Sedra Smith Solutions 4th Edition

and

Solutions

for

Microelectronic

Circuits

FOURTHEDITION

Kenneth

C.

Smith

and

Solutions

for

Microelectronic

Circuits

FOURTHEDITION

Kenneth

C.

Smith

and

Solutions

for

Microelectronic

Circuits

FOURTH EDITION

Sedra

_/

Smith

Kenneth

C.

Smith

University

_of

Toronto

Hong Kong University

_of

Science

and

Technology

New

York

Oxford

OXFORD UNIVERSITY PRESS

Calcutta Cape Town DaresSalaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madras Madrid Melbourne

Mexico City Nairobi Paris Singapore Taipei Tokyo Toronto Warsaw

and associated companies in

Berlin Ibadan

Copyright ©

1998,

1992

by Oxford University

Press, Inc. Published by Oxford University Press, Inc.,

198Madison Avenue, New York, New York, 10016 http://www.oup-usa.org

1-800-334-4249

Oxfordisaregisteredtrademarkof Oxford University Press

Allrightsreserved. Nopartofthis publicationmaybe reproduced, storedinaretrievalsystem,ortransmitted, inany form or byanymeans,

electronic, mechanical,photocopying, recording,orotherwise, without the priorpermissionofOxford University Press. ISBN 0-19-511771-9

98765432

Printedinthe United States of America onacid-freepaper

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II

Yal&es-IOVERVIEW

•

THE MANUAL FORMAT

This manual, "KC's Problems and Solutions", isacollectionofproblemsandsolutionswith compiledanswers,

designed to accompany the Text "Microelectronics Circuits", fourth edition, by Sedra and Smith, Oxford University Press, 1997.

The goal of this Manual, captured in its former subtitle "Trial andSuccess",istomotivate and assist in

thedynamicprocessofactivelearning.

The mechanism provided here includes three parts: I: Problems, II: Solutions, III: Answers.

Specifically:

Part I: Problems, consists ofacollection ofproblems keyedto the Textinavariety of ways:

Most obviously, the problems are grouped according to the Sections of the Text. Possibly less apparentis their relationship bothto segments of the Text andto the end-of-chapter problems con¬

tainedthere,aboutwhichmorewillbe said shortly. As well,the problemsarecodedtoindicateCom¬

plexity (C),Length(L),and Designcontent (D),with an appended asterisk notationto indicatethe

intensity oftheassociated attribute.

PartII: Solutions provides solutions which are relatively detailed. While the presentation is

usuallyinasomewhatcompressedformat,attention has been giventorevealingintermediate analytical and computational steps. As well, additional comments on the interpretation of the Text, and the

direction foradditional workarerelativelycommon.

Part III:Answers allows readers to conveniently evaluate their success at problem solving

withoutthe inevitable hints that skimmingtheactual solution mightprovide.

•

AN APOLOGY TO

THE

USER

-

THE LIKELYHOOD OF ERRORS

InaManualsuchas this, intendedas an aidtothe student inaprocess ofactive learning,the issue of

errors isavery criticalone. Obviously,errorsembodied in the problem solutions presentedherecanbe very

disconcertingtoanyone who is lessthansecurein hisorher knowledge of thesubjectmatter. Thus the reduc¬

tion oferrors has been, andwill continue tobe,ahigh priority. Itis inthe lattersense that your indulgence and helparesought inthe conjoinedprocesses oferror detectionanderror recovery. Certainly Iwillbemost

grateful foryourhelp in reportingthem!

In this process oferror compensation,it is possibly usefultoidentify thetypesoferrorsyou will inevit¬

ablyfind. In order of increasing subtlety and criticality,theyare:

Typographicalerrors:

Therearemanytypes of possibletypographical errors whichcanbe broadly characterizedas

omission,exchange,and replacement, either inword,number,symbol, phraseor sentence con¬ structs. While unnecessarilyconfusing,they usually have thevirtueofbeing easilydetectable and correctable incontext. To assist the detection process at its lowest level, solutions are

relativelydetailed with lots of intermediatecalculations,relativelyconsistentvariable naming, and relatively completeuseof units for numerical results. Unfortunately, however, you may

possibly findmissingsolution lines,aswell.

Arithmetic Errors:

These occur betweenstepsina computationas a result ofcalculator misuseor transcription

error in the originalwork. They aredistinguishedfrom typographicalerrors by the fact that they propagate. They can be detected only by carefully checking and reproducing the

preceedingsubstitutional and computationalsteps. Often the integrity of the following solu¬

tionstructureremains,butnotalways. One ofthegenericmethods Iusetohelpensure struc¬

turalintegrityisanoveralltestforphysicalplausibility,orreasonableness, though this is often

notdocumented. However,anexplicit demonstration of theattempttorevealsuch errorsisin the useof frequent Check comments which typically employ a recent result ina

somewhat-global verificationprocess. Incidentally,this isagood approach

_for

you touseinyour solu¬ tions,aswell!

ConceptualErrors:

Theseareoftwokinds,either localorglobal. Theformer occur usually as aresultofmisin¬

terpretation ofasymbol,orofthe scopeofaquestion. Occasionallyyoumay findapieceof a questionthat was not answeredat all,or answered inaless than complete fashion. The

only virtue of this sin isthat itis normally detectable. Onafarmoreserious scale willbe the

occasional occurrence of totally wrong solution methods. These are quite insidious and

confusing to anovice, since they caneasily bemistakento be avalid alternative approach.

While thesearerelativelyunlikely, theyarealmostcertainlypresent.

For allof theseerrors,pleaseaccept myapologies. WhileIhave utilizedmanyapproaches tominimiz¬ ing them, thelimitations of availabletimeandresourceshaveproduced theresult youseebeforeyou. All that remainstobe said, again, is that Ibeg your indulgence, and look forwardtoyourhelpinimproving the situa¬ tion!

•

SOLUTION-PRESENTATION FORMAT

As youwillnote,the solution formatinPartII:SolutionsinthisManualisoften less-than-ideal, being

basically a run-onstring ofwhat would ideally beseparatedlines. This choicewas madeinview of theneed

toreducetheoverallsizeofthe Manualwhilemaking the solutionrelativelycomplete, with lots ofintermedi¬

atesteps. Obviouslyfewerstepsina morestructured formatwouldbe more readable, and certainlymorebeau¬

tiful, but probably lessinformative! To helpin interpreting the stringformat, asomewhat-variableattemptat

theuseof bridging language,sentence structure,andpunctuationhas been made. Forinstructive variety,some

solutionsarepresentedmoreelegantly,includingmoreexplicit language, bothwithrespect tophysicalarrange¬

mentanddescription,aswellasmathematicalstructure.

IIADVICE TO THE STUDENT

•

COPING WITH ERRORS

Asnoted earlier, Iregretthat youarelikelytofinderrorsin thesolutionspresented here. Myregret con¬ cerns thefactthat Iamdistressingly awarethat anerrorofminecanbedifficulttoseparatefromaconceptual

difficultyyoumay have. The onlypositivething Ican say is that learningtocope withimperfectionis "good

for thesoul". Certainlyalot hasbeenwritten aboutthepositiveeffects ofmoderatestress onmental (andphy¬

Butwhat canyou do? Certainly comparenoteswithyour colleagues! Revel inthe possibility that this

Manualisan ideal candidate forleisure-timeconversation, afterahard day in classorstudy hall! More seri¬

ously,it is certain that aminor degreeof cross-checkingwith others cancertainly avoid wasted time. Then,

and even on your own,if your solution andmine differ, certainly bepreparedfor aquick check of obvious things

-

typos,arithmetic,etc. If you do notfindthe source of thediscrepancyquickly, goontoanotherone,

as a way to test yourself. If you have trouble there as well, suspect your own need for more reading and review of theText. Otherwiseabitmorework on checkingthe solutions isappropriate. Bearinmind, that it isregrettable, buttrue,that thereare errorsintheseSolutions. Feel goodaboutyourselfinfindingthem! Feel sadness (andcompassion) for myfailure to do so! Inany case, report them (throughour WWW page). We

will be grateful!

•

THE ROLE OF CIRCUIT-RELATED SKETCHING IN

ELECTRONICS-PROBLEM SOLUTION

Themerits ofsketching inthesolution ofproblems inElectronicscannotbeoveremphasized! Properly

organized,sketching constitutes a highly-efficient information-transmission mechanism, a language in which relativelycomplexissues in electronics designand analysiscanbepresentedandcommunicated. As well, par¬

ticularly for those broadly conversant with its idioms anddialects, circuit-related sketching can provide the

basis for anenrichingaesthetic experience, manifestingakindof"poetry",or"music fortheeyes",sotospeak. Thisidea isavery important elementinthe graphicpresentation styleseenintheText"MicroelectronicsCir¬ cuits", where a lotof useis made of schematic-circuit andwaveformsketches. As well, the roleof sketching

in laboratoryworkis madequite explicit in the associatedLaboratory Manual"Laboratory Explorations"

.

Regrettably, here in thisManual,"TrialandSuccess",it has notbeenpossibletoproperly present any¬

thing likeacomplete view of the potential of sketchingaslanguage. Therearetworeasons,oneeconomic,and

onepaedogogical.

The paedogogical issue appears first in problem presentations, in the use of circuit sketches in PartI:

Problems. Thus, there, you see some problems posed almost exclusively in tenns of circuit sketches. To

betterappreciate circuit sketches as language, pausefor a moment to reflect on how to presentproblems like

these,withoutasketch! For largeelectronic assemblages, thiscanbeavery dauntingproblem: Forexample, for those ofyoufamiliar with SPICEas aCircuitSimulator,contrastthe sterility of the SPICEinput file

-

the connection-specification list used in basic simulators (for example in Appendix D of the Text)

-

with the

aesthetic elementsofthe circuit sketch itattemptstodescribe. Itis for thisreasonthat schematic-circuitinput

to circuit simulators is becoming more common, as you can see, for example,in the Electronic Workbench

material,byInteractive Technologies,Inc.,providedwith the Text.

It is for exactly this reason that the graphical user interface provided in "Electronic Workbench" is recommended for practicalwork associated withthe Text,particularly as areplacement for (or adjunct to) a

"hands-on" laboratory.

Onthe other hand,tocommunicate situational detailusingspoken andwritten languageis alsoimportant!

Certainly as a student of Electronics, or of engineering ingeneral, you must be able to handle problems

presented inspoken-language style. However one

_of

the best ways

_of

dealing with such a word problem

presentedtoyou, is

_first

toprepareasketch of the situation described. Incidentally, for apersonproficient in the process of circuit sketching, suchasketch would normally becreatedincrementally asthe textdescription

isscanned, then augmented and checked later,asthetextisreread.

Inspite of all this, economic issueassociated with the creation of well-formed drawings inapublished

work suchasthis isa very realone. Regrettably, because of the relatively-highcostofproductionandpresen¬ tation,there are farfewer sketch-based problems providedtoyou in thisManualthan goodpaedogogywould

suggest. In particular,as well, thereisalotof referencetoexisting figuresinthe Text. Notice,however,that

this isagood exampleofanimportant engineering principle,that reuseofacostly resourceisa logicalpartof agood engineering solutiontoany(engineering) problem!

Morecritically, interms ofillustratingthe beststylefor you toemulate, Imust emphasize that there are

far

too

_few

sketches usedinthe Solutions part of this Manual. The ones seen usually arise inresponse to a

directrequestforasketch. While this is paedogogicallywrong, it iseconomically necessary. More concretely,

inyourwork in Electronics, normally without these constraints, the very best and most-effectivestyle Iwould recommend isto always try asketch. "When in doubt, sketch", would notbetoostrong arecommendationto

follow. Notice that in the Text,an aspect ofthis idea is embedded inthe recurring idea of "workingon the diagram" that appears there, for example on pages 248 (numerically) and 267 (analytically). As isillustrated occasionally in the Solutions to follow, it is generally a very good idea to notatecircuit sketches with small calculationsor notations, whose role it isto present,memorably, incontext,circuit-specific data. For example,

aconvenient way to notateeventtiming on digitalor pseudo-digitalcircuits is illustratedon page 364 here in

the Solutions. Ina very broadsense, ingeneral, butcertainly inthe solution of the relatively intricate prob¬ lems which appear inthis Manual, first try tocapture the specified situationas asketch. Then,ator nearthe

appropriate nodeof the circuit, possibly connected byapointer lineorother referencenotation, do the calcula¬ tions that you can doeasily, suchas those,for example,relativetobias-point analysis, signal limits,etc. Use these (possibly approximate) results, then,toguideyour moreelegantandformal solution, and,as well,topro¬ vide arough checkonthe plausibility ofyourfinal results.

•

SOLVING A

PROBLEM

-

SOME

GENERAL

ADVICE

Readthe Problem carefully to seeifyouunderstand thegeneralideaitattemptstopresent. As notedear¬

lier,try topresentthe situation describedinalabelled sketch. Thepreparation of this sketch may besomewhat

iterative

—

firstaroughidea withsome labels(tobe

_left

inplaceonyourpage), thena

_refined

version added, with complete labelling. Note the idea

_of

progression withouterasure. Asa generalrule, don't eliminateear¬

lierwork,either by erasure or abandonment, for itrepresentsthe pathof your progress,thehistory of the pro¬

cess ofyour "learningtolearn",the shouldersonwhichyour finalsolutionstands, theavailableevidenceofthe

logicalprocess youcan usewhenreviewingyour work, andso on. Perhaps,later, you maywant to makeyour

solution more beautiful for final presentation, but this is often not necessary in the engineering workplace,

except for very formalreportsrequiredby top management. Noticealso that inthe phrase "to be

_left

in place",

Ihave attempted to suggest avoiding the scraps of paper, the legendary "back of theenvelope", and so on,

which are relatively inappropriate ina modern responsible decision-path-traceable engineering-design process.

Itis for thesereasons that workingengineers oftenuse a bound "Engineering Workbook" torecord their pro¬

gress.

• Ingeneral,itis oftenagoodideatoredrawthe circuitpresented inthe originalproblem specification(or

photocopy it with segmentationandenlargement, if complex),andthen doyour work while lookingatit,

andworkingonit, ifthatis convenient.

•

Prepare aninformalsummary table of thesymbolic and numeric values ofspecified variables andofthe valueswhichyoumust findinyour calculations. Itis often usefultoorganize the solutiontoyour prob¬

lem by first preparinga tabular format inwhich you might wish to present the results. Certainly from the pointof view of real engineering problem solving, this isa very credible and effective way toboth organize your thinking and toprepare for the ultimatepresentationof your work to the "boss". Bearin mind, ofcourse,that while all of this isa good idea(elseIwould nothave written about it!), it is often difficultto do,andmay be overkillina simplesituation. Whether youusethe idea,ornot,dependson

your particular situation, in the same sense as does the use of refined sketches. If it helps, do it! Notice,in general,thatmostof life'sproblemsarcamenabletomorethanonesolutionstyle!

•

As a generalization of the detailed comments above, always attempt to make the specifications of any

problem you face, whether here, now, or later in real life, as explicit as you can. That is what the

sketchesand tables arc allabout! Set yourself up,asmuchas youcan,for amultisensory input,for the possibility thatarapidreviewofthe situationthrough, say, aquick glanceat acircuit diagramcan crys-talize the issue beforeyou, thereby avoiding the forgotten fact, the potential omission, the unnecessary rework,etc.

IIIGENERAL

INFORMATION

•

RELATIONSHIP OF THE PROBLEMS HERE TO THE EXERCISES

AND

PROBLEMS

IN THE TEXT

Theproblemsinthis Manualareintentionally coupled inavariety of ways to the ExercisesandProb¬ lemsinthe Text:

•

First, you will see that a fraction of the Problems aredirect variations of those inthe Text. By and large,these canbeseentorepresentseveral situations: Oneis of the acknowledged existence ofasetof relatively basic, classic problems that bear repeating. Anotheriswhereproblem variety insome subject is somehow limited. Another isa concern for representing, by example,ageneral approachto creating numerically-different problems inan areawhere that isoftennotstraightforward. Another isto provide,

in conjunction with the Exercises or Problems inthe Text, an opportunity tosee the bigger pictureas

influenced by aparticular set of circuit-design parameters, and thereby experience the issue of design variants,by viewingafewsample pointsinarelated "designspace".

• Second, a fraction of the Problemspresentedare coupled moresubtley to those in theText by being

expansions, extensions,ordecompositionsofthem. By expansion,Iimplythemoredetailedexamination

of an interesting aspect of the Text problem. By extension, Iimply the posing of questions which enlarge the domain of analysis, of design,or of application. Bydecomposition, Irefer to the reuseof

selected parts ofaTextproblem,oftenover awiderdomain of deviceparameters,loads,frequencies,etc.

The enlargeddimensionality implied by the words expansion and extension isindicativeof thefact that the Problemspresented areoften relatively complex. The arguments, insupport of the intendedcom¬

plexity,are many:that reallifeis complex, that complexity mayreinforcein-depthand long-chain think¬ ing, that complexity by added partsimplieschoice, and,Anally, that the existence of Solutions asaids, allareintendedtojustify andsupportacomplexsituation that could otherwise be quite difficult.

•

AIDS TO

SIMULATION

You maynoticethat alarge numberof the circuit schematics usedin this Manualhave been prepared

using software associated with "Electronics Workbench" by Interactive Image Technologies, Ltd. A major

benefit ofthisapproach istheavailability ofthese circuits inaform-compatiblewith simulationusingElectron¬

ics Workbench. In thenearfuture,weproposedtomake such material selectively availablethroughourWWW

site {sedrasmith.org} andinaCD-ROM.

•

SOME FACTS

OF

INTEREST

ACKNOWLEDGEMENTS

Iwould liketoexpress myparticularappreciationtosomeof thosewho madethis workpossible:

• To Laura Fujino, the love of my life, Iam indebted for countless hours of discussion on the

processes of problem creation andpresentation, aswell as for the final camera-ready production,

both of this and the firstedition.

• To RaymundoTangTang,who haspreparedamajorityof thecircuitschematics youwillsee, both intheProblemsandintheSolutions using ElectronicsWorkbench.

•

To Franky Leung, who has solved all of our continuing computer problems, both hardware and software.

• To theComputerSystemsResearchInstituteattheUniversity ofToronto,whose facilitiesandser¬

viceswereusedsointensively in preparingthefirsteditionofthiswork.

• To the Department of Electrical and Electronic Engineeringat the Hong Kong University of Sci¬

enceandTechnology,wherethissecondeditionwasprepared.

•

Tothese and othersmoreperipherally involved, Iam mostgrateful.

But, fortheerrors andomissions,youwilldoubtlessfind here, Ialoneamresponsible. For them, Imust

againapologize, and thankyouinadvanceforyour tolerance and forebearanceinenduring andreportingthem.

Kenneth CarlessSmith,PhD,LFIEEE,PEng

Departmentof Electrical and Computer Engineering University of Toronto

10King's College Rd. Toronto, Ontario, M5S1A4

Canada

FAX: 416 971 2286

Email: [email protected]

PROBLEMS

pages

1

to

131

CHARACTERIZATION CODE

C

Complex

D

Design

L

Long

Where

suffixes

_*

and

_**

indicate

indicate

more and much more

INTRODUCTION

TO

ELECTRONICS

SECTION

1.1: SIGNALS

L

1.1 Forthe following circuits, identify thesignal-sourceform, whether Thevenin or Norton,and provide,in anorganized two-columntable,sketchesofboth standard forms. Whereappropriate,reducethecircuitto

its single-source,single-impedance form. Be carefulwith the polaritiesofvoltageandcurrent generators.

Q1-1a R1 R2 -VSA/

-

Wv-vs(t) Q1-1c 2 s/yVs(t) C Q1-1b Q1-1d 2

—

•

v/yVstt) Q1-1e w vOJVS(t) Q1-1h

SECTION 1.2:

FREQUENCY

SPECTRUM OF SIGNALS

1.2 For the following signals whose frequency is expressed either inradians per second or Hertz, find the

corresponding value in the alternate form. Provide your answers in a neat five-column format, a line labelatthe left,Hznextleft,rad/satmiddle right,and 2 blank columnsat thefarright.

(a) 60Hz, (b) 754 rad/s,(c) 2513.3 rad/s,(d) 1010 kHz,(e)97.30 MHz, (f) 1Hz,(g) 377 rad/s, (h) 1

rad/s, (i) 1GHz,(j)400 GHz.

-L

1.3 Foreachpartoftheprevious question findthe periodofthesignal. Express it insecondsintwo ways,

using 3 significant digits:

a) with oneleft ofthe decimal point and withanappropriate powerof 10,and

b) using the standard names for subdivisions (seconds(s), milliseconds(ms), microseconds(ps), nanoseconds(ns),picoseconds(ps),femptoseconds (fs)).

Create youranswerintwoways:

i) directly from the specifications giveninthepreviousquestion,

ii) theeasiest way,usingdatafromyour table.

Use the 2 far-right columns in theanswer table of PI.2 above for youranswer (firstusing powers of 10, then names).

1.4 An oscillator,operating inaninstrumentat 10.7 MHz, issaidtobestablewithin3 parts-per-million

per-degree-Celsius variation intemperature. What change ofperiodwould youexpectfromthemomentit is firstturnedonina roomat25°C,untilit finally reachesitsinternaloperatingtemperatureat50°C? 1.5 Three individuals, when askedtocharacterize differentsine-wavesignals presentedtothem,state:

a) 0.20Vpeak-to-peakat 1000Hz, b) 2.12V rms,witha20jisecperiod,

c) 1.0 Vpeakamplitude, andafrequencyof 12.57 rad/s.

Find the amplitude andfrequencyratios which characterize the3signals usinga)as thereference. 1.6 What fraction of theenergy inasquarewaveoffrequency

_/

and 10 V amplitude is containedinharmon¬

ics above

_9/

? atandabove 3

_/

?

1.7 An ideal low-pass filter with cutoff frequency

_/

passesall signalenergy below/,and rejects all signal

energy above. Findthecutoff frequency ofalow-pass filter such that square wavesat 1khz and 2kHz, withamplitudesof 1.1V and 1.2V respectively, provide nearlythesameoutput-power levels.

SECTION 1.3: ANALOG AND DIGITAL SIGNALS

1.8 Asquare waveatfrequency

_/

canbe consideredtobe theresultof samplingasinewaveoffrequency

_/

twice percycle (at auniformrateof 2/), and extending the measured value until the nextsample. For

this interpretation, characterize the result of samplingaIVrmssinewave:

a) exactlyatitspeaks,

b) at90°fromanegative-goingzerocrossing,

c) at45°fromapositive-goingzerocrossing.

Whatwaveformresultsforcase a)ifthesamplingfrequency is i) doubled, ii)halved?

1.9 A designerwants to representalldecimalnumbers from 0to33. How many bitsareneeded? What are

the binaryrepresentationsfor 0, 7,15,31and 33? What is the largest value thatcanbe represented?

C

1.10 A second designer involvedincreatingalow-cost version of theapplicationsituationintroduced inP1.9 above, realizes that only the even numbers from 0 to 30 must be represented. How many bits are

needed? Whatarethe binary representations shecan usefor 0, 8, 14, 28? What is the largest value that

canberepresentedin thislow-costversion?

-2-1.11 Consider the 8-bit digital-signal representation shown in Figure 1.8ofthe Text. If the most-significant

bit (MSB)issent first (at time0),what value D is represented ifa) all bitsarepositive,b) all but the

MSB ispositive; and the MSBhasanegative weight (that is, b„ is negative,while

_b\

through

_blt

arc

positive). In eachcase,what is the valuerepresented ifthe MSBis reversed(thusbecoming logic0)?

1.12 Reconsiderthe situation presentedin PI.11above,butwith the MSB (b0)appearing lastin time. What isthe value ofD

,

thenumber represented? What value D isrepresentedifa)allbitsarepositive,b)the

MSB(alone)hasanegative weight,c)the MSB is consideredto bea sign bit withzero weight, 1 being the negative sign. What values are represented in each of these three interpretations, if the MSB is reversed(thatis,totakeonthe logicvalue 1)?

1.13 For a 5-bit digital representation, what are the largest and smallest numbers that can be represented?

What decimal value Dcorrespondstothe 5-bit number 01101 writteninconventionalform. Inamodern instrumentation system usinga 3V supply, the digit voltages are 0V and 3V for logic 0 and logic 1

respectively. Foranassociated 5-bit DAC circuit, the most-significantdigit(alone)producesan outputof

2/1 = 1.5V. To what outputvoltage does thenumber 01101correspond? What is the highest available

voltage-output value? What is the smallest non-zero output value? What availableoutput is closest to

1.00V? Towhat digital inputtothe DAC doesthis correspond?

SECTION 1.4: AMPLIFIERS

1.14 Measurements madeon asetofamplifiers,labelleda)throughe),provide the attributes tabulatedbelow.

Calculatethose missingelements neededtocharacterize each. Each amplifier uses

±

10Vsupplies with

nodc ground connection. Signalconnections arewith respect toground,however. Signalsareassumed

tobesinewaveswhosepeak valuesaregiven. Amplifier a)has been completelycharacterizedby way of

example.

Supply Input Output 4, Ap Eff.

#

/+

/_ P

w

_<1

Rin

Pin

_lO

Ploud

P_out ratio dB ratio dB ratio dB %

mA mA raW mV _Pa k£2 (Iw V mA mW V/mV mA/|lA mW/pw

a 3 3 60 1 i i .<XK>5 2 20 0.1 20 2 66 20 86

4xl04

76 33

b 1 20 .01 1 1

c

103

0.1 10 10 10

d 2(X) .01 10 40 0.2

c 10 0.5 10 0.1 20

1.15 An amplifier operatingfrom

±

10Vsupplieshasalineartransfercharacteristic passing through(0,0),but

withoutput saturation at +7V and -9V. If the amplifier gain is 50V/V, what is the largest sine-wave

-inputhavingnodccomponent,thatcanbeappliedwithout clipping?

1.16 For the situation describedin PI.15 above, it is desiredtohave the largest possible undippedoutput, and adc componentcan be tolerated. What isthe rmsvalue of the largest possible sinewave at the output

andatthe input? What isthedcoutputcomponent? Towhatdcvaluemusttheinput be biassed? 1.17 Anamplifier havingatransfercharacteristic

D0 =8

-

4(U/

-

l)2

with

1£_D/

<

t)o

+

1

.

D0 ÿ₀

istooperate withadcoutputvoltageof 4V. Foran outputsignalof <1 voltpeak amplitudeat theinput

frequency to, what % second-harmonic distortion results? (HINT:Sec Problem 1.15 on page 30inthe Text)

1.18 RepeatExample1.2onpage17 ofthe Text, forthe situation in which Do =5

-

10"10

e40"'

for_x>i

_>

0and_{v0 £ D/} with theoutputbiassedat

_VG

= +S2volts. Find V), L+, L-, the peak magni¬ tude

_Vi

oftheoutputsinewaveallowed,andthe voltage gain

_Au

atthebiaspoint.

SECTION 1.5:

CIRCUIT MODELS FOR AMPLIFIERS

1.19 A voltage amplifier connectedtoaparticularsource

_vs

hasano-load voltage gain of 100 V/V and again of70 V/Vwitha1 k£2 load. What is itsoutputresistance? What is its gainwitha500£2load?

1.20 A voltage amplifier, when connectedtoa 10k£2source,hasanoverall gain(o„A>.f) of 1667 V/V. When

asecond identical amplifierisconnectedinparalleltothesame source,thecorrespondinggain for eachis

foundtobe 909 V/V. Estimate theinputresistance of theamplifiers.

1.21 A voltage amplifier has anopen-circuit voltage gainof A„„, aninput resistance /?,

,

andan output resis¬

tance

_R0.

Find the conditionunder which acascade of n of theseamplifiers has the same open-circuit gainas asingle amplifier.

D

1.22 A designis required ofavoltageamplifier tooperatebetweena 1M£2source anda 100 £2 load. You

have two amplifiers, each with again 10 V/V, butwith the input andoutput resistances ofA!being 1

M£2and 10 k£2,respectively, andof

_A2

being 10 k£2and 100 £2,respectively. There are two possible

ways to connect the two amplifiers betweenthe source and load. Which is best? What isthe highest

overallgain? Contrastthis with the gain using only oneamplifieratatime? Ifagoodfairy grantedyou

onewish

—

todouble(or halve)anyonepropertyof either amplifier

—

isthere abest choicetobe made? Why?

1.23 A voltage amplifier withabasic gain of80dB,hasan outputresistance of 10k£2. What is the voltage gain which results for loads of 1M£2, 10 k£2, 10£2? What is its equivalent transconductance when operating intoazero-ohmload?

DL*

1.24 This problem is intendedto provideyou with a basis for insight into Problem 1.21 on page 51in the

Text.

-(a) Evaluate the gain v„/vs for each of the amplifier stages described there interposed individually betweenthe statedsource and load.

(b) Fromthe processand results of(a),identify where the least loss occurs,whether at the source or

load, for each amplifier. Use these observationsto make 3 listsof amplifiers (inwhich amplifiers

areputindescending order ofmerit), as input-stagecoupler,output-stagecoupler, andas provider ofgain.

(c) Now consider adesignwith apairof amplifiers,picking,as input,anamplifierhighonlist 1 and

reasonableon list3,and,as output, onehighon list 2 and reasonableon list 3. (d) Whatis the highest gainyoucan get fromtwostages?

(e) Reconsiderthe process outlined above,inan attempt toseeifyoucouldreach thesameconclusion by simply thinkingabout it, rather than by makingexplicit lists.

DL*

1.25 You arerequiredtodesignatwo-stage currentamplifier tooperatebetweenacurrent source havinga 10 kfl internal resistance andaloadof 10k£2. Threetypesof amplifierstageareavailable:

(1) A low-input-resistancetype,with

_Rt

=10 £2,R„ = 10kfi and

_Ais

=100A/A (2) Ahigh-gaintype,withRj=10 k£2,R„ = 1 k£2and

_Ais

=1000A/A

(3) Ahigh-outputresistancetype,with /?; =10 kQ,R„ =100kQand

_Ais

=100A/A. How manytwo-stage amplifiercombinationsarethere? Rank them by available gain.

D

1.26 Reconsider Problem

amplifiers) which is

.25 above. Rank the 3 amplifiers on the basis of afigure

_of

merit (for current

Ais

XR„

-

-

-

.

Selectthe two amplifiers oflowest rank, anduseonly those types to

re¬

design a two-stage current amplifier of highest-possible gain between a 10kfisource and 10k£2load.

Whatis the highest availablegain? D

1.27 Reconsider the threeamplifiersintroduced in Problem 1.25 aboveastransconductanceamplifiers. Restate

the specifications of each as atransconductance amplifier. Identify afigure of meritfor atransconduc¬

tance amplifier like that suggested inProblem 1.26 above for a current amplifier. Usethis to rank the threeastransconductance amplifiers.

1.28 Using the results of Example 1.4 (on page 25 of the Text) for a BJT, characterize its use with E

grounded, B as input andC as output, bothas acurrent amplifier and as atransconductance amplifier. Use

_rn

= 5k£2and (3 =200. Whatare

_Ais

and

_Gm

respectively?

1.29 For the BJT circuit shown in FigureEl.14onpage 28 ofthe Text, findexpressionsfor the voltage gain

Vj/Vfr and the resistanceseenby resistor

Re

connected between the emitter and ground. (Hint: tofindthe latter,use a testvoltageasinExamplel.4 inthe Text)

1.30 For the BJTcircuitshownin FigureEl.14on page 28of the Text, findexpressions for the voltage gain

Vt/vb

,

and the resistanceseenby

_RL

.

1.31 Use the results ofExercise 1.14 onpage 28 of the Text and those from P1.29 above, to findanexpres¬

sionfor thevoltage gain when asource v,

,

whose sourceresistance is

_Rs

,

isconnectedtothe base.

What is the value of

Rs

for which VgA>s is half the value of

ve/vh

foundinPI.29above.

-SECTION 1.6:

_FREQUENCY

RESPONSE OF AMPLIFIERS

1.32 In passing throughaparticular amplifier,aninput sine waveof 2 mV peak-to-peak amplitudeat 1kHz

emerges with thesame wave shape, an amplitude increased to 2V peak,andevidence that is hasbeen

delayed by 0.2ms. For theamplifier transmission, what is themagnitude? What isthephase?

1.33 A direct-coupled(dc)amplifier (onewhose responseextends downtozero frequency)hasanupper 3 dB

frequency of 100kHz. What is its bandwidth? When coupledtoasignalsource usingacapacitor, its frequency response is foundtodeteriorateat low frequencies, the response being reduced by 3 dB at20

kHz. What is the overallbandwidthofthisarrangement?

1.34 ConsiderthecircuitsofFig.1.22(onpage31oftheText). Inaparticularsystemapplication,a newout¬ put Vou, =Vj

-

V„ is createdin eachcase. What is thetype ofthecorrespondingoutput Vou, for circuit

a)? circuitb)?

1.35 An amplifier, consideredtohave ahigh-frequency responsewhichcanbe characterizedas STC, is meas¬

uredat 3frequencies, 1kHz, 10kHz and20 kHz,atwhichthegain magnitude is foundtobe 11 x

lO3,

8

x

103,

and 4x 10

3V/V,

respectively. Estimate the 3 dB frequency and thefrequency at which the gain

canbeexpectedtodropto 1. At what frequencydoesaphaselag of60°or soappear? CDL

1.36 Considerone stageofthe amplifiercascadeinFig.P1.37(onpage54)oftheText. At what frequency is

its response3dB down from themidband value? For2stagesincascade,what docs the 3 dB frequency

become? Foramodified2-stagecascadeinwhich oneof the resistors isdecreasedto kR (k<l),find a

processtocalculate what the frequency becomes. Forwhat value ofk doesfjjg ofthe modified 2-stage

0.95 „

cascadehaveavalue 2nRC

1.37 A voltage amplifier has the transfer function

T(f)₌ 1000

1 +j

105

1

+

10 j

_f

On a Bode magnitude plot, sketch asymtotes representingeach of the terms shown. Then sketch the

overall (sum) response. What do each ofthe three terms contribute(indB) at

_/

=1,10, 100,

104,

10s

and

106

Hz. What isthe overallresponseat thesame frequencies? What isthe 3 dB bandwidthof the

amplifier? Overwhat frequency rangeisthe phase0

±

6°?

1.38 Avoltageamplifier has the transfer function

101

Jf

T(f) =

[if

+

io5)

JL

₁₀

+

i

Note that this is not in the most useful standard form. Without converting it explicitly, what are the upper and lower 3 dB frequencies and what is the midband gain (i.e. the gain between the upper and lowercutoffs)? Now reduce T(f) to standard form, and consider the same questions: Do you havea

preference for oneformoverthe other? D

1.39 Consider thetransconductance amplifier inTable 1.1(onpage 24) of the Text driving aload capacitance of C

_-

lOpF and driven by a 10 kQ source,

_Rs.

Findexpressions for the gain at low frequencies and

the associated upper 3 dB frequency. For oneparticular amplifying device,namelya BJT, both /?,• and

-6-R„areinversely proportionaltobiascurrent/,while G„, is directly proportiontoit. Typically,

Ri

=ÿj~,

R„ = and

_Gm

=40/

Designthe circuit biascurrentso that the resultingupper 3dB frequency is 1MHzor more. What is the midband gain

AM

that results? Using the expressions you have derived, find the product of gain and

bandwidth. What is interesting about it? Use this resultto state the gainofan amplifier whose biasis adjusted fora3dBfrequencyof10 MHz. Whatcurrentis needed?

DC

1.40 Considerthe circuit of Figure 1.25 ofthe Text in whichthe outputis augmented intwo ways: capacitor

C2

couples

Rl

to anotherload resistor /?2, and C, (asmall capacitance)is shunted by arelatively large capacitor

_C\.

Here,

_Rs

= 20k£2, Rj

₌

lOOkil,R„ = 20012,

_RL

₌ lk£2,

_R2=

lk!2 and p=100V/V

.

Whatis the nominalgainatmidband frequencies, where the effects of

_C\

and

_C2

are ignored, that is,Cj

is consideredtobe very small, and

_C2

isconsideredtobe very large? Find values for C,and

_C2

sothat theamplifierhasarelativelynarrowmidband region extending from 20kHzto80kHz. What gain results

at 40kHz? Over what frequency range is the gain within ldB of the midband value. Here, the 3dB bandwidthisdesignedto be80

-

20= 60kHz. Whatisthe ldBbandwidth? (Hint: Followthegeneral

appraoch implied in Equation 1.24onpage34 oftheTextandin Exercise 1.17on page38there. 1.41 Find the transfer function of thecircuitshown: Sketchits magnitude and phase.

SECTION 1.7: THE DIGITAL LOGIC INVERTER

D

1.42 An amplifier, operatingfroma5V supply limits 1.5Vfromthe uppersupply rail(at 5V)and 0.5Vfrom thelowerrail(at 0V). It hasarelatively constantgainof -10V/V in the transition regionwhich iscen¬

tered at_{"0/ = 2.5V. Using} the three-segment-transfer-characteristic inverter model of Fig. 1.29of the Text,find

_{V0l< Voh> Vil>}

_Vih>

NMl,

_NMh.

Howwide isthe transitionregion? If the transitionregion is doubledin width duetoamanufacturing error, what do the noisemargins become? By what factordo theychange? Ifyou,as adesigner hadachoice of relocating thecenterthe transition region, what value wouldyouchoseinordertoequalizetheimpactoflower gainonnoise margins?

1.43 For aparticular logicinvertermodelled by the circuit of Fig.1.31c)ofthe Text,

_VDD

= 5V, R ₌ lk£2,

Ron

-

50£2, V_0ffSel

-

50mV. Find

_V0h

and

_VOL.

Whatstatic power is dissipated forinput high? For

input low? Ifthe switch also hasa5k£2 leakage,what does Vqh become? What isthe average static power loss of this "leaky inverter" for 50% dutycycle?

1.44 Foralogic inverter whoseoperationismodelled by the complementary-switch circuits of Fig.1.32 of the

Text,

_Vdd

~ 5V and R„„= 50£2. Find VOL, Vow, and the average static power dissipation of the

-7-inverter. If eachswitchhasa5kO leakage,what do

_V0l

,

_Voh

and theaveragepowerbecome? D

1.45 Consider the switched-current logic represented in Fig.1.33 oftheText. For

_Iee

—

4mA,what values of

Rc

iand

Ret

arerequiredto achieve a IVlogic swing? For

Vcc

-

OV, what valuesof

Vol

and Vqh

result? To achieve equal noise margins, at what value of \)/ should the switch be made to operate? (Note that the switch is usually modelledtohave

_V/l

=Vm-) If

_Vee

—

5V, what isthe average static

power dissipation in the circuit? Provided operation is otherwise OK, does switch resistance affect the

total power dissipation of thegate?

1.46 Reconsider the situationdescribed inPi.44aboveinwhich the logic gate, loaded by a lOpF capacitor,

operates at 100MHz. What is the dynamic power dissipation which results? Estimate the transition

times andpropagationdelay for this inverterfollowingthe definition in Fig.1.35of the Text andassum¬ ingthat theswitchesoperateinstantaneouslyat_O/ =Vdq/1.

1.47 Reconsiderthe situationpresented in PI.44above for

_VDD

reduced from 5V to3V,withtheswitches still operatingat

_VDD/1.

1.48 A current-mode-logic gatemodelledby the circuit in Fig.1.33ofthe Text,uses

_Iee

-

4mA,

_VCc

= OV,

Vee

= 5Vand

_Rc\

=

Rci

—

250£2. The logic load connectedtoeachoutput canbe modelledby a3pF

capacitor. Sketch and labelthe outputwaveforms that result for asequence of 2 switch reversals.Esti¬

mate values for Vql,

_Voh

,_{hui> 'rwz.}

.

{plhi {phl for each output, assuming switch operation to occur

instantaneouslyatitsoperatingthreshold. For thisgateoperatingat200MHz with50%duty cycle,what arethe static, dynamic and totalpowerconsumptions?

-OPERATIONAL AMPLIFIERS

SECTION 2.1: THE OP

AMP TERMINALS

2.1 Whatis the number of op ampsthatcanbeaccomodatedinan8-pinIC package? Ina 14-pinpackage? How manyunusedpinsarethere in eachcase?

SECTION 2.2: THE

IDEAL OP AMP

2.2 An otherwise-idealop amp,knowntohaveagainof

104

V/V,ismeasuredinacircuittohavean output

voltage of -3 V. While it would bedifficult to measure, what would you expect the voltage from the

negativeinput pintothepositiveonetobe? Ifthevoltage atthepositive pin is knowntobe +100 mV,

whatis the voltageyouwouldexpectatthenegative one?

2.3 For theamplifier described in P2.2 above,connected inthe circuitshown inFig. P2.2(onpage 110 of theText),what voltagei)/ would berequiredatthe inputto_{produce o0 =}3.5 V?

SECTION 2.3:

ANALYSIS OF CIRCUITS CONTAINING IDEAL

OP AMPS

-THE INVERTING CONFIGURATION

2.4 An invertingop-amp circuitwith thetopology of Fig.2.4 onpage65 of the Text, has R|=4.7 k£2and

R2=47 kil What closed-loop gain would you expect? In the laboratory, a student accidentally

exchangesthesetworesistors. What gain wouldyouexpecthimtofind?

2.5 Thecircuit shown in Fig. P2.8c), (onpage 111 oftheText)usinganop ampwithagainof

104

V/V, is

foundtohavean outputvoltage of +10V. Whatis the voltage requiredatthe inverting input terminal of the op amp for thistooccur? Whatis thecurrentthrough the grounded 10 kill resistor? What is thepre¬

cise input voltage, U/, you would expect? (Hint: First, consider this question assuming that the gain

(104)is very very high. Then, refine your answerwithacalculationinwhichavery smallerror correc¬

tionismade).

D

2.6 Designanop-amp circuitwitha gainof-2 V/V,usingthree 100 k£2resistors. How many solutionsare

there? What is theinputresistance of each?

D

2.7 Designan inverting op-amp circuit with a gainwhose magnitude is 10 V/V usingone 220 k£2 resistor and anotherresistorno greater than 1 M£2.

CD

2.8 Designanamplifier withagain of-20 V/V,aninput resistance of 100 k£2,andnoresistorgreaterthan 1

MQ. (Hint: youneedmorethan2resistors! Butnot4!)

2.9 An invertingop-amp circuit is designed touse one 10k£2andone 100kS2resistor. What are the two

possibleclosed-loop gains you wouldexpectwith anideal op amp? What gains do you get with anop amp whoseopen-loop gain is only 100 V/V?

2.10 An inverting op-amp circuit designed for a nominal gain of -100V/V uses a very high-frequency

amplifier whose open-loop gain isrelatively low. Whatmusttheamplifiergainbe iftheclosed-loop gain istoliewithin 10%ofthenominalvalue? Within 1%ofnominal?

-2.11 For the invertingamplifier showninFig.2.6inthe Text, find the input resistance/?,• of the feedback cir¬ cuit connectedto therightmostend of R|(namely theamplifier with gain -A andfeedbackresistor R2).

[Hint:Followthegeneral approachusedintheanalysis leadingtoEquation 2.1 with /?,• beingthe ratio of

the voltage at the negative input terminal and the current inR2.] The mechanism, that causes

_Rt

to be quite small is called theMiller

_Effect.

UseR, withRiandA to calculate G

.

Comparethe result with

Equation 2.1.

2.12 Arelativelyideal op amp withopen-loop gain A is connected inacircuitwithitspositive inputgrounded and an unmarked resistor

_Rf

connected between its output and negative-input terminals. A 10)1A test

current is injected into the negative-input connection, where a voltage of 10.1mV is measured. A

correspondingmeasurement at_{the output shows o0} tobe-978mV. Estimate the valueoftheequivalent input resistanceat the negative-input node, the amplifier open-loop gainA, and the actual value of the feedback resistor

_Rf.

What is likely to be the nominal value of

_Rfl

What isits corresponding toler¬ ance? For what value of resistor joining a source Mr to the negative input terminal is

VoA>s

=

-

10.00V/V. D

2.13 D

Designanamplifier with again of +200V/V and aninputresistance of 100 kfi using 2 op amps and resistorsnolarger than 1 M£2. Share the gainasmuchasisconvenient between thetwoamplifiers. 2.14 Reconsider P2.13 above if

_Rin

mustbe2M£2. Useaminimumnumber of resistors.

CD

2.15 Design the circuit of Fig. 2.8 onpage 69 of theTexttohaveaninput resistance of 1 MOandagainof

-22 V/V using resistorsnolargerthan 1MO. Ifresistorsnosmaller than 100 kOareavailable,whatdo you do?

2.16 Consider the circuit of Fig2.8 of theText with the grounded end of

R3

connected to inputu2,and t>i

connectedto

_R\.

Use the approach in Example 2.2(onpage 69 oftheText)andsupeiposition,tofindan

expressionfor v0 intermsof\)2alone,and oft)jandx>2 together.

SECTION 2.4: OTHER APPLICATIONS OF THE INVERTING CONFIGURATION

L

2.17 Find thetransferfunctionofthe following circuit:

What is the condition for which the out¬

putis independentof frequency? Sketch Bode magnitude plots (in rad/s) for 3

cases:

a)

_C2

= 0.1C,= 0.1|iF,

R2

= 10/?|= 100k£2;

b)

_R2

is raisedto 1M£2; c)

_R2

isloweredto lOkfi.

2.18 A Miller integratorfor which the timeconstantis 1ms isdriven byapositivestepof 1volt amplitude. What does theoutputdo? Atwhat rate? If the initialoutputvoltage is 10 V, howlongdoes it take for the outputtoreach 0 V?

10-2.19 A Miller integrator witha timeconstant of 10msis driven by a60 Hz sinewaveof0.1 V peak ampli¬ tude. Describetheresultingoutputwaveform, in amplitude and phase. Is the output leadingor lagging

theinput? C

2.20 Consideradifferentiatorcircuitsuchasthatshownin Fig. 2.14a),onpage79 oftheText,havinga5ms

timeconstant. For whatrateofchangeofinputsignalis theoutput+1 V? Aninput signal beginstorise fromzerovoltsat/ =0attherateof 1 V/ms, reachesavalueof20 V, thenfallsatthe sameratetozero volts. Sketchand label theresultingoutput waveform overaninterval of 50ms.

L

2.21 The differentiatorcircuit of Fig 2.14a)of the Textisaugmentedby aresistor r= 100 £2 in series with C =1.0

_JJ.F.

Resistor/? =10kfl. Sketch and label theoutputifthe input is:

a) apositivepulse of 0.1 Vamplitudeand 10ps duration,

b) anegative pulse of 50 mVamplitudeand 0.1sduration.

2.22 Designacircuit with 3 inputstoprovidean output_u0=

_-

(Uj

₊

_{2 u2}

₊

3 1)3)using 10kfiasthe smal¬ lest resistor.

D

2.23 Designacircuittocombine3inputsto_{form u0}=

+

2 u2

-

3 u3. Useonly inverting amplifiers, with

10kftas thesmallest resistor. There ismorethanoneway! Findonewhich minimizesthe total resis¬

tanceused.

2.24 For the following circuit, find anexpressionfor theoutputv0 intermsof U|andu2,assuminganideal op amp. v1 10kQ v2 5kQ

•

-

VvV 0.1|iF

Hh-_T

vo

SECTION

2.5:

THE

NONINVERTING CONFIGURATION

2.25 A non-invertingop-ampcircuitwith the topology of Fig 2.16,onpage82 of theText, hasR₁₌4.7 kfi and R_{2 =}47 k£L What closed-loop gain wouldyou expect? In the laboratory,a student accidentally exchanges thesetworesistors. Whatgain would youexpect hertofind?

D

2.26 Design anon-inverting amplifier with again of 1.5 V/V using three 1 k£2 resistors. Sketch two solu¬ tions.

CDL

2.27 Usethe circuit idea shown in Fig P2.44(on page 116 ofthe Text) to design acircuit whose output is

u0 =D|

+

2i)2

-

3w3, with 10kflas the smallestresistor used. There areseveral possible ways! Find

one.

-DL*

2.28 Use the generalresult outlinedin P2.44onpage 116 ofthe Text for thearrangement shownthere inFig

P2.44to create acircuittoprovidean output_D0 =10(Di-d2). (Hint:Useanadditional positive input.) Haveyouseenthiscircuit before? What is it called? Youmayfindthe latter questionsmorestraightfor¬ ward afteryouhave read thenextSection of the Text.

D

2.29 A designer, needing to provide aunity-gain buffer,considers the use of the circuit topology shown in Fig. 2.19onpage84 ofthe Text. However, the amplifier he has available hasanopen-loop gain of only 10. What closed-loop gain would thesimple circuitproduce? Hisbosssuggeststhat he consider the cir¬

cuitof Fig2.16onpage82asasolution. As well, sherequeststhat thesmallest resistor used be 10 kO. What design would result?

SECTION 2.6:

EXAMPLES OF OP-AMP

CIRCUITS

CD

2.30 A designer wishes to use asimple modification of the circuit of Fig2.20 on page 86 of the Text to

implementa centre-zerovoltmeter whose scale endsare±1 volt. Themetermovementprovided isa_{0 to}

1mA unit witharesistance of 50£2. Her bosssuggests thatasolution is possible usingasingle addi¬ tional resistor andoneofthe ±10 V supplies from which theop amp is powered. What is the value of the additional resistor? To what supply is it connected? To what circuit nodeis the additional resistor

connected? What is therequired value of R ? CD

2.31 An analog-circuit designer requires a+5 V powersource from which to runa small amount of digital logic requiring 20mA at +5V. The analogsystem uses±15 V supplies whicharequite well-regulated

(thatisstableover time andtemperature and reasonably independent ofload). Suggest asimpleop-amp

circuit, usingaresistor network operatingat0.5 mA,todo the job. If the opamprequiresabiascurrent

of 2 mA from its supplies at noload,what is its total powerdissipation when fully loaded at themax¬

imumcurrentrequired bythelogic?

2.32 For a particular difference amplifier using the topology of Fig 2.21 on page 86 of the Text, Do

Ri

—

R4

=100 k£2and

_R\

=

_R3

=10 k£L What is thegain,G=

-

,youwould expect? (Be

care-Dl-V)2 fulof what isasked!).

D

2.33 The difference amplifier described in P2.32 above is connectedto twosources,\)s₁and O52.eachhaving

Do

a 10k£2internalresistance. What is thegain

-

which results? What mustyoudo toachievea

Dsi-dS2

source-to-output gainofmagnitude 10. As well, thesourceresistanceofUy2is foundto be only 8k£2.

What elsemustyou dotoachievetruedifference action? L

2.34 Reconsider the difference amplifier analyzed in Example 2.6 onpage 86 of theText, usingFig 2.21 and Fig 2.22, under the condition that resistor

_R4

is connected to a 3rd input, 03. Find the expression

/J2

R4

correspondingtoEquation2.13for Do. Simplify it for thecasein which

——

=

—

—

.

R1 "3

12-L

2.35 Considerthecircuit shown here which employsanidealop amp.

Whatisthe_{value of u0} for a) Dj=v2= 5V, b) _{= -u2 =}0V,

c) v,= +3 V,_{v2 =}-2 V?

Do your analysis from first principles.

Afterward, consider using the answer to

P2.34above.

D

2.36 Usingthecircuit of Fig 2.25 onpage90 of the Text,design aninstrumentation amplifier withadiffer¬

encegain of 100V/Vshared equally betweentheinput andoutput stages. Employ 10 kOasthe smallest

resistor. For yourdesign, what voltages appearontheoutputsof Aiand

A2

for =5.0 Vandx>2=4.9

V? 2.37

Show that the input resistance of the circuit shown is

R\

Y

Rin

=

-

_1?3—

,

assumingtheopamptobeideal. (Hint: Use

R2

a test _{voltage Ux} atnodeX and find the current itmustsup¬

ply.) To appreciate the significance ofanegative resistance,

connectitinserieswitharesistor

_R4

toasignalsource

at node W. Sketchthecircuit. Findexpressions fortheinput resistance Rj seenbythe signalsource at

W,and for the voltageratios

_UxA>w

and What do these become for 7?1=

7?2

anda)7?4=2/?3,b)

7?4=s7?3,c)7?4=7?

3*2?

For whatvalueof

R4

isthevoltage gainUyA>iy equalto+10V/V?

2.38

For the circuit shown with input D/, find the Norton equivalent circuitatnodeX. Assume the op amptobeideal.

(Hint: Proceedas at the beginningof above.) What current

willflow inanimpedance Z connectedtonode X? Find the

corresponding expression for the transmission from W to X in general, and when Z isacapacitorC,intermsofcomplex frequency s. Note that the latter circuit is actually a nonin-verting integrator. What is its integrator time constant? What is itsunity-gain frequency?

2.39 A differential amplifier hasacomposite inputsignal consisting of 2 sine-wave componentsat different frequencies (60Hzand 1kHz)ateach ofits inputs: Both haveacommon componentof8 voltspeak at

60Hz. At 1kHz,each hasacomponentof lmV amplitude, but of 180° relative phase. The output con¬

sists ofa0.6V peakcomponentat60Hzanda60mVpeakcomponentat 1kHz. Find the difference-mode gain, andthe common-mode gain. Using the definition ofthe Common-Mode-RejectionRatio(CMRR)

provided inProblem2.60 onpage 118of the Text, calculate the CMRR in dB.

v1 v2

•—

R1 100kQ R3 100kQ

—

w.

—

R2 100kQ -Wr-vo

—

« R4b +15V 300kQ

T

—

VA

-

1 R4a 150kQ

|

vw

-

13-2.40 A differentialamplifier is characterized by the first equation in Problem2.60 on page 118of the Text where CMRR is also defined. It is found to have a difference-mode gain of 200V/V and a CMRR of lOOdB. For whatamplitude of input common-mode signal is the unwantedoutputsignal only 1%ofthe

desired difference-modeoutputof2Vpp?

SECTION 2.7:

EFFECT OF FINITE

OPEN-LOOP

GAIN AND BANDWIDTH ON

CIRCUIT

PERFORMANCE

2.41 An internally-compensated op amp hasf, of 10MHzandadc gain of

106

V/V. What is the 3 dB fre¬

quency of its open-loop gain? If this amplifier is to be operated at 100kHz, what open-loop gain is

available?

2.42 The op amp in P2.41 above is to be used in aclosed-loop amplifier having again of 20dB. What

corresponding break frequencies would you observe in the inverting and non-inverting versions? For

what frequencies is the phaseshiftofthe corresponding amplifier less than 6 degrees?

2.43 Theopampdescribed in P2.41 above istobeusedina systemforwhich low-frequency operation should extend (within 3 dB) to 10 kHz. What is the maximum closed-loop gain available from a single amplifier? From2 identical amplifiers used in cascade? (See the result for 2 amplifiers in cascade developed in Problem2.73 on page 119ofthe Text).

2.44 A measurement of the closed-loop gain of an amplifier shows it to be -25 V/V at 120kHz and-100 V/V at 5 kHz. Estimate theclosed-loopgainat lowfrequencies and the corresponding3 dB frequency.

What isf, fortheop ampused? (Be careful!)

2.45 Anamplifier intended for very-high-frequency operation,yetcharacterizedbyasingle-pole rolloff, has/,

=

100MHzand

_A0

₌20 V/V. Foradesign inwhichthe actual (rather than the nominal)closed-loop gain is -10V/V,what3dB frequency results?

SECTION 2.8: LARGE-SIGNAL OPERATION OF OP AMPS

2.46 Anop-ampcircuit operating from±10V supplies has L+andL-of +8 Vand -8.5 Vrespectively, anda

closed-loop gain of -10 V/V. What is the peak-to-peak value of the largest possible inputsine wave

havingzeroaverage,for whichthe outputisnotdistorted?

2.47 Anop amphasaslewrateof 10 V/psec. What is the highest frequency atwhich it can reproducea6-V

peak-to-peaktrianglewaveatits output?

2.48 Findanexpression for the amplitude of the sine wave for which the small-signal and large-signal (SR-limited)bandwidthsare thesame. When the small-signal bandwidthis0.5 MHzandthe slewrateis2 V/psec, what is the amplitude for which equal bandwidths result?

SECTION 2.9: DC IMPERFECTIONS

D

2.49 For an amplifier operating with ±4 V saturation limits at aclosed-loop gain of -100 V/V, what input

offset voltage is requiredto assurelessthan 1%reduction inoutputswingcapabilityduetooffset?

D

2.50 An inverting amplifier withgain of-100V/V andaninput resistance of 100 k£2,usesanop amp with 1 mV offset,abiascurrent of 30 nA andanoffsetcurrentof 3 nA. What output offset results witha) a

basic uncompensated designb) abias-current-compensateddesign? In the lattercase,what compensating

14-resistor doyou use? Which offset sourcedominates in eachcase? What is the net outputoffsetif the

dominantsourceis halved? D

2.51 If the amplifier in P2.50aboveis capacitor-coupled at the input,what output offset resultsinthe basic and compensated designs? What compensation resistor should be used?

CD

2.52 Designadirect-coupled invertingop amp withagainof -100 V/V,the highest possible input resistance,

and an output offset 20.5 V, usingan op amp with 2 mV offset, and bias currents of 1pAequal to

within±10%. What is /?;„ of your design?

A basic integrator circuit suchas that shown inFig.2.11on page74 of the Text, operates from ±12V supplies. Theop ampsaturates at±10V,hasaninput offset voltage of±2mV,abiascurrent of lOOnA (directedinto theinputterminals), andanoffsetcurrent of±10nA. For R = 10k£2andC= 0.1p.F,an

inputvoltage of zero, andaninitial chargeof0Vonthecapacitor,whatis the minimum time itwilltake

fortheoutputtosaturate,ifimperfections leadto a)positive limiting,b)negativelimiting. Considerthe

circuitshownas ameansfor improving operation.

L 2.53 LD 2.54 Vl R + 12V

1

-t12V

Assuming /?/,

»

Ra, what valueof

_Ru

should be used?What

doyouexpectthetimes tosaturation tobecomenow? If the

bias current doubles, while the offset current remains the

same,what (if anything)happens? For the offsetvoltage and

biascurrentassumedtobe stableattheirmost extremevalues

whichcause positivesaturationat the output, and withR/, =

10ML1,towhat voltageshould the wiper on

_Rc

be adjustedin order to reduce the rate of output-voltage change to essen¬

tially zero?

A non-invertingamplifier using resistorsof lOkQand 1MDtoachieve ahigh gain isfoundto have an

output offset voltage of +1.8V with input grounded. When a 10k£2resistor is used in series with the

positive input (and grounded), the output offset reduces to +0.6V.Estimate the nominal gain of the amplifier,and theinput-biascurrent. Whatcanyou sayabout theinputoffset voltage and offset current? If thevalue of all3 resistorsisreduced by afactor of 10,the output offset reduces to0.4V. What do youestimatetheinputoffset voltagetobe? Now,if the 10ki2resistor connectedtothe amplifier'snega¬

tive input terminal is capacitor-coupled to ground, what does the output offset voltage become? What

mustyounowdotocompensate? Whatdoestheoutputoffset voltagenowbecome?

-NOTES

16-DIODES

SECTION 3.1: THE IDEAL DIODE

3.1 Forthe followingcircuits employing ideal diodes, find thelabelledcurrents,I,andvoltages, V,measured withrespecttoground.

+5V 1kQ Va :la (a) +5V 1kQ Vb ib 5V (b) |C 10V (C) +5V 1kQ Vc Yd

—

•

:1kQ

*

Id (d) + 5V ie Ve

-•

:ikQ

-

5V 11 (0 + 6V

3.2 For the following logicgatesusingideal diodes:

i) If =

_VE

= 5V,and

_VB

=

_Vc

=

_VD

=0V,what is the value of

_VY

produced? ii) If logic'1' = 5V andlogic'0'=0 V,identifythe logic function performed. iii) Iflogic '1' =0 V andlogic'0' = 5V,identify thelogicfunction performed.

-M-B

—

M-B

—

N-Y D

-

—

M-i

_—

(a)

,

i"

R ÿ(b) + 5V

-K-J-r

—

(c)i + 5V + 6V Y

i(d)

A

•HC

E

—

H-c

•—

«-Y

J-,

_—

(«)

,

- 17

3.3 B + 6V D1

Hf-D2

H4-D3

©

100pA 04 D5 +5V

©

100_nA Q 06

—

M-D 07

—

W-©

5V

For the conditions statedinP3.2ii) above,(ind_anexpression

for the logic function

_Y=f

(A,B,C

,

D

,

E) of the circuit shown. Inparticular,fortheinputlogicvalues stated, what is the logicoutputvalue?

50pA

3.4

In thebattery-charger circuitshown, thesinewave input

_vs

is

12Vrms,whilethe battery voltage varies from 12 V to 14 V fromthe dischargedtofully-chargedstates. R$

-

1012 is the

charging-source resistance, D is an ideal diode and

Rc

=50Q,isacurrent-controllingresistor established by the designer. Sketch and label the diode-current waveform for

Vb

=12V. Whatareits peak and average values? What do thepeak and average diodecurrentsbecome when

_VB

reaches

14V?

3.5 Find the currents /j, /2, 13,14 in each of the diodes D1,D2, D3,

D4

of the circuit shown. What

V0

results? The diodesareassumedtobeideal.

+8V +8V

-SECTION

3.2:

TERMINAL CHARACTERISTICS

OF

JUNCTION

DIODES

3.6 Averysmalldiscretesilicon diode(a"100pAdiode")is foundtoconduct 100 pAat0.700 Vand 1 mA

at0.815V. Findthe values ofn and /$ whichcorrespond.

3.7 A diodeforwhichn₌1conducts0.1 mAat 0.7 V. Find its voltage dropat 1mA. For whatcurrentis

itsvoltagedrop equalto0.815 V?

3.8 A 10-Asilicondiode for which n= 2 is known to haveaforward voltage drop of 0.700 V at 10A. What isthe junction voltageatwhich it conducts10mA? 10 pA?

3.9 A particular "1 mA diode", whichat 25" Cconducts 1 mA at 0.7V, is operatedat 95° C inacircuit

whichprovidesita constant 100 pAcurrent. What does itsjunction voltage become ifn₌2?

3.10 Forthe diode described in P3.9above,the leakagecurrent at25° Cis 1nA. What does it becomeat95° C? at 100° C?

SECTION

3.3: PHYSICAL OPERATION OF DIODES

NOTE:Forasummary ofimportant relationshipsandvalues of particular parameters or physical con¬

stantsnotstated explicitly inthe followingproblems, pleaseconsultTable 3.1onpage156oftheText.

3.11 Ataparticulartemperature, thefractionofionizedatoms inapieceofsilicon is 10"". If thematerialis

dopedto alevel of 1 in 10m withacceptor atoms,what isthenetconcentration ofholesandelectrons in the resulting material?

3.12 UsingEquations3.6and supporting data following it, find the intrinsic carrier density «,• at200K, 300K and400K,that isinthe

±

100°Crangeatand around roomtemperature. What isthe%increaseincon¬

centrationforthe 100°Criseaboveroomtemperature? At 127°C,what fractionofthesiliconatomsare

ionized?

3.13 Find the resistivity of a) intrinsic silicon and b) n-type silicon with

_ND

=10[6/cm3. Use

«,• = 1.5 x

I0l0/cm3

with p„ =1350

cm*/Vs

and\ip = 480

cmVV,,

for intrinsic silicon,andmobility reduc¬ tionto80%for the doped material. Towhat values will the resistivity change in eachcasefora 100°C

riseintemperature of the material?

3.14 Fora pnjunction inwhich the n regionisdopedat ten times the concentrationofthe p region,inwhat

region is the depletion regionlargest? Bywhat factor?

3.15 For ajunction in which the built-in voltage is 0.7V, what are the doping-concentrations in the two

regions if:a) they areequal,b) they areinthe ratio 10to 1. [Hint: UseEq.3.18 inthe Text.] For each case,what isthewidth of thedepletionregion andthe distance itextendseach sideofthejunction? For ajunction that is 30 pm by50pm in size, what is the magnitude of the uncovered chargeoneachside? 3.16 For a particular reverse-biasedpn junction, the terminal current is 10 nA. If the drift current at the

operating temperature is 15 nA,what mustthe voltage-dependent diffusion current beat this particular

reverse voltage? CL*

3.17 Findanexpressionforthe chargeqjformedoneither side of the junction intermsoftheapplied reverse voltage VR, as represented inFig. 3.14 of the Text. Calculate the value of qj which applies to the

19-junctions describedinP3.15 above,for

_V*

= OV, 10Vand 11V. Use the latterpairofvalues toestimate

the junction capacitance. Calculate thismoredirectly at

_VR

₌ 10.5V,usingEquations 3.25and 3.26 on

pages 148and149 ofthe Text. Ifthejunction isnotabrupt, buthasagrading coefficientm= 1/3,what aretheexpected capacitancesalt

_VR

= 10.5 V? At

_VR

= 100V?

3.18 At aparticular operating pointof areverse-biasedpit junction, achange of 1 volt produces atransient

currentincreasecorrespondingtoanetchargeflowof 0.1 pC. What is the correspondingdepletioncapa¬

citance ofthejunction atthis operatingvoltage?

3.19 Foraparticularjunction for which m=1.6,acapacitance

C;

of 1.8pF is measured for areversejunction voltageof2 V, and 0.2pF foravoltage of 10V. Whatarcthe corresponding values of

Vo

, Cjo

andCj

atOV?

3.20 A particularpnjunction for which the breakdown voltage is 120V,candissipate50mW while maintain¬ ingits junction temperatureat avaluelow enoughtoavoid permanentjunction damage. What continu¬

ous reverse current flow appears likely tocause permanentfailure? Ifreversecurrentflows only 10%of thetimeat the peaks ofacyclicapplied voltage, what peakcurrentcanbe tolerated?

3.21 Inadiode intended for high-speed switching, theexcess-minority-carrier lifetime for holes is 1ns.Using the valueofhole mobilityindoped silicon from Ex.3.12onpage 143 of the Text, andthe Einstein rela¬ tion(inEq. 3.12onpage 141),findanestimate of the diffusionlengthinthe forward-conductingdiode.

For this diffusion length,at what distance from the depletion-region edge will the excess hole density reach10% of its value there?

3.22 Fora 3|iwt x 5\lm junction, with

_NA

=

10l7/c/n3

and

_ND

=

1016/cm3,

inwhich minority-carrier lifetimes

are

xp

—

1nsandT„ = 2ns,hole and electron mobilitiesare400and 1100

cmWs

,respectively, find

_Is.

3.23 UsingEq. 3.6 of theText, evaluate the temperaturedependence of

Is

(as definedinEq.3.34 there) in

%/'Catroomtemperature(say 300K).

3.24 For the diode in P3.22above,conducting a 1mA current, what fractions of the current arecarried by holesand by electrons? Estimateboth the hole and electronminority stored charges. What is themean

transit time Tr of the diode? What istheassociated small-signal diffusion capacitance?

3.25 Forajunction conducting 1mAat 700 mV, for which«= 2andadiffusioncapacitanceof IpFisasso¬

ciated, whatis the value of

_xr

which applies? Forajunction 10X larger what would iT be? In theori¬ ginaljunction, what is the total stored chargeat 1mA? At 10mA?

3.26 Usetherelationships givenfor chargeQ in Eq. 3.38onpage 154 ofthe Text and thereafter,tocalculate thediffusioncapacitance ofajunctioncharacterizedbyn,D,iin the diodeequation.

SECTION 3.4: ANALYSIS OF DIODE CIRCUITS

3.27 A diode described by the exponential characteristic of Fig. 3.20on page 159oftheText isconnectedtoa sourcewhoseThevenin-equivalentvoltage is

_VT

and resistance is

_Rr-

{Notethat

_VV

isaThevcnin vol¬

tage, notathermalvoltage!} Drawloadlinesand findoperatingpoints(VD, ID)for: (a)

_VT

=1 V,

_Rr

=100 £2,

(b)

_VT

= 0.9V,

_Rt

a_{100 £2,}