the diode the in-ductor will swing the collector to a largepositive voltage when the switch is opened,most likely exceeding the collector-emitterbreakdown voltage, as the inductor tries tomaintain its "on" current from Vcc to thecollector (seethe discussion of inductors inSection 1.31).Figure 2.4. Always use a suppression diodewhen switching an inductive load.Transistor switches enable you to switchvery rapidly, typically in a small fraction ofa microsecond. Also, you can switch manydifferent circuits with a single control sig-nal. One further advantage is the possibil-ity of remote cold switching, in which onlydc control voltages snake around throughcables to reach front-panel switches, ratherthan the electronically inferior approachof having the signals themselves travelingthrough cablesand switches(if you run lotsof signals through cables, youre likely toget capacitive pickup as well as some sig-nal degradation)."Transistor man"Figure 2.5 presents a cartoon that will helpyou understand some limits of transistorFigure 2.5. "Transistor man" observes the basecurrent, and adjusts the output rheostat in anattempt to maintain the output current ILFEtimes larger.behavior. The little mans perpetual taskin life is to try to keep Ic = hFEIB;however, he is only allowed to turn theknob on the variable resistor. Thus hecan go from a short circuit (saturation)to an open circuit (transistor in the "offstate), or anything in between, but he isntallowed to use batteries, current sources,etc. One warning is in order here: Dontthink that the collector of a transistor
  • looks like a resistor. It doesnt. Rather,it looks approximately like a poor-qualityconstant-current sink (the value of currentdepending on the signal applied to thebase), primarily because of this little mansefforts.Another thing to keep in mind is that,at any given time, a transistor may be (a)cut off (no collector current), (b) in theactive region (some collector current, andcollector voltage more than a few tenthsof a volt above the emitter), or (c) insaturation (collector within a few tenths ofa volt of the emitter). See Appendix G ontransistor saturation for more details.2.03 Emitter followerFigure 2.6 shows an example of an emitterfollower. It is called that because the out-put terminal is the emitter, which followsthe input (the base), less one diode drop:VEz VB- 0.6 voltThe output is a replica of the input, but 0.6to 0.7 volt less positive. For this circuit,V,, must stay at +0.6 volt or more, orelse the output will sit at ground. Byreturning the emitter resistor to a negativesupply voltage, you can permit negativevoltage swings as well. Note that there isno collector resistor in an emitter follower.Figure 2.6. Emitter follower.At first glance this circuit may appearuseless, until you realize that the inputimpedance is much larger than the out-put impedance, as will be demonstratedSOME BASIC TRANSISTOR CIRCUITS2.03 Emitter followershortly. This means that the circuit re-quires less power from the signal sourceto drive a given load than would be thecase if the signal source were to drive theload directly. Or a signal of some inter-nal impedance (in the ThCvenin sense) cannow drive a load of comparable or evenlower impedance without loss of amplitude(from the usual voltage-divider effect). Inother words, an emitter follower has cur-rent gain, even though it has no voltagegain. It has power gain. Voltage gain isnteverything!Impedances of sources and loadsThis last point is very important and isworth some more discussion before wecalculate in detail the beneficial effects ofemitter followers. In electronic circuits,youre always hooking the output of some-thing to the input of something else, assuggested in Figure 2.7. The signal sourcemight be the output of an amplifier stage(with Thevenin equivalent series imped-ance ZOut),driving the next stage or per-haps a load (of some input impedance Zin).In general, the loading effect of the follow-ing stage causes a reduction of signal, as wediscussed earlier in Section 1.05. For thisreason it is usually best to keep Zo,t << Zin(a factor of 10 is a comfortable rule ofthumb).In some situations it is OK to forgothis general goal of making the source stiffcompared with the load. In particular, ifthe load is always connected (e.g., withina circuit) and if it presents a known andconstant Zi,, it is not too serious if it"loads" the source. However, it is alwaysnicer if signal levels dont change whena load is connected. Also, if Zin varieswith signal level, then having a stiff source(Zout<< Zin) assures linearity, where oth-erwise the level-dependent voltage dividerwould cause distortion.Finally, there are two situations whereZOut<< Zi, is actually the wrong thing to
  • TRANSISTORS66 Chapter 2t ~ r s t;iriipl~fwr second a m p l ~ f ~ e rFigure 2.7. Illustrating circuit "loading" as a voltage divider.do: In radiofrequency circuits we usuallymatch impedances (Z,,t = Zin), forreasons well describe in Chapter 14. Asecond exception applies if the signal beingcoupled is a current rather than a voltage.In that case the situation is reversed, andone strives to make Zi, << Zout (ZOut=oo,for a current source).Input and output impedances of emitterfollowersAs you have just seen, the emitterfollower is useful for changing impedancesof signals or loads. To put it bluntly, thatsthe whole point of an emitter follower.Lets calculate the input and outputimpedances of the emitter follower. Inthe preceding circuit we will consider Rto be the load (in practice it sometimes isthe load; otherwise the load is in parallelwith R, but with R dominating the parallelresistance anyway). Make a voltage changeAVBat the base; the corresponding changeat the emitter is AVE = AVB. Then thechange in emitter current is(using IE= IC+I B ) The input resistanceis AVB/AIB. ThereforeThe transistor beta (hfe) is typicallyabout 100, so a low-impedance load lookslike a much higher impedance at the base;it is easier to drive.In the preceding calculation, as in Chap-ter 1, we have used lower-case symbolssuch as hf e to signify small-signal (incre-mental) quantities. Frequently one con-centrates on the changes in voltages(or currents) in a circuit, rather than thesteady (dc) values of those voltages (orcurrents). This is most common whenthese "small-signal" variations representa possible signal, as in an audio amplifier,riding on a steady dc "bias" (see Section2.05). The distinction between dc cur-rent gain (hFE) and small-signal currentgain (h ,) isnt always made clear, and theterm beta is used for both. Thats alright,since hfe z hFE (except at very high fre-quencies), and you never assume you knowthem accurately, anyway.Although we used resistances in thepreceding derivation, we could generalizeto complex impedances by allowing AVB,AIB, etc., to become complex num-bers. We would find that the same
  • SOME BASIC TRANSISTOR CIRCUITS2.03 Emitter follower 67transformation rule applies for imped- EXERCISE 2.2ances: Zi, = (hf,+l)Zl,,d. Use a follower with base driven from a voltageWe could do a similar calculation to divider to provide a stiff source of +5 volts fromfind that the output impedance zOUtof an an available regulated +I5 volt supply. Loademitter follower (the impedance looking current (ma() = 25mA. Choose Your resistorvalues so that the output voltage doesnt dropinto the emitter) driven from a source of morethan 50,0 under full load.internal impedance ZsOurceis given byZsourceZout = -hfe + 1Strictly speaking, the output impedance ofthe circuit should also include the parallelresistance of R, but in practice ZOut (theimpedance looking into the emitter) dom-inates.EXERCISE 2.1Show that the preceding relationship is correct.Hint: Hold the source voltage fixed, and findthe changein output current for a given changein output voltage. Remember that the sourcevoltage is connected to the base through aseries resistor.Because of these nice properties, emit-ter followers find application in manysituations, e.g., making low-impedance sig-nal sources within a circuit (or at out-puts), making stiff voltage references fromhigher-impedance references (formed fromvoltage dividers, say), and generally isolat-ing signal sources from the loading effectsof subsequent stages.Figure 2.8. An npn emitter follower can sourceplenty of current through the transistor, but cansink limited current only through its emitterresistor.Important points about followers1. Notice (Section 2.01, rule 4) that inan emitter follower the npn transistor canonly "source" current. For instance, inthe loaded circuit shown in Figure 2.8 theoutput can swing to within a transistorsaturation voltage drop of Vcc (about+9.9V), but it cannot go more negativethan -5 volts. That is because on theextreme negative swing, the transistor cando no more than turn off, which it does at-4.4 volts input (-5V output). Furthernegative swing at the input results inbackbiasing of the base-emitter junction,but no further change in output. Theoutput, for a 10 volt amplitude sine-waveinput, looks as shown in Figure 2.9.InputoutputFigure 2.9. Illustrating the asymmetrical cur-rent drive capability of the npn emitter fol-lower.Another way to view the problem isto say that the emitter follower has lowsmall-signal output impedance. Its large-signal output impedance is much larger(as large as RE). The output impedancechanges over from its small-signal value toits large-signal value at the point where thetransistor goes out of the active region (inthis case at an output voltage of -5V). Toput this point another way, a low value ofsmall-signal output impedance doesnt
  • TRANSISTORS68 Chapter 2necessarily mean that the circuit cangenerate large signal swings into a low-resistance load. Low small-signal outputimpedance doesnt imply large output cur-rent capability.Possible solutions to this probleminvolve either decreasing the value ofthe emitter resistor (with greater powerdissipation in resistor and transistor),using a pnp transistor (if all signals arenegative only), or using a "push-pull"configuration, in which two comple-mentary transistors (one npn, one pnp),are used (Section 2.15). This sort of prob-lem can also come up when the load ofan emitter follower contains voltage orcurrent sources of its own. This happensmost often with regulated power sup-plies (the output is usually an emitter fol-lower) driving a circuit that has otherpower supplies.2. Always remember that the base-emit-ter reverse breakdown voltage for silicontransistors is small, quite often as littleas 6 volts. Input swings large enough totake the transistor out of conduction caneasily result in breakdown (with conse-quent degradation of ~ F E )unless aprotective diode is added (Fig. 2.10).Figure 2.10. A diode prevents base-emitterreverse voltage breakdown.3. The voltage gain of an emitter followeris actually slightly less than 1.O, becausethe base-emitter voltage drop is not reallyconstant, but depends slightly on collectorcurrent. You will see how to handle thatlater in the chapter, when we have theEbers-Moll equation.2.04 Emitter followers as voltageregulatorsThe simplest regulated supply of voltageis simply a zener (Fig. 2.11). Some currentmust flow through the zener, so you chooseK n - VoutR> routBecause V,, isnt regulated, you use thelowest value of V,, that might occur forthis formula. This is called worst-casedesign. In practice, you would also worryabout component tolerances, line-voltagelimits, etc., designing to accommodatethe worst possible combination that wouldever occur.wit;o7T "our (= "zener(unregulated,ripple)Figure 2.11. Simple zener voltage regulator.The zener must be able to dissipateAgain, for worst-case design, you woulduse V,, (max), Rmin, and rout (min).EXERCISE 2.3Design a +I0 volt regulated supply for loadcurrents from 0 to 100mA; the input voltage is+20 to +25 volts. Allow at least 10mA zenercurrent under all (worst-case)conditions. Whatpower rating must the zener have?This simple zener-regulated supply issometimes used for noncritical circuits, orcircuits using little supply current. How-ever, it has limited usefulness, for severalreasons:1. Vout isnt adjustable, or settable to aprecise value.2. Zener diodes give only moderate ripplerejection and regulation against changes of
  • SOME BASIC TRANSISTOR CIRCUITS2.05 Emitter follower biasing 6input or load, owing to their finite dynamicimpedance.3. For widely varying load currents a high-power zener is often necessary to handlethe dissipation at low load current.By using an emitter follower to isolatethe zener, you get the improved circuitshown in Figure 2.12. Now the situa-tion is much better. Zener current can bemade relatively independent of load cur-rent, since the transistor base current issmall, and far lower zener power dissipa-tion is possible (reduced by as much asl/hFE).The collector resistor Rc can beadded to protect the transistor from mo-mentary output short circuits by limitingthe current, even though it is not essentialto the emitter follower function. ChooseRc so that the voltage drop across it isless than the drop across R for the highestnormal load current.(unregulated)source, which is the subject of Section 2.06.An alternative method uses a low-passfilter in the zener bias circuit (Fig. 2.13).R is chosen to provide sufficient zener cur-rent. Then C is chosen large enough sothat RC >> l/friPpl,. (In a variation ofthis circuit, the upper resistor is replacedby a diode.)"I" 0(unregulated)Figure 2.13. Reducing ripple in the zenerregulator.Later you will see better voltage reg-ulators, ones in which you can vary theoutput easily and continuously, using feed-back. They are also better voltage sources,with output impedances measured in milli-ohms, temperature coefficients of a fewparts per million per degree centigrade,etc.Figure 2.12. Zener regulator with follower,for increased output current. Rc protects thetransistor by limitingmaximum output current.EXERCISE 2.4Design a +10 volt supply with the same specifi-cationsasinExercise2.3. Useazener andernit-ter follower. Calculate worst-case dissipationin transistor and zener. What is the percentagechange in zener current from the no-load con-dition to full load? Compare with your previouscircuit.A nice variation of this circuit aimsto eliminate the effect of ripple current(through R) on the zener voltage by sup-plying the zener current from a currentFigure 2.142.05 Emitter follower biasingWhen an emitter follower is driven from apreceding stage in a circuit, it is usuallyOK to connect its base directly to the
  • TRANSISTORS70 Chapter 2previous stages output, as shown in Figure2.14.Because the signal on Q17scollector isalways within the range of the power sup-plies, Qzs base will be between Vcc andground, and therefore Q2 is in the activeregion (neither cut off nor saturated), withits base-emitter diode in conduction andits collector at least a few tenths of a voltmore positive than its emitter. Sometimes,though, the input to a follower may notbe so conveniently situated with respect tothe supply voltages. A typical example is acapacitively coupled (or ac-coupled) signalfrom some external source (e.g., an audiosignal input to a high-fidelity amplifier).In that case the signals average voltage iszero, and direct coupling to an emitter fol-lower will give an output like that in Figure2.15.I inputFigure 2.15. A transistor amplifier poweredfrom a single positive supply cannot generatenegative voltage swings at the transistor outputterminal.It is necessary to bias the follower(in fact, any transistor amplifier) so thatcollector current flows during the entiresignal swing. In this case a voltage divideris the simplest way (Fig. 2.16). R1 and R2are chosen to put the base halfway betweenground and Vcc with no input signal,i.e., R1 and R2 are approximately equal.The process of selecting the operatingvoltages in a circuit, in the absence ofapplied signals, is known as setticg thequiescent point. In this case, as in mostcases, the quiescent point is chosen toallow maximum symmetrical signal swingof the output waveform without clipping(flattening of the top or bottom of thewaveform). What values should R1 andR2 have? Applying our general principle(Section 1.05), we make the impedance ofthe dc bias source (the impedance lookinginto the voltage divider) small comparedwith the load it drives (the dc impedancelooking into the base of the follower). Inthis case,This is approximately equivalent to sayingthat the current flowing in the voltagedivider should be large compared with thecurrent drawn by the base.Figure 2.16. An ac-coupled emitter follower.Note base bias voltage divider.Emitter follower design exampleAs an actual design example, lets make anemitter follower for audio signals (20Hz to20kHz). Vcc is +15 volts, and quiescentcurrent is to be 1mA.Step 1. Choose VE. For the largest possiblesymmetrical swing without clipping, VE =0.5Vcc, or +7.5 volts.Step 2. Choose RE. For a quiescentcurrent of lmA, RE = 7.5k.Step 3. Choose R1 and Rz. Vg is VE+0.6, or 8.1 volts. This determines the ratioof R1 to R2 as 1:1.17. The precedingloading criterion requires that the parallelresistance of R1 and R2 be about 75kor less (one-tenth of 7.5k times hFE).
  • SOME BASIC TRANSISTOR CIRCUITS2.05 Emitter follower biasing 71Suitable standard values are R1 = 130k,R2 = 150k.Step 4. Choose C1. C1 forms a high-passfilter with the impedance it sees as a load,namely the impedance looking into thebase in parallel with the impedance look-ing into the base voltage divider. If weassume that the load this circuit will driveis large compared with the emitter resistor,then the impedance looking into the baseis hFERE, about 750k. The divider lookslike 70k. So the capacitor sees a load ofabout 63k, and it should have a value ofat least 0.15pF so that the 3dB point willbe below the lowest frequency of interest,20Hz.Step 5. Choose C2. C2 forms a high-pass filter in combination with the loadimpedance, which is unknown. However,it is safe to assume that the load impedancewont be smaller than RE,which gives avalue for Cz of at least 1.OpF to put the3dB point below 20Hz. Because there arenow two cascaded high-pass filter sections,the capacitor values should be increasedsomewhat to prevent large attenuation(reduction of signal amplitude, in this case6dB) at the lowest frequency of interest.C1 = 0.5pF and Cz = 3.3pF might begood choices.Followers with split suppliesBecause signals often are "near ground," itis convenient to use symmetrical positiveand negative supplies. This simplifiesbiasing and eliminates coupling capacitors(Fig. 2.17).Warning: You must always provide a dcpath for base bias current, even if it goesonly to ground. In the preceding circuit itis assumed that the signal source has a dcpath to ground. If not (e.g., if the signalis capacitively coupled), you must providea resistor to ground (Fig. 2.18). RB couldbe about one-tenth of hFERE, as before.signal(near --I=ground) outputground)Figure 2.17. A dc-coupledemitterfollowerwithsplit supply.EXERCISE 2.5Design an emitter follower with *I5 volt sup-plies to operate over the audio range (20Hz-2OkHz). Use 5mA quiescent current and capac-itive input coupling.Figure 2.18Bad biasingUnfortunately, you sometimes see circuitslike the disaster shown in Figure 2.19. RBwas chosen by assuming a particular valuefor hFE (loo), estimating the base cur-rent, and then hoping for a 7 volt dropacross RB. This is a bad design; ~ F Eisnot a good parameter and will vary con-siderably. By using voltage biasing witha stiff voltage divider, as in the detailedexample presented earlier, the quiescentpoint is insensitive to variations in tran-sistor beta. For instance, in the previousdesign example the emitter voltage will in-crease by only 0.35 volt (5%) for a transis-tor with hFE = 200 instead of the nominal
  • TRANSISTORSChapter 2hFE= 100. AS with this emitter followerexample, it is just as easy to fall into thistrap and design bad transistor circuits inthe other transistor configurations (e.g., thecommon-emitter amplifier, which we willtreat later in this chapter).Figure 2.19. Dont do this!2.06 Transistor current sourceCurrent sources, although often neglected,are as important and as useful as voltagesources. They often provide an excellentway to bias transistors, and they are un-equaled as "active loads" for super-gainamplifier stages and as emitter sources fordifferential amplifiers. Integrators, saw-tooth generators, and ramp generatorsneed current sources. They provide wide-voltage-range pull-upswithin amplifier andregulator circuits. And, finally, there areapplications in the outside world thatrequire constant current sources, e.g.,electrophoresis or electrochemistry.Resistor plus voltage sourceThe simplest approximation to a currentsource is shown in Figure 2.20. As longas Rload << R (in other words, qoad<<V), the current is nearly constant and isapproximatelyThe load doesnt have to be resistive. Acapacitor will charge at a constant rate, aslong as Vcapacito,<< V; this is just the firstpart of the exponential charging curve ofan RC.Figure 2.20There are several drawbacks to a simpleresistor current source. In order to makea good approximation to a current source,you must use large voltages, with lots ofpower dissipation in the resistor. In ad-dition, the current isnt easily programma-ble, i.e., controllable over a large range viaa voltage somewhere else in the circuit.EXERCISE 2.6If youwanta currentsourceconstantto1%overa load voltagerangeof 0to +10 volts,how largea voltage source must you use in series with asingle resistor?EXERCISE 2.7Suppose you want a 10mA current in the pre-ceding problem. How muchpoweris dissipatedin the series resistor? How much gets to theload?Transistor current sourceFortunately, it is possible to make a verygood current source with a transistor (Fig.2.21). It works like this : Applying VB tothe base, with VB > 0.6 volt, ensures thatthe emitter is always conducting:VE = VB - 0.6 voltSoIE = VE/RE = (VB - 0.6 vOlt)/REBut, since IE z IC for large hFE,Ic W (VB- 0.6 volt)/RE
  • SOME BASIC TRANSISTOR CIRCUITS2.06 Transistor current source 73independent of Vc, as long as the transis-tor is not saturated (Vc > VE+0.2 volt).Figure 2.21. Transistor current source: basicconcept.Current-source biasingThe base voltage can be provided in anumber of ways. A voltage divider isOK, as long as it is stiff enough. Asbefore, the criterion is that its impedanceshould be much less than the dc impedancelooking into the base (hFERE). Or youcan use a zener diode, biased from Vcc,or even a few forward-biased diodes inseries from base to the correspondingemitter supply. Figure 2.22 shows someexamples. In the last example (Fig. 2.22C),a pnp transistor sources current to a loadreturned to ground. The other examples(using npn transistors) should properly becalled current sinks, but the usual practiceis to call all of them current sources.["Sink" and "source" simply refer to thedirection of current flow: If a circuitsupplies (positive) current to a point, it is asource, and vice versa.] In the first circuit,the voltage-divider impedance of -1.3k isvery stiff compared with the impedancelooking into the base of about lOOk (forhFE= loo), SO any changes in beta withcollector voltage will not much affect theoutput current by causing the base voltageto change. In the other two circuits thebiasing resistors are chosen to provideseveral milliamps to bring the diodes intoconduction.ComplianceA current source can provide constantcurrent to the load only over some finiterange of load voltage. To do otherwisewould be equivalent to providing infinitepower. The output voltage range overwhich a current source behaves well iscalled its output compliance. For thepreceding transistor current sources, thecompliance is set by the requirement thatFigure 2.22. Transistor-current-source circuits, illustrating three methods of base biasing; npntransistors sink current, whereas pnp transistors source current. The circuit in C illustrates a loadreturned to ground.
  • TRANSISTORS74 Chapter 2the transistors stay in the active region.Thus in the first circuit the voltage at thecollector can go down until the transistoris almost in saturation, perhaps +1.2 voltsat the collector. The second circuit, withits higher emitter voltage, can sink currentdown to a collector voltage of about +5.2volts.In all cases the collector voltage canrange from a value near saturation all theway up to the supply voltage. For exam-ple, the last circuit can source current tothe load for any voltage between zero andabout +8.6 volts across the load. In fact,the load might even contain batteries orpower supplies of its own, carrying the col-lector beyond the supply voltage. ThatsOK, but you must watch out for transistorbreakdown (VCE must not exceed BVcEo,the specified collector-emitter breakdownvoltage) and also for excessive power dis-sipation (set by IcVcE). As you will seein Section 6.07, there is an additional safe-operating-area constraint on power transis-tors.EXERCISE 2.8You have +5 and +15 volt regulated suppliesavailable in a circuit. Design a 5mAnpn currentsource (sink) using the +5 volts on the base.What is the output compliance?A current source doesnt have to havea fixed voltage at the base. By varyingVB you get a voltage-programmable cur-rent source. The input signal swing vi,(remember, lower-case symbols mean vari-ations) must stay small enough so that theemitter voltage never drops to zero, if theoutput current is to reflect input voltagevariations smoothly. The result will be acurrent source with variations in outputcurrent proportional to the variations ininput voltage, iOut= vin/REDeficiencies of current sourcesTo what extent does this kind of cur-rent source depart from the ideal? Inother words, does the load current varywith voltage, i.e., have a finite (RTh< m)ThCvenin equivalent resistance, and if sowhy? There are two kinds of effects:1. Both VBE (Early effect) and hFE varyslightly with collector-to-emitter voltage ata given collector current. The changes inVBE produced by voltage swings across theload cause the output current to change,because the emitter voltage (and thereforethe emitter current) changes, even with afixed applied base voltage. Changes inh~~ produce small changes in output (col-lector) current for fixed emitter current,since Ic = IE- IB; in addition, thereare small changes in applied base voltageproduced by the variable loading of thenonzero bias source impedance as hFE(and therefore the base current) changes.These effects are small. For instance, thecurrent from the circuit in Figure 2.22Avaried about 0.5% in actual measurementswith a 2N3565 transistor. In particular, forload voltages varying from zero to 8 volts,the Early effect contributed 0.5%,and tran-sistor heating effects contributed 0.2%. Inaddition, variations in hFE contributed0.05% (note the stiff divider). Thus thesevariations result in a less-than-perfect cur-rent source: The output current dependsslightly on voltage and therefore hasless than infinite impedance. Later youwill see methods that get around thisdifficulty.2. V B ~and also h~~ depend on temper-ature. This causes drifts in output currentwith changes in ambient temperature; inaddition, the transistor junction tempera-ture varies as the load voltage is changed(because of variation in transistor dissipa-tion), resulting in departure from ideal cur-rent source behavior. The change of V B ~with ambient temperature can be compen-sated with a circuit like that shown inFigure 2.23, in which Qzs base-emitterdrop is compensated by the drop in emit-ter follower Q1, with similar tempera-ture dependence. R3, incidentally, is a
  • SOME BASIC TRANSISTOR CIRCUITS2.06 Transistor current source 75cc0loadFigure 2.23. One method of temperature-compensating a current source.pull-up resistor for Q1, since Q2s basesinks current, which Q1 cannot source.Improving current-source performanceIn general, the effectsof variability in VBE,whether caused by temperature depen-dence (approximately -2mVI0C) or by de-pendence on VCE (the Early effect, givenroughly by AVBE N" -0.0001 AVCE),can be minimized by choosing the emittervoltage to be large enough (at least lV,say) so that changes in VBE of tens ofmillivolts will not result in large fractionalchanges in the voltage across the emitterresistor (remember that the base voltageis what is held constant by your circuit).For instance, choosing VE = 0.1 volt (i.e.,applying about 0.7V to the base) wouldcause 10% variations in output currentfor lOmV changes in VBE, whereas thechoice VE = 1.0 volt would result in1% current variations for the same VBEchanges. Dont get carried away, though.Remember that the lower limit of outputcompliance is set by the emitter voltage.Using a 5 volt emitter voltage for a currentsource running from a +10 volt supplylimits the output compliance to slightlyless than 5 volts (the collector can go fromabout VE+ 0.2V to Vcc, i.e., from 5.2Vto 10V).Figure 2.24. Cascode current source for im-proved current stability with load voltage vari-ations.Figure 2.24 shows a circuit modifica-tion that improves current-source perfor-mance significantly. Current source Q1functions as before, but with collector volt-age held fixed by Q2s emitter. The loadsees the same current as before, since Q2scollector and emitter currents are nearlyequal (large hFE). But with this circuitthe VCE of Q1 doesnt change with loadvoltage, thus eliminating the small changesin VBE from Early effect and dissipation-induced temperature changes. Measure-ments with 2N3565s gave 0.1% currentvariation for load voltages from 0 to 8volts; to obtain performance of this accu-racy it is important to use stable 1% resis-tors, as shown. (Incidentally, this circuitconnection also finds use in high-frequencyamplifiers, where it is known as the "cas-code.") Later you will see current sourcetechniques using op-amps and feedbackthat circumvent the problem of VBE vari-ation altogether.The effects of variability of h~~ canbe minimized by choosing transistors withlarge h F ~ ,SO that the base current contri-bution to the emitter current is relativelysmall.Figure 2.25 shows one last currentsource, whose output current doesnt
  • TRANSISTORS76 Chapter 2depend on supply voltage. In this circuit,Qls VBE across R2 sets the output cur-rent, independent of Vcc:R1 biases Q2 and holds Qls collector attwo diode drops below Vcc, eliminatingEarly effect as in the previous circuit. Thiscircuit is not temperature-compensated;the voltage across R2 decreases approxi-mately 2.lmV/"C, causing the output cur-rent to decrease approximately 0.3%/OC.Figure 2.25. Transistor VBE-referenced currentsource.2.07 Common-emitter amplifierConsider a current source with a resistoras load (Fig. 2.26). The collector voltage isWe could capacitively couple a signal tothe base to cause the collector voltage tovary. Consider the example in Figure2.27. C is chosen so that all frequencies ofinterest are passed by the high-pass filterit forms in combination with the parallelresistance of the base biasing resistors (theFigure 2.26impedance looking into the base itself willusually be much larger because of the waythe base resistors are chosen, and it can beignored); that is,The quiescent collector current is l.OmAbecause of the applied base bias and the1.0k emitter resistor. That current putsthe collector at +10 volts (+20V, minusl.OmA through 10k). Now imagine anapplied wiggle in base voltage VB. Theemitter follows with VE = VB, whichcauses a wiggle in emitter currentand nearly the same change in collectorcurrent (hf,is large). So the initial wigglein base voltage finally causes a collectorvoltage wiggleAha! Its a voltage amplijier, with a voltageamplification (or "gain") given bygain = vOut/vin= -&/REIn this case the gain is -10,000/1000,or -10. The minus sign means that apositive wiggle at the input gets turned intoa negative wiggle (10 times as large) at theoutput. This is called a common-emitteramplifier with emitter degeneration.
  • SOME BASIC TRANSISTOR CIRCUITS2.08 Unity-gain phase splitter 77signalsignalin1.ovFigure 2.27. An ac common-emitter amplifierwith emitter degeneration. Note that the outputterminal is thecollector,rather than the emitter.Input and output impedance of thecommon-emitter amplifierWe can easily determine the input andoutput impedances of the amplifier. Theinput signal sees, in parallel, 11Ok, 1Ok,and the impedance looking into the base.The latter is about lOOk (hf,times RE),so the input impedance (dominated by the1Ok) is about 8k. The input couplingcapacitor thus forms a high-pass filter, withthe 3dB point at 200Hz. The signal drivingthe amplifier sees 0.1pF in series with8k, which to signals of normal frequencies(well above the 3dB point) just looks like8k.The output impedance is 10k in paral-lel with the impedance looking into thecollector. What is that? Well, remem-ber that if you snip off the collector resis-tor, youre simply looking into a currentsource. The collector impedance is verylarge (measured in megohms), and so theoutput impedance is just the value of thecollector resistor, 10k. It is worth remem-bering that the impedance looking into atransistors collector is high, whereas theimpedance looking into the emitter is low(as in the emitter follower). Although theoutput impedance of a common-emitteramplifier will be dominated by the collec-tor load resistor, the output impedance ofan emitter follower will not be dominatedby the emitter load resistor, but rather bythe impedance looking into the emitter.2.08 Unity-gain phase splitterSometimes it is useful to generate a signaland its inverse, i.e., two signals 180 outof phase. Thats easy to do - just usean emitter-degenerated amplifier with again of -1 (Fig. 2.28). The quiescentcollector voltage is set to 0.75Vcc, ratherthan the usual 0.5Vcc, in order to achievethe same result - maximum symmetricaloutput swing without clipping at eitheroutput. The collector can swing from0.5Vcc to Vcc, whereas the emitter canswing from ground to 0.5Vcc.Figure 2.28. Unity-gain phase splitter.Note that the phase-splitter outputsmust be loaded with equal (or very high)impedances at the two outputs in order tomaintain gain symmetry.Phase shifterA nice use of the phase splitter is shownin Figure 2.29. This circuit gives (fora sine wave input) an output sine waveof adjustable phase (from zero to 180°),but with constant amplitude. It can bebest understood with a phasor diagramof voltages (see Chapter 1); representingthe input signal by a unit vector along
  • TRANSISTORS78 Chapter 2the real axis, the signals look as shown inFigure 2.30.outputk-Figure 2.29. Constant-amplitudephase shifter.Signal vectors v~ and vc must be atright angles, and they must add to forma vector of constant length along the realaxis. There is a theorem from geometrythat says that the locus of such pointsis a circle. So the resultant vector (theoutput voltage) always has unit length,i.e., the same amplitude as the input, andits phase can vary from nearly zero tonearly 180 relative to the input wave asR is varied from nearly zero to a valuemuch larger than Zc at the operatingfrequency. However, note that the phaseshift also depends on the frequency ofthe input signal for a given setting of thepotentiometer R. It is worth noting that asimple RC high-pass (or low-pass) networkcould also be used as an adjustable phaseshifter. However, its output amplitudewould vary over an enormous range as thephase shift was adjusted.An additional concern here is the abilityof the phase-splitter circuit to drive theRC phase shifter as a load. Ideally, theload should present an impedance thatis large compared with the collector andemitter resistors. As a result, this circuitis of limited utility where a wide rangeof phase shifts is required. You will seeimproved phase-splitter techniques inChapter 4.Figure 2.30. Phasor diagram for phase shifter.2.09 TransconductanceIn the preceding section we figured out theoperation of the emitter-degenerated am-plifier by (a) imagining an applied basevoltage swing and seeing that the emittervoltage had the same swing, then (b) calcu-lating the emitter current swing; then, ig-noring the small base current contribution,we got the collector current swing and thus(c) the collector voltage swing. The voltagegain was then simply the ratio of collector(output) voltage swing to base (input) volt-age swing.1lok Lsignal outr--signalinFigure 2.31. The common-emitter amplifier isa transconductance stage driving a (resistive)load.Theres another way to think aboutthis kind of amplifier. Imagine breaking itapart, as in Figure 2.31. The first part is avoltage-controlled current source, withquiescent current of 1.OmA and gain
  • EBERS-MOLL MODEL APPLIED TO BASIC TRANSISTOR CIRCUITS2.10 Improved transistor model: transconductanceamplifier of -1mAlV. Gain means the ratio out-putlinput; in this case the gain has unitsof currentlvoltage, or llresistance. The in-verse of resistance is called conductance(the inverse of reactance is susceptance,and the inverse of impedance is admit-tance) and has a special unit, the siemens,which used to be called the mho (ohmspelled backward). An amplifier whosegain has units of conductance is calleda transconductance amplifier; the ratioIOut/V,,is called the transconductance,9,.Think of the first part of the circuit as atransconductance amplifier, i.e., a voltage-to-current amplifier with transconductanceg, (gain) of 1mAIV (IOOOpS, or lmS,which is just l/RE). The second part of thecircuit is the load resistor, an "amplifier"that converts current to voltage. Thisresistor could be called a transresistanceamplifier, and its gain (r,) has units ofvoltagelcurrent, or resistance. In this caseits quiescent voltage is Vcc, and its gain(transresistance) is 10kVIA (IOkR), whichis just Rc. Connecting the two partstogether gives you a voltage amplifier. Youget the overall gain by multiplying the twogains. In this case G = gmRc = RcIRE,or -10, a unitless number equal to theratio (output voltage)/(input voltage).This is a useful way to think about anamplifier, because you can analyze perfor-mance of the sections independently. Forexample, you can analyze the transconduc-tance part of the amplifier by evaluatingg, for different circuit configurations oreven different devices, such as field-effecttransistors (FETs). Then you can analyzethe transresistance (or load) part by consid-ering gain versus voltage swing trade-offs.If you are interested in the overall voltagegain, it is given by Gv = g,r,, wherer , is the transresistance of the load. Ulti-mately the substitution of an active load(current source), with its extremely hightransresistance, can yield one-stage volt-age gains of 10,000 or more. The cascodeconfiguration, which we will discuss later,is another example easily understood withthis approach.In Chapter 4, which deals with opera-tional amplifiers, you will see further ex-amples of amplifiers with voltages or cur-rents as inputs or outputs; voltage ampli-fiers (voltage to voltage), current amplifiers(current to current), and transresistanceamplifiers (current to voltage).Turning up the gain: limitations of thesimole model- ,The voltage gain of the emitter-degener-ated amplifier is -Rc/RE, according toour model. What happens as RE is re-duced toward zero? The equation pre-dicts that the gain will rise without limit.But if we made actual measurements ofthe preceding circuit, keeping the quies-cent current constant at lmA, we wouldfind that the gain would level off at about400 when RE is zero, i.e., with the emit-ter grounded. We would also find that theamplifier would become significantly non-linear (the output would not be a faithfulreplica of the input), the input impedancewould become small and nonlinear, andthe biasing would become critical and un-stable with temperature. Clearly our tran-sistor model is incomplete and needs to bemodified in order to handle this circuit sit-uation, as well as others we will talk aboutshortly. Our fixed-up model, which we willcall the transconductance model, will beaccurate enough for the remainder of thebook.EBERS-MOLL MODEL APPLIED TOBASIC TRANSISTOR CIRCUITS2.10 Improved transistor model:transconductance amplifierThe important change is in property 4(Section 2.01), where we said earlier thatIc= hFEIB. We thought of the transistor
  • TRANSISTORS80 Chapter 2as a current amplifier whose input circuitbehaved like a diode. Thats roughly cor-rect, and for some applications its goodenough. But to understand differential am-plifiers, logarithmic converters, tempera-ture compensation, and other importantapplications, you must think of the transis-tor as a transconductance device - collectorcurrent is determined by base-to-emittervoltage.Heres the modified property 4:4. When rules 1-3 (Section 2.01) areobeyed, Ic is related to VBE byIc = Is exp -[ (?)-lIwhere VT = k T / q = 25.3mV at roomtemperature (6g°F, 20°C), q is the elec-tron charge (1.60 x 10-l9 coulombs), k isBoltzmanns constant (1.38 xjoules/"K), T is the absolute temperaturein degrees Kelvin (OK ="C + 273.16), andIs is the saturation current of the partic-ular transistor (depends on T). Then thebase current, which also depends on VBE,can be approximated bywhere the "constant" hFE is typically inthe range 20 to 1000, but depends ontransistor type, Ic, VCE, and temperature.Is represents the reverse leakage current.In the active region Ic >> Is, andtherefore the -1 term can be neglected incomparison with the exponential.The equation for Ic is known as theEbers-Moll equation. It also approximate-ly describes the current versus voltage fora diode, if VT is multiplied by a correc-tion factor m between 1 and 2. For tran-sistors it is important to realize that thecollector current is accurately determinedby the base-emitter voltage, rather thanby the base current (the base current isthen roughly determined by hFE), and thatthis exponential law is accurate over anenormous range of currents, typically fromnanoamps to milliamps. Figure 2.32makes the point graphically. If you mea-sure the base current at various collectorcurrents, you will get a graph of hFE ver-sus Ic like that in Figure 2.33.Figure 2.32. Transistor base and collectorcurrents as functions of base-to-emittervoltageVBE.log scalel o O t - I L I 1 , 1 110 10 10 = 10 10 10 10Figure 2.33. Typical transistor current gain( ~ F E )versus collector current.Although the Ebers-Moll equation tellsus that the base-emitter voltage "pro-grams" the collector current, this propertymay not be directly usable in practice (bi-asing a transistor by applying a base volt-age) because of the large temperature co-efficient of base-emitter voltage. You willsee later how the Ebers-Moll equation pro-vides insight and solutions to this problem.Rules of thumb for transistor designFrom the Ebers-Moll equation we can get
  • EBERS-MOLL MODEL APPLIED TO BASIC TRANSISTOR CIRCUITS2.11 The emitter follower revisited 81several important quantities we will beusing often in circuit design:1. The steepness of the diode curve. Howmuch do we need to increase VBE to in-crease Ic by a factor of lo? From theEbers-Moll equation, thats just VT log, 10,or 60mV at room temperature. Base volt-age increases 60rnV per decade of collectorcurrent. Equivalently, Ic = ~ ~ ~ e ~ ~ / ~ ~ ,where AV is in millivolts.2. The small-signal impedance lookinginto the emitter, for the base held at a fixedvoltage. Taking the derivative of VBE withrespect to Ic, you getre = VT/IC = 25/Ic ohmswhere Ic is in milliamps. The numericalvalue 25/Ic is for room temperature. Thisintrinsic emitter resistance, re,acts as if itis in series with the emitter in all transistorcircuits. It limits the gain of a groundedemitter amplifier, causes an emitter fol-lower to have a voltage gain of slightly lessthan unity, and prevents the output imped-ance of an emitter follower from reachingzero. Note that the transconductance of agrounded emitter amplifier is g, = l/re.3. The temperature dependence of VBE.A glance at the Ebers-Moll equation sug-gests that VBE has a positive temperaturecoefficient. However, because of the tem-perature dependence of Is, VBE decreasesabout 2.1mV/OC. It is roughly proportionalto l/T,b,, where Tabsis the absolute tem-perature.There is one additional quantity wewill need on occasion, although it is notderivable from the Ebers-Moll equation. Itis the Early effect we described in Section2.06, and it sets important limits oncurrent-source and amplifier performance,for example:4. Early effect. VBE varies slightly withchanging VCE at constant Ic. This effectis caused by changing effective base width,and it is given, approximately, bywhere cr =0.0001.These are the essential quantities weneed. With them we will be able to handlemost problems of transistor circuit design,and we will have little need to refer to theEbers-Moll equation itself.2.11 The emitter follower revisitedBefore looking again at the common-emit-ter amplifier with the benefit of our newtransistor model, lets take a quick lookat the humble emitter follower. TheEbers-Moll model predicts that an emit-ter follower should have nonzero out-put impedance, even when driven by avoltage source, because of finite re(item 2, above). The same effect alsoproduces a voltage gain slightly lessthan unity, because re forms a voltage di-vider with the load resistor.These effectsare easy to calculate. Withfixed base voltage, the impedance look-ing back into the emitter is just Rout =d v ~ , q / d I ~ ;but IE M IC, SO Rout Xre, the intrinsic emitter resistance [re =251Ic(mA)]. For example, in Figure2.34A, the load sees a driving impedanceof re = 25 ohms, since Ic = 1mA. (Thisis paralleled by the emitter resistor RE,if used; but in practice RE will alwaysbe much larger than re.) Figure 2.34Bshows a more typical situation, with finitesource resistance Rs (for simplicity weveomitted the obligatory biasing components- base divider and blocking capacitor -which are shown in Fig. 2.34C). In thiscase the emitter followers output imped-ance is just re in series with R,/(hfe+ 1)(again paralleled by an unimportant RE,if present). For example, if R, = lk andIc = lmA, Rout = 35 ohms (assuminghf = 100). It is easy to show that the in-trinsic emitter re also figures into an emit-ter followers input impedance, just as ifit were in series with the load (actually, par-allel combination of load resistor and
  • TRANSISTORS82 Chapter 2emitter resistor). In other words, for theemitter follower circuit the effect of theEbers-Moll model is simply to add a seriesemitter resistance re to our earlier results.The voltage gain of an emitter followeris slightly less than unity, owing to thevoltage divider produced by re and theload. It is simple to calculate, becausethe output is at the junction of re andRload: GV = vout/vin = R ~ / ( r e+ RL).Thus, for example, a follower runningat 1mA quiescent current, with lk load,has a voltage gain of 0.976. Engineerssometimes like to write the gain in termsof the transconductance, to put it in a formthat holds for FETs also (see Section 3.07);in that case (using g, = l/re) you getGV = R ~ g m / ( l+RL~,).4loads~gnalsourceB+ "cc -load--LFigure 2.342.12 The common-emitter amplifierrevisitedPreviously we got wrong answers for thevoltage gain of the common-emitter am-plifier with emitter resistor (sometimescalled emitter degeneration) when we setthe emitter resistor equal to zero.The problem is that the transistor has25/Ic(mA) ohms of built-in (intrinsic)emitter resistance re that must be addedto the actual external emitter resistor. Thisresistance is significant only when smallemitter resistors (or none at all) are used.So, for instance, the amplifier we consid-ered previously will have a voltage gain of-lOk/re, or -400, when the exter-nal emitter resistor is zero. The input
  • EBERS-MOLL MODEL APPLIED TO BASIC TRANSISTORCIRCUITS2.12 The common-emitter amplifier revisited 83impedance is not zero, as we would havepredicted earlier (h ,RE); it is approxi-mately hf,r,, or in this case (1mA quies-cent current) about 2.5k.The terms "grounded emitter" and"common emitter" are sometimes used in-terchangeably, and they can be confusing.We will use the phrase "grounded emitteramplifier" to mean a common-emitter am-plifier with RE = 0. A common-emitteramplifier stage may have an emitter resis-tor; what matters is that the emitter circuitis common to the input circuit and the out-put circuit.Shortcomings of the single-stagegrounded emitter amplifierThe extra voltage gain you get by usingRE = 0 comes at the expense of otherproperties of the amplifier. In fact, thegrounded emitter amplifier, in spite of itspopularity in textbooks, should be avoidedexcept in circuits with overall negativefeedback. In order to see why, considerFigure 2.35.t--- signal outsignal inFigure 2.35. Common-emitter amplifier with-out emitter degeneration.1. Nonlinearity. The gain is G =-gmRc = -Rc/re = -RcIc(mA)/25,so for a quiescent current of lmA, thegain is -400. But Ic varies as theoutput signal varies. For this example,the gain will vary from -800 (VOut= 0,IC= 2mA) down to zero (VOut= Vcc,Ic = 0). For a triangle-wave input, theoutput will look like that in Figure 2.36.The amplifier has high distortion, or poorlinearity. The grounded emitter amplifierwithout feedback is useful only for smallsignal swings about the quiescent point. Bycontrast, the emitter-degenerated amplifierhas gain almost entirely independent ofcollector current, as long as RE >> re, andcan be used for undistorted amplificationeven with large signal swings.- time +Figure 2.36. Nonlinear output waveform fromgrounded emitter amplifier.2. Input impedance. The input impedanceis roughly Zi, = hf,r, = 25 hf,/Ic(mA)ohms. Once again, Ic varies over the sig-nal swing, giving a varying input imped-ance. Unless the signal source driving thebase has low impedance, you will windup with nonlinearity due to the nonlinearvariable voltage divider formed from thesignal source and the amplifiers input im-pedance. By contrast, the input impedanceof an emitter-degenerated amplifier is con-stant and high.3. Biasing. The grounded emitter ampli-fier is difficult to bias. It might be tempt-ing just to apply a voltage (from a volt-age divider) that gives the right quiescentcurrent according to the Ebers-Moll equa-tion. That wont work, because of the tem-perature dependence of VnE (at fixed Ic),which varies about 2.1mV/"C (it actuallydecreases with increasing T because of thevariation of Is with T; as a result, VB,gis roughly proportional to l/T, the abso-lute temperature). This means that thecollector current (for fixed VBE) will in-crease by a factor of 10 for a 30°C rise
  • TRANSISTORS84 Chapter 2in temperature. Such unstable biasing isuseless, because even rather small changesin temperature will cause the amplifier tosaturate. For example, a grounded emitterstage biased with the collector at half thesupply voltage will go into saturation if thetemperature rises by 8OC.EXERCISE 2.9Verify that an 8OC rise in ambient temperaturewillcausea base-voltage-biasedgroundedemit-ter stage to saturate, assuming that it was ini-tially biased for Vc = 0.5Vcc.Some solutions to the biasing problemwill be discussed in the following sections.By contrast, the emitter-degenerated am-plifier achieves stable biasing by applying avoltage to the base, most of which appearsacross the emitter resistor, thus determin-ing the quiescent current.Emitter resistor as feedbackAdding an external series resistor to theintrinsic emitter resistance re (emitter de-generation) improves many properties ofthe common-emitter amplifier, at the ex-pense of gain. You will see the same thinghappening in Chapters 4 and 5 , whenwe discuss negative feedback,an importanttechnique for improving amplifier charac-teristics by feeding back some of the outputsignal to reduce the effective input signal.The similarity here is no coincidence; theemitter-degenerated amplifier itself uses aform of negative feedback. Think of thetransistor as a transconductance device,determining collector current (and there-fore output voltage) according to the volt-age applied between the base and emitter;but the input to the amplifier is the voltagefrom base to ground. So the voltage frombase to emitter is the input voltage, mi-nus a sample of the output (IERE). Thatsnegative feedback, and thats why emitterdegeneration improves most properties ofthe amplifier (improved linearity and sta-bility and increased input impedance; alsothe output impedance would be reduced ifthe feedback were taken directly from thecollector). Great things to look forward toin Chapters 4 and 5!2.13 Biasing the common-emitteramplifierIf you must have the highest possible gain(or if the amplifier stage is inside a feed-back loop), it is possible to arrange suc-cessful biasing of a common-emitter am-plifier. There are three solutions that canbe applied, separately or in combination:bypassed emitter resistor, matched biasingtransistor, and dc feedback.Figure 2.37. A bypassed emitter resistor can beused to improve the bias stability of a groundedemitter amplifier.Bypassed emitter resistorUse a bypassed emitter resistor, biasing asfor the degenerated amplifier, as shown inFigure 2.37. In this case RE has beenchosen about 0.1Re,for ease of biasing;if RE is too small, the emitter voltagewill be much smaller than the base-emitterdrop, leading to temperature instability ofthe quiescent point as VBE varies withtemperature. The emitter bypass capacitoris chosen by making its impedance small
  • EBERS-MOLL MODEL APPLIED TO BASIC TRANSISTOR CIRCUITS2.13 Biasing the common-emitteramplifier 85compared with re (not RE)at the lowestfrequency of interest. In this case itsimpedance is 25 ohms at 650Hz. At signalfrequencies the input coupling capacitorsees an impedance of 10k in parallel withthe base impedance, in this case hf, times25 ohms, or roughly 2.5k. At dc, theimpedance looking into the base is muchlarger (hf, times the emitter resistor, orabout look), which is why stable biasingis possible.Figure 2.38A variation on this circuit consists of us-ing two emitter resistors in series, one ofthem bypassed. For instance, suppose youwant an amplifier with a voltage gain of50, quiescent current of lmA, and Vcc of+20 volts, for signals from 20Hz to 20kHz.If you try to use the emitter-degeneratedcircuit, you will have the circuit shown inFigure 2.38. The collector resistor is cho-sen to put the quiescent collector voltage at0.5Vcc. Then the emitter resistor is cho-sen for the required gain, including the ef-fects of the reof 25/Ic(mA). The problemis that the emitter voltage of only 0.175volt will vary significantly as the -0.6 voltof base-emitter drop varies with temper-ature (-2.lmVI0C, approximately), sincethe base is held at constant voltage by R1and Rg;for instance, you can verify thatan increase of 20°C will cause the collectorcurrent to increase by nearly 25%.The solution here is to add some by-passed emitter resistance for stable biasing,with no change in gain at signal frequen-cies (Fig. 2.39). As before, the collectorresistor is chosen to put the collector at10 volts (0.5Vcc). Then the unbypassedemitter resistor is chosen to give a gainof 50, including the intrinsic emitter resis-tance r, = 25/Ic(mA). Enough bypassedemitter resistance is added to make stablebiasing possible (one-tenth of the collectorresistance is a good rule). The base voltageis chosen to give 1mA of emitter current,with impedance about one-tenth the dc im-pedance looking into the base (in this caseabout 100k). The emitter bypass capacitoris chosen to have low impedance comparedwith 180+25 ohms at the lowest signal fre-quencies. Finally, the input coupling ca-pacitor is chosen to have low impedancccompared with the signal-frequency inputimpedance of the amplifier, which is equalto the voltage divider impedance in paral-lel with (180 + 25)hfe ohms (the 8200 isbypassed, and looks like a short at signalfrequencies).Figure 2.39. A common-emitter amplifiercombining bias stability, linearity, and largevoltage gain.An alternative circuit splits the signaland dc paths (Fig. 2.40). This lets you varythe gain (by changing the 1800 resistor)without bias change.
  • TRANSISTORS86 Chapter 2Figure 2.40. Equivalent emitter circuit forFigure 2.39.Matched biasing transistorUse a matched transistor to generate thecorrect base voltage for the required col-lector current; this ensures automatic tem-perature compensation (Fig. 2.41). Qlscollector is drawing ImA, since it is guar-anteed to be near ground (about one VBEdrop above ground, to be exact); if Q1and Q2 are a matched pair (available asa single device, with the two transistorson one piece of silicon), then Q2 will alsobe biased to draw ImA, putting its collec-tor at +10 volts and allowing a full f10volt symmetrical swing on its collector.Changes in temperature are of no impor-tance, as long as both transistors are at thesame temperature. This is a good reasonfor using a "monolithic" dual transistor.Feedback at dcUse dc feedback to stabilize the quiescentpoint. Figure 2.42 shows one method. Bytaking the bias voltage from the collector,rather than from Vcc, you get somemeasure of bias stability. The base sits onediode drop above ground; since its biascomes from a 10:1 divider, the collector isat 11 diode drops above ground, or about7 volts. Any tendency for the transistorFigure 2.41. Biasing scheme with compensatedVBEdrop.R,-11 V,, lor -7V)68k___I1Figure 2.42. Bias stability is improved byfeedback.
  • EBERS-MOLL MODEL APPLIED TO BASIC TRANSISTOR CIRCUITS2.13 Biasing the common-emitteramplifierto saturate (e.g., if it happens to haveunusually high beta) is stabilized, sincethe dropping collector voltage will reducethe base bias. This scheme is acceptableif great stability is not required. Thequiescent point is liable to drift a volt or soas the ambient (surrounding) temperaturechanges, since the base-emitter voltagehas a significant temperature coefficient.Better stability is possible if several stagesof amplification are included within thefeedback loop. You will see examples laterin connection with feedback.A better understanding of feedback isreally necessary to understand this circuit.For instance, feedback acts to reduce theinput and output impedances. The inputsignal sees Rls resistance effectively re-duced by the voltage gain of the stage. Inthis case it is equivalent to a resistor ofabout 300 ohms to ground. In Chapter4 we will treat feedback in enoughdetail so that you will be able to figurethe voltage gain and terminal impedanceof this circuit.Note that the base bias resistor valuescould be increased in order to raise theinput impedance, but you should thentake into account the non-negligible basecurrent. Suitable values might be R1 =220k and R2 = 33k. An alternativeapproach might be to bypass the feedbackresistance in order to eliminate feedback(and therefore lowered input impedance)at signal frequencies (Fig. 2.43).Comments on biasing and gainOne important point about grounded emit-ter amplifier stages: You might think thatthe voltage gain can be raised by increas-ing the quiescent current, since the intrin-sic emitter resistance re drops with risingcurrent. Although re does go down withincreasing collector current, the smallercollector resistor you need to obtain thesame quiescent collector voltage just can-cels the advantage. In fact, you can showFigure 2.43. Eliminating feedback at signalfrequencies.that the small-signal voltage gain of agrounded emitter amplifier biased to0.5Vcc is given by G = 20Vcc, indepen-dent of quiescent current.EXERCISE 2.10Show that the preceding statement is true.If you need more voltage gain in onestage, one approach is to use a currentsource as an active load. Since its imped-ance is very high, single-stage voltage gainsof 1000 or more are possible. Such an ar-rangement cannot be used with the bias-ing schemes we have discussed, but mustbe part of an overall dc feedback loop, asubject we will discuss in the next chap-ter. You should be sure such an amplifierlooks into a high-impedance load; other-wise the gain obtained by high collectorload impedance will be lost. Somethinglike an emitter follower, a field-effect tran-sistor (FET), or an op-amp presents a goodload.In radiofrequency amplifiers intendedfor use only over a narrow frequencyrange, it is common to use a parallel LCcircuit as a collector load; in that casevery high voltage gain is possible, sincethe LC circuit has high impedance (likea current source) at the signal frequency,with low impedance at dc. Since the LC
  • TRANSISTORS88 Chapter 2is "tuned," out-of-band interfering signals(and distortion) are effectively rejected.Additional bonuses are the possibility ofpeak-to-peak output swings of 2Vcc andthe use of transformer coupling from theinductor.EXERCISE 2.11Design a tuned common-emitteramplifierstageto operate at 100kHr. Use a bypassed emitterresistor,and set thequiescentcurrentat1.OmA.Assume Vcc = +15 voltsand L = 1.OmH,andput a 6.2k resistor across the LC to set Q = 10(toget a10% bandpass; see Section1.22). Usecapacitive input coupling.user programsa current 1,Figure 2.44. Classic bipolar-transistormatched-pair current mirror. Note the com-mon convention of referringto the positivesup-ply as Vcc,even when pnp transistorsare used.2.14 Current mirrorsThe technique of matched base-emitter bi-asing can be used to make what is called acurrent mirror (Fig. 2.44). You "program"the mirror by sinking a current from Qlscollector. That causes a V B ~for Q1 ap-propriate to that current at the circuit tem-perature and for that transistor type. Q2,matched to Q1 (a monolithic dual tran-sistor is ideal), is thereby programmed tosource the same current to the load. Thesmall base currents are unimportant.One nice feature of this circuit is voltagecompliance of the output transistor currentsource to within a few tenths of a volt ofVcc, since there is no emitter resistor dropto contend with. Also, in many applica-tions it is handy to be able to program acurrent with a current. An easy way to gen-erate the control current Ip is with a resis-tor (Fig. 2.45). Since the bases are a diodedrop below Vcc, the 14.4k resistor pro-duces a control current, and therefore anoutput current, of 1mA. Current mirrorscan be used in transistor circuits when-ever a current source is needed. Theyrevery popular in integrated circuits, where(a) matched transistors abound and (b) thedesigner tries to make circuits that willwork over a large range of supply voltages.There are even resistorless integrated cir-cuit op-amps in which the operating cur-rent of the whole amplifier is set by oneexternal resistor, with all the quiescent cur-rents of the individual amplifier stages in-side being determined by current mirrors.Figure 2.45Current mirror limitations due to EarlyeffectOne problem with the simple current mir-ror is that the output current varies a bitwith changes in output voltage, i.e., theoutput impedance is not infinite. This isbecause of the slight variation of VBE withcollector voltage at a given current in Q2(due to Early effect); in other words, the
  • EBERS-MOLL MODEL APPLIED TO BASIC TRANSISTOR CIRCUITS2.14 Current mirrors 89curve of collector current versus collector-emitter voltage at a fixed base-emitter volt-age is not flat (Fig. 2.46). In practice, theFigure 2.46current might vary 25% or so over theoutput compliance range - much poorerperformance than the current source withemitter resistor discussed earlier.Figure 2.47. Improved current mirror.One solution, if a better current sourceis needed (it often isnt), is the circuitshown in Figure 2.47. The emitter resis-tors are chosen to have at least a few tenthsof a volt drop; this makes the circuit a farbetter current source, since the small vari-ations of VBEwith VCEare now negligiblein determining the output current. Again,matched transistors should be used.Wilson mirrorAnother current mirror with very constantcurrent is shown in the clever circuit ofFigure 2.48. Q1 and Qz are in the usualmirror configuration, but Q3 now keepsQls collector fixed at two diode dropsFigure 2.48. Wilson current mirror. Good sta-bility with load variations is achieved throughcascode transistor Q g , which reduces voltagevariations across Q1.below Vcc. That circumvents the Early ef-fect in Q1, whose collector is now the pro-gramming terminal, with Q2 now sourc-ing the output current. Qg does not af-fect the balance of currents, since its basecurrent is negligible; its only function isto pin Qls collector. The result is thatboth current-determining transistors (Q1and Q2)have fixed collector-emitter drops;you can think of Qg as simply passingthe output current through to a variable-voltage load (a similar trick is used in thecascode connection, which you will seelater in the chapter). Qj, by the way, doesnot have to be matched to Q1 and Q2.Multiple outputs and current ratiosCurrent mirrors can be expanded to source(or sink, with npn transistors) current toseveral loads. Figure 2.49 shows the idea.Note that if one of the current sourcetransistors saturates (e.g., if its load isdisconnected), its base robs current fromthe shared base reference line, reducingthe other output currents. The situation is
  • TRANSISTORS90 Chapter 2controlcurrentFigure 2.49. Current mirror with multipleoutputs. This circuit is commonly used toobtain multiple programmable current sources.load 1 4load 2TcontrolcurrentAloadcontrolcurrentBFigure 2.51. Current mirrors with currentratios other than 1:1.Figure 2.50rescued by adding another transistor (Fig.2.50).Figure 2.51 shows two variations onthe multiple-mirror idea. These circuitsmirror twice (or half) the control current.In the design of integrated circuits, currentmirrors with any desired current ratiocan be made by adjusting the size of theemitter junctions appropriately.Texas Instruments offers complete mo-nolithic Wilson current mirrors in conve-nient TO-92 transistor packages. TheirTL 011 series includes 1:1, 1:2, 1:4, and2:1 ratios, with output compliance from1.2 to 40 volts. The Wilson configurationgives good current source performance -atconstant programming current the outputcurrent increases by only 0.05O/o per volt -and they are very inexpensive (50 cents orless). Unfortunately, these useful devicesare available in npn polarity only.1. = 20pA(programmingcurrent)Figure 2.52. Modifying current-source outputwith an emitter resistor. Note that the outputcurrent is no longer a simple multiple of theprogamming current.Another way to generate an output cur-rent that is a fraction of the programming
  • SOME AMPLIFIER BUILDING BLOCKS2.15 Push-pull output stages 91current is to add a resistor in the emittercircuit of the output transistor (Fig. 2.52).In any circuit where the transistors are op-erating at different current densities, theEbers-Moll equation predicts that the dif-ference in VBEdepends only on the ra-tio of the current densities. For matchedtransistors, the ratio of collector currentsequals the ratio of current densities. Thegraph in Figure 2.53 is handy for determin-ing the difference in base-emitter drops insuch a situation. This makes it easy to de-sign a "ratio mirror."Figure 2.53. Collector current ratios formatched transistors as determined by the dif-ference in applied base-emitter voltages.EXERCISE 2.12Show that the ratio mirror in Figure 2.52 worksas advertised.SOME AMPLIFIER BUILDING BLOCKS2.15 Push-pull output stagesAs we mentioned earlier in the chapter, annpn emitter follower cannot sink current,and a pnp follower cannot source current.The result is that a single-ended followeroperating between split supplies can drivea ground-returned load only if a highquiescent current is used (this is sometimescalled a class A amplifier). The quiescentcurrent must be at least as large as themaximum output current during peaks ofthe waveform, resulting in high quiescentpower dissipation. For instance, Figure2.54 shows a follower circuit to drivean 8 ohm load with up to 10 watts ofaudio. The pnp follower Q1 is includedto reduce drive requirements and to cancelQzs VBEoffset (zero volts input giveszero volts output). Q1 could, of course,be omitted for simplicity. The heftycurrent source in Qls emitter load isused to ensure that there is sufficientbase drive to Q2 at the top of the signalswing. A resistor as emitter load wouldbe inferior because it would have to be arather low value (500 or less) in order toguarantee at least 50mA of base drive toQzat the peak of the swing, when loadcurrent would be maximum and the dropacross the resistor would be minimum; theresultant quiescent current in Q1 would beexcessive.loudspeakersignalin8RFigure 2.54. A 10 watt loudspeaker amplifier,built with a single-ended emitter follower, dis-sipates 165 watts of quiescent power!The output of this example circuit canswing to nearly f15 volts (peak) in both
  • TRANSISTORS92 Chapter 2directions, giving the desired output power(9V rms across 8R). However, the out-put transistor dissipates 55 watts with nosignal, and the emitter resistor dissipatesanother 110 watts. Quiescent power dissi-pation many times greater than the maxi-mum output power is characteristic of thiskind of class A circuit (transistor always inconduction); this obviously leaves a lot tobe desired in applications where any sig-nificant amount of power is involved.Figure 2.55. Push-pull emitter follower.Figure 2.55 shows a push-pull followerto do the same job. Q1 conducts on posi-tive swings, Q2 on negative swings. Withzero input voltage, there is no collectorcurrent and no power dissipation. At 10watts output power there is less than 10watts dissipation in each transistor.crossoversignal outFigure 2.56. Crossover distortion in the push-pull follower.Crossover distortion in push-pull stagesThere is a problem with the precedingcircuit as drawn. The output trails thesignal -inFigure 2.57. Biasing the push-pull follower toeliminate crossover distortion.input by a VBEdrop; on positive swingsthe output is about 0.6 volt less positivethan the input, and the reverse for negativeswings. For an input sine wave, the outputwould look as shown in Figure 2.56. Inthe language of the audio business, this iscalled crossover distortion. The best cure(feedback offers another method, althoughit is not entirely satisfactory) is to bias thepush-pull stage into slight conduction, asin Figure 2.57.The bias resistors R bring the diodesinto forward conduction, holding Qllsbase a diode drop above the input signaland Q2s base a diode drop below the inputsignal. Now, as the input signal crossesthrough zero, conduction passes from Qzto Q1; one of the output transistors isalways on. R is chosen to provide enoughbase current for the output transistors atthe peak output swing. For instance, withf20 volt supplies and an 8 ohm loadrunning up to 10 watts sine-wave power,the peak base voltage is about 13.5 volts,and the peak load current is about 1.6amps. Assuming a transistor beta of 50(power transistors generally have lowercurrent gain than small-signal transistors),the 32mA of necessary base current willrequire base resistors of about 220 ohms(6.5Vfrom Vcc to base at peak swing).
  • SOME AMPLIFIER BUILDING BLOCKS2.15 Push-pull output stages 93Thermal stability in class 8 push-pullamplifiersThe preceding amplifier (sometimes calleda class B amplifier, meaning that eachtransistor conducts over half the cycle)has one bad feature: It is not thermallystable. As the output transistors warm up(and they will get hot, because they aredissipating power when signal is applied),their VBEdrops, and quiescent collectorcurrent begins to flow. The added heat thisproduces causes the situation to get worse,with the strong possibility of what is calledthermal runaway (whether it runs awayor not depends on a number of factors,including how large a "heat sink" is used,how well the diode temperature tracks thetransistor, etc.). Even without runaway,better control over the circuit is needed,usually with the sort of arrangement shownin Figure 2.58.setbias 1RFigure 2.58. Small emitter resistors improvethermal stability in the push-pull follower.For variety, the input is shown comingfrom the collector of the previous stage; R1now serves the dual purpose of being Qlscollector resistor and providing current tobias the diodes and bias-setting resistor inthe push-pull base circuit. Here Rg andR4, typically a few ohms or less, provide a"cushion" for the critical quiescent currentbiasing: The voltage between the basesof the output transistors must now be abit greater than two diode drops, and youprovide the extra with adjustable biasingresistor R2(often replaced by a third seriesdiode). With a few tenths of a volt acrossEls and R4, the temperature variation ofVBEdoesnt cause the current to rise veryrapidly (the larger the drop across R3 andR4, the less sensitive it is), and the circuitwill be stable. Stability is improved bymounting the diodes in physical contactwith the output transistors (or their heatsinks).You can estimate the thermal stabilityof such a circuit by remembering thatthe base-emitter drop decreases by about2. lmV for each 1°C rise and that thecollector current increases by a factorof 10 for every 60mV increase in base-emitter voltage. For example, if R2 werereplaced by a diode, you would have threediode drops between the bases of Q2andQ3, leaving about one diode drop acrossthe series combination of Rg and R4.(The latter would then be chosen to givean appropriate quiescent current, perhaps50mA for an audio power amplifier.) Theworst case for thermal stability occursif the biasing diodes are not thermallycoupled to the output transistors.Let us assume the worst and calculatethe increase in output-stage quiescent cur-rent corresponding to a 30°C temperaturerise in output transistor temperature.Thats not a lot for a power amplifier, bythe way. For that temperature rise, theVBEof the output transistors will decreaseby about 63mV at constant current, rais-ing the voltage across R3 and R4by about20% (i.e., the quiescent current will riseby about 20°/0). The corresponding figurefor the preceding amplifier circuit withoutemitter resistors (Fig. 2.57) will be a factorof 10 rise in quiescent current (recall that
  • TRANSISTORS94 Chapter 2Ic increases a decade per 60mV increasein VBE), i.e., 1000°/o. The improved ther-mal stability of this biasing arrangement isevident.This circuit has the additional advan-tage that by adjusting the quiescentcurrent, you have some control over theamount of residual crossover distortion. Apush-pull amplifier biased in this way toobtain substantial quiescent current at thecrossover point is sometimes referred toas a class AB amplifier, meaning that bothtransistors conduct simultaneously duringa portion of the cycle. In practice, youchoose a quiescent current that is a goodcompromise between low distortion andexcessive quiescent dissipation. Feedback,the subject of the next chapter, is almostalways used to reduce distortion still fur-ther.setFigure 2.59. Biasing a push-pull output stagefor low crossover distorion and good thermalstability.An alternative method for biasing apush-pull follower is shown in Figure 2.59.Q4 acts as an adjustable diode: The baseresistors are a divider, and therefore Qqscollector-emitter voltage will stabilize at avalue that puts 1 diode drop from base toemitter, since any greater VCE will bringit into heavy conduction. For instance, ifboth resistors were lk, the transistor wouldturn on at 2 diode drops, collector to emit-ter. In this case, the bias adjustment letsyou set the push-pull interbase voltage any-where from 1 to 3.5 diode drops. The10pF capacitor ensures that both outputtransistor bases see the same signal; sucha bypass capacitor is a good idea for anybiasing scheme you use. In this circuit,Qls collector resistor has been replacedby current source Q5. Thats a useful cir-cuit variation, because with a resistor it issometimes difficult to get enough base cur-rent to drive Q2near the top of the swing.A resistor small enough to drive Q2 suffi-ciently results in high quiescent collectorcurrent in Q1 (with high dissipation), andalso reduced voltage gain (remember thatG = -Rcollector/Remitter).Another SOIU-tion to the problem of Q2s base drive isthe use of bootstrapping, a technique thatwill be discussed shortly.Figure 2.60. Darlington transistor configura-tion.2.16 Darlington connectionIf you hook two transistors together asin Figure 2.60, the result behaves like asingle transistor with beta equal to the
  • SOME AMPLIFIER BUILDING BLOCKS2.16 Darlington connection 95product of the two transistor betas. Thiscan be very handy where high currentsare involved (e.g., voltage regulators orpower amplifier output stages), or for inputstages of amplifiers where very high inputimpedance is necessary.For a Darlington transistor the base-emitter drop is twice normal, and thesaturation voltage is at least one diodedrop (since Qls emitter must be a diodedrop above Q2s emitter). Also, thecombination tends to act like a rather slowtransistor because Q1 cannot turn off Qzquickly. This problem is usually taken careof by including a resistor from base toemitter of Q2 (Fig. 2.61). R also preventsleakage current through Q1 from biasingFigure 2.61. Improving turn-off speed in aDarlington pair.Q2 into conduction; its value is chosen sothat Qls leakage current (nanoamps forsmall-signal transistors, as much as hun-dreds of microamps for power transistors)produces less than a diode drop across Rand so that R doesnt sink a large propor-tion of Qzs base current when it has adiode drop across it. Typically R might bea few hundred ohms in a power transistorDarlington, or a few thousand ohms for asmall-signal Darlington.Darlington transistors are available assingle packages, usually with the base-emitter resistor included. A typical ex-Figure 2.62. Sziklai connection ("complemen-tary Darlington").ample is the npn power Darlington2N6282, with current gain of 2400 (typi-cally) at a collector current of 10 amps.Sziklai connectionA similar beta-boosting configuration isthe Sziklai connection, sometimes referredto as a complementary Darlington (Fig.2.62). This combination behaves like annpn transistor, again with large beta. It hasonly a single base-emitter drop, but it alsocannot saturate to less than a diode drop.A small resistor from base to emitter of Q2is advisable. This connection is commonin push-pull power output stages wherethe designer wishes to use one polarity ofoutput transistor only. Such a circuit isshown in Figure 2.63. As before, R1 isQls collector resistor. Darlington Q2Q3behaves like a single npn transistor withhigh current gain. The Sziklai connectedpair Q4Q5 behaves like a single high-gainpnp power transistor. As before, Rg andR4 are small. This circuit is sometimescalled a pseudocomplementary push-pullfollower. A true complementary stagewould use a Darlington-connected pnp pairfor Q4Q5.Superbeta transistorThe Darlington connection and its nearrelatives should not be confused with theso-called superbeta transistor, a device
  • TRANSISTORS96 Chapter 2with very high h F ~achieved throughthe manufacturing process. A typicalsuperbeta transistor is the 2N5962, with aguaranteed minimum current gain of 450at collector currents from lOpA to 10mA; 1it belongs to the 2N5961-2N5963 series;with a range of maximum VCEs of 30to 60 volts (if you need higher collectorvoltage, you have to settle for lower beta).Superbeta matched pairs are available foruse in low-level amplifiers that requirematched characteristics, a topic we willdiscuss in Section 2.18. Examples are theLM394 and MAT-01 series; these providehigh-gain npn transistor pairs whose VBEsare matched to a fraction of a millivolt(as little as 50pV in the best versions) andwhose ~ F ~ Sare matched to about 1%. TheMAT-03 is a pnp matched pair.Some commercial devices (e.g., the LM11and LM316 op-amps) achieve base biascurrents as low as 50 picoamps this way.21 2.17 BootstrappingWhen biasing an emitter follower, for in-stance, you choose the base voltage dividerresistors so that the divider presents a stiffvoltage source to the base, i.e., their paral-lel impedance is much less than the imped-ance looking into the base. For this reasonthe resulting circuit has an input imped-ance dominated by the voltage divider -the driving signal sees a much lower im-pedance than would otherwise be neces-sary. Figure 2.64 shows an example. TheinputFigure 2.63. Push-pull power stage using onlynpn output transistors.It is possible to combine superbetatransistors in a Darlington connection.Figure 2.64resistance of about 9k is mostly due to thevoltage-divider impedance of 10k. It isalways desirable to keep input impedanceshigh, and anyway its a shame to loadthe input with the divider, which, afterall, is only there to bias the transistor.Bootstrapping is the colorful name given toa technique that circumvents this problem(Fig. 2.65). The transistor is biased bythe divider RlRz through series resistorR3. C2 is chosen to have low impedanceat signal frequencies compared with thebias resistors. As always, bias is stableif the dc impedance seen from the base(in this case 9.7k) is much less than thedc impedance looking into the base (in
  • SOME AMPLIFIER BUILDING BLOCKS2.17 Bootstrapping 97this case approximately 100k). But nowthe signal-frequency input impedance isno longer the same as the dc impedance.Look at it this way: An input wiggle vi,results in an emitter wiggle VE = vi,. Sothe change in current through bias resistorR3 is 2 = (vin - ~,q)/R3z 0, i.e., Zi,(due to bias string) = vi,/ii, z infinity.Weve made the loading (shunt) impedanceof the bias network very large at signalfrequencies.In practice the value of Rg is effectivelyincreased by a hundred or so, and theinput impedance is then dominated by thetransistors base impedance. The emitter-degenerated amplifier can be bootstrappedin the same way, since the signal onthe emitter follows the base. Note thatthe bias divider circuit is driven by thelow-impedance emitter output at signalfrequencies, thus isolating the input signalfrom this usual task.Figure 2.65. Raising the input impedance ofan emitter follower at signal frequencies bybootstrapping the base bias divider.Another way of seeing this is to noticethat R3 always has the same voltage acrossit at signal frequencies (since both endsof the resistor have the same voltagechanges), i.e., its a current source. Buta current source has infinite impedance.Actually, the effective impedance is lessthan infinity because the gain of a followeris slightly less than 1. That is so becausethe base-emitter drop depends on collectorcurrent, which changes with the signallevel. You could have predicted the sameresult from the voltage-dividing effect ofthe impedance looking into the emitter[re = 25/Ic(mA) ohms] combined withthe emitter resistor. If the follower hasvoltage gain A ( A z 1) the effective valueof R3 at signal frequencies isFigure 2.66. Bootstrapping driver-stage collec-tor load resistor in a power amplifier.Bootstrapping collector load resistorsThe bootstrap principle can be used to in-crease the effective value of a transistorscollector load resistor, if that stage drivesa follower. That can increase the voltagegain of the stage substantially [recall thatGv = -gmRc, with g, = 1/(RE+re)].Figure 2.66 shows an example of a boot-strapped push-pull output stage similar tothe push-pull follower circuit we saw ear-lier. Because the output follows Qns base
  • TRANSISTORS98 Chapter 2signal, C bootstraps Qls collector load,keeping a constant voltage across R2 as thesignal varies (C must be chosen to havelow impedance compared with R1 and R2at all signal frequencies). That makes Rzlook like a current source, raising Qlsvoltage gain and maintaining good basedrive to Q2,even at the peaks of the signalswing. When the signal gets near Vcc, thejunction of R1and R2 actually rises aboveVcc because of the stored charge in C. Inthis case, if Rl = R2(not a bad choice) thejunction between them rises to 1.5 timesVcc when the output reaches Vcc. Thiscircuit has enjoyed considerable popular-ity in commercial audio amplifier design,although a simple current source in placeof the bootstrap is superior, since it main-tains the improvement at low frequenciesand eliminates the undesirable electrolyticcapacitor.2.18 Differential amplifiersThe differential amplifier is a very com-mon configuration used to amplify the dif-ference voltage between two input signals.In the ideal case the output is entirelyindependent of the individual signal lev-els - only the difference matters. Whenboth inputs change levels together, thatsa common-mode input change. A differen-tial change is called normal mode. A gooddifferential amplifier has a high common-mode rejection ratio (CMRR), the ratio ofresponse for a normal-mode signal to theresponse for a common-mode signal of thesame amplitude. CMRR is usually speci-fied in decibels. The common-mode inputrange is the voltage level over which theinputs may vary.Differential amplifiers are important inapplications where weak signals are con-taminated by "pickup" and other miscella-neous noise. Examples include digital sig-nals transferred over long cables (usuallytwisted pairs of wires), audio signals (theterm "balanced" means differential, usu-ally 6000 impedance, in the audio busi-ness), radiofrequency signals (twin-lead ca-ble is differential), electrocardiogram volt-ages, magnetic-core memory readout sig-nals, and numerous other applications. Adifferential amplifier at the receiving endrestores the original signal if the common-mode signals are not too large. Differen-tial amplifiers are universally used in op-erational amplifiers, which we will cometo soon. Theyre very important in dcamplifier design (amplifiers that amplifyclear down to dc, i.e., have no coupling ca-pacitors) because their symmetrical designis inherently compensated against thermaldrifts.Figure 2.67 shows the basic circuit.The output is taken off one collector withrespect to ground; that is called a single-ended output and is the most commonconfiguration. You can think of thisamplifier as a device that amplifies adifference signal and converts it to a single-ended signal so that ordinary subcircuits(followers, current sources, etc.) can makeuse of the output. (If, instead, a differentialoutput is desired, it is taken between thecollectors.)Figure 2.67. Classic transistor differentialamplifier.What is the gain? Thats easy enoughto calculate: Imagine a symmetrical inputsignal wiggle, in which input 1 rises by
  • SOME AMPLIFIER BUILDING BLOCKS2.18 Differential amplifiers 99vi, (a small-signal variation) and input 2drops by the same amount. As long asboth transistors stay in the active region,point A remains fixed. The gain is then de-termined as with the single transistor am-plifier, remembering that the input changeis actually twice the wiggle on either base:GdiE= Rc/2(re +RE). Typically RE issmall, 100 ohms or less, or it may be omit-ted entirely. Differential voltage gains of afew hundred are typical.The common-mode gain can be deter-mined by putting identical signals vi, onboth inputs. If you think about it correctly(remembering that R1 carries both emittercurrents), youll find G C ~= -Rc/(2R1+RE). Here weve ignored the small re, be-cause R1 is typically large, at least a fewthousand ohms. We really could have ig-nored RE as well. The CMRR is roughlyRl/(r, +RE). Lets look at a typical ex-ample (Fig. 2.68) to get some familiaritywith differential amplifiers.Rc is chosen for a quiescent currentof 100pA. As usual, we put the collectorthe (differential) input is zero. From theformulas just derived, this amplifier hasa differential gain of 30 and a common-mode gain of 0.5. Omitting the 1.0kresistors raises the differential gain to150, but drops the (differential) inputimpedance from about 250k to about 50k(you can substitute Darlington transistorsin the input stage to raise the impedanceinto the megohm range, if necessary).Remember that the maximum gain ofa single-ended grounded emitter amplifierbiased to 0.5Vcc is 20Vcc. In the caseof a differential amplifier the maximumdifferential gain (RE = 0) is half thatfigure, or (for arbitrary quiescent point)20 times the voltage across the collectorresistor. The corresponding maximumCMRR (again with RE = 0) is equal to20 times the voltage across R1.EXERCISE 2.13Verify that these expressionsare correct. Thendesign a differential amplifier to your own spec-ifications.at 0.5Vcc for large dynamic range. Qls The differential amplifier is sometimescollector resistor can be omitted, since called a "long-tailed pair," because if theno output is taken there. R1 is chosen length of a resistor symbol indicated itsto give total emitter current of 200pA, magnitude, the circuit would look likesplit equally between the two sides when Figure 2.69. The long tail determines theinput 1QFinput 2"out RcG,,,,= -= -v , - v, 2(RE + r e )G,=-Rc2R1 + RE + r eR1CMRR 5 ----RE + reFigure 2.68. Calculating differential amplifier performance.
  • TRANSISTORS100 Chapter 21long tailFigure 2.69common-mode gain, and the small inter-emitter resistance (including intrinsicemitter resistance re) determines the dif-ferential gain.Current-source biasingThe common-mode gain of the differentialamplifier can be reduced enormously bysubstituting a current source for R1. ThenR1 effectively becomes very large, andthe common-mode gain is nearly zero.If you prefer, just imagine a common-mode input swing; the emitter currentsource maintains a constant total emittercurrent, shared equally by the two collectorcircuits, by symmetry. The output istherefore unchanged. Figure 2.70 shows anexample. The CMRR of this circuit, usingan LM394 monolithic transistor pair forQ1 and Qz and a 2N5963 current sourceis 100,000:1 (100dB). The common-modeinput range for this circuit goes from -12volts to +7 volts; it is limited at thelow end by the compliance of the emittercurrent source and at the high end by thecollectors quiescent voltage.Be sure to remember that this amplifier,like all transistor amplifiers, must have adc bias path to the bases. If the input is ca-pacitively coupled, for instance, you musthave base resistors to ground. An addi-tional caution for differential amplifiers,Figure 2.70. ImprovingCMRR of the differen-tial amplifier with a current source.particularly those without inter-emitterresistors: Bipolar transistors can tolerateonly 6 volts of base-emitter reverse biasbefore breakdown; thus, applying a differ-ential input voltage larger than this willdestroy the input stage (if there is no inter-emitter resistor). An inter-emitter resistorlimits the breakdown current and preventsdestruction, but the transistors may be de-graded (in hfe, noise, etc.). In either casethe input impedance drops drastically dur-ing reverse conduction.Use in single-ended dc amplifiersA differential amplifier makes an excellentdc amplifier, even for single-ended inputs.You just ground one of the inputs and con-nect the signal to the other (Fig. 2.7 1). Youmight think that the "unused" transistorcould be eliminated. Not so! The dif-ferential configuration is inherently com-pensated for temperature drifts, and evenwhen one input is at ground that transis-tor is still doing something: A tempera-ture change causes both VBEs to changethe same amount, with no change in bal-ance or output. That is, changes in VBEare not amplified by Gdiff(only by GCM,
  • SOME AMPLIFIER BUILDING BLOCKS2.18 Differential amplifiers 101which can be made essentially zero). Fur-thermore, the cancellation of VBEs meansthat there are no 0.6 volt drops at the inputto worry about. The quality of a dc ampli-fier constructed this way is limited only bymismatching of input VBEs or their tem-perature coefficients. Commercial mono-lithic transistor pairs and commercial dif-ferential amplifier ICs are available withextremely good matching (e.g., the MAT-01 npn monolithic matched pair has a typ-ical drift of VBE between the two transis-tors of 0.15pVI0C and 0.2pV per month).dc input(noninverting)Figure 2.71. A differentialamplifiercan be usedas a precision single-ended dc amplifier.Either input could have been groundedin the preceding circuit example. Thechoice depends on whether or not theamplifier is supposed to invert the signal.(The configuration shown is preferableat high frequencies, however, because ofMiller efect; see Section 2.19.) Theconnection shown is noninverting, and sothe inverting input has been grounded.This terminology carries over to op-amps,which are simply high-gain differentialamplifiers.Current mirror active loadAs with the simple grounded emitter am-plifier, it is sometimes desirable to have asingle-stage differential amplifier with veryhigh gain. An elegant solution is a cur-rent mirror active load (Fig. 2.72). Q1Q2is the differential pair with emitter cur-rent source. Qg and Qq, a current mir-ror, form the collector load. The high ef-fective collector load impedance providedby the mirror yields voltage gains of 5000or more, assuming no load at the ampli-fiers output. Such an amplifier is usuallyused only within a feedback loop, or as acomparator (discussed in the next section).Be sure to load such an amplifier with ahigh impedance, or the gain will drop enor-mously.Figure 2.72. Differential amplifier with activecurrent mirror load.Differential amplifiers as phase splittersThe collectors of a symmetrical differen-tial amplifier generate equal signal swingsof opposite phase. By taking outputs fromboth collectors, youve got a phase splitter.Of course, you could also use a differen-tial amplifier with both differential inputsand differential outputs. This differentialoutput signal could then be used to drivean additional differential amplifier stage,with greatly improved overall common-mode rejection.
  • TRANSISTORS102 Chapter 2Differential amplifiers as comparatorsBecause of its high gain and stable char-acteristics, the differential amplifier is themain building block of the comparator, acircuit that tells which of two inputs islarger. They are used for all sorts of ap-plications: switching on lights and heaters,generating square waves from triangles, de-tecting when a level in a circuit exceedssome particular threshold, class D ampli-fiers and pulse-code modulation, switchingpower supplies, etc. The basic idea is toconnect a differential amplifier so that itturns a transistor switch on or off, depend-ing on the relative levels of the input sig-nals. The linear region of amplificationis ignored, with one or the other of thetwo input transistors cut off at any time.A typical hookup is illustrated in the nextsection by a temperature-controlling cir-cuit that uses a resistive temperature sen-sor (thermistor).2.19 Capacitance and Miller effectIn our discussion so far we have used whatamounts to a dc, or low-frequency, modelof the transistor. Our simple currentamplifier model and the more sophisti-cated Ebers-Moll transconductance mod-el both deal with voltages, currents, andresistances seen at the various terminals.With these models alone we have managedto go quite far, and in fact these simplemodels contain nearly everything you willever need to know to design transistor cir-cuits. However, one important aspect thathas serious impact on high-speed and high-frequency circuits has been neglected: theexistence of capacitance in the external cir-cuit and in the transistor junctions them-selves. Indeed, at high frequencies the ef-fects of capacitance often dominate circuitbehavior; at 100 MHz a typical junctioncapacitance of 5pF has an impedance of320 ohms!We will deal with this important sub-ject in detail in Chapter 13. At this pointwe would merely like to state the problem,illustrate some of its circuit incarnations,and suggest some methods of circumvent-ing the problem. It would be a mistaketo leave this chapter without realizing thenature of this problem. In the course ofthis brief discussion we will encounter thefamous Miller eflect and the use of config-urations such as the cascode to overcomeit.Junction and circuit capacitanceCapacitance limits the speed at which thevoltages within a circuit can swing ("slewrate"), owing to finite driving impedanceor current. When a capacitance is drivenby a finite source resistance, you see RCex-ponential charging behavior, whereas a ca-pacitance driven by a current source leadsto slew-rate-limited waveforms (ramps).As general guidance, reducing the sourceimpedances and load capacitances and in-creasing the drive currents within a circuitwill speed things up. However, there aresome subtleties connected with feedbackcapacitance and input capacitance. Letstake a brief look.+ "ccI+- outputFigure 2.73. Junction and load capacitancesina transistor amplifier.The circuit in Figure 2.73 illustratesmost of the problems of junction capac-itance. The output capacitance forms a
  • time constant with the output resistanceRL (RL includes both the collectorand load resistances, and CL includesboth junction and load capacitances),giving a rolloff starting at some frequencyf = 1I2rRLCL. The same is true for theinput capacitance in combination with thesource impedance Rs.Miller effectCCbis another matter. The amplifier hassome overall voltage gain Gv,so a smallvoltage wiggle at the input results in awiggle Gv times larger (and inverted) atthe collector. This means that the signalsource sees a current through CCbthat isGv+ 1 times as large as if CCbwere con-nected from base to ground; i.e., for thepurpose of input rolloff frequency calcu-lations, the feedback capacitance behaveslike a capacitor of value Ccb(Gv+ 1) frominput to ground. This effective increase ofCcbis known as the Miller effect. It of-ten dominates the rolloff characteristics ofamplifiers, since a typical feedback capaci-tance of 4pF can look like several hundredpicofarads to ground.There are several methods available tobeat the Miller effect. It is absent alto-gether in a grounded base stage. You candecrease the source impedance driving agrounded emitter stage by using an emit-ter follower. Figure 2.74 shows two otherpossibilities. The differential amplifier cir-cuit (with no collector resistor in Q1) hasno Miller effect; you can think of it as anemitter follower driving a grounded baseamplifier. The second circuit is the famouscascode configuration. Q1 is a groundedemitter amplifier with RL as its collectorresistor. Q2 is interposed in the collectorpath to prevent Qls collector from swing-ing (thereby eliminating the Miller effect)while passing the collector current throughto the load resistor unchanged. V+ is afixed bias voltage, usually set a few voltsabove Qls emitter voltage to pin QlsSOME AMPLIFIER BUILDING BLOCKS2.19 Capacitance and Miller effecttoutputFigure 2.74. Two circuit configurations thatavoid Miller effect. Circuit B is the cascode.collector and keep it in the active region.This fragment is incomplete as shown; youcould either include a bypassed emitterresistor and base divider for biasing (aswe did earlier in the chapter) or includeit within an overall loop with feedback atdc. V+might be provided from a divideror Zener, with bypassing to keep it stiff atsignal frequencies.EXERCISE 2.14Explain in detail why there is no Miller effectin either transistor in the preceding differentialamplifier and cascode circuits.Capacitive effects can be somewhatmore complicated than this brief introduc-tion might indicate. In particular: (a) Therolloffs due to feedback and output capaci-tances are not entirely independent; in theterminology of the trade there is pole split-ting, an effect we will explain in the nextchapter. (b) The input capacitance still
  • TRANSISTORS104 Chapter 2has an effect, even with a stiff input sig-nal source. In particular, current that flowsthrough Cb, is not amplified by the tran-sistor. This base current "robbing" by theinput capacitance causes the transistorssmall-signal current gain hf, to drop athigh frequencies, eventually reaching unityat a frequency known as fT. (c) To com-plicate matters, the junction capacitancesdepend on voltage. Cb, changes so rapidlywith base current that it is not even spec-ified on transistor data sheets; fT is giveninstead. (d) When a transistor is operatedas a switch, effects associated with chargestored in the base region of a saturatedtransistor cause an additional loss of speed.We will take up these and other topics hav-ing to do with high-speed circuits in Chap-ter 13.2.20 Field-effect transistorsIn this chapter we have dealt exclusivelywith bipolar junction transistors (BJTs),characterized by the Ebers-Moll equation.BJTs were the original transistors, and theystill dominate analog circuit design. How-ever, it would be a mistake to continuewithout a few words of explanation aboutthe other kind of transistor, the field-effecttransistor (FET), which we will take up indetail in the next chapter.The FET behaves in many ways likean ordinary bipolar transistor. It is a 3-terminal amplifying device, available inboth polarities, with a terminal (the gate)that controls the current flow between theother two terminals (source and drain).It has a unique property, though: Thegate draws no current, except for leakage.This means that extremely high inputimpedances are possible, limited only bycapacitance and leakage effects. WithFETs you dont have to worry aboutproviding substantial base current, as wasnecessary with the BJT circuit design ofthis chapter. Input currents measured inpicoamperes are commonplace. Yet theFET is a rugged and capable device, withvoltage and current ratings comparable tothose of bipolar transistors.Most of the available devices fabricatedwith transistors (matched pairs, differen-tial and operational amplifiers, compara-tors, high-current switches and amplifiers,radiofrequency amplifiers, and digitallogic) are also available with FET construc-tion, often with superior performance.Furthermore, microprocessors and mem-ory (and other large-scale digital electron-ics) are built almost exclusively with FETs.Finally, the area of micropower design isdominated by FET circuits.FETs are so important in electronic de-sign that we will devote the next chapterto them, before treating operational ampli-fiers and feedback in Chapter 4. We urgethe reader to be patient with us as we laythe groundwork in these first three difficultchapters; that patience will be rewardedmany times over in the succeeding chap-ters, as we explore the enjoyable topics ofcircuit design with operational amplifiersand digital integrated circuits.SOME TYPICAL TRANSISTOR CIRCUITSTo illustrate some of the ideas of thischapter, lets look at a few examples ofcircuits with transistors. The range ofcircuits we can cover is necessarily limited,since real-world circuits often use negativefeedback, a subject we will cover inChapter 4.2.21 Regulated power supplyFigure 2.75 shows a very common config-uration. R1 normally holds Q1 on; whenthe output reaches 10 volts, Q2 goes intoconduction (base at 5V), preventing fur-ther rise of output voltage by shunting basecurrent from Qls base. The supply can bemade adjustable by replacing R2 and R3
  • SOME TYPICAL TRANSISTOR CIRCUITS2.22 Temperature controller 105Q1+12V to +25V 2N3055 - +1OV-(unregulated) 0 to 1OOrnAFigure 2.75. Feedback voltage regulator.by a potentiometer. This is actually anexample of negative feedback: Q2 "looksat" the output and does something aboutit if the output isnt at the right voltage.2.22 Temperature controllerThe schematic diagram in Figure 2.76shows a temperature controller based ona thermistor sensing element, a device thatchanges resistance with temperature. Dif-ferential Darlington Q1 - Q4compares thevoltage of the adjustable reference dividerR4-Rs with the divider formed from thethermistor and R2. (By comparing ratiosfrom the same supply, the comparison be-comes insensitive to supply variations; thisparticular configuration is called a Wheat-stone bridge.) Current mirror QsQs pro-vides an active load to raise the gain, andmirror Q7Q8provides emitter current. Qgcompares the differential amplifier outputwith a fixed voltage, saturating DarlingtonQloQll, which supplies power to the heat-er, if the thermistor is too cold. R9 is acurrent-sensing resistor that turns on pro-tection transistor Q12 if the output cur-rent exceeds about 6 amps; that removesbase drive from QloQll, preventingdamage.+50V (unregulated)-R90.1R+15VR l15k1OR50Wheater5--- -- Figure 2.76. Temperature controller for 50 watt heater.
  • TRANSISTORS106 Chapter 2seat Figure 2.77. Both diodes and tran-sistors are used to make digital logic"gates" in this seat-belt buzzer circuit.10- 1 I I I I1OMA 100pA 1mA lOrnA 1OOmA 1 Acollector current, lcFigure 2.78. Curves of typical transistor current gain, ~ F E ,for a selection of transistors fromTable 2.1. These curves are taken from manufacturers literature. You can expect productionspreads of +100°/o, -50% from the "typical" values graphed.
  • Figure 2.79SELF-EXPLANATORYCIRCUITS2.25 Bad circuits 1072.23 Simple logic with transistorsand diodesFigure 2.77 shows a circuit that performsa task we illustrated in Section 1.32:sounding a buzzer if either car door is openand the driver is seated. In this circuit thetransistors all operate as switches (eitheroff or saturated). Diodes Dl and D2form what is called an OR gate, turningoff Q1 if either door is open (switchclosed). However, the collector of Ql staysnear ground, preventing the buzzer fromsounding unless switch S3 is also closed(driver seated); in that case R2 turns QQon, putting 12 volts across the buzzer. D3provides a diode drop so that Q1is off withS1or S2closed, and D4protects Q3fromthe buzzers inductive turn-off transient.In Chapter 8 we will discuss logic circuitryin detail.Table 2.1 presents a selection of usefuland popular small-signal transistors; Fig-ure 2.78 shows corresponding curves ofcurrent gain. See also Appendix K.SELF-EXPLANATORY CIRCUITS2.24 Good circuitsFigure 2.80 shows a couple of circuit ideasthat use transistors.2.25 Bad circuitsA lot can be learned from your ownmistakes or someone elses mistakes. Inthis section we present a gallery of blunders(Fig. 2.81). You can amuse yourselfby thinking of variations on these badcircuits, and then avoiding them!ADDITIONAL EXERCISES(I) Design a transistor switch circuit thatallows you to switch two loads to groundvia saturated npn transistors. Closingswitch A should cause both loads to bepowered, whereas closing switch B shouldpower only one load. Hint: Use diodes.
  • TABLE 2.1. SELECTEDSMALL-SIGNALTRANSISTORSaMetal PlasticIC Ccb f~ TO-5e TO-18 TO-92h"CEO maX hFE lc typCtypdGain(V) (mA) typb(mA) (pF) (MHz) curve npn PnP nPn PnP nPn PnPGeneral 20 500 100 150 16 200 - - - - - -purpose 25 200 200 2 1.8-2.8 300 4 - - - - 4124 412640 200 200 10 1.8-2.8 300 - - 3947 3251 3904 3906High gain, 25 50 300 10 2-7 150 -- - - 3 3 9 1 ~ ~ , 3 7 0 7 ~4 0 5 8 ~low noise 25 300 250 50 4 300 - - - - 6008~ 6009~25 50 500 5 1.5-4 500 - - - - 5089 -40 20 700 1 14 200 2 LM394 - - - - -45 50 1000 10 1.5 300 1 - - - - 5962 -50 50 350 5 1.8 400 3 - - 2848 3965 4967,5210 4965,5087High 30-60 600 150 150 5 300 5 2219 2905 2222 2907,3251 4401 4403current 50 1000 100 200 7 450 3725 5022 4014 - - -60 1000 70 80 15 100 2102,3107 4036 - - - -75 2000 70 500 20 60 7,9 5320 5322 - - - -High 150 600 100 10 3-6 250 - 4929 - 5550 5401-voltage 300 1000 50 50 10 50 3439 5416 - - - -High 12 50 80 3 0.7 1500 6 - - -5179 3662h -speed 12 100 50 8 1.5 900 8 - - 918 4208 5770 -12 200 75 25 3 500 - - 2369 2894 5769 5771(a) all transistors are 2Nxxx numbers, except for the LM394 dual transistor. Devices listed on a single row are similar in characteristics and in some casesare electrically identical. (b) see figure 2.76. 6)at VcB=lOV. (d)see figure 13.4. or TO-39. () or TO-72, TO-46. (h) TO-92 and its variants havetwo basic pinouts: EBC and ECB. Transistors with superscript hare ECB; all others are EBC.
  • TRANSISTORS110 Chapter 2(2) Consider the current source in Figure2.79. (a) What is Iload? What is theoutput compliance? Assume V B ~is 0.6volt. (b) If hFE varies from 50 to 100for collector voltages within the outputcompliance range, how much will theoutput current vary? (There are two effectshere.) (c) If VBE varies according toAVBE = -0.0001 AVcE (Early effect),how much will the load current vary overthe compliance range? (d) What is thetemperature coefficient of output currentassuming that hFE does not vary withtemperature? What is the temperaturecoefficient of output current assuming thathFE increases from its nominal value of100 by 0.4°/o/0C?(3) Design a common-emitter npn ampli-fier with voltage gain of 15, Vcc of +15volts, and Ic of 0.5mA. Bias the collectorat 0.5Vcc, and put the low-frequency 3dBpoint at 1OOHz.(4) Bootstrap the circuit in the precedingproblem in order to raise the input imped-ance. Choose the rolloff of the bootstrapappropriately.(5) Design a dc-coupled differential am-plifier with voltage gain of 50 (to a single-ended output) for input signals nearground, supply voltages of f15 volts, andquiescent currents of O.1mA in each tran-sistor. Use a current source in the emitterand an emitter follower output stage.(6) In this problem you will ultimately de-sign an amplifier whose gain is controlledby an externally applied voltage (in Chap-ter 3 you will see how to do the samething with FETs). (a) Begin by design-ing a long-tailed pair differential amplifierwith emitter current source and no emitterresistors (undegenerated). Use f15 voltsupplies. Set Ic (each transistor) at lmA,and use Rc = 1.0k. Calculate the volt-age gain from a single-ended input (otherinput grounded) to a single-ended output.(b) Now modify the circuit so that an ex-ternally applied voltage controls the emit-ter current source. Give an approximateg 1Figure 2.82+ 2v+ "cc-in4 0, 1 - t o furtherstagesFigure 2.83. Base-current cancellation scheme,commonly used in high-quality operationalamplifiers.formula for the gain as a function ofcontrolling voltage. (In a real circuit youmight arrange a second set of voltage-controlled current sources to cancel thequiescent-point shift that gain changesproduce in this circuit, or a differential-input second stage could be added to yourcircuit.)(7) Disregarding the lessons of this chap-ter, a disgruntled student builds the am-plifier shown in Figure 2.82. He adjustsR until the quiescent point is 0.5Vcc. (a)What is Zi, (at high frequencies whereZc e O)? (b) What is the small-signal volt-age gain? (c) What rise in ambient temper-ature (roughly) will cause the transistor tosaturate?
  • SELF-EXPLANATORYCIRCUITS2.25 Bad circuits 111(8) Several commercially available pre- differential amplifier is shown in detail; thecision op-amps (e.g., the venerable OP- other half works the same way). Explain07 and the recent LT1012) use the circuit how the circuit works. Note: Q1 and Qzin Figure 2.83 to cancel input bias cur- are a beta-matched pair. Hint: Its all donerent (only half of the symmetrical-input with mirrors.
  • Ch3: Field-Effect TransistorsINTRODUCTIONField-effect transistors (FETs) are differentfrom the ordinary transistors (sometimescalled "bipolar transistors," "bipolar junc-tion transistors," or BJTs, to distinguishthem from FETs) that we talked aboutin the last chapter. Broadly speaking,however, they are similar devices,which we might call charge-control de-vices: In both cases we have a 3-terminaldevice in which the conduction betweentwo electrodes depends on the availabil-ity of charge carriers, which is controlledby a voltage applied to a third controlelectrode.Heres how they differ: In an npn BJTthe collector-base junction is back-biased,so no current normally flows. Forward-biasing the base-emitter junction by ~ 0 . 6volts overcomes its diode "contact poten-tial barrier," causing electrons to enter thebase region, where they are strongly at-tracted to the collector; although some basecurrent results, most of these "minoritycarriers" are captured by the collector.This results in a collector current, con-trolled by a (smaller) base current. Thecollector current is proportional to therate of injection of minority carriers intothe base region, which is an exponentialfunction of the BE potential difference (theEbers-Moll equation). You can think ofa bipolar transistor as a current amplifier(with roughly constant current gain, hFE)or as a transconductance device (Ebers-Moll).In a FET, as the name suggests, conduc-tion in a channel is controlled by an elec-tricjield, produced by a voltage applied tothe gate electrode. There are no forward-biased junctions, so the gate draws no cur-rent; this is perhaps the most importantadvantage of the FET. As with BJTs, thereare two polarities, n-channel FETs (con-duction by electrons) and p-channel FETs(conduction by holes). These two polari-ties are analogous to the familiar npn andpnp bipolar transistors, respectively. In ad-dition, however, FETs tend to be confusingat first because they can be made with twodifferent kinds of gates (thus JFETs andMOSFETs), and with two different kindsof channel doping (leading to enhancementand depletion modes). Well sort out thesepossibilities shortly.
  • FIELD-EFFECT TRANSISTORS114 Chapter 3First, though, some motivation and per-spective: The FETs nonexistent gate cur-rent is its most important characteristic.The resulting high input impedance (whichcan be greater than 1 0 ~ ~ 0 )is essential inmany applications, and in any case itmakes circuit design simple and fun. Forapplications like analog switches and am-plifiersof ultrahigh input impedance, FETshave no equal. They can be easily used bythemselves or combined with bipolar tran-sistors to make integrated circuits: In thenext chapter well see how successful thatprocess has been in making nearly perfect(and wonderfully easy to use) operationalampl$ers, and in Chapters 8-11 well seehow digital electronics has been revolu-tionized by MOSFET integrated circuits.Because many FETs using very low currentcan be constructed in a small area, theyare especially useful for large-scale integra-tion (LSI) digital circuits such as calculatorchips, microprocessors, and memories. Inaddition, high-current MOSFETs (30A ormore) of recent design have been replacingbipolar transistors in many applications,often providing simpler circuits with im-proved performance.3.01 FET characteristicsBeginners sometimes become catatonicwhen directly confronted with the confus-ing variety of FET types (see, for exam-ple, the first edition of this book!), a vari-ety that arises from the combined choicesof polarity (n-channel or p-channel), formof gate insulation (semiconductor junction[JFET]or oxide insulator[MOSFET]), andchannel doping (enhancement or depletionmode). Of the eight resulting possibilities,six could be made, and five actually are.Four of those five are of major importance.It will aid understanding (and sanity),however, if we begin with one type only,just as we did with the npn bipolar tran-sistor. Once comfortable with FETs, wellhave little trouble with their family tree.FET V-l curvesLets look first at the n-channel enhance-ment-mode MOSFET, which is analogousto the npn bipolar transistor (Fig. 3.1). Innormal operation the drain collector) ismore positive than the source (-emitter).No current flows from drain to sourceunless the gate base) is brought positivewith respect to the source. Once thegate is thus "fonvard-biased" there will bedrain current, all of which flows to thesource. Figure 3.2 shows how the draincurrent IDvaries with drain-source voltageVDs, for a few values of controlling gate-source voltage VGS.For comparison, thecorresponding "family" of curves of Icversus VBEfor an ordinary npn bipolartransistor is shown. Obviously threre area lot of similarities between n-channelMOSFETs and npn bipolar transistors.d r a ~ n collectorsource emittern~channelMOSFET npn b~polartransistorFigure 3.1Like the npn transistor, the FET has ahigh incremental drain impedance, givingroughly constant current for VDs greaterthan a volt or two. By an unfortunatechoice of language, this is called the "satu-ration" region of the FET and correspondsto the "active" region of the bipolar tran-sistor. Analogous to the bipolar transistor,larger gate-to-source bias produces largerdrain current. If anything, FETs behavemore nearly like ideal transconductancedevices (constant drain current for con-stant gate-source voltage) than do bipolar
  • INTRODUCTION3.01 FET characteristics 1150 10 20 0 0 1 0 2v,, IVI v,, IV,BFigure 3.2. Measured MOSFETItransistor characteristic curves.A. VN0106 n-channel MOSFET: ID versus VDS for various values of VGS.B. 2N3904 npn bipolar transistor: Ic versus VCE for various values of VBE.transistors; the Ebers-Moll equation pre-dicts perfect transconductance characteris-tics for bipolar transistors, but that idealbehavior is degraded by the Early effect(Section 2.10).So far, the FET looks just like the npntransistor. Lets look closer, though. Forone thing, over the normal range of cur-rents the saturation drain current increasesrather modestly with increasing gate volt-age (VGS). In fact, it is proportional to(VGS- VT)~,where VT is the "gate thresh-old voltage" at which drain current begins(VT M 1.63V for the FET in Fig. 3.2);compare this mild quadratic law with thesteep exponential transistor law, as givento us by Ebers and Moll. Second, there iszero dc gate current, so you mustnt thinkof the FET as a device with current gain(which would be infinite). Instead, think
  • FIELD-EFFECT TRANSISTORS116 Chapter 3of the FET as a transconductance device,with gate-source voltage programming thedrain current, as we did with the bipolartransistor in the Ebers-Moll treatment; re-call that the transconductance g, is sim-ply the ratio id/vgS (recall the conven-tion of using lower-case letters to indicate"small-signal" changes in a parameter; e.g.,id/vgs = GId/SVss). Third, the gate of aMOSFET is truly insulated from the drain-source channel; thus, unlike the situationfor bipolar transistors (or JFETs, as wellsee), you can bring it positive (or negative)at least 10 volts or more without worryingabout diode conduction. Finally, the FETdiffers from the bipolar transistor in theso-called linear region of the graph, whereit behaves rather accurately like a resistor,even for negative VDs;this turns out to bequite useful because the equivalent drain-source resistance is, as you might guess,programmed by the gate-source voltage.Two examplesFETs have more surprises in store forus. Before getting into more details,though, lets look at two simple switchingapplications. Figure 3.3 shows the MOS-FET equivalent of Figure 2.3, our first sat-urated transistor switch. The FET circuitis even simpler, because we dont haveto concern ourselves with the inevitablecompromise of providing adequate basedrive current (considering worst-case min-imum hFEcombined with the lamps coldresistance) without squandering excessivepower. Instead, we just apply a full-swingdc voltage drive to the cooperative high-impedance gate. As long as the switched-on FET behaves like a resistance smallcompared with the load, it will bring itsdrain close to ground; typical power MOS-FETs have RON< 0.2 ohm, which is finefor this job.Figure 3.4 shows an "analog switch"application, which cannot be done at allwith bipolar transistors. The idea here is toswitch the conduction of a FET from open-Figure 3.3. MOSFET switch.15. s w ~ t c hONIground. s w ~ t c hOFF --&-.-Figure 3.4circuit (gate reverse-biased) to short-circuit(gate fonvard-biased), thus blocking orpassing the analog signal (well see plentyof reasons to do this sort of thing later).In this case we just arrange for the gateto be driven more negative than any in-put signal swing (switch open), or a fewvolts more positive than any input signalswing (switch closed). Bipolar transistorsarent suited to this application, becausethe base draws current and forms diodeswith the emitter and collector, producingawkward clamping action. The MOSFETis delightfully simple by comparison,needing only a voltage swing into the(essentially open-circuit) gate. Warning:
  • INTRODUCTION3.02 FET types 117Iconducting n ~ t y p eregionforms here when gate ISbrought pos~tiveFigure 3.5. An n-channel MOSFET.Its only fair to mention that our treat-ment of this circuit has been somewhatsimplistic, for instance ignoring the effectsof gate-channel capacitance and thevariation of RONwith signal swing. Wellhave more to say about analog switcheslater.3.02 FET typesn-channel, p-channelNow for the family tree. First of all, FETs(like BJTs) can be fabricated in both po-larities. Thus, the mirror twin of our n-channel MOSFET is a p-channel MOSFET.Its behavior is symmetrical, mimickingpnp transistors: The drain is normally neg-ative with respect to the source, and draincurrent flows if the gate is brought at leasta volt or two negative with respect to thesource. The symmetry isnt perfect be-cause the carriers are holes, rather thanelectrons, with lower "mobility" and "mi-nority carrier lifetime." These are semi-conductor parameters of importance intransistor performance. The consequenceis worth remembering - p-channel FETsusually have poorer performance,manifested as higher gate threshold vol-tage, higher RON, and lower saturationcurrent.MOSFET, JFETIn a MOSFET ("Metal-Oxide-Semicon-ductor Field-Effect Transistor") the gateregion is separated from the conductingchannel by a thin layer of SiOz (glass)grown onto the channel (Fig. 3.5). Thegate, which may be either metal or dopedsilicon, is truly insulated from the source-drain circuit, with characteristic inputresistance >loi4 ohms. It affects channelconduction purely by its electric field.MOSFETs are sometimes called insulated-gate FETs, or IGFETs. The gate insulatinglayer is quite thin, typically less than awavelength of light, and can withstandgate voltages up to f20 volts or more.MOSFETs are easy to use because the gatecan swing either polarity relative to thesource without any gate current flowing.They are, however, quite susceptible todamage from static electricity; you candestroy a MOSFET device literally bytouching it.The symbols for MOSFETs are shownin Figure 3.6. The extra terminal is the"body," or "substrate," the piece of sili-con in which the FET is fabricated (seeFig. 3.5). Because the body forms a diodejunction with the channel, it must be heldat a nonconducting voltage. It can betied to the source, or to a point in the
  • FIELD-EFFECT TRANSISTORS118 Chapter 3dra~n drainsource sourcedrain draingateA 6.d~ gate 1 +bodysource sourceA.n-channel MOSFET B. p-channel MOSFETFigure 3.6circuit more negative (positive) than thesource for n-channel @-channel) MOS-FETs. It is common to see the bodyterminal omitted; furthermore, engineersoften use the symbol with the symmetricalgate. Unfortunately, with whats left youcant tell source from drain; worse still,you cant tell n-channel from p-channel!We will use the lower set of schematicsymbols exclusively in this book to avoidconfusion, although we will often leave thebody pin unconnected.In a JFET ( "Junction Field-Effect Tran-sistor") the gate forms a semiconductorjunction with the underlying channel. Thishas the important consequence that a JFETgate should not be forward biased with re-spect to the channel, to prevent gate cur-rent. For example, diode conduction willoccur as the gate of an n-channel JFETapproaches +0.6 volt with respect to themore negative end of the channel (which isusually the source). The gate is thereforeoperated reverse-biased with respect to thechannel, and no current (exceptdiode leak-age) flows in the gate circuit. The cir-cuit symbols for JFETs are shown in Fig-ure 3.7. Once again, we favor the symbolwith offset gate, to identify the source. Aswell see later, FETs (both JFET and MOS-FET) are nearly symmetrical, but the gate-drain capacitance is usually designed tobe less than the gate-source capacitance,making the drain the preferred outputterminal.drain Isourcedraingate 4 gate 4,(4source I Isource IA. n-channel JFETordraingate 4sourceB. p-channel JFETFigure 3.7Enhancement, depletionThe n-channel MOSFETs with which webegan the chapter were nonconducting,with zero (or negative) gate bias, and weredriven into conduction by bringingthe gatepositive with respect to the source. Thiskind of FET is known as enhancementmode. The other possibility is to manu-facture the n-channel FET with the chan-nel semiconductor "doped" so that thereis plenty of channel conduction even withzero gate bias, and the gate must be reverse-biased a few volts to cut off the drain cur-rent. Such a FET is known as depletionmode. MOSFETs can be made in eithervariety, since there is no restriction on gatepolarity. But JFETs permit only reversegate bias and therefore can be made onlyin depletion mode.A graph of drain current versus gate-source voltage, at a fixed value of drainvoltage, may help clarify this distinction(Fig. 3.8). The enhancement-mode devicedraws no drain current until the gate
  • INTRODUCTION3.03 Universal FET characteristics 119is brought positive (these are n-channelFETs) with respect to the source, whereasthe depletion-mode device is operating atnearly its maximum value of drain currentwhen the gate is at the same voltage as thesource. In some sense the two categoriesare artificial, because the two curves areidentical except for a shift along the VGSaxis. In fact, it is possible to manufacture"in-between" MOSFETs. Nevertheless,the distinction is an important one whenit comes to circuit design.log plotVenhancementCFigure 3.8Note that JFETs are always depletion-mode devices and that the gate cannot bebrought more than about 0.5 volt morepositive (for n-channel) than the source,since the gate-channel diode will conduct.MOSFETs could be either enhancement ordepletion, but in practice you rarely seedepletion-mode MOSFETs (the exceptionsbeing n-channel GaAs FETs and "dual-gate" cascodes for radiofrequency applica-tions). For all practical purposes, then, youhave to worry only about (a) depletion-mode JFETs and (b) enhancement-modeMOSFETs; they both come in the two po-larities, n-channel and p-channel.3.03 Universal FET characteristicsA family tree (Fig. 3.9) and a map (Fig.3.10) of inputloutput voltage (sourcegrounded) may help simplify things. Thedifferent devices (including garden-varietynpn and pnp bipolar transistors) are drawnin the quadrant that characterizes their in-put and output voltages when they are inthe active region with source (or emitter)grounded. You dont have to rememberthe properties of the five kinds of FETs,though, because theyre all basically thesame.A An-channel p~channel depletion enhancementIn-channeln-channel p-channelFigure 3.9output+4n~channeldepletion n-channel enhancementn-channel JFET npn transistorsIinput -- a-++ inputp-channel enhancementpnp transistorst-outputFigure 3.10First, with the source grounded, a FETis turned on (brought into conduction)by bringing the gate voltage "toward" theactive drain supply voltage. This is true forall five types of FETs, as well as the bipolartransistors. For example, an n-channelJFET (which is automatically depletion-mode) uses a positive drain supply, as doall n-type devices. Thus a positive-goinggate voltage tends to turn on the JFET.
  • FIELD-EFFECT TRANSISTORS120 Chapter 3The subtlety for depletion-mode devices isthat the gate must be (negatively) back-biased for zero drain current, whereasfor enhancement-mode devices zero gatevoltage is sufficient to give zero draincurrent.Second, because of the near symmetryof source and drain, either terminal can actas the effective source (exception: not truefor power MOSFETs, where the body isinternally connected to the source). Whenthinking of FET action, and for purposesof calculation, the effective source terminalis always the one most "away" from theactive drain supply. For example, supposea FET is used to switch a line to ground,and both positive and negative signals arepresent on the switched line, which is usu-ally selected to be the FET drain. If theswitch is an n-channel MOSFET (thereforeenhancement), and a negative voltage hap-pens to be present on the (turned-off)drainterminal, then that terminal is actually the"source" for purposes of gate turn-on volt-age calculation. Thus a negative gate volt-age larger than the most negative signal,rather than ground, is needed to ensureturn-off.The graph in Figure 3.1 1 may help yousort out all these confusing ideas. Again,the difference between enhancement anddepletion is merely a question of displace-ment along the VGS axis - i.e., whetherthere is a lot of drain current or no draincurrent at all when the gate is at the samepotential as the source. The n-channel andp-channel FETs are complementary in thesame way as npn and pnp bipolar transis-tors.In Figure 3.11 we have used standardsymbols for the important FET parame-ters of saturation current and cutoff volt-age. For JFETs the value of drain currentwith gate shorted to source is specified onthe data sheets as IDssand is nearly themaximum drain current possible. (IDssmeans current from drain to source withthe gate shorted to the source. Throughoutthe chapter you will see this notation, inwhich the first two subscripted letters des-ignate the pair of terminals, and the thirdspecifies the condition.) For enhancement-mode MOSFETs the analogous specifica-tion is ID(ON),given at some forward gatevoltage ("IDss" would be zero for anyenhancement-mode device).log plotenhancement-5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5VP v, v , VPVGS-Figure 3.1 1For JFETs the gate-source voltage atwhich drain current approaches zero iscalled the "gate-source cutoff voltage,"VGS(OFF),or the "pinch-off voltage," Vp,and is typically in the range of -3 to -10volts (positive for p-channel, of course).For enhancement-mode MOSFETs theanalogous quantity is the "threshold volt-age," VT (or the gate-source volt-age at which drain current begins to flow.VTis typically in the range of 0.5 to 5 volts,in the "forward" direction, of course. In-cidentally, dont confuse the MOSFET VTwith the VT in the Ebers-Moll equationthat describes bipolar transistor collectorcurrent; they have nothing to do with eachother.With FETs it is easy to get confusedabout polarities. For example, n-channeldevices, which usually have the drain
  • INTRODUCTION3.04 FET drain characteristics 121positive with respect to the source, canhave positive or negative gate voltage, andpositive (enhancement) or negative (deple-tion) threshold voltages. To make mat-ters worse, the drain can be (and oftenis) operated negative with respect to thesource. Of course, all these statements goin reverse for p-channel devices. In or-der to minimize confusion, we will alwaysassume n-channel devices unless explicitlystated otherwise. Likewise, because MOS-FETs are nearly always enhancement-mode, and JFETs are always depletion-mode, well omit those designations fromnow on.3.04 FET drain characteristicsIn Figure 3.2 we showed a family of curvesof IDversus VDs that we measured fora VN0106, an n-channel enhancement-mode MOSFET. (The VNOl comes invarious voltage ratings, indicated by thelast two digits of the part number. Forexample, a VN0106 is rated at 60V.) Weremarked that FETs behave like prettygood transconductance devices over mostof the graph (i.e., IDnearly constant for agiven VGS), except at small VDs, wherethey approximate a resistance (i.e., IDproportional to VDs). In both cases theapplied gate-source voltage controls thebehavior, which can be well describedby the FET analog of the Ebers-Mollequation. Lets look at these two regionsa bit more closely.Figure 3.12 shows the situation sche-matically. In both regions the drain cur-rent depends on VGS - VT, the amountby which the applied gate-source voltageexceeds the threshold (or pinch-off) volt-age. The linear region, in which draincurrent is approximately proportional toVDS, extends up to a voltage VDs(s,t),after which the drain current is approx-imately constant. The slope in the lin-ear region, ID/VDs, is proportional to thegate bias, VGS - VT. Furthermore, thedrain voltage at which the curves enterthe "saturation region," VDs(,at), equalsVGS-VT, making the saturation drain cur-rent, ID(,,,), proportional to (VGS- VT)~,the quadratic law we mentioned earlier.For reference, here are the universal FETdrain-current formulas:(linear region)ID= ~ ( V G S- (saturation region)1 (near /region 1saturatlon reglon( VGS- V, I = 3vsaturatlon d r a ~ ncurrentI fl p r o p o t o n to vm - V T 2( v,, - V, i = 2v(V,, - V,) = 1vl~nearreglonextends toV ~ ~ , 5 , ~ ~ G SFigure 3.12If we call VGS - VT (the amount bywhich the gate-source voltage exceeds thethreshold) the "gate drive," the importantresults are that (a) the resistance in thelinear region is inversely proportional togate drive, (b) the linear region extends toa voltage equal to the gate drive, and (c)saturation drain current is proportional tothe square of the gate drive. These equa-tions assume that the body is connected tothe source. Note that the "linear region" isnot really linear, because of the V& term;well show a clever circuit fix later.The scale factor k depends on particu-lars such as the geometry of the FET, ox-ide capacitance, and carrier mobility. Ithas a temperature dependence k oc T - ~ / ~ ,which alone would cause IDto decrease
  • FIELD-EFFECTTRANSISTORS22 Chapter 3with increasing temperature. However, V-also depends slightly on temperature (2-SmV/"C); the combined effect producesthe curve of drain current versus tempera-ture shown in Figure 3.13.Sauare root lot30mA 05rnAzero temperature coefflc~ent5 10 v,, (V)extrapolated V,Figure 3.13At large drain currents the negative tem-perature coefficient of Ic causes the draincurrent to decrease with increasing tem-perature - goodbye thermal runaway! Asa consequence, FETs of a given type canbe paralleled without the external current-equalizing ("emitter-ballasting") resistorsthat you must use with bipolar transis-tors (see Section 6.07). This same nega-tive coefficient also prevents thermal run-away in local regions of the junction (aneffect known as "current hogging"), whichseverely limits the power capability of largebipolar transistors, as well see when wediscuss "second breakdown" and "safe op-erating area" in Chapter 6.At small drain currents (where the tem-perature coefficient of VT dominates), IDhas a positive tempco, with a point ofzero temperature coefficient at some draincurrent in between. This. effect is ex-ploited in FET op-amps to minimizetemperature drift, as well see in the nextchapter.Subthreshold regionOur expression given earlier for satura-tion drain current does not apply for verysmall drain currents. This is known asthe "subthreshold" region, where the chan-nel is below the threshold for conduction,but some current flows anyway becauseof a small population of thermally ener-getic electrons. If youve studied physicsor chemistry, you probably know in yourbones that the resulting current is exponen-tial:We measured some MOSFETs over 9decades of drain current (I nA to IA) andplotted the result as a graph of IDversusVGS (Fig. 3.14). The region from InAto ImA is quite precisely exponential;above this subthreshold region the curvesenter the normal saturation region. Forthe n-channel MOSFET (type VNO1) wechecked out a sample of 20 transistors(from four different manufacturing runsspread over 2 years), plotting the extremerange to give you an idea of the variability(see next section). Note the somewhatpoorer characteristics (VT, ID(ON))of the"complementary" VPOI.3.05 Manufacturing spread of FETcharacteristicsBefore we look at some circuits, lets takea look at the range of FET parameters(such as IDssand VT), as well as theirmanufacturing "spread" among devices ofthe same nominal type, in order to geta better idea of the FET. Unfortunately,many of the characteristics of FETs showmuch greater process spread than the cor-responding characteristics of bipolar tran-sistors, a fact that the designer must keepin mind. For example, the VNOl (a typ-ical n-channel MOSFET) has a specifiedVT of 0.8 to 2.4 volts (ID = ImA), com-pared with the analogous VBE spread of
  • INTRODUCTION3.05 Manufacturing spread of FET characteristics 12:Figure 3.14. Measured MOSFET drain currentversus gate-source voltage.0.63 to 0.83 volt (also at Ic = 1mA) foran npn bipolar transistor. Heres what youcan expect:Characteristic Available range SpreadZ ~ s s , 1mA to lOOA x 5RDS(ON) 0.050 to 10k x 5gm @ 1mA 500-3000~s x 5Vp (JFETs) 0.5-1OV 5VVT (MOSFETs) 0.5-5V 2VB ~ D S ( O F F ) 6-1OOOVB ~ G S ( O F F ) 6-125VRD(ON)is the drain-source resistance(linear region, i.e., small VDs) when theFET is conducting fully, e.g., with thegate grounded in the case of JFETs orwith a large applied gate-source voltage(usually specified as IOV) for MOSFETs.IDssand ID(ON)are the saturation-region(large VDs) drain currents under the sameturned-on gate drive conditions. Vp is thepinch-off voltage (JFETs), VT is the turn-on gate threshold voltage (MOSFETs),andthe BVs are breakdown voltages. As youcan see, a JFET with grounded source maybe a good current source, but you cantpredict very well what the current willbe. Likewise, the VGS needed to producesome value of drain current can varyconsiderably, in contrast to the predictable(e0.6V) VBE of bipolar transistors.Matching of characteristicsAs you can see, FETs are inferior to bipo-lar transistors in VGS predictability, i.e.,they have a large spread in the VGS re-quired to produce a given ID. Deviceswith a large process spread will, in gen-eral, have larger offset (voltage unbalance)when used as differential pairs. For in-stance, typical run-of-the-mill bipolar tran-sistors might show a spread in VBE of50mV or so, at some collector current,for a selection of off-the-shelf transistors.The comparable figure for MOSFETs ismore like 1 volt! Because FETs have somevery desirable characteristics otherwise, itis worthwhile putting in some extra effortto reduce these offsets in specially manu-factured matched pairs. IC designers usetechniques like interdigitation (two devicessharing the same general piece of IC realestate) and thermal-gradient cancellationschemes to improve performance (Fig.3.15).The results are impressive. AlthoughFET devicesstill cannot equal bipolar tran-sistors in VGSmatching, their performanceis adequate for most applications. For ex-ample, the best available matched FET hasa voltage offset of 0.5mV and tempco of5,uVI0C (max), whereas the best bipolarpair has values of 25,uV and 0.6,uV1°C(max), roughly 10 times better. Opera-tional amplifiers (the universal high-gaindifferential amplifiers well see in the nextchapter) are available in both flavors; youwould generally choose one with bipolarinnards for high precision (because of its
  • FIELD-EFFECTTRANSISTORS24 Chapter 3FET 1FET 2A. interdigitationheat8.temperature-gradient cancellationFigure 3.15flowclose input-transistor VBE matching),whereas a FET-input op-amp is the ob-vious choice for high-impedance applica-tions (because its inputs - FET gates -draw no current). For example, the inex-pensive JFET-input LF411 that we will useas our all-around op-amp in the next chap-ter has a typical input current of 50pA andcosts $0.60; the popular MOSFET-inputTLC272 costs about the same and has atypical input current of only lpA! Com-pare this with a common bipolar op-amp,the pA741, with typical input current of80,000pA (80nA).Tables 3.1-3.3 list a selection of typi-cal JFETs (both single and dual) andsmall-signal MOSFETs. Power MOSFETs,which we will discuss in Section 3.14, arelisted in Table 3.5.BASIC FET CIRCUITSNow were ready to look at FET circuits.You can usually find a way to converta circuit that uses BJTs into one usingFETs. However, the new circuit may notbe an improvement! For the remainderof the chapter wed like to illustrate cir-cuit situations that take advantage ofthe unique properties of FETs, i.e., cir-cuits that work better with FETs, or thatyou cant build at all with bipolar transis-tors. For this purpose it may be helpful- -to group FET applications into catego-ries; here are the most important, as wesee it:High-impedance/low-current. Buffers oramplifiers for applications where the basecurrent and finite input impedance of BJTslimit performance. Although you canbuild such circuits with discrete FETs,current practice favors using integratedcircuits built with FETs. Some of theseuse FETs as a high-impedance front-endfor an otherwise bipolar design, whereasothers use FETs throughout.Analog switches. MOSFETs are excellentvoltage-controlled analog switches, as wehinted in Section 3.01. Well look brieflyat this subject. Once again, you shouldgenerally use dedicated "analog switch"ICs, rather than building discrete circuits.Digital logic. MOSFETs dominate micro-processors, memory, and most high-performance digital logic. They are usedexclusively in micropower logic. Here,too, MOSFETs make their appearance inintegrated circuits. Well see why FETs arepreferable to BJTs.Power switching. Power MOSFETs are of-ten preferable to ordinary bipolar powertransistors for switching loads, as we sug-gested in our first circuit of the chapter.For this application you use discrete powerFETs.Variable resistors; current sources. In the"linear" region of the drain curves, FETsbehave like voltage-controlled resistors; inthe "saturation" region they are voltage-controlled current sources. You can exploitthis intrinsic behavior of FETs in yourcircuits.
  • BASIC FET CIRCUITS3.06 JFET current sources 125TABLE 3.1. JFETsIDSS VGS(OFF),VPChs Cn.BVGss min max min max max maxType (V) @A) (mA) (V) (V) (PF) (PF) Commentsn-channel2N4117A- 40 0.03 0.09 0.6 1.8 32N4119A 40 0.24 0.6 2 6 45low leakage: 1pA (max)1.52N4416 30 5 15 2.5 6 4 0.8 VHF low noise: <2dB@100MHz2N4867A- 40 0.4 1.2 0.7 2 25 5 low freq, low noise:2N4869A 40 2.5 7.5 1.8 5 25 5 10n~/d~z(max)@10Hz2N5265- 60 0.5 1 - 3 7 2 series of 6, tight I,,, spec;2N5270 60 7 14 8 7 2 2N5358-64 p-chan complement-2N5432 25 150 - 4 10 30 15 switch: RoN=5R(max)2N5457- 25 1 5 0.5 6 7 3 general purpose;2N5459 25 4 16 2 8 7 3 2N5460-2 p-chan complement2N5484- 25 1 5 0.3 3 5 12N5486 25 8 20 2 6 5low noise RF; inexpensive2SK117 50 0.6 14 0.2 1.5 13 3 ultra low noise: 1nVldHz2SK147 40 5 30 0.3 1.2 75 15 ultra low noise: 0 . 7 n ~ l d ~ zp-channel2N5114 30 30 90 5 10 25 7 switch: RoN=75Q(max)2N5358- 40 0.5 1 0.5 3 6 2 series of 7, tight lDssspec;2N5364 40 9 18 2.5 8 6 2 2N5265-70 n-chan complement2N5460- 40 1 5 0.75 6 7 2 general purpose;2N5462 40 4 16 1.8 9 7 2 2N5457-9 n-chan complement2SJ72 25 5 30 0.3 2 185 55 ultra low noise: 0.7n~ldHzGeneralized replacement for bipolar tran-sistors. You can use FETs in oscillators,amplifiers, voltage regulators, and radio-frequency circuits (to name a few), wherebipolar transistors are also normally used.FETs arent guaranteed to make a bettercircuit - sometimes they will, sometimesthey wont. You should keep them in mindas an alternative.Now lets look at these subjects. Welladopt a slightly different order, for clarity.3.06 JFET current sourcesJFETs are used as current sources withinintegrated circuits (particularly op-amps),and also sometimes in discrete designs.The simplest JFET current source is shownin Figure 3.16; we chose a JFET, ratherthan a MOSFET, because it needs no gatebias (its depletion mode). From a graph ofFET drain characteristics (Fig. 3.17) youcan see that the current will be reasonably
  • FIELD-EFFECT TRANSISTORS126 Chapter 3TABLE 3.2. SELECTED MOSFETs8c.E V ~ ~ ( t h ) I~(onn R ~ ~ ( o n ) (vDS.1 bv) c,.g max @VGS min max rnln rnax BVDs BVGs I,,,Type Mfga% (n) (V) (V) (V) (mA) (PF) (V) (V) (nA) Commentsn-channel3SK38A TO3N170 ILSD210 SISD211 SIVN1310 STIT1750 ILVN2222L SICD3600 RC2N3796 MO2N4351 MO+250.010.1 low RON10 low RON0.1 small VMOS; D-S diode0.010.1 small VMOS; D-S diode0.01 equiv to 4007 array0.001 depletion; IDss=l.5mA0.01 popular- --p-channel3N163 IL - 250 20 2 5 5 0.7 40 40 0.01VP1310 ST - 25 10 1.5 3.5 250 5 100 20 0.1 small VMOS; D-S diodeIT1700 IL - 400 10 2 5 2 1.2 40 40 0.01CD3600 RC 500 10 1.8 - 1.3 0.8 15 15 0.02 equiv to 4007 array2N4352 MO+ - 600 10 1.5 6 2 2.5 25 35 0.01 popular3N172 IL 250 20 2 5 5 1 40 40 0.2 popular(a) see footnotesto Table 4.1. (1 typical.Figure 3.16constant for VDslarger than a couple ofvolts. However, because of ID^^ spread,the current is unpredictable. For example,the 2N5484 (a typical n-channel JFET) hasa specified IDss of 1mA to 5mA. Still,the circuit is attractive because of the sim-plicity of a two-terminal constant-currentdevice. If that appeals to you, youre inluck. You can buy "current-regulatordiodes" that are nothing more thanJFETs with gate tied to source, sortedaccording to current. Theyre the cur-rent analog of a Zener (voltage regulator)diode. Here are the characteristics of the1N5283-lN5314 series:Currents available 0.22mA to 4.7mATolerance 10%Temperaturecoefficient f0.4%1°CVoltage range 1V-2.5V min, IOOVmaxCurrent regulation 590typicalImpedance 1M typical (for 1mA device)We plotted I versus V for a IN5294(rated at 0.75mA); Figure 3.18A shows
  • BASIC FET CIRCUITS3.06 JFET current sources 127. .-0 1 0 2 0V,, IV1A0 0 1 0 2 0 3 0 4 0 5VU, IV1BFigure 3.17. Measured JFET characteristiccurves. 2N5484 n-channel JFET: ID versusVDSfor various values of VGS.good constancy of current up to the break-down voltage (140V for this particularspecimen), whereas Figure 3.18B showsthat the device.reaches full current withsomewhat less than 1.5 volts across it.Well show how to use these devices tomake a cute triangle-wave generator in Sec-tion 5.13. Table 3.4 is a partial listing ofthe lN5283 series.Source self-biasingA variation of the previous circuit (Fig.3.19) gives you an adjustable currentFigure 3.18. IN5294 "current regulatordiode."Figure 3.19source. The self-biasing resistor R back-biases the gate by IDR,reducing IDandbringing the JFET closer to pinch-off. Youcan calculate R from the drain curves forthe particular JFET. This circuit allows you
  • FIELD-EFFECT TRANSISTORS28 Chapter 3TABLE 3.3. DUAL MATCHEDn-CHANNEL JFETsl ~ s s VGS(OFF), VP en CrssV,, Drift (VDG=20V) CMRR (10Hz) (VDG=lOV)max max max min min max max maxType (mV) (pV1-C) (PA) (dB) (V) (V) (nJldHz) (PF) Comments(a) at 100Hz. (b) at lkHz. () at lOkHz. at 30V. (e) at 20V. (1 typical.Siliconixgen purp, low driftpopularlow gate leakagelow noise at high freqlow noise at low freqcascode: low C,,,ultra low noiseto set the current (which must be less thanloss), as well as to make it more pre-dictable. Furthermore, the circuit is a bet-ter current source (higher impedance) be-cause the source resistor provides "current-sensing feedback" (which well learn aboutin Section 4.07), and also because FETstend to be better current sources anywaywhen the gate is back-biased (as can per-haps be seen from the flatness of the lowerdrain-current curves in Figs. 3.2 and 3.17).Remember, though, that actual curves ofIDfor some value of VGS obtained witha real FET may differ markedly from thevalues read from a set of published curves,owing to manufacturing spread. You maytherefore want to use an adjustable sourceresistor, if it is important to have a specificcurrent.EXERCISE 3.1Usethe 2N5484measuredcurvesin Figure3.17todesign a JFETcurrentsource todeliver1mA.Now ponder the fact that the specified IDssofa 2N5484is 1mA (min),5mA (max).A JFET current source, even if builtwith source resistor, shows some variationof output current with output voltage; i.e.,it has finite output impedance, rather thanthe desirable infinite ZOut.The measuredcurves of Figure 3.17, for example, suggestthat over a drain voltage range of 5 to20 volts, a 2N5484 shows a drain currentvariation of 5% when operated with gatetied to source (i.e., loss). This might dropto 2% or so if you use a source resistor.The same trick used in Figure 2.24 canbe used with JFET current sources andis shown in Figure 3.20. The idea (aswith BJTs) is to use a second JFET tohold constant the drain-source voltage ofthe current source. Q1 is an ordinaryJFET current source, shown in this casewith a source resistor. Q2 is a JFET oflarger IDss, connected "in series" with thecurrent source. It passes Qls (constant)drain current through to the load, whileholding Qls drain at a fixed voltage -namely the gate-source voltage that makesQ2 operate at the same current as Q1.Thus Q2 shields Q1 from voltage swings
  • BASIC FET CIRCUITS3.07 FET amplifiers 129TABLE 3.4. CURRENT-REGULATORDIODESaImpedance(25V) Vmi,IP min (I r 0.8 lp)Type (mA) (MQ) (V)(a)all operate to 100V and 600mW, and look likediodes in the reverse directionat its output; since Q1 doesnt see drainvoltage variations, it just sits there andprovides constant current. If you lookback at the Wilson mirror (Fig. 2.48),youll see that it uses this same voltageclamping idea.You may recognize this JFET circuitas the "cascode," which is normally usedto circumvent Miller effect (Section 2.19).A JFET cascode is simpler than a BJTcascode, however, because you dont needa bias voltage for the gate of the upperFET: Because its depletion-mode, you cansimply ground the upper gate (comparewith Fig. 2.74).EXERCISE 3.2Explain why the upper JFET in a cascode musthave higher IDss than the lower JFET. It mayFigure 3.20. Cascode JFET current sink.help to consider a JFET cascode with no sourceresistor.It is important to realize that a goodbipolar transistor current source will givefar better predictability and stability than aJFET current source. Furthermore, the op-amp-assisted current sources well see inthe next chapter are better still. For exam-ple, a FET current source might vary 5%over a typical temperature range and loadvoltage variation, even after being set tothe desired current by trimming the sourceresistor, whereas an op-amp/transistor (orop-ampIFET) current source is predictableand stable to better than 0.5% withoutgreat effort.3.07 FET amplifiersSource followers and common-source FETamplifiers are analogous to the emitter fol-lowers and common-emitter amplifiersmade with bipolar transistors that wetalked about in the last chapter. How-ever, the absence of dc gate current makes
  • FIELD-EFFECT TRANSISTORS130 Chapter 3it possible to realize very high input im-pedances. Such amplifiers are essentialwhen dealing with the high-impedance sig-nal sources encountered in measurementand instrumentation. For some specializedapplications you may want to build follow-ers or amplifiers with discrete FETs; mostof the time, however, you can take advan-tage of FET-input op-amps. In either caseits worth knowing how they work.With JFETs it is convenient to use thesame self-biasing scheme as with JFETcurrent sources (Section 3.06), with asingle gate-biasing resistor to ground (Fig.3.21); MOSFETs require a divider fromthe drain supply, or split supplies, justas we used with BJTs. The gate-biasingresistors can be quite large (a megohm ormore), because the gate leakage current ismeasured in nanoamps.Figure 3.21FET transconductance can be estimatedfrom the characteristic curves, either bylooking at the increase in ID from onegate-voltage curve to the next on the familyof curves (Fig. 3.2 or 3.17), or, moresimply, from the slope of the ID-VGS"transfer characteristics" curve (Fig. 3.14).The transconductance depends on draincurrent (well see how, shortly) and is, ofcourse,(Remember that lower-case letters indicatequantities that are small-signal variations.)From this we get the voltage gainjust the same as the bipolar transistor re-sult in Section 2.09, with load resistor Rcreplaced by RD. Typically, FETs havetransconductances of a few thousand mi-crosiemens (micromhos) at a few milli-amps. Because g, depends on drain cur-rent, there will be some variation of gain(nonlinearity) over the waveform as thedrain current varies, just as we have withgrounded emitter amplifiers (where g, =llr,, proportional to Ic). Furthermore,FETs in general have considerably lowertransconductance than bipolar transistors,which makes them less suitable as ampli-fiersand followers. Lets look at this a littlefurther.Transconductance Transconductance of FETs versus BJTsThe absence of gate current makes trans-conductance (the ratio of output currentto input voltage: g, = iout/vin) thenatural gain parameter for FETs. Thisis in contrast to bipolar transistors in thelast chapter, where we at first flirted withthe idea of current gain (iout/iin), thenintroduced the transconductance-orientedEbers-Moll model: Its useful to thinkof BJTs either way, depending on theapplication.To make our last remark quantitative, con-sider a JFET and a BJT, each operatingat 1mA. Imagine they are connected ascommon source (emitter) amplifiers, witha drain (collector) resistor of 5k to a +10volt supply (Fig. 3.22). Lets ignore detailsof biasing and concentrate on the gain.The BJT has an re of 25 ohms, hence ag, of 40 mS, for a voltage gain of -200(which you could have calculated direct-ly as -Rc/re). A typical JFET (e.g., a
  • BASIC FET CIRCUITS3.07 FET amplifiers 131Figure 3.222N4220) has a g, of 2mS at a drain cur-rent of lmA, giving a voltage gain of -10.This seems discouraging by comparison.The low g, also produces a relatively largeZoutin a follower configuration (Fig. 3.23):The JFET hasZout = l/gmwhich in this case equals 500 ohms (inde-pendent of signal source impedance), to becompared with the BJT, which hasZout =Rs/hfe +re = Rs/hfe + l/g,equal to Rs/h e+ 25 ohms (at 1mA). Fortypical transistor betas, say hfe = 100,and reasonable signal sources, say withR, < 5k, the BJT follower is an orderof magnitude stiffer (Z,,t = 250 to 750).Note, however, that for R, > 50k theJFET follower will be better.To see what is happening, lets look backat the expressions for FET drain currentversus gate-source voltage and comparewith the equivalent expression (Ebers-Moll) for BJT collector current versus base-emitter voltage.BJT: The Ebers-Moll equation,IC= Is{~xP(VBE/VT)- 11,with VT = kT/q = 25 mVpredicts g, = dIC/dVBE = Ic/VTfor collector currents large compared with"leakage" current Is. This is our familiarresult re(ohms)= 25/Ic(mA), since g, =1/re-FET: In the "subthreshold" region ofvery low drain current,which, being exponential like Ebers-Moll,also gives a transconductance proportional-1- Figure 3.23. Follower output- impedance.
  • FIELD-EFFECT TRANSISTORS132 Chapter 3to current. However, for real-world val-ues of k (which is determined by FET ge-ometry, carrier mobility, etc.) the FETstransconductance is somewhat lower thanthe BJTs, about I/40mV for p-channelMOSFETs and I/60mV for n-channelMOSFETs, as compared with I/25mV forBJTs. As the current is increased, theFET enters the normal "saturation" re-gion, whereID= k(VGs -which gives gm = 2(k1~)/~. That is,the transconductance increases only as thesquare root of IDand is well below thetransconductance of a bipolar transistorat the same operating current; see Fig-ure 3.24. Increasing the constant k inour preceding equations (by raising thewidthllength ratio of the channel) increasesthe transconductance (and the drain cur-rent, for a given VGS)in the region abovethreshold, but the transconductance stillremains less than that of a bipolar tran-sistor at the same current.Figure 3.24. Comparison of gm for bipolartransistorsand FETs.EXERCISE 3.3Derive the foregoing expressions for gm bydifferentiating IOutwith respect to v,.The problem of low voltage gain inFET amplifiers can be circumvented byresorting to a current-source (active) load,but once again the bipolar transistor willbe better in the same circuit. For thisreason you seldom see FETs used as simpleamplifiers, unless its important to takeadvantage of their unique input properties(extremely high input resistance and lowinput current).Note that FET transconductance in thesaturation region is proportional to VGS-VT; thus, for example, a JFET with gateoperated halfway to pinch-off has a trans-conductance approximately half thatshown on the data sheet (where it is alwaysgiven for ID= loss, i.e., VGS= 0).Differential amplifiersMatched FETs can be used to constructhigh-input-impedance front-end stages forbipolar differential amplifiers, as well asthe important op-amps and comparatorswell meet in the next chapter. As we men-tioned earlier, the substantial VGS offsetsof FETs will generally result in larger inputvoltage offsets and offset drifts than with acomparable amplifier constructed entirelywith bipolar transistors, but of course theinput impedance will be raised enormously.OscillatorsIn general, FETs have characteristics thatmake them useful substitutes for bipolartransistors in almost any circuit that canbenefit from their uniquely high input im-pedance and low bias current. A particularinstance is their use in high-stability LCand crystal oscillators; well show examplesin Sections 5.18, 5.19, and 13.11.Active loadJust as with BJT amplifiers, it is possibleto replace the drain-load resistor in a FETamplifier with an active load, i.e., a current
  • BASIC FET CIRCUITS3.08 Source followers 13:source. The voltage gain you get that waycan be very large:Gv = -gmRo(with a drain resistor as load)GV = -9mR0(with a current source as load)where Rois the impedance looking into thedrain (called "goSs"), typically in the rangeof look to 1M.One possibility for an active load isa current mirror as the drain load for adifferential FET pair (see Section 2.18); thecircuit is not bias-stable, however, withoutoverall feedback. The current mirror canbe constructed with either FETs or BJTs.This configuration is often used in FET op-amps, as well see in the next chapter. Youwill see another nice example of the activeload technique in Section 3.14 when wediscuss the CMOS linear amplifier.3.08 Source followersBecause of the relatively low transconduc-tance of FETs, its often better to use aFET "source follower" (analogous to anemitter follower) as an input buffer to aconventional BJT amplifier, rather thantrying to make a common-source FET am-plifier directly. You still get the high in-put impedance and zero dc input currentof the FET, and the BJTs large transcon-ductance lets you achieve high single-stagegain. Furthermore, discrete FETs (i.e.,those that are not part of an integratedcircuit) tend to have higher interelectrodecapacitance than BJTs, leading to greaterMiller effect (Section 2.19) in common-source amplifiers; the source follower con-figuration, like the emitter follower, has noMiller effect.FET followers, with their high input im-pedance, are commonly used as inputstages in oscilloscopes as well as other mea-suring instruments. There are many ap-plications in which the signal sourceimpedance is intrinsically high, e.g., ca-pacitor microphones, pH probes, charged-particle detectors, or microelectrode sig-nals in biology and medicine. In thesecases a FET input stage (whether discreteor part of an integrated circuit) is a goodsolution. Within circuits there are situa-tions where the following stage must drawlittle or no current. Common examplesare analog "sample-and-hold" and "peakdetector" circuits, in which the level isstored on a capacitor and will "droop"if the next amplifier draws significantinput current. In all these applicationsthe negligible input current of a FETis more important than its low transcon-ductance, making source followers (oreven common-source amplifiers) attrac-tive alternatives to the bipolar emitterfollower.Figure 3.25Figure 3.25 shows the simplest sourcefollower. We can figure out the outputamplitude, as we did for the emitter fol-lower in Section 2.11, using the transcon-ductance. We havesince ig is negligible; but
  • FIELD-EFFECT TRANSISTORS134 Chapter 3For Rr, >> llg, it is a good follower(v, x v,), with gain approaching, butalways less than, unity.Output impedanceThe preceding equation for v, is preciselywhat you would predict if the sourcefollowers output impedance were equalto l/gm (try the calculation, assuminga source voltage of v, in series withllg, driving a load of RL). This isexactly analogous to the emitter followersituation, where the output impedance wasre = 25/Ic, or llg,. It can be easilyshown explicitly that a source follower hasoutput impedance l/g, by figuring thesource current for a signal applied to theoutput with grounded gate (Fig. 3.26). Thedrain current istypically a few hundred ohms at currentsof a few milliamps. As you can see, FETsource followers arent nearly as stiff asemitter followers.Figure 3.26There are two drawbacks to this circuit:1. The relatively high output impedancemeans that the output swing may be signif-icantly less than the input swing, even withhigh load impedance, because RL aloneforms a divider with the sources outputimpedance. Furthermore, because thedrain current is changing over the signalwaveform, g, and therefore the outputimpedance will vary, producing some non-linearity (distortion) at the output. The sit-uation is improved if FETs of hightransconductance are used, of course, but acombination FET-bipolar follower is oftena better solution.2. Because the VGS needed to producea certain operating current is a poorlycontrolled parameter in FET manufacture,a source follower has an unpredictable dcoffset, a serious drawback for dc-coupledcircuits.Active loadThe addition of a few components im-proves the source follower enormously.Lets take it in stages:clj3or (better)1Sf"k +- "ss -vssA BFigure 3.27First, replace RL with a (pull-down)current source (Fig. 3.27). The constantsource current makes VGS approximatelyconstant, thus reducing nonlinearities.You can think of this as the previous casewith infinite RL, which is what a currentsource is. The circuit on the right hasthe advantage of providing low output imp-edance,while still providing a(rough1y)con-stant source current of VBE/RB. We stillhave the problem of unpredictable (andtherefore nonzero) offset voltage (from in-put to output) of VGS (VGS + VBE for
  • BASIC FET CIRCUITS3.09 FET gate current 13the circuit on the right). Of course, wecould simply adjust Isinkto the particu-lar value of IDssfor the given FET (inthe first circuit) or adjust RB (in the sec-ond). This is a poor solution, for tworeasons: (a) It requires individual adjust-ment for each FET. (b) Even so, ID mayvary by a factor of two over the normaloperating temperature range for a givenVGS-A better circuit uses a matched FET pairto achieve zero offset (Fig. 3.28). Q1and Q2 are a matched pair, on a singlechip of silicon. Qz sinks a current exactlyappropriate to the condition VGS = 0.So, for both FETs, VGS = 0, and Q1is therefore a follower with zero offset.Because Q2 tracks Q1 in temperature, theoffset remains near zero independent oftemperature.input 4.l+-- outputFigure 3.28You usually see the preceding circuitwith source resistors added (Fig. 3.29). Alittle thought should convince you that R1is necessary and that R1 = R2guaranteesthat VOut= V,, if Ql and Q2are matched.This circuit modification gives better IDpredictability, allows you to set the draincurrent to some value less than l o s s ,and gives improved linearity, since FETsare better current sources when operatedbelow loss. This follower circuit ispopular as the input stage for oscilloscopevertical amplifiers.For the utmost in performance youcan add circuitry to bootstrap the drain(eliminating input capacitance) and usea bipolar output stage for low outputimpedance. That same output signal canthen be used to drive an inner "guard"shield in order to effectively eliminatethe effects of shielded-cable capacitance,which would otherwise be devastating forthe high source impedances that you mightsee with this sort of high-impedance inputbuffer amplifier.input -Co1Figure 3.293.09 FET gate currentWe said at the outset that FETs in general,and MOSFETs in particular, have essen-tially zero gate current. This is perhapsthe most important property of FETs, andit was exploited in the high-impedance am-plifiers and followers in the previous sec-tions. It will prove essential, too, in ap-plications to follow - most notably analogswitches and digital logic.Of course, at some level of scrutiny wemight expect to see some gate current.Its important to know about gate current,because a naive zero-current model isguaranteed to get you in trouble sooner orlater. In fact, finite gate current arises from
  • FIELD-EFFECT TRANSISTORS136 Chapter 350 0 50temperature ("C)several mechanisms: Even in MOSFETsthe silicon dioxide gate insulation is notperfect, leading to leakage currents in thepicoampere range. In JFETs the gate "in-sulation" is really a back-biased diode junc-tion, with the same impurity and junctionleakage current mechanisms as ordinarydiodes. Furthermore, JFETs (n-channel inparticular) suffer from an additional effectknown as"impact-ionization" gate current,which can reach astounding levels. Finally,both JFETs and MOSFETs have dynamicgate current, caused by ac signals drivingthe gate capacitance; this can cause Millereffect, just as with bipolar transistors.In most cases gate input currents arenegligible in comparison with BJT basecurrents. However, there are situationsin which a FET may actually have higherinput current! Lets look at the numbers.Gate leakageThe low-frequency input impedance of aFET amplifier (or follower) is limited bygate leakage. JFET data sheets usuallyspecify a breakdown voltage, BVGss, de-fined as the voltage from gate to channelFigure 3.30. The input currentof a FET amplifier is gateleakage, which doubles every(source and drain connected together) atwhich the gate current reaches 1pA. Forsmaller applied gate-channel voltages, thegate leakage current, IGsS,again measuredwith the source and drain connected to-gether, is considerably smaller, droppingquickly to the picoampere range for gate-drain voltages well below breakdown.With MOSFETs you must never allow thegate insulation to break down; instead,gate leakage is specified as some maximumleakage current at a specified gate-channelvoltage. Integrated circuit amplifiers withFETs (e.g., FET op-amps) use the mislead-ing term "input bias current," I g , to spec-ify input leakage current; its usually in thepicoampere range.The good news is that these leakage cur-rents are in the picoampere range at roomtemperature. The bad news is that they in-crease rapidly (in fact, exponentially) withtemperature, roughly doubling every 1O°C.By contrast, BJT base currents arent leak-age, and in fact tend to decrease slightlywith increasing temperature. The compar-ison is shown graphically in Figure 3.30,a plot of input current versus tempera-ture for several IC amplifiers (op-amps).
  • BASIC FET CIRCUITS3.09 FET gate current 13The FET-input op-amps have the lowestinput currents at room temperature (andbelow), but their input current rises rapidlywith temperature, crossing over the curvesfor amplifiers with carefully designed BJTinput stages like the LMl 1 and LT1012.These BJT op-amps, along with "premi-um" low-input-current JFET op-amps likethe OPAI 11 and AD549, are fairly expen-sive. However, we also included everyday"jellybean" op-amps like the bipolar 358and JFET LF411 in the figure to give anidea of input currents you can expect withinexpensive (less than a dollar) op-amps.JFET impact-ionization currentIn addition to conventional gate leakage ef-fects, n-channel JFETs suffer from ratherlarge gate leakage currents when operatedwith substantial VDsand ID (the gate leak-age specified on data sheets is measuredunder the unrealistic conditions Vos =ID= O!). Figure 3.31 shows what happens.The gate leakage current remains near theIGss value until you reach a critical drain-gate voltage, at which point it rises pre-cipitously. This extra "impact-ionization"current is proportional to drain current,and it rises exponentially with voltage andtemperature. The onset of this current oc-curs at drain-gate voltages of about 25% ofBVGss, and it can reach gate currents ofa microamp or more. Obviously a "high-impedance buffer" with a microamp of in-put current is worthless. Thats what youwould get if you used a 2N4868A as a fol-lower, running 1mA of drain current froma 40 volt supply.This extra gate leakage current afflictsprimarily n-channel JFETs, and it occursat higher values of drain-gate voltage.Some cures are to (a) operate at low drain-gate voltage, either with a low-voltagedrain supply or with a cascode, (b) use ap-channel JFET, where the effect is muchsmaller, or (c) use a MOSFET. The mostimportant thing is to be aware of the effectso that it doesnt catch you by surprise.Figure 3.31. JFET gate leakage increasesdisastrously at higher drain-gate voltages andis proportional to drain current.Dynamic gate currentGate leakage is a dc effect. Whatever isdriving the gate must also supply an accurrent, because of gate capacitance. Con-sider a common-source amplifier. Justas with bipolar transistors, you can havethe simple effect of input capacitance toground (called Cis,), and you can havethe capacitance-multiplying Miller effect(which acts on the feedback capacitanceC,,,). There are two reasons why capaci-tive effects are more serious in FETs thanin bipolar transistors: First, you use FETs(rather than BJTs) because you want verylow input current; thus the capacitive cur-rents loom relatively larger for the samecapacitance. Second, FETs often haveconsiderably larger capacitance than equiv-alent bipolar transistors.To appreciate the effect of capacitance,consider a FET amplifier intended for asignal source of lOOk source impedance.
  • FIELD-EFFECTTRANSISTORS138 Chapter 3At dc theres no problem, because the pi-coampere currents produce only microvoltdrops across the signal sources internalimpedance. But at IMHz, say, an inputcapacitance of 5pF presents a shunt imped-ance of about 30k, seriously attenuatingthe signal. In fact, any amplifier is in trou-ble with a high-impedance signal at highfrequencies, and the usual solution is tooperate at low impedance (50R is typical)or use tuned LC circuits to resonate awaythe parasitic capacitance. The point to un-derstand is that the FET amplifier doesntlook like a 1012ohm load at signal frequen-cies.CMOS d ~ g ~ t a llog~cnv~0+ 1ov- 1mA, max+ I+Figure 3.32As another example, imagine switchinga 10 amp load with a power MOSFET(there arent any power JFETs), in the styleof Figure 3.32. One might naively as-sume that the gate could be driven froma digital logic output with low current-sourcing capability, for example the so-called CMOS logic, which can supply out-put current on the order of ImA with aswing from ground to +10 volts. In fact,such a circuit would be a disaster, sincewith IrnA of gate drive the 350pFfeedbackcapacitance of the 2N6763 would stretchthe output switching speed to a leisurely20ps. Even worse, the dynamic gate cur-rents (Igate= CdVD/dt) would force cur-rents back into the logic devices output,possibly destroying it via a perverse effectknown as "SCR latchup" (more of whichin Chapters 8 and 9). Bipolar power tran-sistors turn out to have comparable ca-pacitances, and therefore comparable dy-namic input currents; but when youdesign a circuit to drive a 10-amp powerBJT, youre expecting to provide 500mAorso of base drive (via a Darlington or what-ever), whereas with a FET you tendto take low input current for granted. Inthis example, once again, the ultra-high-impedance FET has lost some of its luster.EXERCISE 3.4Show that the circuit of Figure 3.32 switchesin about 20ps, assuming 1mA of available gatedrive.3.10 FETs as variable resistorsFigure 3.17 showed the region of JFETcharacteristic curves (drain current versusVDs for a small family of VGS voltages),both in the normal ("saturated") regimeand in the "linear" region of small VDs.We showed the equivalent pair of graphsfor a MOSFET at the beginning of thechapter (Fig. 3.2). The ID-versus-VDscurves are approximately straight lines forVDs smaller than VGS - VT, and theyextend in both directions through zero,i.e., the device can be used as a voltage-controlled resistor for small signals ofeither polarity. From our equation for IDversus VGS in the linear region (Section3.04) we easily find the ratio (ID/VDs) tobeThe last term represents a nonlinearity,i.e., a departure from resistive behavior(resistance shouldnt depend on voltage).However, for drain voltages substantiallyless than the amount by which the gateis above threshold (VDs -+ O), the last
  • BASIC FET CIRCUITS3.10 FETs as variable resistors 13term becomes unimportant, and the FETbehaves approximately like a resistance:Because the device-dependent parameter kisnt a quantity you are likely to know, itsmore useful to write RDs aswhere the resistance RDs at any gatevoltage VG is written in terms of the(known) resistance Roat some gate voltageVGO-EXERCISE 3.5Derive the preceding "scaling" law.From either formula you can see thatthe conductance (= l/RDs) is propor-tional to the amount by which the gatevoltage exceeds threshold. Another usefulfact is that RDs = llg,, i.e., the channelresistance in the linear region is the inverseof the transconductance in the saturatedregion. This is a handy thing to know,because g, is a parameter nearly alwaysspecified on FET data sheets.EXERCISE 3.6Show that RDs = l/gm by finding the trans-conductance from the saturation drain-currentformulain Section 3.04.Typically, the values of resistance youcan produce with FETs vary from a fewtens of ohms (as low as O.1R for powerMOSFETs) all the way up to an opencircuit. A typical application might bean automatic-gain-control (AGC)circuit inwhich the gain of an amplifier is adjusted(via feedback) to keep the output withinthe linear range. In such an AGC circuityou must be careful to put the variable-resistance FET at a place in the circuitwhere the signal swing is small, preferablyless than 200mV or so.The range of VDs over which the FETbehaves like a good resistor depends onthe particular FET and is roughly propor-tional to the amount by which the gatevoltage exceeds Vp (or VT). Typically, youmight have nonlinearities of about 2% forVDS < O.l(VGs- Vp), and perhaps 10%nonlinearity for VDs -" 0.25(VGs - Vp).Matched FETs make it easy to design aganged variable resistor to control severalsignals at once. JFETs intended for useas variable resistors are available (SiliconixVCR series) with resistance tolerances of30°/o, specified at some VGS.It is possible to improve the linearity,and simultaneously the range of VDs overwhich a FET behaves like a resistor, bya simple compensation scheme. Wellillustrate with an application.Linearizing trick: electronic gain controlBy looking at the preceding equation forl/RDs, you can see that the linearity willbe nearly perfect if you can add to thegate voltage a voltage equal to one-half thedrain-source voltage. Figure 3.33 showstwo circuits that do exactly that. In thefirst, the JFET forms the lower half of aresistive voltage divider, thus forming avoltage-controlled attenuator (or "volumecontrol"). R1and Rzimprove the linearityby adding a voltage of 0.5Vos to VGS, asjust discussed. The JFET shown has anON resistance (gate grounded) of 60 ohms(max), giving the circuit an attenuationrange of 0 to 40dB.The second circuit uses a MOSFET as avariable emitter resistance in an emitter-degenerated ac amplifier. Note the useof a constant-dc-current emitter pulldown(Wilson mirror or FET current-regulatordiode); this (a) looks like a very high im-pedance at signal frequencies, thus lettingthe variable-resistance FET set the gainover a wide range (including Gv << I),and (b) provides simple biasing. By us-ing a blocking capacitor, weve arrangedthe circuit so that the FET affects only the
  • FIELD-EFFECT TRANSISTORS140 Chapter 3Figure 3.33. Variable-gain circuits.-ac (signal) gain. Without the capacitor,the transistor biasing would vary with FETresistance.outEXERCISE 3.7The VN13 has an ON resistance (VGS= +5V)of 15 ohms(max). Whatis the rangeof amplifiergain in the second circuit (assume that thecurrent sink looks like 1MR)? What is the low-frequency3dB point when the FET is biased sothat the amplifier gain is (a) 40dB or (b) 20dB?56k- 125OPAv4(4:l current- m~rror)-VCO~,,OI VN13(positive1The linearization of RDs with a resis-tive gate divider circuit, as above, is re-markably effective. In Figure 3.34 wevecompared actual measured curves of IDversus VDs in the linear (low-VDs) regionfor FETs with and without the linearizingcircuit. The linearizing circuit is essentialfor low-distortion applications with signalswings of more than a few millivolts.When considering FETs for an appli-cation requiring a gain control, e.g., anAGC or "modulator" (in which the am-plitude of a high-frequency signal is var-ied at an audio rate, say), it is worth-while to look also at "analog-multiplier"ICs. These are high-accuracy devices withgood dynamic range that are normally usedto form the product of two voltages. Oneof the voltages can be a dc control sig-nal, setting the multiplication factor of thedevice for the other input signal, i.e., thegain. Analog multipliers exploit the g,-versus-Ic characteristic of bipolar transis-tors [g, = Ic(mA)/25 siemens], usingmatched arrays to circumvent problemsof offsets and bias shifts. At very highfrequencies (1OOMHz and above), passive"balanced mixers" (Section 13.12) are of-ten the best devices to accomplish the sametask.It is important to remember that aFET in conduction at low VDs behaveslike a good resistance all the way downto zero volts from drain to source (thereare no diode drops or the like to worryabout). We will see op-amps and digitallogic families (CMOS) that take advantageof this nice property, giving outputs thatsaturate cleanly to the power supplies.FET SWITCHESThe two examples of FET circuits thatwe gave at the beginning of the chapterwere both switches: a logic-switching ap-plication and a linear signal-switchingcir-cuit. These are among the most importantFET applications and take advantage ofthe FETs unique characteristics: high gateimpedance and bipolarity resistive conduc-tion clear down to zero volts. In practice
  • FET SWITCHES3.11 FET analog switches 1410 0 1 0 2 0 3 0.4 0 5vu,,, cvr/ JFETFigure 3.34. Measured curves of ID versus Vos for bare and linearized FETS.A. 2N5484 JFETB. VN0106 MOSFETyou usually use MOSFET integrated cir-cuits (rather than discrete transistors) inall digital logic and linear switch appli-cations, and it is only in power switch-ing applications that you resort to discreteFETs. Even so, it is essential (and fun!)to understand the workings of these chips;otherwise youre almost guaranteed tofall prey to some mysterious circuitpathology.3.11 FET analog switchesA common use of FETs, particularly MOS-FETs, is as analog switches. Their combi-nation of low ON resistance (all the way tozero volts), extremely high OFF resistance,low leakage currents, and low capacitancemakes them ideal as voltage-controlledswitch elements for analog signals. Anideal analog, or linear, switch behaves like
  • FIELD-EFFECT TRANSISTORS142 Chapter 3a perfect mechanical switch: In the ONstate it passes a signal through to a loadwithout attenuation or nonlinearity; in theOFF state it is an open circuit. It shouldhave negligible capacitance to ground andnegligible coupling to the signal of theswitching level applied to the control in-put.signalout47kovcontrolFigure 3.35Lets look at an example (Fig. 3.35). Q1is an n-channel enhancement-mode MOS-FET, and it is nonconducting when the gateis grounded or negative. In that state thedrain-source resistance (ROFF)is typicallymore than 10,00OM, and no signal getsthrough (though at high frequencies therewill be some coupling via drain-source ca-pacitance; more on this later). Bringingthe gate to +15 volts puts the drain-sourcechannel into conduction, typically 25 to100 ohms (RON) in FETs intended for useas analog switches. The gate signal levelis not at all critical, as long as it is suffi-ciently more positive than the largest sig-nal (to maintain RONlow), and it could beprovided from digital logic circuitry (per-haps using a FET or BJT to generate a full-supply swing) or even from an op-amp (whose f13V output swing would donicely, since gate breakdown voltages inMOSFETs are typically 20V or more).Swinging the gate negative (as from anop-amp output) doesnt hurt, and in facthas the added advantage of allowing theswitching of analog signals of either polar-ity, as will be described later. Note thatthe FET switch is a bidirectional device;signals can go either way through it. Or-dinary mechanical switches work that way,too, so it should be easy to understand.The circuit as shown will work forpositive signals up to about 10 volts; forlarger signals the gate drive is insufficientto hold the FET in conduction (RONbegins to rise), and negative signals wouldcause the FET to turn on with the gategrounded (it would also forward bias thechannel-body junction; see Section 3.02).If you want to switch signals that are ofboth polarities (e.g., signals in the range-10V to +lOV), you can use the samecircuit, but with the gate driven from -15volts (OFF) to +15 volts (ON); the bodyshould then be tied to -15 volts.With any FET switch it is important toprovide a load resistance in the range oflk to lOOk in order to reduce capacitivefeedthrough of the input signal that wouldotherwise occur during the OFF state. Thevalue of the load resistance is a compro-mise: Low values reduce feedthrough, butthey begin to attenuate the input signalbecause of the voltage divider formed byRONand the load. Because RON variesover the input signal swing (from changingVGS),this attenuation also produces someundesirable nonlinearity. Excessively lowload resistance appears at the switch input,of course, loading the signal source as well.Several possible solutions to this problem(multiple-stage switches, RON cancella-tion) are shown in Sections 3.12 and 4.30.An attractive alternative is to use a secondFET switch section to connect the outputto ground when the series FET is off, thuseffectively forming an SPDT switch (moreon this in the next section).CMOS linear switchesFrequently it is necessary to switch sig-nals that may go nearly to the supply volt-ages. In that case the simple n-channelswitch circuit just described wont work,since the gate is not forward-biased at the
  • FET SWITCHES3.11 FET analog switches l rpeak of the signal swing. The solution isto use paralleled complementary MOSFET("CMOS") switches (Fig. 3.36). The tri-angular symbol is a digital inverter, whichwell discuss shortly; it inverts a HIGHinput to a LOW output, and vice versa.When the control input is high, Q1 is heldON for signals from ground to within a fewvolts of VDD(where R O ~starts increas-ing dramatically). Q2 is likewise held ON(by its grounded gate) for signals from VDDto within a few volts of ground (where itsRON increases dramatically). Thus, sig-nals anywhere between VDDand groundare passed through with low series resis-tance (Fig. 3.37). Bringing the control sig-nal to ground turns off both FETs, pro-viding an open circuit. The result is ananalog switch for signals between groundand VDD.This is the basic constructionof the 4066 CMOS "transmission gate." Itis bidirectional, like the switches describedearlier; either terminal can be the input.signal in(Out) 7open <cl:~kF+controlsignal out(in)Figure 3.36. CMOS analog switch.There is a variety of integrated circuitCMOS analog switches available, with var-ious switch configurations (e.g., several in-dependent sections with several poleseach). The 4066 is the classic 4000-seriesCMOS"analog transmission gate," just an-other name for an analog switch for sig-nals between ground and a single positivesupply. The IH5040 and IH5140 seriesfrom Intersil and Harris and the DG305and DG400 series from Siliconix are veryconvenient to use; they accept logic-level(OV = LOW, > 2.4V = HIGH) controlsignals, they will handle analog signals tof15 volts (compared with only f7.5V forthe 4000 series), they come in a varietyof configurations, and they have relativelylow ON resistance (25R for some mem-bers of these families). Analog Devices,Maxim, and PMI also manufacture niceanalog switches.p-channel n channelsignal -voltageFigure 3.37MultiplexersA nice application of FET analog switchesis the "multiplexer" (or MUX), a circuitthat allows you to select any of several in-puts, as specified by a digital control signal.The analog signal present on the selectedinput will be passed through to the (sin-gle) output. Figure 3.38 shows the basicscheme. Each of the switches SWO throughSW3 is a CMOS analog switch. The "se-lect logic" decodes the address and en-ables (jargon for "turns on") the addressedswitch only, disabling the remainingswitches. Such a multiplexer is usuallyused in conjunction with digital circuitrythat generates the appropriate addresses.A typical situation might involve a data-acquisition instrument in which a numberof analog input voltages must be sampledin turn, converted to digital quantities, andused as input to some computation.Because analog switches are bidirec-tional, an analog multiplexer such as this is
  • FIELD-EFFECTTRANSISTORS44 Chapter 31 address decoderI"address" of LSBselect input [ MSBFigure 3.38. Analog multiplexer.outputalso a "demultiplexer": A signal can befed into the "output" and will appear onthe selected "input." When we discussdigital circuitry in Chapters 8 and 9, youwill see that an analog multiplexer suchas this can also be used as a "digitalmultiplexer/demultiplexer," because logiclevels are, after all, nothing but voltagesthat happen to be interpreted as binary 1sand 0s.Typical of analog multiplexers are theDG506-509 series and the IH6108 and6116 types, 8- or 16-input MUX circuitsthat accept logic-level address inputs andoperate with analog voltages up tof15 volts. The 4051-4053 devices in theCMOS digital family are analog multi-plexers/demultiplexers with up to 8 inputs,but with 15 volt pp maximum signal lev-els; they have a VEEpin (and internal levelshifting) so that you can use them withbipolarity analog signals and unipolarity(logic-level)control signals.Other analog switch applicationsVoltage-controlled analog switches formessential building blocks for op-amp cir-integrators, sample-and-hold circuits, andpeak detectors. For example, with op-amps we will be able to build a "true" in-tegrator (unlike the approximation to anintegrator we saw in Section 1.15): A con-stant input generates a linear ramp output(not an exponential), etc. With such an in-tegrator you must have a method to resetthe output; a FET switch across the inte-grating capacitor does the trick. We wonttry to describe these applications here; be-cause op-amps form essential parts of thecircuits, they fit naturally into the nextchapter. Great things to look forward to!3.12 Limitations of FET switchesSpeedFET switches have ON resistances R O ~of 25 to 200 ohms. In combination withsubstrate and stray capacitances, this resis-tance forms a low-pass filter that limits op-erating speeds to frequencies of the orderof IOMHz or less (Fig. 3.39). FETs withlower RONtend to have larger capacitance(up to 50pF with some MUX switches),so no gain in speed results. Much of therolloff is due to protection components -current-limiting series resistance, and ca-pacitance of shunt diodes. There are afew "RFIvideo" analog switches that ob-tain higher speeds, probably by eliminat-ing some protection. For example, theRON= 300RInputnoutputc,,,= 5pFI IC,,,,= 22pF- -- -- 24MHzf3dB= ---2aRonCou,Hl-508 analog rnultlplexer - ON valuescuits well see in the next chapter - Figure 3.39
  • FET SWITCHES3.12 Limitations of FET switches 145IH5341 and IH5352 switches handle ana-log signals over the usual f15 volt rangeand have a bandwidth of 100MHz; the74HC4051-53 series of "high-speed"CMOS multiplexers also provide a 3dBanalog bandwidth of lOOMHz, but handlesignals only to f5 volts. The MAX453-5from Maxim combine a video multiplexerwith an output video amplifier,so you candrive low-impedance cables or loads (usu-ally 75R) directly; they have 5OMHz typ-ical bandwidth and are intended for f1volt low-impedance video signals.ON resistanceCMOS switches operated from a relativelyhigh supply voltage (15V, say) will havelow RONover the entire signal swing, be-cause one or the other of the transmis-sion FETs will have a forward gate biasat least half the supply voltage. However,when operated with lower supply voltages,the switchs RONvalue will rise, the max-imum occurring when the signal is abouthalfway between the supply and ground(or halfway between the supplies, for dual-supply voltages). Figure 3.40 shows why.As V D ~is reduced, the FETs begin tohave significantly higher ON resistance (es-pecially near VGS = VDD/~),since forenhancement-mode FETs VT is at least afew volts, and a gate-source voltage of asmuch as 5 to 10 volts is required to achievelow RON.Not only will the parallel re-sistances of the two FETs rise for signalvoltages between the supply voltage andground, but also the peak resistance (athalf VDD)will rise as VDDis reduced, andfor sufficiently low VDD the switch willbecome an open circuit for signals nearVDD/~.signal voltage LFigure 3.40There are various tricks used by the de-signers of analog switch ICs to keep RONlow, and approximately constant (for lowdistortion), over the signal swing. For ex-ample, the original 4016 analog switchused the simple circuit of Figure 3.36, pro-ducing RONcurves that look like those inFigure 3.41. In the improved 4066 switchthe designers added a few extra FETs sothat the n-channel body voltage follows thesignal voltage, producing the RONcurvesof Figure 3.42. The "volcano"shape, with= 1ov4016 analog switch6 soone0 l I Io 5 10 15 Figure 3.41. ON resistancefor 4016signal voltage CMOS switch.
  • FIELD-EFFECT TRANSISTORS146 Chapter 3Figure 3.42. ON resistance for theI , , , improved 4066 CMOS switch; noteo 5 10 15 change of scale from previouss~gnalvoltage figure.1 I 1 I- 10 5 0 + 5 +10signal voltageits depressed central R o ~ ,replaces the"Everest" shape of the 4016. Sophisti-cated switches like the IH5140 series (orAD7510 series), intended for serious ana-log applications, succeed even better,with gentle RONcurves like those shownin Figure 3.43. The recent DG400series from Siliconix achieves an ex-cellent RONof 20 ohms, at the expenseof increased "charge transfer" (see thelater section on glitches); this switchfamily (like the IH5140 series) has theadditional advantage of zero quiescentcurrent.Figure 3.43. ON resistance for theIH5140-series bipolarity analogswitches; note vertical scale.CapacitanceFET switches exhibit capacitance frominput to output (CDs), from channel toground (CD, Cs), from gate to channel,and from one FET to another within oneIC package (Coo, Css); see Figure 3.44.Lets look at the effects:CDs: Capacitance from input to output.Capacitance from input to output causessignal coupling in an OFF switch, risingat high frequencies. Figure 3.45 shows theeffect for the IH5140 series. Note the use
  • FET SWITCHES3.12 Limitations of FET switches 147Figure 3.44. Analog switch capacitances -AD7510 4-channel switch.frequency (Hz11 2 0 -- 100-8 0 --mD2 6 0 -.Figure 3.45OFF isolationIH5140 serlesof a stiff 50 ohm load, common in radiofre-quency circuits, but much lower than nor-mal for low-frequency signals, where a typ-ical load impedance is IOk or more. Evenwith a 50 ohm load, the feedthrough be-comes significant at high frequencies(at 30MHz 1pF has a reactance of 5k,giving -40dB of feedthrough). And,of course, there is significant attenua-tion (and nonlinearity) driving a 50ohm load, since RONis typically 30 ohms(75R worst-case). With a 10k load thefeedthrough situation is much worse, ofcourse.P v""Tlvo",--Figure 3.46Figure 3.47EXERCISE 3.8Calculate the feedthrough into 10k at lMHz,assuming CDs= 1pF.In most low-frequency applications ca-pacitive feedthrough is not a problem. Ifit is, the best solution is to use a pairof cascaded switches (Fig. 3.46) or, bet-ter still, a combination of series and shuntswitches, enabled alternately (Fig. 3.47).The series cascade doubles the attenuation(in decibels), at the expense of additionalRON,whereas the series-shunt circuit (ef-fectively an SPDT configuration) reducesfeedthrough by dropping the effectiveloadresistance to RONwhen the series switchis off.EXERCISE 3.9Recalculate switch feedthrough into 10k at1MHz, assuming CDs= 1pFand RON= 50ohms, for the configurationof Fig. 3.47.CMOS SPDT switches with controlledbreak-before-make are available commer-cially in single packages; in fact, yod can
  • FIELD-EFFECT TRANSISTORS148 Chapter 3get a pair of SPDT switches in a singlepackage. Examples are the DG188 andIH5142, as well as the DG191, IH5143,and AD7512 (dual SPDT units). Becauseof the availability of such convenientCMOSswitches, it is easy to use this SPDTconfiguration to achieve excellent perfor-mance. The RFIvideo switches mentionedearlier use a series-shunt circuit internally.CD, Cs: Capacitance to ground. Shuntcapacitance to ground leads to the highfrequency rolloff mentioned earlier. Thesituation is worst with a high-impedancesignal source, but even with a stiff sourcethe switchs RONcombines with the shuntcapacitance at the output to make a low-pass filter. The following problem showshow it goes.EXERCISE 3.10An AD7510 (here chosen for its complete ca-pacitance specifications, shown in Fig. 3.44) isdriven by a signal source of 10k,with a load im-pedance of 1OOk at the switchs output. Whereis the high-frequency -3dB point? Now repeatthe calculation,assuming a perfectly stiff signalsource, and a switch RONof 75 ohms.Capacitance from gate to channel. Ca-pacitance from the controlling gate to thechannel causes a different effect, namelythe coupling of nasty little transients intoyour signal when the switch is turned onor off. This subject is worth some seriousdiscussion, so well defer it to the nextsection on glitches.CDD, Css: Capacitance betweenswitches. If you package several switcheson a single piece of silicon the size of akernel of corn, it shouldnt surprise you ifthere is some coupling between channels("cross-talk"). The culprit, of course, iscross-channel capacitance. The effect in-creases with frequency and with signal im-pedance in the channel to which the signalis coupled. Heres a chance to work it outfor yourself:EXERCISE 3.11Calculate the coupling, in decibels, between apair ofchannelswith CDD= Css =0.5pF(Fig.3.44) for the source and load impedancesof thelast exercise. Assume that theinterfering signalis 1MHz. In eachcasecalculatethe coupling for(a) OFF switch to OFF switch, (b) OFF switch toON switch, (c)ON switch to OFF switch, and (d)ON switch to ON switch.It should be obvious from this examplewhy most. broadband radiofrequency cir-cuits use low signal impedances, usually50 ohms. If cross-talk is a serious prob-lem, dont put more than one signal on onechip.GlitchesDuring turn-on and turn-off transients,FET analog switches can do nasty things.The control signal being applied to thegate(s) can couple capacitively to the chan-nel(~),putting ugly transients on your sig-nal. The situation is most serious if thesignal is at high impedance levels. Multi-plexers can show similar behavior duringtransitions of the input address, as well asmomentary connection between inputs ifturn-off delay exceeds turn-on delay. A re-lated bad habit is the propensity of someswitches (e.g., the 4066) to short the inputto ground momentarily during changes ofstate.Lets look at this in a bit moredetail. Figure 3.48 shows a typical wave-form you might see at the output of ann-channel MOSFET analog switch circuitsimilar to Figure 3.35, with an inputdrive I 1Figure 3.48
  • FET SWITCHES3.12 Limitations of FET switches 149signal levelof zero voltsand an output loadconsisting of 10k in parallel with 20pC re-alistic values for an analog switch circuit.The handsome transients are caused bycharge transferred to the channel, throughthe gate-channel capacitance, at the tran-sitions of the gate. The gate makes a sud-den step from one supply voltage to theother, in this case between f15 volt sup-plies, transferring a slug of chargeQ = CGc [VG(finish) - VG(start)]CGC is the gate-channel capacitance,typically around 5pE Note that the amountof charge transferred to the channel de-pends only on the total voltage change atthe gate, not on its rise time. Slowingdown the gate signalgives rise to a smaller-amplitude glitch of longer duration, withthe same total area under its graph. Low-pass filtering of the switchs output signalhas the same effect. Such measures mayhelp if the peak amplitude of the glitchmust be kept small, but in general they areineffective in eliminating gate feedthrough.In some cases the gate-channel capacitancemay be predictable enough for you tocancel the spikes by coupling an invertedversion of the gate signal through a smalladjustable capacitor.The gate-channel capacitance is distri-buted over the length of the channel, whichmeans that some of the charge is coupledback to the switchs input. As a result, thesize of the output glitch depends on thesignal source impedance and is smallestwhen the switch is driven by a voltagesource. Of course, reducing the size ofthe load impedance will reduce the size ofthe glitch, but this also loads the sourceand introduces error and nonlinearity dueto finite RON. Finally, all other thingsbeing equal, a switch with smaller gate-channel capacitance will introduce smallerswitching transients, although you pay aprice in the form of increased RON.Figure 3.49 shows an interesting com-parison of gate-induced charge transfersfor three kinds of analog switches, includ-ing JFETs. In all cases the gate signalis making a full swing, i.e., either 30volts or the indicated supply voltage forMOSFETs, and a swing from -15 voltsto the signal level for the n-channel JFETswitch. The JFET switch shows a strongFigure 3.49. Chargetransfer for various, FET linear switches-15 - 10 - 5 o + 5 + 10 +15 as a function of signalv,,,,, (V) voltage.
  • FIELD-EFFECT TRANSISTORS150 Chapter 3CMOS -c~rcuitT -dependence of glitch size on signal, be-cause the gate swing is proportional to thelevel of the signal above -15 volts. Well-balanced CMOS switches have relativelylow feedthrough because the charge contri-butions of the complementary MOSFETstend to cancel out (one gate is rising whilethe other is falling). Just to give scale tothese figures, it should be pointed out that30pC corresponds to a 3mV step across a0.01pF capacitor. Thats a rather large fil-ter capacitor, and you can see that this is areal problem, since a 3mV glitch is prettylarge when dealing with low-level analogsignals.Latchup and input currentAll CMOS integrated circuits have someform of input protection circuit, becauseotherwise the gate insulation is easily de-stroyed (see the later section on handlingprecautions). The usual protection net-work is shown in Figure 3.50: Although itmay use distributed diodes, the network isequivalent to clamping diodes to Vss andto VDD, combined with resistive currentlimiting. If you drive the inputs (or out-puts) more than a diode drop beyond thesupply voltages, the diode clamps go intoconduction, making the inputs (or outputs)look like a low impedance to the respec-tive supplies. Worse still, the chip canbe driven into "SCR latchup," a terrifying(and destructive) condition well describein more detail in Section 14.16. For now,all you need to know about it is that youdont want it! SCR latchup is triggered* I .outputFigure 3.50. CMOSinputloutput protectionnetworks. The seriesresistor at the output isoften omitted.by input currents (through the protectionnetwork) of roughly 20mA or more. Thus,you must be careful not to drive the analoginputs beyond the rails. This means, forinstance, that you must be sure the powersupply voltages are applied before any sig-nals that have significant drive current ca-pability. Incidentally, this prohibition goesfor digital CMOS ICs as well as the analogswitches we have been discussing.The trouble with diode-resistor protec-tion networks is that they compromiseswitch performance, by increasing RON,shunt capacitance, and leakage. Withclever chip design (making use of "dielec-tric isolation") it is possible to eliminateSCR latchup without the serious perfor-mance compromises inherent in traditionalprotection networks. Many of the neweranalogswitch designsare "fault protected";for example, Intersils IH5108 and IH5116analog multiplexers claim you can drivethe analog inputs to f25 volts, even withthe supply at zero (you pay for this robust-ness with an RONthat is four times higherthan that of the conventional IH6108116).Watch out, though, because there are plen-ty of analog switch ICs around that arenot forgiving!You can get analog switches and multi-plexers built with n-channel JFETs ratherthan complementary MOSFETs. Theyperform quite well, improving on CMOSswitches in several characteristics. In par-ticular, the series of JFET switches fromPMI has superior constancy of RONver-sus analog voltage, complete absence of
  • FET SWITCHES3.13 Some FET analog switch examples 151latchup, and low susceptibility to electro-static damage.Other switch limitationsSome additional characteristics of analogswitches that may or may not be impor-tant in any given application are switch-ing time, settling time, break-before-make delay, channel leakage current(both ON and OFF; see Section 4.19,RON matching, temperature coefficientof R O ~ ,and signal and power supplyranges. Well show unusual restraintby ending the discussion at this point,leaving the reader to look into these de-tails if the circuit application demandsit.the output impedance is high. Youll seehow to make "perfect" followers (precisegain, high Zin,low ZOut,and no VBEoff-sets, etc.) in the next chapter. Of course,if the amplifier that follows the filter hashigh input impedance, you dont need thebuffer.4-lnput MUXInputoutput ?.----4+ 1 .>--2 - b ~ tI IL,addressFigure 3.513.13 Some FET analog switch examplesAs we indicated earlier, many of the nat-ural applications of FET analog switchesare in op-amp circuits, which we will treatin the next chapter. In this section wewill show a few switch applications thatdo not require op-amps, to give a feelingfor the sorts of circuits you can use themin.Figure 3.52 shows a simple variation inwhich weve used four independentswitches, rather than a 4-input multiplexer.With the resistors scaled as shown, you cangenerate 16 equally spaced 3dB frequen-cies by turning on binary combinations ofthe switches.SwitchableRC low-pass filterFigure 3.51 shows how you could make asimple RC low-pass filter with selectable3dB points. Weve used a multiplexer toinputpI I 80kselect one of four preset resistors, via a2-bit (digital) address. We chose to put 1 1 outputthe switch at the input, rather than after O.0lpFthe resistors, because there is less charge A, A, A , AO I- -injection at a point of lower signal imped- -rolloff frequencyance. Another possibility, of course, is to selectuse FET switches to select the capacitor.TO generate a very wide range of time con- Figure 3.52. RC low-pass filter with choice ofstants you might have to do that, but the 15 equally spaced time constants.switchs finite RONwould limit attenua-tion at high frequencies, to a maximumof RoN/Rseries. Weve also indicated a EXERCISE 3.12unity-gain buffer, following the filter, since What are the 3dB points for this circuit?
  • FIELD-EFFECT TRANSISTORS152 Chapter 3Figure 3.53. An analog multi-plexer selects appropriateemitter degeneration resistorsto achieve decade-switchablegain.buffer bufferI-"" hold-Figure 3.54. Sample-and-hold.Switchable gain amplifier Sample-and-holdFigure 3.53 shows how you can apply thesame idea of switching resistors to pro-duce an amplifier of selectable gain. Al-though this idea is a natural for op-amps,we can use it with the emitter-degeneratedamplifier. We used a constant-current sinkas emitter load, as in an earlier exam-ple, to permit gains much less than unity.We then used the multiplexer to sel-ect one of four emitter resistors. Notethe blocking capacitor, needed to keepthe quiescent current independent ofgain.Figure 3.54 shows how to make a "sample-and-hold" circuit, which comes in handywhen you want to convert an analog signalto a stream of digital quantities ("analog-to-digital conversion") - youve got tohold each analog level steady while youfigure out how big it is. The circuit issimple: A unity-gain input buffer generatesa low-impedance copy of the input signal,forcing it across a small capacitor. Tohold the analog level at any moment, yousimply open the switch. The high inputimpedance of the second buffer (which
  • FET SWITCHES3.14 MOSFET logic and power switches 153should have FET input transistors, to keep get you up to speed on them in Chaptersinput current near zero) prevents loading 8-11!).of the capacitor, so it holds its voltage untilthe switch is again closed.3.14 MOSFET logic and power switchesEXERCISE 3.13 The other kinds of FET switch applicationsThe input buffermust supplycurrent to keep the are logic and Power switching circuits. Thecapacitor following a varying signal. Calculate distinction is simple: In analog signalthe bufferspeak output current when the circuit switching you use a FET as a series switch,is driven by an input sine wave of 1 volt passing or blocking a signal that has someamplitudeat 10kHz. range of analog voltage. The analog signalis usually a low-level signal,at insignificantFlying-capacitor voltage converterHeres a nice way (Fig. 3.55) to generate aneeded negative power-supply voltage in acircuit that is powered by a single positivesupply. The pair of FET switches on theleft connects C1across the positive supply,charging it to V,,, while the switches onthe right are kept open. Then the inputswitches are opened, and the switches onthe right are closed, connecting chargedC1 across the output, transferring someof its charge onto C2. The switchesare diabolically arranged so that C1 getsturned upside down, generating a negativeoutput! This particular circuit is availablepower levels. In logic switching, on theother hand, MOSFET switches open andclose to generate full swings between thepower supply voltages. The "signals" hereare really digital, rather than analog-theyswing between the power supply voltages,representing the two states HIGH andLOW. In-between voltages are not usefulor desirable; in fact, theyre not evenlegal! Finally, "power switching" refers toturning on or off the power to a load suchas a lamp, relay coil, or motor winding;in these applications, both voltages andcurrents tend to be large. Well take logicswitching first.as the 7662 voltage converter chip, which Logic awnchingwell talk about in Sections 6.22 and14.07. The device labeled "inverter" turns Figure 3.56 shows the simplest kind ofa HIGH voltage into a LOW voltage, and logic switching with MOSFETs: Bothvice versa. Well show you how to make circuits use a resistor as load and performone in the next section (and well really the logical function of inversion - a HIGHm -- Figure 3.55. Flying-capacitor voltagelnverter inverter.
  • FIELD-EFFECT TRANSISTORS154 Chapter 3Figure 3.56. NMOS and PMOS logic inverters.input generates a LOW output, and viceversa. The n-channel version pulls the out-put to ground when the gate goes HIGH,whereas the p-channel version pulls theresistor HIGH for grounded (LOW) in-put. Note that the MOSFETs in these cir-cuits are used as common-source invert-ers, rather than as source followers. Indigital logic circuits like these we are usu-ally interested in the output voltage ("logiclevel") produced by a certain input volt-age; the resistor serves merely as a passivedrain load, to make the output swing to thedrain supply when the FET is off. If, onthe other hand, we replace the resistor bya light bulb, relay, printhead hammer, orsome other hefty load, weve got a power-switching application (Fig. 3.3). Althoughwere using the same "inverter" circuit, inthe power switching application were in-terested instead in turning the load on andoff.CMOS inverterThe NMOS and PMOS inverters of thepreceding circuits have the disadvantageof drawing current in the ON state andhaving relativelyhigh output impedance inthe OFF state. You can reduce the outputimpedance (by reducing R), but only atthe expense of increased dissipation, andvice versa. Except for current sources,of course, its never a good idea to havehigh output impedance. Even if the in-tended load is high impedance (anotherMOSFET gate, for example), you are invit-ing capacitive noise pickup problems, andyou will suffer reduced switching speedsfor the ON-to-OFF ("trailing") edge (be-cause of stray loading capacitance). In thiscase, for example, the NMOS inverter witha compromise value of drain resistor, say10k, would produce the waveform shownin Figure 3.57.Figure 3.57The situation is reminiscent of thesingle-ended emitter follower in Section2.15, in which quiescent power dissipationand power delivered to the load were in-volved in a similar compromise. The so-lution there - the push-pull configuration- is particularly well suited to MOSFETswitching. Look at Figure 3.58, which youmight think of as a push-pull switch: In-put grounded cuts off the bottom transis-tor and turns on the top transistor, pullingthe output HIGH. A HIGH input (+VDo)does the reverse, pulling the output toground. Its an inverter with low output
  • FET SWITCHES3.14 MOSFET logic and power switches 155source inverters, whereas the complementarybipolar transistors in the push-pull circuits ofSection 2.15 are (non-inverting) emitter foilow-input T$outputers. Try drawing a "complementary BJT in-verter," analogous to the CMOS inverter. Whywont it work?Well be seeing much more of digitalCMOS in the chapters on digital logic andmicroprocessors (Chapters 8-11). For now,- it should be evident that CMOS is a lowFigure 3.58. CMOS logic inverter. power logic family (with zero quiescentpower) with high-impedance inputs, andimpedance in both states, and no quiescentcurrent whatsoever. Its called a CMOS(complementary MOS) inverter, and it isthe basic structure of all digital CMOSlogic, the logic family that has becomedominant in large-scale integrated circuits(LSI), and seems destined to replace ear-lier logic families (with names like "TTL")based on bipolar transistors. Note thatthe CMOS inverter is two complementaryMOSFET switches in series, alternatelyenabled, while the CMOS analog switch(treated earlier in the chapter) is two com-plementary MOSFET switches in parallel,enabled simultaneously.with stiff outputs that swing the full supplyrange. Before leaving the subject, however,we cant resist the temptation to show youone additional CMOS circuit (Fig. 3.59).This is a logic NAND gate, whose outputgoes LOW only if input A AND input Bareboth HIGH. The operation is surprisinglyeasy to understand: If A and B are bothHIGH, series NMOS switches Q1 and Q2are both ON, pulling the output stifflyto ground; PMOS switches Qg and Qqcooperate by being OFF; thus, no currentflows. However, if either A or B (or both) isLOW, the corresponding PMOS transistoris ON, pulling the output HIGH; since one(or both) of the series chain QIQz is OFF,EXERCISE 3.14 no current flows.The complementary MOS transistors in the This is called a "NAND" gate becauseCMOS inverter are both operating as common- it performs the logical AND function, butoutputQ = F B+QZL--Figure 3.59. CMOSNAND gate, AND gate.
  • FIELD-EFFECTTRANSISTORS156 Chapter 3with inverted ("NOT") output - its aNOT-AND, abbreviated NAND. Althoughgates and their variants are properly asubject for Chapter 8, you will enjoy tryingyour hand at the following problems.EXERCISE 3.15Draw a CMOS AND gate. Hint: AND = NOT-NAND.EXERCISE 3.16Now draw a NOR gate: The output is LOW ifeither A OR B (or both) is HIGH.EXERCISE 3.17You guessed it -draw a CMOS OR gate.EXERCISE 3.18Draw a 3-input CMOS NAND gate.The CMOS digital logic well be see-ing later is constructed from combinationsof these basic gates. The combination ofvery low power dissipation and stiff rail-to-rail output swing makes CMOS logicthe family of choice for most digital cir-cuits, accounting for its popularity. Fur-thermore, for micropower circuits (suchas wristwatches and small battery-poweredinstruments) its the only game in town.Lest we leave the wrong impression,however, its worth noting that CMOSlogic is not zero-power. There are twomechanisms of current drain: During tran-sitions, a CMOS output must supply atransient current I = CdVldt to chargeany capacitance it sees (Fig. 3.60). You getload capacitance both from wiring ("stray"capacitance) and from the input capaci-tance of additional logic that you are driv-ing. In fact, because a complicated CMOSchip contains many internal gates, eachdriving some on-chip internal capacitance,there is some current drain in any CMOScircuit that is making transitions, even ifthe chip is not driving any external load.Not surprisingly, this "dynamic" currentdrain is proportional to the rate at whichtransitions take place. The second mecha-nism of CMOS current drain is shown inFigure 3.61: As the input jumps betweenthe supply voltage and ground, there is aregion where both MOSFETs are conduct-ing, resulting in large current spikes fromVoDto ground. This is sometimes called"class-A current" or "power supply crow-barring." You will see some consequencesof this in Chapters 8, 9, and 14. As longas were dumping on CMOS, we shouldmention that an additional disadvantageof CMOS (and, in fact, of all MOSFETs)is its vulnerability to damage from staticelectricity. Well have more to say aboutthis in Section 3.15.Figure 3.60. Capacitive charging current.0, alone,,10 v," voo0 , conducting0, conduct~ng0Figure 3.61. Class-A CMOS conduction.CMOS linear amplifierCMOS inverters - and indeed all CMOSdigital logic circuits - are intended to be
  • FET SWITCHES3.14 MOSFET logic and power switches 157used with digital signal levels. Except dur-ing transitions between states, therefore,the inputs and outputs are close to groundor VDD (usually +5V). And except duringthose transitions (with typical durations ofa few nanoseconds), there is no quiescentcurrent drain.The CMOS inverter turns out to havesome interesting properties when used withanalog signals. Look again at Figure 3.61.You can think of Q1 as an active (current-source) load for inverting amplifier Q2,and vice versa. When the input is nearVDD or ground, the currents are grosslymismatched, and the amplifier is in satu-ration (or "clipping") at ground or VDD,respectively. This is, of course, the nor-mal situation with digital signals. How-ever, when the input is near half the sup-ply voltage, there is a small region wherethe drain currents of Q1and Q2are nearlyequal; in this region the circuit is an in-verting linear amplifier with high gain. Itstransfer characteristic is shown in Figure3.62. The variation of Rloadand g, withdrain current is such that the highest volt-age gain occurs for relatively low draincurrents, i.e., at low supply voltages (say5V).This circuit is not a good amplifier; ithas the disadvantage of very high outputimpedance (particularly when operated atlow voltage), poor linearity, and unpre-dictable gain. However, it is simple andinexpensive (CMOS inverters are available6 to a package for under half a dollar),and it is sometimes used to amplify smallinput signals whose waveforms arent im-portant. Some examples are proximityswitches (which amplify 60Hz capacitivepickup), crystal oscillators, and frequency-sensing input devices whose output is afrequency that goes to a frequency counter(see Chapter 15).To use a CMOS inverter as a linearamplifier, its necessary to bias the inputso that the amplifier is in its active re-gion. The usual method is with a large-very h ~ y hgainfor small signals1 2 3 4 5AV," (V)v+= 3v50 -40I 3 0 -v+= 1ovgain(dB) 20-10 -I I I 1 I10 100 l k lOk look l M lOM lOOMfrequencyBFigure 3.62value resistor from output to input (whichwell recognize as "dc feedback" in thenext chapter), as shown in Figure 3.63.That puts us at the point VOut = V,, inFigure 3.62. As well learn later, such aconnection (circuit A) also acts to lowerthe input impedance, through "shunt feed-back," making circuit B desirable if a highinput impedance at signal frequencies isimportant. The third circuit is the clas-sic CMOS crystal oscillator, discussed inSection 5.13. Figure 3.64 shows a vari-ant of circuit A, used to generate a cleanlOMHz full-swing square wave (to drivedigital logic) from an input sine wave. Thecircuit works well for input amplitudesfrom 50mV rms to 5 volts rms. This is agood example of an "I dont know the gain,and I dont care" application. Note theinput-protection network, consisting of acurrent-limiting series resistor and clamp-ing diodes.
  • FIELD-EFFECT TRANSISTORS158 Chapter 3A BFigure 3.63. CMOS linear amplifier circuits.0.001 100lOMHz in0.05-5"rms wvrr74HC04 74HC04Figure 3.64Power switchingMOSFETs work well as saturated switches,as we suggested with our simple circuit inSection 3.01. Power MOSFETs are nowavailable from many manufacturers, mak-ing the advantages of MOSFETs (high in-put impedance, easy paralleling, absenceof "second breakdown") applicable topower circuits. Generally speaking, powerMOSFETs are easier to use than conven-tional bipolar power transistors. However,there are some subtle effects to consider,and cavalier substitution of MOSFETs inswitching applications can lead to promptdisaster. Weve visited the scenes of suchdisasters and hope to avert their repetition.Read on for our handy guided tour.than a few tens of milliamps, until thelate 1970s, when the Japanese introduced"vertical-groove" MOS transistors. PowerMOSFETs are now manufactured by allthe manufacturers of discrete semiconduc-tors (e.g, GE, IR, Motorola, RCA, Sili-conix, Supertex, TI, along with Europeancompanies like Amperex, Ferranti, Sie-mens, and SGS, and many of the Japanesecompanies), with names like VMOS,TMOS, vertical DMOS, and HEXFET.They can handle surprisingly high voltages(up to IOOOV), and peak currents to 280amps (continuous currents to 70A), withRON as low as 0.02 ohm. Small powerMOSFETs sell for much less than a dollar,and theyre available in all the usual tran-sistor packages, as well as multiple tran-Power MOSFETs. FETs were feeble low- sistors packaged in the convenient DIPcurrent devices, barely able to run more (dual in-line package) that most integrated
  • FET SWITCHES3.14 MOSFET logic and power switches 15C/-- B Figure 3.65. A large-junction-area transistorcan be thought of asmany paralleled small-E area transistors.circuits come in. Ironically, it is nowdiscrete low-level MOSFETs that are hardto find, there being no shortage of powerMOSFETs. See Table 3.5 for a listing ofrepresentative power MOSFETs.High impedance, thermal stability. Thetwo important advantages of the powerMOSFET, compared with the bipolarpower transistor, are its high input imped-ance (but watch out for high input capac-itance, particularly with high-current de-vices; see below) and its complete absenceof thermal runaway and second breakdown.This latter effect is very important in powercircuits and is worth understanding: Thelarge junction area of a power transistor(whether BJT or FET) can be thought ofas a large number of small junctions inparallel (Fig. 3.65), all with the same ap-plied voltages. In the case of a bipolarpower transistor, the positive temperaturecoefficientof collector current at fixed VBE(approximately +9°/o/0C, see Section 2.10)means that a local hot spot in the junc-tion will have a higher current density,thus producing additional heating. At suf-ficiently high VCE and Ic, this "currenthogging" can cause local thermal runaway,known as second breakdown. As a result,bipolar power transistors are limited to a"safe operating area" (on a plot of collectorcurrent versus collector voltage) smallerthan that allowed by transistor power dis-sipation alone (well see more of this inChapter 6). The important point here isthat the negative temperature coefficientof MOS drain current (Fig. 3.13) preventsthese junction hot spots entirely. MOS-FETs have no second breakdown, and theirsafe operating area (SOA) is limited onlyby power dissipation (see Fig. 3.66, whereweve compared the SOAs of an npn andan NMOS power transistor of the sameImax,Vmax,and Pdiss).For the same rea-son, MOSFET power amplifiers dont havethe nasty runaway tendencies that weveall grown to love in bipolar transistors (seeSection 2.15), and as an added bonus,power MOSFETs can be paralleled with-out the current-equalizing "emitter-ballasting" resistors that are necessary withbipolar transistors (see Section 6.07).Power switching examples and cautions.You often want to control a power MOS-FET from the output of digital logic. Al-though there are logic families that gen-erate swings of 10 volts or more ("4000-series CMOS"), the most common logicfamilies use levels of +5 volts ("high-speedCMOS") or +2.4 volts ("TTL"). Figure3.67 shows how to switch loads from thesethree logic families. In the first circuit, the+10 volt gate drive will fully turn on anyMOSFET, so we chose the VN0106, an in-expensive transistor that specifies RON< 5ohms at VGS = 5 volts. The diode protectsagainst inductive spike (Section 1.31); theseries gate resistor, though not essential, isa good idea, because MOSFET drain-gatecapacitance can couple the loads inductivetransients back to the delicate CMOS logic(more on this soon). In the second circuitwe have 5 volts of gate drive, still fine forthe VNOl/VPOl series; for variety weve
  • FIELD-EFFECTTRANSISTORS160 Chapter 31 2 5 10 20 50 100 a0 nCV,,. V ~ s( v ~ down.3.66.sufferPower MOSFETsfrom second break-used a p-channel MOSFET, driving a load +5 volt -swing from the TTL output,returned to ground. which then drives a normal MOSFET;The last two circuits show two ways alternatively, we can use something liketo handle the +2.4 volt (worst-case; its the TN0106, a "low-threshold" MOSFETusually around +3.5V)HIGH output from designed for logic-level drive. Watch out,TTL digital logic: We can use a pullup though, for misleading specifications. Forresistor to +5 volts to generate a full exam~le.the TNOl svecifies V~9/+h =
  • FET SWITCHES3.14 MOSFET logic and power switches 161Magnecraft W97Cpx-2power relay1N4002+ 1ovI 0.3 V maxwhen on40h=GVNO106-10V CMOSVP0106RON= 150 (maxl@ v,, = - 5 v5V loadFigure 3.67. MOSFETs can switch power loads when driven from digital logic levels.1.5 volts (max)," which sounds fine untilyou read the fine print ("at ID = 1mA").It takes considerably more gate voltagethan VGS(th) to turn the MOSFET onfully (Fig. 3.68). However, the circuit willprobably work OK, because (a) a HIGHTTL output is rarely less than +3 volts,and typically more like +3.5 volts, and (b)the TNOl further specifies RoN(typ) =50 at VGS= 3V."This example illustrates a frequent de-signers quandary, namely a choice be-tween a complicated circuit that meets thestrict worst-case design criterion, and istherefore guaranteed to work, and a sim-ple circuit that doesnt meet worst-casespecifications, but is overwhelmingly likelyto function without problems. There aretimes when you will find yourself choosingthe latter, ignoring the little voice whisper-ing into your ear.Capacitance. In the preceding exampleswe put a resistor in series with the gatewhen there was an inductive load. As wementioned earlier in the chapter (Section
  • FIELD-EFFECTTRANSISTORS162 Chapter 3ioutput characterist~cs3.0 - transfer characteristics2.4 -1.8 --50.1.2 -0.6 -0Figure 3.68. Drain characteristics of an n-channel low-threshold MOSFET (type TNO104).The series resistance is a compromisebetween speed and protection, with valuesof 100 ohms to 10k being typical. Evenwithout inductive loads there is dynam-ic gate current, of course: The capaci-tance to ground, Cis,, gives rise to I =CissdVGs/dt,while the (smaller) feedbackcapacitance, C,,,, produces an input cur-rent I = CTs,dVDG/dt.The latter maydominate in a common-source switch, be-cause A V D ~is usually much larger thanthe AVGs gate drive (Miller effect).EXERCISE 3.19An IRF520 MOSFET controlling a 2 amp loadis switched off in 100ns (by bringing the gatefrom +10V to ground), during which the draingoes from 0 to 50 volts. What is the averagegate current during the 1OOns, assuming CGS(alsocalledCis,)is 450pF,and CDG(alsocalledCTss)is 50pF?3.09), MOSFETs have essentially infinitegate resistance,but finite impedance owingto gate-channel capacitance. With high-current MOSFETs the capacitance can bestaggering: Compared with 45pF of inputcapacitance for the 1 amp VNO1, the 10amp IRF520 has Ci, = 450pF, and themacho 70 amp SMM70N05 from Siliconixhas Cin = 4300pF! A rapidly-changingdrain voltage can produce milliamps oftransient gate current, enough to overdrive(and even damage, via "SCR crowbarring")delicate CMOS driver chips.0 5 10 15gate charge (nC1Figure 3.69. Gate charge versus VGS.In a common-source switch, the Miller-effect contribution to gate current oc-curs entirely during the drain transitions,whereas the gate-source capacitance causescurrent whenever the gate voltage is chang-ing. These effects are often plotted as agraph of "gate charge versus gate-sourcevoltage," as in Figure 3.69. The horizon-tal portion occurs at the turn-on voltage,where the rapidly falling drain forces the
  • FET SWITCHES3.14 MOSFET logic and power switches 163gate driver to supply additional charge toCrss(Miller effect). If the feedback capaci-tance were independent of voltage, the hor-izontal portion would be proportional todrain voltage, after which the curve wouldcontinue at the previous slope. In fact,feedback capacitance Crssrises rapidly atlow voltage (Fig. 3.70), which means thatmost of the Miller effect occurs during thelow-voltage portion of the drain waveform.This explains the change in slope of thegate charge curve, as well as the fact thatthe horizontal portion is almost indepen-dent of drain voltage.IRF520VGS= 0C,,, = C,, + Cgd,CdsshortedCgsCgdcoss = Cd, + -Cgs + Cgd" Cds + cgdI I I I J0 1 0 2 0 3 0 4 0 5 0v,, (V)Figure 3.70. Power MOSFET capacitances.EXERCISE 3.20How does the voltage dependence of Crssexplain the change in slope of the gate chargecurves?Other cautions. Power MOSFETs havesome additional idiosyncrasies you shouldknow about. All manufacturers of powerMOSFETs seem to connect the body in-ternally to the source. Because the bodyforms a diode with the channel, this meansthat there is an effective diode from drainto source (Fig. 3.71); some manufactur-ers even draw the diode explicitly in theirMOSFET symbol so that you wont for-get. This means that you cannot use powerMOSFETs bidirectionally, or at least notwith more than a diode drop of reversedrain-source voltage. For example, youcouldnt use a power MOSFET to zero anintegrator driven with a bipolarity signal,and you couldnt use a power MOSFETas an analog switch for bipolarity signals.This problem does not occur with inte-grated circuit MOSFETs (analog switches,for example), where the body is connectedto the most negative power-supply termi-nal.Figure 3.71. Power MOSFETs connect body tosource, forming a drain-source diode.Another trap for the unwary is thefact that gate-source breakdown voltages(f20V is a common figure) are lower thandrain-source breakdown voltages (whichrange from 20V to 1000V). This doesntmatter if youre driving the gate from thesmall swings of digital logic, but you getinto trouble immediately if you think youcan use the drain swings of one MOSFETto drive the gate of another.Finally, the issue of gate protection: Aswe discuss in the final section of this chap-ter, all MOSFET devices are extremely sus-ceptible to gate oxide breakdown, causedby electrostatic discharge. Unlike JFETsor other junction devices, in which junc-tion avalanche current can safely dischargethe overvoltage, MOSFETs are damagedirreversibly by a single instance of gatebreakdown. For this reason it is a verygood idea to use gate series resistors oflk-lOk, particularly when the gate signal
  • FIELD-EFFECTTRANSISTORS164 Chapter 3comes from another circuit board. This stantial dc gate current. Another precau-greatly reduces the chances of damage; it tion is to make sure you dont leave MOS-also prevents circuit loading if the gate FET gates unconnected, because they areis damaged, because the most common much more susceptible to damage whensymptom of a damaged MOSFET is sub- floating (there is then no circuit path for-TABLE 3.5. POWER MOSFETsContdrain Turn-onCUrr RDS(O~)@"GSVGS(~II) Ciss Crss chargeBVDSa max mar max tYP tYP tYP(V) (A) (R) (V) (V) (pF) (pF) (nC) caseb Type/Commentscn-channel30 0.8 1.8 5 2.5 110 35 - DIP-14 ~ ~ 3 0 0 1J; 2N, 2P in DIP40 4 2.5 5 1.5 60 5 0.8 TO-92 TN0104N3; low threshold60 0.2 6 5 2.5 60 5 - TO-92 ~ ~ 0 6 1 0 ~ ~ ;gate protec; sim to VN222260 0.4 5 5 2.5 60 10 - DIP-14 ~ ~ 1 0 0 4 ~ uad in DIP60 15 0.14 5 2 900 180 ,4.- TO-220 RFP15NO6L , low thresholdVN1310N3, BSS100VN0210N3IRFDl2ORFP~NIOL~;low thresholdIRF510, MTP4N10, VNIllON5,2SK295IRF520, BUZ72A, 2SK383, VN121ON5IRF540,MTP25N10IRF150,2N6764VNEOOSA120 0.2 10 2.5 2 125 20 - TO-92 ~ ~ 1 2 0 6 ~ ;low threshold
  • FET SWITCHES3.14 MOSFET logic and power switches 165Contdrain Turn-onCU" RDS(O~)@~GSVGS(~~)Ciss Crss chargeBVDSamax max max tYP tYP tYP(V) (A) (a) (V) (V) (pF) (pF) (nC) caseb Type/Commentscp-channel30 0.6 2 12 4.5 150 60 - DIP-14 ~ ~ 3 0 0 1J ; 2N, 2P in DIP60 0.4 5 10 4.5 150 20 - DIP-14 ~ ~ 2 0 0 4 ~ ;quad in DIPBVGSis +20V, except (I +40V, (*) k1OV, (3) +15, -0.3V, and (4) k15V(b) QJA:DIP-4=12O0CMI;DIP-14=10O"C/W;TO-92=200C/W; OJC:TO-220=2.5C/W; TO-3=0.8C/W.Pdiss@ Tamb=75C: DIP-4=0.6W; DIP-14=0.8W; TO-92=0.3W; Pdiss@ Tcase=75C:TO-220=30W; TO-3=90W.() expect var~at~onsin characteristics between manufacturers; those shown are typical. (m) maximum.static discharge, which otherwise providesa measure of safety). This can happenunexpectedly if the gate is driven fromanother circuit board. The best practice isto connect a pulldown resistor (say lOOk to1M)from gate to source of any MOSFETswhose gates are driven from an off-cardsignal source.MOSFETs versus BJTs as high-currentswitches. Power MOSFETs are attractivealternatives to conventional power BJTsmost of the time. They currently costsomewhat more, for the same capability;but theyre simpler to drive, and theydont suffer from second breakdown andconsequently reduced safe-operating-area(SOA) constraints (Fig. 3.66).Keep in mind that an ON MOSFETbehaves like a small resistance, ratherthan a saturated bipolar transistor, forsmall values of drain voltage. This canbe an advantage, because the "saturationvoltage" goes clear to zero for small draincurrents. There is a general perception thatMOSFETs dont saturate as well at highcurrents, but our research shows this to belargely false. In Table 3.6 weve chosencomparable pairs (npn versus n-channelMOSFET), for which weve looked up thespecified VcE(sat) or RDs(,,). The low-current MOSFET makes a poor showingwhen compared with its "small-signal" npncousin, but in the range of 10-50 amps, 0-100 volts, the MOSFET does better. Noteparticularly the enormous base currents
  • FIELD-EFFECT TRANSISTORS166 Chapter 3TABLE 3.6. BJT-MOSFETCOMPARISONV,t(max)tout(25°C) (125C) (10V) PriceClass TYPe 1c.b (v) (v) 1,. VGS max (100 PC)60V, 0.5A NPN - 2N4400 0.5A 0.75NMOS - VN0610 0.5A 2.560V, 10A NPN - 2N3055 10A 3NMOS - MTP3055A 1OA 1.51OOV, 50A NPN - 2N6274 20A 1NMOS - VNE003A 20A 0.7400V, 1 5 ~ NPN - 2N6547 15A 1.5NMOS - IRF350 15A 3needed to bring the bipolar power transis-tor into good saturation - 10% or more ofthe collector current (!) - compared withthe (zero-current) 10 volt bias at whichMOSFETs are usually specified. Note alsothat high-voltage MOSFETs (say, BVDs >200V) tend to have larger RDs(,,), withlarger temperature coefficients, than thelower-voltage units. Along with saturationdata, weve listed capacitances in the ta-ble, because power MOSFETs often havemore capacitance than BJTs of the samerated current; in some applications (partic-ularly if switching speed is important) youmight want to consider the product of ca-pacitance and saturation voltage as a figureof merit.Remember that power MOSFETs canbe used as BJT substitutes for linear powercircuits, for example audio amplifiers andvoltage regulators (well treat the latter inChapter 6). Power MOSFETs are alsoavailable as p-channel devices, althoughthere tends to be a greater variety availableamong the (better performing) n-channeldevices.Some MOSFET power switching exam-ples. Figure 3.72 shows three ways to usea MOSFET to control the dc power tosome sub-circuit that you want to turn onand off. If you have a battery-operatedinstrument that needs to make some mea-surements occasionally, you might usecircuit A to switch the power-hungrymicroprocessor off except during thoseintermittent measurements. Here weveused a PMOS switch, turned on by a 5 voltlogic swing to ground. The "5V logic" ismicropower CMOS digital circuitry, keptrunning even when the microprocessor isshut off (remember, CMOS logic has zerostatic dissipation). Well have much moreto say about this sort of "power-switching"scheme in Chapter 14.In the second circuit (B), were switch-ing dc power to a load that needs +12volts, at considerable current; maybe itsa radio transmitter, or whatever. Becausewe have only a 5 volt logic swing avail-able, weve used a small n-channel switchto generate a full 12 volt swing, which thendrives the PMOS gate. Note the high-valueNMOS drain resistor, perfectly adequatehere because the PMOS gate draws no dccurrent (even a beefy 10A brute), and wedont need high switching speed in an ap-plication like this.The third circuit (C) is an elaborationof circuit B, with short-circuit current lim-iting via the pnp transistor. Thats alwaysa good idea in power supply design, be-cause its easy to slip with the oscilloscopeprobe. In this case, the current limiting
  • FET SWITCHES3.14 MOSFET logic and power switches 1675 v -logickr-to 12V loadcircuit+ lav0 . 5 0 VP121ZV load1OOk-10k -Figure 3.72. dc power switching with MOSFETs.also prevents momentary short-circuiting Figure 3.73A shows a simple MOSFETof the +12 volt supply by the initially switching example, one that takes advan-uncharged bypass capacitor. See if you can tage of the high gate impedance. You mightfigure out how the current limiting circuit want to turn on exterior lighting automat-works. ically at sunset. The photoresistor has lowresistance in sunlight, high resistance inEXERCISE 3.21darkness. You make it part of a resis-How doesthe currentlimiting circuitwork? Howmuch load current does it allow? Why is thetive divider, driving the gate directly (noNMOS drain resistor split in two? dc loading!). The light goes on when thegate voltage reaches the value that pro-The limited gate breakdown voltages ofMOSFETs (usually f20V) would createa real problem here if you attempted tooperate the circuit from higher supplyvoltage. In that case you could replace thelOOk resistor with lOk (allowing operationto 40V), or other appropriate ratio, alwayskeeping the VP12 gate drive less than 20volts.duces enough drain current to close the re-lay. Sharp-eyed readers may have noticedthat this circuit is not particularly preciseor stable; thats OK, because the photore-sistor undergoes an enormous change inresistance (from 1Ok to lOM, say) when itgets dark. The circuits lack of a preciseand stable threshold just means that thelight may turn on a few minutes early or
  • FIELD-EFFECT TRANSISTORS168 Chapter 3Figure 3.73. Ambient-light-controlled power switch.to 120V aclampl~ghtingcircu~t (or relay)1OOk s 6-bL--m~ O O ~ H Z Figure 3.74. MOSFET piezo1OMt*4 )late. Note that the MOSFET may have todissipate some power during the time thegate bias is inching up, since were operat-ing in the linear region. That problem isremedied in Figure 3.73B, where a pair ofcascaded MOSFETs delivers much highergain, augmented by some positive feed-back via the 10M resistor; the latter causesthe circuit to snap on regeneratively as itreaches threshold.Figure 3.74 shows a real power MOS-FET job: A 200 watt amplifier to drivea piezoelectric underwater transducer at0power driver.-----200kHz. Weve used a pair of hefty NMOStransistors, driven alternately to create acdrive in the (high-frequency) transformerprimary. The bipolar push-pull gate dri-vers, with small gate resistors, are neededto overcome capacitive loading, since theFETs must be turned on fully in somethingless than a microsecond.Finally, in Figure 3.75 we show a linearcircuit example with power MOSFETs.Ceramic piezoelectric transducers are of-ten used in optical systems to producecontrolled small motions; for example,
  • FET SWITCHES3.15 MOSFET handling precautions 169180pFo r 0 +1ov3.3k- use five resistors- In series-protection 0- 1kV piezo dr~vercircuit lOOOV pp to 1kHzFigure 3.75. IkV low-power piezo driver.in adaptive optics you might use a piezo-electrically controlled "rubber mirror" tocompensate for local variations in the in-dex of refraction of the atmosphere. Piezotransducers are nice to use, because theyrevery stiff. Unfortunately, they require akilovolt or more of voltage to produce sig-nificant motions. Furthermore, theyrehighly capacitive - typically 0.01pF ormore - and have mechanical resonancesin the kilohertz range, thus presenting anasty load. We needed dozens of suchdriver amplifiers, which for some reasoncost a few thousand dollars apiece if youbuy them commercially. We solved ourproblem with the circuit shown. The BUZ-50B is an inexpensive ($4) MOSFET, goodfor 1kV and 2 amps. The first transistor isa common-source inverting amplifier, driv-ing a source follower. The npn transis-tor is a current-limiter and can be a low-voltage unit, since it floats on the output.One subtle feature of the circuit is the factthat its actually push-pull, even though itpiezoCLc 10,OOOpFlooks single-ended: You need plenty of cur-rent to push 10,000pF around at 2 voltsper microsecond (how much?); the outputtransistor can source current, but the pull-down resistor cant sink enough (look backto Section 2.15, where we motivated push-pull with the same problem). In this circuitthe driver transistor is the pulldown, viathe gate-source diode! The rest of the cir-cuit involves feedback (with an op-amp),a forbidden subject until the next chapter;in this case the magic of feedback makesthe overall circuit linear (100V of outputper volt of input), whereas without it theoutput voltage would depend on the (non-linear) ID-versus-VGs characteristic of theinput transistor.3.15 MOSFET handling precautionsThe MOSFET gate is insulated by a layerof glass (SOa) a few thousand angstroms(1A = 0.lnm) thick. As a result it hasvery high resistance, and no resistive or
  • FIELD-EFFECT TRANSISTORS170 Chapter 3junction-like path that can discharge staticelectricity as it is building up. In a classicsituation you have a MOSFET (or MOS-FET integrated circuit) in your hand. Youwalk over to your circuit, stick the deviceinto its socket, and turn on the power, onlyto discover that the FET is dead. Youkilled it! You should have grabbed onto thecircuit board with your other hand beforeinserting the device. This would have dis-charged your static voltage, which in win-ter can reach thousands of volts. MOS de-vices dont take kindly to "carpet shock,"which is officially called electrostatic dis-charge (ESD). For purposes of static elec-tricity, you are equivalent to lOOpF in se-ries with 1.5k; in winter your capacitormay charge to lOkV or more with a bit ofshuffling about on a fluffy rug, and evena simple arm motion with shirt or sweatercan generate a few kilovolts (see Table 3.7).TABLE 3.7.TYPICAL ELECTROSTATICVOLTAGESaElectrostatic voltage10%-20% 650-90%humidity humidityAction (J) (J)tion. (If the spark comes from your finger,your additional lOOpF only adds to the in-jury.) Figure 3.76 (from a series of ESDtests on a power MOSFET) shows the sortof mess this can make. Calling this "gatebreakdown" gives the wrong idea; the col-orful term "gate rupture" is closer to themark!highpower (X1200)Figure 3.76. Scanning electron micrograph ofa 6 amp MOSFET destroyed b y IkV charge o n"human body equivalent" (1.5k in series with100pF) applied t o its gate. (Courtesy o f Motor-ola, Inc.)walk on carpet 35,000 1,500walk on vinyl floor 12,000 250work at bench 6,000 100handle vinyl envelope 7,000 600pick up poly bag 20,000 1,200shift position on foam chair 18,000 1,500(a) adapted from Motorola Power MOSFET Data Book.Although any semiconductor device canbe clobbered by a healthy spark, MOS de-vices are particularly susceptible becausethe energy stored in the gate-channel ca-pacitance, when it has been brought up tobreakdown voltage, is sufficient to blow ahole through the delicate gate oxide insula-The electronics industry takes ESD veryseriously. It is probably the leading causeof nonfunctional semiconductors in instru-ments fresh off the assembly line. Booksare published on the subject, and you cantakes courses on it. MOS devices, as wellas other susceptible semiconductors (whichincludes just about everything; e.g., it takesabout 10 times as much voltage to zapa BJT), should be shipped in conductivefoam or bags, and you have to be carefulabout voltages on soldering irons, etc., dur-ing fabrication. It is best to ground solder-ing irons, table tops, etc., and use conduc-tive wrist straps. In addition, you can get"antistatic" carpets, upholstery, and even
  • clothing (e.g., antistatic smocks containing2% stainless steel fiber). A good antistaticworkstation includes humidity control, airionizers (to make the air slightly conduc-tive, which keeps things from charging up),and educated workers. In spite of all this,failure rates increase dramatically in win-ter.Once a semiconductor device is safelysoldered into its circuit, the chances fordamage are greatly reduced. In addition,most small-geometry MOS devices (e.g.,CMOS logic devices, but not power MOS-FETs) have protection diodes in the inputgate circuits. Although the internal pro-tection networks of resistors and clampingdiodes (or sometimes zeners) compromiseperformance somewhat, it is often worth-while to choose those devices because ofthe greatly reduced risk of damage by staticelectricity. In the case of unprotecteddevices, for example power MOSFETs,small-geometry (low current) devices tendto be the most troublesome, because theirlow input capacitance is easily brought tohigh voltage when it comes in contact witha charged lOOpF human. Our personalSELF-EXPLANATORY CIRCUITS3.17 Bad circuits 171experience with the small-geometry VN13MOSFET has been so dismal in this regardthat we no longer use it in production in-struments.It is hard to overstate the problemof gate damage due to breakdown inMOSFETs. Luckily, MOSFET designersrealize the seriousness of the problemand are responding with new designs withhigher BVGs; for example, Motorolasnew "TMOS IV" series features f50 voltgate-source breakdown.SELF-EXPLANATORY CIRCUITS3.16 Circuit ideasFigure 3.77 presents a sampling of FETcircuit ideas.3.17 Bad circuitsFigure 3.78 presents a collection of badideas, some of which involve a bit ofsubtlety. Youll learn a lot by figuring outwhy these circuits wont work.
  • Ch4: Feedback and Operational AmplifiersINTRODUCTIONFeedback has become such a well-knownconcept that the word has entered the gen-eral vocabulary. In control systems, feed-back consists in comparing the output ofthe system with the desired output andmaking a correction accordingly. The "sys-tem" can be almost anything: for instance,the process of driving a car down the road,in which the output (the position and ve-locity of the car) is sensed by the driver,who compares it with expectations andmakes corrections to the input (steeringwheel, throttle, brake). In amplifier cir-cuits the output should be a multiple of theinput, so in a feedback amplifier the inputis compared with an attenuated version ofthe output.4.01 Introduction to feedbackNegative feedback is the process of cou-pling the output back in such a way asto cancel some of the input. You mightthink that this would only have the effectof reducing the amplifiers gain and wouldbe a pretty stupid thing to do. HaroldS. Black, who attempted to patent nega-tive feedback in 1928, was greeted withthe same response. In his words, "Ourpatent application was treated in the samemanner as one for a perpetual-motion ma-chine." (See the fascinating article in IEEESpectrum, December 1977.) True, it doeslower the gain, but in exchange it also im-proves other characteristics, most notablyfreedom from distortion and nonlinearity,flatness of response (or conformity to somedesired frequency response), and predict-ability. In fact, as more negative feedbackis used, the resultant,amplifier character-istics become less dependent on the char-acteristics of the open-loop (no-feedback)amplifier and finally depend only on theproperties of the feedback network itself.Operational amplifiers are typically usedin this high-loop-gain limit, with open-loopvoltage gain (no feedback) of a million orSO.A feedback network can be frequency-dependent, to produce an equalizationamplifier (with specific gain-versus-frequency characteristics, an examplebeing the famous RIAA phono amplifier175
  • FEEDBACK AND OPERATIONAL AMPLIFIERS176 Chapter 4characteristic), or it can be amplitude-dependent, producing a nonlinear ampli-fier (a popular example is a logarithmicamplifier, built with feedback that exploitsthe logarithmic VBEversus IC of a diodeor transistor). It can be arranged to pro-duce a current source (near-infinite out-put impedance) or a voltage source (near-zero output impedance), and it can be con-nected to generate very high or very low in-put impedance. Speaking in general terms,the property that is sampled to producefeedback is the property that is improved.Thus, if you feed back a signal propor-tional to the output current, you will gen-erate a good current source.Feedback can also be positive; thatshow you make an oscillator, for instance.As much fun as that may sound, it sim-ply isnt as important as negative feed-back. More often its a nuisance, since anegative-feedback circuit may have largeenough phase shifts at some high frequencyto produce positive feedback and oscil-lations. It is surprisingly easy to havethis happen, and the prevention of un-wanted oscillations is the object of whatis called compensation, a subject we willtreat briefly at the end of the chapter.Having made these general comments,we will now look at a few feedback exam-ples with operational amplifiers.types, with the universal symbol shownin Figure 4.1, where the (+) and (-) in-puts do as expected: The output goes posi-tive when the noninverting input (+)goesmore positive than the inverting input (-),and vice versa. The (+) and (-) sym-bols dont mean that you have to keep onepositive with respect to the other, or any-thing like that; they just tell you the rela-tive phase of the output (which is impor-tant to keep negative feedback negative).Using the words "noninverting" and "in-verting," rather than "plus" and "minus,"will help avoid confusion. Power-supplyconnections are frequently not displayed,and there is no ground terminal. Oper-ational amplifiers have enormous voltagegain, and they are never (well, hardly ever)used without feedback. Think of an op-amp as fodder for feedback. The open-loop gain is so high that for any reason-able closed-loop gain, the characteristicsdepend only on the feedback network. Ofcourse, at some level of scrutiny this gen-eralization must fail. We will start witha naive view of op-amp behavior and fillin some of the finer points later, when weneed to.4.02 Operational amplifiersMost of our work with feedback will in-volve operational amplifiers, very highgain dc-coupled differential amplifiers withsingle-ended outputs. You can think ofthe classic long-tailed pair (Section 2.18)with its two inputs and single output asa prototype, although real op-amps havemuch higher gain (typically lo5 to lo6)and lower output impedance and allow theoutput to swing through most of the sup-ply range (you usually use a split supply,most often f15V).Operational amplifiersare now available in literally hundreds ofFigure 4.1There are literally hundreds of differentop-amps available, offering various perfor-mance trade-offs that we will explain later(look ahead to Table 4.1 if you want tobe overwhelmed by whats available). Avery good all-around performer is thepopular LF411 ("411" for short), origi-nally introduced by National Semi-conductor. Like all op-amps, it is a weebeastie packaged in the so-called mini-DIP (dual in-line package), and it looks
  • BASIC OP-AMP CIRCUITS4.04 Inverting amplifier 177Figure 4.2. Mini-DIP integrated circuit.as shown in Figure 4.2. It is inexpensive(about 60 cents) and easy to use; it comesin an improved grade (LF411A) and alsoin a mini-DIP containing two independentop-amps (LF412, called a "dual" op-amp).We will adopt the LF411 throughout thischapter as our "standard" op-amp, and werecommend it as a good starting point foryour circuit designs.d 411offset null 1 top viewFigure 4.3Inside the 411 is a piece of silicon con-taining 24 transistors (21 BJTs, 3 FETs),11 resistors, and 1 capacitor. The pin con-nections are shown in Figure 4.3. The dotin the corner, or notch at the end of thepackage, identifies the end from which tobegin counting the pin numbers. As withmost electronic packages, you count pinscounterclockwise, viewing from the top.The "offset null" terminals (also known as"balance" or "trim") have to do with cor-recting (externally) the small asymmetriesthat are unavoidable when making the op-amp. You will learn about this later in thechapter.4.03 The golden rulesHere are the simple rules for working outop-amp behavior with external feedback.Theyre good enough for almost everythingyoull ever do.First, the op-amp voltage gain is sohigh that a fraction of a millivolt betweenthe input terminals will swing the outputover its full range, so we ignore that smallvoltage and state golden rule I:I. The output attempts to do whatever isnecessary to make the voltage differencebetween the inputs zero.Second, op-amps draw very little inputcurrent (0.2nA for the LF411; picoampsfor low-input-current types); we roundthis off, stating golden rule 11:II. The inputs draw no current.One important note of explanation:Golden rule I doesnt mean that the op-amp actually changes the voltage at its in-puts. It cant do that. (How could it, andbe consistent with golden rule II?) What itdoes is "look" at its input terminals andswing its output terminal around so thatthe external feedback network brings theinput differential to zero (if possible).These two rules get you quite far. Wewill illustrate with some basic and impor-tant op-amp circuits, and these will prompta few cautions listed in Section 4.08.BASIC OP-AMP CIRCUITS4.04 Inverting amplifierLets begin with the circuit shown inFigure 4.4. The analysis is simple, if youremember your golden rules:1. Point B is at ground, so rule I impliesthat point A is also.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS178 Chapter 42. This means that (a) the voltage acrossR2 is VOutand (b) the voltage across R1 isVn-Figure 4.4. Inverting amplifier.3. So, using rule 11, we haveIn other words,voltage gain = Vout/Kn= -R2/R1Later you will see that its often betternot to ground B directly, but through aresistor. However, dont worry about thatnow.Our analysis seems almost too easy! Insome ways it obscures what is actuallyhappening. To understand how feedbackworks, just imagine some input level, say+1 volt. For concreteness, imagine thatR1 is 1Ok and R2 is 100k. Now, supposethe output decides to be uncooperative,and sits at zero volts. What happens? R1and R2form a voltage divider, holding theinverting input at +0.91 volt. The op-amp sees an enormous input unbalance,forcing the output to go negative. Thisaction continues until the output is at therequired -10.0 volts, at which point bothop-amp inputs are at the same voltage,namely ground. Similarly, any tendencyfor the output to go more negative than-10.0 volts will pull the inverting inputbelow ground, forcing the output voltageto rise.What is the input impedance? Simple.Point A is always at zero volts (its calleda virtual ground). So Zin= R1. At thispoint you dont yet know how to figure theoutput impedance; for this circuit, its afraction of an ohm.Note that this analysis is true evenfor dc - its a dc amplifier, So if youhave a signal source offset from ground(collector of a previous stage, for instance),you may want to use a coupling capacitor(sometimes called a blocking capacitor,since it blocks dc but couples the signal).For reasons you will see later (having to dowith departures of op-amp behavior fromthe ideal), it is usually a good idea to use ablocking capacitor if youre only interestedin ac signals anyway.This circuit is known as an invertingamplifier. Its one undesirable feature isthe low input impedance, particularly foramplifiers with large (closed-loop) voltagegain, where R1 tends to be rather small.That is remedied in the next circuit (Fig.4.5).Figure 4.5. Noninverting amplifier.4.05 Noninverting amplifierConsider Figure 4.5. Again, the analysis issimplicity itself:VA = KnBut VAcomes from a voltage divider:VA= VoutRl/(Rl+R2)Set VA= V,,, and you getgain = Vout/Kn= 1 +R2IR1This is a noninverting amplifier. In theapproximation we are using, the inputimpedance is infinite (with the 411 itwould be 1012R or more; a bipolar op-amp
  • BASIC OP-AMP CIRCUITS4.06 Follower 179will typically exceed 108R). The outputimpedance is still a fraction of an ohm.As with the inverting amplifier, a detailedlook at the voltages at the inputs willpersuade you that it works as advertised.Once again we have a dc amplifier. Ifthe signal source is ac-coupled, you mustprovide a return to ground for the (verysmall) input current, as in Figure 4.6. Thecomponent values shown give a voltagegain of 10 and a low-frequency 3dB pointof 16Hz.Figure 4.6Figure 4.7An ac amplifierAgain, if only ac signals are being ampli-fied, it is often a good idea to "roll offthe gain to unity at dc, especially if theamplifier has large voltage gain, in orderto reduce the effects of finite "input off-set voltage." The circuit in Figure 4.7 hasa low-frequency 3dB point of 17Hz, thefrequency at which the impedance of thecapacitor equals 2.0k. Note the large ca-pacitor value required. For noninvertingamplifiers with high gain, the capacitor inthis ac amplifier configuration may be un-desirably large. In that case it may bepreferable to omit the capacitor and trimthe offset voltage to zero, as we will dis-cuss later (Section 4.12). An alternativeis to raise R1 and R2, perhaps using a Tnetwork for the latter (Section 4.18).In spite of its desirable high input im-pedance, the noninverting amplifier con-figuration is not necessarily to be preferredover the inverting amplifier configurationin all circumstances. As we will see later,the inverting amplifier puts less demandon the op-amp and therefore gives some-what better performance. In addition, itsvirtual ground provides a handy way tocombine several signals without interac-tion. Finally, if the circuit in question isdriven from the (stiff) output of anotherop-amp, it makes no difference whetherthe input impedance is 10k(say)or infinity,because the previous stage has no troubledriving it in either case.outFigure 4.8. Follower.4.06 FollowerFigure 4.8 shows the op-amp version of anemitter follower. It is simply a noninvert-ing amplifier with R1 infinite and Rz zero(gain = 1). There are special op-amps, us-able only as followers, with improved char-acteristics (mainly higher speed), e.g., theLM310 and the OPA633, or with simpli-fied connections, e.g., the TL068 (whichcomes in a 3-pin transistor package).An amplifier of unity gain is sometimescalled a bufler because of its isolating
  • FEEDBACK AND OPERATIONAL AMPLIFIERS180 Chapter 4properties (high input impedance, lowoutput impedance).(from a voltage divideror perhaps a signal)Figure 4.9I II IIIII -I tR2I powerI supplyIRcorn -II I4.07 Current sourcesThe circuit in Figure 4.9 approximates anideal current source, without the VBE off-set of a transistor current source. Nega-tive feedback results in Kn at the invert-ing input, producing a current I = Kn/Rthrough the load. The major disadvan-tage of this circuit is the "floating" load(neither side grounded). You couldnt gen-erate a usable sawtooth wave with respectto ground with this current source, for in-stance. One solution is to float the wholecircuit (power supplies and all) so that youcan ground one side of the load (Fig. 4.10).II-The circuit in the box is the previous cur-rent source, with its power supplies shownexplicitly. R1 and Rg form a voltage di-vider to set the current. If this circuitseems confusing, it may help to remindyourself that "ground" is a relative con-cept. Any one point in a circuit could becalled ground. This circuit is useful forgenerating currents into a load that is re-turned to ground, but it has the disadvan-tage that the control input is now floating,so you cannot program the output currentwith an input voltage referenced to ground.Some solutions to this problem are pre-sented in Chapter 6 in the discussion ofconstant-current power supplies.1 IICurrent sources for loadsreturned to groundL 1Figure 4.10. Current source with grounded loadand floating power supply.With an op-amp and external transistor itis possible to make a simple high-qualitycurrent source for a load returned toground; a little additional circuitry makesit possible to use a programming input ref-erenced to ground (Fig. 4.11). In the firstcircuit, feedback forces a voltage Vcc -Knacross R, giving an emitter current (andtherefore an output current) IE= (VCC-Kn)/R.There are no VBE offsets, or theirvariations with temperature, Ic, VCE,etc.,to worry about. The current source is im-perfect (ignoring op-amp errors: Ib, V,,)only insofar as the small base current mayvary somewhat with VCE(assuming theop-amp draws no input current), not toohigh a price to pay for the convenience of agrounded load; a Darlington for Q1 wouldreduce this error considerably. This errorcomes about, of course, because the op-amp stabilizes the emitter current, whereasthe load sees the collectorcurrent. A varia-tion of this circuit, using a FET instead ofa bipolar transistor, avoids this problem al-together, since FETs draw no gate current.
  • BASIC OP-AMP CIRCUITS4.07 Current sources 181With this circuit the output current isproportional to the voltage drop belowVcc applied to the op-amps noninvertinginput; in other words, the programmingvoltage is referenced to Vcc, which is fineif K, is a fixed voltage generated by a volt-age divider, but an awkward situation ifan external input is to be used. This isremedied in the second circuit, in which asimilar current source with npn transistoris used to convert an input voltage (refer-enced to ground) to a Vcc-referenced in-put to the final current source. Op-ampsand transistors are inexpensive. Dont hes-itate to use a few extra components to im-prove performance or convenience in cir-cuit design.One important note about the last cir-cuit: The op-amp must be able to operatewith its inputs near or at the positive sup-ply voltage. An op-amp like the 307, 355,or OP-41 is good here. Alternatively, theop-amp could be powered from a separateV+ voltage higher than Vcc.source. It has the advantage of zerobase current error, which you get withFETs, without being restricted to outputcurrents less than IDS(ON).In this circuit(actually a current sink), Q2 begins toEXERCISE 4.1What is the output current in the last circuit for Figure 4.12. FETtbipolar Current source suit-a given input voltage &? able for high currents.Figure 4.12 shows an interesting vari- conduct when Q1 is drawing about 0.6mAation on the op-ampltransistor current drain current. With Qls minimum IDss
  • FEEDBACK AND OPERATIONAL AMPLIFIERS182 Chapter 4of 4mA and a reasonable value for Qzsbeta, load currents of lOOmA or morecan be generated (Q2 can be replaced bya Darlington for much higher currents,and in that case R1 should be reducedaccordingly). Weve used a JFET in thisparticular circuit, although a MOSFETwould be fine; in fact, it would be better,since with a JFET (which is a depletion-mode device) the op-amp must be runfrom split supplies to ensure a gate voltagerange sufficient for pinch-off. Its worthnoting that you can get plenty of currentwith a simple power MOSFET ("VMOS");but the high interelectrode capacitances ofpower FETs may cause problems that youavoid with the hybrid circuit here.Even so, its performance is limited by theCMRR of the op-amp. For large outputcurrents, the resistors must be small, andthe compliance is limited. Also, at highfrequencies (where the loop gain is low, aswell learn shortly) the output impedancecan drop from the desired value of infinityto as little as a few hundred ohms (the op-amps open-loop output impedance). Asclever as it looks, the Howland currentsource is not widely used.4.08 Basic cautions for op-amp circuits1. In all op-amp circuits, golden rules Iand I1 (Section 4.03) will be obeyed onlyif the op-amp is in the active region, i.e.,inputs and outputs not saturated at one ofHowland current source the supply voltages.For instance, overdriving one of theFigure 4.13 shows a nice "textbook" cur- amplifier configurations will cause outputrent source. If the resistors are chosen ,-lipping at output swings near vcc orso that = R4/Ri7then it can be V . During clipping, the inputs willshown that Iload= -Kn/R2. no longer be maintained at the sameFigure 4.13. Howland current source.EXERCISE 4.2Show that the preceding result is correct.This sounds great, but theres a hitch:The resistors must be matched exactly;otherwise it isnt a perfect current source.voltage. The op-amp output cannot swingbeyond the supply voltages (typicallyit canswing only to within 2V of the supplies,though certain op-amps are designed toswing all the way to one supply or theother). Likewise, the output complianceof an op-amp current source is set bythe same limitation. The current sourcewith floating load, for instance, can puta maximum of Vcc - V;,, across theload in the "normal" direction (currentin the same direction as applied voltage)and V,, - VEEin the reverse direction(the load could be rather strange, e.g.,it might contain batteries, requiring thereverse sense of voltage to get a forwardcurrent; the same thing might happenwith an inductive load driven by changingcurrents).2. The feedback must be arranged sothat it is negative. This means (amongother things) that you must not mix up theinverting and noninverting inputs.
  • AN OP-AMP SMORGASBORD4.09 Linear circuits 1833. There must always be feedback at dc inan op-amp circuit. Otherwise the op-ampis guaranteed to go into saturation.For instance, we were able to put acapacitor from the feedback network toground in the noninverting amplifier (toreduce gain at dc to 1, Fig. 4.7), butwe could not similarly put a capacitor inseries between the output and the invertinginput.4. Many op-amps have a relatively smallmaximum differential input voltage limit.The maximum voltage difference betweenthe inverting and noninverting inputsmight be limited to as little as 5 volts in ei-ther polarity. Breaking this rule will causelarge input currents to flow, with degrada-tion or destruction of the op-amp.We will take up some more issues of thistype in Section 4.11 and again in Section7.06 in connection with precision circuitdesign.AN OP-AMP SMORGASBORDIn the following examples we will skip thedetailed analysis, leaving that fun for you,the reader.4.09 Linear circuitsOptional inverterThe circuits in Figure 4.14 let you invert,or amplify without inversion, by flippinga switch. The voltage gain is either + I or-1, depending on the switch position.EXERCISE 4.3Show that the circuits in Figure 4.14 work asadvertised.Follower with bootstrapAs with transistor amplifiers, the bias pathcan compromise the high input impedanceyou would otherwise get with an op-amp,Figure 4.14Figure 4.15particularly with ac-coupled inputs, wherea resistor to ground is mandatory. If thatis a problem, the bootstrap circuit shownin Figure 4.15 is a possible solution. Asin the transistor bootstrap circuit (Section2.17), the 0.lpF capacitor makes the upper1M resistor look like a high-impedancecurrent source to input signals. The low-frequency rolloff for this circuit will beginat about lOHz, dropping at 12dB peroctave for frequencies somewhat belowthis. Note: You might be tempted to
  • FEEDBACK AND OPERATIONAL AMPLIFIERS184 Chapter 4reduce the input coupling capacitor, sinceits load has been bootstrapped to highimpedance. However, this can generatea peak in the frequency response, in themanner of an active filter (see Section5.06).Ideal current-to-voltageconverterRemember that the humble resistor is thesimplest I-to-V converter. However, it hasthe disadvantage of presenting a nonzeroimpedance to the source of input current;this can be fatal if the device providingthe input current has very little complianceor does not produce a constant currentas the output voltage changes. A goodexample is a photovoltaic cell, a fancyname for a sun battery. Even the garden-variety signal diodes you use in circuitshave a small photovoltaic effect (there areamusing stories of bizarre circuit behaviorfinally traced to this effect). Figure 4.16shows the good way to convert currentphotovoltaicdiode-- Figure 4.16to voltage while holding the input strictlyat ground. The inverting input is a vir-tual ground; this is fortunate, since a pho-tovoltaic diode can generate only a fewtenths of a volt. This particular circuithas an output of 1 volt per microamp ofinput current. (With BJT-input op-ampsyou sometimes see a resistor connected be-tween the noninverting input and ground;its function will be explained shortly inconnection with op-amp shortcomings.)Of course, this transresistance configu-ration can be used equally well for devicesthat source their current via some positiveexcitation voltage, such as Vcc. Photo-multiplier tubes and phototransistors (bothdevices that source current from a positivesupply when exposed to light) are oftenused this way (Fig. 4.17).LPT 100(no baseconnection)PFigure 4.17EXERCISE 4.4Use a 411 and a 1mA (full scale) meter toconstruct a "perfect" current meter (i.e., onewith zero input impedance) with 5mA full scale.Design the circuit so that the meter will neverbe driven more than f150% full scale. Assumethatthe411 outputcan swingto f 13volts(* 15Vsupplies) and that the meter has 500 ohmsinternalresistance.Differential amplifierThe circuit in Figure 4.18 is a differentialamplifier with gain R2/R1. As with thecurrent source that used matched resistorratios, this circuit requires precise resistormatching to achieve high common-moderejection ratios. The best procedure isto stock up on a bunch of lOOk 0.01%resistors next time you have a chance.All your differential amplifiers will haveunity gain, but thats easily remedied withfurther (single-ended) stages of gain. Wewill treat differential amplifiers in moredetail in Chapter 7.
  • AN OP-AMP SMORGASBORD4.09 Linear circuits 185Figure 4.18. Classic differential amplifier.Summing amplifierThe circuit shown in Figure 4.19 is just avariation of the inverting amplifier. PointX is a virtual ground, so the input currentis Vl/R + V2/R + V3/R. That givesVOut = -(Vl + V2 + V3). Note thatthe inputs can be positive or negative.Also, the input resistors need not be equal;if theyre unequal, you get a weightedsum. For instance, you could have fourinputs, each of which is +I volt or zero,representing binary values 1, 2, 4, and8. By using input resistors of 10k, 5k,2.5k, and 1.25k you will get an outputin volts equal to the binary count input.This scheme can be easily expanded toseveral digits. It is the basis of digital-to-analog conversion, although a differentinput circuit (an R - 2R ladder) is usuallyused.EXERCISE 4.5Show how to make a two-digit digital-to-analogconverter by appropriately scaling the inputresistors in a summing amplifier. The digitalinput represents two digits, each consisting offour lines that represent the values 1, 2, 4, and8 for the respectivedigits. An input line is eitherat +1 volt or at ground, i.e., the eight input linesrepresent 1,2,4,8,10,20,40,and 80. Becauseop-ampoutputsgenerallycannotswingbeyondf13 volts, you will have to settle for an outputin volts equal to one-tenththe value of the inputnumber.Figure 4.19L - -- - - - - -frequency (log scale) -BFigure 4.20. Op-amp RIAA phono playbackamplifier.RIAA preampThe RIAA preamp is an example of an am-plifier with a specificallytailored frequencyresponse. Phonograph records are cut withapproximately flat amplitude characteris-tics; magnetic pickups, on the other hand,respond to velocity, so a playback ampli-fier with rising bass response is required.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS186 Chapter 4Power boosterThe circuit shown in Figure 4.20 produces VVVFor high output current, a power transis-tor follower can be hung on an op-ampoutput (Fig. 4.21). In this case a nonin-verting amplifier has been drawn; the fol-lower can be added to any op-amp configu-ration. Notice that feedback is taken fromthe emitter; thus, feedback enforces the de-sired output voltage in spite of the VBEdrop. This circuit has the usual problemthat the follower output can only sourcecurrent. As with transistor circuits, theremedy is a push-pull booster (Fig. 4.22).You will see later that the limited speedwith which the op-amp can move its out-put (slew rate) seriously limits the speedthe required response. The RIAA play-Figure 4.23+ VCCof this booster in the crossover region,creating distortion. For slow-speed appli-cations you dont need to bias the push-pull pair into quiescent conduction, be-cause feedback will take care of most ofthe crossover distortion. Commercial op-amp power boosters are available, e.g., theLT1010, OPA633, and 3553. These areunity-gain push-pull amplifiers capable of200mA of output current and operation tolOOMHzand above. You can include theminside the feedback loop without any wor-ries (See Table 7.4).back amplifier frequency response (relativeto OdB at 1kHz) is shown in the graph,with the breakpointsgiven in terms of timeconstants. The 47pF capacitor to ground e outputrolls off the gain to unity at dc, where itwould otherwise be about 1000; as we have -hinted earlier, the reason is to avoid ampli-fication of dc input "offsets." The LM833is a low-noise dual op-amp intended for - VEEaudio applications (a "gold-plated" op- Figure 4.22amp for this application is the ultra-low-noise LT1028, which is 13dB quieter, and 2N3055 t heat sinklOdB more expensive, than the 833!)., 1 I/,input output+ v c c t 1 2 V to t30V-7 ;+1OV (regulated)(unregulated) O t o l A10k0 41output1.Ok- -- -Figure 4.21
  • AN OP-AMPSMORGASBORD4.10 Nonlinear circuits 187Power supplyAn op-amp can provide the gain for afeedback voltage regulator (Fig. 4.23). Theop-amp compares a sample of the outputwith the zener reference, changing thedrive to the Darlington "pass transistor"as needed. This circuit supplies 10 voltsregulated, at up to 1 amp load current.Some notes about this circuit:1. The voltage divider that samples theoutput could be a potentiometer, for ad-justable output voltage.2. For reduced ripple at the zener, the 10kresistor should be replaced by a currentsource. Another approach is to bias thezener from the output; that way you takeadvantage of the regulator you have built.Caution: When using this trick, you mustanalyze the circuit carefully to be sure itwill start up when power is first applied.3. The circuit as drawn could be damagedby a temporary short circuit across the out-put, because the op-amp would attempt todrive the Darlington pair into heavy con-duction. Regulated power supplies shouldalways have circuitry to limit "fault" cur-rent (see Section 6.05 for more details).4. Integrated circuit voltage regulators areavailable in tremendous variety, fromthe time-honored 723 to the convenient 3-terminal adjustable regulators with inter-nal current limit and thermal shutdown(see Tables 6.8-6.10). These devices,complete with temperature-compensatedFigure 4.24internal zener reference and pass transis-tor, are so easy to use that you will almostnever use a general-purpose op-amp as aregulator. The exception might be to gen-erate a stable voltage within a circuit thatalready has a stable power-supply voltageavailable.In Chapter 6 we will discuss voltageregulators and power supplies in detail,including special ICs intended for use asvoltage regulators.4.10 Nonlinear circuitsPower-switching driverFor loads that are either on or off, a switch-ing transistor can be driven from an op-amp. Figure 4.24 shows how. Note thediode to prevent reverse base-emitterbreakdown (op-amps easily swing morethan -5V). The 2N3055 is everyonespower transistor for noncritical high-current applications. A Darlington (orpower MOSFET) can be used if currentsgreater than about 1 amp need to bedriven,Active rectifierRectification of signals smaller than adiode drop cannot be done with a sim-ple diode-resistor combination. As usual,op-amps come to the rescue, in this caseby putting a diode in the feedback loop(Fig. 4.25). For Enpositive, the diode pro-vides negative feedback; the output followsthe input, coupled by the diode, but with-out a VBEdrop. For V,, negative, the op-amp goes into negative saturation and VOutis at ground. R could be chosen smaller forlower output impedance, with the tradeoffof higher op-amp output current. A bettersolution is to use an op-amp follower atthe output, as shown, to produce very lowoutput impedance regardlessof the resistorvalue.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS188 Chapter 4Figure 4.25. Simple active rectifier.VCCr 1 diode d r o ~Figure 4.26. Effect of finite slew rate on thesimple active rectifier.There is a problem with this circuit thatbecomes serious with high-speed signals.Because an op-amp cannot swing its outputinfinitely fast, the recovery from negativesaturation (as the input waveform passesthrough zero from below) takes some time,during which the output is incorrect. Itlooks something like the curve shown inFigure 4.26. The output (heavy line) is anaccurate rectified version of the input (lightline), except for a short time interval afterthe input rises through zero volts. Duringthat interval the op-amp output is racingup from saturation near -VEE, so the cir-cuits output is still at ground. A general-purpose op-amp like the 411 has a slew rate(maximum rate at which the output canchange) of 15 volts per microsecond; re-covery from negative saturation thereforetakes about Ips, which may introduce sig-nificant output error for fast signals. Acircuit modification improves the situationconsiderably (Fig. 4.27).uFigure 4.27. Improved active rectifier.Dl makes the circuit a unity-gaininverter for negative input signals. D2clamps the op-amps output at one diodedrop below ground for positive inputs, andsince Dl is then back-biased, VOutsits atground. The improvement comes becausethe op-amps output swings only two diodedrops as the input signal passes throughzero. Since the op-amp output has to slewonly about 1.2 volts instead of VEE volts,the "glitch" at zero crossings is reducedmore than tenfold. This rectifier is invert-ing, incidentally. If you require a nonin-verted output, attach a unity-gain inverterto the output.The performance of these circuits is im-proved if you choose an op-amp with ahigh slew rate. Slew rate also influencesthe performance of the other op-amp ap-plications weve discussed, for instance thesimple voltage amplifier circuits. At thispoint it is worth pausing for a while to seein what ways real op-amps depart from theideal, since that influences circuit design,as we have hinted on several occasions. Agood understanding of op-amp limitationsand their influence on circuit design andperformance will help you choose your op-amps wisely and design with them effec-tively.A DETAILED LOOK ATOP-AMP BEHAVIORFigure 4.28 shows the schematic of the741, a very popular op-amp. Its circuit is
  • A DETAILED LOOK AT OP-AMP BEHAVIOR4.11 Departure from ideal op-amp performance 185relatively straightforward, in terms of thekinds of transistor circuits we discussedin the last chapter. It has a differentialinput stage with current mirror load,followed by a common-emitter npnstage (again with active load) that pro-vides most of the voltage gain. A pnpemitter follower drives the push-pull emit-ter follower output stage, which includescurrent-limiting circuitry. This circuitis typical of many op-amps now avail-able. For many applications the prop-erties of these amplifiers approach idealop-amp performance characteristics. Wewill now take a look at the extentto which real op-amps depart from theideal, what the consequences are for circuitdesign, and what to do about it.4.11 Departure from ideal op-ampperformanceThe ideal op-amp has these characteristics:I. Input impedance (differential or com-mon mode) = infinity2. Output impedance (open loop) = 03. Voltage gain = infinity4. Common-mode voltage gain = 05. VOut= 0 when both inputs are at thesame voltage (zero "offset voltage7)6. Output can change instantaneously(infinite slew rate)offsetnullboffsetnullFigure 4.28. Schematic of the 741 op-amp. (Courtesy of Fairchild Camera and Instrument Corp.)
  • FEEDBACK AND OPERATIONAL AMPLIFIERS190 Chapter4All of these characteristics are indepen- for high-speed operation have higher biasdent of temperature and supply voltage currents.changes.Real op-amps depart from these char- currentacteristics in the following ways (see Table4.1 for some typical values). Input offset current is a fancy name forthe difference in input currents betweenthe two inputs. Unlike input bias current,Input current the offset current, I,,, is a result of man-The input terminals sink (or source, de-pending on the op-amp type) a smallcurrent called the input bias current, IB,which is defined as half the sum of the in-put currents with the inputs tied together(the two input currents are approximatelyequal and are simply the base or gate cur-rents of the input transistors). For theJFET-input 411 the bias current is typi-cally 50pA at room temperature (but asmuch as 2nA at 70°C), while a typical BJT-input op-amp like the OP-27 has a typicalufacturing variations, since an op-ampssymmetrical input circuit would otherwiseresult in identical bias currents at the twoinputs. The significance is that even whenit is driven by identical source impedances,the op-amp will see unequal voltage dropsand hence a difference voltage between itsinputs. You will see shortly how this influ-ences design.Typically, the offset current is one-halfto one-tenth the bias current. For the 411,IOffset= 25pA, typical.bias current of 15nA, varying little withtemperature. As a rough guide, BJT-input Input impedanceop-amps have bias currents in the tens of Input impedance refers to the differentialnanoamps, while FET-in~utop-amps have input resistance (impedance looking intoinput currents in the tens of ~ i c o a m ~ s(i.e-9 one input, with the other input grounded),1000 times lower). Generally speaking, which is usually much less than the corn-you can ignore input current with FET op- man-mode resistance (a typical input stageamps, but not with bi~olar-in~utop-amps. looks like a long-tailed pair with currentThe significance of input bias Wrrent source). For the FET-input 411 it is aboutis that it causes a voltage drop across 1012 ohms, while for B J T - ~ ~ ~ ~op-ampsthe resistors of the feedback network, bias like the 741 it is about 2 ~ 0 .Because ofnetwork, or source impedance- How small the input bootstrapping effect of negativea resistor this restricts you to depends on feedback (it attempts to keep both inputsthe dc gain of your circuit and how much at the same voltage, thus eliminating mostoutput variation you can tolerate. YOUwill of the differential input signal), zi, insee how this works later. practice is raised to very high values andOp-amps are available with input bias usually is not as important a parameter ascurrents down to a nanoamp or less for input bias current.(bipolar) transistor-input circuit types ordown tb a few picoamps ( I O - ~ ~ A )forFET-input circuit types. The very lowest Common-mode input rangebias cuirents are typified by the superbeta The inputs to an op-amp must stay withinDarlington LM11, with a maximum input a certain voltage range, typically less thancurrent of 50pA, the AD549, with an the full supply range, for proper operation.input current of 0.06pA, and the MOSFET If the inputs go beyond this range, theICH8500, with an input current of 0.OlpA. gain of the op-amp may change drastically,In general, transistor op-amps intended even reversing sign! For a 411 operating
  • A DETAILED LOOK AT OP-AMP BEHAVIOR4.11 Departure from ideal op-amp performance 191from f15 volt supplies, the guaranteedcommon-mode input range is f11 voltsminimum. However, the manufacturerclaims that the 411 will operate withcommon-mode inputs all the way to thepositive supply, though performance maybe degraded. Bringing either input downto the negative supply voltage causes theamplifier to go berserk, with symptoms likephase reversal and output saturation to thepositive supply.There are op-amps available with com-mon-mode input ranges down to the neg-ative supply, e.g., the LM358 (a good dualop-amp) or the LM10, CA3440, or OP-22,and up to the positive supply, e.g., the 301,OP-41, or the 355 series. In addition to theoperating common-mode range, there aremaximum allowableinput voltages beyondwhich damage will result. For the 411 theyare f15 volts (but not to exceed the nega-tive supply voltage, if it is less).or sometimes just a few values for typi-cal load resistances. Many op-amps haveasymmetrical output drive capability, withthe ability to sink more current than theycan source (or vice versa). For the 411,output swings to within about 2 volts ofVcc and VEE are possible into load resis-tances greater than about lk. Load resis-tances significantly less than that will per-mit only a small swing. Some op-amps canproduce output swings all the way downto the negative supply (e.g., the LM358), aparticularly useful feature for circuits op-erated from a single positive supply, sinceoutput swings all the way to ground arethen possible. Finally, op-amps with MOStransistor outputs (e.g., the CA3130, 3160,ALD1701, and 1CL761x)can swing all theway to both rails. The remarkable bipo-lar LM 10shares this property, without thelimited supply voltage range of the MOSop-amps (usually f8V max).Differential input range Voltage gain and phase shiftSome bipolar op-amps allow only a lim- Typically the voltage gain A,, at dc isited voltage between the inputs, sometimes 100,000 to 1,000,000 (often specified inas small as f0.5 volt, although most are decibels), dropping to unity gain at a fre-more forgiving, permitting differential in- quency (called fT) of lMHz to IOMHz.puts nearly as large as the supply voltages. This is usually given as a graph of open-Exceeding the specified maximum can de- loop voltage gain as a function of frequen-grade or destroy the op-amp. cy. For internally compensated op-ampsthis graph is simply a 6dBfoctave rolloffOutput impedance; output swingversus load resistanceOutput impedance Ro means the op-ampsintrinsic output impedance without feed-back. For the 411 it is about 40 ohms,but with some low-power op-amps it canbe as high as several thousand ohms (seeFig. 7.16). Feedback lowers the output im-pedance into insignificance(or raises it, fora current source); so what usually mattersmore is the maximum output current, withtypical values of 20mA or so. This is fre-quently given as a graph of output voltageswing V,, as a function of load resistance,beginningat some fairly low frequency (forthe 411 it begins at about IOHz), an inten-tional characteristic necessary for stability,as you will see in Section 4.32. This rolloff(the same as a simple RC low-pass filter)results in a constant 90" lagging phase shiftfrom input to output (open-loop) at all fre-quencies above the beginningof the rolloff,increasing to 120"to 160° as the open-loopgain approaches unity. Since a 180 phaseshift at a frequency where the voltage gainequals 1 will result in positive feedback(oscillations), the term "phase margin" isused to specify the difference between thephase shift at fT and 180".
  • FEEDBACK AND OPERATIONAL AMPLIFIERS192 Chapter 4lnput offset voltageOp-amps dont have perfectly balanced in-put stages, owing to manufacturing vari-ations. If you connect the two inputs to-gether for zero input signal, the output willusually saturate at either Vcc or VEE (YOUcant predict which). The difference in in-put voltages necessary to bring the outputto zero is called the input offset voltageV,, (its as if there were a battery of thatvoltage in series with one of the inputs).Usually op-amps make provision for trim-ming the input offset voltage to zero. For a411 you use a 10k pot between pins 1 and5, with the wiper connected to VEE.Of greater importance for precision ap-plications is the drift of the input offsetvoltage with temperature and time, sinceany initial offset can be trimmed to zero.A 411has a typical onset voltage of 0.8mV(2mV maximum), with temperature coeffi-cient ("tempco") of 7pVI0C and unspec-ified coefficient of offset drift with time.The OP-77, a precision op-amp, is laser-trimmed for a typical offset of 10 micro-volts, with temperature coefficient TCV,,of 0.2pVI0C and long-term drift of0.2pVlmonth.Slew rateThe op-amp "compensation" capacit-ance (discussed further in Section 4.32)and small internal drive currents act to-gether to limit the rate at which the outputcan change, even when a large input unbal-ance occurs. This limiting speed is usuallyspecified as slew rate or slewing rate (SR).For the 41 1 it is 15VIps; low-power op-amps typically have slew rates less thanIVIps, while a high-speed op-amp mightslew at 1OOVIps, and the LH0063C "damnfast buffer" slews at 6000VIps. The slewrate limits the amplitude of an undistortedsine-wave output swing above some criti-cal frequency (the frequency at which thefull supply swing requires the maximumslew rate of the op-amp, Fig. 4.29), thusexplaining the "output voltage swing asa function of frequency" graph. A sinewave of frequency f hertz and amplitudeA volts requires a minimum slew rate of27rAf volts per second.at zero cross~ng14VFigure 4.29. Slew-rate-induced distortion.For externally compensated op-ampsthe slew rate depends on the compensationnetwork used. In general, it will be lowestfor "unity gain compensation," increasingto perhaps 30 times faster for x 100 gaincompensation. This is discussed further inSection 4.32.Temperature dependenceAll these parameters have some temper-ature dependence. However, this usuallydoesnt make any difference, since smallvariations in gain, for example, are almostentirely compensated by feedback. Fur-thermore, the variations of these param-eters with temperature are typically smallcompared with the variations from unit tounit.The exceptions are input offset voltageand input offset current. This will mat-ter, particularly if youve trimmed the off-sets approximately to zero, and will ap-pear as drifts in the output. When highprecision is important, a low-drift "instru-mentation" op-amp should be used, withexternal loads kept above 10k to minimize
  • A DETAILED LOOK AT OP-AMP BEHAVIOR4.12 Effects of op-amp limitations on circuit behavior 193the horrendous effects on input-stage per-formance caused by temperature gradients.We will have much more to say about thissubject in Chapter 7.For completeness, we should mentionhere that op-amps are also limited in com-mon-mode rejection ratio (CMRR), power-supply rejection ratio (PSRR), input noisevoltage and current (en, in), and outputcrossover distortion. These become signif-icant limitations only in connection withprecision circuits and low-noise amplifiers,and they will be treated in Chapter 7.4.12 Effects of op-amp limitations oncircuit behaviorLets go back and look at the invertingamplifier with these limitations in mind.You will see how they affect performance,and you will learn how to design effectivelyin spite of them. With the understandingyou will get from this example, you shouldbe able to handle other op-amp circuits.Figure 4.30 shows the circuit again.Figure 4.30Open-loop gainBecause of finite open-loop gain, the volt-age gain of the amplifier with feedback(closed-loop gain) will begin dropping ata frequency where the open-loop gain ap-proaches R2/R1 (Fig. 4.31). For garden-variety op-amps like the 411, this meansthat youre dealing with a relatively lowfrequency amplifier; the open-loop gain isdown to 100 at SOkHz, and fT is 4MHz.Note that the closed-loop gain is alwaysless than the open-loop gain; this means,for instance, that a x 100 amplifier builtwith a 411 will show a noticeable falloff ofgain for frequencies approaching 5OkHz.Later in the chapter (Section 4.25), whenwe deal with transistor feedback circuitswith finite open-loop gains, we will have amore accurate statement of this behavior.105open-looplo4C gain f rf 3 < 1 ~=C.- 1 / G (closed looplg, lo3-.closed-loopin gainfrequency (Hz1Figure 4.31. LF411 gain versus frequency("Bode plot")., ,drops as 1IfL:Ym 8a40l k 10k look 1M 10Mfrequency (Hz)Figure 4.32. Output swing versus frequency(LF411).Slew rateBecause of limited slew rate, the maximumundistorted sine-wave output swing dropsabove a certain frequency. Figure 4.32shows the curve for a 411, with its 15Vlps
  • FEEDBACK AND OPERATIONAL AMPLIFIERS194 Chapter 4slew rate. For slew rate S, the outputamplitude is limited to A(pp) 5 Slrf fora sine wave of frequency f , thus explainingthe llf dropoff of the curve. The flatportion of the curve reflects the power-supply limits of output voltage swing.As an aside, the slew-rate limitation ofop-amps can be usefully exploited to filtersharp noise spikes from a desired signal,with a technique known as nonlinear low-pass&filtering By deliberately limiting theslew rate, the fast spikes can be dramati-cally reduced without any distortion of theunderlying signal.Output currentBecause of limited output current capabil-ity, an op-amps output swing is reducedfor small load resistances. Figure 4.33shows the graph for a 411. For precisionapplications it is a good idea to avoid largeoutput currents in order to prevent on-chipthermal gradients produced by excessivepower dissipation in the output stage.load resistance (k)output could be as large as f0.2 volt whenthe input is grounded (V,, = 2mV max).Solutions: (a) If you dont need gain at dc,use a capacitor to drop the gain to unity atdc, as in Figure 4.7, as well as the RIAAamplifier circuit (Fig. 4.20). In this caseyou could do that by capacitively couplingthe input signal. (b) Trim the voltageoffset to zero using the manufacturersrecommended trimming network. (c) Usean op-amp with smaller V,,. (d) Trimthe voltage offset to zero using an externaltrimming network as described in Section7.06 (Fig. 7.5).Input bias currentEven with a perfectly trimmed op-amp(i.e., V,, = O), our inverting amplifier cir-cuit will produce a non-zero output volt-age when its input terminal is connectedto ground. That is because the finite inputbias current, IB, produces a voltage dropacross the resistors, which is then ampli-fied by the circuits voltage gain. In thiscircuit the inverting input sees a drivingimpedance of R1 11 R2,so the bias currentproduces a voltage v/;,= IB(RI 11 R2),which is then amplified by the gain at dc,-R2/R1.With FET-input op-amps the effect isusually negligible, but the substantial inputcurrent of bipolar op-amps can cause realproblems. For example, consider an in-verting amplifier with R1 = 10kand R2=1M; these are reasonable valuesfor an inverting stage, where we mightlike to keep Zin at least 1Ok. If wechose the low-noise bipolar LM833, theFigure 4.33. Output swingversusload (LF411). output (for grounded input) could be aslarge as 100x 1000nAx9.9k. or 0.99 voltOffset voltage-(GdcX~Runbalance),which is unacceptable.By comparison, for our jellybean LF411Because of input offset voltage, a zero (JFET-input) op-amp the correspondinginput produces an output of Vout = worst-case output (for grounded input) isGd,Vo,. For an inverting amplifier with 0.2mV; for most applications this is neg-voltage gain of 100 built with a 411, the ligible, and in any case is dwarfed by the
  • A DETAILED LOOK AT OP-AMP BEHAVIOR4.12 Effects of op-amp limitations on circuit behavior 19!V,,-produced output error (200mV, worst-case untrimmed, for the LF411).There are several solutions to the prob-lem of bias-current errors. If you must usean op-amp with large bias current, it is agood idea to ensure that both inputs seethe same dc driving resistance, as in Fig-ure 4.34. In this case, 9.lk is chosen asthe parallel resistance of 10k and 100k. Inaddition, it is best to keep the resistance ofthe feedback network small enough so thatbias current doesnt produce large offsets;typical values for the resistance seen fromthe op-amp inputs are lk to lOOk or so.A third cure involves reducing the gain tounity at dc, as in the RIAA amplifier ear-lier.1OOk--Figure 4.34. With bipolar op-amps, use acompensation resistor to reduce errors causedby input bias current.In most cases, though, the simplest so-lution is to use op-amps with negligible in-put current. Op-amps with JFET or MOS-FET input stages generally have input cur-rents in the picoamp range (watch out forits rapid rise versus temperature, though,roughly doubling every 10°C), and manymodern bipolar designsuse superbeta tran-sistors or bias-cancellation schemes toachieve bias currents nearly as low, de-creasing slightly with temperature. Withthese op-amps, you can have the advan-tages of bipolar op-amps (precision,low noise) without the annoying problemscaused by input current. For example,the precision low-noise bipolar OP-27 hasIB=10nA (typ), the inexpensive bipolarLM312 has IB=I .5nA (typ), and its im-proved bipolar cousins (the LT1012 andLM11) have IB= 30pA (typ). Among in-expensive FET op-amps, the JFET LF411has IB= 50pA (typ), and the MOSFETTLC270 series, priced under a dollar, haveIB= IPA (~YP)-Input offset currentAs we just described, it is usually best todesign circuits so that circuit impedances,combined with op-amp bias current, pro-duce negligible errors. However, occasion-ally it may be necessary to use an op-ampwith high bias current, or to deal with sig-nals of extraordinarily high ThCvenin im-pedances. In that case the best you cando is to balance the dc driving resistancesseen by the op-amp at its input termi-nals. There will still be some error at theoutput (GdcIoffsetRsource),due to unavoid-able asymmetry in the op-amp input cur-rents. In general, Ioffsetis smaller thanIbiasby a factor of 2 to 20 (with bipolarop-amps generally showing better match-ing than FET op-amps).In the preceding paragraphs we havediscussed the effectsof op-amp limitations,taking the example of the simple invert-ing voltage amplifier circuit. Thus, forexample, op-amp input current caused avoltage error at the output, In a differentop-amp application you may get a differenteffect; for example, in an op-ampintegrator circuit, finite input currentproduces an output ramp (rather thana constant) with zero applied input.As you become familiar with op-amp cir-cuits you will be able to predict the ef-fects of op-amp limitations in a givencircuit and therefore choose which op-amp to use in a given application. Ingeneral, there is no "best" op-amp (evenwhen price is no object): For example,
  • TABLE 4.1. OPERATIONAL AMPLIFIERSTotal Voltageo SUPPlY Current# per n u voltage Supp Offset5 3DriApkgben0 curr Bias Offset @lkHz.E ;;.e min max max typ max typ max max maxType Mfga 1 2 4 c W Z (V) (V) (mA) (mV) (mVi (pVI C) (pVInC) ("A) (nA) n?!HzBIPOLAR, PRECISIONOP-07A PM+ A -OP-07E PM+ A -OP-21A PM A AOP-27E PM+ A AOP-27G PM+ A AOP-37E PM+ .A -OP-50E PM - -OP-77E PM A AOP-90E PM A AOP-97E PM - -MAX400M MA - -LM607A NS - -AD707C AD A -AD8466 AD - -LT1001A LT * A -LT1007A LT * - -LT1012C LT+ A -LT1028A LT - -LT1037A LT - -RC4077A RA - -HA5134A HA - -HA5135 HA * - -HA5147A HA - -BIPOLAR, LOW-BIAS (see also "bipolar, precision7OP-08E PM - - - U 10 40 0.5 0.07 0.15LMlO NS+ a - - a - 1 1 45 0.4 0.3 2LMl1 NS+ - - " 1 5 40 0.6 0.1 0.3OP-12E PM+ - - - - 1 10 40 0.5 0.07 0.15LM308 NS+ * A - - * U 10 36 0.8 2 7.5LM312 NS+ * - - * 1 10 40 0.8 2 7.5LP324 NS - - - - 1 4 32 0.25 2 4BIPOLAR, SINGLE-SUPPLY324A NS+ A A * - - 1 3 3 2 3 2 3LP324 NS - - - - 1 4 32 0.25 2 4LT1013C LT - * A - - 1 4 44 1 0.06 0.3HA5141A HA * A A - - 1 2 40 0.07 0.5 2BIPOLAR, SINGLE-SUPPLY PRECISIONLT1006A LT • - 1 2.7 44 0.5 0.02 0.05LT1013A LT - * A - - 1 4 44 1 0.04 0.15
  • Swing tosupplies?JSlew Max Max -ratee fT CMRR PSRR Gain output diffl In Outtyp typ min min min curr inputf-Type (Vtps) (MHz) (dB) (dB) (dB) (mA) (V) + - + - CommentsOP-08ELMlOLM11OP-12ELM308LM312LP324low powerlow noisecheap gradelow noise, decomp OP-27high current, low noiseimproved OP-07micropowerlow power OP-77lowest non-chopper V,,improvedOP-07; dual = 708current feedback; fastlow noise, -0P-27improved 312; dual = 1024ultra low noisedecomp 1007, -0P-37lowest non-chopper V,,quad, low noiselow noise, high speed, uncomp0.12 0.8 104 104 98 5 0.5 - - - - precision 3080.12 0.1 93 90 102 20 40 - 1Vop-amp; precision; volt. ref.0.3 0.5 110 100 100 2 0.5 - - - - precision; lowest bias bipolar0.12 0.8 104 104 98 5 0.5 - - - - precision 3120.15 0.3 80 80 88 5 0.5 - - - - original low-bias (superbeta)0.15 0.3 80 96 88 5 0.5 - - - - compensated 3080.05 0.1 80 90 94 5 32 - - low power, single supply0.5 1 65 65 88 20 30 - - • a classic; duaL358A0.05 0.1 80 90 94 5 32 - - low power, low bias0.4 0.8 97 100 122 25 30 - - improved 3581324;quad = 10141.5 0.4 80 94 94 1 7 -*-• micropower0.4 1 100 106 120 20 30 -*-• optional I, = 9 0 M0.4 0.8 100 103 124 25 30 -*-• improved 3581324;quad = 1014
  • TABLE 4.1 (contd)Total Voltageo supply Current#per E u voltage Supp Offset Drifi enpkgb Q % curr -Bias Offset @lkHzE - c min rnax rnax typ rnax typ rnax rnax rnaxType Mfga :d f (V) (V) (mA) (mV) (mV) (pVInC) (pVIsC) ("A) (nA) nd?HzBIPOLAR, HIGH-SPEEDOP-62E PM - -OP-63E PM - -OP-64E PM - -OP-65E PM - -CLC400 CL - -AD509K AD - -SL541B PL - -VA705L VT A AVA706K VT A AVA707K VT A ALM837 NS - -AD840K AD - -AD841K AD - -AD847J AD * - -AD848J AD a - -AD849J AD - -HA2539 HA - -SL2541B PL - -HA2541 HA - -HA2542 HA - -HA2544 HA - -CA3450 RC - -HA5101 HA A AHA5111 HA * A AHA5147A HA * - -HA5195 HA - -LM6361 NS - -LM6364 NS - -LM6365 NS - -BIPOLAR, OTHEROP-20B PM - A A * - 1 4 36 0.08 0.06 0.25 0.75 1.5LM833 NS - - - 1 1 0 36 8 0.3 5 2CA3193A RC - - - 1 7 36 3.5 0.14 0.2 1 3XR4560 XU - - - - 1 8 36 2 0.5 6HA5151 HA * A A - - 1 2 40 0.25 2 3 3NE5534 SN+ A - 3 6 44 8 0.5 4MC33078 MO - A - - 1 10 36 5 0.15 2 2MC33171 MO A A - 1 3 44 0.25 2 4.5 10MC34071A MO A A - 1 3 44 2.5 0.5 1.5 10
  • Swing tosupplies?gSlew Max Max -ratee f, CMRR PSRR Gain output diffl In Outtyp typ min min min curr inputf-Type (Vlps) (MHz) (dB) (dB) (dB) (mA) (V) + - + - Commentsprecisiontransimpedance; decomp=401fastfast, videovideo, drives 50Q; fast settlevideo, drives 50R; fast settledecornp, fast, 50Qlow noise, low distortiondecornp 841;842 has G>2fast settle; decomp versionsfast settle; decomp versionsdecomp 847uncornp 847low noise, sim to 2540has uncommitted unity gain buffast settle, low distortionfast settle, decompvideovideo amptline driverlow noiselow noise, uncomplow noise, precision, uncompElantec EL2195 = improvedvertical PNPvertical PNPvertical PNP30 -.-- accurate low power30 - - - - low noise, low distortion5 - - - -30 - - - - intended for audio7 ---. low power0.5 - - - - low noise, intended for audio36 - - - - low noise, low distortion44 - .- -44 -.-- drives 0.01pF
  • TABLE 4.1 (contd)Total Voltageo S~PP~Y Current#per g U voltage Supp Offset Drift enpkgb 8 w curr Bias Offset @lkHz.k ;.5 rnin rnax rnax typ rnax typ rnax rnax rnaxType Mfga 1 2 4 c IU S (V) (V) (mA) (mV) (mV) (pVI C) (pVI°C) (nA) (nA) n:%HzBIPOLAR, OBSOLESCENTOP-OIE PM * - - * - 1 1 0 44 3 1OP-02E PM A - - 1 1 0 44 2 0.3OP-05E PM+ A - - 1 6 44 4 0.2OP-l1E PM --• - - 1 1 0 44 6 0.3307 NS+ 0 - - - - 1 1 0 44 2.5 2LM318 NS+ - - 1 10 40 10 4349 NS --. - - 5 10 36 4.5 1AD517L AD - - - 1 1 0 36 3 -AD518J AD * - - 1 10 40 10 4NE530 SN A - - 1 1 0 36 3 2NE531 SN - - • U 12 44 10 2NE538 SN A - - 5 10 36 2.8 2pA725 FA+ - - U 6 44 3 0.5pA739 FA - - - U 8 3 6 1 4 1741C FA+ * A A * - 1 10 36 2.8 2748C FA+ - - U 10 36 3.3 2pA749 FA - - - U 8 3 6 1 0 11435 TP * - - * * l o 24 32 30 21456 MO .-- .-1 1 0 36 3 5HA2505 HA - - r n . 1 20 40 6 4HA2515 HA - - 0 . 1 20 40 6 5HA2525 HA - - - 3 20 40 6 5HA2605 HA - - * * I 1 0 4 5 4 3HA2625 HA - - 0 5 5 1 0 4 5 4 3CA3100 RC - - 10 13 36 11 14558 RA+ - a - - - 1 8 36 5.6 2NE5535 SN A - - 1 1 0 36 2.8 25539 SI+ - - - * 7 6 24 15 2.5JFET, PRECISIONOP-41E PM * - - * - 1 10 36 1 0.2 0.25 2.5 5OP-43E PM - - - 1 10 36 1 0.2 0.25 2.5 5OPAlOlB BB - - - 1 1 0 40 8 0.05 0.25 3 5OPAlllB BB A - * - 1 10 36 3.5 0.05 0.25 0.5 1AD547L AD A - - 1 5 36 1.5 - 0.25 - 1AD548C AD A - - 1 9 36 0.2 0.1 0.25 - 2OPA627B BB - - - 1 9 36 8 0.04 0.1 0.5 0.8AD711C AD * A A - 1 9 36 2.8 0.1 0.25 2 3AD845K AD - - - 1 9.5 36 12 0.1 0.25 1.5 5LT1055A LT * - - - 1 1 0 40 4 0.05 0.15 1.2 4HA5170 HA - - - 1 9 44 2.5 0.1 0.3 2 5
  • Swing tosupplies?gSlew Max Max -rateefT CMRR PSRR Gain output diffl In Outtyp typ min min min curr inputf-Type (Vlps) (MHz) (dB) (dB) (dB) (mA) (V) + - + - CommentsOP-41EOP-43EOPAl01BOPA111BAD547LAD548COPA627BAD711CAD845KLT1055AHA5170fast, precisionprecision, low currentprecision quada classic; uncomp=301was populardecomp 348 (quad 741)fast; dual=5530fast; dual=5538original precision op-amplow noise, intended for audioold classic; dual=1458, quad=348uncomp 741sim to 739fast settlefast 1458fastsmall output swinglow bias, low dist; OP-43 fasterlow bias, low dist; OP-41 stablerlow noise; decomp = OPA102low noise, low biasdual = AD642,647improved LF441; dual = AD648fastimproved LF41112fastLT1056 is 20% fasterlow noise
  • TABLE 4.1 (contd)Total Voltagel2 Supply Current# per nu: voltage Supp Offset Driftpkgb s enu curr Bias Offset elkHz.E .E min max max typ max typ max max maxType Wga 1 2 4 c LU S (V) (V) (mA) (mV) (mV) (pVi C) (yVI.C) (nA) A ) n$!HzJFET, HIGH-SPEEDOP-42E PM - - - 1 15 40 6.5 0.3 0.75 4 10OP-44E PM - - - 3 16 40 6 0.03 0.75 4 103578 NS+ .-- * - 5 1 0 36 7 3 5 5AD380K AD - - U 12 40 15 - 1 10LF401A NS - - 1 15 36 12 - 0.2OPA404B BB - - . - - 1 10 36 10 0.26 0.75 3LF457B NS - - - 5 10 36 10 0.18 0.4 3 4OPA602C BB - - - 1 10 36 4 0.1 0.25 1 2OPA605K BB - - * * 5 0 0 40 9 0.25 0.5 5OPA606L BB - - - 1 10 36 9.5 0.1 0.5 3 5AD744C AD A - 2 9 36 4 0.1 0.25 2 3AD843B AD - - - 1 9 36 12 0.5 1 15AD845K AD - - - 1 9.5 36 10.2 0.1 0.25 1.5 3LT1022A LT * - 1 20 40 7 0.08 0.25 1.3 5HA5160 HA * - - - U 14 40 10 1 3 20MC34080A MO A A - 2 6 44 3.4 0.3 0.5 10MC34081A MO A A - 1 6 44 3.4 0.3 0.5 10JFET, OTHERTL031C TITLO5lC TITLO61C TI+TL071C TI+TLO8lB TI+OPA121 BBOPA128L BBLF351 NS+355B NS+3568 NS+LF411 NS+LFnnn NSLF441 NSLF455B NSLF456B NSAD549L ADAD611K ADLT1057A LTHA5180 HAMC34001A MOMC34181 MO* A A - 1 10 36 0.28 0.5 1.5 6* A A - 1 10 36 3.2 0.6 1.5 8* A A .- 1 4 36 0.25 3 15 10* A A * - 1 7 36 2.5 3 10 10- A A * - 1 7 36 2.8 2 3 10.-- .-1 1 0 36 4 0.5 2 3 10.--.- 1 10 36 1.5 0.14 0.5 5A A - 1 10 36 3.4 5 10 10.--. - 1 1 0 36 4 3 5 5.--. - 1 1 0 36 7 3 5 5A - . - 1 10 36 3.4 0.8 2 7 20-.- - - 1 6 36 25 1* A A • - 1 10 36 0.25 1 5 10 20.--. - 1 1 0 36 4 0.18 0.4 3 4.--. - 1 10 36 8 0.18 0.4 3 4.--.- 1 10 36 0.7 0.3 0.5 5 10.--.- 1 10 36 2.5 0.25 0.5 5 10- . A - - 1 20 40 3.8 0.15 0.45 1.8 7.--.- 1 10 40 1 0.1 0.5 5* A A * - 1 8 36 2.5 1 2 10- A A * - 1 3 36 0.2 0.5 2 10
  • Swing tosupplies?gSlew Max Max -ratee fT CMRR PSRR Gain output diffl In Outtyp typ min min min curr inputf-Type (Vlps) (MHz) (dB) (dB) (dB) (mA) (V) + - + - CommentsTL031C 3TL051C 24TLO61C 3.5TL071C 13TL081B 13OPA121 2OPA128L 3LF351 133558 53568 12LF411 15LFnnn 20LF441 1LF455B 5LF456B 12.5AD549L 3AD611K 13LT1057A 13HA5180 7MC34001A 13MC34181 10low Zoutdecornp 356hybrid, fast, 50Raccurateaccurate quadlow noise; drives 0.01~Flow bias, fast settleuncornpimproved LF356very low dist (3pprn); fast settlefast settlefast settlelow biasVi, > V.+4V; decornp 34081vi, > v-+4vlow power; improved TL061low dist; improved TL0711081low powerlower noiselow noisevery low bias353=dual, 347=quadpopularfaster 355jellybeanlowest noise JFETlow current jellybeanlow noise; drives 0.01pFlow noise; drives 0.01pFelectrometer; guard pinlow dist, gen purp JFETaccurate duallquad JFETvery low bias over temp; noisylow power, fast, low dist.
  • TABLE 4.1 (contd)Total Voltagesupply# per voltage Supp Offset Driftpkgb 8 - currE - c min max max typ max typ max= X .-Type Mfga 1 2 4 + U B (V) (V) (rnA) (mV) (rnV) (pV1C) (pV1-C)JFET, OBSOLESCENTOP-15E PM+ A -OP-16E PM+ - -AD515L AD - -AD542L AD - -AD544L AD - -AD545L AD - -ICH8500A IL - -MOSFETOP-80E PM - -TLC27L2A TI A ATLC27M2A TI A ATLC272A TI A ATLC279C TI - -LMC660A NS - - .TLC1078C TI - AALDl701 AL - -ALD1702 AL - -CA3140A RC A -CA3160A RC A -CA3410A RC - -CA3420A RC * - -CA5160A RC A -CA5420A RC * - -CA5422 RC - -ICL7612B IL+ * - -ICL7641B IL+ A ACHOPPERSTABILIZEDMAX420E MA - -MAX422E MA - -LMC668A NS - -TSC9OOA TS - -TSC901 TS A ATSC911A TS A ATSC915 TS - -TSC918 TS - -LTCl050 LT - -LTCl052 LT - -ICL7650 IL+ - -ICL765OS IL - -ICL7652 IL+ - -ICL7652S IL - -TSC76HV52TS - -CurrentenBias Offset @IkHzmax max(nA) ( A ) n%z
  • Swing tosupplies?gSlew Max Max -ratee fT CMRR PSRR Gain output diffl In Outtyp typ min min min curr inputt-Type (Vlys) (MHz) (dB) (dB) (dB) (mA) (V) + - + - CommentsOP-15E 17 6 86 86 100 15 40 - - - - precision fast 355OP-16E 25 8 86 86 100 20 40 - - - - precision fast 356 (OP-17=decomp)AD515L 1 0.4 70 74 94 10 20 - - - - very low bias, precisionAD542L 3 1 80 80 110 10 20 - - - - precisionAD544L 13 2 80 80 94 15 20 - - - - precision, low noiseAD545L 1 0.7 76 74 92 10 20 - - - - precisionICH8500A 0.5 0.5 60 80 100 10 0.5 - - - - ultra low biasMAX420EMAX422ELMC668ATSCSOOATSC9OlTSC911ATSC915TSC918LTC1050LTC1052ICL7650ICL765OSICL7652ICL7652STSC76HV52electrometer; 1,<20pA @ 125°CCMOS jellybeansCMOS jellybeansCMOS jellybeansbest V,, of 272-seriesquad CMOS jellybeanlow offsetrail-to-rail; specs @ +5V supplyrail-to-rail; specs @ +5V supplyMOS inlout (3130=uncomp)high speed 324-type replacementlow lb,good input protec.CMOS outputsimilar to 3420unusual 2-section designprogrammable; inlout to both railsgen purp, low voltagef15V V,; 0.1yvlmo; 430 has Cintf15V V,; 0.1yV/mo; 432 has C,,,low powerk15V supply; int capsint caps, noisyk15V supplyinexpensiveint caps; 50nVldmonthimproved 7652; 0.1yV/month0.1yV1monthimproved 7650; 0.1yVlmonth0.15yVImonthimproved 7652; 0.15yVlmonthk15V supply 20!
  • TABLE 4.1 (contd)Total VoltageSupply Current# per voltage Supp Offset Drift enpkgb 8 w curr Bias Offset @IkHz.i.;; .s rnin rnax rnax typ max typ max max rnaxType Mfga 1 2 1 c IU I (V) (V) (mA) (mV) (mV) (pVIC) (1VI.C) (nA) (nA) n?JHzHIGH VOLTAGELM343 NSLM344 NSOPA445B BB1436 MO+HA2645 HA3580 BB3581 BB3582 BB3583 BB3584 BBMONOLITHIC POWERLM12 NS * - - - - 1 20 80 80 2 7 50OPA541B BB - - 1 2 0 80 25 0.1 1 15 30LM675 NS - - - - 10 16 60 50 1 10 25SG1173 SG • - - 1 1 0 50 20 2 4 - 30(a)manufacturersare as follows (a "+"suffix designates multiple sources):AD - Analog Devices HO - HoneywellAL - Advanced Linear Devices HS - Hybrid SystemsAM - Advanced Micro Devices ID - Integrated Device TechnologyAN - Analogic IL - GEIlntersilAP - Apex IN - IntelBB - Burr-Brown IR - International RectifierBT - Brooktree KE - M.S.Kennedy CorpCL - Comlinear LT - Linear Technology CorpCR - Crystal Semiconductor MA - MaximCY - Cypress MN - Micro NetworksDA - Datel MO - MotorolaEL - Elantec MP - Micro Power SystemsFA - Fairchild (National) NE - NECFE - Ferranti NS - NationalSemiconductorGE - General Electric OE - Optical Electronics IncGI - General Instrument PL - PlesseyHA - Harris PM - Precision MonolithicsHI - Hitachi RA - RaytheonRC - GEIRGARO - RockwellSG - Silicon GeneralSI - SiliconixSN - SigneticsSO - SonyST - SupertexTI -Texas InstrumentsTM - TelmosTO - ToshibaTP - Teledyne PhilbrickTQ - TriQuintTR - TRWTS - Teledyne SemiconductorVT - VTCXI - XicorXR - ExarZI - Zilog
  • Swing tosupplies?gSlew Max Max -ratee fT CMRR PSRR Gain output diffl In Outtyp typ min min min curr inputf-Type (Vlps) (MHz) (dB) (dB) (dB) (mA) (V) + - + - Commentsmonolithicuncomp 343low-bias, monolithicmonolithicmonolithichybridhybridhybridfast JFET, hybriduncomp JFET, hybridLM12 9 0.7 75 80 94 10A 80 - - - - full output protectionOPA541B 10 1.6 95 100 90 10A 80 - - - - isolated case; no int. protec.LM675 8 5.5 70 70 70 3000 60 - - - - full output protectionSG1173 0.8 1 76 80 92 3500 50 - - - - thermal shutdown(b) the symbol indicates the number of op-amps per package for the part number shown; an " A indicates theavailability of other quantities of op-amps per package from the same manufacturer; some electricalcharacteristics (particularly offset voltage) may be degraded somewhat in multiple packages.() pins are provided for external compensation.(d) a number gives the minimum closed-loopgain without instability. Op-amps with pins for external compensationcan generally be operated at lower gain, if an appropriateext comp network is used. The letter U means thatthe op-amp is uncompensated- external capacitance is necessary for any small value of closed-loopgain.(e) at minimum stable closed-loop gain (usually unity gain), unless otherwise noted.() the maximum value without damage to the chip; not to exceed the total supply voltage used, if that is less.(9) a dot in an IN column means that the input operating common-moderange includes that supply rail;a dot in an OUT column means that the op-amp can swing its output all the way to the corresponding supply rail.(h) resistor-diode network draws input current for input differential greater than +1V.(j) pV pp, 0.1-1OHz.(k) current-sensing inverting input ("current feedback"configuration);the bias currents at the two inputs may differwidely. The listed bias current is for the non-inverting input.(I) "raw" output (no current limit) available at pin 8, in addition to the conventional (protected)output at pin 6;the latter is limited to fl5mA.minlmax (worst case).(1 typical.
  • TABLE 4.2. RECOMMENDED OP-AMPSTotalsupplyAmps per Offset Offset Input voltage Supply en,typ Slewpackageb voltage drift curr curr rate f~max max max min max max lOHz lkHz typ tYPType Mfga 1 2 4 (mV) (yV/"C) (nA) (V) (V) (mA) (nVldHz) ( n ~ l d ~ z )(V/p) (MHz) CommentsLF411 NS A -AD711K AD A -LM358A NS+ - ATLC27M2A TI A AOP-27E PM+ A AOP-37E PM+ A -HA5147A HA - -OP-77E PM A ALT1028A LT - -LTlOl3A LT - ALT1055A LT - -LTlOl2C LT+ A -OPAlllB BB A -AD744K AD - -LTC1052 IL+ - -OP-90E PM A ACA3440A RC - -AD549L AD - -LMlO NS+ - -10 36 3.49 36 33 32 1.23 18 0.68 44 58 44 58 44 46 44 28 44 9.54 44 110 40 44 40 0.610 36 3.59 36 44.8 16 21.6 36 0.024 15 (d)10 36 0.71.1 40 0.4(a)see footnotes to Table 4.1. (b) = this part number; A = available. () G>10. (d) programmable 0.02pA-10yA.(m) rninlrnax. () typical.4 general purpose jellybean4 improved LF4111 single supply jellybean0.7 CMOS jellybean8 precision, low-noise63h ditto, faster (decomp, min. gain = 5)140 ditto, still faster (min.gain = 10)0.6 precision75 precision ultra-low-noise0.8 precision single-supply5 precision JFET0.8 precision low-bias2 precision low-bias JFET13 ultra low dist, stable, fast settle1.2 chopper0.02 precision micropower0.005e nanopower (programmable)1 ultra low input current JFET0.4 low supply voltage, rail-to-rail output
  • A DETAILED LOOK AT OP-AMP BEHAVIOR4.12 Effects of op-amp limitations on circuit behavior 209op-amps with the very lowest input cur- Limitations imply trade-offsrents (MOSFET types) generally have poorvoltage offsets, and vice versa. Good cir- The limitations of op-amp performance wecuit designers choose their components have talked about will have an influencewith the right trade-offs to optimize perfor- on component values in nearly all circuits.mance, without going overboard on un- For instance, the feedback resistors mustnecessary "gold-plated" parts. be large enough so that they dont load the"Here Yesterday, Gone Today"In its untiring quest for better and fancier chips, the semiconductor industry can sometimes causeyou great pain. It might go something like this: Youve designed and prototyped a wonderful newgadget; debugging is complete, and youre ready to go into production. When you try to order theparts, you discover that a crucial IC has been discontinued by the manufacturer! An even worsenightmaregoes like this: Customershave beencomplainingabout late delivery on some instrumentthat youve been manufacturing for many years. When you go to the assembly area to find outwhats wrong, you discover that a whole production run of boards is built, except for one IC that"hasnt come in yet." You then ask purchasing why they havent expedited the order; turns out theyhave, just havent receivedit. Then you learn from the distributor that the part was discontinued sixmonths ago, and that none is available!Why does this happen, and what do you do about it? Weve generally found four reasons thatICsare discontinued:I. Obsolescence: Much better parts come along, and it doesnt make much sense to keep makingthe old ones. This has beenparticularly true with digital memory chips (e.g., small static RAMSandEPROMs, which are superseded by denser and faster versions each year), though linear ICshavenot entirelyescapedthe purge. In these cases there is often apin-compatibleimproved version thatyou can plug into the old socket.2. Not selling enough: Perfectly good ICs sometimes disappear. If you are persistent enough, youmaygetanexplanationfrom themanufacturer- "there wasnt enoughdemand," or somesuchstory.You might characterize this as a case of "discontinued for the convenience of the manufacturer."Weve been particularly inconvenienced by Harriss discontinuation of their splendid HA4925 - afine chip, the fastest quad comparator, now gone, with no replacement anything like it. Harris alsodiscontinued the HA2705 - another great chip, the fastest low-power op-amp, now gone without atrace! Sometimes a good chip is discontinued when the wafer fabrication line changes over to alarger wafer size (e.g., from the original 3" diameter wafer to a 5" or 6" wafer). Weve noticed thatHarris has a particular fondness for discontinuing excellent and unique chips; lntersil and GE havedone the same thing.3. Lostschematics: You might not believeit, but sometimesthe semiconductorhouse loses track ofthe schematic diagram of some chip and cant make any more! This apparently happened with theSolid State Systems SSS-4404CMOS &stage divider chip.4. Manufacturer out ofbusiness: This also happenedto the SSS-4404!If youre stuck with a board and no available IC, youve got several choices. You can redesignthe board (and perhaps the circuit) to use somethingthat is available. This is probably best if youregoinginto production with a new design or if you arerunning a largeproduction of an existing board.A cheap and dirty solution is to make a little "daughterboard" that plugs into the empty IC socketand includes whatever it takes to emulate the nonexistent chip. Although this latter solution isntterribly elegant, it gets the job done.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS210 Chapter 4output significantly, but they must not beso large that input bias current producessizable offsets. High impedances in thefeedback network also increase suscepti-bility to capacitive pickup of interferingsignals and increase the loading effects ofstray capacitance. These trade-offs typi-cally dictate resistor values of 2k to lOOkwith general-purpose op-amps.Similar sorts of trade-offs are involvedin almost all electronic design, includingthe simplest circuits constructed with tran-sistors. For instance, the choice of quies-cent current in a transistor amplifier is lim-ited at the high end by device dissipation,increased input current, excessive supplycurrent, and reduced current gain, whereasthe lower limit of operating current is lim-ited by leakage current, reduced currentgain, and reduced speed (from stray capac-itance in combination with the high resis-tance values). For these reasons you typ-ically wind up with collector currents inthe range of a few tens of microamps toa few tens of milliamps (higher for powercircuits, sometimes a bit lower in "mi-cropower" applications), as mentioned inChapter 2.In the next three chapters we will lookmore carefully at some of these problemsin order to give you a good understandingof the trade-offs involved.EXERCISE 4.6Draw a dc-coupledinverting amplifier with gainof 100 and Zi, = 10k. Include compensationfor input bias current, and show offset voltagetrimming network (10k pot between pins 1 and5, wiper tied to V-). Now add circuitry so thatZi, > lo8ohms.4.13 Low-power andprogrammable op-ampsFor battery-powered applications thereis a popular group of op-amps known as"programmable op-amps," because all ofthe internal operating currents are set byan externally applied current at a biasprogramming pin. The internal quiescentcurrents are all related to this bias currentby current mirrors, rather than by internalresistor-programmed current sources. Asa consequence, such amplifiers can beprogrammed to operate over a wide rangeof supply currents, typically from a fewPOPULAR OP-AMPSSometimes a new op-amp comes along at just the right time, filling a vacuum with its combinationof performance, convenience, and price. Several companies begin to manufacture it (it becomes"second-sourced"),designers become familiar with it, and you have a hit. Here is a list of somepopular favorites of recent times:301 First easy-to-use op-amp; first use of "lateralpnp." Externalcompensation. National.741 The industry standardfor many years. Internal compensation. Fairchild.1458 Motorolas answer to the 741; two 741s in a mini-DIP, with no offset pins.308 Nationals precision op-amp. Low power, superbeta, guaranteeddrift specifications.324 Popular quad op-amp (358=dual, mini-DIP).Single-supply operation. National.355 All-purpose bi-FET op-amp (356, 357 faster). Practically as precise as bipolar, but fasterand lower input current. National. (Fairchild tried to get the FET ball rolling with their 740,which flopped because of poor performance. Would you believe 0.1V input offset?)TL081 Texas Instruments answer to the 355 series. Low-cost comprehensiveseries of singles,duals, quads; low power, low noise, many packagestyles.LF411 Nationals improved bi-FET series. Low offset, low bias, fast, low distortion, high outputcurrent, low cost. Dual (LF412)and low-power variants (LF4411214).
  • A DETAILED LOOK AT OP-AMP BEHAVIOR4.13 Low-powerand programmableop-amps 21microamps to a few milliamps. Theslew rate, gain-bandwidth product fT,and input bias current are all roughlyproportional to the programmed operatingcurrent. When programmed to operate ata few microamps, programmable op-ampsare extremely useful in battery-poweredcircuits. We will treat micropower designin detail in Chapter 14.The 4250 was the original programma-ble op-amp, and it is still a good unit formany applications. Developed by UnionCarbide, this classic is now "second-sourced" by many manufacturers, and iteven comes in duals and triples (the 8022and 8023, respectively). As an example ofthe sort of performance you can expect foroperation at low supply currents, lets lookat the 4250 running at 1OpA. To get thatoperating current, we have to supply a biascurrent of 1.5pA with an external resistor.When it is operated at that current, fT is75kHz, the slew rate is 0.05V/ps, and theinput bias current IB is 3nA. At low op-erating currents the output drive capabil-ity is reduced considerably, and the open-loop output impedance rises to astound-ing levels, in this case about 3.5k. At lowTHE 741 AND ITS FRIENDSBob Widlardesignedthe first really successfulmonolithic op-amp back in1965,the FairchildpA709.It achieved greatpopularity,but it had some problems, in particular thetendencyto go into alatch-upmode when the input was overdriven and its lack of output short-circuit protection. It also requiredexternalfrequencycompensation(twocapacitors andoneresistor) andhadaclumsy offset trimmingcircuit (againrequiring three external components). Finally, its differential input voltage was limitedto 5 volts.Widlar moved from Fairchild to National, where he went on to design the LM301, an improvedop-amp with short-circuit protection, freedom from latch-up, and a 30-volt differential input range.Widlar didnt provide internal frequency compensation, however, because he liked the flexibility ofuser compensation. The 301 could be compensatedwith a single capacitor, but because there wasonly one unused pin remaining, it still required three external components for offset trimming.Meanwhile, over at Fairchild the answer to the 301 (the now-famous 741) was taking shape. Ithad the advantagesof the 301, but Fairchild engineers opted for internal frequency compensation,freeing two pins to allow simplifiedoffset trimming with a single external trimmer. Since most circuitapplications dont require offset trimming (Widlar was right), the 741 in normal use requires nocomponents other than the feedback network itself. The rest is history - the 741 caught on likewildfire and became firmly entrenched as the industry standard.There are now numerous741-typeamps, essentially similar in design and performance, but withvarious features such as FET inputs, dual or quad units, versions with improved specifications,decompensatedand uncompensatedversions, etc. We list some of them here for reference and asademonstration of mans instinct to clutch onto the coattails of the famous(seeTable 4.1 for a morecomplete listing).Single units741sMC741NOP-024132LF13741748NE530TL081LF411Dual unitsfast ( l0VIps) 747low noise OP-04precision 1458low power (35pA) 4558FET low input current TL082uncompensatedfast (25VIps) LF412FET, fast (similar to LF35 1)FET, fastQuad unitsdual 74 1 MC4741 quad 741(alias 348)precision OP-11 precisionmini-DIP package 4136 fast (3MHz)fast (15VIps) HA4605 fast (4VIps)FET, fast (similar TL084 FET, fast (similarto LF353) to LF347)FET, fast
  • FEEDBACK AND OPERATIONAL AMPLIFIERS212 Chapter 4operating currents the input noise voltagerises, while the input noise current drops(see Chapter 7). The 4250 specificationsclaim that it can run from as little as 1volt total supply voltage, but the claimedminimum supply voltages of op-amps maynot be terribly relevant in an actual circuit,particularly where any significant outputswing or drive capability is needed.The 776 (or 3476) is an upgraded 4250,with better output-stage performance atlower currents. The 346 is a nice quadprogrammable op-amp, with three sectionsprogrammed by one of the programminginputs, and the fourth programmed by theother. Some other programmable op-ampsconstructed with ordinary bipolar transis-tors are the OP-22, OP-32, HA2725, andCA3078. Programmable CMOS op-ampsinclude the ICL7612, TLC251, MC14573,and CA3440. These feature operatipn atvery low supply voltage (down to 1V forthe TLC251)and, for the astounding 3440,operation at quiescent currents down to20 nanoamps. The 7612 and 251 use avariation of the usual programmingscheme; their quiescent current is pin-selectable (lOpA, 100pA, or ImA),according to whether the programmingpin is connected to V+ or V- or is leftopen.In addition to these op-amps, there areseveral nonprogrammable op-amps thathave been designed for low supply currentsand low-voltage operation and shouldbe considered for low-power applications.Notable among these is the outstandingbipolar LMIO, an op-amp that is fullyspecified at 1 volt total supply voltage(f0.5V, for example). This is extraordi-nary, considering that VBE increaseswith decreasing temperature and isclose to 1 volt at -55OC, the lower limitof the LMlOs operating range. Someother excellent "micropower" op-amps(and their operating currents) are theprecision OP-20 (40pA), OP-90 (12pA),and LT1006 (90pA), the inexpensive quadLP324 (20,uA per amplifier), the JFETLF4411214 (150pA per amplifier), andthe MOSFET TLC27L4 (10pA per ampli-fier).output- 1.OV/decadeFigure 4.35. Logarithmic converter. QI and Qz compose a monolithic matched pair.
  • A DETAILED LOOK AT SELECTED OP-AMP CIRCUITS4.14 Logarithmic amplifier 213TABLE 4.3. HIGH-VOLTAGE OP-AMPSTotal supply DifflESlew Output Pdiss =inputb8 f, rate current (50C)min max max L ~ . E typ typ max maxType Mfga (V) (V) (V) k w c (MHz) (Vlps) (mA) (W) CaseCCommentsTO-220TO-99TO-99TO-31TO-3TO-31TO-31TO-99TO-3P-DIPTO-3TO-99TO-99TO-3TO-31P-DIPTO-3TO-31TO-3TO-3TO-31TO-31TO-31monolithic pwr op-ampsuperbetasuperbetamonolithic high-powerVMOS outputmonolithic high-pwroriginal, still goodVMOS outputVMOS outputfast unity-gain cornpsame as Philbrick 1332monolithic; miniDlP alsocurrent limitVMOS output; curr limlow V,,, low enlow IQ,Vo,, en,VMOSlow V,,, low en, VMOS(a) see notes to Table 4.1. (b) not to exceed total supply voltage. () "I" = isolated. (d) when cornp for G>10. (e)when cornp for G>100.A DETAILED LOOK AT SELECTEDOP-AMP CIRCUITSThe performance of the next few circuits isaffected significantly by the limitations ofop-amps; we will go into a bit more detailin their description.4.14 Logarithmic amplifierThe circuit shown in Figure 4.35 exploitsthe logarithmic dependence of VB,y onIc to produce an output proportional tothe logarithm of a positive input voltage.R1 converts K, to a current, owing tothe virtual ground at the inverting input.That current flows through Q1, puttingits emitter one VBEdrop below ground,according to the Ebers-Moll equation. Q2,which operates at a fixed current, providesa diode drop of correction voltage, whichis essential for temperature compensation.The current source (whichcan be a resistor,since point B is always within a few tenthsof a volt of ground) sets the input currentat which the output voltage is zero. Thesecond op-amp is a noninverting amplifierwith a voltage gain of 16, in order to givean output voltage of -1.0 volt per decadeof input current (recall that VBEincreases60mV per decade of collector current).Some further details: Qls base couldhave been connected to its collector, butthe base current would then have causedan error (remember that Ic is an accurateexponential function of VBE). In this
  • FEEDBACK AND OPERATIONAL AMPLIFIERS214 Chapter 4--TABLE 4.4. POWER OP-AMPS05.-- f Vsupply0 c.SR fT pwr VOs(max)5+.E I,,, min max Pdiss typ typ BWType MfgaE kC pkgb (A) (V) (V) (W) (Vlps) (MHz) (kHz) (mV) (pVIoC) (pVMI)-PA03 AP - * * PD 30 15 75 500 10 5 70 3 30 20PA04A AP - - PD 20 15 100 200 50 2 90 5 30 10OPA512 BB - - - 31 15 10 50 125 4 4 20 3 40 20LM12 NS * - - 3 10 10 40 90 9 0.7 60 7 50 50OPA501 BB - - - 31 10 10 40 80 1.4" 1 16 5 40 35OPA512B BB - - - 31 10 10 50 125 4 4 20 6 65 20OPA541B BB - 31 10 10 40 90 10 2 55 2 30 601468 TP - - - 3 10 10 50 125 4 4 20 6 65 20PAISA AP - - 31 5 15 40 70 900 100 3500 0.5 10 20OPA511 BB - - - 31 5 10 30 67 1.8 1 23 10 65 20PAO9A AP - 31 4 10 40 78 400 75 2500 0.5 10SG1173 SG * - - 220 3.5 5 25 20 0.8 1 4 30LM675 NS - - 220 3 8 30 40 8 5.5 10 25 25LHOlOl NS - - 3 2 5 20 62 10 5 300 3 10 1503572 BB - * - 31 2 15 40 60 3 0.5 16 2 40 203573 BB - - - 31 2 10 34 45 1.5 1 23 10 65LH0021 NS - - - 3 1 5 15 23 3 1 20 3 25 15MSK792 KE --• 3 1 5 22 5 2 1 11 0.1 21463 TP - 3 1 15 40 40 165 17 5 201461 TP - * * PD 0.75 15 40 12OOU 1000" 5 50LH0061 NS --• 3 0.5 - 15 20 70 - 1000 4 5 5WAOlA AP - - 31 0.4 12 16 10 4000 1000 150000 5 25 10CLC203 CL - - - PD 0.2 9 20 6000 5000 60000 1.5 151460 TP --• 3 0.15 15 40 2.5 300U1000U 1500 5 5035548 BB - 31 0.15 5 18 5 1200 100 19000 1 15HA2542 HA - D 0.1 5 15 1.6 375 120 4700" 10" 20LH4101 NS - D 0.1 - 15 4 250 28 - 15 25LH4104 NS - C 0.1 - 15 2.5 40 18 - 5 201480 TP - * * 3 0.08 15 150 100 20 120 3 1001481 TP - * * 3 0.08 15 75 15 25 4.5 50 3 25CA3450 RC - D 0.08 - 7 1.5 420 190 10000 153583 BB - * . 31 0.08 40 140 10 30 5 60 3 23OP-50E PM - D 0.07 5 18 0.5 3 25 20 0.03 0.3 -3580 BB - * * 31 0.06 15 35 4.5 15 5 100 10 30AMP-01E PM - D 0.05 5 15 0.5 4.5 1 20 0.05 0.3 -3581 BB - 31 0.03 32 75 4.5 20 5 60 3 25358214 BB - 31 0.02 70 150 4.5 201150 7 301135 3 25(a) see Table 4.1 notes. (b) 3 - TO-3; 220 - TO-220; PD - power DIP; D - DIP; I - isolated; C -metal can.(C) current limit: T- thermallimit; E -external adjust. min or max. () typical. uncompensated.
  • A DETAILED LOOK AT SELECTED OP-AMP CIRCUITS4.14 Logarithmic amplifier 215-t, (~YP)m"sat2 5 ~ T,,, 11imc eType (nA) (nA) (V) @ (A) (ps) to (%) (A) CommentsPA03 0.05PA04A 0.02OPA512 20LM12 300OPA501 20OPA512B 30OPA541B 0.051468 30PA19A 0.05OPA511 40PAO9A 0.02SG1173 500LM675 2lALHOl01 0.33572 0.13573 40LH0021 100MSK792 1001463 0.21461 0.1LH0061 100WAOlA lOpACLC203 20pA1460 10pA3554B 0.05HA2542 35pALH4101 0.5LH4104 0.61480 0.21481 0.1CA3450 3503583 0.02OP-50E 53580 0.05AMP-O1E 33581 0.02358214 0.02a mighty brutehigh voltage brutePA-12 similarPA-51 similarmonolithic JFETVMOS output, wideband, precPA-01 similarfastPA-02 similarPA-07 similar; 3571 to 1APA-73 similarext compVMOS outputVMOS output; ext compext compfast settle, wideband, precVMOS output; ext compfastdecomp (G>2)LH4105 has VO,<0.5mVhigh voltagevideo amphigh voltagelow noise, precisionlow noise, prec inst amphigh voltage
  • FEEDBACK AND OPERATIONAL AMPLIFIERS216 Chapter 4circuit the base is at the same voltage asthe collector because of the virtual ground,but there is no base-current error. Q1and Q2 should be a matched pair, ther-mally coupled (a matched monolithic pairlike the LM394 or MAT-01 is ideal). Thiscircuit will give accurate logarithmic out-put over seven decades of current or more(1nA to 1OmA, approximately), providingthat low-leakagetransistors and a low-bias-current input op-amp are used. An op-amplike the 741 with 80nA of bias current isunsuitable, and a FET-input op-amp likethe 411 is usually required to achieve thefull seven decades of linearity. Further-more, in order to give good performanceat low input currents, the input op-ampmust be accurately trimmed for zero off-set voltage, since V,, may be as small asa few tens of microvolts at the lower limitof current. If possible, it is better to use acurrent input to this circuit, omitting R1altogether.The capacitor C1 is necessary to stabi-lize the feedback loop, since Q1contributes voltage gain inside the loop.Diode Dl is necessary to prevent base-emitter breakdown (and destruction) of Q1in the event the input voltage goes nega-tive, since Q1 provides no feedback pathfor positive op-amp output voltage. Boththese minor problems are avoided if Q1 iswired as a diode, i.e., with its base tied toits collector.Temperature compensation of gainQ2compensates changes in Qls VBEdropas the ambient temperature changes,but the changes in the slope of thecurve of VBEversus ICare not compen-sated. In Section 2.10 we saw that the"60mVldecade" is proportional to abso-lute temperature. The output voltage ofthis circuit will look as shown in Figure4.36. Compensation is perfect at an inputcurrent equal to lo, Q2s collector current.A change in temperature of 30°C causes aFigure 4.3610°/o change in slope, with correspondingerror in output voltage. The usual solu-tion to this problem is to replace R2 witha series combination of an ordinary resis-tor and a resistor of positive temperaturecoefficient. Knowing the temperature co-efficient of the resistor (e.g., the TG 118type manufactured by Texas Instrumentshas a coefficient of +0.67%I0C) allows youto calculate the value of the ordinary resis-tor to put in series in order to effect perfectcompensation. For instance, with the 2.7kTG 118 type "sensistor" just mentioned, a2.4k series resistor should be used.There are several logarithmic convertermodules available as complete integratedcircuits. These offer very good perfor-mance, including internal temperaturecompensation. Some manufacturers areAnalog Devices, Burr-Brown, Philbrick,Intersil, and National Semiconductor.EXERCISE 4.7Finishup the log converter circuitby (a)drawingthe current source explicitly and (b) using a TG118 resistor (+0.67%I0C tempco) for thermalslope compensation. Choose values so thatVOut= +1 volt per decade, and provide anoutput offset control so that Voutcan be set tozeroforanydesiredinputcurrent(dothiswithaninvertingamplifier offsetcircuit, notby adjusting10).
  • A DETAILED LOOK AT SELECTED OP-AMP CIRCUITS4.15 Active peak detector 2174.15 Active peak detectorThere are numerous applications in whichit is necessary to determine the peakvalue of some input waveform. Thesimplest method is a diode and capacitor(Fig. 4.37). The highest point of the inputwaveform charges up C, which holds thatvalue while the diode is back-biased.Figure 4.39Figure 4.37This method has some serious problems.The input impedance is variable and isvery low during peaks of the input wave-form. Also, the diode drop makes the cir-cuit insensitive to peaks less than about 0.6volt and inaccurate (by one diode drop) forlarger peak voltages. Furthermore, sincethe diode drop depends on temperatureand current, the circuits inaccuracies de-pend on the ambient temperature and onthe rate of change of output; recall thatI = C(dV/dt). An input emitter followerwould improve the first problem only.Figure 4.38 shows a better circuit, usingfeedback. By taking feedback from thevoltage at the capacitor, the diode dropdoesnt cause any problems. The sort ofoutput waveform you might get is shownin Figure 4.39.Figure 4.38. Op-amp peak detector.Op-amp limitations affect this circuit inthree ways: (a) Finite op-amp slew ratecauses a problem, even with relativelyslowinput waveforms. To understand this, notethat the op-amps output goes into negativesaturation when the input is less positivethan the output (try sketching the op-ampvoltage on the graph; dont forget aboutdiode forward drop). So the op-ampsoutput has to race back up to the outputvoltage (plus a diode drop) when the inputwaveform next exceedsthe output. At slewrate S, this takes roughly (Vo - V-)IS,where V- is the negative supply voltageand Vois the output voltage. (b) Input biascurrent causes a slow discharge (or charge,depending on the sign of the bias current)of the capacitor. This is sometimes called"droop," and it is best avoided by usingop-amps with very low bias current. Forthe same reason, the diode must be a low-leakage type (e.g., the FJT1100, with lessthan 1pAreverse current at 20V, or a "FETdiode"such as the PAD-1 from Siliconix orthe ID101from Intersil), and the followingstage must also present high impedance(ideally it should also be a FET or FET-input op-amp). (c) The maximum op-ampoutput current limits the rate of change ofvoltageacross the capacitor, i.e., the rate atwhich the output can follow a rising input.Thus, the choice of capacitor value is acompromise between low droop and highoutput slew rate.For instance, a 1pF capacitor used inthis circuit with the common 741 (which
  • FEEDBACK AND OPERATIONAL AMPLIFIERS218 Chapter 4would be a poor choice because of its highbias current) would droop at dV/dt =IB/C = 0.08VIs and would follow inputchanges only up to dV/dt = IoutPut/C=0.02VIps. This maximum follow rate ismuch less than the op-amps slew rate of0.5V/ps7 being limited by the maximumoutput current of 20mA driving 1pE Bydecreasing C you could achieve greateroutput slewing rate at the expense ofgreater droop. A more realistic choice ofcomponents would be the popular LF355FET-input op-amp as driver and outputfollower (30pA typical bias current, 20mAoutput current) and a value of C = 0.01pEWith this combination you would get adroop of only 0.006VIs and an overallcircuit slew rate of 2VIps. For betterperformance, use a FET op-amp like theOPA111 or AD549, with input currents of1pA or less. Capacitor leakage may thenlimit performance even if unusually goodcapacitors are used, e.g., polystyrene orpolycarbonate (see Section 7.05).A circuit cure for diode leakagevoltage on the capacitor follows a risinginput waveform: IC1 charges the capaci-tor through both diodes and is unaffectedby IC2s output. When the input dropsbelow the peak value, IC1 goes into neg-ative saturation, but IC2 holds point Xat the capacitor voltage, eliminating leak-age altogether in D2. Dls small leakagecurrent flows through R1,with negligibledrop across the resistor. Of course, bothop-amps must have low bias current. TheOPAll lB is a good choice here, with itscombination of precision (V,, = 250pV,max) and low input current (lpA, max).This circuit is analogous to the so-calledguard circuits used for high-impedance orsmall-signal measurements.Note that the input op-amps in bothpeak-detector circuits spend most of theirtime in negative saturation, only poppingup when the input level exceeds the peakvoltage previously stored on the capacitor.However, as we saw in the active rectifiercircuit (Section 4.10) the journey fromnegative saturation can take a while (e.g.,Ips-2ps for the LF411). This may restrictyour choice to high-slew-rate op-amps.Quite often a clever circuit configurationcan provide a solution to problems causedby nonideal behavior of circuit compo- R1nents. Such solutions are aesthetically 47kpleasing as well as economical. At thispoint we yield to the temptation to takea closer look at such a high-performance Vln -design, rather than delaying until Chapter7, where we treat such subjects under theheading of precision design.Suppose we want the best possible per-formance in a peak detector, i-e., highestratio of output slew rate to droop. If the -lowest-input-current op-amps are used in -a peak-detector circuit (some are available Figure 4.40with bias currents as low as O.OlpA), thedroop will be dominated by diode leakage;i.e., the best available diodes have higher a peak detectorleakage currents (see Table 1.1) than theop-amps bias currents. Figure 4.40 shows In practice it is usually desirable to reseta clever circuit solution. As before, the the output of a peak detector in some way.
  • A DETAILED LOOK AT SELECTED OP-AMP CIRCUITS4.15 Active peak detector 219One possibility is to put a resistor across to the base then zeros the output. A FETthe output so that the circuits output switch is often used instead. For example,decays with a time constant RC. In this in Figure 4.38 you could connect an n-way it holds only the most recent peak channel MOSFET across C; bringing thevalues. A better method is to put a gate momentarily positive then zeros thetransistor switch across C; a short pulse capacitor voltage.FET inp~lr.signal15VInputToutputacquisitiontime I-charge droopinjection("hold step")capacitorvoltagehold sample hold sample-time-outputs , yinputI0.OOlpF(external) Figure 4.41. Sample-and-hold.A. standard configuration,-- with exaggerated waveform.B. LF398 single-chip S/H.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS220 Chapter 44.16 Sample-and-hold and the follower cause Cs voltage toClosely related to the peak detector is the"sample-and-hold" (S/H) circuit (some-times called "follow-and-hold"). These areespeciallypopular in digital systems, whereyou want to convert one or more analogvoltages to numbers so that a computercan digest them: The favorite method isto grab and hold the voltage(s), then dothe digital conversion at your leisure. Thebasic ingredients of a S/H circuit are anop-amp and a FET switch; Figure 4.41Ashows the idea. IC1 is a follower to providea low-impedance replica of the input. Q1passes the signal through during "sample"and disconnects it during "hold."Whatever signal was present when Q1 wasturned OFF is held on capacitor C. IC2is a high-input-impedance follower (FETinputs), so that capacitor current during"hold" is minimized. The value of C isa compromise: Leakage currents in Q1"droop" during the hold interval, accord-ing to dV/dt = II,,~,,/C. Thus C shouldbe large to minimize droop. But Qls ONresistance forms a low-pass filter in com-bination with C, so C should be small ifhigh-speed signals are to be followed ac-curately. IC1 must be able to supply Cscharging current I = CdV/dt and musthave sufficient slew rate to follow the in-put signal. In practice, the slew rate ofthe whole circuit will usually be limited byIC17soutput current and Qls ON resis-tance.EXERCISE 4.8Suppose IC1 can supply lOmA of output cur-rent, and C = O.01pF. What is the maximuminput slewrate the circuit can accuratelyfollow?If Q1 has 50 ohms ON resistance, what will bethe output error for an input signal slewing atO.lVIps? If the combined leakage of Q1 andDIELECTRIC ABSORPTIONCapacitors are not perfect. The most commonly appreciated shortcomings are leakage (parallelresistance), series resistance and inductance,and nonzero temperature coefficientof capacitance.A more subtleproblem is dielectric absorption,an effect that manifests itself clearlyas follows: Takea large-value tantalum capacitor that is charged up to 10 volts or so, and rapidly discharge it bymomentarily putting a 100 ohm resistor across it. Remove the resistor, and watch the capacitorsvoltage on a high-impedance voltmeter. You will be amazed to see the capacitor charge back up,reaching perhaps a volt or so after a few seconds!The origins of dielectric absorption (or dielectric soakage, dielectric memory) are not entirelyunderstood, but the phenomenon is believed to be related to remnant polarization trapped ondielectric interfaces; mica, for example, with its layered structure, is particularly poor in this regard.Fromacircuit point of view, this extra polarization behaves like a set of additionalseries RCsacrossthe capacitor (Fig. 4.42A), with time constants generallyin the range of x100ps to severalseconds.Dielectrics vary widely in their susceptibility to dielectric absorption; Figure 4.42B shows data forseveralhigh-qualitydielectrics, plotted as voltage memory versus time after a 10 volt step of 1Oopsduration.Dielectricabsorption can cause significanterrors in integrators and other analogcircuits that relyon theidealcharacteristics of capacitors. In the case of a samplelholdfollowed by precision analog-to-digital conversion,theeffectcanbe devastating. Insuchsituationsthe best approachistochooseyour capacitors carefully (Teflon dielectric seems to be best), retaining a healthy skepticism untilproven wrong. In extreme cases you may have to resort to tricks such as compensation networksthat use carefully trimmed RCs to electrically cancel the capacitors internal dielectric absorption.This approach is used in some high-quality samplelhold modules made by Hybrid Systems.
  • A DETAILED LOOK AT SELECTED OP-AMP CIRCUITS4.18 Absolute-valuecircuit 221ICn is InA, what is the droop rate during the +15"holdwstate? IFor both the samplelhold circuit andthe peak detector, an op-amp drives a v,"capacitive load. When designing suchcircuits, make sure you choose an op-amp that is stable at unity gain whenloaded by the capacitor C. Some op-amps,(e.g., the LF35516)are specificallydesignedto drive large (0.OlpF) capacitive loads --directly. Some other tricks you can use arediscussed in Section 7.07 (see Fig. 7.17). Figure 4.43u"glitches"O. r / Figure 4.44available, if you need better performancepolystyrene than the LF398 offers; for example, theE 0.01 AD585 from Analog Devices includes anrn internal capacitor and guarantees a max-imum acquisition time of 3ps for 0.01%accuracy following a 10 volt step.lolls 1 0 0 ~ ~ 1ms lOmstime after pulse 4.17 Active clampBFigure 4.43 showsa circuit that is an activeFigure 4.42. Dielectricabsorptionin capaci- version of the clamp function we discussedtors. A. model B. measured properties for sev- in Chapter 1. For the values shown,era1dielectrics. (AfterHybrid Systems HS9716 V,, < +10 volts puts the op-amp outputdata sheet.) at positive saturation, and VOut= I$,.When q, exceeds +10 volts the diodeYou dont have to design SIH circuits closes the feedback loop, clamping thefrom scratch, because there are nice mono- output at 10 volts. In this circuit, op-amplithic ICs that contain all the parts YOU slew-ratelimitations allow small glitchesasneed except for the capacitor. Nationals the input reaches the clamp voltage fromLF398 is a popular part, containing the below (Fig. 4.44).FET switch and two op-amps in an inex-pensive (S2) -pin package Figure 441B 4-18 *bsolute-va,ue circuitshows how to use it. Note how feedbackcloses the feedback loop around both op- The circuit shown in Figure 4.45 gives aamps. There are plenty of fancy SIH chips positive output equal to the magnitude of
  • FEEDBACK AND OPERATIONAL AMPLIFIERS222 Chapter 4the input signal; it is a full-wave rectifier.As usual, the use of op-amps and feedbackeliminates the diode drops of a passivefull-wave rectifier.input.Figure 4.45. Active full-wave rectifier.outputFigure 4.46EXERCISE 4.9Figure out how the circuit in Figure 4.45 works.Hint: Applyfirst apositiveinput voltage, andseewhat happens; then do negative.Figure 4.46 shows another absolute-value circuit. It is readily understandableas a simple combination of an optionalinverter (IC1) and an active clamp (ICz).For positive input levels the clamp isout of the circuit, with its output atnegative saturation, making IC1 a unity-gain inverter. Thus the output is equalto the absolute value of the input voltage.By running IC2 from a single positivesupply, you avoid problems of slew-ratelimitations in the clamp, since its outputmoves over only one diode drop. Note thatno great accuracy is required of Rg.Figure 4.47. Integrator.4.19 IntegratorsOp-amps allow you to make nearly perfectintegrators, without the restriction thatVout << K,. Figure 4.47 shows how itsdone. Input current V,,/R flows throughC. Because the inverting input is a virtualground, the output voltage is given byK n / R = -C(dVout/dt)1Vout= J K. dt +constantThe input can, of course, be a current,in which case R will be omitted. Oneproblem with this circuit as drawn is thatthe output tends to wander off, even withthe input grounded, due to op-amp offsetsand bias current (theres no feedback atdc, which violates rule 3 in Section 4.08).This problem can be minimized by usinga FET op-amp for low input current andoffset, trimming the op-amp input offsetvoltage, and using large R and C values.In addition, in many applications the in-tegrator is zeroed periodically by closing a
  • A DETAILED LOOK AT SELECTED OP-AMP CIRCUITS4.19 Integrators 22:+15nresetreset1 - l o r-"n-channel MOSFETp!{positive.outputonly-4.48. Op-amp integrators with reset switches.switch placed across the capacitor (usuallya FET), so only the drift over short timescales matters. As an example, an inex-pensive FET op-amp like the LF411 (25pAtypical bias current) trimmed to a voltageoffset of 0.2mV and used in an integratorwith R =lOMR and C = lOpF will pro-duce an output drift of less than 0.003 voltin 1000seconds.If the residual drift of the integrator isstill too large for a given application, itmay be necessary to put a large resistor R2across C to provide dc feedback for sta-ble biasing. The effect is to roll off theintegrator action at very low frequencies,f <11R2C. Figure 4.48 shows integratorswith FET zeroing switch and with resis-tor bias stabilization. The feedback resis-tor may become rather large in this sortof application. Figure 4.49 shows a trickfor producing the effect of a large feedbackresistor using smaller values. In this casethe feedback network behaves like a sin-gle lOMR resistor in the standard invert-ing amplifier circuit giving a voltage gain(Section 4.09). For example, the circuit ofFigure 4.49, driven from a high-impedancesource (e.g., the current from a photodi-ode, with the input resistor omitted), hasan output offset of 100 times V,,, whereasthe same circuit with a 10Ma feedback re-sistor has an output equal to v,, (assumingthe offset due to input current is negligi-ble).Figure 4.49of -100. This technique has the advan-tage of using resistors of convenient values A circuit cure for FET leakagewithout the problems of stray capacitance, In the integrator with a FET reset switchetc., that occur with very large resistor val- (Fig. 4.48), drain-source leakage sources aues. Note that this "T-network" trick may small current into the summing junctionincrease the effective input offset voltage, even when the FET is OFF With an ultra-if used in a transresistance configuration low-input-current op-amp and low-leakage
  • FEEDBACK AND OPERATIONAL AMPLIFIERS224 Chapter 4capacitor, this can be the dominant error small leakage passes to ground through R2in the integrator. For example, the ex- with negligible drop. There is no leakagecellent AD549 JFET-input "electrometer" current at the summing junction becauseop-amp has a maximum input current of Qls source, drain, and substrate are all0.06pA, and a high-quality 0.01pF metal- at the same voltage. Compare this circuitlized Teflon or polystyrene capacitor spec- with the zero-leakage peak-detector circuitifies leakage resistance as 10 megohms, of Figure 4.40.minimum. Thus the integrator, exclusiveof reset circuit, keeps stray currents at thesumming junction below IpA (for a worst-case 10V full-scale output), correspondingto an output dV/dt of less than O.OlmV/s.Compare this with the leakage contribu-tion of a MOSFET such as the popular2N4351(enhancement mode), which spec- +?-fJ-ifies a maximum leakage current of lOnAat VDs= 10V and VGS= OV! In other Figure 4.51words, the FET contributes 10,000 timesas much leakage as everything else com-bined. 4.20 DifferentiatorsCRC tvpe J93(1, = 60fA, max)--Figure 4.50Differentiators are similar to integrators,but with R and C reversed (Fig. 4.51).Since the inverting input is at ground, therate of change of input voltage producesa current I = C(dV,/dt) and hence anoutput voltageDifferentiators are bias-stable, but theygenerally have problems with noise andinstabilities at high frequencies because ofthe op-amps high gain and internal phaseshifts. For this reason it is necessary toroll off the differentiator action at somemaximum frequency. The usual methodis shown in Figure 4.52. The choiceof the rolloff components R1 and C2depends on the noise level of the signaland the bandwidth of the op-amp. AtFigure 4.50 shows a clever circuit solu- high frequencies this circuit becomes antion. Although both n-channel MOSFETs integrator, due to R1 and C2.are switched together, Q1 is switched withgate voltages ofzero and +15 volts so thatgate leakage (as well as drain-source leak- ,-JOP-AMP OPERATION WITHage) is entirely eliminated during the OFF A SINGLE POWER SUPPLYstate (zero gate voltage). In the ON statethe capacitor is discharged as before, but Op-amps dont require f15 volt regulatedwith twice RON. In the OFF state, Q2s supplies. They can be operated from split
  • OP-AMP OPERATION WITH A SINGLE POWER SUPPLY4.22 Single-supplyop-amps 225Figure 4.52supplies of lower voltages, or from un-symmetrical supply voltages (e.g, +12 and-3), as long as the total supply voltage(V+ - V-) is within specifications (see Ta-ble 4.1). Unregulated supply voltages areoften adequate becauseof the high "power-supply rejection ratio" you get from nega-tive feedback (for the 411 its 90dB typ).But there are many occasions when itwould be nice to operate an op-amp froma single supply, say +12 volts. This can bedone with ordinary op-amps by generatinga "reference" voltage above ground, if youare careful about minimum supply volt-ages, output swing limitations, and max-imum common-mode input range. Withsome of the more recent op-amps whoseinput and output ranges include the neg-ative supply (i.e., ground, when run froma single positive supply), single-supply op-eration is attractive because of its sim-plicity. Keep in mind, though, that oper-ation with symmetrical split supplies re-mains the usual technique for nearly allapplications.4.21 Biasing single-supply ac amplifiersFor a general-purposeop-amp like the 411,the inputs and output can typically swingto within about 1.5 volts of either supply.With V- connected to ground, you canthave either of the inputs or the output atground. Instead, by generating a referencevoltage (e.g., 0.5V+) you can bias the op-amp for successful operation (Fig. 4.53).This circuit is an audio amplifier with40dB gain. Vref= 0.5V+ gives an outputswing of about 17 volts pp before onset ofclipping. Capacitive coupling is used atthe input and output to block the dc level,which equals Vref.inputFigure 4.534.22 Single-supply op-ampsThere is a class of op-amps that permitsimplified operation with a single positivesupply, because they permit input voltagesall the way down to the negative rail(normally tied to ground). They can befurther divided into two types, accordingto the capability of the output stage: Onetype can swing all the way down to V-,and the other type can swing all the way toboth rails:1. The LM324(quad) 1LM358 (dual),LT1013, and TLC270 types. These haveinput common-mode ranges all the waydown to 0.3 volt below V-, and the outputcan swing down to V-. Both inputs andoutput can go to within 1.5 volts of V+. If
  • FEEDBACK AND OPERATIONAL AMPLIFIERS226 Chapter 4instead you need an input range up to V+,use something like an LM3011307, OP-41, or a 355; an example is illustrated inSection 6.24 in the discussion of constant-current supplies. In order to understandsome of the subtleties of this sort of op-amp, it is helpful to look at the schematic(Fig. 4.54). It is a reasonably straight-forward differential amplifier, with currentmirror active load on the input stage andpush-pull complementary output stagewith current limiting. The special thingsto remember are these (calling V- ground):Inputs: The pnp input structure allowsswings of 0.3 volt below ground; if thatis exceeded by either input, weird thingshappen at the output (it may go negative,for instance).Output: QISpulls the output down andcan sink plenty of current, but it goesonly to within a diode drop of ground.Outputs below that are provided by the50pA current sink, which means you cantdrive a load that sources more than 50pAand get closer than a diode drop aboveinputsground. Even for "nice" loads (an opencircuit, say), the current source wont bringthe output lower than a saturation voltage(0.1V) above ground. If you want theoutput to go clear down to ground, the loadshould sink a small current to ground; itcould be a resistor to ground, for instance.Recent additions to the family of pnp-input single-supply op-amps include theprecision LT1006 and LT1014 (single andquad, respectively) and the micropowerOP-20 and OP-90 (both single), and LP324(quad).We will illustrate the use of these op-amps with some circuits, after mentioningthe other kind of op-amp that lends itselfwell to single-supply operation.2. The LMlO (bipolar) or CA513015160(MOSFET) complementary-output-stageop-amps. When saturated, they look likea small resistance from the output to thesupply (V+ or V-). Thus the output canswing all the way to either supply. Inaddition, the inputs can go 0.5 volt be-low V-. Unlike the LM10, the CA5130outputFigure 4.54. Schematic of the popular 324 and 358 op-amps. (NationalSemiconductorCorp.)
  • OP-AMP OPERATION WITH A SINGLE POWER SUPPLY4.22 Single-supplyop-amps 2270 to 5V for0 to 500nARl1OM-L-- Figure 4.55.Single-supply photometer.battery+ 5 to + 1 56and 5160 are limited to 16 volts (max) to-tal supply voltage and f8 volts differen-tial input voltage. Although most CMOSop-amps permit rail-to-rail output swings,watch out for some varieties that can onlyswing all the way to one rail; also note thatthe input common-mode range of mostCMOS op-amps, like ordinary bipolar op-amps, includes at most one power-supplyrail. For example, the popular TLC27xxAseries from TI has input and output ca-pability to the negative rail only, whereasthe LMC660 from National, along with theIntersil ICL76xx series and RCAs CMOSop-amps, has output swing to both rails(but input common-mode range only tothe negative rail). Unique among op-ampsare the CMOS ICL7612 and ALD170112,which claim both input and output opera-tion to both rails.--photodtode +-A--- -- TLC251CFigure 4.56. Output stagesc D used in single-supplyop-amps.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS228 Chapter 4Figure 4.57. Connecting a load to a single-supply op-amp. All single-supply types (A-D)can swing all the way to ground while sourcingcurrent. Some types (A and B) can swing nearlytoground whilesinking moderateor substantialcurrents; type C can sink up to 50pA, and typeD requiresa load resistor returned to ground tooperate near ground.is convenient. We discussed a similar cir-cuit earlier under the heading of current-to-voltage converters. Since a photocellcircuit might well be used in a portablelight-measuring instrument, and since theoutput is known to be positive only, thisis a good candidate for a battery-operatedsingle-supplycircuit. R1 sets the full- scaleoutput at 5 volts for an input photocur-rent of 0.5pA. No offset voltage trim isneeded in this circuit, since the worst-caseuntrimmed offset of lOmV corresponds toa negligible 0.2% of full-scale meter indi-cation. The TLC251 is an inexpensivemicropower (1OpA supply current) CMOSop-amp with input and output swings tothe negative rail. Its low input current(IpA, typ, at room temperature) makesit good for low-current applications likethis. Note that if you choose a bipolarop-amp for an application like this, betterperformance at low light levels results ifthe photodiode is connected as in thecircuit shown in Figure 4.945.When using "single-supply" op-amps,watch out for misleading statements aboutoutput swing to the negative rail (ground).There are really four different kinds ofoutput stages, all of which "swing downExample: single-supply photometerto ground," but they have very differentproperties (Fig. 4.56): (a) Op-amps withFigure 4.55 shows a typical example of a complementary MOS output transistorscircuit for which single-supply operation give true rail-to-rail swing; such a stage is"single-supplyop-amppositiveinput(OK to OVI- positiveIoutputIOK to OV)-- --1---- Figure 4.58. Single-supply dc amplifier.
  • COMPARATORS AND SCHMIIT TRIGGER4.23 Comparators 22capable of pulling its output to ground,even when sinking moderate current. Someexamples are the ICL76xx, the LMC660,and CA5160. (b) Op-amps with an npncommon-emitter transistor to ground be-have similarly, i.e., they can pull their out-put to ground even while sinking current.Examples are the LMIO, CA5422, andLT1013114. Both kinds of output stagescan, of course, handle an open circuit ora load that sinks current to ground. (c)Some op-amps, notably the 358 and 324,use a pnp follower to ground (which canonly pull down to within a diode drop ofground), in parallel with an npn currentsink (with compliance clear to ground). Inthe 358, the internal current sink is setat 50pA. Such a circuit can swing cleardown to ground as long as it doesnt haveto sink more than 50pA from the load.If the load sources more current, the out-put only works to within a diode drop ofground. As before, this kind of output cir-cuit is happy sourcing current to a loadthat is returned to ground (as in the pho-tometer example earlier). (d) Finally, somesingle-supply op-amps (e.g., the OP-90) usea pnp follower to ground, without the par-allel current sink. Such an output stage canswing to ground only if the load helps outby sinking current, i.e., by being returnedto ground. If you want to use such an op-amp with a load that sources current, youhave to add an external resistor to ground(Fig. 4.57).A note of caution: Dont make the mis-take of assuming that you can make anyop-amps output work down to the nega-tive rail simply by providing an externalcurrent sink. In most cases the circuitrydriving the output stage does not permitthat. Look for explicit permission in thedata sheet!Example: single-supply dc amplifierFigure 4.58 shows a typical single-supplynoninverting amplifier to amplify aninput signal of known positive polarity.The input, output, and positive supply areall referenced to ground, which is the neg-ative supply voltage for the op-amp. Theoutput "pulldown" resistor may be neededwith what we called type-1 amplifiers to en-sure output swing all the way to ground;the feedback network or the load itselfcould perform this function. An importantpoint: Remember that the output cannotgo negative; thus you cannot use this am-plifier with, say, ac-coupled audio signals.Single-supply op-amps are indispens-able in battery-operated equipment. Wellhave more to say about this in Chapter 14.COMPARATORS AND SCHMITT TRIGGERIt is quite common to want to know whichof two signals is larger, or to know whena given signal exceeds a predeterminedvalue. For instance, the usual method ofgenerating triangle waves is to supplypositive or negative currents into a ca-pacitor, reversing the polarity of the cur-rent when the amplitude reaches a presetpeak value. Another example is a digitalvoltmeter. In order to convert a voltage toa number, the unknown voltage is appliedto one input of a comparator, with a lin-ear ramp (capacitor + current source) ap-plied to the other. A digital counter countscycles of an oscillator while the ramp isless than the unknown voltageand displaysthe result when equality of amplitudes isreached. The resultant count is propor-tional to the input voltage. This is calledsingle-slope integration; in most sophisti-cated instruments a dual-slope integrationis used (see Section 9.21).4.23 ComparatorsThe simplest form of comparator is a high-gain differential amplifier, made eitherwith transistors or with an op-amp (Fig.4.59). The op-amp goes into positive or
  • FEEDBACK AND OPERATIONAL AMPLIFIERS230 Chapter 4Figure 4.59negative saturation according to the differ-ence of the input voltages. Because thevoltage gain typically exceeds 100,000, theinputs will have to be equal to within afraction of a millivolt in order for the out-put not to be saturated. Although an ordi-nary op-amp can be used as a comparator(and frequently is), there are special inte-grated circuits intended for use as com-parators. Some examples are the LM306,LM311, LM393, NE527, and TLC372.These chips are designed for very fast re-sponse and arent even in the same leagueas op-amps. For example, the high-speedNE521 slews at several thousand volts permicrosecond. With comparators, the term"slew rate" isnt usually used; you talk in-stead about "propagation delay versus in-put overdrive."Comparators generally have more flexi-ble output circuits than op-amps. Whereasan ordinary op-amp uses a push-pull out-put stage to swing between the supply volt-ages (f13V, say, for a 411 running fromf15V supplies), a comparator chip usu-ally has an "open-collector" output withgrounded emitter. By supplying an exter-nal "pullup" resistor (thats accepted ter-minology, believe it or not) connected toa voltage of your choice, you can have anoutput swingfrom +5 volts to ground, say.You will see later that logic circuits havewell-defined voltages they like to operatebetween; the preceding example would beideal for driving a TTL circuit, a populartype of digital logic. Figure 4.60 shows thecircuit. The output switchesfrom +5 voltsto ground when the input signal goes nega-tive. This use of a comparator is really anexample of analog-to-digital conversion.Figure 4.60This is the first example we have pre-sented of an open-collector output; this isa common configuration in logic circuits,as you will see throughout Chapters 8-11.If you like, you can think of the externalpullup resistor as completing the compara-tors internal circuit by providing a collec-tor load resistor for an npn output tran-sistor. Since the output transistor operatesas a saturated switch, the resistor value isnot at all critical, with values typically be-tween a few hundred ohms and a few thou-sand ohms; small values yield improvedswitching speed and noise immunity at theexpense of increased power dissipation.Incidentally, in spite of their superficialresemblance to op-amps, comparatorsare never used with negative feedbackbecause they would not be stable (seeSections 4.32-4.34). However, somepositive feedback is often used, as youwill see in the next section.Comments on comparatorsSome points to remember: (a) Becausethere is no negative feedback, golden ruleI is not obeyed. The inputs are not at thesame voltage. (b) The absence of negativefeedback means that the (differential) in-put impedance isnt bootstrapped to thehigh values characteristic of op-amp cir-cuits. As a result, the input signal sees achanging load and changing (small)input current as the comparator switches;if the driving impedance is too high,
  • strange things may happen. (c) Some com-parators permit only limited differentialinput swings, as little as f5 volts in somecases. Check the specs! See Table 9.3 andthe discussion in Section 9.07 for the prop-erties of some popular comparators.J inputtrlgger point(voltage at other Inputof comparator)Figure 4.61without feedbackAwith feedbackBFigure 4.624.24 Schmitt triggerThe simple comparator circuit in Figure4.60 has two disadvantages. For a veryCOMPARATORS AND SCHMITT TRIGGER4.24 Schmitt trigger 23slowly varying input, the output swing canbe rather slow. Worse still, if the inputis noisy, the output may make severaltransitions as the input passes throughthe trigger point (Fig. 4.61). Both theseproblems can be remedied by the use ofpositive feedback (Fig. 4.62). The effectof RJ is to make the circuit have twothresholds, depending on the output state.In the example shown, the threshold whenthe output is at ground (input high) is4.76 volts, whereas the threshold with theoutput at +5 volts is 5.0 volts. A noisyinput is less likely to produce multipletriggering (Fig. 4.63). Furthermore, thepositive feedback ensures a rapid outputtransition, regardless of the speed of theinput waveform. (A small "speedup"capacitor of 10-100pF is often connectedacross Rgto enhance switching speed stillfurther.) This configuration is knownas a Schmitt trigger. (If an op-ampwere used, the pullup would be omitted.)h~ghthreshold+4 76Figure 4.63inputFigure 4.64The output depends both on the input volt-age and on its recent history, an effectcalled hysteresis. This can be illustratedwith a diagram of output versus input,as in Figure 4.64. The design procedure
  • FEEDBACK AND OPERATIONAL AMPLIFIERS232 Chapter 4is easy for Schmitt triggers that have asmall amount of hysteresis. Use the cir-cuit of Figure 4.62B. First choose a resis-tive divider (R1, R2) to put the thresholdat approximately the right voltage; if youwant the threshold near ground, just use asingle resistor from noninverting input toground. Next, choose the (positive) feed-back resistor Rg to produce the requiredhysteresis, noting that the hysteresisequalsthe output swing, attenuated by a resistivedivider formed by R3and R111R2. Finally,choose an output pullup resistor R4 smallenough to ensure nearly full supply swing,taking account of the loading by Rg. Forthe case where you want thresholds sym-metrical about ground, connect an off-setting resistor of appropriate valuefrom the noninverting input to the nega-tive supply. You may wish to scale allresistor values in order to keep theoutput current and impedance levels with-in a reasonable range.Figure 4.65outputDiscrete-transistor Schmitt triggerA Schmitt trigger can also be made simplywith transistors (Fig. 4.65). Q1 and Q2share an emitter resistor. It is essentialthat Qls collector resistor be larger thanQ2s. In that way the threshold to turnon Q1, which is one diode drop abovethe emitter voltage, rises when Q1 isturned off, since the emitter current ishigher with Q2 conducting. This produceshysteresis in the trigger threshold, just asin the preceding integrated circuit Schmitttrigger.EXERCISE 4.10DesignaSchmitttriggerusinga311comparator(open-collector output) with thresholdsat +1.0voltand +1.5 volts. Use a1.Ok pullupresistorto+5 volts, and assume that the 311 is poweredfrom f15 volt supplies.FEEDBACK WITHFINITE-GAIN AMPLIFIERSWe mentioned in Section 4.12 that the fi-nite open-loop gain of an op-amp limits itsperformance in a feedback circuit. Specifi-cally, the closed-loopgain can never exceedthe open-loop gain, and as the open-loopgain approaches the closed-loop gain, theamplifier begins to depart from the idealbehavior we have come to expect. In thissection we will quantify these statementsso that you will be able to predict theperformance of a feedback amplifier con-structed with real (less than ideal) compo-nents. This is important also for feedbackamplifiers constructed entirely with dis-crete components (transistors), where.theopen-loop gain is usually much less thanwith op-amps. In these cases the outputimpedance, for instance, will not be zero.Nonetheless, with a good understandingof feedback principles you will be able toachieve the performance required in anygiven circuit.4.25 Gain equationLets begin by considering an amplifier offinite voltage gain, connected with feed-back to form a noninverting amplifier(Fig. 4.66). The amplifier has open-loopvoltage gain A, and the feedback networksubtracts a fraction B of the output voltagefrom the input. (Later we will generalize
  • FEEDBACK WITH FINITE-GAIN AMPLIFIERS4.26 Effects of feedback on amplifier circuits 23things so that inputs and outputs can becurrents or voltages.) The input to the gainblock is then V,, - BVout. But the outputis just the input times A:In other words,and the closed-loop voltage gain, Vout/Vn,is justSome terminology: The standard designa-tions for these quantities are as follows:G = closed-loopgain, A = open-loop gain,AB = loop gain, 1 + AB = return differ-ence, or desensitivity. The feedback net-work is sometimes called the beta network(no relation to transistor beta, hf,).Figure 4.664.26 Effects of feedback onamplifier circuitsLets look at the important effects of feed-back. The most significant are predictabil-ity of gain (and reduction of distortion),changed input impedance, and changedoutput impedance.Predictability of gainThe voltage gain is A/(l + AB). In thelimit of infinite open-loop gain A, G =11B. We saw this result in the noninvert-ing amplifier configuration, where a volt-age divider on the output provided thesignal to the inverting input (Fig. 4.69).The closed-loop voltage gain was just theinverse of the division ratio of the volt-age divider. For finite gain A, feedbackstill acts to reduce the effects of variationsof A (with frequency, temperature, ampli-tude, etc.). For instance, suppose A de-pends on frequency as in Figure 4.67. ThisFigure 4.67will surely satisfy anyones definition of apoor amplifier (the gain varies over a fac-tor of 10 with frequency). Now imagine weintroduce feedback, with B = 0.1 (a sim-ple voltage divider will do). The closed-loop voltage gain now varies from 1000/[1+(1000x0.1)], or 9.90, to 10,000/[1 +(10,000x0.1)], or 9.99, a variation of just1% over the same range of frequency! Toput it in audio terms, the original amplifieris flat to flOdB, whereas the feedback am-plifier is flat to f0.04dB. We can now re-cover the original gain of 1000with nearlythis linearity by just cascading three suchstages. It was for just this reason (namely,the need for extremely flat telephone re-peater amplifiers) that negative feedbackwas invented. As the inventor, HaroldBlack, described it in his first open publica-tion on the invention (Electrical Engineer-ing, 53:114, 1934),"by building an ampli-fier whose gain is made deliberately, say40 decibels higher than necessary (10,000-fold excess on energy basis) and then feed-ing the output back to the input in sucha way as to throw away the excess gain, ithas been found possible to effect extraordi-nary improvement in constancy of ampli-fication and freedom from nonlinearity."
  • FEEDBACK AND OPERATIONAL AMPLIFIERS234 Chapter 4Figure 4.68It is easy to show, by taking the partialderivativeof G with respect to A (BGJaA),that relative variations in the open-loopgain are reduced by the desensitivity:Thus, for good performance the loop gainAB should be much larger than 1. Thatsequivalent to saying that the open-loopgain should be much larger than the closed-loop gain.A very important consequence of this isthat nonlinearities, which are simply gainvariations that depend on signal level, arereduced in exactly the same way.goes to infinity or zero, respectively. Thisis easy to understand, since voltage feed-back tends to subtract signal from the in-put, resulting in a smaller change (by thefactor AB) across the amplifiers input re-sistance; its a form of bootstrapping. Cur-rent feedback reduces the input signal bybucking it with an equal current.Lets see explicitly how the effective in-put impedance is changed by feedback.We will illustrate the case of voltage feed-back only, since the derivations are similarfor the two cases. We begin with an op-amp model with (finite) input resistance asshown in Figure 4.68. An input V;,, is re-duced by BVOUt,putting a voltage Vdiff=V;,, - BVOutacross the inputs of the am-plifier. The input current is thereforegiving an effective input resistanceinput impedanceFeedback can be arranged to subtract avoltage or a current from the input (theseare sometimes called seriesfeedback andshunt feedback, respectively). The nonin-verting op-amp configuration, for instance,subtracts a sample of the output voltagefrom the differential voltage appearing atthe input, whereas in the inverting con-figuration a current is subtracted from theinput. The effects on input impedance areopposite in the two cases: Voltage feed-back multiplies the open-loop input im-pedance by 1 +AB, whereas current feed-back reduces it by the same factor. In thelimit of infinite loop gain the input im-pedance (at the amplifiers input terminal)Figure 4.69The classic op-amp noninverting amplifieris exactly this feedback configuration, asshown in Figure 4.69. In this circuit,B = R1/(R1 + R2), giving the usualvoltage-gain expression G, = 1+ R2/R1and an infinite input impedance for theideal case of infinite open-loop voltagegain
  • FEEDBACK WITH FINITE-GAIN AMPLIFIERS4.26 Effects of feedback on amplifier circuits 23A. For finite loop gain, the equations aspreviously derived apply.The opamp inverting amplifier circuitis different from the noninverting circuitand has to be analyzed separately. Itsbest to think of it as a combination ofan input resistor driving a shunt feedbackstage(Fig. 4.70). The shunt stage alone hasits input at the "summing junction" (theinverting input of the amplifier), where thecurrents from feedback and input signalsare combined (this amplifier connectionis really a "transresistance" configuration;it converts a current input to a voltageoutput). Feedback reduces the impedancelooking into the summing junction, R2,bya factor of 1 +A (see if you can prove this).In cases of very high loop gain (e.g, an op-amp) the input impedance is reduced to afraction of an ohm, a good characteristicfor a current-input amplifier. Some goodexamples are the photometer amplifier inSection 4.22 and the logarithmic converterin Section 4.14.The classic op-amp inverting amplifierconnection is a combination of a shuntfeedback transresistance amplifier and aseries input resistor, as in the figure. As aresult, the input impedance equals the sumof R1and the impedance looking into thesumming junction. For high loop gain, Rinapproximately equals R1.Fpi*- -- z,,= -A 1 + A R2Z (open loop)Z,,= R , + -ZO", =1 + A1 + A Z (open loop1Z.", = 1 + A 6Figure 4.70. Input and output impedances for(A) transresistance amplifier and (B) invertingamplifier.It is a straightforward exercise to derivean expression for the closed-loop voltagegain of the inverting amplifier with finiteloop gain. The answer isG = -A(1 - B ) / ( l + AB)where B is defined as before, B =R1/(R1+Rz).In the limit of large open-loop gain A, G = - 1/B+ 1 (i.e., G =-R2/R1).EXERCISE 4.11Derive the foregoing expressions for inputimpedance and gain of the inverting amplifier.Figure 4.71Output impedanceAgain, feedback can extract a sample ofthe output voltage or the output current.In the first case the open-loop outputimpedance will be reduced by the factor1 + AB, whereas in the second case itwill be increased by the same factor. Wewill illustrate this effect for the case ofvoltagesampling. We begin with the modelshown in Figure 4.7 1 . This time we haveshown the output impedance explicitly.The calculation is simplified by a trick:Short the input, and apply a voltage Vto the output; by calculating the outputcurrent I , we get the output impedance= VII. Voltage V at the output
  • FEEDBACK AND OPERATIONAL AMPLIFIERS236 Chapter 4puts a voltage -BV across the amplifiers desired output impedance. This equationinput, producing a voltage -ABV in the reduces to the previous results for the usualamplifiers internal generator. The output situation in which feedback is derivedcurrent is therefore from either the output voltage or theV - (- ABV) V ( 1 + AB) output current.I = --Ro Ro Loading by the feedback networkgiving an effective output impedanceIn feedback computations, you usually as-Rb = V / I= Ro/(l+ AB) sume that the beta network doesnt loadIf feedback is connected instead to the amplifiers output. If it does, thatsample the output current, the expression must be taken into account in ComPut-becomes ing the open-loop gain. Likewise, if theconnection of the beta network at the am-Rb = &(l + AB) plifiers input affects the open-loop gain~t is possible to have multiple feedback (feedback removed, but network still con-paths, sampling both voltage and current.nected), You must use the modified open-In the general case the output impedance loop gain. Finally, the preceding expres-is given by Blackmans impedance relation sions assume that the beta network is uni-directional, i.e., it does not couple signalRb = &1+(AB)sc from the input to the output.1 + (AB)oc4.27 Two examples of transistorwhere (AB)sc is the loop gain with thewit,, feedbackoutput shorted to ground and (AB)ocis the loop gain with no load attached. Figure 4.72 shows a transistor amplifierThus, feedback can be used to generate a with negative feedback.signalinFigure 4.72. Transistor power amplifier with negative feedback.
  • FEEDBACK WITH FINITE-GAIN AMPLIFIERS4.27 Two examples of transistor amplifiers with feedback 23Circuit description important to make sure that the dc re-It may look complicated, but it is extreme- sistances seen from the inputs are equal,ly straightforward in design and is rela- as shown (a Darlington input stage wouldtively easy to analyze. Q1 and Q2 form probably be better here).a differential pair, with common-emitteramplifier Q3 amplifying its output. Rs is AnalysisQ3s collector load resistor, and push-pull analyze this circuit in detail, de-pair Q4 an Q5 form the output emitter termining the gain, input and outputfollower. The output voltage is sampled by impedances, and distortion. T~ illustratethe feedback network consisting of voltage the utility of feedback, we will find thesedivider R4 and Ra, with C2 included to parameters for both the open-loop andreduce the gain at dc for closed-loop situations (recognizingthat bi-biasing. R3 sets the quiescent current inasing would be hopeless in the open~loopthe differential pair, and since overall feed- ca,). To get a feeling for the linearizingback guarantees that the quiescent Output effect of the feedback, the gain will bevoltage is at ground, Q3s quie~centcur- culated at + 10volts and -10volts output,rent is seen be lomA ( V ~ ~ as well as the quiescent point (zero volts).R6,approximately). As we have discussedearlier (Section 2.151, the diodes bias the Open loop. Input impedance: We cutpush-pull pair intoconduction, leaving One the feedback at point X and ground thediode drop across the series pair R7 and right side of R4. The input signal sees 1OOkR8, i.e., 60mA quiescent current. Thats in parallel with the impedance looking intoclass AB operation, good for minimizing the base. The latter is hfe times twicecrossover distortion, at the cost of 1 watt the intrinsic emitter resistance thestandby dissipation in each Output transis- impedance seen at Q27S emitter due to thetor. feedback network at Q2s base. For hfe =From the point of view of our earlier 250, zi, 250~[(2~25)+(3.3k/250)];circuits, the only unusual feature is Q17s i.e., zin 16k.quiescent collector voltage, one diode drop Output impedance: Since the imped-below Vcc. That is where it must sit in ance looking back into Q3s collector isorder to hold Q3 in conduction, and the high, the output transistors are driven byfeedback path ensures that it will. (For a 1.5k source (R6). The output impedanceinstance, if Q1 were to pull its ~ollector is about 15 ohms (hfe x 100) plus the 5closer to ground, Q3 would conduct heav- ohm emitter resistance, or 20 ohms. Theily, raising the output voltage, which in intrinsic emitter resistance of 0.4 ohm isturn would force Q2to conduct more heav- negligible.ily, reducing QIs collector current and Gain: The differential input stage seeshence restoring the status quo.) R2 was a load of R2 paralleled by Q3s base re-chosen to give a diode drop at QIs quies- sistance. Since Q3 is running lOmA quies-cent current in order to keep the collector cent current, its intrinsic emitter resistancecurrents in the differential pair approxi- is 2.5 ohms, giving a base impedance ofmately equal at the quiescent point. In about 250 ohms (again, hf, =loo). Thethis transistor circuit the input bias current differential pair thus has a gain ofis not negligible (4pA), resulting in a 0.4volt drop across the lOOk input resistors. 25011620or 3.5In transistor amplifier circuits like this, in 2 xwhich the input currents are considerably The second stage, Q3, has a voltage gain oflarger than in op-amps, it is particularly 1.5W2.5ohms,or 600. The overall voltage
  • FEEDBACK AND OPERATIONAL AMPLIFIERS238 Chapter 4gain at the quiescent point is 3.5 x 600,or 2100. Since Q3s gain depends onits collector current, there is substantialchange of gain with signal swing, i.e.,nonlinearity. The gain is tabulated in thefollowingsection for three values of outputvoltage.Closed loop. Input impedance: Thiscircuit uses series feedback, so the inputimpedance is raised by (1 + loop gain).The feedback network is a voltage dividerwith B = 1/30 at signal frequencies, so theloop gain AB is 70. The input impedanceis therefore 70 x 16k, still paralleled bythe lOOk bias resistor, i.e., about 92k.The bias resistor now dominates the inputimpedance.Output impedance: Since the outputvoltage is sampled, the output impedanceis reduced by (1 + loop gain). The outputimpedance is therefore 0.3 ohm. Notethat this is a small-signal impedance anddoes not mean that a 1 ohm load could bedriven to nearly full swing, for instance.The 5 ohm emitter resistors in the outputstage limit the large signal swing. Forinstance, a 4 ohm load could be drivenonly to 10 volts pp, approximately.Gain: The gain is A/(1 +AB). Atthe quiescent point, that equals 30.84,using the exact value for B. In order toillustrate the gain stability achieved withnegative feedback, the overall voltage gainof the circuit with and without feedbackis tabulated at three values of output levelat the end of this paragraph. It shouldbe obvious that negative feedback hasOpen loop Closed loopVout -10 0 +I0 -10 0 $10Zi, 16k 16k 16k 92k 92k 92kZout 200 200 200 0.30 0.30 0.30Gain 1360 2100 2400 30.60 30.84 30.90Series feedback pairFigure 4.73Figure 4.73 shows another transistor am-plifier with feedback. Thinking of Q1 asan amplifier of its base-emitter voltagedrop (thinking in the Ebers-Moll sense),the feedback samples the output voltageand subtracts a fraction of it from the inputsignal. This circuit is a bit tricky becauseQ2s collector resistor doubles as the feed-back network. Applying the techniques weused earlier, you should be able to showthat G(open loop) =200, loop gain = 20,Zout(openloop) =1Ok, Zout(closedloop)=500 ohms, and G(c1osed loop) =9.5.brought about considerable improvementin the amplifiers characteristics, although soMEp P l c A ~O ~ - ~ M Pc l R c " l ~ ~in fairness it should be pointed out thatthe amplifier could have been designedfor better open-loop performance, e-g., by 4.28 General-purpose lab amplifier- - - .using a current source for Q3s collector Figure 4.74 shows a dc-coupled "decadeload and degenerating its emitter, by using amplifier" with settable gain, bandwidth,a current source for the differential-pair and wide-range dc output offset. IC1 isemitter circuit, etc. Even so, feedback a FET-input op-amp with noninvertingwould still make a large improvement. gain from unity (OdB) to x100 (40dB) in
  • SOME TYPICAL OP-AMP CIRCUITS4.28 General-purposelab amplifier 23accurately calibrated lOdB steps; a vernieris provided for variable gain. IC2 is aninverting amplifier; it allows offsetting theoutput over a range of f10 volts, accu-rately calibrated via R14, by injecting cur-rent into the summing junction. C2- C4set the high-frequency rolloff, since it isoften a nuisance to have excessive band-width (and noise). IC5 is a power boosterfor driving low-impedance loads or cables;it can provide fl5OmA output current.Some interesting details: A lOMR in-put resistor is small enough, since the biascurrent of the 411 is 25pA (0.3mV errorwith open input). R2,in combination withDl and D2,limits the input voltage at theop-amp to the range V- to V++ 0.7. D3is used to generate a clamp voltage atV- +0.7, since the input common moderange extends only to V- (exceedingV- causes the output to reverse phase).With the protection components shown,the input can go to f150 volts withoutdamage.offsetl-JFigure 4.74. Laboratory dc amplifier with output offset.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS240 Chapter 4EXERCISE 4.12 is HIGH and open-circuited when the out-Check that the gain is as advertised. How does put is LOW.the variable offset circuitry work? An unusual feature of this circuit is itsoperation from a single positive supply.4.29 Voltage-controlled oscillatorFigure 4.75 shows a clever circuit, bor-rowed from the application notes ofseveral manufacturers. IC1 is an inte-grator, rigged up so that the capacitorcurrent (Vin/200k) changes sign, butnot magnitude, when Q1 conducts. IC2is connected as a Schmitt trigger, withthresholds at one-third and two-thirdsof V+. Q1 is an n-channel MOSFET,used here as a switch; it is simpler touse than bipolar transistors in this sortof application, but an alternative cir-cuit using npn transistors is shown in ad-dition. In either case, the bottom side ofR4 is pulled to ground when the output0 4 V,, 4 2 ( V +- 1.5V)The 3160 (internally compensated versionof the 3130) has FETs as output transis-tors, guaranteeing a full swing between V+and ground at the output; this ensuresthat the thresholds of the Schmitt dontdrift, as they would with an op-amp ofconventional output-stage design, with itsill-defined limits of output swing. In thiscase this means that the frequency and am-plitude of the triangle wave will be sta-ble. Note that the frequency depends onthe ratio &,/V+; this means that if v,is generated from V+ by a resistive di-vider (made from some sort of resistivetransducer, say), the output frequencywont vary with V+, only with changes inresistance.a n r 8"49.9k 1OOk1%-Lbipolar substitute V+for FET Q,Itriangle out al.nJ-Lrground"sauare out2N412447kFigure 4.75. Voltage-controlled waveform- -- - generator.
  • SOME TYPICAL OP-AMP CIRCUITS4.30 JFET linear switch with RONcompensation 241EXERCISE 4.13Show that the output frequency is given byf(Hz) = 150F,/V+. Along the way,verify thatthe Schmitt thresholds and integrator currentsare as advertised.4.30 JFET linear switchwith RONcompensationIn Chapter 3 we considered MOSFETlinear switches in some detail. It is alsopossible to use JFETs as linear switches.However, you have to be more carefulabout gate signals so that gate conductiondoesnt occur. Figure 4.76 shows a typicalarrangement. The gate is held well belowground to keep the JFET pinched off. Thismeans that if the input signals go negative,the gate must be held at least Vp belowthe most negative input swing. To bringthe FET into conduction, the control inputis brought more positive than the mostpositive input excursion. The diode is thenreverse-biased,and the gate rides at sourcevoltage via the 1M resistor.outputground- 15Figure 4.76The awkwardness of this circuit prob-ably accounts for much of the popularityof MOSFETs in linear switch applications.However, it is possible to devise an elegantJFET linear switch circuit if you use an op-amp, since you can tie the JFET source tothe virtual ground at the summing junctionof an inverting amplifier. Then you simplybring the gate to ground potential to turnthe JFET on. This arrangement has theadded advantage of providing a methodof canceling precisely the errors caused byfinite RONand its nonlinearity. Figure4.77 shows the circuit.Figure 4.77. JFET-switched amplifier withRONcancellation.R ,10k 1% 0,L -There are two noteworthy features ofthis circuit: (a) When Q1 is ON (gategrounded), the overall circuit is an inverterwith identical impedances in the input andfeedback circuits. That results in the can-cellation of any effects of finite or non-linear ON resistance, assuming the FETsare matched in RON.(b) Because of thelow pinch-off voltage of JFETs, the circuitwill work well with a control signal of zeroto +5 volts, which is what you get withstandard digital logic circuits (see Chap-ters 8 and 9). The inverting configuration,with Q17ssource connected to a virtualground (the summing junction), simplifiescircuit operation, since there are no sig-nal swings on Qls source in the ON state;Dl prevents FET turn-on for positive in-put swings when Q1 is OFF, and it has noeffect when the switch is closed.There are p-channel JFETs with lowpinch-off voltages available in useful con-figurations at low prices. For example, theIH5009-IH5024 family includes deviceswith four input FETs and one cancellationFET in a single DIP package, with RONof100 ohms and a price less than two dol-lars. Add an op-amp and a few resistorsand youve got a Cinput multiplexer. Notethat the same RONcancellation trick canbe used with MOSFET switches.*11-- --0,.Oz: matched pair+5x,,u T L 1ev.s)ov
  • FEEDBACK AND OPERATIONAL AMPLIFIERS242 Chapter 44.31 TTL zero-crossing detectorThe circuit shown in Figure 4.78 generatesan output square wave for use with TTLlogic (zero to +5V range) from an inputwave of any amplitude up to 100 volts.R1, combined with Dl and D2,limits theinput swing to -0.6 volt to +5.6 volts,approximately. Resistive divider R2R3 isnecessary to limit negative swing to lessthan 0.3 volt, the limit for a 393 compara-tor. Rs and Rg provide hysteresis, withR4 setting the t~iggerpoints symmetricallyabout ground. The input impedance isnearly constant, because of the large R1value relative to the other resistors in theinput attenuator. A 393 is used because itsinputs can go all the way to ground, mak-ing single-supply operation simple.current, for use with a current regulator,metering circuit, or whatever. The voltageacross the 4-terminal resistor Rs goesfromzero to 0.1 volt, with probable common-mode offset due to the effects of resistancein the ground lead (note that the powersupply is grounded at the output). For thatreason the op-amp is wired as a differen-tial amplifier, with gain of 100. Voltageoffset is trimmed externally with Rs, sincethe LT1013doesnt have internal trimmingcircuitry (the single LT1006 does, how-ever). A Zener reference with a few percentstability is adequate for trimming, sincethe trimming is itself a small correction(you hope!). The venerable 358 could havebeen chosen because both inputs and out-put also go all the way to ground. V+couldbe unregulated, since the power-supply re-jection of the op-amp is more than ade-EXERCISE 4.14 quate, loodB (typ) in this case.Verifythatthe trigger points are at f25mVat theinput signal.FEEDBACK AMPLIFIER FREQUENCY4.32 Load-current-sensing circuit COMPENSATIONThe circuit shown in Figure 4.79 provides If you look at a graph of open-loop voltagea voltage output proportional to load gain versus frequency for several op-amps,posit~veprotection center hysteres~srnax.IN914negative-protection -nto log~cgates, etc4.7MS2R6 225rnV hysteresis (at lnput)4.7kp-Figure 4.78. Zero-crossinglevel detector with input protection.
  • FEEDBACK AMPLIFIER FREQUENCY COMPENSATION4.33 Gain and phase shift versus frequency 243t12V to t30V (unrequlated OK)youll see something like the curves inFigure 4.80. From a superficial look atsuch a Bode plot (a log-log plot of gainR ,100 1%frequency (Hz)Figure 4.80vi&Vo = /L (Rs-3! A-R3 74100 1% 10k 1%---/I6.2VIN5234 7Land phase versus frequency) you mightconclude that the 741 is an inferior op-amp, since its open-loop gain drops offsorapidly with increasing frequency. Infact, that rolloff is built into the op-ampintentionally and is recognizable as theJ-same -6dbloctave curve characteristic ofan RC low-pass filter. The 748, by corn-parison, is identical with the 741 exceptthat it is uncompensated (as is the 739).Op-amps are generally available in inter-nally compensated varieties and uncom-pensated varieties; lets take a look at thisbusiness of frequency compensation.source4.33 Gain and phase shiftversus frequency- ---An op-amp (or, in general, any multistageamplifier) will begin to roll off at somefrequency because of the low-pass filtersformed by signals of finite source imped-ance driving capacitive loads within theamplifier stages. For instance, it is corn-mon to have an input stage consisting ofa differential amplifier, perhaps with cur-rent mirror load (see the LM358 schematicin Fig. 4.54), driving a common-emittersecond stage. For now, imagine that thecapacitor labeled Cc in that circuit is re-moved. The high output impedanceof the input stage, in combination with4 terminal- Figure 4.79. High-powerreslstor 1ow ground at oufput terminal current-sensingamplifier.power/
  • FEEDBACK AND OPERATIONAL AMPLIFIERS244 Chapter 4junction capacitance Ci,and feedback ca-pacitance Ccb(Miller effect, see Sections2.19 and 13.04) of the following stage,forms a low-pass filter whose 3dB pointmight fall somewhere in the range oflOOHz to 10kHz.The decreasing reactance of the capac-itor with increasing frequency gives riseto the characteristic 6dbloctave rolloff: Atsufficiently high frequencies (which may bebelow IkHz), the capacitive loading domi-nates the collector load impedance, result-ing in a voltage gain GV = g,Xc, i.e.,the gain drops off as llf. It also producesa 90 lagging phase shift at the output rel-ative to the input signal. (You can thinkof this as the tail of an RC low-pass fil-ter characteristic, where R represents theequivalent source impedance driving thecapacitive load. However, it is not nec-essary to have any actual resistors in thecircuit.)Figure 4.81-0-;m--C_ma0-tgIn a multistage amplifier there will beadditional rolloffs at higher frequencies,caused by low-pass filter characteristics inthe other amplifier stages, and the over-all open-loop gain will look something likethat shown in Figure 4.81. The open-loop gain begins dropping at 6dBloctaveat some low frequency fl, due to capac-itive loading of the first-stage output. ItI I l $ - - Lcontinues dropping off with that slope un-til an internal RC of another stage rears itsugly head at frequency fi, beyond whichthe rolloff goes at 12dB/octave, and so on.f 1frequency (log scale)I-20 t frequency (log scale)IFigure 4.82. Bode plot: gain and phase versusfrequency.I Ifrequency (log) Figure 4.83What is the significance of all this?Remember that an RC low-pass filterhas a phase shift that looks as shown inFigure 4.82. Each low-pass filter withinthe amplifier has a similar phase-shiftcharacteristic, so the overall phase shift ofthe hypothetical amplifier will be as shownin Figure 4.83.
  • FEEDBACK AMPLIFIER FREQUENCY COMPENSATION4.34 Amplifier compensation methods 245Now heres the problem: If you wereto connect this amplifier as an op-ampfollower, for instance, it would oscillate.Thats because the open-loop phase shiftreaches 180 at some frequency at whichthe gain is still greater than 1 (negativefeedback becomes positive feedback at thatfrequency). Thats all you need to generatean oscillation, since any signal whatsoeverat that frequency builds up each timearound the feedback loop, just like a publicaddress system with the gain turned up toofar.Stability criterionThe criterion for stability against oscilla-tion for a feedback amplifier is that itsopen-loop phase shift must be less than180 at the frequency at which the loopgain is unity. This criterion is hardest tosatisfy when the amplifier is connected asa follower, since the loop gain then equalsthe open-loop gain, the highest it can be.Internally compensated op-amps are de-signed to satisfy the stability criterion evenwhen connected as followers; thus they arestable when connected for any closed-loopgain with a simple resistive feedback net-work. As we hinted earlier, this is accom-plished by deliberately modifying an exist-ing internal rolloff in order to put the 3dBpoint at some low frequency, typically 1Hzto 20Hz. Lets see how that works.4.34 Amplifier compensation methodsDominant-pole compensationThe goal is to keep the open-loop phaseshift much less than 180 at all frequenciesfor which the loop gain is greater than1. Assuming that the op-amp may beused as a follower, the words "loop gain"in the last sentence can be replaced by"open-loop gain." The easiest way todo this is to add enough capacitance atthe point in the circuit that produces theinitial 6dBloctave rolloff, so that the open-loop gain drops to unity at about the 3dBfrequency of the next "natural" RC filter.In this way the open-loop phase shift isheld at a constant 90 over most of thepassband, increasing toward 180" only asthe gain approaches unity. Figure 4.84increase C1OOdBE60dB00-& 40dB20d BCOdB tFigure 4.84shows the idea. Without compensationthe open-loop gain drops toward 1, first at6dB/octave, then at 12dB/octave, etc., re-sulting in phase shifts of 180" or more be-fore the gain has reached 1. By moving thefirst rolloff down in frequency (forming a"dominant pole"), the rolloff is controlledso that the phase shift begins to rise above90° only as the open-loop gain approachesunity. Thus, by sacrificing open-loop gain,you buy stability. Since the natural rolloffof lowest frequency is usually caused byMiller effect in the stage driven by the in-put differential amplifier, the usual methodof dominant-pole compensation consistssimply of adding additional feedback ca-pacitance around the second-stage transis-tor, so that the combined voltage gain of
  • FEEDBACK AND OPERATIONAL AMPLIFIERS246 Chapter 4the two stages is gmXc or gm/2.rrf C,,,,over the compensated region of the am-plifiers frequency response (Fig. 4.85). Inpractice, Darlington-connected transistorswould probably be used for both stages.+ "ccFigure 4.85. Classic op-amp input stage withcompensation.which it intersects the unity-gain axis (Fig.4.86).dont know (or care)pck C,,,,,,, forgaln out hereOdB 1frequency (log) Figure 4.86Uncompensated op-ampsIf an op-amp is used in a circuit withclosed-loop gain greater than 1 (i.e., nota follower), it is not necessary to put thepole (the term for the "corner frequency"of a low-pass filter)at such a low frequency,since the stability criterion is relaxed be-cause of the lower loop gain. Figure 4.87shows the situation graphically.By putting the dominant-pole unity-gain1(uncompensated)crossingat the 3dB point of the next rolloff,open loop galn(compensated for 30dB)you get a phase margin of about 45" in l o o d ethe worst case (follower), since a single 8odB!RC filter has a 45" lagging phase shift at G closed loop qalnits 3dB frequency, i.e., the phase margin !6 0 d B -(51equals 180"- (90 + 45"), with the 90" Zcoming from the dominant pole. ? 4odeAn additional advantage of using a 20dB [Miller-effect pole for compensation is that closed loop qaln( u n ~ t ygaln compensat~on)the compensation is inherently insensitive O ~ B- frequency ( I O ~ )to changes in voltage gain with temper- Iature, or manufacturing spread of gain:Higher gain causes the feedback capaci- Figure 4-87tance to look larger, moving the pole down-ward in frequency in exactly the right way For a closed-loop gain of 30dB, the loopto keep the unity-gain crossing frequency gain (which is the ratio of the open-loopunchanged. In fact, the actual 3dB fre- gain to the closed-loop gain) is less thanquency of the compensation pole is quite for a follower, so the dominant pole can beirrelevant; what matters is the point at placed at a higher frequency. It is chosen
  • FEEDBACK AMPLIFIER FREQUENCY COMPENSATION4.35 Frequency response of the feedback network 247so that the open-loop gain reaches 30dB(rather than OdB) at the frequency of thenext natural pole of the op-amp. As thegraph shows, this means that the open-loopgain is higher over most of the frequencyrange, and the resultant amplifier will workat higher frequencies. Some op-ampsare available in uncompensated versions[e.g., the 748 is an uncompensated 741;the same is true for the 308 (312), 3130(3160), HA5102 (HA5112), etc.], withrecommended external capacitance valuesfor a selection of minimum closed-loopgains. They are worth using if you need theadded bandwidth and your circuit operatesat high gain. An alternative is to use"decompensated" (a better word might be"undercompensated") op-amps, such asthe 357, which are internally compensatedfor closed-loop gains greater than someminimum (Av> 5 in the case of the 357).t -- -- -- -Ifrequency (log)Figure 4.88amplifier to move upward somewhat infrequency, an effect known as "pole split-ting." The frequency of the canceling zerowill be chosen accordingly.4.35 Frequency response of thefeedback network7Pole-zero compensationIt is possible to do a bit better than withdominant-pole compensation by using acompensation network that begins drop-ping (6dB/octave, a "pole") at some lowfrequency, then flattens out again (it has a"zero") at the frequency of the second nat-ural pole of the op-amp. In this way theamplifiers second pole is "canceled,"giv-ing a smooth 6dBloctave rolloff up to theamplifiers third pole. Figure 4.88 showsa frequency response plot. In practice,the zero is chosen to cancel the amplifierssecond pole; then the position of the firstpole is adjusted so that the overall responsereaches unity gain at the frequency of theamplifiers third pole. A good set of datasheets will often give suggested componentvalues (an R and a C) for pole-zero com-pensation, as well as the usual capacitorvalues for dominant-pole compensation.As you will see in Section 13.06, movingthe dominant pole downward in frequencyactually causes the second pole of theIn all of the discussion thus far we haveassumed that the feedback network hasa flat frequency response; this is usuallythe case, with the standard resistive volt-age divider as a feedback network. How-ever, there are occasions when some sortof equalization amplifier is desired (inte-grators and differentiators are in this cat-egory) or when the frequency response ofthe feedback network is modified to im-prove amplifier stability. In such cases itis important to remember that the Bodeplot of loop gain versus frequency is whatmatters, rather than the curve of open-loop gain. To make a long story short, thecurve of ideal closed-loop gain versus fre-quency should intersect the curve of open-loop gain, with a difference in slopes of6dBloctave. As an example, it is com-mon practice to put a small capacitor (afew picofarads) across the feedback resis-tor in the usual inverting or noninvertingamplifier. Figure 4.89 shows the circuitand Bode plot.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS248 Chapter 4lOOdB80dB +open loop galnm... .. kedbac, network wif,o,,= ruaa +(closed loop galn.>20dBBFigure 4.89with C,uncompensated op-amps. It is simplestto use the compensated variety, and thatsthe usual choice. You might considerthe internally compensated LF411 first.If you need greater bandwidth or slewrate, look for a faster compensated op-amp(see Table 4.1 or 7.3 for many choices).If it turns out that nothing is suitable,and the closed-loop gain is greater thanunity (as it usually is), you can use anuncompensated op-amp, with an externalcapacitor as specified by the manufacturerfor the gain you are using.A number of op-amps offer anotherchoice: a "decompensated" version, re-quiring no external compensation compo-nents, but only usable at some minimumgain greater than unity. For example, thepopular OP-27 low-noiseprecision op-amp(unity-gain-compensated) is available asthe decompensated OP-37 (minimum gainof 5), offering roughly seven times thespeed, and also as the decompensatedHA-5147 (minimum gain of lo), with 15times the speed.The amplifier would have been close to Example: 60Hz power sourceinstability with a flat feedback network,since the loop gain would have beendropping at nearly 12dBloctave where thecurves meet. The capacitor causes the loopgain to drop at 6dBloctave near the cross-ing, guaranteeing stability. This sort ofconsideration is very important when de-signing differentiators, since an ideal dif-ferentiator has a closed-loopgain that risesat 6dB/octave; it is necessary to roll offthe differentiator action at some moder-ate frequency, preferably going over to a6dBloctave rolloff at high frequencies. In-tegrators, by comparison, are very friendlyin this respect, owing to their 6dBloctaveclosed-loop rolloff. It takes real talent tomake a low-frequency integrator oscillate!What to doIn summary, you are generally faced withthe choice of internally compensated orUncompensated op-amps also give you theflexibility of overcompensating, a simplesolution to the problem of additional phaseshifts introduced by other stuff in thefeedback loop. Figure 4.90 shows a niceexample. This is a low-frequency amplifierdesigned to generate a 115 volt ac poweroutput from a variable 60Hz low-levelsine-wave input (it goes with the 60Hzsynthesizer circuit described in Section8.31). The op-amp, together with R2 andR3, forms a x 100 gain block; this is thenused as the relatively low "open-loopgain"for overall feedback. The op-amp outputdrives the push-pull output stage, whichin turn drives the transformer primary.Low-frequency feedback is taken from thetransformer output via Rlo,in order togenerate low distortion and a stable outputvoltage under load variations. Because of
  • 2.5V rmsInput -50-70Hz~-+16 (unregulated)Figure 4.90. Output amplifier for 60Hz power source.
  • FEEDBACK AND OPERATIONAL AMPLIFIERS250 Chapter 4the unacceptably large phase shifts of sucha transformer at high frequencies, the cir-cuit is rigged up so that at higher fre-quencies the feedback comes from the low-voltage input to the transformer, via C3.The relative sizes of R9 and Rloare cho-sen to keep the amount of feedback con-stant at all frequencies. Even though high-frequency feedback is taken directly fromthe push-pull output, there are still phaseshifts associated with the reactive load (thetransformer primary) seen by the transis-tors. In order to ensure good stability,even with reactive loads at the 115 voltoutput, the op-amp has been overcompen-sated with an 82pF capacitor (30pF is thenormal value for unity gain compensation).The loss of bandwidth that results is unim-portant in a low-frequency application likethis.output voltageVSfrequency+ VS3a output power.-with the transformers finite output imped-ance, causes additional phase shifts withinthe low-frequency feedback loop. Sincethis circuit was built to derive a telescopessynchronous driving motors (highly induc-tive loads), the loop gain was intentionallykept low. Figure 4.91 shows a graph of theac output voltage versus load, which illus-trates good (but not great) regulation.MotorboatingIn ac-coupled feedback amplifiers, stabilityproblems can also crop up at very low fre-quencies, due to the accumulated leadingphase shifts caused by several capacitivelycoupled stages. Each blocking capacitor,in combination with the input resistancedue to bias strings and the like, causes aleading phase shift that equals 45" at thelow-frequency 3dB point and approaches90" at lower frequencies. If there is enoughloop gain, the system can go into a low-frequency oscillation picturesquely knownas "motorboating." With the widespreaduse of dc-coupled amplifiers, motorboatingis almost extinct. However, old-timers cat^tell you some good stories about it.SELF-EXPLANATORY CIRCUITS1050 L I50 55 60 65 70frequency (Hz)power (W)Figure 4.9 1An application such as this represents acompromise, since ideally you would liketo have plenty of loop gain to stabilize theoutput voltage against variations in loadcurrent. But a large loop gain increases thetendency of the amplifier to oscillate, espe-cially if a reactive load is attached. This isbecause the reactive load, in combination4.36 Circuit ideasSome interesting circuit ideas, mostlylifted from manufacturers data sheets, areshown in Figure 4.94.4.37 Bad circuitsFigure 4.95 presents a zoo of intentional(mostly) blunders to amuse, amaze, andeducate you. There are a few real howlershere this time. These circuits are guar-anteed not to work. Figure out why. Allop-amps run from f15 volts unless shownotherwise.
  • SELF-EXPLANATORY CIRCUITS4.37 Bad circuits 251ADDITIONAL EXERCISES(I) Design a "sensitive voltmeter" to haveZin= 1M a and full-scale sensitivities oflOmV to 10V in four ranges. Use a 1mAmeter movement and an op-amp. Trimvoltage offsets if necessary, and calculatewhat the meter will read with input open,assuming (a) IB = 25pA (typical for a411) and (b) IB = 8OnA (typical for a741). Use some form of meter protection(e.g., keep its current less than 200% offull scale), and protect the amplifier inputsfrom voltages outside the supply voltages.What do you conclude about the suitabilityof the 741 for low-level high-impedancemeasurements?(2) Design an audio amplifier, using anOP-27 op-amp (low noise, good foraudio), with the following characteristics:gain = 20dB, Zin = 10k, -3dB point =20Hz. Use the noninverting configuration,and roll off the gain at low frequencies insuch a way as to reduce the effects of in-put offset voltage. Use proper design tominimize the effects of input bias currenton output offset. Assume that the signalsource is capacitively coupled.(3) Design a unity-gain phase splitter (seeChapter 2) using 411s. Strive for highinput impedance and low output imped-ances. The circuit should be dc-coupled.At roughly what maximum frequency canyou obtain full swing (27V pp, with f15Vsupplies), owing to slew rate limitations?(4) El Cheapo brand loudspeakers arefound to have a treble boost, beginning at2kHz (+3dB point) and rising 6dBloctave.Design a simple RC filter, buffered withAD611 op-amps (another good audio chip)as necessary, to be placed between preampand amplifier to compensate this rise.Assume that the preamp has ZOut= 50kand that the amplifier has Zin = IOk,approximately.(5) A 741 is used as a simple compara-tor, with one input grounded; i.e., it is azero-crossing detector. A 1 volt amplitudesine wave is fed into the other input(frequencylkHz). What voltage(s) will theinput be when the output passes throughzero volts? Assume that the slew rate isO.5Vlps and that the op-amps saturatedoutput is f13 volts.(6) The circuit in Figure 4.92 is an exam-ple of a "negative-impedance converter."(a) What is its input impedance? (b) Ifthe op-amps output range goes from V+ toV-, what range of input voltages will thiscircuit accommodate without saturation?Figure 4.92(7) Consider the circuit in the precedingproblem as the 2-terminal black box (Fig.4.93). Show how to make a dc amplifierwith a gain of -10. Why cant you make adc amplifier with a gain of +lo? (Hint:The circuit is susceptible to a latchupcondition for a certain range of sourceresistances. What is that range? Can youthink of a remedy?)Figure 4.93
  • Ch 5: Active Filters and OscillatorsWith only the techniques of transistors andop-amps it is possible to delve into a num-ber of interesting areas of linear (as con-trasted with digital) circuitry. We believethat it is important to spend some time do-ing this now, in order to strengthen yourunderstanding of some of these difficultconcepts (transistor behavior, feedback,op-amp limitations, etc.) before introduc-ing more new devices and techniques andgetting into the large area of digital elec-tronics. In this chapter, therefore, we willtreat briefly the areas of active filters andoscillators. Additional analog techniquesare treated in Chapter 6 (voltage regula-tors and high-current design), Chapter 7(precision circuits and low noise), Chap-ter 13 (radiofrequency techniques), Chap-ter 14 (low-power design), and Chapter15 (measurements and signal processing).The first part of this chapter (active filters,Sections 5.01-5.11) describes techniquesof a somewhat specialized nature, and itcan be passed over in a first reading. How-ever, the latter part of this chapter (oscil-lators, Sections 5.12-5.19) describes tech-niques of broad utility and should not beomitted.ACTIVE FILTERSIn Chapter 1 we began a discussion of fil-ters made from resistors and capacitors.Those simple RC filters produced gentlehigh-pass or low-pass gain characteristics,with a 6dBloctave falloff well beyondthe -3dB point. By cascading high-passand low-pass filters, we showed how toobtain bandpass filters, again with gentle6dBloctave "skirts." Such filters are suffi-cient for many purposes, especially if thesignal being rejected by the filter is farremoved in frequency from the desiredsignal passband. Some examples are by-passing of radiofrequency signals in audiocircuits, "blocking"capacitors for elimina-tion of dc levels, and separation of mod-ulation from a communications "carrier"(see Chapter 13).5.01 Frequency response with RC filtersOften, however, filters with flatter pass-bands and steeper skirts are needed. Thishappens whenever signals must be filteredfrom other interfering signals nearby in263
  • ACTIVE FILTERS AND OSCILLATORS264 Chapter 5frequency. The obvious next question iswhether or not (by cascading a numberof identical low-pass filters, say) we cangenerate an approximation to the ideal"brick-wall" low-pass frequency response,as in Figure 5.1.Figure 5.1We know already that simple cascadingwont work, since each sections inputimpedance will load the previous sectionseriously, degrading the response. Butwith buffers between each section (or byarranging to have each section of muchhigher impedance than the one precedingit), it would seem possible. Nonetheless,the answer is no. Cascaded RC filters doproduce a steep ultimate falloff, but the"knee" of the curve of response versusfrequency is not sharpened. We mightrestate this as "many soft knees do nota hard knee make." To make the pointgraphically, we have plotted some graphsof gain response (i.e., VOut/V,,) versusfrequency for low-pass filters constructedfrom 1, 2, 4, 8, 16, and 32 identical RCsections, perfectly buffered (Fig. 5.2).The first graph shows the effect of cas-cading several RC sections, each with its3dB point at unit frequency. As moresections are added, the overall 3dB pointis pushed downward in frequency, as youcould easily have predicted. To comparefilter characteristics fairly, the rolloff fre-quencies of the individual sections shouldbe adjusted so that the overall 3dB pointis always at the same frequency. The othergraphs in Figure 5.2, as well as the next fewgraphs in this chapter, are all "normalized"in frequency, meaning that the -3dB pointfrequency (Hz)AL I I I0 1 2 3normallzed frequencyBnormaltzed frequency (log scale)CFigure 5.2. Frequency responses of multisec-tion RCfilters. GraphsA and Bare linear plots,whereas C is logarithmic. The filter responsesin B and C have been normalized (or scaled)for 3dB attenuation at unit frequency.
  • ACTIVE FILTERS5.02 Ideal performance with LC filters 265frequency (kHz)Figure 5.3. An unusually good passive bandpass filter implemented from inductorsand capacitors(inductances in mH,capacitances in pF). Bottom: Measured response of the filter circuit. [Basedon Figs. 11 and 12 from Orchard, H. J., and Sheahan,D. E, ZEEE Journal of Solid-State Circuits,Vol. SC-5, NO. 3 (1970).](or breakpoint, howeverdefined) is at a fre-quency of 1 radian per second (or at 1Hz).To determine the response of a filter whosebreakpoint is set at some other frequency,simply multiply the values on the frequen-cy axis by the actual breakpoint frequencyf,. In general, we will also stick to thelog-log graph of frequency response whentalking about filters, because it tells themost about the frequency response. Itlets you see the approach to the ultimaterolloff slope, and it permits you to readoff accurate values of attenuation. In thiscase (cascaded RC sections) the normal-ized graphs in Figures 5.2B and 5.2C dem-onstrate the soft knee characteristic of pas-sive RC filters.5.02 Ideal performance with LC filtersAs we pointed out in Chapter 1, filtersmade with inductors and capacitors canhave very sharp responses. The parallelLC resonant circuit is an example. Byincluding inductors in the design, it is pos-sible to create filters with any desired flat-ness of passband combined with sharpnessof transition and steepness of falloff out-side the band. Figure 5.3 shows an exam-ple of a telephone filter and its character-istics.Obviously the inclusion of inductors in-to the design brings about some magic thatcannot be performed without them. Inthe terminology of network analysis, thatmagicconsists in the use of "off-axis poles."Even so, the complexity of the filter in-creases according to the required flatnessof passband and steepness of falloff outsidethe band, accounting for the large numberof components used in the preceding fil-ter. The transient response and phase-shiftcharacteristics are also generally degradedas the amplitude response is improved to
  • ACTIVE FILTERS AND OSCILLATORS266 Chapter 5approach the ideal brick-wall characteris-tic.The synthesis of filters from passivecomponents (R, L, C) is a highly devel-oped subject, as typified by the authorita-tive handbook by Zverev (see chapter ref-erences at end of book). The only problemis that inductors as circuit elements fre-quently leave much to be desired. They areoften bulky and expensive, and they de-part from the ideal by being"lossy," i.e., byhaving significant series resistance, as wellas other "pathologies" such as nonlinear-ity, distributed winding capacitance, andsusceptibility to magnetic pickup of inter-ference.What is needed is a way to makeinductorless filters with the characteristicsof ideal RLC filters.5.03 Enter active filters: an overviewBy using op-amps as part of the filter de-sign, it is possible to synthesize any RLCfilter characteristic without using induc-tors. Such inductorless filters are knownas active filters because of the inclusion ofan active element (the amplifier).Active filters can be used to make low-pass, high-pass, bandpass, and band-rejectfilters, with a choice of filter types accord-ing to the important features of the re-sponse, e.g., maximal flatness of passband,steepness of skirts, or uniformity of timedelay versusfrequency (more on this short-ly). In addition, "all-pass filters" with flatamplitude response but tailored phase ver-sus frequency can be made (theyie alsoknown as"delay equalizers"), as well as theopposite - a filter with constant phase shiftbut tailored amplitude response.Negative-impedance converters andgyratorsTwo interesting circuit elements thatshould be mentioned in any overview arethe negative-impedance converter (NIC)and the gyrator. These devices can mimicthe properties of inductors, while usingonly resistors and capacitors in addition toop-amps.Once you can do that, you can build in-ductorless filters with the ideal propertiesof any RLC filter, thus providing at leastone way to make active filters.The NIC converts an impedance to itsnegative, whereas the gyrator converts animpedance to its inverse. The followingex-ercises will help you discover for yourselfhow that works out.EXERCISE 5.1Show that the circuit in Figure 5.4 is a negative-impedance converter, in particular that Zin =-2. Hint: Apply some input voltage V, andcompute the input current I. Thentakethe ratioto find Zin= V / I .Figure 5.4. Negative-impedanceconverter.R2Z," = 7 R- NIC -T 11Figure 5.5EXERCISE 5.2Show that the circuit in Figure 5.5 is a gyrator,in particular that Zin = R2/Z. Hint: You cananalyzeit as a set of voltagedividers,beginningat the right.
  • ACTIVE FILTERS5.04 Key filter performance criteria 265The NIC therefore converts a capacitorto a "backward" inductor:i.e., it is inductive in the sense of generat-ing a current that lags the applied voltage,but its impedance has the wrong frequencydependence (it goes down, instead of up,with increasing frequency). The gyrator,on the other hand, converts a capacitor toa true inductor:i.e., an inductor with inductance L =CR2.The existence of the gyrator makes itintuitively reasonable that inductorless fil-ters can be built to mimic any filter us-ing inductors: Simply replace each induc-tor by a gyrated capacitor. The use ofgyrators in just that manner is perfectlyOK, and in fact the telephone filter illus-trated previously was built that way. In ad-dition to simple gyrator substitution intopreexisting RLC designs, it is possible tosynthesize many other filterconfigurations.The field of inductorless filter design is ex-tremely active, with new designs appearingin the journals every month.Sallen-and-Key filterFigure 5.6 shows an example of a simpleand even partly intuitive filter. It is knownas a Sallen-and-Key filter, after its inven-tors. The unity-gain amplifier can be anop-amp connected as a follower, or just anemitter follower. This particular filter is a2-pole high-pass filter. Note that it wouldbe simply two cascaded RC high-pass fil-ters except for the fact that the bottom ofthe first resistor is bootstrapped by the out-put. It is easy to see that at very low fre-quencies it falls off just like a cascaded RC,since the output is essentially zero. As theoutput rises at increasing frequency, how-ever, the bootstrap action tends to reducethe attenuation, giving a sharper knee. Ofcourse, such hand-waving cannot substi-tute for honest analysis, which luckily hasalready been done for a prodigious varietyof nice filters. We will come back to activefilter circuits in Section 5.06.Figure 5.65.04 Key filter performance criteriaThere are some standard terms that keepappearing when we talk about filters andtry to specify their performance. It is worthgetting it all straight at the beginning.Frequency domainThe most obvious characteristic of a filteris its gain versus frequency, typified bythe sort of low-pass characteristic shownin Figure 5.7.The passband is the region of frequen-cies that are relatively unattenuated by thefilter. Most often the passband is con-sidered to extend to the -3dB point, butwith certain filters(most notably the "equi-ripple"types) the end of the passband maybe defined somewhat differently. Withinthe passband the response may show vari-ations or ripples, defining a ripple band, asshown. The cutoffrequency, f,, is the endof the passband. The response of the filterthen drops off through a transition region(alsocolorfullyknown as the skirt of the fil-ters response) to a stopband, the region ofsignificant attenuation. The stopband maybe defined by some minimum attenuation,e.g., 40dB.Along with the gain response, the otherparameter of importance in the frequency
  • ACTIVE FILTERS AND OSCILLATORS268 Chapter 5ripple4 1bandcIp :itsi rion regionlog frequency -Afrequency (linear) - frequency (linear) ----tFigure 5.7. Filter characteristics versus frequency.graph of phase shift and amplitude for alow-pass filter that is definitely not a linear-phase filter. Graphs of phase shift versusfrequency are best plotted on a linear-frequency axis.domain is the phase shift of the output terms for some undesirable properties ofsignal relative to the input signal. In other filters.words, we are interested in the complexresponse of the filter, which usually goes -Time domainby the name of H(s), where s = jw, where s-MH, s, and w all are complex. Phase is ;, 0.8important because a signal entirely within -$ -the passband of a filter will emerge with 0.6 -its waveform distorted if the time delay of "a -0.4different frequencies in going through theufilter is not constant. Constant time delay ,z0.2-corresponds to a phase shift increasing "E,linearly with frequency; hence the term IAs with any ac circuit, filters can bedescribed in terms of their time-domainproperties: rise time, overshoot, ringing,and settling time. This is of particularimportance where steps or pulses may beused. Figure 5.9 shows a typical low-pass-filter step response. Here, rise timeis the time required to reach 90% of thefinal value, whereas settling time is thetime required to get within some specifiedamount of the final value and stay there.Overshoot and ringing are self-explanatory4n3n :a.-p-2~ ccI- n rmaoFigure 5.8. Phase and amplitude responsefor an 8-pole Chebyshev low-pass filter (2dBpassband ripple).0linear-phase $filter applied to a filter ideal0.5 1.O 1.5 2.0normalized frequencyin this respect. Figure 5.8 shows a typical (linear scale)5.05 Filter typesSuppose you want a low-pass filter withflat passband and sharp transition to thestopband. The ultimate rate of falloff,well into the stopband, will always be6ndBloctave, where n is the number of"poles." You need one capacitor (orinductor) for each pole, so the requiredultimate rate of falloff of filter responsedetermines, roughly, the complexity of thefilter.Now, assume that you have decidedto use a 6-pole low-pass filter. You areguaranteed an ultimate rolloff of 36dBloctave at high frequencies. It turns out
  • ACTIVE FILTERS5.05 Filter types 26915%1over,sbotsettle to 5%time ----cFigure 5.9that the filter design can now be optimizedfor maximum flatness of passband re-sponse, at the expense of a slow transitionfrom passband to stopband. Alternatively,by allowing some ripple in the passbandcharacteristic, the transition from pass-band to stopband can be steepened con-siderably. A third criterion that may beimportant is the ability of the filter to passsignalswithin the passband without distor-tion of their waveforms caused by phaseshifts. You may also care about rise time,overshoot, and settling time.There are filter designs available to opti-mize each of these characteristics, or com-binations of them. In fact, rational filterselection will not be carried out as just de-scribed; rather, it normally begins with aset of requirements on passband flatness,attenuation at some frequency outside thepassband, and whatever else matters. Youwill then choose the best design for thejob, using the number of poles necessaryto meet the requirements. In the next fewsections we will introduce the three popu-lar favorites, the Butterworth filter (max-imally flat passband), the Chebyshev fil-ter (steepest transition from passband tostopband), and the Bessel filter (maximallyflat time delay). Each of these filter re-sponses can be produced with a variety ofdifferent filter circuits, some of which wewill discuss later. They are all availablein low-pass, high-pass, and bandpass ver-sions.Butterworth and Chebyshev filtersThe Butterworth filter produces the flattestpassband response, at the expense of steep-ness in the transition region from passbandto stopband. As you will see later, it alsohas poor phase characteristics. The ampli-tude response is given bywhere n is the order of the filter (numberof poles). Increasing the number of polesflattens the passband response and steep-ens the stopband falloff,as shown in Figure5.10.normalized frequencyFigure 5.10. Normalized low-pass Butterworth-filter response curves. Note the improvedattenuation characteristics for the higher-orderfilters.The Butterworth filter trades off every-thing else for maximum flatness of re-sponse. It starts out extremely flat at zerofrequency and bends over near the cut-off frequency fc (fc is usually the -3dBpoint).In most applications, all that really mat-ters is that the wiggles in the passband re-sponse be kept less than some amount, say1dB. The Chebyshev filter responds to thisreality by allowing some ripples through-out the passband, with greatly improved
  • ACTIVE FILTERS AND OSCILLATORS270 Chapter 5sharpness of the knee. A Chebyshev filteris specified in terms of its number of polesand passband ripple. By allowing greaterpassband ripple, you get a sharper knee.The amplitude is given bywhere C, is the Chebyshev polynomialof the first kind of degree n, and 6 isa constant that sets the passband ripple.Like the Butterworth, the Chebyshev hasphase characteristics that are less thanideal.normalized frequencyAnormalized frequencyFigure 5.11. Comparison of some common6-pole low-pass filters. The same filters areplotted on both linear and logarithmicscales.Figure 5.11 presents graphs comparingthe responses of Chebyshev and Butter-worth 6-pole low-pass filters. As you cansee, theyre both tremendous improve-ments over a 6-pole RC filter.Actually, the Butterworth, with its max-imally flat passband, is not as attractiveas it might appear, since you are alwaysaccepting some variation in passband re-sponse anyway (with the Butterworth itis a gradual rolloff near f,, whereas withthe Chebyshev it is a set of ripples spreadthroughout the passband). Furthermore,active filters constructed with componentsof finite tolerance will deviate from thepredicted response, which means that areal Butterworth filter will exhibit somepassband ripple anyway. The graph in Fig-ure 5.12 illustrates the effectsof worst-casevariations in resistor and capacitor valueson filter response.frequency (linear) ---,Figure 5.12. The effect of component toleranceon active filter performance.Viewed in this light, the Chebyshev isa very rational filter design. It is some-times called an equiripple filter: It man-ages to improve the situation in the transi-tion region by spreading equal-size ripplesthroughout the passband, the number ofripples increasing with the order of the fil-ter. Even with rather small ripples (aslittleas 0.ldB) the Chebyshev filter offers con-siderably improved sharpness of the knee
  • ACTIVE FILTERS5.05 Filter types 271-mVI01C.-m0)I 1fCYtOff fEIOP Figure 5.13. Specifying filter fre-frequency (log scale) - quency response parameters.as compared with the Butterworth. Tomake the improvement quantitative, sup-pose that you need a filter with flatness toO.ldB within the passband and 20dB at-tenuation at a frequency 25% beyond thetop of the passband. By actual calculation,that will require a 19-pole Butterworth, butonly an 8-pole Chebyshev.The idea of accepting some passbandripple in exchange for improved steep-ness in the transition region, as in the equi-ripple Chebyshev filter, is carried to its log-ical limit in the so-called elliptic (or Cauer)filter by trading ripple in both passbandand stopband for an even steeper tran-sition region than that of the Chebyshevfilter. With computer-aided design tech-niques, the design of elliptic filters is asstraightforward as for the classic Butter-worth and Chebyshev filters.Figure 5.13 shows how you specify fil-ter frequency response graphically. In thiscase (a low-pass filter) you indicate the al-lowable range of filter gain (i.e., the ripple)in the passband, the minimum frequen-cy at which the response leaves the pass-band, the maximum frequency at whichthe response enters the stopband, andthe minimum attenuation in the stop-band.Bessel filterAs we hinted earlier, the amplitude re-sponse of a filter does not tell the wholestory. A filter characterized by a flat ampli-tude response may have large phase shifts.The result is that a signal in the passbandwill suffer distortion of its waveform. Insituations where the shape of the wave-form is paramount, a linear-phase filter(or constant-time-delay filter) is desirable.A filter whose phase shift varies linearlywith frequency is equivalent to a constanttime delay for signals within the passband,i.e., the waveform is not distorted. TheBessel filter (alsocalled the Thomson filter)had maximally flat time delay within itspassband, in analogy with the Butterworth,which has maximally flat amplitude re-sponse. To see the kind of improvement intime-domain performance you get with theBessel filter, look at Figure 5.14 for a com-parison of time delay versus normalizedfrequency for 6-pole Bessel and Butter-worth low-pass filters. The poor time-delayperformance of the Butterworth gives riseto effects such as overshoot when drivenwith pulse signals. On the other hand, theprice you pay for the Bessels constancyof time delay is an amplitude response
  • ACTIVE FILTERS AND OSCILLATORS272 Chapter 5with even less steepness than that ofthe Butterworth in the transition regionbetween passband and stopband.frequency (radiansisor w )Figure 5.14. Comparison of time delays for6-pole Bessel and Butterworth low-pass filters.The excellent time-domain performance ofthe Bessel filter minimizes waveform distor-tion.There are numerous filter designs thatattempt to improve on the Bessels goodtime-domain performance by compromis-ing some of the constancy of time delay forimproved rise time and amplitude-versus-frequency characteristics. The Gaussianfilter has phase characteristics nearly asgood as those of the Bessel, with improvedstep response. In another class there are in-teresting filters that allow uniform ripplesin the passband time delay (in analogy withthe Chebyshevs ripples in its amplitude re-sponse) and yield approximately constanttime delays even for signals well into thestopband. Another approach to the prob-lem of getting filters with uniform time de-lays is to use all-pass filters, also knownas delay equalizers. These have constantamplitude response with frequency, witha phase shift that can be tailored to in-dividual requirements. Thus, they can beused to improve the time-delay constancyof any filter, including Butterworth andChebyshev types.Filter comparisonIn spite of the preceding comments aboutthe Bessel filters transient response, it stillhas vastly superior properties in the timedomain, as compared with the Butterworthand Chebyshev. The Chebyshev, with itshighly desirable amplitude-versus-frequen-cy characteristics, actually has the poor-est time-domain performance of the three.The Butterworth is in between in both fre-quency and time-domain properties. Table5.1 and Figure 5.15 give more informationabout time-domain performance for thesethree kinds of filters to complement thefrequency-domain graphs presented earlier.They make it clear that the Bessel is a verydesirable filter where performance in thetime domain is important.%0F: -6-pole Chebyshev (0.5dB ripple)E6-pole Butterworth6-pole Besselcm0 0.5 1.0 1.5 2.0 2.5 3.0time (s)Figure 5.15. Step-response comparison for 6-pole low-pass filters normalized for 3dB atten-uation at 1Hz.ACTIVE FILTER CIRCUITSA lot of ingenuity has been used in invent-ing clever active circuits, each of whichcan be used to generate response functionssuch as the Butterworth, Chebyshev, etc.You might wonder why the world needsmore than one active filter circuit. Thereason is that various circuit realizationsexcel in one or another desirable property,so there is no all-around best circuit.Some of the features to look for in activefilters are (a) small numbers of parts, both
  • ACTIVE FILTER CIRCUITS5.06 VCVS circuits 273TABLE 5.1. TIME-DOMAIN PERFORMANCE COMPARISON FOR LOW-PASS FILTERSaStep Settling time Stopband attenuationrise time Over-f 3 d ~ (0 to 90%) shoot to 1% to 0.1% f = 2f, f = lof,Type (Hz) Poles (s) (%I (s) (S) (dB) (dB)Bessel 1.O 2 0.4 0.4 0.6 1.1 10 36(-3.0dBat 1.0 4 0.5 0.8 0.7 1.2 13 66f, = 1.OHz) 1.0 6 0.6 0.6 0.7 1.2 14 921.O 8 0.7 0.3 0.8 1.2 14 114Butterworth 1.0 2 0.4 4 0.8 1.7 12 40(-3.0dBat 1.0 4 0.6 11 1.0 2.8 24 80f, = 1.OHz) 1.0 6 0.9 14 1.3 3.9 36 1201.O 8 1.1 16 1.6 5.1 48 160Chebyshev 1.39 2 0.4 11 1.1 1.6 8 370.5dB ripple 1.09 4 0.7 18 3.0 5.4 31 89(-0.5dBat 1.04 6 1.1 21 5.9 10.4 54 141f, = 1.OHz) 1.02 8 1.4 23 8.4 16.4 76 193Chebyshev 1.07 2 0.4 21 1.6 2.7 15 442.0dB ripple 1.02 4 0.7 28 4.8 8.4 37 96(-2.0dBat 1.01 6 1.1 32 8.2 16.3 60 148f, = 1.OHz) 1.01 8 1.4 34 11.6 24.8 83 200(a) a design procedure for these filters is presented in Section 5.07.active and passive,(b) ease of adjustability,(c) small spread of parts values, especiallythe capacitor values, (d) undemanding useof the op-amp, especially requirements onslew rate, bandwidth, and output imped-ance, (e) the ability to make high-Q fil-ters, and (f)sensitivity of filter characteris-tics to component values and op-amp gain(in particular, the gain-bandwidth product,fT).In many ways the last feature is one ofthe most important. A filter that requiresparts of high precision is difficult to ad-just, and it will drift as the componentsage; in addition, there is the nuisance thatit requires components of good initial ac-curacy. The VCVS circuit probably owesmost of its popularity to its simplicity andits low parts count, but it suffers from highsensitivity to component variations. Bycomparison, recent interest in more com-plicated filter realizations is motivated bythe benefits of insensitivity of filter prop-erties to small component variability.In this section we will present severalcircuits for low-pass, high-pass, and band-pass active filters. We will begin with thepopular VCVS, or controlled-source type,then show the state-variable designs avail-able as integrated circuits from severalmanufacturers, and finally mention thetwin-T sharp rejection filter and some in-teresting new directions in switched-capacitor realizations.5.06 VCVS circuitsThe voltage-controlled voltage-source(VCVS) filter, also known simply as acontrolled-source filter, is a variation of theSallen-and-Keycircuit shown earlier. It re-places the unity-gain follower with a non-inverting amplifier of gain greater than 1.Figure 5.16 shows the circuits for low-pass,high-pass, and bandpass realizations. Theresistors at the outputs of the op-ampscreate a noninverting voltage amplifier
  • ACTIVE FILTERS AND OSCILLATORS274 Chapter 5(dc-coupled)I-low-pass filterhigh-pass filter1--band~assfilterFigure 5.16. VCVS active filter circuits.of voltage gain K, with the remainingRs and Cs contributing the frequency re-sponse properties for the filter. These are2-pole filters, and they can be Butterworth,Bessel, etc., by suitable choice of compo-nent values, as we will show later. Anynumber of VCVS 2-pole sections may becascaded to generate higher-order filters.When that is done, the individual filter sec-tions are, in general, not identical. In fact,each section represents a quadratic poly-nomial factor of the nth-order polynomialdescribing the overall filter.There are design equations and tables inmost standard filter handbooks for all thestandard filter responses, usually includingseparate tables for each of a number ofripple amplitudes for Chebyshev filters.In the next section we will present aneasy-to-use design table for VCVS filtersof Butterworth, Bessel, and Chebyshevresponses (0.5dB and 2dB passband ripplefor Chebyshev filters) for use as low-passor high-pass filters. Bandpass and band-reject filters can be easily made fromcombinations of these.5.07 VCVS filter design using oursimplified tableTo use Table 5.2, begin by deciding whichfilter response you need. As we mentionedearlier, the Butterworth may be attractiveif maximum flatness of passband is de-sired, the Chebyshev gives the fastest roll-off from passband to stopband (at theTABLE 5.2. VCVS LOW-PASSFILTERSChebyshev ChebyshevButter- Bessel (0.5dB) (2.0dB)4 worth0P K f n K f n K f n K2 1.586 1.272 1.268 1.231 1.842 0.907 2.114
  • ACTIVE FILTER CIRCUITS5.07 VCVS filter design using our simplified table 275expense of some ripple in the passband),and the Bessel provides the best phase char-acteristics, i.e., constant signal delay inthe passband, with correspondingly goodstep response. The frequency responses forall types are shown in the accompanyinggraphs (Fig. 5.17).To construct an n-pole filter (n is aneven number), you will need to cascaden/2 VCVS sections. Only even-orderfilters are shown, since an odd-order filterrequires as many op-amps as the nexthigher-order filter. Within each section,R1 = R2 = R, and C1 = Cz = C. As isusual in op-amp circuits, R will typicallybe chosen in the range 10k to 100k. (It isbest to avoid small resistor values, becausethe rising open-loop output impedance ofthe op-amp at high frequencies adds tothe resistor valuesand upsets calculations.)Then all you need to do is set the gain, K ,of each stage according to the table entries.For an n-pole filter there are n/2 entries,one for each section.Butterworth low-pass filtersIf the filter is a Butterworth, all sectionshave the same values of R and C, givensimply by R C = 1127~f,, where f, is thedesired -3dB frequency of the entire filter.To make a 6-pole low-pass Butterworthfilter, for example, you cascade three of thelow-pass sections shown previously, withgains of 1.07, 1.59, and 2.48 (preferablyin that order, to avoid dynamic rangeproblems), and with identical Rs and Csto set the 3dB point. The telescope drivecircuit in Section 8.31 shows such anexample, with f, = 88.4Hz (R = 180k,C = 0.OlpF).Bessel and Chebyshev low-pass filtersTo make a Bessel or Chebyshev filter withthe VCVS, the situation is only slightlymore complicated. Again we cascade sev-eral 2-pole VCVS filters, with prescribedgains for each section. Within each sec-tion we again use R1 = R2 = R, andC1 = C2 = C. However, unlike the sit-uation with the Butterworth, the RC prod-ucts for the different sections are differentand must be scaled by the normalizing fac-tor fn (given for each section in Table 5.2)according to R C =l12.rrfnf,. Here fc isagain the -3dB point for the Bessel filter,whereas for the Chebyshev filter it definesthe end of the passband, i.e., it is the fre-quency at which the amplitude responsefalls out of the ripple band on its way intothe stopband. For example, the responseof a Chebyshev low-pass filter with 0.5dBripple and fc = lOOHz will be flat within+OdB to -0.5dB from dc to 100Hz, with0.5dB attenuation at lOOHz and a rapidfalloff for frequencies greater than 1OOHz.Values are given for Chebyshev filters with0.5dB and 2.0dB passband ripple; the lat-ter have a somewhat steeper transition intothe stopband (Fig. 5.17).High-pass filtersTo make a high-pass filter, use the high-pass configuration shown previously, i.e.,with the Rs and Cs interchanged. For But-terworth filters, everything else remainsunchanged (use the same values for R, C,and K). For the Bessel and Chebyshev fil-ters, the K values remain the same, but thenormalizing factors f, must be inverted,i.e., for each section the new fn equalsll(fn listed in Table 5.2).A bandpass filter can be made by cas-cading overlapping low-pass and high-passfilters. A band-reject filter can be madeby summing the outputs of nonoverlap-ping low-pass and high-pass filters. How-ever, such cascaded filters wont work wellfor high-Q filters (extremely sharp band-pass filters) because there is great sensi-tivity to the component values in the in-dividual (uncoupled) filter sections. Insuch cases a high-Q single-stage bandpasscircuit (e.g., the VCVS bandpass circuit
  • ACTIVE FILTERS AND OSCILLATORS276 Chapter 50.1 1.o 10normalized frequencyAnormallzed frequencyB1.o(2.0dB ripple)normalized frequency normalized frequencyDFigure 5.17. Normalized frequency response graphs for the 2-, 4-, 6-, and 8-pole filtersin Table 5.2. The Butterworth and Bessel filters are normalized to 3dB attenuation at unitfrequency, whereas the Chebyshev filters are normalized to 0.5dB and 2dB attenuations.illustrated previously, or the state-variable sensitivity to component values and am-and biquad filters in the next section) plifier gain, and they dont lend themselvesshould be used instead. Even a single-stage well to applications where a tunable filter2-pole filter can produce a response with of stable characteristics is needed.an extremely sharp peak. ~nformationon such filter design is available in thestandard references.VCVS filters minimize the number ofcomponents needed (2 poleslop-amp) andoffer the additional advantages of nonin-verting gain, low output impedance, smallspread of component values, easy adjusta-EXERCISE 5.3Design a 6-pole Chebyshev low-pass VCVSfilter with a 0.5dB passband ripple and lOOHzcutoff frequency fc. What is the attenuation at1.5fc?5.08 State-variable filtersbility of gain, and the ability to operate at The 2-pole filter shown in Figure 5.18 ishigh gain or high Q. They suffer from high far more complex than the VCVS circuits,
  • ACTIVE FILTER CIRCUITS5.08 State-variablefilters 277bandpass&- Figure 5.18. State-variable active filter.but it is popular because of its improvedstability and ease of adjustment. It iscalled a state-variable filter and is availableas an IC from National (the AFlOO andAF150), Burr-Brown (the UAF series), andothers. Because it is a manufacturedmodule, all components except RG, RQ,and the two RFS are built in. Amongits nice properties is the availability ofhigh-pass, low-pass, and bandpass outputsfrom the same circuit; also, its frequencycan be tuned while maintaining constantQ (or, alternatively, constant bandwidth)in the bandpass characteristic. As withthe VCVS realizations, multiple stagescan be cascaded to generate higher-orderfilters.Extensivedesign formulas and tables areprovided by the manufacturers for the useof these convenient ICs. They show howto choose the external resistor values tomake Butterworth, Bessel, and Chebyshevfilters for a wide range of filter orders, forlow-pass, high-pass, bandpass, and band-reject responses. Among the nice featuresof these hybrid ICs is integration of thecapacitors into the module, so that onlyexternal resistors need be added.Bandpass filtersThe state-variable circuit, in spite of itslarge number of components, is a goodchoice for sharp (high-Q) bandpass filters.It has low component sensitivities, doesnot make great demands on op-amp band-width, and is easy to tune. For example, inthe circuit of Figure 5.18, used as a band-pass filter, the two resistors RF set the cen-ter frequency, while RQ and RG togetherdetermine the Q and band-center gain:RF = 5.03 x 107/fo ohmsRQ = 105/(3.48~+G - 1) ohmsRG= 3.16 x ~ O ~ Q / GohmsSo you could make a tunable-frequency,constant-Q filter by using a 2-section vari-able resistor (pot) for RF. Alternatively,you could make RQadjustable, producinga fixed-frequency, variable-Q (and, unfor-tunately, variable-gain) filter.
  • ACTIVE FILTERS AND OSCILLATORS278 Chapter 5(Figure 5.19.-- dently settablebandpassoutA filtergain andC--4-Cinputbandpass- -- Figure 5.20. BiquadwithQ.active filter.indepen-EXERCISE 5.4Calculateresistor values in Figure5.18 to makea bandpass filter with fo = 1kHz, Q = 50, andG = 10.Figure 5.19 shows a useful variant ofthe state-variable bandpass filter. The badnews is that it uses four op-amps; the goodnews is that you can adjust the bandwidth(i.e., Q) without affecting the midbandgain. In fact, both Q and gain are set witha single resistor each. Q, gain, and centerfrequency are completely independent andare given by these simple equations:Biquad filter. A close relative of the statevariable filter is the so-called biquad fil-ter, shown in Figure 5.20. This circuitalso uses three op-amps and can be con-structed from the state-variable ICs men-tioned earlier. It has the interesting prop-erty that you can tune its frequency (viaRF) while maintaining constant bandwidth(rather than constant Q). Here are the de-sign equations:fo = 1/2rRFCBW = 1/2rRBCG = RB/RGfo = 1/2?rR~C The Q is given by fo/BW and equals& = R ~ / R Q RB/RF. AS the center frequency is variedG = R1/& (via RF), the Q varies proportionately,R x 1Ok(noncritical, matched) keeping the bandwidth Qfo constant.
  • ACTIVE FILTER CIRCUITS5.09 Twin-T notch filters 279When you design a biquad filter from Higher order bandpass filtersscratch (rather than with an active filter ICAs with our earlier low-pass and high-that already contains most of the parts),the general procedure goes something like pass filters, it is possible to build higherthis: order bandpass filters with approximatelyI. Choose an op-amp whose bandwidth fTflat bandpass and steep transition to theis at least 10 to 20 times Gfo. stopband.You do this by cascading several lower-2* Pick a rOund-number in order bandpass filters,the tai-the vicinity of lored to realize the desired filter type (But-- - .C = lo/ fo p F terworth, Chebyshev, or whatever). As be-fore, the Butterworth is "maximally flat,"3. Use the desired center frequency to whereas the Chebyshev sacrifices passbandcalculate the corresponding RF from the flatness for steepness of skirts. Both thefirst equation given earlier. VCVS and state-variablelbiquad bandpass4. Use the desired bandwidth to calculate filters just considered are second orderRE from the second equation given ear- (two pole). As You increase the filtersharp-lier. ness by adding sections, you generally de-5. Use the desired band-center gain to grade the transient response and phasecalculate RGfrom the third equation given characteristics. The "bandwidth7 of aearlier. bandpass filter is defined as the width be-You may have to adjust the capacitor tween -3dB points, except for e q u i r i ~ ~ l evalue if the resistor values become awk- filters, for which it is the width betweenwardly large or small. F~~instance, in frequencies at which the response falls outa high-Q filter you may need to increase the passbandC somewhat to keep RE from becoming Can find tables and design proce-too large (or you can use the T-network dLlres for constructing complex filters intrick described in section 4-19). N~~~that standard books on active filters, or in theRF, RE,and RGeach act as op-amp loads, data sheets for active filter ICs. There areand should not become less than, say, 5k, also some very nice filter design programswhen jugglingcomponent values, you may that run on inexpensive workstations (IBMfind it easier to satisfy requirement 1 PC, Macintosh).by decreasingintegrator gain (increase RF)and simultaneously increasingthe inverter- 5-09 Twin-T notch filtersstage gain (increase the 10kfeedback resis-tor). The passive RC network shown in FigureAs an example, suppose we want to 5.21 has infinite attenuation at a frequencymake a filter with the same characteristics fc = 1/2rRC- Infinite attenuation isas in the last exercise. We would begin byprovisionally choosing C = 0.01pE Thenwe find RF = 15.9k (fo = 1kHz) andRE = 796k (Q = 50; BW=20Hz). Finally, inRG = 79.6k (G = 10).I,qoEXERCISE 5.5 Ti-Designa biquadbandpassfilter with fo= 60Hz,-BW=1 Hz, and G = 100. Figure 5.21. Passive twin-T notch filter.
  • ACTIVE FILTERS AND OSCILLATORS280 Chapter 5uncharacteristic of RC filters in general;this one works by effectively adding twosignals that have been shifted 180" out ofphase at the cutoff frequency. It requiresgood matching of components in order toobtain a good null at f,. It is called atwin-T, and it can be used to remove aninterfering signal, such as 6OHz power-line pickup. The problem is that it hasthe same "soft" cutoff characteristics as allpassive RC networks, except, of course,near f,, where its response drops like arock. For example, a twin-T driven bya perfect voltage source is down lOdBat twice (or half) the notch frequencyand 3dB at four times (or one-fourth) thenotch frequency. One trick to improveits notch characteristic is to "activate" itin the manner of a Sallen-and-Key filter(Fig. 5.22). This technique looks good inprinciple, but it is generally disappointingin practice, owing to the impossibility ofmaintaining a good filter null. As the filternotch becomes sharper (more gain in thebootstrap), its null becomes less deep.Twin-T filters are available as prefabmodules, going from 1Hz to SOkHz, withnotch depths of about 60dB (with some de-terioration at high and low temperatures).They are easy to make from components,but resistors and capacitors of good stabil-ity and low temperature coefficient shouldbe used to get a deep and stable notch.One of the components should be madetrimmable.The twin-T filter works fine as a fixed-frequency notch, but it is a horror to maketunable, since three resistors must be si-multaneously adjusted while maintainingconstant ratio. However, the remarkablysimple RC circuit of Figure 5.23A, whichbehaves just like the twin-T, can be ad-justed over a significant range of frequency(at least two octaves) with a single poten-tiometer. Like the twin-T (and most activefilters) it requires some matching of com-ponents; in this case the three capacitorsmust be identical, and the fixed resistormust be exactly six times the bottom (ad-justable) resistor. The notch frequency isthen given byfnotch = 1 1 2 ~ ~JZZFigure 5.23B shows an implementationthat is tunable from 25Hz to 100Hz.The 50k trimmer is adjusted (once) formaximum depth of notch.As with the passive twin-T, this filter(known as a bridged diferentiator) has agently sloping attenuation away from thenotch and infinite attenuation (assumingperfect matching of component values)at the notch frequency. It, too, can be"activated," by bootstrapping the wiper ofthe pot with a voltage gain somewhat lessthan unity (as in Fig. 5.22). Increasing
  • ACTIVE FILTER CIRCUITS5.11 Switched capacitor filters 281trim~n A out50k 10% 464k 1%Figure 5.23. Bridged differentiator tunable-notch filter. The implementation in B tunesfrom 25Hz to 100Hz.the bootstrap gain toward unity narrowsthe notch, but also leads to an undesirableresponse peak on the high frequency sideof the notch, along with a reduction inultimate attenuation.5.10 Gyrator filter realizationsAn interesting type of active filter is madewith gyrators; basically they are used tosubstitute for inductors in traditional filterdesigns. The gyrator circuit shown inFigure 5.24 is popular. Z4will ordinarilybe a capacitor, with the other impedancesFigure 5.24. Gyrator.being replaced by resistors, creating an in-ductor L = k c , where k = R1R3R5/R2.It is claimed that these gyrator-substitutedfiltershave the lowest sensitivity to compo-nent variations, exactly analogous to theirpassive RLC prototypes.5.11 Switched capacitor filtersOne drawback to these state-variable orbiquad filters is the need for accuratelymatched capacitors. If you build thecircuit from op-amps, youve got to getpairs of stable capacitors (not ceramic orelectrolytic), perhaps matched as closelyas 2% for optimum performance. Youalso have to make a lot of connections,since the circuits use at least three op-amps and six resistors for each 2-polesection. Alternatively, you can buy afilter IC, letting the manufacturer figureout how to integrate matched lOOOpFcapacitors into his IC. IC manufacturershave solved those problems, but at a price:The AFlOO "Universal Active Filter" ICfrom National is a hybrid IC and costsabout $10 apiece.
  • ACTIVE FILTERS AND OSCILLATORS282 Chapter 5- 1V,,, = - [V,. dt- RC.Figure 5.25. A. Switched-capacitorintegratorB. conventional integrator.Theres another way to implement theintegrators that are needed in the state-variable or biquad filter. The basic idea isto use MOS analog switches, clocked froman externally applied square wave at somehigh frequency (typically 100 times fasterthan the analog signals of interest), asshown in Figure 5.25. In the figure, thefunny triangular object is a digital inverter,which turns the square wave upside downso that the two MOS switches are closedon opposite halves of the square wave.The circuit is easy to analyze: When S1is closed, C1 charges to G,, i.e., hold-ing charge CIQn; on the alternate halfof the cycle, C1 discharges into the vir-tual ground, transferring its charge to C2.The voltage across C2 therefore changes byan amount AV = AQ/Cz = QnC1/C2.Note that the output voltagechange duringeach cycle of the fast square wave is pro-portional to Q, (which we assume changesonly a small amount during one cycle ofsquare wave), i.e., the circuit is an integra-tor! It is easy to show that the integratorsobey the equations in the figure.EXERCISE 5.6Derive the equations in Figure 5.25There are two important advantages tousing switched capacitors instead of con-ventional integrators. First, as hinted ear-lier, it can be less expensive to implementon silicon: The integrator gain dependsonly on the ratio of two capacitors, noton their individual values. In general itis easy to make a matched pair of any-thing on silicon, but very hard to make asimilar component (resistor or capacitor)of precise value and high stability. As aresult, monolithic switched-capacitor filterICs are very inexpensive - Nationals uni-versal switched-capacitor filter (the MF10)costs $2 (compared with $10 for the con-ventional AF100) and furthermore givesyou two filters in one package!The second advantage of switched-capacitor filters is the ability to tune thefilters frequency (e.g., the center frequencyof a bandpass filter, or the -3dB point ofa low-pass filter) by merely changing thefrequency of the square wave ("clock") in-put. This is because the characteristic fre-quency of a state-variable or biquad filteris proportional to (and depends only on)the integrator gain.Switched-capacitor filters are availablein both dedicated and "universal"configu-rations. The former are prewired with on-chip components to form bandpass or low-passfilters, while the latter have various in-termediate inputs and outputs brought outso you can connect external componentsto make anything you want. The price youpay for universality is a larger IC packageand the need for external resistors. For ex-ample, Nationals self-contained MF4 But-terworth low-pass filter comes in an 8-pinDIP ($1.30), while their MF5 universal fil-ter comes in a 14-pin DIP ($ l .45), requir-ing 2 or 3 external resistors (depending onwhich filterconfiguration you choose). Fig-ure 5.26 shows just how easy it is to use thededicated type.
  • ACTIVE FILTER CIRCUITS5.11 Switched capacitor filters 283sig l n , l - i n MF,-100 o u l l ~sig out(low-pass.f,,, = 1kHz)Figure 5.26Now for the bombshell: Switched-capacitor filters have three annoying char-acteristics, all related and caused by thepresence of the periodic clocking signal.First, there is clock feedthrough, the pres-ence of some output signal (typically about1OmVto 25mV)at the clock frequency, in-dependent of the input signal. Usually thisdoesnt matter, because it is far removedfrom the signal band of interest. If clockfeedthrough is a problem, a simple RC fil-ter usually gets rid of it. The second prob-lem is more subtle: If the input signal hasany frequency components near the clockfrequency, they will be"aliased" down intothe passband. To state it precisely, any in-put signalenergy at a frequency that differsfrom the clock frequency by an amountcorresponding to a frequency in the pass-band will appear (unattenuated!) in thepassband. For example, if you use anMF4 as a lkHz low-pass filter (i.e., setfclock = lOOkHz), any input signal energyin the range of 99kHz- 101kHz will appearin the output band of dc-1kHz. No filter atthe output can remove it! You must makesure the input signal doesnt have energynear the clock frequency. If this isnt natu-rally the case, you can usually use a simpleRC filter, since the clock frequency is typi-cally quite far removed from the passband.The third undesirable effect in switched-capacitor filters is a general reduction insignal dynamic range (an increase in the"noise floor") due to incomplete cancella-tion of MOS switch charge injection (seeSection 3.12). Typical filter ICs have dy-namic ranges of 80dB-90dB.Like any linear circuit, switched-capaci-tor filters (and their op-amp analogs) suf-fer from amplifier errors such as input off-set voltage and l/f low-frequency noise.These can be a problem if, for example,you wish to low-pass filter some low-levelsignal without introducing errors or fluc-tuations in its average dc value. A nicesolution is provided by the clever folks atLinear Technology, who dreamed up theLTC1062 "DC Accurate Low-Pass Filter"(or the MAX280, with improved offsetvoltage). Figure 5.27 shows how you useit. The basic idea is to put the filter out-side the dc path, letting the low-frequencysignal components couple passively to theoutput; the filter grabs onto the signal lineonly at higher frequencies, where it rollsoff the response by shunting the signal tosig outIIL------,Jfclk d k f 3 d ~= fclk/l O0- ;v Figure 5.27. LTC1062 "dc-accurate"low-pass filter.
  • ACTIVE FILTERS AND OSCILLATORS284 Chapter 5ground. The result is zero dc error, andswitched-capacitor-type noise only in thevicinity of the rolloff (Fig. 5.28).0.1 1 1 0 100 l k 10kfrequency (Hz)Figure 5.28Switched-capacitor filter ICs are widelyavailable, from manufacturers such asAMI-Gould, Exar, LTC, National, andEGG-Reticon. Typically you can put thecutoff (or band center) anywhere in therange of dc to a few tens of kilohertz, as setby the clock frequency. The characteristicfrequency is a fixed multiple of the clock,usually 50fclk or 100fclk. Most switched-capacitor filter ICs are intended for low-pass, bandpass, or notch (band-stop) use,though a few (e.g., the AM1 3529) are de-signed as high-pass filters. Note that clockfeedthrough and discrete (clock frequency)output waveform quantization effects areparticularly bothersome in the latter case,since theyre both in-band.OSCILLATORS5.12 Introduction to oscillatorsWithin nearly every electronic instrumentit is essential to have an oscillator or wave-form generator of some sort. Apart fromthe obvious case of signal generators, func-tion generators, and pulsegenerators them-selves, a source of regular oscillations isnecessary in any cyclical measuring instru-ment, in any instrument that initiates mea-surements or processes, and in any instru-ment whose function involves periodicstates or periodic waveforms. That in-cludes just about everything. For exam-ple, oscillators or waveform generators areused in digital multimeters, oscilloscopes,radiofrequency receivers, computers, ev-ery computer peripheral (tape, disk, prin-ter, alphanumeric terminal), nearly everydigital instrument (counters, timers, calcu-lators, and anything with a "multiplexeddisplay"), and a host of other devices toonumerous to mention. A device withoutan oscillator either doesnt do anythingor expects to be driven by something else(which probably contains an oscillator). Itis not an exaggeration to say that an oscil-lator of some sort is as essential an ingre-dient in electronics as a regulated supplyof dc power.Depending on the application, an oscil-lator may be used simply as a source ofregularly spaced pulses (e.g., a "clock" fora digital system), or demands may be madeon its stability and accuracy (e.g., the timebase for a frequency counter), its adjusta-bility (e.g., the local oscillator in a trans-mitter or receiver), or its ability to produceaccurate waveforms (e.g., the horizontal-sweep ramp generator in an oscilloscope).In the following sections we will treatbriefly the most popular oscillators, fromthe simple RC relaxation oscillators to thestable quartz-crystal oscillators. Our aimis not to survey everything in exhaustivedetail, but simply to make you acquaintedwith what is available and what sorts of 0s-cillators are suitable in various situations.5.13 Relaxation oscillatorsA very simple kind of oscillator can bemade by charging a capacitor through a
  • OSCILLATORS5.13 Relaxation oscillators 28:Figure 5.29. Op-amp relaxation oscillator.resistor (or a current source), then dis-charging it rapidly when the voltagereaches some threshold, beginning the cy-cle anew. Alternatively,the external circuitmay be arranged to reverse the polarity ofthe charging current when the threshold isreached, thus generating a triangle waverather than a sawtooth. Oscillators basedon this principle are known as relaxationoscillators. They are inexpensive and sim-ple, and with careful design they can bemade quite stable in frequency.In the past, negative-resistance devicessuch as unijunction transistors and neonbulbs were used to make relaxation oscil-lators, but current practice favors op-ampsor special timer ICs. Figure 5.29 shows aclassic RC relaxation oscillator. The oper-ation is simple: Assume that when poweris first applied, the op-amp output goes topositive saturation (its actually a toss-upwhich way it will go, but it doesnt mat-ter). The capacitor begins charging up to-ward V+, with time constant RC. When itreachesone-half the supply voltage, the op-amp switches into negative saturation (itsa Schmitt trigger), and the capacitor beginsdischarging toward V- with the same timeconstant. The cycle repeats indefinitely,with period 2.2RC, independent of sup-ply voltage. ACMOS output-stage op-amp(see Sections 4.11 and 4.22) was chosenbecause its outputs saturate cleanly at thesupply voltages. The bipolar LMlO alsoswings rail-to-rail and, unlike CMOS op-amps, allows operation at a full f15 volts;however, it has a much lower fT (0.1MHz).EXERCISE 5.7Show that the period is as stated.By using current sources to charge thecapacitor, a good triangle wave can begenerated. A clever circuit using thatprinciple was shown in Section 4.29."CMOS inverters"(each is of a 74HC04;6powered from + 5V)Figure 5.30Sometimes you need an oscillator withvery low noise content (also called "lowsideband noise"). The simple circuit ofFigure 5.30 is good in this respect. Ituses a pair of CMOS inverters (a form ofdigital logic well use extensivelyin Chapters 8-11) connected together toform an RC relaxation oscillator withsquare wave output. Actual measurements
  • ACTIVE FILTERS AND OSCILLATORS286 Chapter 574HCU04 (lower no~se74HC04 (lower current1Figure 5.31. Low-noise oscillator.on this circuit running at IOOkHzshow close-in sideband noise powerdensity (power per square root hertz,measured 1OOHz from the oscillatorfrequency), down at least 85dB rela-tive to the carrier. You sometimes seea similar circuit, but with Rz and Cinterchanged. Although it still oscillatesfine, it is extremely noisy by compari-son.The circuit of Figure 5.31 has even lowernoise and furthermore lets you modulatethe output frequency via an external cur-rent applied to the base of Q1. In thiscircuit Q1operates as an integrator, gener-ating an asymmetrical triangle waveformat its collector. The inverters operate asa noninverting comparator, alternating thepolarity of the base drive each half cy-cle. This circuit has close-in noise densityof - 9 0 d B c / a measured lOOHz fromthe 15OkHz carrier, and -1 0 0 d ~ c / f imeasured at an offset of 300Hz. Al-though these circuits excel in low side-band noise, the oscillation frequency hasmore supply-voltage sensitivity thanother oscillators discussed in this chap-ter.5.14 The classic timer chip: the 555The next level of sophistication involvesthe use of timer or waveform-generator ICsas relaxation oscillators. The most popularchip around is the 555 (and its successors).It is also a misunderstood chip, and weintend to set the record straight with theequivalent circuit shown in Figure 5.32.Some of the symbols belong to the digitalworld (Chapter 8 and following), so youwont become a 555 expert for a while yet.But