iiPream

bleT

hiscourse

coversa

numberofdiverse

topics.Some

oftheseare

practicalandyou

willneed

theskills

forprojectsin

futureyears.O

therssim

plydidn’tfitinto

othercoursesand

were

collectedhere!

These

arethe

main

subjects.

1.U

seof

theC

adenceO

rCA

DPC

BD

esignersuite

todraw

,simulate

andlay

outdesignson

printedcircuitboards

(laboratoriesonly).

2.A

nalogue-to-digitalanddigital-to-analogue

converters(lectures

andtest,sem

ester1).

3.Pow

ersupplies

andpassive

components

(lecturesand

test,semester2).

4.T

hedesign

projectitself:research,design,constructionand

test(preliminary

laboratory,design

assignmentand

finallaboratories).

There

isno

complicated

mathem

aticsin

thiscourse.

Itry

tokeep

thetopics

practicalbutyoucan’tdesign

oruseeithera

powersupply

orananalogue-to-digitalconverterw

ithoutsome

ideaofhow

itoperates.T

hem

aterialoverlapsconsiderably

with

othercoursesbecause

ofchangesin

thecurriculum

inthe

pastfewyears.In

particular,powersupplies

andrelated

topicsare

alsocovered

inPow

erE

lectronics2.B

othcourses

coverabroad

rangeofm

aterialandw

ehope

thattherepetition

will

behelpful.A

glancew

illshow

youthat

thishandout

isnot

acollection

oflecture

slides.T

henotes

containfarm

orem

aterialthanthe

lectures.Insteadoftrying

tocovereverything

inclass

Ishallconcentrate

onthe

important

concepts,leavingthe

detailsfor

youto

study.T

hisleads

tothe

obviousquestion:

Whatshould

Ilearn

forthe

tests?Pasttests

areon

moodle

andyou

willsee

thatthequestions

arevery

similarto

theexam

plesin

eachchapter.

This

handoutis

more

likea

textbook,partly

becauseno

singlebook

coversthe

courseat

therightlevel.

Bonnie

Baker’s

book[1]

isgood

butalotof

them

aterialistoo

advanced.Y

oushould

alsobecom

efam

iliarw

ithThe

ArtofE

lectronics[4],another

wonderfulbook.

Seethe

chapterFurther

readingon

page143

forotherbooksand

applicationnotes

thatmightbe

useful.T

heseitem

sare

referencedin

thetextby

numbers

insquare

brackets,suchas

[1]and[4]above.

Pleasetake

careofthis

handoutbecausea

lotofthetopics

areim

portantforfutureprojects.

Prerequisites

These

arethe

main

prerequisitesfrom

firstyear.We

shalldrawon

allthism

aterialinthe

project.

B

asicbehaviour

ofthe

standardcom

ponents–

resistors,capacitors

andinductors,

Ohm

’slaw

andso

on(E

lectronicE

ngineering1X

).This

includestheirbehaviourin

time,

notjustinfrequency.

Impedance

isusefulonly

forsine

waves

(orsignals

thatcaneasily

beconstructed

fromthem

,as

youw

illlearn

inm

athematics

thisyear)

butm

anyof

thecurrents

andvoltages

thatwe

considerarenothing

likesine

waves.

G

eneralrelationbetw

eencurrentand

charge–

notjustQ

DI

T.

B

asiccircuitanalysis–

Kirchoff’slaw

s,Thévenin’stheorem

,nodalanalysisandthe

like.

iii

Tim

e-dependenceofR

Ccircuits

–the

way

inw

hicha

capacitorchargesand

dischargesthrough

aresistor(E

lectronicE

ngineering1Y

).This

willbe

revisedin

ElectricalC

ircuits2.Inductors

arem

ajorcomponents

inm

anypow

ersuppliesand

we’llneed

tolook

attheirbehaviourin

time

asw

ell.

O

perationalamplifiers

–w

eneed

touse

some

unfamiliar

circuitsbut

theycan

allbe

analysedusing

theprinciples

thatyouw

eretaughtin

Electronic

Engineering

1Y.Pleasedo

yourselvesa

favourand

forgettherubbish

thatyouw

eretaughtin

Higher

Physics:It

won’tw

ork.(It’snotyourteachers’faultbutthe

SQA

.)

O

perationofa

bipolardiode

andtransistor

–outline

only,nodetails

(Electronic

En-

gineering1Y

).You

will

learna

greatdeal

more

inE

lectronicD

evices2

andA

nalogueE

lectronics2.

M

icrocontrollers–

usedin

thefinal

project.T

hem

aterialfrom

Electronic

Engineer-

ing1Y

will

becarried

furtherin

Em

beddedProcessors

2.T

hem

icrocontrollerw

illbe

programm

edin

theC

language,taughtinIntroductory

Programm

ingE

E1.

Look

backatyour

notesfrom

lastyearor

astandard

textbookif

youhave

forgottenany

basictheory.Y

ouw

illneeditforyourothercoursesand

Imay

wellquiz

youaboutthese

topicsduringthe

course.

Formaldescription

The

university’sform

aldescriptionofthe

courseis

containedin

thecourse

specification,which

canbe

foundin

thecourse

catalogue.A

linkis

providedfrom

moodle.

Here

arethe

most

importantsections.

Minim

umR

equirementforA

ward

ofCredits

A

ttendanceatalltests,gaining

anonzero

mark

C

ompletion

oflaboratorieson

printedcircuitboard

design

A

ttendanceatallsessions

fortheproject,m

akinga

worthw

hilecontribution

tothe

team’s

work

Tim

elysubm

issionofprojectreports

andan

acceptablelaboratory

recordbook

The

onlyunusual

itemhere

isthe

thirdone.

Iw

illnot

tolerate‘passengers’

onthe

projectbecause

itisnotfairto

theotherstudents

inthe

team.

Course

Aim

sT

hiscourse

addressesm

anyof

theissues

thatarisein

thedesign

ofa

realpieceof

electronicequipm

ent.These

include:

provision

ofapow

ersupply

interface

between

analoguesignals

anddigitalcom

ponents(such

asm

icrocontrollers)

iv

layoutofa

circuitona

printedcircuitboard

interpretation

ofam

anufacturer’sdata

sheet

selection

anduse

ofsimple

components,w

ithheatsink

ifrequired

These

issuesare

broughttogetherina

project,carriedoutin

asm

allteam,w

hichalso

draws

onm

aterialtaughtinotherelectronics

courses.

IntendedLearning

Outcom

esofC

ourseB

ythe

endofthis

coursestudents

willbe

ableto:

Printedcircuitboard

design

draw

circuitsusing

schematic

capture,with

about20com

ponents

sim

ulatea

one-transistoramplifierand

compare

theresults

with

analyticalestimates

lay

outa

printedcircuit

board,using

localdesign

rules,for

singleand

double-sidedboards,using

manualand

automatic

routing

Power

suppliesandpassive

components

E

xplainoperation

oftraditionaloff-linepow

ersupply:transistor,rectifierandsm

oothingcapacitor

C

alculateratings

ofallcomponents

required

D

esignshuntregulatorusing

Zenerdiode

andresistor

D

escribeoperation

oflinearregulatorandstate

itskey

specifications

L

istbasictypes

ofswitching

regulatoranddescribe

when

theyare

appropriate

E

xplainthem

aldissipation,calculatelim

itson

operationof

devicesand

specifysuitable

heatsink

D

escribebasic

passivecom

ponents(resistor,capacitor,inductor),their

differentpracticatypes,and

choosean

appropriatecom

ponentforanapplication

D

escribeconstruction

ofa

basicprinted

circuitboard(PC

B)

anddifferentpackages

form

oderncom

ponents

Analogue-to-digitaland

digital-to-analogueconverters

State

mathem

aticalexpressionsforan

analogue-to-digitalconverter(AD

C)and

adigital-

to-analgoueconverter(D

AC

)

D

istinguishbetw

eenresolution

andaccuracy

with

applicationto

AD

Cs

andD

AC

s

D

escribecom

mon

typesof

AD

Cand

DA

C(flash,

pipeline,successive-approxim

ation(SA

R),sigm

a-deltaand

integratingA

DC

s;string,current-steeringand

sigma-delta

DA

Cs)

v

E

xplainprincipleofoperation

ofaSA

RA

DC

anddescribe

itsinputcharacteristics

State

Nyquistcriterion

toavoid

aliasingand

needforanti-aliasing

filter

D

educekey

parameters

ofanA

DC

fromits

datasheet

Project

D

eviseapproach

toaddress

givenrequirem

ents

Perform

appropriatepreparatory

experiments

D

esignsignalconditioning

andspecify

AD

C

D

esigncom

pletesystem

,includingpow

ersupply,decouplingcapacitors

etc

L

ayoutprinted

circuitboard

Populate

printedcircuitboard,testforcontinuity,rew

orkas

necessary,includingsurface-

mountdevices

W

ritesoftw

areform

icrocontrollerwith

appropriatestructure

anddocum

entation

Testand

debugcom

plete,mixed-signalsystem

C

ontributeto

writing

ofuser’sm

anualandteam

report

W

orkeffectively

asa

mem

berofateam

of3or4

students

K

eepan

individuallaboratorybook

This

courseaddresses

many

ofthem

oregeneralgraduate

attributessetoutby

theU

niversity.

Sum

mative

Assessm

entMethods

50%

–Tw

oclass

tests,each1

hour(numerous

pastpapersand

solutionsare

providedon

moodle)

10%

–L

aboratoryon

PCB

design

40%

–Project(practicalw

ork,teamreports

andindividuallaboratory

recordbook)

There

aretw

ospecialconditions

fortheassessm

ent.

Itis

notpossibleto

offerreassessmentofthe

projectbecauseitis

carriedoutin

teams.

To

receivea

gradeD

inthis

course,students

must

achieveat

leasta

gradeE

inevery

componentofassessm

entlisted.The

resultwillbe

cappedatE

1otherw

ise.

The

secondcondition

isim

posedby

ourProfessional

Engineering

Institution,the

Institutionof

Engineering

andTechnology,

who

accreditthe

programm

esin

electronicsand

computing

science.T

heyare

concernedthat

nobodyshould

beable

to‘pass’

thecourse

overall,w

hilefailing

asignificantpartofit.To

getagrade

Doverall(typically

40T

hesespecial

conditionsaffect

onlyabout

onestudent

peryear

andare

ofno

concernto

anybodyw

hotakes

thecourse

seriously.

viLearningand

TeachingM

ethodsT

helist

givesthe

number

ofcontact

hoursand

(estimated

notionallearning

hours–

thetotal

time

thatyouare

expectedto

devoteto

thiscourse).

L

ectures:10(40)

Tutorials:2

(10)

L

aboratoryw

ork:10(10)

Projectw

ork:20(30)

E

xaminations:2

(10)

Contents

ID

ataconversion

1

1Introduction

todata

conversion2

2G

eneralfeaturesofanalogue-to-digitalconverters6

2.1Input–outputcharacteristic

ofanidealA

DC

..

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.6

2.2R

esolution,precisionand

accuracy.

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.9

2.3Sum

mary

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.10

2.4E

xamples

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.10

3B

asictypesofanalogue-to-digitalconverter

123.1

Introduction.

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.12

3.2C

omparators

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143.3

Flashconverters

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163.4

Pipelineconverters

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183.5

Successive-approximation

(SAR

)converters.

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203.6

Practicalissuesw

ithSA

RA

DC

s.

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233.7

Integratingconverters

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.26

3.8Sum

mary

ofclassicalAD

Cs

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.29

3.9E

xamples

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.30

4Sam

pling,oversampling

andsigm

a–deltaconverters

314.1

Sampling

rateand

theN

yquistfrequency.

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314.2

Sigma–delta

converters.

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.33

4.3Practicalissues

with

sigma–delta

converters.

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344.4

Summ

aryofsigm

a–deltaconverters

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.35

4.5R

eflectionon

AD

Cs

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364.6

Exam

ples.

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36

5Sum

mary:Selection

ofanA

DC

37

vii

viiiC

ontents

6Signalconditioning

396.1

Am

plification.

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396.2

Single-supplyop-am

ps.

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6.3C

ircuitsw

ithsingle-supply

op-amps

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6.4Filters

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.46

6.5C

omparators

andSchm

itttriggers.

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.47

6.6Sam

ple-and-holdcircuit.

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.50

6.7Sum

mary

ofsignalconditioning.

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516.8

Exam

ples.

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51

7C

omplete

systemsw

ithA

DC

s53

7.1Voltage

reference.

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537.2

Ratiom

etricm

easurements

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557.3

Measurem

entofabsolutevoltages

with

asim

pleA

DC

..

..

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557.4

Worked

example:Tem

peraturesensorw

ithL

M35

and8-bitA

DC

..

..

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..

567.5

Worked

example:M

easurementoftem

peratureusing

atherm

istor.

..

..

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587.6

Worked

example:sensorw

ithgiven

rangeofvoltages.

..

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.61

7.7W

orkedexam

ple:Sensorforaw

eighingm

achine.

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.62

7.8E

xamples

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.64

8D

igital-to-analogueconverters

668.1

Introduction.

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.66

8.2G

eneralfeaturesofdigitalto

analogueconverters

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668.3

Pulsew

idthm

odulation.

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8.4Types

ofdigitaltoanalogue

converter.

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.69

8.5Sum

mary

ofDA

Cs

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768.6

Exam

ples.

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77

IIPow

ersuppliesand

passivecom

ponents78

9Pow

ersupplies

799.1

Introduction.

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.79

10B

atteries82

10.1Introduction

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8210.2

Capacity

ofbatteries.

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8310.3

How

shouldyou

choosea

battery?.

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.85

10.4Forw

hatvoltageshould

youdesign

abattery-pow

eredcircuit?

..

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.86

10.5Supercapacitors

..

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8710.6

Worked

example:pulsed

currentdrawn

froma

coincell

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10.7E

xamples

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.89

Contents

ix

11R

ectifiers90

11.1Transform

ers.

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9011.2

Rectifiers

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11.3Sm

oothing.

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Calculation

ofinputvoltage.

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11.5C

onclusion.

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11.6E

xamples

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.96

12L

inearregulators

9812.1

Zenerdiode

regulator.

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9812.2

Seriestransistorregulator

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.101

12.3L

owdropoutregulators

(LD

Os)

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.104

12.4Packaged

regulators.

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.105

12.5E

xamples

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.106

13H

owto

reada

datasheet

10713.1

Generaldescription

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10713.2

Connection

diagrams

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.108

13.3O

rderinginform

ation.

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Typicalapplications.

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.108

13.5A

bsolutem

aximum

ratings.

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.109

13.6E

lectricalcharacteristics.

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Typicalperformance

characteristics.

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diagram.

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14Sw

itchingpow

ersupplies

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inductorconverters.

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omplete

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ontents

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.142

Furtherreading

143

Data

sheetsprovided147

Solutionstoexam

plesondata

conversion148

Solutionstoexam

plesonpow

ersuppliesand

passivecom

ponents156

PartI

Data

conversion

1

1

Introductionto

dataconversion

Avery

largenum

berofelectronicsystem

shave

theoverallstructure

shown

infigure

1.1.These

arethe

main

functionalblocks.

1.A

nalogueinputcom

esfrom

asensor

(temperature,m

icrophone,antenna,...).

2.T

hisanalogue

signalisconverted

toa

digitalvalueby

ananalogue-to-digitalconverter

(A-to-D

,AD

C,A

/D).

3.T

hesignal

isprocessed

digitally.It

may

alsobe

storedor

comm

unicatedto

anothersystem

.

4.T

heprocessed

valueis

returnedto

ananalogue

signalbya

digital-to-analogueconverter

(D-to-A

,DA

C,D

/A).

5.Finally,a

transduceroractuator

(controlvalve,speaker,...)isdriven

with

theanalogue

output.

Am

orespecific

example

isshow

nin

figure1.2

onthe

facingpage.

This

isa

digitalweighing

machine,

which

was

theproject

forthis

courselong

ago.In

thiscase

theoutput

isonly

toa

processingA

DC

DA

Ctransducer(output)

sensor(input)

storage

comm

unication

(analogue)(analogue)

Figure1.1

Ageneralized

systemw

ithanalogue

inputfroma

sensor,digitalprocessing,storageand

comm

unication,andanalogue

outputtoa

transducer.

2

Chapter1

Introductionto

dataconversion

3

VC

C

v-

v+

R+dR

R-dR

R-dR

R+dR

Vout

analog todigital

converter

micro-

controller

LC

Dcon-

trolleram

plifiersensor

set zerogram

s / ounces

weight

liquidcrystaldisplay

Figure1.2

Block

diagramofa

digitalweighing

machine.

displayalthough

therew

ouldprobably

bea

digitalinterface

toa

computer

ina

comm

ercialsystem

.Itshows

abitm

oredetailofthe

analogueinput,w

hichw

illbecovered

inchapter6.

The

complete

systemw

ouldhave

operatedon

analoguesignals

inthe

past.For

example,

televisionused

tobe

ananalogue

signalandw

asstored

inthis

formon

VH

Stapes.

The

same

was

trueof

sound.C

ontrolsystem

sw

erealso

entirelyanalogue

(thedepartm

entow

nedan

analoguecom

puterw

henI

arrivedin

1986).A

controllerfor

thetem

peratureof

anindustrial

processw

ouldhave

usedan

analoguesensor,processed

thesignalusing

op-amps

with

feedbacknetw

orks,andproduced

ananalogue

outputtodrive

theheater.

The

circuitwith

theop-am

psw

ouldbe

designedspecifically

toachieve

thedesired

functionand

thecom

ponentsw

ouldneed

tobe

changedifa

differentcontrollaww

asneeded.C

ontrollersused

tobe

made

with

terminals

onthe

backso

thatthecriticalcom

ponentscould

beexchanged

easily.N

owthe

trendis

todo

asm

uchas

possiblew

ithdigitalsignals.

Televisionis

againa

goodexam

ple.A

naloguetransm

issionw

illcease

inthe

nextfew

yearsand

allbroadcasts

will

bedigital.Program

mes

cannow

berecorded

indigitalform

onhard

disksorD

VD

s.This

haslong

beenthe

caseforaudio,w

hereC

Ds

were

introducedaboutthirty

yearsago.H

erethe

amplifiers

usedto

beanalogue

systemsbuteven

thatischanging,andm

anyaudio

poweram

plifiersarenow

‘classD’system

s,which

usevariousform

sofpulsem

odulation(such

aspulsew

idthm

odulationor

PWM

).The

conversionback

toan

analoguesignaltakes

placeatthe

lastpossiblepoint,in

thespeakeritself.T

hesam

etrend

canbe

seenon

theinputside

ofsystem

sas

well.

Forexam

ple,itiscon-

venientform

anufacturersof

mobile

phonesif

theycan

beadapted

with

minim

alefforttothe

varioussystem

sin

usearound

thew

orld.T

heradio

receiverstherefore

doas

littleas

possiblein

theanalogue

domain

beforethey

convertthe

signalto

digitalform

.It

isrelatively

easyto

reprogramm

ea

digitalsignalprocessortow

orkin

theU

SAratherthan

theU

K,forinstance.

4Introduction

todata

conversionC

hapter1

AV

CC

am

pli-fier

digitalsystem

low-

passfilter

sensor(input)

sample

and hold (S/H

)

analogueto digital converter

DV

CC

analogueground

digitalground

Figure1.3

Block

diagramof

adata

acquisitionsystem

,includingthe

functionsneeded

tocon-

ditionthe

signalfortheconverteritself.

This

allmakes

itseemas

thoughanalogue

electronicsis

beingpushed

tothe

peripheryof

many

systems

(apartfromthe

powersupply,although

eventhey

usean

increasinglevelofdig-

italcontrol).

While

thisis

partlytrue,

itrequires

veryhigh

performance

fromthe

analoguecircuitry

thatremains.

Major

electronicscom

paniestherefore

promote

theiranalogue

productsvigorously.Forexam

ple,TexasInstrumentsis

probablybestknow

nfordigitalsignalprocessors

(DSPs)now

adaysbutthe

titleofits

home

web

pageis

currentlyA

nalogTechnologies,Sem

icon-ductors,

Digital

SignalP

rocessing.A

nalogueis

unavoidable!O

ftenthe

interfacebetw

eena

sensorand

theA

DC

isthe

most

difficultpart

ofa

systemto

design.It

canbe

verytricky

toelim

inatenoise

andpresent

aclean

signalof

thecorrect

magnitude

tothe

analogueto

digitalconverter.Y

ouw

illhaveto

handleallthis

infuture

projects.A

greatdealmore

thanjustan

AD

Cis

neededto

turna

signalfromthe

analoguevoltage

ofasensorto

adigitaloutputforfurtherprocessing.

Some

ofthisw

asshow

nin

figure1.2

andfigure

1.3show

san

expandedversion

ofatypicalsystem

.N

oteveryblock

may

beneeded

andthe

ordermay

varyslightly.H

ereis

anoutline

ofthefunction

ofeachblock.

1.T

heinputcom

esfrom

asensor

ofsome

sort.The

outputisoften

avoltage

butsometim

esa

currentor

changein

resistance,capacitance

orinductance

–an

enormous

varietyof

sensorsis

available.

2.M

anysensors

producevery

small

outputs,perhaps

onlyµV,

andan

amplifier

may

benecessary

toraise

themto

asuitable

levelfortheA

DC

.

3.A

low-passfilter

isalm

ostalways

neededfortw

oreasons.

To

remove

noisefrom

thesignal.

Typicallythe

signalhas

alow

frequency,in

which

caseany

highfrequencies

presentareunw

antednoise

andcan

besuppressed

with

alow

-passfilter.Some

typesofnoisehave

aw

ell-definedfrequency,such

asthem

ainsat50

Hz

andharm

onics.A

notchfiltercan

beused

toelim

inatethese.

Some

typesofA

DC

operatein

aw

aythatrem

ovesparticularfrequencies

intrinsically.

To

avoidaliasing.Ifthe

signalissam

pledatfrequency

fs ,then

frequenciesgreater

than12f

s mustnorm

allybe

eliminated

fromthe

inputbeforeitis

sampled.T

hisw

illbe

explainedin

section4.1.

4.T

heinputto

theA

DC

shouldbe

heldconstantw

hileitis

beingconverted

toensure

thatthe

sample

refersto

aw

ell-definedtim

e.T

hesam

ple-and-hold(S/H

)circuit

doesthis

Chapter1

Introductionto

dataconversion

5

undercontrolfromthe

AD

C.M

anytypes

ofAD

Cactas

theirown

S/Hcircuitand

donot

needan

externalone.

5.Finally,the

analogue-to-digitalconverterturns

theanalogue

signalintoa

digitalrepre-sentation.

The

blocksbefore

theA

DC

will

becovered

inchapter

6.N

otethat

theanalogue

anddigi-

talblockshave

separatepow

erand

groundrails

(supplies).T

hiskeepa

them

easurementfree

ofdigital

noise.T

heA

DC

isthe

interfacebetw

eenthe

analogueand

digitalw

orldsand

may

thereforeneed

bothpow

ersuppliesand

grounds.

2

Generalfeatures

ofanalogue-to-digitalconverters

Acom

puterprocessesdigitaldata,w

hichhas

aw

ell-definedvalue

thatdependson

thebits

usedto

representit.H

owever,m

ostdatain

therealw

orldis

analogue,with

acontinuous

variationbetw

eensom

elim

its.The

numberoflevels

thatcanbe

detecteddepends

onlyon

theresolution

ofthem

easuringinstrum

ent.Conversion

between

thetw

oform

sis

doneby

digital-to-analogue(D

AC

,D

-to-A,

D/A

)and

analogue-to-digital(A

DC

,A

-to-D,

A/D

)converters.

These

usea

varietyof

methods

thatdifferin

resolution,speed,accuracyand

price.D

AC

sare

simpler

butw

e’llstartwith

AD

Cs

becausethey

arem

uchm

orecom

mon.

We

shouldconsider

some

importantgeneralfeatures

ofanalogue-to-digitalconversion

be-fore

we

lookatthe

operationofparticulartypes

ofconverter.

T

heinputvoltage

isa

continuousquantity,w

hichm

eansthatitcan

takeany

value(w

ithina

practicalrange),buttheoutputisan

integer–

adigitalvalue

with

agiven

numberofbits,

which

cantake

onlya

finiterange

ofvalues.Information

istherefore

lostonsam

pling.

Sim

ilarly,theinputvoltage

isa

continuousfunction

oftim

ebutthe

outputisa

discretesequence.Sam

plesm

ustbetaken

atasufficiently

highrate

togeta

faithfulrepresentationofthe

input.

A

llAD

Cs

compare

theirinputagainstareference

voltage.T

heoutputvalue

isa

ratioof

theinputto

thisreference,notan

absolutevalue.

Thus

theinput

v.t/

toan

AD

Cis

acontinuous

quantitythatvaries

continuouslyin

time,w

hilethe

outputN

AD

CŒn

is

alist

ofintegers.

The

processof

convertingv.t/

toN

AD

CŒn

is

calledsam

plingand

canbe

analysedm

athematically

todeterm

inehow

much

information

islost

inam

plitudeand

time.Ishalldo

onlya

littleofthe

theorybutthe

basicfacts

areessential.

2.1Input–outputcharacteristic

ofanidealA

DC

The

behaviourofanelectronic

systemis

expressedm

athematically

byits

transfercharacteristic

ortransferfunction,the

functionthatgives

itsoutputin

terms

ofitsinput.Foran

AD

Cthe

input

6

Section2.1

Input–outputcharacteristicofan

idealAD

C7

input voltage, VA

DC

0V

FS

000001010011100101110111

digital output, NADC

range of input values that all give 101 output

VFS

8

(1000)

LSB

=

LSB

12L

SB32

LSB

= 8

LSB

Figure2.1

Relation

between

analogueinputand

digitaloutput(transferfunction)

foran

ideal3-bitconverter.T

hiscan

produce8

digitalvaluesand

thereforehas

LSB

DV

FS =8.T

hestraight

lineshow

sthe

idealtransferfunctionw

ithoutquantization.

isa

voltage,V

AD

C ,andthe

outputisa

(binary)number,

NA

DC .Tw

oparam

etersofthe

AD

Care

neededbefore

we

canw

ritedow

nthe

transferfunction.

N

umber

ofbitsinthe

output,N

.An

outputofN

bitscan

represent2

Ndistinctvalues.

Full-scale

voltageofinput,

VFS .T

heA

DC

isdesigned

forwork

forinputvoltagesfrom

zeroto

VFS .

The

full-scalevoltage

istypically

thesam

eas

thereference

voltageV

ref .(Som

eA

DC

shave

differentinputranges,asI’llm

entionlater.)

Itseems

reasonablethat

VA

DC D

0should

giveN

AD

C D0,and

thatV

AD

C DV

FSshould

giveN

AD

CD

2N

forthe

maxim

umvalue.

Afirst

stabat

thetransfer

functionis

thenthe

simple,

linearrelation

NA

DC D

2N

VA

DC

VFS

(conceptual)(2.1)

Unfortunately

thiscannotbe

correctbecausethe

inputvoltageV

AD

Cis

acontinuous

quantity,sothe

right-handside

cantake

anyvalue

between

0and

2N

.In

contrast,theleft-hand

sideis

aninteger.A

realisticexpression

istherefore

NA

DC D

nint 2

NV

AD

C

VFS

(2.2)

where

thenint./

functiongives

thenearestintegerto

itsargum

ent.This

isthe

transferfunctionforan

idealAD

C.

Another

complication

isassociated

with

theoutputvalues.

Ifthese

haveN

bits,theycan

represent2

Nvalues,

which

gofrom

0to

2N

1.

Itis

notpossible

torepresent

thenum

ber2

Nw

ithN

bits.For

example,

4D2

2D0b

100,w

hichjustneeds

3bits.

The

largestnumber

8G

eneralfeaturesofanalogue-to-digitalconverters

Chapter2

thatcanbe

representedw

ith2

bitsis

3D0b

11.

The

prefix‘0b’m

eansa

binarynum

berand

isavailable

insom

eprogram

ming

environments

butisnotstandard

C.

The

transferfunction

isoften

expressedin

terms

ofanother

voltage,calledL

SBfor

leastsignificant

bit.U

nfortunatelythe

name

hasa

quitedifferent

meaning

indigital

systems.

Inanalogue

systems,L

SBis

thechange

ininputvoltage

requiredto

changethe

outputbyexactly

onebit.L

ookingatequation

(2.1)or(2.2)shows

that

LSB

DV

FS

2N

:(2.3)

This

isthe

rangeof

inputvoltages

dividedby

thenum

berof

possibleoutput

values.It

isa

convenientquantityforanalysing

thebehaviourofA

DC

sandD

AC

s.The

idealtransferfunctioncan

berew

rittensim

plyin

terms

ofLSB

as

NA

DC D

nint V

AD

C

LSB

;(2.4)

providedthatthe

outputdoesnotgo

outsideits

limits

of0and

2N

1.

As

anexam

ple,figure

2.1on

thepreceding

pageshow

sthe

transfercharacteristic

ofan

ideal3-bit

converter.T

hishas

8possible

digitaloutput

valuesand

thereforeL

SBD

18V

FS .T

hestraight

lineon

theplot

frombottom

leftto

topright

isthe

conceptualtransfer

functionin

equation(2.1),w

hichallow

sthe

outputtotake

anyvalue.

Inreality

theoutputm

ustbean

integer,w

hichturns

thestraight

lineinto

thestaircase

shown

inthe

plot.T

hism

eansthat

arange

ofanalogue

inputsgive

thesam

edigitaloutput,a

featurecalled

quantization.C

onsiderthe

behaviouroftheoutputas

theinputis

raisedfrom

zero.

A

ninputof0

naturallygives

000output.

R

aisingthe

inputatfirstgivesno

changein

outputbecauseofquantization.

T

heoutputjum

psfrom

000to

001w

henthe

inputpassesthrough

12 LSB

D116V

FS ,be-cause

highervaluesare

closerto1

LSB

thanto

0.

T

heoutputrem

ainsat001

untiltheinputrises

above32 L

SB,w

henthe

outputjumps

tothe

nextvalueof

010.T

husa

rangeof

inputvaluesfrom

12 LSB

to32 L

SBgives

thesam

eoutputof001,a

spreadof1

LSB

.

T

hiscontinues

untilwe

reachthe

maxim

umvalue

111ofthe

output,which

appearsw

henthe

inputpasses

through1

32L

SB.

Itshould

continueuntil

theinput

risesto

152

LSB

,at

which

pointtheoutputoughtto

jump

tothe

nextvalue.H

owever,itcan’tbecause

thereare

nom

orevalues.

Thus

theoutputm

ustremain

at111untilthe

inputreachesits

full-scale

valueof8

LSB

.

The

problematthe

endsof

therange

isthata

rangeof

inputsof

only12 L

SBgives

zerooutput,

soan

intervalof32 L

SBis

neededfor

maxim

umoutputto

fillthefullrange

of8

LSB

.Itwould

bem

oreconvenientif

a3-bitconverter

couldgive

9outputvalues,0–8,rather

thanonly

0–7.D

AC

shave

similarbehaviour,as

we

shallseein

section8.2.

Section2.2

Resolution,precision

andaccuracy

9

-4 -3 -2 -1 0 1 2 3 4

signal / LSB

time (continuous)

continuous signal

quantized signal

quantization error

1L

SB

Figure2.2

Quantization

errorincontinuous

time

forasine

wave

ofpeakam

plitude4

LSB

anda

3-bitconverter.The

intervalsatthe

endsare

symm

etricforsim

plicity.

Figure2.2

shows

asine

wave,before

andafter

passingthrough

a3-bit

AD

C.T

hisshow

sclearly

theeffectofquantization

–the

damage

doneto

thesignalby

convertingitfrom

analogueto

digital.T

heintervals

attheends

aresym

metric

forsim

plicity.T

hesine

wave

liesbetw

een˙

4L

SBto

usethe

fullrangeof

inputs.T

hequantization

errorlies

between˙

12 LSB

.Ithas

adistinctpattern

forthis

simple

sinew

avebutlooks

randomfor

aless

predictablesignaland

isoften

calledquantization

noise.

2.2R

esolution,precisionand

accuracyT

hesem

ustbeam

ongthe

technicalterms

thatcausem

ostmisunderstanding!

(Well,there

areother

candidates,suchas

synchronousand

asynchronous...)T

hedistinction

isvital

fordata

converters.

R

esolutionorprecision

tellsyouthe

numberofdistinctoutputvaluesthata

measurem

entcan

provide.This

is2

Nforan

N-bitA

DC

.

Alternatively,itcan

bespecified

asthe

changein

inputthatcorrespondsto

them

inimum

changeof

1bitin

theoutput:

thesm

allestchangein

inputvoltagethatcan

beresolved.

This

isjustL

SB.

A

ccuracytells

youhow

closea

measurem

entis

toits

‘correct’value

–the

valuethat

would

beproduced

byan

idealsystem.

Togive

atrivial

example,

a4-digit

voltmeter

thatgives

areading

of1.234

Vis

more

precisethan

a3-digitm

eter,which

reads1.32

V.On

theother

hand,thesecond

meter

ism

oreaccurate

ifthetrue

voltageis

1.321V.A

practicaldifferenceis

thatitisfairly

easyto

gethighresolution

butmuch

more

difficult(andexpensive)to

gethighaccuracy.

10G

eneralfeaturesofanalogue-to-digitalconverters

Chapter2

The

resolutionor

precisioncan

bequoted

indifferent

ways

foran

AD

C,

dependingon

whether

youare

lookingat

theA

DC

aloneor

itsoverall

behaviorin

thesystem

.C

onsidera

10-bitAD

C,forinstance.

Its

outputisa

binaryvalue

of10

bits,which

canrepresent

21

0D1024

distinctvalues.T

husits

resolutionis

10bits

or1partin

1024.

W

ealso

needto

knowthe

rangeofinputvoltage

todeterm

inethe

resolutionon

theinput,

which

isL

SB.Suppose

thattherange

isfrom

0to

afull-scale

valueof

VFS D

3V

.T

hena

changeofone

bitinthe

outputcorrespondsto

achange

ofLSB

D.3

V/=1

024

3m

Von

theinput.W

ecan

thereforesay

thattheA

DC

convertsits

inputtoa

precisionof3

mV.

Accuracy

ism

uchharder

todefine

andm

easureand

thetopic

rapidlygets

verytechnical;

datasheets

forAD

Cs

arecom

plicated.The

simplestspecification

isthe

totalunadjustederror,

which

isthe

largestdifferencebetw

eenthe

actualtransferfunctionand

theidealstraightline.It

isusually

quotedin

bitsbutsom

etimes

in%

orparts

perm

illion(ppm

).A

nidealA

DC

hasa

totalunadjustederrorof˙

12L

SBas

infigure

2.1.L

argererrors

oftenarise

fromother

partsof

thesystem

,suchas

thevoltage

reference.Y

ouneed

toconsider

allofthese

toevaluate

theoverallaccuracy.

Forinstance,how

accurateis

thegain

oftheam

plifierifyouneed

one?N

oiseis

anothermajorproblem

inpractice.

2.3S

umm

ary

T

heaction

ofanA

DC

ism

ostsimply

expressedin

terms

ofthevoltage

LSB

DV

FS =2

N.

T

heidealtransferfunction

isthen

NA

DC D

nint.VA

DC=L

SB/

within

limits.

M

akesure

thatyouknow

thedifference

between

precision(resolution)and

accuracy.

R

esolution(precision)can

beexpressed

asthe

numberofbits

inthe

outputorasL

SB,the

changein

analogueinputthatcorresponds

toa

changeofa

singlebitin

theoutput.

T

hetotalunadjusted

erroristhe

simplestm

easureofaccuracy

foranA

DC

.

A

complete

dataacquisition

systemhas

many

sourcesoferror,notjustthe

AD

C.

2.4E

xamples

Exam

ple2.1

A12-bitA

DC

hasa

full-scalerange

from0.0–3.3

V.Whatis

itsresolution

involtage

(LSB

)?

Exam

ple2.2

Calculate

thedigitaloutputin

hexadecimalfrom

a12-bitA

DC

with

arange

of5

Vw

henthe

inputvoltageis

(i)0.1V

(ii)1V

(iii)4V,(iv)5

V.Rem

emberthatthe

outputmust

bean

integer.[0x052]

Exam

ple2.3

An

8-bitAD

Chasa

full-scalerange

of0–2.048V.W

hatrangesofinputvoltagesw

ouldgive

hexadecimaloutputs

of(i)

0x00,(ii)0x09,(iii)

0xAB

and(iv)

0xFF?Q

uoteyour

answers

tothe

nearestmillivolt.

[0–4m

V]

Section2.4

Exam

ples11

Exam

ple2.4

An

AD

Cis

requiredto

convertavoltage

between

zeroand

1.8V

with

aresolu-

tionof1

mV.Specify

theconverter.

Exam

ple2.5

Why

doesanidealA

DC

havea

totalunadjustederrorof

12L

SBratherthan

zero?

3

Basic

typesofanalogue-to-digitalconverter

3.1Introduction

These

arethe

comm

ontypes

ofAD

Cin

currentuse.

Flash

–fast,low

precision,highpow

er

Pipeline

–essentially

asequence

oflow-resolution

flashconverters

Successive-approxim

ation(SA

R)

–m

ostpopulargeneral-purpose

AD

C,w

idelyfound

inm

icrocontrollersand

systems

onchip

(SoCs)

Sigm

a–delta(†

–

)–radically

differentapproach,deferredto

chapter4

Integrating

–slow

,highprecision,low

power(fading

away?)

The

listgoesfrom

fast,lowprecision

devicesto

slow,high

precisionand

theirapplicationsare

summ

arizedin

figure3.1

onthe

facingpage.I’llgo

throughthem

inturn,in

more

orlessdetail.

Mostconverters

takesam

plesofthe

inputatthesam

erate

atwhich

theyproduce

outputvaluesand

aresom

etimes

calledN

yquistconverters(w

e’llseew

hyin

chapter4).

Incontrast,sigm

a–delta

converterssam

plethe

inputat

am

uchhigher

ratethan

theyproduce

outputvalues.

We

needto

doa

littlem

oretheory

beforelooking

attheseso

Ishallputthemoffuntilchapter4.

Most

basicA

DC

sw

orkin

essentiallythe

same

way:

theinput

iscom

paredw

itha

setof

known

voltagesand

theclosestm

atchis

found.T

hedifference

isthe

way

inw

hichthe

known

voltagesare

generatedand

whetherthis

isa

sequentialorsimultaneous

process.The

technologyused

togenerate

thevoltageshaschanged

overtheyears.C

urrentsandresistorsw

ereused

inthe

bipolardays,soV

DIR

.Aproblem

with

thisis

thatitisdifficultto

make

accurateresistors

inintegrated

circuits.The

needfora

currentalsom

akesitdifficultto

reducethe

power.N

owadays

thevoltages

aregenerated

byusing

chargeson

capacitorsand

VD

Q=C

.Itiseasy

tofabricate

accuratecapacitors

inM

OS

technology;infactthe

gateofa

MO

SFET

isessentially

acapacitor.

How

ever,this

canlead

toaw

kward

problems

becausethe

inputto

suchan

AD

Clooks

likea

capacitorratherthana

resistor.I’llexplainthis

more

forSAR

AD

Cs

insection

3.6.

12

Section3.1

Introduction13

Figure3.1

Resolution

asa

functionofsam

plingrate

forcomm

ontypes

ofAD

C,show

ingtheir

typicalapplications[from

TexasInstrum

entscatalogue].Flash

AD

Cs

areom

itted.

Before

lookingat

AD

Cs

themselves,

it’sam

usingto

lookat

theircost.

Table3.1

shows

anexam

plefor

afam

ilyof

microcontrollers

with

differentanalogueinputs.

The

MSP430

isa

simple,

16-bitm

icrocontrollerdesigned

forlow

-power

applications[2].

The

cheapestoption

hasonly

acom

paratorrather

thana

trueA

DC

.A10-bitA

DC

nearlydoubles

theprice

andthe

16-bitAD

Ctriples

it.This

tablealso

shows

aninteresting

featureofm

odernintegrated

circuits.Presum

ablyabout$1.00

ofthe$1.50

priceofthe

MSP430F2003

goeson

itsA

DC

.This

istw

o-thirds

ofthe

cost!T

hedigital

partof

asm

allIC

(bycurrent

standards)is

almost

free.Few

standalone16-bitsigm

a–deltaA

DC

scostless

than$1.50

too.Crazy.

The

costisreflected

inthe

areaofthe

chiprequired

foranA

DC

.Figure3.2

onthe

following

pageis

alow

-resolutionim

ageofthe

die(the

baresilicon

chip)ofanM

SP430m

icrocontroller.T

hisis

am

uchlargerdevice

thanthose

listedin

table3.1

andcontains

three16-bitA

DC

s,seenon

theleftofthe

image.E

achofthese

islargerthan

anyotherm

oduleon

thechip

exceptfortheflash

mem

oryin

thecentre.

Even

theC

PUis

smallerthan

asingle

AD

C.T

hecostofm

akinga

chipis

roughlyproportionalto

itsarea,and

AD

Cs

mustbe

extensivelytested

oneach

chip,soI

Table3.1

Priceof

differentm

embers

ofthe

TexasInstrum

entsM

SP430fam

ilyof

microcon-

trollers,which

dependson

theiranalogueinputs.T

hedevices

areotherw

isenearly

identical.

Device

Analogue

inputPrice

MSP430F2001

comparator

$0.55M

SP430F200210-bitsuccessive-approxim

ationA

DC

$0.99M

SP430F200316-bitsigm

a–deltaA

DC

$1.50

14B

asictypes

ofanalogue-to-digitalconverterC

hapter3

Figure3.2

Image

ofthe

die(chip)

foran

MSP430

microcontroller

with

them

ainm

odulesoutlined.

Each

ofthe

threelarge

blockson

theleftis

anA

DC

.The

CPU

isoutlined

inyellow

onthe

right.

suspectthatthecostof

thisdevice

isprobably

dominated

bythe

AD

Cs.

(Ithasthree

AD

Cs

sothatitcan

takethree

measurem

entssim

ultaneously,which

isrequired

form

easuringelectrical

poweraccurately.)E

xploringfurther,table

3.2on

thenextpage

listsa

selectionofA

DC

sfrom

theTexas

Instru-m

entsA

mplifier

andD

ataC

onverterG

uide(2009).

Ichose

thiscatalogue

becauseitincludes

prices,which

isnotalw

aysthe

case;unfortunatelythey

donotm

akeflash

AD

Cs.T

herange

ofspecifications

isim

mense

andthis

isreflected

inthe

price.Ihavetried

tochoose

aleading

edgedevice

(expensive,oftencalled

thebleeding

edge),middle

oftherange

anda

cheapdevice.

3.2C

omparators

Before

lookingatany

ofthe

AD

Cs

listedabove,w

e’lltakew

hatlookslike

adiversion

andex-

plorethe

analoguecom

parator.This

forms

partofmany

typesofconverterand

cansom

etimes

beused

asa

substitutefor

a‘real’

AD

C.T

heobvious

advantageis

cost:a

comparator

ism

uchsim

plerandtherefore

cheaperthana

trueA

DC

,asshow

nby

table3.1.W

hypay

foranA

DC

ifa

comparatorw

illdothe

job?A

comparatoris

roughlylike

anop-am

pused

withoutnegative

feedback.T

helack

offeed-back

means

thatmostofthe

usualrulesaboutcircuits

with

op-amps

nonotapply.Forexam

ple,you

cannotassume

thatVC

DV

asfor

anop-am

pw

ithnegative

feedback.In

factrealcom-

paratorsuse

alittle

positivefeedback

ratherthan

negativefeedback

tohelp

theiroutputs

tochange

quickly.T

hesym

bolandits

outputasa

functionof

theinputs

areshow

nin

figure3.3.

Section3.2

Com

parators15

Table3.2

Approxim

ateprice

ofa

selectionof

AD

Cs

fromTexas

Instruments

(2009Q

1).T

hespeed

ism

easuredin

samples

persecond(sps).

Device

Architecture

Resolution

(bits)Speed

(sps)Price

AD

S5474pipeline

14400M

$161A

DS6122

pipeline12

65M$12

AD

S8422SA

R16

4M$24

AD

S7883SA

R12

3M$2.5

AD

S7885SA

R8

3M$1

AD

S1281sigm

a–delta31

4k$30

AD

S1248sigm

a–delta24

2k$5

AD

S1100sigm

a–delta16

128$2

The

‘crossedS’is

oftenom

itted,inw

hichcase

thesym

bolisthe

same

asan

op-amp.

Inw

ords,the

comparator

tellsyou

whether

thedifference

involtage

between

itsinputs,

VC

V,is

positiveornegative:

the

outputgoesto

ground(orthe

negativesupply),logicalzero,if

VC<

V

the

outputgoeshigh

(toV

CC

here),logicalone,ifVC

>V

.

The

transitionoccurs

overavery

smallrange

ofdifferencesVC

V

.C

omparators

areused

insidem

osttypesofA

DC

,asw

eshallsee.In

factaone-bitA

DC

canbe

made

froma

comparator.Tie

theinput

Vto

areference

at12V

FS ,where

VFS

isthe

full-scalevoltage.T

hecom

paratornowacts

asa

one-bitAD

Cforthe

inputV

AD

C DVC

asfollow

s:

output=

0if

VA

DC

<12V

FS

output=

1if

VA

DC

>12V

FS .

I’llsaym

oreaboutcom

paratorsand

giveexam

plesoftheiruse

insection

6.5.

+-

V+

V-

Vout

VC

C

Vout

VC

C

0V+ -

V-

Figure3.3

The

symboland

behaviourofananalogue

comparator.

16B

asictypes

ofanalogue-to-digitalconverterC

hapter3

VFS

- +- +- +- +- +- +- +

VA

DC

RRRRRRR 12 R 32

priority encoder

latch

clock

comparators

‘thermometer code’

digital output

1 1 1 0 0 0 0

7654321

011

12L

SB

52L

SB

72L

SB

NADC

32L

SB

Figure3.4

Structureof

a3-bit

flashA

DC

.T

heinput

voltageV

AD

Clies

between

52 LSB

and72 L

SB.

3.3Flash

convertersF

lashor

parallelconvertersare

thefastesttype

ofA

DC

atthecostof

alarge

number

ofcom

-parators:

onefor

eachof

the2

Npossible

outputvalues

exceptzero,

notjust

onefor

eachof

theN

bits.T

heirstructure

isstraightforw

ard,shown

infigure

3.4for

a3-bit

AD

C.T

hishas

23D

8possible

outputsand

thereforeneeds

81D

7com

parators.Achain

ofresistors,con-nected

between

Vref and

ground,generatesa

setof7voltages

thatdefinethe

transitionsbetw

eenone

outputvalue

andthe

next.T

hesevoltages

were

shown

infigure

2.1on

page7

andlie

at12 L

SB,

32 LSB

andso

on,separated

byL

SBD

18V

ref ,up

to1

32L

SB(but

not1

52L

SB!).

Each

voltagefeeds

thenegative

inputof

acom

parator,whose

positiveterm

inalis

connectedto

theinputvoltage

VA

DC

.T

heoutputof

eachcom

paratoris

1if

VA

DC

ishigher

thanits

subdividedreference

voltageand

0ifthe

inputislow

er.Look

attheoutputs

ofthesetofcom

paratorsas

VA

DC

israised

fromzero

toV

ref .

A

llcomparators

give0

ifV

AD

C<

12 LSB

.

C

omparator1

gives1

andallothers

remain

at0if

12 LSB

<V

AD

C<

32 LSB

.

Section3.3

Flash

converters17

C

omparators

1and

2give

1and

allothersstay

at0if

32 LSB

<V

AD

C<

52 LSB

.

...and

soon

until

A

llcomparators

give1

if1

32L

SB<

VA

DC

.

Thus

theoutput

fromthe

comparators

typicallyhas

aset

of1s

fromthe

lower

valuesand

0sfrom

theupper

values,which

isaptly

calledtherm

ometer

code.T

hisis

aninefficient

way

ofrepresenting

thevalue

becauseitrequires

onebitper

nonzerovalue,so

7bits

here.C

ombina-

tionallogicistherefore

usedto

convertthetherm

ometercode

intoa

more

compactform

,suchas

straightforward

binarycode.

This

needsto

pickoutthe

highestnonzeroinput,w

hichis

astan-

dardfunction

calleda

priorityencoder.Y

oushould

recallthisfrom

DigitalE

lectronics2.Ihave

shown

alatch

onthe

outputofthe

priorityencoder,w

hichis

drivenby

aclock

tosynchronize

theA

DC

with

thedigitalsystem

.Flash

AD

Cs

arefast.T

hecom

paratorsgive

onlyone

delaybecause

theyare

inparallel,plus

furthercontributionsfrom

the(sim

ple)priorityencoderand

latch.The

obviousdisadvantage

iscom

plexitybecause

som

anycom

paratorsare

needed.This

typicallylim

itsflash

AD

Cs

to8

bits(255

comparators).

Another

issueis

thepow

erconsum

ptionof

thecom

paratorsbecause

theyneed

ahigh

currentfora

fastresponse.T

hevoltage

inputmustdrive

theload

presentedby

allthe

comparators

inparallel,w

hichcan

bea

problemtoo.

FlashA

DC

sare

thereforerestricted

toapplications

thatneedhigh

speedand

lowprecision,and

where

thelarge

powerconsum

ptioncan

betolerated.

Afeature

ofthe

resistorchain

infigure

3.4on

thefacing

pagem

ayhave

caughtyoureye.

Mostof

theresistors

havethe

same

valueR

butthelow

estis12R

andthe

highestis32R

.T

hisis

necessaryto

givethe

usualtransferfunction,which

was

shown

infigure

2.1.Rem

emberthat

thebottom

stepis

narrowerthan

usualandthe

topstep

isw

ider.Straightforw

ardflash

convertersare

rarelyused

now.

The

largenum

berof

comparators

means

thattheyare

expensiveto

make

andconsum

ea

lotofpow

er.N

ewer

devicesreduce

thenum

berofcomparators

byusing

techniquescalled

interpolationand

folding.An

example

isthe

NationalSem

iconductorAD

C083000,an

8-bitconverterthatcanproduce

310

9sam

plesper

second(3

Gsps).A

tthatrateitcould

digitizedirectly

thelow

erfrequencyused

byG

SMm

obilephones,900

MH

z,andis

almostfastenough

forthe

higherfrequency

of1.8

GH

z.(O

fcourse

youhave

togetallthatdata

outoftheA

DC

andprocess

itinsom

ew

ay...)Its

datasheetis

onthe

web

ifyouw

anttofind

outmore.Itdissipates

nearly2

Wfrom

a1.9

Vsupply.

Mobile

phonesystem

sillustrate

thesort

ofapplication

forw

hichthe

AD

C083000

isin-

tended.T

heidea

isto

buildradio

systems

where

thesignalfrom

theantenna

isdigitized

with-

outany

processingin

itsanalogue

form,

exceptperhaps

amplification.

All

theprocessing

isdone

digitallyin

sucha

software

radio.A

greatadvantageis

thattheycan

‘trivially’be

repro-gram

med

tosw

itchbetw

eenthe

two

widely

usedsystem

sform

obilephones,G

SMand

CD

MA

.E

venbetter,a

software

radiocan

processthe

two

simultaneously!

This

technologyis

alreadybeing

testedin

basestations

form

obilephones.

Itmay

arrivein

yourhandsetbefore

toolong,

giventhe

generaladvanceof

digitalprocessing,butthepow

erconsum

ptionrem

ainsa

seriousproblem

.

18B

asictypes

ofanalogue-to-digitalconverterC

hapter3

S +

-A

DC

DA

CT

/H

k = 2 bits of digital output

analogueinput from

previous

stage

amplified

residualanalogueoutput to next stage

¥ 4

Figure3.5

One

stageofa

pipelineA

DC

thatproduceskD

2bits.

3.4P

ipelineconverters

Pipelineconverters

arefast

butm

uchsm

allerthan

fullflash

converters.T

hebasic

ideais

tom

akea

coarseflash

conversionof

theinput

(onlya

fewbits)

andsubtract

theconverted

partof

thevoltage

toleave

arem

ainder.T

hisis

passedto

thenextstage

ofthe

pipeline,where

theprocess

isrepeated

toim

provethe

resolution.T

hereare

asm

anystages

asneeded

toget

thedesired

number

ofbits.

Itis

something

likedoing

divisionby

hand:Y

oufirst

operateon

them

ostsignificantdigit,thenon

therem

ainder(thenextm

ostsignificantdigit)andso

on,untilthecom

pletedivision

hasbeen

performed

down

tothe

leastsignificantdigit.A

defectof

pipelineconverters

islatency:

The

complete

outputis

notavailable

untilthe

signalhas

passedthrough

allstages

ofthe

pipeline.H

owever,

oncethe

firstvalue

hasbeen

completed,subsequentoutputs

appearasfastas

eachstage

canrun.Pipelines

areused

where

acontinuous

streamofconversions

isneeded

andvideo

signalsare

agood

example.

Figure3.5

shows

theprinciple

indetail.T

hisis

astage

inthe

middle

ofapipeline;the

finalone

would

needonly

anA

DC

.

1.T

hetrack-and-hold

circuit(T/H

)holdsthe

inputtothe

AD

Cconstantduring

eachconver-

sion.Itopens

totransfer

thesignalfrom

theprevious

stagew

henthe

conversionin

thisstage

hasbeen

completed

anditis

readyforthe

nextsample.

2.T

heA

DC

makes

aflash

conversionof

theinputand

producesa

k-bitoutput.T

hism

aybe

onlya

singlebitbutis

usuallym

ore(often

‘112 ’,w

hichis

trickyto

explain).I

havechosen

kD2

forthesketch.

3.T

heD

AC

convertsthe

k-bitcode

backto

ananalogue

voltage.T

hisis

thepart

ofthe

analogueinputvoltage

thatisincluded

inthe

k-bitdigitaloutput.

4.T

hesubtractor

givesthe

differencebetw

eenthe

inputand

theoutput

ofthe

DA

C.T

hisis

theresidualpartof

theanalogue

inputthatisnotincluded

inthe

digitaloutputandis

passedto

thenextstage.

5.T

heam

plifierboosts

theresidual

signalback

tothe

rangeof

theinput.

Fork

D2

theaverage

magnitude

ofthe

residualis14

thatofthe

input.A

nam

plifierw

itha

gainof

4com

pensatesforthis

andallow

thecircuits

foreachstage

tobe

identical.

The

operationis

illustratedin

figure3.6

onthe

facingpage

foratw

o-stagepipeline

andan

inputof

0:4

VFS .E

achflash

converterusesvoltage

levelsof

14V

FS ,12V

FSand

34V

FS .

Section3.4

Pipeline

converters19

VFS0

VA

DC =

0.4V

FS

VFS

14 VFS

12 VFS

34

convertedpart

convertedpart

remainder

remainder

firstflashlevels

first flash result:

01

secondflashlevels

second flash result:

10

remainder

amplifiedby 4

11100100

11100100

amplifier

stage 1 AD

Cstage 2 A

DC

subtractor

convertedpart

subtracted

Figure3.6

Operation

ofa

2-stagepipeline

AD

Cw

ithan

inputofV

AD

C D0:4

VFS

anda

2-bitflash

AD

Cin

eachstage.

1.T

heinputis

compared

with

thevoltage

levelsofthe

firstflashconverter.

2.T

hevoltage

liesbetw

een14V

FSand

12V

FSso

theoutputofthis

stageis

01,which

givesthe

mostsignificantpairofbits.

3.T

hedifference

betwen

theinputvalue

andthe

nearestvoltagelevelbelow

isam

plifiedby

4forthe

nextstage.Here

thedifference

is0:4

VFS

14V

FS D0:1

5V

FS ,which

isam

plifiedto

0:6

VFS .

4.T

heam

plifiedrem

ainderis

compared

with

theusualsetof

voltagelevels

inthe

secondflash

converter.

5.T

hevoltage

liesbetw

een12V

FSand

34V

FSso

theoutputofthis

stageis

10,which

givesthe

leastsignificantpairofbits.

6.T

herem

ainderof

0:1

VFS

would

beam

plifiedand

passedto

thenext

stagein

alonger

pipeline.

The

overallconverterincludeslogicto

accumulate

thebitsproduced

byeach

stageand

assemble

thecom

pletedigitaloutput.

Inpractice

thisneeds

heavyerror

correctionbecause

ofthe

DA

C,

subtractorand

amplifier

ineach

stage.A

‘small’

errorin

thefirststage

would

almostcertainly

belarger

thanthe

valuerepresented

bythe

bitsfurther

downstream

.N

astyerrors

suchas

lackofm

onotonicityand

missing

codesw

ouldarise

iftherew

ereno

correction.H

owm

uchsim

plerisa

pipelinethan

afullflash

converter?Suppose

thatwe

want12

bits.

20B

asictypes

ofanalogue-to-digitalconverterC

hapter3

A

fullflashconverterw

ouldneed

21

21D

4095

comparators,w

hichis

afrighteningly

largenum

ber.

A

ssume

thatthepipeline

uses2-bitconverters.

Itthereforeneeds

6stages

toproduce

12bits

intotal.

Each

2-bitflash

convertergives

4possible

outputsand

thereforeneeds

3com

parators.This

requires18

comparators

intotal.

The

pipelinerequires

adram

aticallysm

allernum

berof

comparators.

Of

courseit

isnot

thissim

plebecause

thepipeline

needsD

AC

s,subtractors

andam

plifiersas

well.

Areal

pipelineconverteralso

needsm

orestages

toproduce

extrabits

fortheerror-correcting

logic.Table

3.2on

page15

shows

typicalspecifications.

PipelineA

DC

sproduce

8–14bits

at50–500

Msps

(megasam

plespersecond).T

heinputs

may

besingle-ended

ordifferential.They

areoften

usedin

image

processingand

high-frequencyw

irelesscom

munication

systems.

Spe-cialized

circuitdesignis

neededto

getgoodresults

atthesehigh

frequencies,which

goesfar

beyondthis

course.

3.5S

uccessive-approximation

(SA

R)converters

Successive-approximation

convertersare

currentlythe

standardchoice

fora

general-purposeA

DC

.T

heirresolution

istypically

8–16bits

andthe

speedreaches

megasam

plesper

sec-ond

(Msps),

asshow

nin

table3.2

onpage

15.For

some

reasonthe

name

isexpanded

into‘successive-approxim

ationregister’so

thatitcanbe

contractedinto

SAR

.T

heoperation

isconceptually

relatedto

thatofa

pipelineconverter,buta

pipelinehas

nu-m

eroussets

ofhardw

areso

thatitcanoperate

likea

productionline

onnum

eroussam

plesat

thesam

etim

e,w

hilea

SAR

makes

successiveoperations

usinga

singleset

ofhardw

arefor

economy

attheexpense

ofspeed.Y

ouare

more

likelyto

usea

SAR

AD

Cthan

anyothertype

ofAD

Cso

itgetsthe

mostspace

inthese

notes.I’llgothrough

theiroperationin

thissection

anddescribe

some

practicalaspectsin

thenext.

They

arew

idelyavailable

asdiscrete

components

orbuilt

intom

icrocontrollersand

othersystem

s-on-chip.T

heN

XP

LPC

1768m

icrocontrollerin

them

bedm

odulehas

an8-channel,12-bitSA

RA

DC

.SA

RA

DC

sw

orkby

‘homing

in’on

theresultusing

binarychopping,w

hichis

astandard

way

offindingsolutions

toequations

oftheform

f.x

/D0.T

hisis

illustratedfora

4-bitSAR

AD

Cin

figure3.7

onthe

nextpage.H

ereis

thesequence

ofoperations

foran

inputvoltageof

VA

DC D

0:4

VFS .

1.T

heinputvoltage

VA

DC

iscom

paredw

iththe

midpoint

12V

FSofthe

fullrange.Inthis

caseV

AD

C<

12V

FSso

them

ostsignificantbit(msb)=

0.

2.W

enow

knowthatthe

inputliesbetw

een0

and12V

FS .T

heinputis

nextcompared

with

them

idpointofthisrange,

14V

FS .We

findV

AD

C>

14V

FSso

thenextbitis

1.

3.N

oww

eknow

thattheinputlies

between

14V

FSand

12V

FS .T

heinputis

nextcompared

with

them

idpointofthisrange,

38V

FS .We

findV

AD

C>

38V

FSso

thisbitis

1again.

Section3.5

Successive-approximation

(SAR

)converters21

VFS0

VA

DC

time

① Full range: com

pare input with (1/2)V

FS .

16 intervals of resolution (LSB

)

input

0

msb

FindV

in smaller so bit =

0

①

② H

alve range: compare input w

ith (1/4)VFS .

VFS

14

②

FindV

in larger so bit = 1

1

③ H

alve range: compare input w

ith (3/8)VFS .

VFS

38③

FindV

in larger so bit = 1

1

④ H

alve range: compare input w

ith (7/16)VFS .

VFS

716④

FindV

in smaller so bit =

0

0lsb=

output

Figure3.7O

perationofa

4-bitsuccessiveapproxim

ationA

DC

with

aninputof

VA

DC D

0:4

VFS .

The

behaviourattheextrem

evalues

hasbeen

simplified.

4.N

oww

eknow

thattheinputliesbetw

een38V

FSand

12V

FS .The

inputisthereforecom

paredw

iththe

midpointofthis

range,716V

FS .This

time

VA

DC

<716V

FSso

thisbitis

0.Itisthe

leastsignificantbit(lsb)fora4-bitconverter.

This

processis

repeatedfor

eachbit,halving

therange

eachtim

e.E

achstep

typicallyrequires

oneclock

cycle(som

etimestw

o)tom

akea

comparison

andsetup

thenew

voltage.An

overheadis

requiredto

starttheconversion,particularly

tosam

plethe

inputvoltage.T

hebits

ofoutput

aregenerated

insequence,starting

with

them

ostsignificantbit,msb.T

hisfits

naturallyinto

anA

DC

with

serialoutput.

Operation

ofasw

itched-capacitorS

AR

AD

CT

hreem

ainfunctions

arerequired

insidea

SAR

AD

C:

logicto

controlthe

operation,som

ew

ayof

generatingthe

voltagesfor

comparison

anda

comparator.

Back

inthe

bipolardays

thevoltagesw

eregenerated

usinga

DA

C,often

with

anR

–2R

ladder(tobe

explainedin

section8.4

onpage

73).Ingenious

arrangements

ofsw

itchedcapacitors

arenow

usedinstead

tostore

theinput,generate

thevoltages

andm

akethe

comparisons.

Ifyou

would

liketo

knowthe

detail,take

alook

atanapplication

notefrom

TexasInstrum

ents[16]

orsection

12of

theFreescale

M68H

C11

Reference

Manual[15].

Atypical,m

odernSA

Rconverter

usesa

setofcapacitors

andsw

itchesto

redistributetheir

charge,asshow

nin

figure3.8

onthe

nextpage.This

isa

4-bitconvertertom

atchthe

operationsshow

nin

figure3.7.I’llassum

ethe

same

inputvoltageas

well,

VA

DC D

0:4

VFS .T

hevalues

of

22B

asictypes

ofanalogue-to-digitalconverterC

hapter3

C 12C 14

C 18C 18

CS3

S2

S1

S0

S0 ¢

Vin

Vref

-+S

A

VA

to

logic

Figure3.8

Circuitofa

4-bit,charge-redistributionSA

RA

DC

.The

switches

arein

thepositions

tosam

plethe

input.

thecapacitors

areC

,12C

,14C

andso

onto

givethe

binarychopping

sequence.T

heirswitches

arelabelled

with

thenum

berof

thecorresponding

bitin

theoutput.

An

extracapacitor

with

thesm

allestvalueatsw

itchS

00brings

thetotalcapacitance

to2C

,which

isim

portantforthe

detailedoperation.T

hereference

voltageis

equaltothe

full-scalevoltage

forthiscircuit,

VFS D

Vref .

The

switches

areconstructed

fromM

OSFE

Ts.

The

onlyother

analoguecom

ponentisa

comparator,w

hichis

connectedthe

wrong

way

aroundin

figure1

oftheapplication

note[16].I

havenotshow

nthe

clocknorthe

logicneeded

tooperate

thesw

itchesand

storethe

result.This

includesthe

successive-approximation

registerthatgivesthe

converteritsnam

e.T

hefirst

stepis

tosam

plethe

input.A

llcapacitors

areconnected

toV

AD

Cand

switch

Ais

closedto

connectthenegative

inputofthe

comparator

toground

asin

figure3.8.

The

‘top’plates

ofthe

capacitorsare

groundedand

their‘bottom

’plates

arecharged

toV

AD

C .T

hevital

featureis

thattheinputofa

SAR

AD

Cis

acapacitance.

I’llexplainw

hythis

isim

portantinsection

3.6.In

thesecond

step,sw

itchA

isopened

todisconnect

groundfrom

thetop

platesof

thecapacitors.

The

individualswitches

arethen

moved

sothatthe

bottomplates

ofthe

capacitorsare

connectedto

groundinstead.

The

resultingcircuit

isshow

nin

figure3.9.

The

chargeon

thecapacitors

remains

fixedbecause

nocurrents

flow.

This

means

thatthevoltage

acrossthe

capacitorsalso

remains

thesam

e.T

husthe

potentialdifference

between

thebottom

andtop

platesis

stillV

AD

Cbut

nowthe

bottomplates

aregrounded

sothe

topplates

areforced

to

C 12C 14

C 18C 18

CS3

S2

S1

S0

S0 ¢

Vin

Vref

-+S

A

VA

Figure3.9

Holding

phaseofa

4-bit,charge-redistributionSA

RA

DC

.

Section3.6

Practicalissues

with

SAR

AD

Cs

23

C 12C 14

C 18C 18

CS3

S2

S1

S0

S0 ¢

Vin

Vref

-+S

A

VA

Figure3.10

Finalconfiguration

ofa

4-bit,charge-redistribution

SAR

AD

Cfor

aninput

ofV

AD

C D0:4

VFS ,w

hichgives

abinary

outputof0110.

VA D

V

AD

C .N

extcomes

theconversion

itself.Each

ofthesuccessive

approximations

ism

adeby

moving

oneof

thesw

itchesfrom

groundto

Vref .

The

firststepuses

thelargestcapacitor.

Moving

S3

fromground

toV

ref addsa

voltageof

12V

ref toV

Abecause

thenetw

orkof

capacitorsacts

likea

potentialdivider.(I’m

notgoingto

explainthe

details.)T

husthe

overallvoltageon

thetop

platesbecom

esV

AD

12V

ref V

AD

C .T

hecom

paratorcom

paresthis

with

ground,w

hichis

effectivelythe

same

ascom

paringV

AD

Cw

ith12V

ref .T

hisis

justwhatw

ew

antforthe

firststepofthe

binarychopping.H

erew

efind

thatV

AD

C<

12V

ref soS

3is

moved

backto

ground.T

hisis

repeatedforthe

remaining

bits.Moving

S2

fromground

toV

ref compares

VA

DC

with

14V

ref becausethe

capacitanceis

only12C

,andso

on.Figure3.10

shows

thefinalconfiguration

ofthesw

itchesfor

VA

DC D

0:4

VFS .

3.6P

racticalissuesw

ithS

AR

AD

Cs

SAR

AD

Cs

areprobably

them

oststraightforward

typeofA

DC

.Frequentlyyou

won’thave

tow

orryaboutsom

eofthe

detailsbecause

theconverteris

buriedin

am

icrocontroller,butevenin

thesecases

youm

ustreadthe

datasheetthoroughly!

Ihaven’tprovided

anexam

pleof

adata

sheetbecauseyou

arem

orelikely

touse

theSA

RA

DC

ina

microcontroller.

The

inputsare

usuallysingle-ended

butsom

etimes

differential.T

hefull-scale

voltageis

usuallythe

same

asthe

referencevoltage,

VFS D

Vref ,butoccasionally

VFS D

2V

ref .O

utputsm

aybe

parallelor

serial,often

usingSPI

orI²C

.Serialoutput

startingw

iththe

msb

ism

ostcom

mon

andconveniently

matches

theoperation

oftheA

DC

.Ofcourse

youjustread

aregister

iftheA

DC

isin

am

icrocontroller.

Choose

thefrequency

ofoperationA

sw

ehave

justseen,theoperation

ofaSA

RA

DC

relieson

thestorage

ofchargeon

switched

capacitors.T

hisleads

totw

olim

itson

thefrequency

ofthe

clockbecause

noneof

thecom

po-nents

areideal.

T

heconversion

must

becom

pletedbefore

significantcharge

hasleaked

away

fromthe

capacitors.The

inputofthecom

paratordraws

asm

allcurrent,opensw

itchesdo

nothave

24B

asictypes

ofanalogue-to-digitalconverterC

hapter3

infiniteresistance

andnordo

thecapacitors

themselves.T

heclock

musttherefore

notbetoo

slow.

O

nthe

otherhand,closed

switches

donothave

zeroresistance.

Time

musttherefore

beallow

edfor

chargeto

redistributethrough

themso

thatthevoltages

havestabilized

andthe

outputofthecom

paratorisvalid.T

husthe

clockcannotbe

toofasteither.

The

clockfrequency

thereforehasupperand

lowerlim

its.Some

discreteSA

RA

DC

shavebuilt-

inclocks

sothis

isnotan

issue.O

thers,particularlyw

ithserialoutput,need

anexternalclock

tosynchronize

thetransm

issionofthe

resultandthis

mustlie

ina

specifiedrange.

Puta

capacitoracross

theanalogue

inputT

hedata

sheetmay

adviseyou

toconnecta

capacitorbetw

eenthe

analogueinputand

groundfortw

om

ainreasons.

T

hecapacitor

actsas

areservoir

andm

akesitfaster

tocharge

theinternalcapacitance,

especiallyifthe

sourcehas

ahigh

internalresistance.I’llexplainthis

shortly.

Itsuppresses

noise.This

appliesboth

toexternalnoise,w

hichw

oulddisturb

them

easure-m

ent.Italsosuppresses

noisegenerated

bythe

sampling

process,which

couldaffectthe

sensorandothersensitive

electronics.This

isnota

trivialpoint:some

earlydigitalsignal

processingsystem

sproved

unusablebecause

som

uchsw

itchingnoise

came

outoftheir

inputs.

The

following

adviceis

takenfrom

thedata

sheetfortheFreescale

MC

9S08QG

andis

typical.

Em

piricaldata

shows

thatcapacitors

onthe

analoginputs

improve

performance

inthe

presenceof

noiseor

when

thesource

impedance

ishigh.

Use

of0.01

µFcapacitors

with

goodhigh-frequency

characteristicsis

sufficient.T

hesecapacitors

arenotnecessary

inallcases,butw

henused

theym

ustbeplaced

asnearaspossibleto

thepackage

pinsand

bereferenced

toV

SSA .

There

isalw

aysa

disadvantage:acapacitorslow

sthe

responseto

changesin

theinput.A

notherpotentialproblem

isthatthe

analogueinputto

theA

DC

may

come

fromthe

outputofan

am-

plifier.Mostop-am

psdo

notlikedriving

capacitativeloads,forreasons

thatyouw

illencounterin

ControlE

E3

andE

lectronicSystem

Design

3.Asm

allresistance,typically10–50

,should

thereforebe

installedbetw

eenthe

outputoftheam

plifierandthe

capacitoracrossthe

input.You

may

remem

beraresistoron

theoutputofthe

op-amp

inthe

microphone

amplifierin

Electronic

Engineering

1Y.This

was

includedforthe

same

reason.

Allow

sufficienttime

forthe

inputtocharge

thecapacitance

The

inputto

acharge-redistribution

SAR

AD

Cis

acapacitor.

This

must

becharged

‘fully’before

theconversion

starts.T

hetim

erequired

comm

onlysets

them

aximum

speedof

conver-sions.T

hestaffatthe

TexasInstrum

entsE

uropeanProductInform

ationC

entretold

me

thatoneof

theirm

ostcom

mon

problems

isthat

engineersdo

notallow

enoughtim

efor

sampling

theinputby

anA

DC

andIhave

heardthe

same

fromA

pplicationsE

ngineersatFreescale.

Section3.6

Practicalissues

with

SAR

AD

Cs

25

V0

VC (t)

t2t

3tt

V0

VC (t)

t

V0

VC (t)

charge

discharge

dischargechargeRC

Figure3.11

Charging

anddischarging

anR

Ccircuit.

How

longshould

beallow

edforthis?

You

shouldofcourse

knowthe

equationforcharging

acapacitor

byheart.

Justin

caseyou

don’t,here

arethe

equationsfor

chargingan

initiallyuncharged

capacitorC

througha

resistorR

froma

supplyat

V0

anddischarging

itfrom

aninitialvoltage

ofV

0 :

Vcharge .t/

DV

0 1

exp t

(3.1)

Vdischarge .t/

DV

0exp

t :

(3.2)

The

time-constant

DR

C.Figure

3.11should

remind

youofthese

curves.N

owapply

theseequations

toan

AD

C.Its

inputcapacitancem

ustbecharged

bythe

appliedvoltage.

The

worstcase

isw

henthe

capacitanceis

initiallyuncharged

andthe

appliedvoltage

isthe

maxim

umvalue.

We

cantherefore

useequation

(3.1)w

ithV

0 DV

FS .T

heexponential

functioninside

thesquare

bracketsshow

sthe

differencebetw

eenthe

presentvoltage

andits

finalvalue,when

thecapacitor

isfully

charged,andis

oftencalled

thecharging

defect.T

hisis

theerror

involtage

dueto

incomplete

chargingfor

theA

DC

andcan

neverbe

eliminated

completely.

The

usualcriterionis

thattheerror

shouldbe

reducedbelow

12L

SBso

thatitwill

notaffect

thedigital

outputin

most

cases.M

athematically

thisrequires

thatthe

time

tchargeallow

edforcharging

theinputcapacitance

obeys

VFS

exp tcharge

<

LSB2

D12

VFS

2N

D2

.NC

1/V

FS :(3.3)

The

full-scalevoltage

cancelsfrom

bothsides

toleave

arequirem

entforthefractionalerrordue

toincom

pletecharging

foranN

-bitAD

C,

exp tcharge

<

2 .N

C1

/:(3.4)

26B

asictypes

ofanalogue-to-digitalconverterC

hapter3

VC

CVin

Rth R

1

thermistor

(a)T

hévenin equivalent circuit of sensor and input to A

DC

(b) Potential divider to Thévenin equivalent

Rin

Cin

Rs

Vs

AD

C input

Vin

sensor

Rs

Vs

Figure3.12

(a)T

héveninequivalent

circuitof

asensor,feeding

theequivalent

circuitfor

theinputof

aSA

RA

DC

.(b)M

anysim

plesensors

takethe

formof

apotentialdivider,w

hichcan

beconverted

toits

Thévenin

equivalentcircuit.

Takenaturallogarithm

sofboth

sidesto

eliminate

theexponentialfunction:

tcharge

<

.N

C1/log

e2:

(3.5)

Multiply

throughoutby

and

cancelthe

minus

signs,rem

embering

toreverse

theinequality

signas

well.T

hisgives

thefinalresult

tcharge> .N

C1/log

e2

:(3.6)

Supposethat

we

areusing

atypical

SAR

AD

Cw

itha

resolutionof

10bits.

Then

.NC

1/log

e2D

7:6so

tcharge>

7:6.In

words,atleast7.6

time-constants

shouldbe

allowed

forthecapacitorto

charge.This

isa

greatdeallongerthanthe

usual‘ruleofthum

b’of3

becausethat

would

leavethe

capacitoronly

95%charged,w

hichisn’tgood

enoughfora

10-bitconversion:itm

ustbeatleast99.95%

charged.T

henextproblem

isto

identifythe

valuesthatenter

theusualexpression

DR

Cfor

thetim

e-constant.T

hecapacitance

isthe

inputcapacitanceof

theSA

Rnetw

ork,C

AD

C ,which

isgiven

inthe

datasheet.

The

resistancecom

esfrom

thesw

itchesinside

theconverter

RA

DC ,

which

isalso

inthe

datasheet,plus

theoutputresistance

Rs ofthe

sourcethatdrives

theA

DC

.T

hisis

illustratedin

figure3.12(a).

You

may

needto

doa

littlecircuit

analysisto

convertthe

actualcircuit

ofthe

sensorinto

itsT

héveninequivalent

(Electronic

Engineering

1X).For

example,tem

peraturem

aybe

measured

usinga

thermistor,w

hichis

typicallyconnected

ina

potentialdividerasin

figure3.12(b).See

chapter7on

page53.

The

otherquestionis

howm

uchtim

ethe

systemallow

sforthe

capacitortocharge.Itis

notthe

fullconversiontim

ebutonly

thetim

efor

which

thecapacitor

isconnected

tothe

inputinthe

sample

mode

(figure3.9).

This

may

beonly

afew

cyclesof

theA

DC

clockand

isagain

specifiedin

thedata

sheet.Sometim

esthe

usercanconfigure

thesam

plingtim

eofan

AD

C.

3.7Integrating

convertersT

heseare

thetraditional

high-resolutionA

DC

s.T

heyw

erew

idelyfound

inm

ultimeters,for

instance,but

havenow

beenlargely

supersededby

sigma–delta

converters.T

heiroperation

Section3.7

Integratingconverters

27

-+

C

RiR (t)

iC (t)

vout (t)

vin (t)

vC (t)

vR (t)

v+

v–

Figure3.13

Op-am

pconnected

asan

integrator.

dependson

analogueintegration,

which

isbased

onthe

circuitshow

nin

figure3.13.

You’ll

studythis

inA

nalogueE

lectronics2

buthere

isa

quickdescription

ofhow

itw

orks.It

allfollow

sfrom

theusualrules

foranalysingcircuits

with

idealop-amps

andnegative

feedback.

0.C

heckthatnegative

feedbackis

present:itis,althoughthrough

acapacitorratherthan

theusualresistor.

1.T

henoninverting

inputterminalofthe

op-amp

isconnected

toground

sovC

D0.

2.T

heinverting

inputterm

inalof

theop-am

pis

thereforea

virtualground

(virtualearth)

becausethe

op-amp

triesto

keepits

inputsatthe

same

voltageso

v DvC

D0.

3.N

ocurrentflow

sinto

theinverting

inputterminalso

iR.t/C

iC.t/D

0.

The

voltagesacross

theresistorand

capacitoraregiven

by

vR

Dv

in v D

vin

(3.7)v

CD

vout

v Dv

out(3.8)

sothe

currentsthrough

themare

iRD

vRR

Dv

in

R(3.9)

iCD

Cdv

C

dt

Ddv

out

dt

(3.10)

The

currentsatthe

invertinginputare

thereforerelated

by

0DiR

.t/CiC

.t/Dv

in

RC

Cdv

out

dt

(3.11)

sodv

out

dt

D

vin

RC

:(3.12)

Integratingthis

with

respecttotim

egives

vout .t/D

1

RC Z

t

vin .t 0/d

t 0:(3.13)

28B

asictypes

ofanalogue-to-digitalconverterC

hapter3

-+

C

R

VA

DC

–Vref

+-

control logic

clockf

countern

output

S1

S2

overflowenable, clear

vout (t)

Figure3.14

Dual-slope

integratingA

DC

.

The

factorofR

Cis

theusualtim

econstant.

Thisanalysisshow

sthattheoutputvoltage

isproportionaltothe

integraloftheinputvoltage.

Itneeds

aboundary

conditionor

constantof

integration,like

allindefinite

integrals.T

hisis

appliedby

short-circuitingthe

capacitortodischarge

it,which

setsv

out D0

atachosen

time.

The

integratorw

orksfor

anyvariation

ofv

in .t/on

itsinput

butI

shallassum

ethat

itis

constanttoanalyse

theintegrating

AD

Cand

willw

ritev

in .t/DV

AD

Cbelow

.Figure

3.14show

showthe

integratorisusedin

anA

DC

.Thisiscalled

adual-slope

converterfor

reasonsthatw

illbecome

obvious.T

heclock

hasfrequency

fand

periodT

D1=f

.H

ereis

thesequence

ofoperations,illustratedin

figure3.15

onthe

facingpage

fortwo

valuesofthe

inputvoltageV

AD

C .

1.Sw

itchS

2is

closedto

zerothe

integratorandthe

counteriscleared.

2.Sw

itchS

1is

connectedto

theinputvoltage

VA

DC ,

S2

isopened

andthe

counterisenabled

attD

0.The

outputvoltageofthe

integratorfallslinearly

with

time

togive

vout .t/D

V

AD

Ct

RC

:(3.14)

3.T

hiscontinues

untilthecounter

hasgone

throughits

rangeN

andoverflow

edafter

time

NT

.The

outputvoltageofthe

integratorisnow

vout .N

T/D

V

AD

CN

T=.R

C/.

4.Sw

itchS

1is

thanchanged

totake

theinputfrom

thereference

voltageV

ref .

5.T

hecounter

restartsfrom

zeroand

theoutput

voltageof

theintegrator

nowrises

with

slopeCV

ref =R

C.

6.T

hecom

paratordetects

when

theoutput

ofthe

integratorreaches

zeroand

stopsthe

counteratn

so

tDn

T.T

hechange

involtage

attheoutputofthe

integratoristherefore

vout D

CV

ref nT

=.R

C/.

Section3.8

Summ

aryofclassicalA

DC

s29

slope = –VA

DC

RC

slope =V

ref

RC

NT

nTt

vout (t)

small

largeV

AD

C

Figure3.15

Operation

ofdual-slopeintegrating

AD

Cfortw

ovalues

oftheinputvoltage

VA

DC .

Equating

thechange

involtage

attheoutputofthe

integratorduringthe

two

phasesshow

sthat

VA

DCN

T

RC

DV

ref nT

RC

sothat

VA

DC D

nNV

ref :(3.15)

Thus

thevalue

nin

thecounter

isthe

convertedvalue

within

ascaling

factor.T

hisshow

svery

clearlyhow

theconvertergives

theratio

oftheinputto

thereference

voltage.Som

ecleverfeatures

ofthisdesign

assistittogive

preciseresults.

T

hevalues

ofR

,C

andT

cancelinthe

convertedresult.T

husnone

needbe

particularlyaccurate,

which

isw

hythe

dual-slopem

ethodis

used.T

hevalues

must

allbe

stable,how

ever,which

means

thattheym

ustremain

constantduringthe

measurem

ent.In

par-ticular,the

capacitormustnotleak

andits

valuem

ustnotchangeas

afunction

ofvoltage.Im

perfectionsofthe

capacitoroftenlim

ittheperform

anceofthe

converter.

T

heinputissam

pledforthe

fixedtim

erequired

forthecounterto

rollover.The

frequencyof

theclock

canbe

chosenso

thatthissam

plingtim

ecancels

interferenceof

aparticular

frequencyin

theinput.

Forexam

ple,pickupfrom

the50

Hz

mains

isa

major

problemin

multim

eters.W

etherefore

arrangefor

theintegration

time

tobe

20m

s,the

periodof

them

ains.T

hisw

illincludeone

fullcycleof

them

ainsand

multiple

fullcyclesof

itsharm

onics.The

averageofa

sinew

aveoverany

numberofcom

pletecycles

iszero

sothis

techniquecancels

interferencew

itha

frequencyof

50H

zand

harmonics.

Unfortunately

youw

illstillhaveproblem

sifyou

move

toa

countryw

ith60

Hz

mains!

Furthertricks

giveextra

accuracybutI

shan’tgointo

thembecause

integratingconverters

arelargely

obsolete.Sigm

a–deltaconverters

providesim

ilarprecision

without

suchdem

andson

theanalogue

components.

How

ever,plentyof

integratingconverters

arestill

inuse

andthey

providea

goodillustration

ofhowop-am

pscan

beused.

3.8S

umm

aryofclassicalA

DC

sT

hishas

beena

lengthychapterso

I’llrepeatthem

ainpoints.

Flash

convertershave

thehighestspeed

butareexpensive

andconsum

ea

highpow

er.

Pipeline

convertersare

usedfor

highersam

plingrates

thanSA

RA

DC

s;they

havehigh

throughputbutsufferfromlatency.

30B

asictypes

ofanalogue-to-digitalconverterC

hapter3

In

practiceyou

arem

ostlikelyto

usea

successive-approximation

(SAR

)AD

C,probably

integratedinto

am

icrocontroller.

M

odernSA

RA

DC

sw

orkby

redistributingcharge

arounda

network

ofswitched

capaci-tors.

Itis

generallystraightforw

ardto

usea

SAR

AD

Cbutthe

capacitativenature

ofits

inputm

aycause

problems:E

nsurethatyou

allowsufficienttim

eforcharging.

Integrating

convertersm

aybe

usefulfor

slow,

high-precisionm

easurements

buthave

largelybeen

displacedby

sigma–delta

converters.

Read

thedata

sheetcarefullybefore

youuse

anyA

DC

(oranycom

ponent,come

tothat).

3.9E

xamples

Exam

ple3.1

A4-bitflash

AD

Chas

afull-scale

rangeof0–5

V.How

many

comparators

doesitcontain

andw

hatvoltagesare

appliedto

them?

Exam

ple3.2

Explain

theoperation

oftheabove

converterwith

aninputof3

V.Calculate

thetherm

ometercode

andfinalbinary

output.[10

(decimal)]

Exam

ple3.3

Repeatthis

fora

4-bitsuccessive-approximation

AD

Cw

iththe

same

voltages.W

orkoutthe

sequenceofcom

parisonsand

thebinary

output.Whatis

wrong

with

theresult?

Exam

ple3.4

Why

doserialSA

RA

DC

ssend

theirmostsignificantbit(m

sb)first?

Exam

ple3.5

A12-bit

SAR

AD

Cis

specifiedas

havingan

inputcapacitance

of40

pFand

inputresistanceof

2k

.W

hatisthe

minim

umsam

plingtim

ethatm

ustbeallow

edto

ensurethat

theerror

dueto

incomplete

chargingis

lessthan

12 LSB

,assuming

thatit

isconnected

toan

idealvoltagesource?

The

AD

Cis

thenconnected

toa

sensorw

ithan

outputresistanceof

10k

.How

doesthis

affectthesam

plingtim

e?

Exam

ple3.6

An

integratingdual-slope

converterusesa

20-bitcounterandthe

voltagerefer-

encehas

am

agnitudeof10.0

V.Atthe

endofa

conversionthe

counterreads838

859(decim

al).W

hatw

asthe

analoginput

voltage?W

hatis

theresolution

ofthis

value?W

hattem

peraturecoefficient

shouldthe

referencevoltage

haveif

theconverter

isto

beaccurate

overthe

range10–35°C

?[7.999

98V,6

digits(1

in10

6or10

µV),

0:0

4ppm

=°C]

4

Sam

pling,oversampling

andsigm

a–deltaconverters

4.1S

ampling

rateand

theN

yquistfrequencyW

ehave

alreadylooked

atprecisionand

accuracyin

theam

plitudeof

sampling.

(What’s

thedifference?)

Another

importantaspectis

therelation

between

thefrequency

ofthe

signalandthe

rateatw

hichitis

sampled.

Rem

ember

thatoneaspectof

usingan

AD

Cis

thatitconvertsa

continuousfunction

oftim

ev.t/

toa

discretesequence

ofsam

plesvŒn

.T

hisclearly

may

‘damage’the

signalinsom

ew

ayand

thissection

shows

theproblem

sthatcan

arise.Let

f

bethe

frequencyofthe

signal,assumed

tobe

asim

plesine

wave

f

s bethe

rateatw

hichitis

sampled,and

Ts D

1=f

s isthe

intervalbetween

samples

The

sampling

frequencyf

s isoften

quotedw

ithunits

of‘samples

persecond’(sps)ratherthanhertz

(Hz)

butthem

eaningis

thesam

e.Suppose

thatf

s D1

kspsto

keepthe

numbers

simple

andconsidera

signalwith

frequencyf

D310

Hz.Figure

4.1(a)onthe

nextpageshow

sa

plotofthe

continuoussignalandthe

discretesam

plesevery1

ms.T

hesam

pleslooklike

areasonable

representationofthe

sinew

ave.N

owsuppose

thatthefrequency

israised

to690

Hz,chosen

because690D

1000

310.T

heoutcom

eis

shown

infigure

4.1(b).The

continuousinputclearly

hasa

higherfrequencybutthe

discretevaluesofthe

samplesare

exactlythe

same

asthoseforthe

310H

zinput!

Inotherw

ords,you

cannottellthedifference

between

thesignals

aftersam

pling.T

hiscalled

aliasingand

isone

ofthe

fundamentalproblem

sof

sampling

datain

time.

The

same

happensfor

frequenciesof

1000C

310D

1310

Hz,

2000˙

310

Hz

andso

on.A

liasingis

illustratedin

anotherway

byfigure

4.2on

thefollow

ingpage,again

forsampling

at1kH

z.Frequenciesfrom

zeroto

500H

zare

sampled

faithfully.Frequenciesin

thenextzone,

500to

1kH

z,are

foldeddow

nbelow

500H

z.T

hism

eansthat

thesam

plesfrom

aninput

at850

Hz

cannotbedistinguished

fromthose

dueto

aninputof150

Hz.In

thenextzone,a

signalat1150

Hz

givesthe

same

samples

asthose

from150

Hz,and

soon.

The

foldedribbon

shows

howdifferentinputfrequencies

giveidenticalsam

ples.U

suallyw

ew

ouldlike

thedata

tobe

sampled

faithfully,meaning

thatthereis

noam

biguityin

thesam

pledsignal.W

em

ustthereforeavoid

aliasing.Supposethatthe

maxim

umfrequency

31

32Sam

pling,oversampling

andsigm

a–deltaconverters

Chapter4

E

EE

E

E

E

EE

E-1 0 1

01

23

45

67

8

E

EE

E

E

E

EE

E-1 0 1

t / ms

V(t) V(t)(a)

f = 310 H

z

(b)f =

690 Hz

Figure4.1

(a)A

sinew

avev.t/

at310

Hz

with

samples

vŒn

taken

every1

ms

shown

bythe

circles.(b)

Sinew

avesat

310H

zand

690H

zsam

pledevery

1m

s.T

hehigher

frequencyis

aliased–

itssam

plesare

identicaltothose

ofthelow

erfrequency.

f

0H

z500

Hz

1000H

z(f

s )

1500H

z

2000H

z

basebandaliasing

folding

folding

Input frequencies that appear to be the sam

e after sampling at 1000

Hz

150H

z

850H

z

1150H

z

1850H

z

(fs /2)

Figure4.2

Aliasing

andfolding

offrequencies

aftersam

plingat

fs D

1ksps.

The

ribbonshow

sthe

frequencyofthe

continuousinputsignaland

thehorizontalscale

shows

theapparent

frequencyof

thesam

pledoutput.

Inputfrequenciesof

150,850,1150H

zand

soon

cannotbedistinguished

aftersam

pling.[A

daptedfrom

Theessentialgude

todata

conversionposter

byA

nalogD

evices.]

Section4.2

Sigma–delta

converters33

inthe

signalisf

max .

Then

theShannon

sampling

theoremstates

thatthesignalcan

berecon-

structedperfectly

fromdiscrete

samples

providedthatthe

sampling

ratef

s obeys

fs

fN D

2fm

ax :(4.1)

The

minim

umacceptable

sampling

rateis

calledthe

Nyquistrate

fN

andis

twice

them

aximum

frequencyin

thesignal.

Turningthis

around,thehighestfrequency

thatcanbe

sampled

with-

outaliasing

ishalf

ofthe

sampling

frequency:f

f

max D

12f

s .In

theexam

pleabove

we

sampled

thedata

at1

kspsso

thefrequency

ofthe

inputm

ustbe

keptbelow

500H

zto

avoidaliasing.(Strictly,the

conditionis

thatthesam

plingrate

shouldbe

atleasttwice

thebandw

idthof

theinputbutI’llassum

ethatw

eare

dealingw

ithbaseband

signals,which

godow

nto

zerofrequency.)

As

anotherexample,w

em

ightwantto

recordaudio

frequenciesin

therange

0–20

kHz.T

hesound

musttherefore

besam

pledata

frequencyof

atleast40kH

z.In

practice,compactdiscs

(CD

s)use

44.1kH

zand

digitalaudio

tape(D

AT

)uses

48kH

z.B

othobey

thiscriterion.

On

theotherhand,som

esystem

ssuch

asN

ICA

M(nearinstantaneous

companded

audiom

ultiplex)and

DA

B(digitalaudio

broadcasting)take

samples

at32kH

zand

thereforecannotreproduce

thesam

erange,butonly

upto

16kH

z.These

highratesofsam

plingw

ouldcreate

problemsw

iththe

limited

mem

oryof

smallem

beddedsystem

sso

thebandw

idthis

usuallyreduced.

Arange

from300–3000

Hz

isconsidered

sufficientfor‘telephonequality’sound

andrequires

sampling

atonly6

ksps.A

nim

portantpart

ofm

ostsystem

sthat

sample

datais

thereforean

anti-aliasingfilter

onthe

inputtosuppress

allfrequenciesthatsufferaliasing,

f>

12f

s .A

naloguefilters

arehard

todesign,particularly

ifasharp

cutoffisneeded.Forexam

ple,thefilteron

aC

Drecordershould

ideallypass

frequenciesup

to20

kHz

orso,butstronglyattenuate

thoseabove

22.05kH

z.Itis

practicallyim

possibleto

designanalogue

filtersw

ithsuch

asharp

cutoff.(D

oyou

remem

berhow

slowly

theoutputofa

RC

low-pass

filterfallsas

afunction

offrequency?)

4.2S

igma–delta

convertersT

hebasic

ideabehind

sigma–delta

(†

butoftenthe

otherway

round,delta–sigma)converters

isto

takea

largenum

berofsamples

atlowresolution

andto

averagethem

toobtain

afinalresult

with

am

uchhigher

resolution.T

hism

eansthatthe

AD

Cin

thecore

ofthe

converteris

verysim

ple,oftenproducing

onlya

singlebitas

output,butitmustrun

much

fasterthan

thefinal

output.T

heratio

ofthe

frequencyatw

hichthe

inputissam

pledto

thefrequency

atwhich

theoutputs

areproduced

iscalled

theoversam

plingfrequency,O

SR.Itis

notunusualtohave

OSR

=1024

soan

outputfrequencyof1

kHz

requiresthe

inputtobe

sampled

atabout1M

Hz.

The

analoguepartofthe

systemis

made

assim

pleas

possiblebutthe

digitalpart,which

car-ried

outtheaveraging,is

more

complicated.Itis

calleda

digitalfilter.Sigma–delta

AD

Cs

were

expensivein

thepastbutthe

sizeofdigitalcircuits

keepsshrinking

andsigm

a–deltaconverters

arenow

more

comm

on.T

heyare

almostuniversally

usedfor

audioapplications

andgeneral-

purpose16-bit

†

AD

Cs

arenow

availablein

£1m

icrocontrollers(table

3.1on

page13).

Figure4.3

onthe

following

pageshow

sthe

main

blocksofa

sigma–delta

converter.

T

heanalogue

inputgoesinto

adifference

amplifier,w

hichsubtracts

(hence‘delta’)

thecurrentvalue

oftheoutputto

leavethe

error.

34Sam

pling,oversampling

andsigm

a–deltaconverters

Chapter4

AD

C

DA

C

low-pass

filterdecim

ator

fmfm

fsanalogueinput

digital signals

+-

integrator

Figure4.3

Block

diagramofa

sigma–delta

analogue-to-digitalconverter.

T

hiserroris

integrated(m

uchthe

same

assum

mation,hence

‘sigma’).

T

heoutput

ofthe

integratoris

convertedfrom

analogueto

digitalin

anA

DC

ata

fre-quency

fm ,

them

odulatoror

oversampling

frequency.T

hisis

performed

bya

one-bitA

DC

,which

isjusta

comparator.

T

hisdigital

signalis

convertedback

toanalogue

ina

DA

Cso

thatit

canbe

subtractedfrom

theinput,form

inga

feedbackloop.T

heone-bitD

AC

isno

more

thana

switch.

These

firstfour

components

inthe

loopform

thesigm

a–deltam

odulator.T

hesecond

partof

theA

DC

handlespurely

digitalsignals.Its

jobis

totake

thefaststream

ofsinglebits

fromthe

modulatorand

convertthemto

aslow

erstreamofm

ulti-bitsamples.In

principlethis

isdone

intw

ostages.

T

hedigital

signalis

processedby

alow

-passfilter.

This

isneeded

becausethe

streamof

samples

fromthe

modulator

canrepresentfrequencies

upto

12f

mbutthe

slower,final

outputcanrepresentfrequencies

onlyup

to12f

s .Thus

we

mustrem

ovefrequencies

above12f

s toavoid

aliasingatthe

finalsampling

rate.

T

hefiltered

digitalsignalisthen

decimated

toreduce

therate

ofsamples

fromf

mto

fs .

The

effectivenum

berofbitsrises

inboth

thesesteps,w

hichis

why

thelines

getthickerinfigure

4.3.Inpractice

thefiltering

anddecim

ationare

combined

inthe

digitalfilter.

4.3P

racticalissuesw

ithsigm

a–deltaconverters

Sigma–delta

convertershave

some

specialfeatures

thatm

ustbe

takeninto

accountin

areal

system.

InputcharacteristicsT

hecircuitofthe

inputisvery

similarto

thatofaSA

RA

DC

(section3.6

onpage

23).Itisagain

acapacitance,w

hichitm

ustbepossible

torecharge

within

theperiod

ofthe

modulator,

1=f

m .Forexam

ple,theinputofthe

sigma–delta

AD

Cin

theM

SP430is

modelled

with

acapacitance

of10

pFin

seriesw

itha

resistanceof

1k

.T

hishas

atim

e-constantD

RC

D10

8s.

The

maxim

umfrequency

ofthem

odulatoris1

MH

z,which

correspondsto

100tim

e-constants.This

lookslike

plentyoftim

eforthe

capacitanceto

chargebutrem

emberthe

externalresistanceand

thatyouw

antavery

accuratevalue.

Section4.4

Summ

aryofsigm

a–deltaconverters

35

Differentialinputs

Most

sigma–delta

AD

Cs

havedifferential

inputs.T

hism

eansthat

theA

DC

operateson

thevoltage

between

theinputs,

VC V

,ratherthanthe

voltagebetw

eena

singleinputand

ground.Y

oucan

always

tieV

toground

ifthisfeature

isnotw

antedbutitis

oftenhelpful.Forexam

ple,the

weighing

machine

backin

figure1.2

onpage

3uses

abridge

forits

sensor.T

hisgives

differentialoutputsnaturally,w

hichcould

beconnected

directlyto

asigm

a–deltaA

DC

.We’ll

lookatthis

insection

7.7on

page62.

Of

coursethere

mustbe

sufficientgain,which

bringsus

tothe

nextpoint.

Program

mable

gainam

plifierM

anysigm

a–deltaA

DC

shave

aprogram

mable

gainam

plifier(PG

A)

ontheir

inputs.T

histypically

hasa

fairlym

odestgain,perhapsup

to32,butitm

aybe

sufficienttoavoid

theneed

foranexternalop-am

p.T

heseam

plifiersare

nothinglike

aclassic

op-amp

with

feedbackresistors.

They

amplify

packetsof

chargerather

thanvoltage

andtheir

inputis

likea

switched-capacitor

SAR

AD

C,

describedin

section3.6

onpage

23.D

onotexpecta

highinputim

pedanceas

ifthere

were

atraditionalinstrum

entationam

plifieronthe

input(section6.1

onpage

39).Aseparate

analoguebufferbased

onan

op-amp

may

beprovided

toboostthe

inputimpedance.

Exam

pleA

wide

rangeofsigm

a–deltaconverters

isavailable

with

anbroad

spreadofsam

plingfrequen-

cies,resolutionand

typesoffilter.Afew

examplesare

listedin

table3.2

onpage

15.Ratherthan

pickouta

‘typical’deviceI’ve

goneforan

extreme.T

hisis

theA

D7788

fromA

nalogD

evices,w

hichhas

16-bitresolution.A

24-bitversion,theA

D7789,is

alsoavailable.

I’veattached

afew

pagesfrom

theirdata

sheet[31].T

heoutputdata

rateis

16.6H

zto

providesim

ultaneousrejection

of50

and60

Hz.

These

may

bethe

slowestsigm

a–deltaconverters

availablebutyou

may

needsom

ethinglike

themto

make

high-precisionm

easurements

fromsensors

infuture

projects.A

udioconverters

arehighly

specializedand

Idon’thave

time

totalk

aboutthem,unfortu-

nately.T

heytend

touse

high-order(fourth

orfifth)

modulators

andsophisticated

digitalfiltersto

ensurea

flatfrequencyresponse

overtheaudible

range.

4.4S

umm

aryofsigm

a–deltaconverters

You

aren’texpectedto

learnthe

detailsof

sigma–delta

convertersbutthey

areso

widely

usedthatIhave

toinclude

them.T

heseare

them

ainpoints

thatyoushould

know.

Sigm

a–deltaconverters

oversample

theinputby

avery

largefactor.

T

hisis

followed

bydigitalfiltering

anddecim

ationto

givegood

resolutionbutlow

speed.

T

heiranalogueparts

aresim

plew

hilethe

digitalfilteriscom

plicatedbuteasy

tofabricate

inV

LSI.

T

heyhave

highresolution

anddifferentialinputs,w

hichsuitm

anytypes

ofsensor.

36Sam

pling,oversampling

andsigm

a–deltaconverters

Chapter4

T

heoversam

plingrate

mustbe

largeenough

forthedesired

numberofbits.

4.5R

eflectionon

AD

Cs

It’sinteresting

tonote

thatthe

AD

Cs

thatI

havechosen

asexam

pleshave

datarates

from16.6

spsto

3G

sps,a

factorof

nearly10

9.T

hepow

erconsum

ptionreflects

this:the

3G

spsA

DC

083000consum

esnearly

2W

while

theslow

AD

7788needs

onlyabout200

µW,a

factorof

10

4.The

resolutiongoes

from8

to24

bits,which

soundslike

afactorofonly

3butis

betterview

edas

22

4=2

8D2

16

10

5.These

figureshighlighttheenorm

ousrangeofA

DC

savailable.T

herange

ofpricesis

largetoo.Istillfind

ithardto

believethata

24-bitAD

C,w

hoseresolution

exceeds1

partin10

7,canbe

boughtfor£3!

4.6E

xamples

Exam

ple4.1

Whatis

meantby

aliasingand

theN

yquistfrequencyf

N ?H

owdoes

fN

dependon

therate

ofsampling?

Exam

ple4.2

An

AD

Cis

requiredto

convertaninputw

hosefrequency

may

gofrom

DC

upto

50kH

z.Whatis

them

inimum

rateofsam

plingthatshould

beused?

Whatw

ouldhappen

ifalow

erratew

ereused?

5

Sum

mary:

Selection

ofanA

DC

Many

aspectsm

ustbe

consideredw

henchoosing

ananalogue

todigital

converter.H

ereis

asum

mary

(more

thanlong

enough!)to

helpyou

when

theneed

arises.

Precision

–T

henum

berof

bitsin

theoutput.

Alternatively,the

resolutionof

thesystem

canbe

definedas

LSB

,thechange

inthe

inputthatcorrespondsto

onebitin

theoutput.

Speed

–H

owm

anysam

plespersecond

doyou

need?Som

econverters

work

overaw

iderange

ofsampling

ratesbutsom

ehave

onlyone.

N

umber

ofinput

channels–

How

many

doyou

need?M

ustthey

besam

pledsim

ul-taneously

(atexactly

thesam

etim

e)or

canthey

betreated

sequentially(one

afterthe

other)?

C

haracteristicsofinput–Severalissues

arisehere.

–W

hatisthe

rangeof

inputvoltages?C

anyou

connecttheinputdirectly

orw

illanam

plifierbeneeded?

–D

oyou

needa

single-endedordifferentialinput?

–Is

theinput

impedance

highenough

notto

loadyour

sourceor

will

abuffer

beneeded?

–Is

asam

ple-and-holdcircuitnecessary,eitherinternal(usually)orexternal?

Type

ofconverter–

Inm

ostcasesthis

willfalloutfrom

thechoices

alreadym

adebut

thereare

some

applicationsforw

hichparticulartypes

ofconverterareespecially

suitable.

Voltage

reference–

Isthere

aninternalvoltage

referenceorm

ustyouprovide

anexternal

one?

Filtering

–Is

filteringnecessary?

You

almostalw

aysneed

afilter

torem

ovenoise

andforanti-aliasing

buttherem

aybe

more

specificrequirem

ents,torejectinterference

fromthe

mains

at50or60

Hz

forinstance.Some

typesofconverterdo

thisintrinsically.

37

38Sum

mary:

Selectionofan

AD

CC

hapter5

A

ccuracy–

Not

thesam

eas

precision!U

suallythe

totalunadjusted

erroris

them

ostappropriate

number

buttheeffective

number

ofbits

(EN

OB

)m

aybe

more

relevantforsigm

a–deltaA

DC

s.

Accuracy

dependson

theoverallsystem

,notjusttheA

DC

itself.T

hevoltage

referenceorgain

ofanam

plifiermay

beless

accuratethan

theA

DC

.

Pow

ersupply

–Particularly

importantin

equipmentpow

eredby

batteries.

–W

hatvoltage

doesthe

converterneed

topow

erit?

Some

havetw

opow

ersupply

pins,oneforanalogue

andone

fordigital,with

two

groundsto

correspond.

–H

owm

uchpow

erdoesthe

converteruse?C

anbe

beshutdow

nto

savepow

er?

Interface

fordigitaloutput

–W

illoftenbe

definedby

thedigitalsystem

tow

hichthe

converterisconnected.C

omm

onoptions

are:

–paralleloutput(usually

asm

anybits

asthere

arein

theA

DC

’soutput)

–serialperipheralinterface

(SPI).This

isa

simple

andcom

mon

way

ofconnectinga

singleperipheralto

am

icrocontroller;3-wire

andM

icrowire

aresim

ilar.

–inter-integrated

circuitbus

(I²C).

This

isanother

comm

onw

ayof

connectingpe-

ripheralsto

am

icrocontrollerbutthisis

abus

andcan

beshared

byseveraldevices;

2-wire

andSM

Bus

aresim

ilar.

Package

–Ifthe

boardis

tobe

assembled

byhand

youshould

lookfora

plasticdual-in-

linepackage

(PDIP),w

hichis

easyto

solder,butforproductionyou

would

probablyw

anta

smaller,surface-m

ountpackage.

Price

–H

owm

uchdoes

itcost?V

eryim

portant!

Clearly

thereare

alotofquestions

toask,although

some

willbe

farmore

importantthan

othersin

agiven

application.L

ookatthe

manufacturers’

web

sites.T

heyhave

selectorsw

hereyou

typein

them

ajorspecifications

andreceive

alist

ofrecom

mended

devices.Follow

thisby

checkingthe

web

pageforlikely

components

anddow

nloadingthe

datasheet.

Manufacturers

alsopublish

applicationnotes

tohelp

youuse

(andbuy!)

theirproducts.

These

canbe

extremely

helpfulandare

oftenm

oreup

todate

thantextbooks.O

lderdatasheets

andapplication

notestend

tobe

more

informative,a

sadreflection

oncost-cutting.

6

Signalconditioning

Itisrarely

possibleto

connectasensororanothersource

directlyto

anA

DC

.An

amplifierw

illoften

beneeded

andusually

afilteras

well.T

hisprocessing

ofthesignalbefore

itisconverted

bythe

AD

Cis

calledsignalconditioning.

6.1A

mplification

An

amplifierw

illbeneeded

iftherange

ofvoltagesfrom

thesensordoes

notmatch

theinputof

theA

DC

.Often

thesignalm

ustbeboth

amplified

andshifted

tom

atch.Y

oualready

knowthe

basiccircuits

constructedusing

op-amps

fromE

lectronicE

ngineering1Y

andw

illstudythem

furtherinA

nalogueE

lectronics2.

Sometim

esthere

isno

needto

amplify

thesignalbutthe

sourceresistance

istoo

highfor

thecapacitance

oftheinputto

chargein

intim

e.This

was

discussedin

section3.6

anda

simple

bufferorvoltagefollow

eronthe

inputeliminates

theproblem

.They

arebuiltinto

some

AD

Cs

andm

icrocontrollers.Y

ouare

expectedto

beable

toanalyse

anddesign

standardcircuits

with

op-amps.Professor

Weaver’srecognition

chartfromE

lectronicE

ngineering1Y

ishelpful.Often

youhave

tochoose

between

invertingand

noninvertingconfigurations.

These

arethe

keyfeatures

ofthe

basiccircuits.

A

noninvertingam

plifierhasa

highinputresistance

becausethe

signalgoesdirectly

toa

terminalofthe

op-amp.

A

ninverting

amplifierhas

avirtualground,w

hichenables

thecircuitto

carryoutsim

plesum

sandotherm

athematicaloperations.Itsinputresistance

isdetermined

bythe

resistorsand

istherefore

lowerthan

anoninverting

amplifier.

Invertingam

plifiercircuitsgenerally

placeless

demand

onthe

op-amp

andshould

thereforebe

chosenif

ahigh

inputresistance

isnot

required.It

usuallydoesn’t

matter

ifthe

signalto

anA

DC

getsinverted

becauseitis

trivialtochange

thesign

ofthedigitalvalue.

39

40Signalconditioning

Chapter6

+ - +-

+ -V

out

V-

V+

R1

R2

R2 R

3R

4

R3

R4

(orV

bias )

Figure6.1

Standardcircuitofan

instrumentation

amplifier.

Instrumentation

amplifier

Often

thedesired

inputisthe

smalldifference

between

two

largevoltages

–a

differentialsignal.A

circuitis

neededto

amplify

thedifference

while

rejectingthe

averagevoltage

onthe

two

wires,

calledthe

comm

on-mode

voltage.T

heoutput

ofa

bridgeis

atypical

example,

asin

thew

eighingm

achineshow

nin

figure1.2

onpage

3.Som

etimes

youcan

usea

singleop-

amp

configuredas

adifference

amplifier

buttheinputresistance

isoften

toolow

;a

lowinput

resistanceacts

likea

potentialdividerandreduces

them

agnitudeofthe

measured

voltage.The

desiredcharacteristics

aretherefore

am

plificationofdifferentialpartofinputsignal

rejection

ofcomm

on-mode

partofinputsignal

high

inputresistance

The

solutionis

astandard

circuitwith

threeop-am

pscalled

aninstrum

entationam

plifier,shown

infigure

6.1.M

ostof

theresistors

arein

matched

pairs.B

othinputs

areconnected

directlyto

non-invertinginputs

ofop-am

ps.Ideally

thesedraw

nocurrent

andin

practicethe

inputresistance

isvery

high.The

outputvoltageofthis

circuitis

Vout D

1C2

R2

R1

R4

R3

.VC

V/:

(6.1)

Often

R4 D

R3 ,in

which

casethe

gainis

determined

justbyR

2 =R

1 .T

heground

connectionon

R4

canbe

replacedby

aconstantvoltage

Vbias to

shifttheoutputifnecessary.

Com

pleteinstrum

entationam

plifierscan

beboughtin

asingle

package.Sometim

esthe

gainis

fixedbutoften

R1

isexternalso

thatthegain

canbe

changed.You

willsee

more

ofthiscircuit

inA

nalogueE

lectronics2

andw

illlearnhow

togetthe

bestoutofinstrum

entationam

plifiersin

Electronic

SystemD

esign3.

Section6.2

Single-supplyop-am

ps41

+ -

VC

C = +15

V

VE

E = -15

V0

V

R1

R2

v+

v-

Vout

Vin

+ -

VC

C = +3

V

0V

R1

R2

v+

v-

Vout

Vin

(a) Dual (split) supply

(b) Single supply

Figure6.2

Standardinverting

amplifiers

using(a)split(dual)and

(b)singlepow

ersupplies.

6.2S

ingle-supplyop-am

psA

llthecircuits

with

op-amps

thatyouhave

studiedin

thepasthave

runfrom

split(dual)supplyvoltages,

typically˙15

V.

These

areoften

calledthe

power

railsand

I’lluse

thenotation

VE

E(negative)

andV

CC

(positive),which

istraditionalfor

bipolarcircuits.

The

power

supplyactually

hasthree

connectionsincluding

theground

railat0V.I’ve

drawn

thefam

iliarcircuitofan

invertingam

plifierinfigure

6.2(a),includingits

powersupplies.(Y

oucan

seew

hyw

edon’t

normally

bothertoshow

these!)T

hevoltage

gainis

ideallyR

2 =R

1 .Split˙

15

Vsupplies

arefine

ifyouhave

abench

powersupply

availablebutare

anuisance

inbattery-pow

eredequipm

ent.T

hevoltage

istoo

large,for

astart.

Besides,

digitalsystem

sm

anagew

itha

single,positive

supplyso

why

shouldw

ehave

toprovide

asecond,

negativesupply

fortheanalogue

components?

Itism

uchm

oreconvenientto

usea

single-supplyop-am

pw

itha

lower

voltageas

infigure

6.2(b).T

hepositive

supplyconnection

ofthe

op-amp,

VC

C ,goes

tothe

batteryas

usualbutthenegative

supplygoes

toground.O

nlytw

oconnections

nowgo

tothe

powersupply

ratherthanthree.

Insom

ew

aysitis

betternotto

concentrateon

the‘single

supply’aspectbuton

thelack

ofa

groundrailin

them

iddleof

thesupply

voltages.T

hisis

whatcauses

mostof

theproblem

sw

hendesigning

circuitsw

ithsingle-supply

op-amps.

Before

lookingat

thesecircuits,

afew

characteristicsofsingle-supply

op-amps

themselves

areim

portant.

Supply

voltageM

osttraditionalop-amps

were

designedto

work

froma˙

15

Vsupply,a

totalrangeof

30V.

Modern

devicesare

typicallyspecifed

ata

totalsupplyvoltage

of3

Vso

thattheyw

orkw

ellfrom

asingle

Li-ion

cell.I’veattached

thedata

sheetoftheST

Microelectronics

TS951

[32]asan

example.

Itsperform

anceisn’tparticularly

specialbutitcomes

ina

PDIP,w

hichm

akesit

easyto

solder(mostm

oderndevices

areproduced

onlyin

impossibly

smallpackages).A

’741,T

L071

orsimilarop-am

pw

illnotwork

atallfroma

single3

Vsupply.

Rail-to-railinput

The

inputsof

anold-fashioned

op-amp

mustnotbe

allowed

tooclose

toeither

VE

Eor

VC

Cto

ensurenorm

albehaviour.M

orem

oderncom

ponentsm

ayperm

itinputsto

reacheither

oneof

42Signalconditioning

Chapter6

VC

C

0

(a) range of inputs(b) range of outputs

old-fashioned(far from

both rails)

‘rail to rail’(not really, but close)

old-fashioned(reaches neither

rail)rail to rail

(and beyond)includes

ground rail

Figure6.3

Illustrationofdifferentranges

of(a)inputsand

(b)outputsavailable

fromop-am

ps,notto

scale.

thesupply

railsor

both.In

facttheycan

oftengo

about0.2V

outsidethe

supplies.T

heterm

rail-to-railinputthereforem

eansw

hatitsays.The

optionsare

illustratedin

figure6.3(a).

You

mightthink

thatitwould

always

bea

goodidea

tochoose

anam

plifierw

itha

rail-to-railinput.

How

ever,theyare

betteravoided

unlessreally

necessary.T

hereason

isthatitis

notpossible

tobuild

asingle

inputstagethatw

orksto

bothrails.A

nop-am

pw

ithrail-to-railinput

thereforeneeds

toinclude

two

inputstagesor

touse

othertricks,w

hichm

ayhave

undesirableside-effects.

Rail-to-railinputis

notalways

neededduring

normaloperation.

The

inputtoa

circuitwith

gainm

ustbesm

allerin

magnitude

thanthe

outputandm

aytherefore

stayclear

ofthe

supplyvoltages.

Sometim

esthe

inputm

aygo

tozero

voltage,w

hichrequires

aninput

rangethat

includesthe

groundrailbutnotthe

supplyrail.A

nexception

isa

bufferwith

unitygain

(voltagefollow

er),w

hichthe

rangeof

boththe

inputand

outputm

ayspan

thesupplies.

Rail-to-rail

inputsm

ayalso

beneeded

ifthevoltage

onan

inputgoesto

oneofthe

suppliesw

henthe

circuitis

turnedon.T

hisw

asthe

casew

iththe

microphone

preamplifierin

Electronic

Engineering

1Y.

Rail-to-railoutput

Ifyourem

emberyourfirstexperim

entson

op-amps,the

outputofanold-fashioned

devicelike

theO

PA177

or’741

cannotgetwithin

1V

orso

ofthe

supplyrails.

This

would

bea

seriousrestriction

with

a3

Vsupply!

Mostm

odernop-am

pstherefore

featurea

so-calledrail-to-rail

output.T

hereason

forthe

‘so-called’is

thatthe

outputcan’t

actuallyreach

groundor

VC

C :R

ail-to-railoutputisan

advertisingterm

only.Inpractice

theoutputgets

within˙

0:1

Vofthe

railsorcloser.A

gainthis

issketched

infigure

6.3.To

make

thebehaviourofa

rail-to-railoutputclearer,figure6.4

onthe

nextpageshow

sthe

inputand

outputvoltages

ofa

single-supplyvoltage

follower

asthe

inputvoltage

isreduced

tozero.

IdeallyV

out DV

inbut

thisfails

asthe

inputfalls

belowabout

0.2V.T

hisparticular

Section6.3

Circuits

with

single-supplyop-am

ps43

Vin / V

Vout / V

0.00.5

0.0

0.1

0.5

ideal

real‘rail-to-rail’output

Figure6.4

Inputandoutputofa

single-supplyvoltage

followerforvoltages

nearground.

op-amp

isunable

topullthe

outputbelow0.1

Vso

aninputof

zerocannotgive

anoutputof

zero.M

anym

odernop-am

pscan

dom

uchbetterthan

this–

perhaps0.01

V–

buttheiroutputscannotactually

reachthe

rails.If

theoutputof

anop-am

pm

ustgoallthe

way

down

toground,a

negativesupply

forV

EE

isunavoidable.

Don’t

worry,

them

anufacturersrealise

thisand

specialIC

sare

availableto

producea

small,negative

supplyvoltage

forthe

op-amp

fromthe

singlepositive

supplyto

therestof

thesystem

.For

example,the

NationalSem

iconductorL

M7705

produces0:2

3V

with

lownoise.Itis

basedon

acharge

pump,described

insection

14.1on

page113.

6.3C

ircuitsw

ithsingle-supply

op-amps

Why

shouldcircuits

with

single-supplyop-am

psbe

anydifferent

fromthose

with

two

sup-plies?

Well,

justlook

backat

thestandard

invertingam

plifierredraw

nfor

asingle

supplyin

figure6.2(b)on

page41.T

heinput

Vin

mustbe

positivebecause

thereare

nonegative

voltagesavailable.

Unfortunately

thism

eansthat

theinverting

amplifier

wants

toproduce

anegative

output,which

itcannotdoforthe

same

reason.Clearly

thisw

illnotwork

asexpected.

+ -R

1R

2

Vout

v+

v-

Vin

Vbias

Figure6.5

Invertingam

plifiercircuitw

iththe

noninvertinginputof

theopam

pconnected

toa

biasvoltage

Vbias ratherthan

ground.

44Signalconditioning

Chapter6

The

basicproblem

isthat

thereis

noreference

voltageavailable

between

thetw

osupply

voltages,likethe

groundrailw

ithdualsupplies.T

hereare

two

ways

aroundthis.

R

edesignthe

circuitsothatitw

orkscorrectly,w

ithallvoltages

positive.

Provide

areference

voltage,m

idway

between

thepow

ersupplies,

anduse

thislike

theground

railina

circuitwith

splitsupplies.Itisoften

calledV

mid .

The

standardinverting

amplifiercan

beredesigned

asin

figure6.5

onthe

precedingpage

sothat

itsnoninverting

inputisconnected

toa

positivebias

voltageV

biasrather

thanground.

It’seasy

toanalyse

thiscircuit

usingthe

usualthree

orfour

steps(good

revision!),assum

ingan

idealopam

p.A

lways

usethe

approachthatw

etaughtyou

inE

lectronicE

ngineering1Y.Forgetthe

rubbishfrom

Higher

Physics

becauseitisw

rong.

0.C

onfirmthatnegative

feedbackis

present.

1.T

hevoltage

atthenoninverting

inputisvC

DV

bias .

2.N

egativefeedback

andthe

infinitegain

ofthe

opamp

causethe

two

inputsof

theopam

pto

come

tothe

same

potential,sov D

vCD

Vbias .

3.T

hefinalstep,as

always,is

nodalanalysisat

v.T

heinputto

theopam

pdraw

snocurrent

becauseitis

ideal.ThusV

in V

bias

R1

CV

out V

bias

R2

C0D

0:

(6.2)

This

canbe

rearrangedinto

differentexpressions:

Vout

D

1CR

2

R1

Vbias

R2

R1

Vin

(6.3)

DV

bias CR

2

R1

.Vbias

Vin /:

(6.4)

Choose

Vbias

sothat

theoutput

remains

positiveover

thedesired

rangeof

inputs.T

hegain

stillhas

itsusual

value.T

heinversion

andshift

arenot

aproblem

ifthe

signalgoes

toan

AD

Cbecause

theoriginal

signalcan

berecovered

bytrivial

arithmetic

onthe

digitalvalue.

Noninverting

amplifiers

with

anoffsetvoltage

canalso

bedesigned

butitisa

littlem

oretricky

[22].M

athematically,

theinclusion

ofV

biasallow

sthe

circuitto

performthe

operationy

Dm

xCc

ratherthanjust

yDm

xfora

simple

amplifier.

The

alternativeapproach

istogenerate

aground

reference,Vm

id .Apotentialdividerbetw

eenground

andV

CC

isthe

simplestm

ethod.Sadly

itisoften

notgoodenough

becausethe

voltagem

ustremain

constant,whateverw

econnectto

it.This

may

needa

‘stiff’dividerwith

verysm

allresistors,w

hichw

astesa

lotofcurrent.

The

simplestsolution

isto

addan

op-amp

asa

voltagefollow

er,asshow

nin

figure6.6

onthe

nextpage.T

hecapacitor

onthe

potentialdivideris

tosuppress

noise.T

hism

ayseem

likea

waste

ofan

op-amp

butthey

usuallycom

ein

multiple

packages.Application

note[23]suggests

bettercircuitsforground

references.N

otethatthe

outputvoltagefrom

theground

referencevaries

with

VC

C .T

hesam

eis

truefor

thepotentialdivider

infigure

6.7.O

ftenthis

isdesirable,as

we

shallseein

section7.2

onpage

55.If

anabsolute

voltageis

needed,w

hichshould

notchange

ifV

CC

varies,a

voltagereference

shouldbe

usedinstead.T

heseare

describedin

section7.1.

Section6.3

Circuits

with

single-supplyop-am

ps45

VC

CRR

groundreference,V

mid

-+

Figure6.6

Ground

referencegenerated

bybuffering

apotentialdivider.

Worked

example:

Analysis

ofasingle-supply

opamp

circuitA

nalysethe

single-supplyam

plifierinfigure

6.7.Calculate

therange

ofinputsoverw

hichthis

circuitworks

correctly.D

oesthe

op-amp

needrail-to-railinputs?

Whatis

thepurpose

ofthis

circuitandw

hyis

astraightforw

ardinverting

amplifiernotused?

The

biasvoltage

Vbias

isprovided

bya

potentialdivider

with

adecoupling

capacitorto

remove

noise.Y

oucould

justput

numbers

intoequation

(6.3)to

analysethe

circuitbut

it’sbetter

todo

thecalculation

fromscratch

becauseit’s

straightforward

andavoids

anyneed

tom

emorise

equations.Followthe

usualsteps.

0.N

egativefeedback

ispresent.

1.Solving

thepotential

dividershow

sthat

thevoltage

atthe

noninvertinginput

isvC

DV

bias D1

V.

2.N

egativefeedback

andthe

infinitegain

ofthe

opamp

causethe

two

inputsof

theopam

pto

come

tothe

same

potential,sov D

vCD

1V

.

3.U

senodalanalysis

atv

,which

gives

Vin

1V

20

k

CV

out 1

V100

k

C0D

0;

-+V

out

Vin

VC

C = 3

V

R2 =

100kW

R1 =

20kW

R3 =

100kW

R4 =

50kW

v+

v-

Vbias

Figure6.7

An

amplifierbased

onan

op-amp

with

asingle

supply.

46Signalconditioning

Chapter6

Vin / V

Vout / V

0.00.0

3.0

1.02.0

3.0

2.0

1.0

0.6 V1.2 V

Figure6.8

Transferfunction

forthe

single-supplyam

pliferin

figure6.7.

The

roundingof

theoutputnear

thesupply

railsis

exaggeratedand

thedifference

between

thesaturated

outputandthe

supplyrails

istoo

smallto

beseen.

5.V

in 1

V/C

.Vout

1V

/D0;

Vout D

6V

5V

in:

(6.5)

This

completes

theanalysis.

The

nexttaskis

tofind

therange

ofinputs

overw

hichthis

amplifier

works

correctly.B

oththe

inputandoutputvoltages

mustlie

within

thesupply

rails.Check

theoutputvoltage

first.

T

heoutputvoltage

cannotnotgobelow

groundso

Vout

0.This

means

that6

V5V

in 0

orV

in 1:2

V.

Sim

ilarly,theoutputvoltage

cannotnotexceedthe

supplyso

Vout

VC

CD

3V

.T

hism

eansthat

6V

5V

in 3

Vor

Vin

0:6

V.

The

inputvoltage

must

thereforelie

inthe

range0:6

V

Vin

1:2

Vto

avoidsaturation

ofthe

output.T

hisrange

doesnotgo

toeither

railsorail-to-railinputs

would

bepointless.

The

amplifier’s

behaviouris

sketchedin

figure6.8.

This

shows

clearlythe

rangeof

inputvoltagesoverw

hichthe

amplifierfunctions

asdesired.

You

were

giventhe

circuitinthisproblem

andasked

tofind

itsbehaviour.Inpractice

youare

more

likelyto

dothe

opposite,designan

amplifier

toperform

agiven

operation.For

example,

youm

ightbetold

thattheinputvoltage

liesbetw

een0.2

Vand

0.3V

andasked

toproduce

anoutputfrom

0V

to3

V.Inthis

caseitis

probablyeasierto

startfromequation

(6.3)or(6.4).

6.4Filters

Ihave

mentioned

alreadythat(alm

ost)allcircuits

fordata

acquisitionneed

alow

-passfilter

torem

ovenoise

andfor

anti-aliasing.T

hetrend

isnow

todo

asm

uchfiltering

aspossible

inthe

Section6.5

Com

paratorsand

Schmitttriggers

47

digitaldomain

butitisalw

aysbetter

togetrid

ofundesired

signalsas

earlyas

possible.G

oodlayoutofthe

circuitcango

along

way

topreventnoise

beingpicked

upin

thefirstplace.

The

onlyrelevant

filtersthat

youhave

studiedare

simple

RC

low-pass

filters.T

heseare

oftensufficient

ifthe

signalof

interestis

atsuch

alow

frequencythat

anti-aliasingis

notan

issue.The

problemis

thattheam

plitudefalls

offslowly

with

frequency,onlyas

1=f

.Itisoften

saidthatthe

responsehas

asingle

pole,which

youw

illlearnaboutin

Com

munication

Systems

3and

Control3.A

betterfilter,meaning

onew

hoseresponse

fallsm

orerapidly

with

frequency,is

oftenneeded

foranti-aliasing.There

arem

anyclassic

filtersw

ithdifferentcharacteristics

thatgo

bythe

names

ofB

utterworth,T

chebychev(m

anyspellings),B

essel,ellipticand

soon.

The

problemis

thatnofilter

isideal.

Forexam

ple,theT

chebychevfilter

givesthe

bestresponseas

afunction

offrequency,m

eaningthatits

amplitude

fallsoff

mostrapidly

with

frequency,butitalso

distortsthe

shapeof

asquare

pulsein

time

mostseverely.

These

filtersusually

includeopam

psand

arecalled

activefilters.Y

ouw

illstudythem

inE

lectronicSystem

Design

4.

6.5C

omparators

andS

chmitttriggers

Icouldn’tthinkofa

logicalplaceforthis

sectionbutw

antedto

includea

littlem

oredetailthan

insection

3.2because

comparators

areoften

neededto

cleanup

thesignalfora

standarddigital

input.T

heunderlying

problemis

thatrealsignalsare

always

analogueso

thisconnection

actsas

asortofim

plicitanalogue-to-digitalconversion.Two

issuesare

comm

on.

T

hevoltage

ona

digitalinput

shouldeither

benear

groundfor

alogical

zeroor

nearV

CC

foralogical1;itshould

changerapidly

fromone

ofthesedefinite

valuesto

another.Voltages

around12V

CC

giveunpredictable

behaviourand

thecircuit

may

evenoscillate.

This

situationarises

ifthe

inputchanges

slowly

–if

thereis

alot

ofcapacitance,

forexam

ple.

R

ealsignalsalwayscontain

noise,which

cancause

multiple

logicaltransitionswhen

thereshould

beonly

one.

The

standardsolution

tothese

problems

isto

connectacom

paratorasa

Schmitttrigger.

Schm

itttriggerFgure

6.9(a)onthe

nextpageshow

sastraightforw

ardcom

paratorworking

froma

singlesupply.

The

signalisconnectedto

theinverting

inputofthecom

parator,which

willm

akeiteasierto

turnthe

circuitintoa

Schmitttrigger.T

henoninverting

inputisconnected

toa

fixedvoltage

derivedfrom

apotentialdivider,w

hichgives

12V

CC

here.This

thethreshold

voltageforthe

comparator,

meaning

thatitsoutputsw

itchesw

henthe

signalpassesthrough

thisvoltage.

The

ideaof

aSchm

itttriggeris

toadd

feedbackfrom

theoutputto

givetw

ovalues

forthe

thresholdvoltage,one

forrisingvoltagesand

oneforfalling

voltages.The

circuitofaninverting

Schmitttriggeris

shown

infigure

6.9(b).Note

thatthefeedback

ispositive,so

don’ttryto

applythe

rulesforanalysing

circuitsw

ithopam

ps!T

heoperation

isillustrated

infigure

6.10on

page49.

I’veassum

eda

3V

supplyand

thatthe

acceptableinputvoltages

arethe

typicalvaluesforC

MO

Slogic:

Voltages

below13V

CC

givelogic

0

48Signalconditioning

Chapter6

+-

V+

V-

VC

C

100kW

¥ 3

Vthreshold (t)

100kW

100kW

50kW

100kW

23 VC

C

(b)Inverting Schm

itt trigger

=V

CC

100 kW

100kW

100kW

100kW

50kW

13 VC

C=

VC

C

(c)T

hreshold network w

hen Vout =

VC

C(d)

Threshold netw

ork when V

out = 0

Vthreshold =

Vthreshold =

100 kW

Vin

Vout

VC

C

+-

V+

V-

VC

C

100kW

Vin

Vout

VC

C100

kW

(a)Inverting com

parator with fixed

threshold voltage

12 VC

CV

threshold =

Figure6.9

(a)C

ircuitofan

invertingcom

paratorw

itha

fixedthreshold

voltage.(b)

InvertingSchm

itttrigger,w

ithfeedback

fromthe

outputto

thethreshold

voltage.T

henetw

orkfor

thethreshold

voltagegives

(c)V

threshold D23V

CC

when

Vout D

VC

Cand

(d)V

threshold D13V

CC

when

Vout D

VC

C .

Voltages

above23V

CC

givelogic

1

Voltages

between

13V

CC

and23V

CC

giveundefined

values.

This

isdiscussed

furtherin

Digital

Electronics

2.T

heconventional

inverterin

figure6.10(a)

givesoutput

voltagesin

theundefined

rangefor

arange

ofinput

voltages.(Y

ouw

illanalyse

itsbehaviour

inE

lectronicC

ircuitDesign

3).N

owcom

parethe

Schmitttrigger.

It’seasiestto

consideraninputvoltage

thatrisessteadily

fromzero

asin

figure6.10(c).

(i)W

ithV

in D0

theoutput

isdefinitely

high,V

out DV

CC .

The

feedbacknetw

orkcan

beredraw

nas

infigure

6.9(c).Tw

oof

theresistors

areconnected

toV

CC

andare

thereforeeffectively

inparallel.

The

joinis

atV

TCD

23V

CC ,w

hichsets

thethreshold

voltageon

VC.

(ii)T

heoutputrem

ainsclose

toV

CC

untiltheinputrises

throughthe

thresholdvoltage,

23V

CC .

The

outputnowfalls

toV

out D0.

This

changesthe

behaviourofthenetw

orkforthe

thresholdvoltage,w

hichnow

behavesas

infigure

6.9(d).Tw

oof

theresistors

arenow

connectedto

groundand

thevoltage

atthe

joinfalls

toV

TD

13V

CC .

The

inputvoltageis

farabove

thisnew

thresholdvoltage,

which

isw

hythe

outputchanges

soabruptly

andpasses

rapidlythrough

theundefined

rangeofvoltages.T

hisis

theeffectofpositive

feedback.

Section6.5

Com

paratorsand

Schmitttriggers

49

logic0

01

23

0 1 2 3

Vin / V

Vout / V

logic1

undefined

01

23

Vin / V

V

T–

VT

+

(a) Conventional inverter

(b) Inverting Schmitt trigger

Vout / V Vin / V

tt

VT

–

VT

+

0 1 2 30 1 2 3 (i)(ii)

(iii)(iv)

(c) Input and output of a Schmitt trigger

(v)

Figure6.10

Transfercharacteristic

(outputvoltageas

afunction

ofinputvoltage)

for(a)

con-ventionalinverterand

(b)Schmitttrigger.T

heSchm

itttriggershows

hysteresisand

nevergivesan

outputw

ithan

undefinedlogic

value.(c)

Inputto

andoutput

froma

Schmitt

triggeras

afunction

oftim

e.T

hetrigger

turnsa

slowly

varyinginputinto

sharptransitions

andelim

inatesnoise.

(iii)T

heinput

voltagerises

toV

CC ,

thenfalls

again.N

othinghappens

asit

passesthrough

VTC

;the

outputdoesnotsw

itchuntilthe

inputfallsbelow

thelow

erthreshold

voltage,V

T.

The

two

thresholdvoltages,one

forrisingand

anotherforfallinginputvoltages,give

theinput–output

characteristicsketched

infigure

6.10(b).T

histype

ofbehaviour

iscalled

hysteresis.

(iv)T

hesecond

halfof

thetrace

shows

theeffectof

a(rather

fanciful)noisy

signal.G

oingupw

ard,theoutputsw

itchesw

hena

spikeofnoise

onthe

inputfirstgoesabove

VTC

.

50Signalconditioning

Chapter6

(v)T

heoutput

remains

lowuntil

anotherspike

onthe

fallingsignal

goesbelow

VT

.T

heSchm

itttriggergivesa

cleanoutputfrom

thisnoisy

inputsignal.

The

resistorsin

thethreshold

network

don’thaveto

beequal,as

Ihave

assumed

here–

itwas

justtom

akethe

arithmetic

simple.

Schmitttriggers

havem

anyother

applications.A

simple

relaxationoscillator

canbe

made

byadding

aresistorand

capacitor,forinstance.You

willsee

thisin

Analogue

Electronics

2.

An

op-amp

isnota

comparator

The

symbols

foran

op-amp

anda

comparator

aresim

ilar(som

etimes

identical)so

youm

ightbe

tempted

touse

anop-am

pas

acom

parator.D

onot.

Their

internalcircuitsare

significantlydifferentbecause

oftheirdifferentfunctions.

A

nop-am

pis

designedto

work

with

negativefeedback.A

syou

knoww

ell,thefeedback

bringsthe

inputsto

almost

thesam

epotential,

VC

V.

The

inputsof

op-amps

aredesigned

with

thisin

mind

andm

anydevices

aredam

agedifjVC

V j

>1

V.

Com

paratorshave

nosuch

restriction;theinputs

arenot‘tied

together’in

thesam

ew

ayand

canbe

drivenindependently

between

VE

Eand

VC

C .

A

nop-am

pis

usedin

linearcircuits

andits

outputcantake

anyvoltage

between

VE

Eto

VC

C(lim

itedby

saturation).Typicallythe

outputcanonly

changeratherslow

ly(the

slewrate).

Com

paratorsare

nonlineardevices

andtheir

outputisdesigned

toprovide

eitherV

EE

orV

CC ,notvoltages

inbetw

een,andto

switch

between

thesevalues

asrapidly

aspossible.

Som

ecom

paratorshave

anopen-collector

output.T

hism

eansthatthe

outputstagecan

pulltheload

down

toV

EE

butnotdriveitup

toV

CC .

Apullup

resistorm

aybe

needed.C

heckthis

carefullyw

henyou

usea

comparator.

Read

thedata

sheetandsee

TheA

rtofE

lectronics[4]forfurtherdetails.

Studentsare

oftencaughtoutby

open-collectoroutputs

inprojects!

Itisn’tanissue

forcom

paratorsbuiltinto

largersystems

suchas

microcontrollers.

Use

thecorrectcom

ponentforthejob.M

anym

icrocontrollerscontain

analoguecom

paratorsor

offerSchmitttriggers

ontheirinputs

toreduce

theim

pactofnoiseorslow

ly-varyingsignals.

6.6S

ample-and-hold

circuitIn

theorya

sample-and-hold

circuitis

acritical

partof

anyanalogue-to-digital

converter.In

practicethey

areincorporated

intom

osttypesofA

DC

andyou

don’thaveto

worry

aboutthem,

which

isw

hyI’ve

leftthemuntilthe

end.A

sample-and-hold

(S/H)

ortrack-and-hold

(T/H

)circuit

islike

theanalogue

equivalentof

atransparentlatch

indigitalelectronics.

Figure6.11

onthe

nextpageshow

san

outlineof

thecircuit

andits

operation.T

hetw

oop-am

psare

connectedas

unitygain

buffers(voltage

followers).

The

firstchargesthe

capacitorto

theinputvoltage

aslong

asthe

switch

isclosed,

inw

hichcase

theoutputfollow

sthe

input.W

henthe

switch

isopened

thecapacitoris

isolated

Section6.7

Summ

aryofsignalconditioning

51

+-

Vout

Vin

close to track or sam

ple

t

Vout

Vin

voltage

trackhold

opento

hold

+-

track

hold

Figure6.11

Basic

track-and-hold(orsam

ple-and-hold)circuitandits

operation.

fromthe

inputandholds

itsvoltage,provided

thattheinputofthe

secondop-am

pdoes

notdrawtoo

much

current.(The

inputcurrentwould

bezero

foranidealop-am

pbutnothing

isideal!)

Sometim

esthese

arecalled

track-and-hold,som

etimes

sample-and

holdcircuits.

Inprin-

ciplea

sample-and-hold

circuitshouldbe

more

likean

edge-triggeredflip-flop

andsam

pleits

inputonlyata

particularpointintim

e(butin

realityduring

ashortintervalcalled

theaperture).

My

impression

isthat

thenam

esare

usedinterchangeably

inpractice

andthat

most

sample-

and-holdsare

reallytrack-and-holds.

They

aretricky

circuitsto

designbutm

ostAD

Cs

donot

needthem

nowadays.Forexam

ple,thenetw

orkofcapacitors

ina

SAR

AD

Cacts

asan

intrinsicsam

ple-and-holdcircuit.

6.7S

umm

aryofsignalconditioning

M

ostdataacquisition

systems

needto

conditionthe

signalinsom

ew

ay.T

heaim

isto

remove

frequenciesthat

would

sufferaliasing,

suppressnoise

andm

atchthe

rangeof

voltagesto

theconverter.

Som

estandard

circuitsneed

tobe

redesignedforsingle-supply

op-amps.

A

comparator

isnotthe

same

asan

op-amp

andshould

beused

toclean

noisysignals

toavoid

spurioustransitions

ondigitalinputs.

6.8E

xamples

Exam

ple6.1

You

couldw

ritedow

nequation

(6.3)fromthe

standardresults

forcircuitsw

ithopam

psusing

superposition–

doyou

seehow

?

Exam

ple6.2

Whatshould

beconnected

tothe

inputofeveryA

DC

?

Exam

ple6.3

An

AD

Cis

neededforan

applicationon

anaeroplane.

The

signalsuffersfrom

interferencefrom

thepow

ersupply,w

hichruns

at400H

z.W

hattypeof

AD

Cand

whatsam

-pling

frequencyw

ouldyou

recomm

endto

minim

izeinterference

fromthe

powersupply?

Exam

ple6.4

Whatare

thecharacteristics

ofaninstrum

entationam

plifier?

52Signalconditioning

Chapter6

-+V

out

Vin

VC

CR

2 =

100 kW

R1 =

10 kW

R3 =

120 kW

R4 =

100 kW

v+

v-

1 µF

Figure6.12

An

amplifierbased

onan

op-amp

with

asingle

supply.

Exam

ple6.5

Analyse

theam

plifierin

figure6.12

basedon

anop-am

pw

itha

single-supplyand

showthat

Vout D

10.V

in 12V

CC/:

(6.6)

Hint:assum

ean

idealop-amp

anduse

theusualthree

orfourstepsthatyou

learntinE

lectronicE

ngineering1Y.D

on’tworry

aboutthecapacitor,w

hichisincluded

tosuppressnoise.C

alculatethe

acceptablerange

ofinputs

tothis

amplifier

assuming

asupply

ofV

CC D

3V

.D

oesthe

op-am

pneed

rail-to-railinputs?

What

isthe

purposeof

thiscircuit

–w

hyis

astraightforw

ardinverting

amplifiernotused?

Exam

ple6.6

Design

anam

plifierto

work

froma

single3

Vsupply.

Itshouldtake

aninput

voltagebetw

een0.2

Vand

0.3V

andam

plifyitto

thefullrange

ofoutputvoltage.

Itmay

beinverting

ornon-invertingatyouroption.

7

Com

pletesystem

sw

ithA

DC

s

Now

itistim

eto

puteverythingtogetherto

make

acom

pletesystem

with

ananalogue-to-digital

converter.W

eshallfirstlook

atvoltagereferences

andhow

toavoid

thembefore

examining

afew

examples

ofsensorandhow

theycan

beconnected

toan

AD

Cto

meeta

givenspecification.

7.1Voltage

referenceR

ecall(again!)thatthe

digitaloutputofanA

DC

isthe

ratioofthe

analogueinputvoltage

toa

referencevoltage,setoutin

equation(2.2):

NA

DC D

nint 2

NV

in

VFS

:(7.1)

The

full-scalevoltage

VFS

isusually

thesam

eas

thereference

voltageV

ref .AllA

DC

stherefore

needa

voltagereference,although

thisis

sometim

eshidden.T

hesam

eis

trueofD

AC

s.In

many

casesthe

(analogue)supplyvoltage

isused

asthe

reference.This

isalm

ostalways

donein

smallm

icrocontrollers,althoughlargerones

offeranexternalconnection

orprovidean

internalreference.Sm

all,discreteA

DC

soften

usethe

supplyas

referencetoo.

Care

mustbe

takento

keepthe

supplyquietin

thesecases.

Alternatively,

aspecial

voltagereference

isused

togive

aprecise,

accuratevalue.

The

simplestcircuitis

aZ

enerdiodew

itha

resistorinseries

togive

asuitable

current.Unfortunately

itsperform

anceis

poor.

T

hevoltage

altersif

thecurrentthrough

thediode

varies,becauseof

changesin

theload

orthevoltage

thatsuppliesthe

resistor.

E

venifthe

currentiskeptconstant,the

voltagechanges

asa

functionoftem

perature.

The

dependenceon

temperature

canbe

cancelledby

placinga

normal,forw

ard-biasseddiode

inseriesw

iththe

(reverse-biassed)Zener.H

owever,you

don’thaveto

worry

aboutthisbecause,asusual,m

anufacturersproduce

specialvoltagereferences.C

heaperonesare

basedon

adifferent

principlecalled

abandgap

referencebutspecial,buried

Zener

diodesare

stillinuse.

The

datasheets

arecom

plexbuttw

ospecifications

areparticularly

important.

53

54C

omplete

systems

with

AD

Cs

Chapter7

Initialaccuracy

–how

closeis

thevoltage

tothe

specifiedvalue.

Tem

peraturecoefficient

–by

howm

uchdoes

thevoltage

change(drift)

with

tempera-

ture.Itisoften

quotedin

unitsofppm

/°C,w

hereppm

isa

standardabbreviation

for‘partsperm

illion’.

Togive

youan

ideaof

whatis

available,hereis

aselection

ofbandgap

referencesfrom

TexasInstrum

ents. 1

T

heycom

ein

voltagesof1.25,2.048,2.5,3.0,3.3

and4.096

V.

For

about$0.50

youget

theR

EF29xx.

Itsinitial

accuracyis

2%w

itha

temperature

coefficientof100ppm

/°C.

Y

oum

ustspend

more

money

ifthis

isn’tgood

enough.Four

gradesof

referenceare

offered,ofw

hichthe

bestisthe

RE

F32xxw

ithan

initialaccuracyof

0.2%and

driftof7

ppm/°C

.The

outputisless

noisyas

well.

Of

courseyou

paym

ore,nearly$2,w

hichm

aybe

more

thanthe

AD

C!

Consider

thetem

peraturecoefficienta

littlefurther.

The

voltagefrom

theR

EF29xx

variesby

100ppm

,10

4or0.01%

ifthetem

peraturechanges

by1°C

.Achange

intem

peratureof100°C

causesthe

referencevoltage

tochange

by10000

ppmor

1%.

This

may

degradethe

overallaccuracy

ofthe

systemseriously.

How

ever,itisalw

aysbestto

studythe

datasheetthoroughly

ratherthanrely

ona

singlenum

ber.Aplotshow

sthatthe

dependenceofvoltage

ontem

peratureis

farfromlinear.In

factit’sm

orelike

aparabola

with

am

aximum

atabout60°C.

These

referencesare

three-terminal

orseries

devices.T

hism

eansthat

theyhave

input,outputand

groundconnectionsare

areused

inthe

same

way

asalinearregulator.T

hedifference

isthatyou

shouldnotdraw

alarge

currentfromthem

.Tw

o-terminalor

shuntdevicesare

usedin

thesam

ew

ayas

asim

pleZ

enerdiode.To

seethe

importance

ofthe

temperature

coefficient,consider

thereference

requiredfor

a10-bit

AD

Cthat

must

remain

accuratebetw

een50

andC100°C

.A

ssume

that‘accurate’

means

thatany

changein

Vref

shouldproduce

lessthan

1bit

errorin

theconverted

value.A

changeof1

bitin2

10

isabout

10

3and

thisis

arange

of150°Cso

thetem

peraturecoefficient

must

beless

than10

3=150

7

10

6=°Cor

7ppm

/°C.

We

would

needto

splashout

onthe

mostexpensive

referenceto

meetthe

specification.A

ctuallyw

eshouldn’tdo

thisw

ithoutfurtherthought:w

eshould

checkthe

datasheetm

orecarefully

becauseofthe

nonlineardepen-dence

ontem

perature.Even

thebestreference

inthis

rangew

ouldnotm

eetthespecification

fora

12-bitconverter.T

hem

oralisthatthe

voltagereference

mustbe

chosencarefully

ifyouw

antasystem

with

high,absoluteaccuracy.

Pleasem

akecertain

thatyoureally

needsuch

highaccuracy:

Would

highprecision

begood

enough?Suppose

thatyouare

designinga

heatingsystem

,forinstance.Y

oum

ightw

antto

resolvechanges

of˙0:1°C

togive

goodcontrol

ofthe

temperature.

On

theother

hand,itmightnotm

atterifthe

selectionof

theabsolute

temperature

isno

betterthan

˙0:5°C

.This

example

needsgood

resolutionbutis

lessdem

andingon

accuracy.T

hebestsortofvoltage

referenceis

onethatyou

don’tneedatall.W

e’llexplorethis

next.1A

littlehistory:

These

components

were

formerly

soldby

Burr–B

rown,

perhapsthe

premier

brandin

analogueelectronics.T

hecom

panyw

asacquired

byTexas

Instruments

andthe

originalname

hasnow

beenelim

inatedfrom

thedocum

entation.Sad.NationalSem

iconductorhasnow

gonethe

same

way.

Section7.2

Ratiom

etricm

easurements

55

(a) Therm

istor in potential divider and AD

C(b) T

hévenin equivalent circuit

Rin

Cin

Rs

Vs

AD

Cinput

Vin

thermistor

network

VC

C = 3

V

Vin

Rth =

10kW

–20kW

Rref =

50kW

thermistor

AD

C, 10 bits

Rin =

7 kWC

in = 5.5 pF

Figure7.1

(a)Therm

istorina

potentialdividerconnectedto

aSA

RA

DC

.(b)Thévenin

equiv-alentcircuit.

7.2R

atiometric

measurem

entsI

havem

entionedseveraltim

esthatsystem

scan

bedesigned

torender

avoltage

referenceun-

necessary.A

san

example,suppose

thatatherm

istorto

measure

temperature

usingthe

circuitshow

nin

figure7.1,w

hoseoperation

willbe

describedin

section7.5

onpage

58.T

hevoltage

fromthe

potentialdivideris

Vin D

Rth

Rref C

Rth

VC

C:

(7.2)

Here,yetagain,is

therelation

between

theinputvoltage

andoutputofthe

AD

C,assum

ingthat

itusesthe

supplyvoltage

VC

Cas

itsreference:

NA

DC D

nint 2

NV

in

VC

C :

(7.3)

Puttingthese

togethergives

NA

DC D

nint 2

N

VC

C

Rth V

CC

Rref C

Rth

Dnint

2N

Rth

Rref C

Rth

:(7.4)

The

criticalfeatureis

thatthereference

voltageV

CC

hasvanished

fromthe

overallbehaviourbecause

itaffectsthe

signalandA

DC

equally.If

VC

Cfalls,the

outputofthe

potentialdividerfalls

butsodoes

thereference

voltageof

theA

DC

andthe

changecancels

outinN

AD

C .T

hiscircuitdoes

notneeda

voltagereference.

Ifyou

looka

littlem

oreclosely,you

willsee

thattheoutput

NA

DC

dependson

theratio

ofR

thto

Rref .

This

istherefore

calleda

ratiometric

measurem

ent.Itis

oftenpossible

todesign

systemsin

thisway

withouta

voltagereference.W

e’llseeanotherexam

pleshortly

insection

7.7on

page62.

7.3M

easurementofabsolute

voltagesw

itha

simple

AD

CT

hetw

opreceding

sectionshave

shown

howto

designtw

osim

plesystem

sw

ithan

AD

C.

56C

omplete

systems

with

AD

Cs

Chapter7

AD

C

signal

Vin

Vabs

VC

C

VA

DC

voltagereference

Figure7.2

AD

Cw

ithtw

oinputs,the

signalofinterest

Vin

andan

absolutevoltage

Vabs .

The

referencevoltage

fortheA

DC

istaken

fromthe

powersupply

atV

CC .

If

thevoltage

fromthe

sensoris

proportionaltoV

CC ,the

referencevoltage

forthe

AD

Cshould

betaken

fromV

CC .

If

thesensor

producesan

absolutevoltage,the

referencevoltage

ofthe

AD

Cshould

betaken

froman

absolutevoltage

reference.

Unfortunately

youoften

needto

measure

anabsolute

voltagebutthe

AD

Ctakes

itsreference

voltagefrom

VC

Cand

thiscannot

bechanged.

An

example

ofthis

isgiven

inthe

following

section.The

outputoftheA

DC

isgiven

byequation

(7.3)andw

illchangeif

VC

Cchanges,even

ifthe

voltageV

infrom

thesensor

remains

thesam

e.H

owshould

thesystem

bedesigned

toelim

inatethis

error?T

hesolution

requiresan

absolutevoltage

reference,which

cannotbeavoided,butitm

ustbeconnected

toa

signalinputofthe

AD

Crather

thanits

referenceinput.

The

systemis

shown

infigure

7.2.Use

theA

DC

tom

easurethe

two

inputvoltages:

Nin D

nint 2

NV

in

VC

C and

Nabs D

nint 2

NV

abs

VC

C :

(7.5)

Dividing

thetw

oand

droppingthe

nint./function

gives

Nin

Nabs D

Vin

Vabs

soV

in DN

in

Nabs V

abs:

(7.6)

Thus

theabsolute

valueof

theinputvoltage

canbe

foundfrom

thetw

om

easurements.

Effec-

tivelyw

eare

usingV

abs tocalibrate

VC

C .T

hesam

em

ethodis

oftenused

tom

easureV

CC

tocheck

thehealth

ofthe

power

supply.It

stillrequiresan

absolutevoltage

referencealthough

itmightnotneed

particularlyhigh

quality.

7.4W

orkedexam

ple:Tem

peraturesensor

with

LM35

and8-bitA

DC

We’llnow

lookata

givensensorand

AD

Cand

investigatehow

thecom

pletesystem

shouldbe

designedto

meeta

specification.Suppose

firstthatwe

wantto

measure

thetem

peratureof

aroom

with

thefollow

ingcom

ponents.

Section7.4

Worked

example:

Temperature

sensorw

ithLM

35and

8-bitAD

C57

LM

35A

DC

+ -90

kW

10kW

AD

CL

M35

(a) Direct connection

(b) With am

plifier of gain +10

VC

C = 3.3

V

Figure7.3

An

LM

35tem

peraturesensor

connectedto

anA

DC

(a)directly

and(b)

througha

noninvertingam

plifierofgain+10.

T

hesensor

isthe

LM

35,w

hichgives

avoltage

proportionalto

temperature

indegrees

celsius,so

that0°C

giveszero

voltage.T

hescaling

factoris

10m

V/°C

,so

theL

M35

gives200

mV

at20°Cand

soon.T

hesensoris

asilicon

IC,nota

thermistor.Its

outputisa

linearfunctionoftem

perature,which

isconvenient,butthe

voltageis

small.

T

heA

DC

isan

8-bitSAR

,comm

onin

smallm

icrocontrollers,suppliedat3.3

V.

We

wish

toresolve

changesof˙

0:1°C

overa

rangeof

5°Cto

30°C.Is

itpossibleto

meetthis

specificationw

ithoutfurthercomponents?

Only

250values

areneeded

soitsounds

trivial–but

isnot.

Supposefirstthatw

econnectthe

outputoftheL

M35

directlyto

theinputofthe

AD

Cas

infigure

7.3(a).Whatvoltages

mustw

em

easure?

T

herange

intem

peratureis

5–30°Cand

thescaling

factoris

10m

V/°C

sothe

outputvaries

from50–300

mV.

A

changein

temperature

of˙0:1°C

scalesto

achange

of˙1

mV

.

Thus

we

needto

measure

50–300m

Vw

itha

resolutionof

1m

V.The

full-scalerange

ofthe

AD

Cis

3.3V.Suppose

thatwe

usethe

maxim

umresolution

of10bits.

This

gives2

10D

1024

possibleoutputs

sothe

resolutionon

theinputis

LSB

D.3

:3V

/=1024

3

mV

.T

hisis

toolarge

sow

ecannot

meet

thespecification.

The

smallest

changein

temperature

thatcould

bedetected

is0.3°C

.T

hebasic

problemis

thatwe

areusing

onlya

smallpartof

theA

DC

’srange,just0.25

Voutof

3.3V.O

ver90%

ofthe

rangeis

wasted

sothis

sensoris

apoor

match

tothe

AD

C.T

hism

ismatch

isillustrated

infigure

7.4(a)onthe

following

page.T

heconclusion

isthata

10-bitAD

Ccannotm

eetthespecification,although

only250

valuesare

neededand

youm

ighthave

hopedthat

an8-bit

AD

Cw

ouldbe

sufficient.H

ereare

two

solutionsto

thisproblem

.

U

sean

externalAD

Cw

ithbetter

resolution.A

ssume

thatitworks

overthe

same

rangeofvoltage,3.3

V.We

needto

resolve1

mV,w

hichneeds

atleast3300outputvalues.T

henextpow

erof

two

abovethis

is4096

D2

12.

A12-bitA

DC

would

thereforem

eetthespecification.

58C

omplete

systems

with

AD

Cs

Chapter7

3.0V

3.3V

2.0V

1.0V

0V

3.0V

3.3V

2.0V

1.0V

0V

output from sensor

input to ADC

input range of ADC

(a) direct connection of sensor(b) w

ith amplifier of gain +

10

0.3V

Figure7.4

Matching

ofoutputof

LM

35to

inputofA

DC

(a)directly

and(b)

througha

nonin-verting

amplifierofgain

+10.

Insertan

amplifierw

itha

gainofC

10

between

thesensorand

theA

DC

asshow

nin

figure7.3(b).

The

sensornow

presentsan

amplified

inputof500

mV

–3000m

Vto

theA

DC

forthe

range5°C

–30°Cas

shown

infigure

7.4(b).T

heA

DC

needonly

resolvea

changeof

10m

V,which

istrivialin

10-bitmode

andalm

ostpossiblein

8-bitmode.

We

cantherefore

meetthe

specificationforresolution

with

anextra

componentbutnotw

ithout.T

hisis

asim

pleexam

pleof

howitis

usuallynecessary

tocondition

asignalbefore

convertingit.

We

shouldalso

includea

capacitorbetw

eenthe

outputofthe

LM

35and

groundto

reducenoise

pickedup

fromthe

environment.T

hedata

sheetsuggestsa

1µF

capacitorinseries

with

a75

resistorforthe

LM

35,butothercomponents

havedifferentrequirem

ents.A

seriousdefectofthis

systemis

thattheoutputofthe

LM

35is

anabsolute

voltagebutthe

AD

Cuses

VC

Cas

itsreference.

The

outputofthe

AD

Cw

illthereforechange

ifV

CC

changes,even

ifthe

temperature

staysthe

same.

The

previoussection

explainshow

toelim

inatethis

error.

7.5W

orkedexam

ple:M

easurementoftem

peratureusing

atherm

istorR

eturnnow

tothe

circuitinfigure

7.1on

page55,w

hichis

usedto

measure

temperature

usinga

thermistor.T

hisis

aresistorm

adeofa

specialmaterialw

hoseresistance

changesstrongly

with

temperature

(theopposite

ofthequality

usuallydesired).

Therm

istorsare

widely

usedbecause

theyare

simple,cheap

andcan

beencapsulated

ina

ruggedpackage.

They

givea

largechange

inresistance,so

thattheycan

oftenbe

connecteddirectly

toan

AD

C;m

ostothersensorsrequire

amplifiers

orm

orecom

plicatedsignalconditioning.

Unfortunately

theresistance

isa

stronglynonlinear

functionof

temperature

soa

lookuptable

may

beneeded.

Acom

mon

applicationis

tom

easurethe

temperature

ofthecoolantin

acarengine.

Atherm

istoris

usuallyconnected

ina

simple

potentialdivider

asin

figure7.1.

(There

doesn’tseemto

bea

standardsym

bolfortherm

istors.)Suppose

thattheresistance

ofthe

ther-m

istorvaries

between

10k

–20k

overthe

operatingrange.

We

shallanalysetw

oaspects

ofthis

system:

Section7.5

Worked

example:

Measurem

entoftemperature

usinga

thermistor

59

the

time

thatshouldbe

allowed

fortheA

DC

tosam

plethe

input

the

rangeof

voltagespresented

tothe

AD

Cand

whether

thiscircuitcan

providea

givenresolution.

Sam

plingtim

eFirst,turn

thepotentialdivider

intoits

Thévenin

equivalentcircuit,asin

figure7.1(b).

Iw

on’texplain

thisbecause

youshould

know–

lookback

atElectronic

Engineering

1Xifnot.

Vs

DR

th

Rth C

Rref V

CC;

(7.7)

Rs

DR

th kR

ref DR

th Rref

Rth C

Rref :

(7.8)

Both

ofthese

dependon

theresistance

ofthe

thermistor.

Startwith

thehighestvalue,

Rth D

20

k

.

1.T

hepotentialdividergives

Vs D

0:8

6V

andR

s D14

k

.

2.T

hetotalresistance

inthe

equivalentcircuitisR

DR

s CR

AD

C D14C

7D21

k

.

3.T

hecapacitance

CD

CA

DC D

5:5

pF.

4.T

hereforethe

time-constantis

DR

CD

21

k

5:5

pFD0:1

2µs.

5.W

efound

earlierthatthe

inputofa

10-bitAD

Cshould

beallow

edto

chargefor

atleast7:6

D0:9

µs;say1

µsforsafety.

This

mustbe

repeatedfor

thelow

estvalueof

resistance,10k

,which

givesV

s D0:5

0V

andR

s D8:3

k

.T

helow

erresistance

allows

theinputof

theA

DC

tocharge

more

quickly,soin

generalwe

shoulduse

thelongersam

plingtim

ecalculated

for20k

.

Resolution

The

previouscalculation

shows

thatthe

outputvoltage

rangesfrom

0.50V

–0.86V,a

spanof

0.36V.T

hisvoltage

entersan

10-bitAD

C,w

hoserange

ofinputsis

0.0–3.0V,so

thetherm

istoruses

only12%

ofthepossible

values.This

isroughly

18 D2

3ofthe

rangeso

itislike

throwing

away

3ofthe

AD

C’s

bitsand

reducingitfrom

a10-bitto

a7-bitdevice.

Another

way

oflooking

atthisis

tocalculate

LSB

D.3

V/=

21

03

mV

.T

henum

berof

outputsover

theoperating

rangeis

givenby

0:3

6V

=LSB

D120.

An

amplifier

isrequired

tom

akebestuse

oftheA

DC

.C

onsideragain

astraightforw

ardnoninverting

amplifier.

The

maxim

uminput

voltageis

0.86V.

The

op-amp

issupplied

from3.0

Vbut

itis

bestto

keepabout

0.1V

away

fromthe

supplyrails

evenifthe

op-amp

hasa

so-calledrail-to-railoutput.T

hem

aximum

gainperm

ittedis

therefore2:9

=0:8

63:4.

Use

again

of3forsim

plicity.T

herange

ofinputvoltagesis

nowfrom

1.50V

–2.58V,varying

by1.08

V.thisis

abig

improvem

entbutwe

stillwaste

more

thanhalfofthe

AD

C’s

range.

60C

omplete

systems

with

AD

Cs

Chapter7

-+

Vout

Vin

R2 =

86 kW

R1 =

12 kW

R3 =

33 kW

R4 =

12 kW

v+

v- V

CC =

3 V

Rth =

10–20 kW

Rref =

50 kWA

DC

, 10 bitsR

in = 7 kW

Cin =

5.5 pFV

bias = 0.79 V

Figure7.5

Invertingam

plifierwith

biasto

match

atherm

istortoan

AD

C.

An

invertingam

plifierw

itha

biasvoltage

shouldbe

usedif

itisim

portanttofillthe

rangeof

theA

DC

.T

hecircuit

isshow

nin

figure7.5

andw

asanalysed

insection

6.3on

page43.

Itshouldtake

aninputfrom

0.50–0.86V

andconvertitto

anoutputfrom

2.9–0.1V,w

hichis

safelyclearofthe

supplyrails.Its

gainshould

be

2:9

0:1

0:5

00:8

6

7:8:

(7.9)

The

gaindoesn’t

haveto

bean

integer.It

isset

bythe

usualpair

ofresistors,

R2 =

R1

infigure

6.5on

page43.

You

willhave

toexperim

entifyou

wish

togetnear

thisvalue

ofgain

with

standardvalues.

Forexam

ple,R

1D

8:6

k

andR

2D

68

k

givea

gainof

7:9or

R1 D

12

k

andR

2 D86

k

give7:2.T

hesecond

choiceis

safer.H

avingfound

thegain,the

nextstepis

tocalculate

thebias

voltage.H

ereis

arem

inderof

equation(6.3):

Vout D

1CR

2

R1

Vbias

R2

R1

Vin :

(7.10)

PutV

in D0:5

V,V

out D2:9

V,R

1 D12

k

andR

2 D86

k

intothis:

2:9

VD

1C86

12

Vbias

86

12

0:5

V;

(7.11)

which

givesV

bias D0:7

9V

.Finally,w

eneed

apotentialdivider

togive

0.79V

from3.0

V.Again

youm

ustexperiment

andIfound

that12k

and33

k

gave0.80

V,which

ispretty

good.These

valuesare

shown

infigure

7.5.W

eseem

tohave

asatisfactory

systembutsadly

ithasa

major

problem.

We

foundearlier

thatthepotentialdivider

hasan

outputresistanceof

about14k

.T

heinputresistance

ofthe

invertingam

plifieris

givenby

R1

D12

k

.T

heam

plifierw

illtherefore

loadthe

potentialdividerseverely

andhave

alarge

effectonthe

voltagem

easured,upto

afactorof2.

This

isan

unacceptableerror

butitispossible

tocalculate

theerror

andapply

acorrection.

Alternatively

avoltage

follower

(unity-gainbuffer),m

eaningan

opamp

connectedto

givea

gainofC

1,canbe

connectedbetw

eenthe

potentialdividerandthe

invertingam

plifier.

Section7.6

Worked

example:

sensorw

ithgiven

rangeofvoltages.

61

7.6W

orkedexam

ple:sensor

with

givenrange

ofvoltages.

This

isa

typicalexample

froma

pasttestpaper.The

outputofatem

peraturesensoris

avoltage

proportionaltoabsolute

temperature

with

ascale

of10

mV

K

1.Itisrequired

tow

orkoverthe

range40°C

toC75°C

.(Take

0°CD

273

K.)

The

outputis

connecteddirectly

toan

AD

C,

whose

full-scalevoltage

issetby

thesingle

powersupply

at5:0

V.

(a)W

hatrangeofvoltages

mustbe

convertedby

theA

DC

?

(b)T

hesystem

isrequired

toresolve

0:5°C

orbetter.How

many

bitsofoutputm

usttheA

DC

produce?

(c)T

hedigital

systemchosen

forthis

applicationhas

onlyan

8-bitA

DC

.Isit

possibleto

meetthe

specificationofthe

systemby

includingsom

etype

ofamplifying

circuit?Ifso,

explainw

hattypeofcircuitshould

beused

andgive

itsspecification

butdonotdesign

thecircuitin

detail.

(d)A

reviewer

suggeststhat

itw

ouldbe

betterto

usean

AD

Cw

itha

separatereference

voltage,ratherthan

areference

derivedfrom

thepow

ersupply.

Explain

whether

thisis

goodadvice

ornot.

(e)T

hedesigneracceptsthe

adviceand

choosesareference

with

avoltage

driftof100

ppm=°C

.E

xplainw

hetherthisis

agood

choiceornot.

The

lowesttem

peratureis

40°C

D233

Kgiving

2.330V

;them

aximum

temperature

isC75°C

D348

K,giving

3.480V.T

herange

istherefore

2.330V

to3.480

V.A

resolutionof

0.5°Cm

eans5

mV

sothe

AD

Cm

ustresolveatleast

5:0

V=5

mV

D1000

values.T

henextpow

erof

2up

is1024,giving

a10-bitA

DC

.Note

thatyoum

ustusethe

fullrange

oftheA

DC

,notjusttherange

ofinputsfrom

thesensor.

The

numberofvaluesto

beresolved

inthe

rangeofinterestis

.75°C

40°C

/=0:5°C

D231

includingboth

endpoints.T

hisis

possiblew

ithan

8-bitA

DC

,which

has256

outputvalues.

The

8-bitA

DC

hasL

SBD

5:0

V=256

19:5

3m

Vso

we

needan

amplifier

with

again

of19:5

3=5D

3:9

06

tom

atchthe

changein

outputfromthe

sensorfor

achange

of0.5°C

toL

SBof

theA

DC

.Asim

plenoninverting

amplifier

will

notw

orkbecause

thisgain

would

increasethe

voltageat+75°C

to13.6

V,which

isfarabove

thesupply

voltage.We

musttherefore

usean

invertingam

plifierwith

anoffsetvoltage

tokeep

theoutputvoltage

within

thesupply

rails.It

isgood

adviceto

usea

separatereference

voltage.T

hecurrent

systemhas

anabsolute

inputvoltageto

theA

DC

butthereference

voltageis

takenfrom

thepow

ersupply,which

may

bepoorly

stabilised.Itis

notaratiom

etricm

easurement.

The

referencevoltage

shouldalso

bean

absolutevalue,w

hichrequires

a‘real’reference.

The

rangeoftem

peraturesis

115°C,giving

afractionalchange

inreference

voltageof

115

100

D11500

ppmD

0:0

115

D1:1

5%.

The

fractionalresolution

ofthe

AD

Cis

1=256

0:0

039D

0:3

9%so

thechange

inreference

voltageis

equivalenttoa

changein

outputof3for

them

aximum

inputacceptedby

theA

DC

.Maybe

notagood

choice.

62C

omplete

systems

with

AD

Cs

Chapter7

VC

C

V-

V+

R+D

R

R-D

R

R-D

R

R+D

R

sensor

VC

C

V-

V+

R+D

R

R-D

R

R-D

R

R+D

R

sensor+- instrum

entationam

plifier

AD

C

VC

C

(a)(b)

Figure7.6

(a)Weightsensorw

ithfourelem

entsconnected

asa

Wheatstone

bridge.(b)Sensorconnected

toan

instrumentation

amplifierand

AD

C.

7.7W

orkedexam

ple:S

ensorfor

aw

eighingm

achineT

hefinalexam

pleis

thesensor

andA

DC

foran

electronicw

eighingm

achine.T

hesensors

areusually

basedon

thepiezoresistive

effect,which

means

thattheresistance

ofam

aterialchangesw

henit

isstrained

(distortedm

echanically).Typically

thesensor

isis

athin

diaphragmof

silicon,fourregionsofw

hichactas

piezoresistivesensors.T

heyare

connectedas

aW

heatstonebridge,w

hichisarranged

sothatthe

resistanceoftw

oelem

entsgoesupw

hena

weightisapplied

andthe

othertwo

goesdow

n.The

circuitisshow

nin

figure7.6(a).

Look

atthevoltage

VCfirst.

IdeallyVC

D12V

CC

and

RD

0w

henno

weightis

present.W

hena

weightis

applied,VCV

CC

DR

C

R

.RC

R

/C.R

R/ D

12 C

R

2R

:(7.12)

The

largestpartofthisis

the12

because

R=R

issm

all.Similarly,

VV

CC

DR

R

.R

R

/C.R

C

R/ D

12

R

2R

:(7.13)

Again,the

largestpartisthe

12 .Instead

oflooking

atVC

andV

themselves,itis

more

illumi-

natingto

work

with

theiraveragevalue

anddifference.T

heaverage

iscalled

thecom

mon-m

odevoltage

andis

givenby

VC

M

VCC

V2

D12

VC

C;

(7.14)

while

thedifference

is

V

VC

V D

RRV

CC:

(7.15)

The

comm

on-mode

voltageis

largebutboring

andw

eare

interestedonly

inthe

smalldifference

V

,which

isa

comm

onsituation.

Atypicalvalue

forthe

sensitivityis

R

=R

D1%

fora

fullloadof

1000g.

Supposethat

we

wish

toresolve

differencesof10

g,which

mightbe

goodenough

fordomestic

kitchenscales

(actuallym

inew

orkto

5g).

This

requiresonly

100intervals,w

hichsounds

trivial.U

nfortu-nately

itistrivialonly

iftherange

ofoutputsfrom

thesensorm

atchesthe

rangeofinputs

tothe

AD

Cperfectly.Ifpossible

we’lluse

asim

ple8-bitA

DC

.

Section7.7

Worked

example:

Sensorfor

aw

eighingm

achine63

Tryfirstto

convertVC

andV

separatelyand

usesubtraction

tofind

thedifference

ofthe

digitalvalues.Whatisthe

rangeof

VCand

byhow

much

doesitchangeasa

functionofw

eight?

VC

D0:5

00

VC

Cw

ithno

weight

VC

D0:5

05

VC

Cw

iththe

maxim

umw

eightof1kg,a

changeof

0:0

05

VC

C

a

changein

weightof10

gtherefore

causesa

changeof

VC

D0:0

00

05

VC

C

Ifthe

AD

Cw

orksbetw

een0

andV

CC ,itneeds

toresolve

1=0:0

00

05D

20

000

values.T

hisw

ouldneed

a15-bitA

DC

,which

seemscrazy

when

we

needonly

100finalvalues!

The

problemis

thatwe

areusing

onlythe

rangefrom

0.500to

0.505of

VC

C ,which

is1=200

ofthe

rangeof

inputsto

theA

DC

.Over99%

ofitsrange

isw

asted.C

learlyw

eare

approachingthis

systemthe

wrong

way.T

hisis

ajob

foraninstrum

entationam

plifier(section6.1

onpage

40)asshow

nin

figure7.6(b).

Itamplifies

thedesired

difference

VD

VC

Vbut

suppressesthe

comm

on-mode

voltageV

CM

D12V

CC .

The

maxim

umdifference

voltageis

V

D0:0

1V

CC

soa

gainof50

(say)would

bringthis

to0:5

VC

C .We

needto

resolve100

valuesw

ithinthe

rangefrom

0to

0:5

VC

C ,which

means

200values

within

thefullrange

from0

toV

CC .T

hisrequires

onlyan

8-bitAD

Cas

desired.W

hynotam

plifythe

outputofthe

bridgeallthe

way

toV

CC ?

The

reasonis

thatpracticalstrain

sensorshave

alarge

offset.T

hism

eansthatthe

fourresistances

inthe

bridgeare

notallequal

when

now

eightis

applied.In

turn,this

implies

that

V¤

0and

itm

aybe

positiveor

negative.W

em

ustcom

pensatefor

theoffset

byadding

anoffset

voltageto

thecircuit

ofthe

instrumentation

amplifier

(Vbias in

figure6.1

onpage

40).T

hiskeeps

theinputto

theA

DC

positive,which

itneedsforvalid

conversions.T

husw

eneed

anam

plifierwith

apotentiom

eterforthe

offsetvoltage.The

potentiometeris

calleda

tarecontroland

isused

toadjustthe

scalesso

thattheyread

zerow

henthe

panis

empty.

Agood

featureofthis

designis

thatboththe

inputvoltagesand

thereference

voltageforthe

AD

Care

takenfrom

VC

C .T

hism

akesita

ratiometric

measurem

entasdescribed

insection

7.2on

page55.N

ovoltage

referenceis

thereforerequired.

Itwould

beeven

betterif

we

couldconnectthe

outputsof

thebridge

directlyto

anA

DC

.W

eneed

two

vitalfeatures:

differentialinputs

forVC

andV

torejectthe

comm

on-mode

voltage

high

resolutionbecause

ofthesm

allchangesin

voltage

This

suitsa

sigma–delta

AD

Cperfectly.Forexam

ple,theA

DC

inthe

MSP430F2003

(table3.1

onpage

13)has

differentialinputs

with

arange

of˙0:6

Vand

16-bitresolution.

ItsL

SBis

therefore.1

:2V

/=2

16D

18

µV.Forcom

parison,achange

inw

eightof10g

changes

R=R

by0.0001.

This

isequalto

V

=V

CC

so

Vchanges

by0.0003

Vor300

µVif

VC

C D3

V.

Infact

we

couldm

easureto

aresolution

of1

g.T

hisA

DC

includesa

programm

ablegain

amplifier,

which

couldim

proveresolution

further.T

heonly

catchis

thatthem

easurementis

nolonger

ratiometric

becausethe

AD

Cin

theM

SP430F2003does

notuseV

CC

foritsreference.

This

shows

theadvantage

ofusing

thecorrecttype

ofA

DC

forthe

job.T

hesigm

a–deltaA

DC

canalso

handlenegative

differencesin

voltagefrom

theoffsetand

we

couldsubtractthe

offsetvoltagedigitally.T

husw

edon’tneed

apotentiom

eter–justa

Tarebutton.

64C

omplete

systems

with

AD

Cs

Chapter7

This

mightsound

abitspecialised

butbridgesensors

arew

idelyused,notjustin

weighing

machines.Pressure

sensorsand

straingauges

arevery

similar.A

notherexample

isthe

mass

airflow

(MA

F)sensorina

car.This

measures

therate

atwhich

airentersthe

engine,which

isone

ofthekey

inputsto

theengine

managem

entsystem.

7.8E

xamples

Exam

ple7.1

Areference

diodehas

atem

peraturecoefficientof0.005%

/°C.O

verwhattem

-perature

rangecould

itbeused

inconjunction

with

(i)an8-bitconverter(ii)a

12-bitconverter?[78°C

,5°C]

Exam

ple7.2

Whattem

peraturecoefficientis

requiredfora

referencevoltage

sourcew

hichis

tobe

usedw

itha

converteroperating

overa

temperature

rangeof

0°Cto

70°Cif

theconverter

has(i)8

bits,(ii)12bits,(iii)16

bits?[5

10

3%=°C

,3

10

4%=°C

,2

10

5%=°C

]

Exam

ple7.3

Whatvalue

shouldbe

chosenforthe

referenceresistor

Rref to

getthem

aximum

changein

voltageforthe

systemin

section7.2

onpage

55,where

Rth

variesbetw

een10

k

and20

k

?W

hatisthe

newchange

involtage?

Hint:

findan

expressionfor

thechange

involtage

andfind

itsm

aximum

asa

functionof

Rref .It’s

straightforward

butmessy.

[About14

k

]

Exam

ple7.4

Whatchange

intem

peraturecould

beresolved

with

thesystem

insection

7.4on

page56

usingthe

AD

Cin

8-bitmode?

Exam

ple7.5

Isa

gainof10

thebestchoice

toresolve

0.1°Cforthe

systemin

section7.4?

Exam

ple7.6

Supposethatthe

rangeoftem

peraturesw

ereextended

to0–30°C

forthesystem

insection

7.4.Isthe

designw

iththe

amplifierstillsatisfactory?

(The

answeris

nottrivial.)

Exam

ple7.7

Asensor

producesan

outputbetween

0.5V

and1.0

V,which

isto

bem

ustbedigitized

with

aprecision

of1

mV

orbetter.

The

AD

Chas

afull-scale

rangefrom

0.0V

–2.5V.

How

many

bitsare

neededif

thesensor

isconnected

directlyto

theA

DC

andw

hatwould

theactualresolution

be?H

oww

ouldthis

changeif

anam

plifierw

ereused

tom

atchthe

outputofthe

sensortothe

fullrangeofinputs

oftheA

DC

?G

ivea

specificationforthe

amplifier.

Exam

ple7.8

Figure7.7

shows

alight-dependentresistor

(LD

R)

connectedin

apotentialdi-

vider.T

heL

DR

hasresistance

1.6k

inthe

lightand100

k

inthe

dark.Find

thevoltage

onthe

potentialdividerand

theoutputresistance

atthesetw

oextrem

es.(In

otherw

ords,findits

Thévenin

equivalentcircuit.)T

heA

DC

isin

theL

PC1768

andhas

aresolution

of12

bits,aninputresistance

of7.5

k

andcapacitance

of15

pF.For

howlong

shouldit

sample

itsinput

toensure

thaterrors

dueto

incomplete

chargingare

negligible?H

owm

anyclock

cyclesis

thisfor

anA

DC

clockat

13M

Hz?

Ifthesystem

hadonly

todistinguish

between

lightanddark,w

hatsimplercom

ponentcouldbe

used?

Section7.8

Exam

ples65

VC

C = 3.3 V

Rref =

5.6kW

RL

DR

Vin

AD

C

Figure7.7

Alight-dependentresistor(L

DR

)connectedin

apotentialdividerand

monitored

byan

AD

C.

Exam

ple7.9

[Hard]

Calculate

theerror

dueto

theinputresistance

ofthe

invertingam

plifierin

figure7.5.H

int:thevoltage

attheinverting

inputoftheop-am

pis

heldfixed

bythe

negativefeedback.

This

issim

ilarto

avirtual

groundbut

thevoltage

isV

biasrather

thanground.

Use

nodalanalysisto

findV

in .Suggestin

principlehow

theerrorcould

becorrected

(detailsare

notrequired).

8

Digital-to-analogue

converters

8.1Introduction

Digital-to-analogue

convertersor

DA

Cs

areused

much

lessthan

AD

Cs,w

hichis

why

I’veput

themat

theend.

Fewm

icrocontrollersprovide

DA

Cs,

forinstance,

althoughthe

LPC

1768has

one.T

hem

ainreason

isthat

pulse-width

modulation

(PWM

)is

goodenough

form

anyapplications

andneeds

onlya

timer,w

hichis

purelydigitaland

thereforem

uchsim

plerthan

atrue

DA

C.

Ofcourse

itisnotalwaysacceptable

touse

digitaloutputtosim

ulatean

analoguesignal.T

hem

ostcom

mon

exceptionin

consumer

productsis

audio,where

power

amplifiers

havealm

ostalw

aysbeen

linearcircuits.

Afficianados

ofthe

‘valvesound’,w

holike

tosee

theanodes

oftheiroutputam

plifiersglow

ingred-hot,are

unlikelyto

switch

allegiancebutm

anyaudio

power

systems

nowuse

PWM

orsom

ethingsim

ilar.T

hem

aindrive

isthe

efficiencyrequired

ifan

audiopow

eramplifieris

tobe

squeezedinto

aflat-screen

television.Itissim

plynotpossible

tocoola

linearamplifiereffectively

ina

thincasing

withouta

fan,whose

noisew

ouldbe

intrusive.

8.2G

eneralfeaturesofdigitalto

analogueconverters

AD

AC

takesin

adigitalvalue

andproduces

ananalogue

output.T

heoutputof

anideal3-bit

DA

Cis

shown

infigure

8.1on

thefacing

page,compared

with

anideal3-bitA

DC

.I’veassum

edthatthe

analoguesignals

areallvoltages

althoughthis

isoften

nottrueforD

AC

s.An

important

differencebetw

eenthe

two

plotsis

thatthe

DA

Chas

onlya

discretenum

berof

inputvalues

while

theinput

tothe

AD

Cis

acontinuous

function.T

husthe

plotfor

theD

AC

hasjust

8points,although

Ihave

joinedthem

with

aline

forclarity.

The

outputvoltageV

out ofan

idealN

-bitDA

Cis

givenby

Vout D

ND

AC

2N

VFS D

ND

AC L

SB;

(8.1)

where

thedigitalinputis

ND

AC

andL

SBis

definedin

exactlythe

same

way

asforA

DC

s(equa-

tion2.3).

This

isthe

analogueof

equation(2.2)

onpage

7butdoesn’tneed

thenint./

functionbecause

itisa

one-to-onerelation

between

inputandoutput.

Adigital

inputof

zerogives

ananalogue

outputof

zero.T

heonly

surpriseis

atthe

thetop

endof

therange.

The

maxim

uminputto

a3-bitD

AC

is0b111

=7

andthere

are2

3D8

66

Section8.3

Pulse

width

modulation

67

0V

FS

000001010011100101110111

digital output

Vin

(a) Digital to analogue converter

0

VFS

000001010011100101110111

analogue output

analogue inputdigital input

(b) Analogue to digital converter

(1000)

(1000)

Figure8.1

Outputas

afunction

ofinput(transferfunction)foranideal3-bitD

AC

andan

AD

C.

possiblevalues

sothe

maxim

umoutputis

78V

FS.

Itisnotpossible

togetthe

full-scaleoutput

VFS

froma

DA

C.T

hesam

eproblem

causestheextra-long

stepatthe

topofthe

rangeofan

AD

C(figure

8.1(b)).N

oD

AC

isidealand

theerrors

arespecified

inthe

same

way

asfor

AD

Cs,so

Iw

on’tsaym

uchm

ore.A

straightforward

number

tocheck

isthe

integralnonlinearity,w

hichgives

them

aximum

deviationin

LSB

sbetw

eenthe

realoutputpointsand

theidealstraightline.

Like

AD

Cs,D

AC

sdo

notproduce‘absolute’

outputsbutneed

areference,w

hichm

aybe

internal,externalortakenfrom

VC

C .The

same

adviceapplies

asforA

DC

s.T

hem

aximum

sampling

frequencyw

asone

oftheim

portantspecificationsofan

AD

C.T

hisis

slightlym

orecom

plicatedin

DA

Cs

becausetw

onum

bersm

aybe

quoted.T

heupdate

ratespecifies

howoften

thedigitalinputm

aybe

loadedbutyou

areprobably

more

interestedin

howrapidly

theoutputchanges.T

hisis

givenby

theoutputvoltage

settlingtim

e,which

may

bea

lotlonger.Itm

ayalso

dependon

thesize

ofthechange

inthe

input.A

notherissue,

becausethe

outputis

analogue,is

itscom

pliance.T

hism

eanshow

much

currentyoucan

draww

ithoutaffectingthe

voltage‘significantly’.T

heoutputofsom

eD

AC

sis

acurrent,in

which

casethe

maxim

umvoltage

isspecified

instead.The

digitalinputsare

usuallyserial,typically

SPIorI²C,butm

aybe

parallel.I’llnow

runthrough

some

ofthem

orecom

mon

typesofD

AC

andthe

methods

thatareused

assubstitutes

forthem

.To

belogicalIoughtto

startwith

a1-bitD

AC

.This

hasan

outputthatcan

beon

oroff–in

otherwords

asw

itch.Astraightforw

arddigitaloutputdoes

this,switching

itsvoltage

between

VSS

andV

DD .

We

havealready

encountereda

1-bitDA

Cin

theloop

ofa

sigma–delta

modulator.Itis

theopposite

ofacom

parator,which

iseffectively

a1-bitA

DC

.

8.3P

ulsew

idthm

odulationPulse

width

modulation

isa

comm

onsubstitute

forreal

digital-to-analogueconversion.

The

loadis

switched

onand

offata

fixedfrequency,w

hichcan

beperform

edw

itha

purelydigital

68D

igital-to-analogueconverters

Chapter8

period = 256

length of pulse = 032: low

power

length of pulse = 128: half pow

er

length of pulse = 224: high pow

er

pulses

0 1

t

average power

duty cycle = 032/256 =

1/8

duty cycle = 128/256 =

1/2

duty cycle = 224/256 =

7/8

output

Figure8.2

Outputasa

functionoftim

eforpulse

width

modulation,show

ingthree

powerlevels.

system.

The

fractionof

time

forw

hichthe

loadis

switched

onis

calledthe

dutycycle

(‘dutyfraction’m

ightbem

oreaccurate)and

isadjusted

togive

thedesired

averagevalue.T

heoutput

issketched

forthreeduty

cyclesin

figure8.2.

Ifno

smoothing

isapplied,the

frequencyof

thesquare

wave

mustbe

highenough

nottobe

noticeable.L

ED

sshould

bem

odulatedat100

Hz

ormore,forinstance,so

thattheeye

doesnotreadily

discernthe

flashing.Many

loadsprovide

theirown

smoothing.Forexam

ple,heatersoften

havea

largetherm

alm

assand

theirtem

peratureonly

respondsslow

ly,sm

oothingout

thechanges

inheatinput.

Many

loadssuch

asm

otorsare

inductiveand

actaslow

-passfilters

themselves.R

emem

berthataninductorobeys

VL D

LdI

L

dt

soI

L D1L Z

VL.t/d

t:(8.2)

The

torqueproduced

bya

simple

motor

isproportionalto

currentandthe

inductanceconverts

thesquare

wave

involtage

intoa

triangularwave

incurrent.T

hisis

lessdisruptive

butyoucan

oftenhearthe

switching

frequencyforthe

tractionm

otorson

trains.The

PWM

frequencym

ustbe

fastenoughnotto

producem

echanicalresonancesor

anythingnasty.

Itispossible

tofilter

thePW

Moutputifa

steady(so-called

DC

)voltageis

reallyneeded.H

owever,a

realDA

Cm

aybe

abettersolution

insuch

cases.

Alm

ostall

microcontrollers,

includingthe

LPC

1768,contain

oneor

more

timers

–often

many

–to

generatew

aveforms

forPW

Min

hardware,

independentlyof

them

ainprocessor.

They

arecontrolled

byspecialfunction

registersin

theusualw

ayand

runautom

aticallyafter

theperiod

andlength

ofpulsehave

beenloaded.

There

arevariations

onthis

conventionalformofPW

M.Som

etimes

thelength

ofthepulse

iskeptconstantand

therepetition

frequencyis

variedto

controltheaverage

power.

Am

plifiersthatuse

PWM

orvariationsare

known

asC

lassD

inaudio

applications.

Section8.4

Typesofdigitalto

analogueconverter

69

VFS

VD

AC

RRRRRRR R

000

001

010

011

100

101

110

111

buffer

ND

AC

Figure8.3

Simple

stringD

AC

.A3

to8

decoderis

alsoneeded

tocontrolthe

switches.

The

inputisN

DA

C D0b010.

8.4Types

ofdigitaltoanalogue

converterI’llnow

runthrough

some

ofthem

orecom

mon

typesofD

AC

.FarfewerD

AC

sthan

AD

Cs

arelisted

inthe

cataloguesand

many

areintended

forspecificapplications.A

lthoughsom

eproduce

voltages,thecore

ofm

anyD

AC

sproduce

currentsinstead.

The

outputfromthe

ICm

aybe

acurrentoran

internalamplifierm

aybe

usedto

turnthe

currentintoa

voltage.

String

DA

Cs

These

areperhaps

thesim

plestDA

Cs

andthe

circuitisroughly

equivalenttoa

flashA

DC

(sec-tion

3.3).They

arealso

known

asvoltage

segmentD

AC

sand

thecircuitis

shown

infigure

8.3.Voltages

aretapped

offa

stringof

equalresistors

between

Vref

andground,

calleda

Kelvin

divider.This

circuithasa

coupleofim

portantfeatures,simple

asitis.

T

heresistors

areallequal,even

thetw

oatthe

ends,incontrastto

thechain

inthe

flashA

DC

.

T

hebottom

ofthe

ladderhas

atap,

which

canbe

selectedto

givean

outputof

zero.

70D

igital-to-analogueconverters

Chapter8

VFS

RRRRRRR R

000

001

010

011

100

101

110

111

VD

AC

00 01 10 11

more

significantbits

lesssignificantbits

R¢ R¢ R¢ R¢

Figure8.4

Interpolatingstring

DA

C.A

3to

8decoderis

neededto

controlthesw

itcheson

them

ainstring

anda

2to

4decoderforthe

interpolator.The

inputisN

DA

C D0b10001.

How

ever,thetop

hasno

tap.This

isbecause

ofthetransferfunction

ofaD

AC

,which

canneverreach

itsfull-scale

valueof

Vref (figure

8.1on

page67).

Asim

plestring

DA

Chas

asingle

chainof

resistorsas

shown

infigure

8.3(a).I

haveincluded

abuffer

(voltagefollow

er),which

ensuresthatthe

outputdoesnotload

theresistors

andaffect

thevoltage.

This

architecturegives

am

onotonicoutputbecause

ahigher

tapcan

nevergive

alow

ervoltage

thana

lower

tap.T

heresistors

must

beidentical

togive

theideal

output.T

heD

AC

needsa

decoderto

takea

3-bitdigitalinputandselectone

ofthe

8sw

itches,which

areM

OSFE

Ts

asusual.T

hisis

theopposite

ofthepriority

encoderusedin

theflash

AD

C.

An

obviousproblem

with

thiscircuit

isthe

number

ofresistors

needed,2

Nfor

anN

-bitD

AC

.This

canbe

reducedby

usingtw

ochains

asshow

nin

figure8.4.

The

secondchain

isconnected

acrosstw

oadjacenttaps

onthe

firstchainand

interpolatesbetw

eenthe

two

voltages.I

haveshow

n4

resistorsin

thesecond

chain,which

raisesthe

totalnumber

ofbits

from3

to5.

This

DA

Cis

slowerbecause

thevoltages

mustpass

throughtw

osets

ofswitches

andbuffers.

You

mightbe

surprisedthatso

primitive-looking

anarchitecture

isw

idelyused.R

esolutionvaries

from8

to16

bitsand

theL

PC1768

offersa

10-bitstring

DA

C.M

ostinclude

abuffer

amplifier

onthe

outputasshow

nin

figure8.3.

Decoding

theinputand

changingthe

internal

Section8.4

Typesofdigitalto

analogueconverter

71

switches

isfastso

thespeed

isgenerally

limited

bythe

slewrate

ofthe

buffer.Y

ouw

illlearnaboutthis

inA

nalogueE

lectronics2.Itm

eansthatthe

outputchangesrapidly

forsmallsteps

inthe

digitalinputbutmore

slowly

forlargesteps.Typicalsettling

times

area

fewµs.

Digitalpotentiom

etersA

naloguepotentiom

etersor

trimm

ersare

oftenused

tom

akesm

alladjustm

entsto

circuitsto

bringthem

intospecification.

This

requiresa

human

toperform

thecalibration,w

hichis

ex-pensive,

andthe

contactson

potentiometers

degradeover

time.

Trimm

ersare

thereforebest

avoided.A

digitalpotentiometer

isa

possiblesubstitute.

Itscircuitis

virtuallythe

same

asa

simple

stringD

AC

withouta

buffer.Ithasone

fewerresistorand

thetop

tapis

connecteddirectly

tothe

Vref input(although

itisno

longercalled

that).T

husthe

outputcanbe

connectedto

eitherone

oftheinputs

ortoany

ofthetaps

between.A

notherdifferenceis

thatthesetting

may

bestored

innon-volatile

mem

oryso

thatitisretained

permanently.O

therwise

thecalibration

would

haveto

berepeated

everytim

ethatpow

erwas

applied.D

igitalpotentiometers

aresom

etimes

calleddigipots

orR

DA

Cs.

They

typicallyoffer

32–1024

settingsw

ithvolatile,one-tim

e-programm

ableor

flashm

emory.

Some

canbe

connectedto

mechanicalpushbuttons

toreplace

apotentiom

eteron

acontrolpanelbutm

osthaveserial

interfacesfor

in-circuitcontrol.T

heyconsum

ecurrent,unlike

mechanicalpotentiom

eters,butthis

may

bebelow

1µA

.T

heprice

isn’tparticularly

lowso

thism

aybe

oneexam

plew

herethe

analogueapproach

ischeaper!

Abasic,volatile,32-position

devicecosts

about$0.40but

fancier,non-volatileones

may

costover$5.

My

impression

isthatthey

havenotcaughton

tothe

extentthatthem

anufacturershoped.

Thermom

eterD

AC

sT

hesehave

nothingto

dow

ithtem

perature!T

henam

erefers

tothe

codethatis

usedto

controlthe

switches

insidethe

DA

C,w

hichis

thesam

eas

ina

flashA

DC

.They

arealso

calledfully-

decodedD

AC

s.T

hisis

thefirstexam

pleof

aD

AC

thatproducescurrentrather

thanvoltage.

The

ideaofa

thermom

eterDA

Cis

simple:

itcontainsa

setofidenticalcurrentsourcesand

therequired

numberofthese

isselected

inparallel.T

hedigitalinputis

convertedinto

thermom

etercode

todrive

thesw

itches.Figure

8.5on

thenext

pageshow

ssom

eof

thecircuits

thatcan

beused

tom

akea

ther-m

ometerD

AC

.The

simplestis

asetofequalcurrentsources

inparallel.Ifthe

digitalinputis2,

then2

sourcesare

connectedto

theoutput.N

otethatonly

3sources

areneeded

fora2-bitD

AC

becausethe

highestinputis3!

Itism

uchbetterto

switch

theoutputofthe

sourcesbetw

eentw

obuses

asin

figure8.5(b)on

thefollow

ingpage

becausea

currentsourcedoes

notliketo

bedis-

connectedfrom

aload

–itis

theequivalentofshort-circuiting

avoltage

source.This

providesa

differentialoutput:currentissw

itchedfrom

oneto

theotheraccording

tothe

digitalinput.The

‘negative’outputI

canbe

groundedifitis

notwanted.

How

dow

egetallthese

currentsources?A

straightforward

way

isto

usea

classiccircuit

calleda

currentmirror,w

hichyou

willanalyse

inE

lectronicC

ircuitDesign

3.T

hesim

plest,

72D

igital-to-analogueconverters

Chapter8

I

IoutI+

I-

VC

C

(a)T

hermom

eter DA

C w

ith single output

(b)T

hermom

eter DA

C w

ith differential outputs

VC

C

Iref

(c)C

urrent mirrors to generate set

of equal currents I = Iref

II

Vref

RR

RR

f

Vout

I

+ -

(d)C

urrents generated by resistors with

amplifier to give voltage output

II

I

Figure8.5

Aselection

ofcircuitsthatfunction

as2-bittherm

ometerD

AC

s:(a)currentsourcesand

single(current)

output,(b)currentsources

with

differentialoutputs,(c)bipolar

transistorm

irrorsas

currentsourcesand

(d)resistorsw

ithan

op-amp

togive

voltageoutput.

reliableequation

forthecollectorcurrentthrough

abipolartransistorin

activem

odeis

Ic D

Is exp

Vbe

VT

:(8.3)

Active

mode

requiresa

sufficientlylarge

collector–emitter

voltage,roughlyV

ce>

0:3

V.

This

isa

bare-bonesversion

ofthe

Ebers–M

ollequation.

The

prefactorI

sis

calledthe

scaleor

saturationcurrent;itdepends

onthe

areaofthe

transistorandthe

way

inw

hichitis

made.T

heotherconstantisthe

thermalvoltage,V

T Dk

BT

=e

26

mV

atroomtem

perature.The

collectorcurrentdoes

notdependon

thecollectorvoltage

inthis

simple

model–

thetransistoracts

likea

currentsource,which

isjustw

hatwe

want.(O

fcoursethis

pictureis

fullofapproximations.)

The

main

pointis

thatthe

collectorcurrent

iscontrolled

bythe

base–emitter

voltageV

be .T

hismeansthatifw

ecollecta

setofidenticaltransistorswith

theirbasesandem

ittersinparallel,

theyfeelthe

same

Vbe

andtheir

collectorcurrents

arethe

same.

Ifw

eapply

aknow

ncurrent

Iref to

onetransistor,its

Vbe adjusts

tothe

appropriatevalue

forthiscurrent,the

othertransistorsexperience

thesam

evalue

ofV

beand

thereforepass

thesam

ecurrent,

ID

Iref .

This

isshow

nin

figure8.5(c).

Ihave

usedpnp

transistorsand

drawn

themupside

down

sothe

emitters

(with

thearrow

s)areatthe

top.This

isso

thatthepositive

supplyis

atthetop

ofthedraw

ing,which

Section8.4

Typesofdigitalto

analogueconverter

73

isconventional.

The

same

method

canbe

usedw

ithM

OSFE

Ts

byconnecting

theirsources

andgates

inparallel.T

hecorresponding

equationforthe

draincurrentin

terms

ofthegate–source

voltageis

Id D

K.V

gs V

t /2;

(8.4)

where

Vt is

thethreshold

voltageatw

hichthe

transistorsw

itcheson

(nottobe

confusedw

iththe

thermalvoltage).

The

MO

SFET

mustbe

insaturation

mode,w

hichis

equivalenttoactive

mode

forabipolartransistor–

aconfusing

nomenclature.T

hisneeds

Vds

>V

gs V

t .L

argercurrents

canbe

obtainedby

connectingtransistors

inparallel.

This

issom

etimes

usedto

producesources

with

binary-weighted

currentsof

I,

2I

,4I

andso

on.T

hesecan

becom

binedto

givethe

desiredcurrent

bysw

itchingeach

sourceaccording

tothe

valueof

thecorresponding

bitinthe

digitalinput.No

decodingis

required.T

hesim

plestw

ayof

generatinga

known

currentis

toconnect

aknow

nvoltage

acrossa

resistorandthiscan

beused

ina

thermom

eterDA

Casw

ell.The

circuitisshown

infigure

8.5(d).Y

oum

aythink

thatitissim

plerto

make

resistorsthan

currentsources,butthisis

notobviousfor

anintegrated

circuit!E

achcurrentis

switched

tothe

outputifrequired

orto

groundif

itisnotneeded.T

hevoltage

acrossthe

resistorsm

ustbekeptconstantforaccurate

currents.This

isachieved

byfeeding

theoutputinto

theinverting

inputofanop-am

p.The

non-invertingterm

inalis

groundedand

negativefeedback

keepsthe

invertingterm

inalatthesam

epotential:

avirtual

ground(rem

ember

that?).T

husthe

voltageacross

theresistors

isheld

atV

ref whether

theyare

connectedto

theoutputorground.

Another

advantageof

switching

unwanted

resistorsto

groundrather

thandisconnecting

themis

thatthe

totalcurrent

drawn

remains

constant.T

hisreduces

errorsdue

tothe

depen-dence

ofV

ref oncurrent.

The

amplifier

hasa

secondfunction,

which

isto

turnthe

currentI

intoa

voltage.T

hiscurrentcannotflow

intothe

op-amp’s

inputsoitm

ustflowthrough

thefeedback

resistor,givingV

out D

Rf I

.N

ow,I

containsa

contributionV

ref =R

fromeach

ofthen

resistorsconnected

tothe

output,so

Vout D

R

f

RV

ref n:

(8.5)

The

full-scaleoutputis

therefore2

N.R

f =R

/Vref .Itis

negativeforthe

circuitasdraw

n,which

isa

problemin

asystem

with

onlya

singlesupply.

Anotherw

ayofanalysing

thecircuitis

totreat

Vref as

avoltage

input.Then

thecircuitlooks

likea

straightforward

invertingam

plifierand

itsgain

isgiven

bythe

usualratioof

resistances,

Rf =

.R=n

/D

.Rf =

R/n.

DA

Cs

basedon

theR

–2Rchain

Figure8.6

onthe

nextpage

shows

aclassic

circuit,the

R–2R

chain,w

hichis

usedin

many

DA

Cs

andform

erlyin

successive-approximation

AD

Cs.

Itiselegantto

analyse.Suppose

thatthe

circuitis

cutalong

thelines

labelledA

–Dand

we

connectan

ohmm

eterto

thepart

thatrem

ainson

theright:w

hatwould

itmeasure?

A.

This

istrivial:the

resistanceis

justR

.

74D

igital-to-analogueconverters

Chapter8

RR

R

2R2R

2RR

AB

CDR

R

2R2R C

DR

2R D

RR

R

RR

R

2R2R

2RR

8I

4I2I

II

(a) Classic R

–2R chain

(b)–(d) Steps in the analysis of a R–2R

chain

(e)R

–2R chain in ‘current m

ode’ BC

D

4I2I

IV

ref

ground

2I4I

RR

R2R

2R2R

R

(f) Com

plete 3-bit DA

C based on R

–2R chain w

ith input of 110

Rf

VD

AC

I

+ -

Vref

1’s4’s

2’s

Figure8.6

The

classicR

–2R

chain:(a)

basiccircuit,

(b)–(d)steps

inthe

reductionof

thecircuit,show

ingthatthe

sectionsto

therightcan

bereplaced

bya

resistanceof

Rateach

stage,(e)currents

throughthe

chain,which

divideby

afactorof2

ineach

stageand

(f)complete

3-bitD

AC

with

transresistanceam

plifiertogive

voltageoutput.

Section8.4

Typesofdigitalto

analogueconverter

75

B.

Now

we

haveall

threeresistors

tothe

rightof

lineB

,supposingthat

thew

irescut

forA

havebeen

solderedback

together.Tw

oresistors

ofR

inseries

give2R

,which

isin

parallelwith

anotherresistorof2R

,and2R

k2R

DR

sow

ew

ouldm

easureR

again.

C.

Now

we

havea

more

complicated

circuit.H

owever,

we

havejust

shown

thatw

ecan

replaceeverything

tothe

rightof

Bw

itha

singleresistor

R,as

shown

infigure

8.6(b).T

hism

akesittrivialto

work

outtheresistance

seenlooking

intoC

becauseitis

thesam

eas

thelastcalculation

andthe

resultisagain

R.

D.

Again,w

ecan

replaceeverything

tothe

rightofC

bya

singleresistor

Ras

in(c).

The

calculationis

thesam

eagain

andthe

apparentresistanceis

R.

Thus

theresistance

issim

plyR

between

theexternalterm

inals,asshow

nin

figure8.6(d).

The

2R

resistorsare

usuallym

adefrom

two

resistorsof

Rin

seriesso

thatallresistorshave

thesam

evalue,w

hichm

akesiteasierto

fabricatethem

accurately.T

hisis

verypretty

butw

hatis

theuse?

Supposethat

we

connectthe

upperterm

inalto

avoltage

reference,V

ref asin

figure8.6(e).

This

feedsa

currentintothe

network,w

hichI’llcall

8I

forconvenience.

Itsvalue

is8I

DV

ref =R

becausew

ehave

justshow

nthat

theoverall

resistanceofthe

network

isR

.How

doesthe

currentflowinside

thenetw

ork?

A

tthefirstnode

thecurrentcan

goeitherthrough

the2R

resistortoground

orthroughthe

restofthe

network

tothe

right.Figure

8.6(c)show

sthatthe

restofthe

network

behaveslike

aresistance

of2R

sothe

currentsplitsequally

with

4I

down

eachbranch.

A

currentof4I

reachesthe

nextnodein

thenetw

orkand

againsplits

equallyforthe

same

reason,giving2I

ineach

branch.

T

hesam

ehappens

atthethird

andfinalnode.

Thus

thecurrents

thatflowthrough

the2R

resistorsto

groundare

dividedby

two

ateachstage.

There

isan

extracurrentw

iththe

smallestvalue,justas

therew

asan

extracapacitor

with

thesm

allestvaluein

thecharge-redistribution

network

ofaSA

RA

DC

(figure3.8

onpage

22).T

hesebinary-w

eightedcurrents

canbe

usedto

make

aD

AC

bysw

itchingand

combining

them.

This

issim

ilarto

atherm

ometer

DA

Cbut

thebinary

weighting

means

thateach

bitin

thedigitalinputdrives

asw

itchdirectly;the

thermom

etercodeis

notneeded.Atransresistance

amplifier

isagain

usedto

collectthecurrents

ataconstantvoltage

(ground)and

transformthe

currentsinto

avoltage.

Ihavedescribed

the‘currentm

ode’ofoperationofan

R–2R

chain.Itcanalso

beoperated

in‘voltage

mode’,

where

theoutput

isa

voltagerather

thana

current.T

hisis

abit

trickierto

explainso

Iw

on’tbother.T

hiscircuitprovided

thevoltages

usedfor

comparisons

inSA

RA

DC

sin

thedays

beforeM

OSFE

Ts

andcapacitors

displacedbipolartransistors

andresistors.

Segm

entedD

AC

sM

anyD

AC

sare

made

usinga

combination

ofcircuits

ratherthan

asingle

architecturefor

thew

holeconverter.

Itissim

pleto

combine

theresistive

thermom

eterD

AC

infigure

8.5(d)w

iththe

R–2R

chainin

figure8.6(e),

forinstance.

The

thermom

eterD

AC

isused

forthe

more

significantbits

andthe

R–2R

chainfor

theless

significantbits.

This

iscalled

asegm

ented

76D

igital-to-analogueconverters

Chapter8

DA

C.A

comm

ercialexample

isthe

18-bitTexasInstrum

entsD

AC

9881,whose

architectureis

describedas

‘anR

–2R

ladderconfiguration

with

thefour

MSB

ssegm

ented’.It

islinear

tow

ithin˙2

LSB

,which

isseriously

impressive.

Anothertype

ofsegmented

DA

Cusesseveralsetsofcurrentsources,each

asinfigure

8.5(b).A

largercurrent

isused

forthe

most

significantbits

anda

smaller

currentforless

significantbits.T

hereare

plentyofvariations

onthese

themes!

Sigm

a–deltaD

AC

sT

heseare

verysim

ilartosigm

a–deltaA

DC

sand

arebased

onthe

same

sortofmodulator.

The

convertertakes

indigital

dataw

ithN

bitsat

thefinal

sampling

frequencyf

s .It

producesa

streamofsingle

bitsatthe

faster,oversampling

(modulator)frequency

fm ,w

hoseaverage

valuem

atchesthatofthe

input.The

sigma–delta

modulatorpushes

thefluctuations

tohigh

frequencyso

thattheanalogue

outputcaneasily

befiltered

tokeep

onlythe

components

belowthe

Nyquist

frequency.The

jargonis

thatthem

odulator‘shapesthe

noise’toenable

easyfiltering.

Sigma–delta

DA

Cs

dominate

particularapplications,notable

audio,andare

spreadinginto

otherfieldsthatrequire

highresolution

butrelativelyslow

analogueoutputs.

Multiplying

DA

Cs

The

outputofallD

AC

sdepends

ona

referenceinputbutusually

thism

ustliew

ithina

fairlynarrow

range.M

ultiplyingD

ACs

acceptaw

iderange

ofreference

inputsand

theoutputis

theproductof

theanalogue

referenceand

thedigitalinput.

The

circuitsbased

onresistors

canbe

usedas

multiplying

DA

Cs

providedthat

thesw

itchesand

amplifiers

canhandle

therange

ofvoltages.

This

soundsa

daftrequirem

entfor

thesw

itchesbut

remem

berthat

theyare

made

fromM

OSFE

Ts,notm

etalcontacts!

Am

plifiersin

DA

Cs

Severalof

thecircuits

describedabove

includean

amplifier.

This

isa

problemif

theoutput

shouldgo

fromrail

torail

becauseno

realam

plifiercan

dothis

ifit

sharesthe

same

power

supplyas

theD

AC

itself(section

6.2).T

hesystem

may

thereforebe

linearover

most

ofits

rangebutw

ithm

uchpoorerperform

anceatthe

two

extremes.

8.5S

umm

aryofD

AC

s

Pulse-width

modulation

(PWM

)is

aw

idelyused

substitutefor

a‘real’

DA

C.M

ostmi-

crocontrollerscontain

hardware

todrive

PWM

automatically.

A

wide

rangeofD

AC

sisavailable,many

ofwhich

producea

currentratherthana

voltage.

M

ultiplyingD

AC

saccepta

wide

rangeof

referenceinputs

andeffectively

multiply

theanalogue

referenceby

thedigitalinput.

D

igitalpotentiometers

work

inthe

same

way

asstring

DA

Cs

andm

aybe

usefulfortrim-

ming

circuits.

Section8.6

Exam

ples77

Ihave

notm

entionedone

important

point,w

hichis

smoothing

theoutput.

The

outputof

anD

AC

changesin

multiples

ofLSB

butasm

oothsignalis

generallydesirable.A

particulartypeoflow

passfilteris

required,calleda

reconstructionfilter,and

needsm

oresophisticated

designthan

Icandescribe

here.

8.6E

xamples

Exam

ple8.1

Calculate

theoutputvoltage

froman

8-bitDA

Cconverterw

itha

full-scaleout-

putof5.00V

when

thedigitalinputin

decimalis

(i)10(ii)150

(iii)200.Whatis

them

aximum

outputvoltage?[0.20

V,2.93V,3.91

V]

Exam

ple8.2

Calculate

theoutput

voltagefrom

a12-bit

DA

Cw

itha

fullscale

outputof

10.00V

when

thedigitalinputin

hexadecimalis

(i)0xBA

D(ii)0xA

CE

(iii)0x0FF.[7.30

V]

Exam

ple8.3

An

outputneeds

tobe

drivenby

am

icrocontrollerw

hosePW

Mm

odulesare

basedon

a16-bit

timer.

The

outputshould

providean

averagevoltage

from0

to5.00

Vthat

canbe

adjustedin

stepsof

10m

V.Itdoesnotneed

aparticularly

steadyvoltage

andPW

Mis

thereforeacceptable.Suggesta

suitableform

atforthePW

Mw

aveform.

Exam

ple8.4

How

many

resistorsw

ouldbe

neededfor

an12-bitsim

plestring

DA

C?

Would

theyallhave

thesam

evalue?

How

would

thischange

ifthe

DA

Cw

eresegm

entedinto

a6-bit

stringand

a6-bitinterpolator?

Exam

ple8.5

A8-bit

thermom

eterD

AC

hasresistors

of100

k

anda

voltagereference

of2.5

V.The

transresistanceam

plifieron

theoutputhas

afeedback

resistorof

1k

.W

hatcom-

plianceis

neededforthe

referencevoltage

(inotherw

ords,howm

uchcurrentneed

itprovide)?W

hatoutputvoltagesdoes

theD

AC

produce?

Exam

ple8.6

Asegm

ented8-bitD

AC

usesindividualcurrentsources

basedon

resistorsfor

them

ostsignificant4bits

anda

R–2R

ladderfortheleastsignificant4

bits.How

many

resistorsare

neededifallare

ofvalueR

?

PartII

Power

suppliesandpassive

components

78

9

Power

supplies

9.1Introduction

All

electronicand

electricalequipm

entneeds

asource

ofenergy:

apow

ersupply.

Exam

plesinclude:

battery:chem

ical!electricalenergy,reversible

ifthebattery

canbe

recharged

converter:electrical!

electrical,with

differentpossiblesources

–A

Cinput!

DC

output,e.g.230

V,50H

z!5

VD

C,as

usedfor

almostallelec-

tronicsystem

sand

chargers

–D

Cinput!

DC

output,e.g.

12V

DC

!5

VD

C,often

usedfor

individualIC

sw

ithina

system,w

herethey

arecalled

pointofloadorPO

Lsupplies

–D

Cinput!

AC

output(inverter),e.g.12

VD

C!

230V

AC

,50H

z,asm

ightbeused

topow

ermains

appliancesin

acaravan.

–A

Cinput!

AC

output,usedto

changethe

frequencyorvoltage

energy

harvestingfrom

theenvironm

ent

–solarcell:light!

electricalenergy

–m

echanicalenergy!electricalenergy,such

as...?

When

analysinga

circuitwe

assume

aperfect(ideal)

supplythathas

aconstantvoltage

inde-pendent

ofthe

loadcurrent

(orinput

voltage).T

hisim

pliesthat

thesupply

haszero

sourceim

pedance,andcan

deliverany

magnitude

ofcurrent–

upto

infinity!In

practiceallsources

havesom

einternal

resistancew

hichlim

itsthe

current.T

hisinternal

orsource

resistance(in

generalanim

pedance)may

affecttheoperation

ofthecircuitunless

itisincluded

inthe

theoret-icalanalysis.

Seefigure

9.1on

thenextpage.

Rem

ember

Thévenin’s

theorem?

The

resistanceis

almostnevera

realcomponentbutrepresents

theresistance

ofthew

indingsofa

transformer,

platesof

acapacitor

andso

on.M

ostpower

supplieshave

electroniccircuits

toregulate

theiroutput,in

which

caseR

s isa

characteristicofthe

whole

circuitratherthana

particularcompo-

nent.

79

80Pow

ersupplies

Chapter9

RL

(a) Ideal(b) Practical (sim

plified)

Rs

RL

VV

s

Figure9.1

An

idealpow

ersupply

andsim

plifiedT

héveninequivalent

circuitof

apractical

powersupply

with

internalresistanceR

s ,connectedto

aload

RL .

The

differencebetw

eenthe

EM

Fof

abattery

andthe

potentialatitsterm

inalsis

calledthe

lostvoltsin

HigherPhysics.Itis

thevoltage

droppedacross

Rs .In

many

applicationsthe

valueof

Rs

must

be‘sm

all’at

allfrequencies

ofinterest

orchanges

inload

currentw

illaffect

thevoltage.T

hisvariation

ofterminalvoltage

with

currentiscalled

regulation.R

egulationcan

bedefined

indifferent

ways,

shown

infigure

9.2.O

neis

interm

sof

thevoltage

atnoload

andfullload.R

eminder:

no

loadm

eanszero

current,nothingconnected,open

circuit,R

L D1

fullload

means

them

aximum

ratedcurrent,low

estpermitted

valueofload

resistance

Then

regulationDV

noload

Vfull

load

Vno

load

100%

:(9.1)

(Sometim

esthe

denominatoris

Vfull

loadinstead;itm

akeslittle

differenceifregulation

isgood.)

We

would

likeas

smalla

valueas

possible.T

heregulation

isa

purenum

berby

thisdefinition,

usuallyexpressed

asa

percentage.A

lternatively,regulationcan

bedefined

interm

sofsm

allchangesaboutthe

ratedoutput,

regulationD

•V•I ˇˇratedoutput :

(9.2)

V

I

Vno load

Vfull load

Ifull load

00

slope = –R

s

Figure9.2

Outputvoltage

ofarealpow

ersupplyas

afunction

ofcurrent,showing

thetw

ow

aysin

which

regulationis

oftendefined.

Section9.1

Introduction81

This

isjust

theT

héveninresistance

Rs

evaluatedat

therated

output.A

sthe

plotshow

s,the

apparentvalueof

Rs varies

with

current.Itistherefore

notaconstantin

arealcircuit,although

we

oftenassum

ethis

tom

akecalculations

simpler.

Again

we

would

likethe

variationto

beas

small

aspossible,

which

requiresR

sto

besm

all.It

ism

easuredin

ohms

becauseit

isa

resistance.T

heregulation

ofcheapplug-in

dcsupplies

(‘wallw

arts’)canbe

spectacularlybad.

Imea-

sureda

9V

supplyonce

andfound

thatitsno-load

voltagew

as13

V.Regulation

canbe

signifi-canteven

inm

ainssupplies

iftheconsum

erisatthe

endofa

longsupply

line:lightsdim

when

aheavy

loadsuch

asa

cookerissw

itchedon

orwhen

them

otorina

vacuumcleanerstarts.

Power

suppliesare

bigbusiness.

Here

isa

quotationfrom

reference[25].

‘Sincepow

ersupplies

areso

widely

usedin

electronicequipm

ent,thesedevices

nowcom

prisea

worldw

idesegm

entof

theelectronics

market

inexcess

of$5

billionannually.’

That

was

in2002

andthe

figurehas

grown

sincethen.

TexasInstrum

ents(form

erlyN

ationalSemiconductor)

hasa

fabricationplant

inG

reenock,w

hichhas

recentlybeen

extendedat

greatexpense,

andtheir

main

businessis

inpow

ersupplies.

Exam

ple9.1

Adc

power

supplyproduces

9.0V

with

noload.

This

dropsto

8.1V

when

a50

load

isattached.C

alculatethe

currentthatflows,the

regulationand

theinternalresistance

Rs (assum

edconstant).W

hatwould

bethe

outputvoltagew

itha

loadof10

?

Exam

ple9.2

Abattery

hasan

opencircuitvoltage

of9

Vand

aninternalresistance

of2

.

Calculate

theoutput

voltageand

percentageregulation

when

theload

is(i)

100

,(ii)

50

,(iii)10

.

[8.82V,2.0%

]

Exam

ple9.3

Provethatthe

regulationdue

toseries

resistanceR

Sis

RS =

.RL C

RS /fora

loadofresistance

RL .

Exam

ple9.4

A12

Vcar

batteryhas

aninternal

resistanceof

0.01

.W

hatis

theterm

inalvoltage

when

startingthe

carifthestarterm

otortakes300

A?

Whatw

ouldhappen

iftheinternal

resistancerose

to0.1

on

areally

coldm

orning?[9

V]

Exam

ple9.5

Atransform

erhasan

opencircuitvoltage

of6.00V,w

hichfalls

to5.62

Vw

hena

loadtaking

50m

Ais

connected.Whatis

itseffective

sourceresistance?

[7.6

]

10

Batteries

10.1Introduction

These

arethe

most

comm

onsource

ofpow

erin

portableequipm

entand

come

intw

om

aincategories.

The

performance

ofalltypes

ofcellhas

advancedsubstantially

duringm

ylifetim

ebutsadly

therate

ofdevelopmentis

much

slowerthan

advancesin

semiconductors.

Prim

arycells

These

areused

onceonly,then

discarded.H

ereare

them

orecom

mon

typesbutm

anyexotic

varietiesare

alsoavailable.E

xtractsfrom

datasheets

areattached.

A

lkaline(A

AA

,A

A,

Cand

soon),

them

ostw

idelyused.

They

produceabout

1.5V

when

freshbutthis

declinesduring

theirlifetime

[34].

L

ithiumcoin

cells(C

R2032

forexample),com

mon

forbackupapplications

andin

small

portableproducts.

They

containlithium

andm

anganesedioxide,

which

produceabout

3.0V

[35].

L

ithiumcylindricalcells

suchas

AA

usedifferent

materials

toproduce

1.5V

sothat

theycan

beinterchanged

with

alkalinecells.T

heiranodeis

lithiumm

etalandthe

cathodeis

irondisulphide.

They

haveaboutdouble

theenergy

densityper

unitmass

ofalkaline

cellsand

work

much

betteratlowtem

perature.

B

uttoncells

areused

incalculators,w

atchesand

thelike.T

heyare

oftenbased

onsilver

oxidebutcheaperversions

arealkaline.U

sually1.5

V.

Secondary

cellsT

heseare

rechargableand

thereforem

oreeconom

icaland

environmentally

friendlybut

ofcourse

acharger

isrequired.

They

usedto

sufferfrom

much

lower

capacitythan

primary

cellsbutthatless

truenow

adays[36].

N

ickelmetalhydride

(NiM

H)cellsare

them

ostcomm

ontype

forgeneraluse,producing1.2

V[37].N

ickel–cadmium

(NiC

d)cellsrem

ainw

idelyavailable

butshouldbe

avoided

82

Section10.2

Capacity

ofbatteries83

becauseofthe

environmentalim

pactofcadmium

andbecause

NiM

Hgenerally

performs

better.

L

ithium-ion

cells(not

just‘lithium

’because

theydo

notcontain

lithiumm

etal)now

dominate

integratedsystem

ssuch

ascom

putersand

mobile

phones.Theirenergy

densityis

much

higherand

theyproduce

around3.6

Vw

henfresh,depending

onthe

chemistry

[38].T

hisdeclines

toabout3.0

Vw

hendischarged.

The

positiveelectrode

isbased

ona

transitionm

etal,typicallyC

o,Mn

orFe

asan

oxideor

phosphatew

hilethe

negativeelectrode

isa

formofcarbon

–graphite

orevennanotubes.M

ostcellsinclude

apolym

erto

separatethe

anodeand

cathodeand

may

becalled

Li-polym

erorLiPo

cells.

L

ead–acidbatteries

arean

oldtechnology

butstill

usedw

hereresistance

toabuse

anda

harshenvironm

entisim

portant,suchas

incars.

They

havea

lowinternalresistance,

which

means

thattheycan

providea

highcurrentforstarterm

otors.Each

cellgivesabout

2V

butofcoursethey

areusually

packagedinto

batteriesfor6

or12V.

The

performance

ofLi-ion

cellsis

seductivebutunfortunately

theyalso

havefam

ousincendiary

tendenciesand

thereforeneed

expertcareand

attention.The

Panasonicw

ebsite

says:

Inorder

toensure

theuse

ofproperly

designedsafety

circuitsw

ithlithium

ionbattery

packs,Panasoniclithium

ioncells

arenotsold

as‘off

theshelf’

productsand

arenot

availableas

astandard

productfrom

distributors.L

ithiumion

cells,how

evercan

beassem

bledinto

packsby

authorizedpack

assembly

centersthat

havebeen

approvedforsafety

circuitassembly

andlithium

ionpack

design.

The

safetyaspect

was

made

abundantlyclear

in2013

bythe

firesin

Boeing

787aeroplanes

causedby

faultsin

theirLi-ion

batteries.L

i-ioncells

mustneverbe

connectedto

asystem

directlybutalw

aysthrough

asupervisory

circuit.T

hisincludes

a‘fuel

gauge’to

ensurethat

thecells

arenever

chargedor

dischargedexcessively.

The

currentm

ustbe

limited

andthe

cellshould

beshut

down

ifits

temperature

risesoutside

specification.T

hesupervisor

mustbe

carefullym

atchedto

theprecise

chemistry

ofthe

cellbecausea

differenceof

0.1V

between

theratings

ofthe

cellandcharger

canlead

toan

explosion.

10.2C

apacityofbatteries

Capacity

isusually

quotedas

theam

ountofcharge

thatcanbe

suppliedby

abattery

beforeit

isexhausted

or‘flat’

–the

voltageis

toolow

tobe

useful.T

hisis

justtheproductof

currentand

time

ifthe

currentisconstantor

anintegralin

general.T

heSI

unitofcharge

iscoulom

bsbutis

neverused

forthe

capacityof

batteries.Instead

itism

easuredin

ampère–hours

(Ah)

orm

Ah.

Forexample,the

capacityofa

carbatterym

ightbequoted

as50

Ah.

This

means

thatitcan

supply

50

Afor1

hour

10

Afor5

hours

500

Afor0.1

hour(inprinciple!)

84B

atteriesC

hapter10

t / s

I / mA 10000

101

I(t)

Iave20

Figure10.1

Variable

currentasa

functionoftim

e,I.t/,and

itsaverage

valueI

ave .

Inpractice

thecapacity

dependson

thecurrentdrain,so

thatmanufacturers

specifythe

capacityata

particularcurrentorwith

aparticularload

asin

thedata

sheet[34].The

symbol

Cis

oftenused

forcapacity,

sothat

acurrent

ofC

=10

means

thecapacity

dividedby

10hours,

which

would

be5

Afor

thiscar

battery.C

apacityalso

dependson

temperature,

beinglow

erat

lowtem

peratures.The

open-circuitvoltagedrops

with

temperature

too.(Putlithium-based

batteriesin

yourcam

eraif

yougo

somew

herecold

–their

performance

ism

uchbetter

thanalkalines

atlow

temperature.)

The

energycapacity

ofabattery

isalsoim

portant.Thisisthe

productofthepow

erdissipatedin

theload

andtim

e,assuming

thatthepow

erisconstant.

Itisquoted

inw

att–hours(W

h)anddepends

onthe

voltageproduced

bythe

batteryas

wellas

thecharge.

Li-ion

cellsgive

about3.6

Vcom

paredw

ith1.2

VforN

iMH

,which

booststheirenergy

capacitysubstantially.

The

chargecapacity

ofabattery

isincreasedby

puttingcellsin

parallel:Two

cellsinparallel

havetw

icethe

capacityof

one,and

soon.

How

ever,putting

cellsin

serieshas

noeffect

onthe

chargecapacity:

Itincreases

thevoltage

instead.It

doublesthe

energycapacity

throughdoubling

thevoltage

ratherthan

thecharge.

Itisnota

goodidea

toputsom

etypes

ofcellin

seriesor

parallelbecause

theload

may

notbe

sharedequally

among

them,

leadingto

nastyside-effects.

Typical(charge)capacitiesformodern

AA

cellsare2500

mA

h(alkaline

primary),2000

mA

h(N

iMH

secondary)butw

itha

wide

range.T

heenergy

capacityis

about2.5W

h.For

compari-

son,thebattery

ofmy

antiquelaptop

hasa

capacityof4400

mA

hat14.8

V,giving65

Wh.A

ninteresting

example

isthe

batteryin

theToyota

Prius(data

fromw

ikipedia).Itproduces

about280

Vw

itha

capacityof6.5

Ah

or1.8kW

h.D

ividethe

capacityby

theaverage

currentto

findthe

lifetime

ofa

battery.T

hisis

trivialif

thecurrentis

constantbutitusuallyvaries

accordingto

thestate

ofthe

system.

Also,m

anysystem

ssw

itchon

andoff

sotheir

currentis

farfrom

constant.O

ftenthere

isa

lowcurrent

while

thesystem

sleepsw

ithbrief

pulsesof

highcurrentw

henactivity

isrequired.

Recallthat

theaverage

ofaperiodic

functioncan

befound

fromthe

integral

Iave D

1T ZI.t/d

t;

(10.1)

where

theintegralistaken

overanyperiod

T.Forexam

ple,supposethata

systemdraw

s100m

Afor1

s,then10

mA

for9s,and

repeatsthis

pattern,which

isillustrated

infigure

10.1.This

sortofprofile

iscom

mon

with

high,shortpeaksofcurrentseparated

bylongerintervals

with

am

uch

Section10.3

How

shouldyou

choosea

battery?85

lowercurrent.T

heperiod

is10

sand

theintegralcan

bedone

bycalculating

thearea

underthecurve.T

hisshow

sthatthe

averagecurrentis

Iave D

100

mA

1

sC10

mA

9

s1

sC9

sD

.100C

90/m

As

10

sD

190

mA

s10

sD

19

mA

:(10.2)

Note

thattheaverage

currentisa

currentandis

thereforem

easuredin

A(orm

Aetc);itdoesn’t

involvetim

e.T

hissystem

ispow

eredby

two

AA

cellsin

series,eachof2500

mA

hcapacity.T

hecapacity

ofthebattery

isnotincreased

byputting

cellsin

seriesso

thelifetim

eis

lifetimeD

capacityaverage

current D2500

mA

h19

mA

D132

h5:5

days:(10.3)

This

isn’tverylong:

Supposethatthe

systemhad

torun

foratleasta

week

withouta

changeof

battery.Is

itm

oreim

portantto

reducethe

currentat

thepeaks

orbetw

eenthem

?In

thiscase

thetw

oregions

ofcurrentmake

almostequalcontributions

tothe

averageso

we

probablyneed

tow

orkon

both.Don’tassum

ethatthe

largercurrentmakes

thebiggercontribution

tothe

average!T

hisdepends

onits

durationas

well.

Often

onepartof

thecycle

givesa

much

largercontribution

tothe

averageand

shouldreceive

mostattention,even

ifitisthe

smallercurrent.

10.3H

owshould

youchoose

abattery?

These

aresom

eofthe

main

pointsto

consider.

W

hatvoltageis

needed?

W

hatcapacityis

needed?

H

owportable

isthe

product?

Is

itpossibleto

usea

rechargablesystem

ratherthanprim

arycells?

Itis

agood

ideato

choosea

batterythatis

easyto

replace:

–alkaline

batteriescan

beboughtatany

cornershop–

rechargeableN

iMH

arealso

easyto

buy,asare

chargers–

some

lithiumcoin

cellsand

buttoncells

arefairly

easyto

findbutexotic

batteriesare

anuisance,even

iftheyhave

wonderfulelectricalproperties!

Here

aresom

eusefulw

ebsites

fordataon

batteries.

w

ww

.duracell.com/oem

/default.asp–

mainly

primary

cellsplus

NiM

Hrechargables.

data.energizer.com

–w

iderange

ofprimary

cellsand

NiM

Hrechargables.

w

ww

.panasonic.com/industrial/battery/oem

–w

iderange

ofprim

aryand

secondarybat-

teries.

w

ww

.batteryuniversity.com–

mainly

rechargablebatteries

86B

atteriesC

hapter10

TE

ST

CO

ND

ITIO

NS

:70°F (21°C

)

SE

RV

ICE

HO

UR

S

VOLTAGE (V)

00.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

2040

6080

100120

140160

3.9 OH

MS

24 OH

MS

62 OH

MS

OH

MS

mA

3.92462

2755020

Typical discharge profile of the DURACELL®alkaline M

N 1500 (“AA” size) cell.

Figure 2

Figure10.2

Discharge

profilesofan

alkalineA

Acell,taken

fromthe

Duracellw

ebsite.

10.4For

whatvoltage

shouldyou

designa

battery-powered

circuit?

This

soundslike

ano-brainer

butthedischarge

curvesin

figure10.2

showthatitis

noteasyto

choosethe

voltageatw

hicha

circuitshouldoperate!

Acom

mon

choiceis

2A

Acells.

This

means

thatthesupply

is3

V,isn’tit?W

ell,no–

notmostofthe

time.

Alkaline

cellsproduce

over1.5

Vw

henthey

arenew

butthisdrops

steadilythrough

theirlife

(which

makes

iteasyto

determine

howm

uchcapacity

isleft).T

heend-pointis

oftentaken

as0.9

V,so2

AA

cellsproduce

only1.8

Vatthe

endof

theirlife!

(Battery

manufacturers

quotethe

capacityto

0.8V

tom

akethe

capacityseem

abithigher,w

hichis

evenw

orse.)T

husa

welldesigned

productthatuses2

AA

cellsshould

becapable

ofoperating

from1.8–3.1

Vifprim

arycells

areperm

itted–

maybe

evendow

nto

1.6V.Som

eproducts

nowcom

ew

ithinstructions

forbiddingthe

useof

alkalinecells,perhaps

sothatthey

canbe

designedfor

2.4V

ratherthan1.8

V.O

thercellshave

differentcharacteristics.Seethe

pagesfrom

datasheets

fordetails.

N

iMH

produceclose

to1.2

Vfairly

constantlyuntilthe

voltageplum

metsw

henthey

havebeen

discharged.Inthis

case2

AA

cellsproduce

2.4V

throughouttheirusefullife.

L

ithiumcoin

cells,asusedin

thenovelty

lightsinE

lectronicE

ngineering1X

,givea

fairlyconstant3.0

Vform

ostoftheirlifebuthave

ahigh

internalresistance.

T

hebehaviour

ofL

i-ionsecondary

cellsis

between

NiM

Hand

alkalinecells.

They

canstartas

highas

4.0V

andthe

voltagedeclines

steadilyto

about3.5V,after

which

itfallsrapidly.T

heyare

typicallyrated

down

to3.0

V.

Section10.5

Supercapacitors87

load

Rbatt =

30W

Vbatt =

2.8V

50mA

load

Rbatt

Vbatt

Rcap

C

(a) Direct connection of load to cell

(b) Reservoir capacitor added to supply

Vload

Vload

IloadIload

Vcap

Figure10.3

Equivalentcircuits

of(a)

coincellconnected

directlyto

pulsedload

and(b)

with

reservoircapacitor.

10.5S

upercapacitorsT

heseare

avariety

ofcapacitorthatusesa

special,double-layerconstructionto

providea

highcapacitance

ina

smallvolum

e.For

example,the

PC10

fromM

axwellTechnologies

measures

3030

5m

mand

hasa

capacitanceof

10F

(that’sfarads,

notm

icrofarads).A

snagis

thatthe

dielectricis

verythin,

which

limits

thew

orkingvoltage

toonly

2.5V

inthis

case.Supercapacitors

arew

idelyused

as‘buffers’

between

them

ainpow

ersource

anda

loadto

provide:

backup

power

while

them

ainsource

isunavailable

–w

hilechanging

abattery,

forin-

stance

extra

currentwhen

aheavy

loadis

applied–

them

ainsupply

needonly

providethe

aver-age

current.W

e’llstudyan

example

shortly.M

anyelectric

vehiclesuse

thisapproach

toprovide

extracurrentforacceleration

andstore

chargefrom

activebraking.

Aproblem

isthatsupercapacitors

arecapacitors,so

theirvoltagedrops

linearlyas

afunction

ofcharge

(VD

Q=C

).Powerelectronics

isusually

requiredto

givea

constantoutputvoltage.

10.6W

orkedexam

ple:pulsed

currentdrawn

froma

coincell

Adom

esticelectronic

productdraws

asteady

currentof3

µAatalltim

es.Italso

draws

pulsesof

50m

Afor

1m

severy

1s.

The

voltagem

ustremain

above2.4

Vfor

correctoperation.T

hedesigner

wishes

touse

aC

R2032

cell.Is

thispossible

withoutextra

components?

Ifnot,w

hatelse

isneeded?

Whatis

theexpected

lifetime?

Aplot

ofcurrent

againsttim

eresem

blesthat

infigure

10.1on

page84

butw

ithdifferent

numericalvalues.

The

datasheetforthe

CR

2032[35]

shows

thatitproducesabove

2.8V

with

aninternalresistance

ofbelow

30

form

ostofits

ratedlifetim

e,givinga

chargecapacity

of200

mA

h.T

heseare

somew

hatarbitrary

choicesfrom

thegradual

curves.T

heanalysis

usesthese

values,ratherthan

thestarting

values,becauseitshould

bebased

onthe

worstcase

andtherefore

them

ostrestrictivevalues.

Ignorethe

steadycurrentfornow

;itmay

affectthelifetim

ebutw

on’totherwise

bea

prob-lem

.Coin

cellshavea

highinternalresistance

andthe

currentof50m

Am

aytherefore

bea

prob-lem

.Figure

10.3(a)show

sthe

equivalentcircuitofthe

cellconnecteddirectly

tothe

load.B

e-

88B

atteriesC

hapter10

causeofthe

internalresistancethe

voltageacross

theload

isgiven

byV

load DV

batt R

batt Iload D

2:8

V

.30

/

.50

mA

/D2:8

1:5D

1:3

V.T

hisis

farbelowthe

limitof2.4

Vforcorrect

operationso

itisnotpossible

toconnectthe

systemdirectly

tothe

coincell.

We

needanother

component

tostore

chargeand

releaseit

toprovide

the50

mA

pulse:a

capacitorconnected

inparallelw

iththe

coincellas

shown

infigure

10.3(b).T

heresistor

Rcap

inseries

with

thecapacitor

representsits

internalresistance,

which

will

beexplained

insec-

tion15.2

onpage

128;ignoreitfornow

.Make

thefollow

ingassum

ptionsto

estimate

thevalue

Cofcapacitance

required.

T

hecapacitor

isfully

chargedto

2.8V

atthestartof

thepulse.

We

mustcheck

laterthat

thereis

time

forittorecharge

fromthe

cellbetween

pulses.

Itprovides

thefull50

mA

duringthe

1m

spulse.T

hisis

aw

orst-caseassum

ptionbecause

thecellprovides

partofthecurrentdirectly.

Itis

dischargedto

them

inimum

acceptablevoltage

of2.4V

attheend

ofthepulse.

The

capacitorm

ustthereforeprovide

acharge

duringthe

pulseof

Q

DI

T

D.5

0m

A/

.1m

s/D50

µC.

Itsvoltage

must

notfall

bym

orethan

2:8

2:4

D0:4

V.

The

definingequation

fora

capacitor,Q

DC

V,also

appliesto

changes,

QD

C

V,so

V

D

Q=C

.T

hism

eansthatw

eneed

V

D

QCD

50

µCC

<0:4

V(10.4)

soC

D

Q

V

>50

µC0:4

VD

125

µF:

(10.5)

This

isa

bitlargerthan

thestandard

valueof

100µF

sow

ew

ouldhave

tochoose

thenextsize

up,220µF.

The

nextquestionis

whether

thecapacitor

canrecharge

between

pulses.T

heload

isdis-

connected,which

leavesthe

classicR

Ccharging

circuitasin

figure3.11

onpage

25.The

time

constant

D.R

batt CR

cap /CD

.30

/

.220

µF/D

7m

s.I

haveneglected

Rcap

inthe

calculationagain.

This

isfar

shorterthan

the1

savailable

between

pulsesso

we

concludethat

thereis

plentyoftim

eforrecharging

andthatthe

circuitshouldoperate

correctly.Finally,

thelifetim

e.B

ycurrent

conservationthe

averagecurrent

drawn

fromthe

cellis

equaltothatdraw

nby

theload;currentflow

sin

andoutof

thecapacitor

buttheaverage

must

bezero.Itis

much

easiertocalculate

theaverage

currentdrawn

bythe

load.The

pulsedpartof

thecurrenthas

aperiod

of1s

=1000

ms

soits

averagevalue

is

hIpulse iD

.50

mA

/.1

ms/C

0999

ms

1000

ms

D50

µA:

(10.6)

Angle

bracketssuch

ashxiare

oftenused

toindicate

anaverage

orexpectedvalue.T

hesteady

currentis3

µAso

thetotalis

53µA

andthe

lifetime

is

TD

QhIi D200

mA

h53

µAD

3800

hD160

days:(10.7)

Clearly

thepulsed

partofthecurrentis

much

more

significantthanthe

steadycurrent.

Section10.7

Exam

ples89

This

example

shows

howa

capacitorcan

beused

tow

orkaround

theproblem

ofthe

highinternalresistance

ofa

battery.T

hisprinciple

isw

idelyused

inother

typesof

power

supplyas

well.

10.7E

xamples

Exam

ple10.1

Roughly

howm

uchpetrol(gasoline)

isneeded

todrive

thecar

thesam

edis-

tanceas

theenergy

inthe

batteryofa

Prius?

Exam

ple10.2

A12

Vcar

batteryhas

acapacity

of50

Ah.

Forhow

longw

illitsupplythe

following

loads?

(a)4

sidelights

(5W

each)plusa

4W

lamp

forthenum

berplate?[25

h]

(b)T

heselights

plustw

o60

Wheadlights?

[4.1h]

(c)A

llthelights

aboveplus

a100

Wheated

rearwindow

?[2.5

h]

Exam

ple10.3

Many

productsare

designedto

runfor

atleast

ayear

(sometim

es10)

ona

singleC

R2032

lithiumcoin

cell.W

hataveragecurrentis

permitted?

Whatresistance

ofload

couldbe

usedifthe

currentwas

steady?

Exam

ple10.4

Atem

peraturesensortransm

itsdata

onceperm

inute.Itdraws

40m

Aw

hileit

runsatfullpow

erduring

eachtransm

ission,which

lasts10

ms.

Betw

eentransm

issionsitgoes

intoa

low-pow

ermode

anddraw

sonly

0.1m

A.H

owlong

willitlastusing

a500

mA

hbattery?

Which

hasthe

more

significanteffectonthe

lifetime,the

low-pow

erortheactive

mode?

Exam

ple10.5

Com

puterm

emory

takesa

standbycurrent

of10

µAand

will

retainthe

dataif

thevoltage

isheld

above3.3

V.The

standbyvoltage

isprovided

bya

1F

capacitor,which

isinitially

chargedto

4.5V.Forhow

longw

illthedata

beheld

inthe

mem

ory?[30

h]

Exam

ple10.6

The

resistanceR

capofthe

capacitorwas

neglectedin

section10.6

onpage

87.A

smallelectrolytic

capacitorm

ayhave

aseries

resistanceof

afew

ohms,say

3

.W

illthishave

asignificantim

pact?[Potentially

yes]

Exam

ple10.7

Sketchthe

currentthrough

theload

andthat

drawn

fromthe

coincell

asa

functionof

time

forthe

systemin

section10.6

onpage

87.Sketch

alsothe

voltageacross

thecapacitor.A

ccuratevalues

arenotrequired,justthe

shapesofthe

curvesand

roughscales.

11

Rectifiers

The

mostcom

mon

typeof

power

supplyunit(PSU

)for

electronicequipm

entproducesa

lowD

Cvoltage

(typically3–15

V)

fromthe

AC

mains

at230

V,50H

z.(T

hisapplies

inE

urope.W

hatisthe

mains

supplyin

North

Am

erica,forinstance?)W

ew

ouldlike

tohave

asupply

with

zerosource

impedance,so

thattheoutputvoltage

doesnotdepend

onthe

loadcurrent;and

togive

aconstantvoltage

when

theinputvoltage

(mains)varies.

The

changefrom

mainsto

DC

requiresseveralfunctions.Traditionallythey

were

performed

inthe

following

sequence:

isolation

between

theequipm

entandthe

mains

forsafety

reduction

involtage

with

atransform

er

rectification

toconvertA

Cto

DC

sm

oothingto

make

theraw

DC

waveform

fromthe

rectifierinto

something

closerto

smooth

DC

regulation

torefine

theoutputby

removing

rippleand

making

thevoltage

lesssensitive

tothe

load

Aproblem

isthatthetransform

ermustoperate

at50H

z,which

makesitlarge,heavy

andexpen-

sive.N

owadays

them

ainsis

usuallyrectified

directly,smoothed

andsupplied

toan

electroniccircuitto

reduceitsvoltage,isolate

andregulate

it.Atransform

erisstillneededbutcan

besm

allbecause

itoperatesathigh

frequency.M

uchof

thePSU

works

atmains

voltageso

keepyour

fingersout.W

e’lllookatthe

traditionalapproachfirst.Itis

nowalm

ostobsoleteforcom

mercial

productsbutrem

ainsattractive

forindividualdesigns.

11.1Transform

ersA

simple

transformer

(figure11.1

onthe

nextpage)

consistsof

two

inductorsw

oundon

thesam

ecore

sothatthe

windings

experiencethe

same

magnetic

flux.T

heinputis

appliedto

the

90

Section11.2

Rectifiers

91

primary

N1 turns

secondaryN

2 turns

110 V

230 V

(a) Transform

er(b) A

utotransformer

Figure11.1

(a)Simple

transformerw

ithprim

ary(input)and

secondary(output)w

indings,and(b)autotransform

er,where

thew

indingsare

shared.

primary

winding

andthe

outputis

takenfrom

thesecondary

winding.

You

will

studytrans-

formers

inE

ngineeringE

lectromagnetics

2.The

voltagesacross

thetw

ow

indingsare

(ideally)proportionalto

thenum

berofturns:

Vsecondary

Vprim

aryD

N2

N1

:(11.1)

The

coreis

made

ofsoft

ironfor

am

ainstransform

erso

theyare

weighty

items.

Asecond

importantfunction

ofatransform

eristo

isolatethe

two

circuits,which

isessentialforsafety

inequipm

entconnectedto

them

ains.A

nautotransform

ershares

thew

indingsas

infigure

11.1(b).T

heseare

widely

usedto

convertbetw

een230

Vand

110V

sothat

North

Am

ericanequipm

entcan

beused

inE

uropeand

viceversa.

The

sharedw

indingsreduce

thew

eight,sizeand

costbuttheydo

notprovideisolation.T

husthe

importantsafety

featureofa

fulltransformeris

lost.

11.2R

ectifiersTraditionalrectifiers

arebased

ondiodes.Ideally

theseallow

currenttopass

onlyin

onedirec-

tion,shown

bythe

arrowin

itssym

bol.A

practicalsilicondiode

dropsabout0.7–0.8

Vw

henconducting

(forward

biassed),assketched

infigure

11.2.V

erylittle

currentpassesin

theop-

positedirection

(reversebias)

unlessthe

voltageexceeds

thebreakdow

nvoltage,w

hichm

ustobviously

beavoided

innorm

aloperation.Schottkydiodes

arem

adein

adifferentw

ayand

havea

lowerforw

ardvoltage

dropofabout0.3

V.

V

I

breakdown

0.7V

Figure11.2

Sketchof

I.V

/fora

conventionalsilicondiode.

92R

ectifiersC

hapter11

load

load

load

(a) Half-w

ave(b) Full-w

ave(c) B

ridge

+-

-

-

+

+

Figure11.3

Standardrectifiercircuits:(a)half-w

ave,(b)full-wave

and(c)bridge.

Three

standardcircuits

areused

forrectifiers,shown

infigure

11.3.

(a)T

hesim

plest,half-wave

circuitusesa

singlediode,w

hichconducts

onlyforthe

positivehalf-cycles.

This

givesan

outputthatis‘D

C’

inthe

sensethatcurrentflow

sonly

inone

direction,butthevoltage

isnow

herenearconstant.Ituses

onlyhalfthe

waveform

,which

givesa

poorqualitysupply

thatrequiresheavy

smoothing.

(b)T

hefull-w

averectifier

usesboth

halvesof

thecycle

butrequiresdouble

thew

indingon

thetransform

er.

(c)T

he4-diode

bridgerectifieris

comm

on,with

thediodes

oftensupplied

asa

singlepack-

age.Itis

alsoa

full-wave

rectifier,meaning

thatitusesboth

halvesof

thew

avefunction,and

thereforem

akesbestuse

ofthe

transformer.

Ithasthe

disadvantagethatthe

voltagesuffers

fromtw

odiode

drops.T

hisis

anincreasing

nuisancebecause

ofthe

lowvoltage

usedby

modern

electroniccircuits.

The

sketchesin

figure11.4

onthe

facingpage

showthe

outputvoltagefor

half-wave

andfull-

wave

orbridge

rectification.I’ve

includeda

small

voltagedrop

acrossthe

diodesbecause

itm

akesthe

curvesclearer.

Allcom

ponentsare

supposedto

beidealapartfrom

that(novoltage

dropin

transformer

forinstance).

These

unsmoothed

waveform

sare

uselessfor

almost

allapplications.

Inparticular,

thehalf-w

averectifier

producesno

voltageat

allfor

halfof

eachperiod

T.

The

voltagedrop

acrossa

diode,ortw

odiodes

fora

bridge,isunacceptable

inm

anylow

-voltage

systems.

Insteadthey

usesynchronous

rectification,where

thediodes

arereplaced

byM

OSFE

Tsthatactassw

itches.These

switchesare

closedforthe

appropriatepartsofeach

cycleto

achieverectification.A

nIC

isneeded

tocontrolthe

system,w

hichincreases

complexity,but

theadvantage

ishigherefficiency.

11.3S

moothing

The

rectifiedw

aveforms

must

besm

oothedto

bringthem

closerto

idealD

C,w

hosevoltage

isstrictly

constantin

time.

The

principleof

smoothing

isto

storeenergy

when

thevoltage

Section11.3

Smoothing

93

V

t

V

t

(a) Half-w

ave(b) Full-w

ave or bridge

AC

in putA

C input

DC

outputD

C output

Figure11.4

Unsm

oothedoutputof(a)half-w

aveand

(b)full-wave

orbridgerectifier.

fromthe

rectifieris

highand

torelease

itagainw

henthe

voltagefrom

therectifier

falls.Tw

obasic

components

storeenergy:capacitors

andinductors.B

othare

used,oftentogether,butthe

simplest

power

supplieshave

onlya

reservoiror

smoothing

capacitorconnected

acrosstheir

output.Figure11.5

shows

ahalf-w

averectifierw

itha

smoothing

capacitor.T

hecapacitor

needsto

havea

largevalue,as

we

shallseeshortly,and

isusually

anelec-

trolytictype.

These

arepolarized,

which

means

thatthey

must

beconnected

theright

way

round.They

explodeifnot!

We’lllook

attypesofcapacitorin

section15.2

onpage

128.Figure

11.6on

thenextpage

shows

theeffectof

smoothing

onthe

voltagesand

currentsin

thecircuit.T

hebottom

curveshow

sthe

currentthatflows

intothe

positiveplate

ofthecapacitor

asa

functionoftim

e.Ithastw

odistinctregions.

Form

uchofthe

time,w

hilethe

voltagefrom

therectifieris

low,the

capacitorsuppliesall

ofthe

currenttothe

load.T

husthe

currentI

cap D

Iload .

Itisnegative

becausecharge

flows

outofthecapacitorinto

theload.T

hecapacitorsupplies

theload

forovertwice

aslong

with

onlya

half-wave

rectifier.

B

etween

theseintervals

areshort,positive

peaksofcurrentw

henthe

capacitorrechargesup

tothe

peakvoltage

fromthe

rectifier.T

hesepeaks

arenarrow

erand

higherthan

theflatregions,so

them

agnitudeofthe

currentism

uchlargerthan

Iload .

The

chargethatflow

sinto

thecapacitorduring

thepeaks

mustbalance

thecharge

thatflows

outto

theload

between

thepeaks

sothatthe

averagecharge

onthe

capacitorremains

constantover

load

+

-+

iload

icap

-

vload

Figure11.5

Bridge

rectifierwith

asm

oothingcapactorand

load.

94R

ectifiersC

hapter11

icap

t

Tv

load00-ioad

capacitor supplies current to load

capacitor recharges from

rectifier

smoothed

(unsmoothed)

positivem

eans that current flow

s into capacitor

Dt

Figure11.6O

utputvoltagefrom

afull-w

aveorbridge

rectifierwith

smoothing,show

ingcurrent

flowin

andoutofcapacitor.

acom

pletecycle.R

emem

berthatchargeand

currentarerelated

ingeneralby

QD Z

I.t/d

t:(11.2)

This

means

thatthe

areabetw

eenthe

peakand

thetim

eaxis,

while

thecapacitor

recharges,should

bethe

same

asthe

areabetw

eenthe

axisand

Iload ,

while

thecapacitor

suppliedthe

load.The

outputvoltagefalls

while

thecapacitoris

dischargingand

supplyingcurrentto

theload.

This

leadsto

a‘saw

tooth’variation

inoutput

voltagecalled

ripple.It

dependson

theload

current,the

sizeof

thecapacitor

andthe

time

forw

hichthe

currentflow

s.T

hevariation

iscalled

theripple

voltageV

rippleand

isalw

aysquoted

asa

peak-to-peakvalue.

Rem

ember

thebasic

equationfor

acapacitor,

VD

Q=C

.T

hisalso

works

forchanges,

V

D

Q=C

.Tocalculate

theripple,

Q

isthe

chargethatthe

capacitorsuppliesto

theload

while

theinputvoltage

islow

.Ifthevoltage

change

Vis

smallthen

we

canassum

ea

constantcurrentinto

theload.T

hisgives

Q

D ZI.t/d

tI

load t;

(11.3)

V

mean

Vripple

Dt

Figure11.7

Ripple

voltagew

ithm

eanvalue

Vm

eanand

peak-to-peakvalue

Vripple .

Section11.4

Calculation

ofinputvoltage95

where

t

isthe

time

forw

hichthe

capacitorsupplies

theload

with

currentI

load .T

heripple

voltageis

thengiven

by

Vripple D

V

DI

load t

C:

(11.4)

Unfortunately

itishard

toestim

ate

tby

hand.E

achperiod

ofthe

voltagefrom

afull-w

averectifier

is12T

D1=.2f

/,halfthe

periodT

ofthe

inputAC

.Clearly

t

isless

thanthis

butitis

difficulttodeterm

inethe

exactvalue.Simulation

shows

that0:6

=.2f

/is

aboutright.We

canuse

thisto

estimate

thesize

ofcapacitorneeded.For

example,

supposethat

we

want

a5

Vsupply

todeliver

100m

Aw

itha

peak-to-peakripple

of0.5V.T

hen

CD

I

t

V

0:6

I

2f

VD

0:6

0:1

250

0:5 D

1200

µF:

(11.5)

This

isa

bigcapacitor!

11.4C

alculationofinputvoltage

The

outputvoltagew

illobviouslydepend

onthe

voltageatthe

input.To

determine

this,work

backfrom

theoutput,adding

upallthe

voltagedrops

togetthe

peakvalue

attheinput.

1.T

hepeak

valueat

theload

inthe

aboveexam

pleis

Vm

ean D5

Vplus

halfof

Vripple D

0:5

V,giving

apeak

outputvoltageof5.25

V.

2.To

thism

ustbe

addedtw

odiode

drops,each

about0.8

V,givinga

totalof

6.8V

(toa

precisionof0.1

V).

3.T

hedrop

acrossthe

sourceresistance

ofthe

transformer

mustfinally

beadded.

This

istricky

becauseofthe

waveform

ofthecurrent,show

nin

figure11.6(c)on

thefacing

page.Typically

itspeak

valueis

roughlythree

times

theload

current,or

about300

mA

.The

internalresistanceofa

smalltransform

ermightbe

around7

,so

thevoltage

droppedis

about2.1V

(againvery

roughly).This

raisesthe

totalvoltageto

8.9V.

4.T

heoutputvoltage

ofatransform

erisalwaysquoted

asanrm

svalue.The

mainsisideally

asine

wave

sow

ecan

divideby

theusualfactor

of p2

toget6.3

V.You

shouldbuy

atransform

erforthisvoltage.

You

cansee

thatthesource

resistanceofthe

transformerhas

alarge

effectonthe

performance.

Itishard

topredictthe

voltagesdropped

bythe

diodesand

transformer

becauseof

thepeaked

natureofthe

current,sothe

resultisunlikely

tobe

accurate.Simulation

may

help.Figure

11.8on

thenext

pageshow

soscilloscope

tracesfrom

measurem

entson

apow

ersupply

with

atransform

er,bridgerectifierand

smoothing

capacitor(formerly

anexperim

entforthis

course).T

hepeaked

natureof

thecurrentis

particularlyclear

inthe

figure11.8(b),w

herethe

currentandvoltage

canbe

compared

onthe

input.The

distortedshape

ofthem

ainsvoltage

inthe

Rankine

Building

isalso

clear.

96R

ectifiersC

hapter11

Figure11.8

Oscilloscope

tracesfrom

apow

ersupply

with

transformer,

bridgerectifier

andsm

oothingcapacitor.

(a)Top

curves(orange

andlightgrey):

outputvoltageshow

ingripple

ofabout

0.6V

;bottom

curves:current

intoload

(blue,nearlyconstant)

andinto

capacitor(dark

grey,stronglypeaked).

(b)Top

curves:A

Cinputvoltage

(lightgrey,roughlya

sinew

ave)and

smoothed

outputvoltage(orange,nearly

constantbutripplevisible);bottom

curves:A

Cinput

current(darkgrey,strongly

peaked)andcurrentinto

load(blue,nearly

constant).

11.5C

onclusionT

hissim

plesupply

describedin

thischapter,w

itha

rectifierandsm

oothingcapacitor,has

poorperform

ance.Its

outputhas

alot

ofripple,

despitea

largecapacitor,

andthe

outputvoltage

dependson

theload

andalso

onthe

inputvoltage.Itisadequate

forundemanding

applications,usually

electricalratherthan

electronic,butisnotsuitable

forpow

eringintegrated

circuitsor

transistors.Aregulatoris

neededas

well.

Another

problemis

theshape

ofthe

currentw

aveformon

theinput.

This

isfar

fromsi-

nusoidal:N

ocurrentflow

sfor

much

ofthe

cycle,with

strongpeaks

asthe

capacitorrecharges

aroundthe

peaksofthevoltage.T

hem

ainssupplyin

theR

ankineB

uildingsuffersseverely

fromthis

becauseof

allthecom

puters,asyou

cansee

fromfigure

11.8.L

egislationhas

made

thisillegalforlargerpow

ersuppliesand

sophisticatedpow

erfactor

correctionis

neededto

controlthe

shapeofthe

currentwaveform

.

11.6E

xamples

Exam

ple11.1

Atransform

ertakesits

inputfromthe

230V

mains

andis

requiredto

produce5.5

Vpeak

outputasthe

inputtoa

5.0V

DC

supply.T

heprim

aryhas

600turns.

How

many

turnsshould

therebe

onthe

secondaryw

inding?(R

emem

berto

convertbothvoltages

torm

sbefore

takingthe

ratio.)

Exam

ple11.2

Draw

upa

tableto

compare

half-wave,

full-wave

andbridge

rectifiersw

iththe

headings:w

indingsneeded

ontransform

er;utilization

oftransform

er;num

berof

diodesneeded;

reversevoltage

ratingof

diodes;voltage

dropacross

diodes(assum

ingtypicalsilicon

components);frequency

ofripple;easeofsm

oothing.

Section11.6

Exam

ples97

Exam

ple11.3

How

largea

capacitorw

ouldbe

neededto

reducethe

rippleto

0.1V

forthe

example

insection

11.3?

Exam

ple11.4

Abridge

rectifieris

requiredto

supplyan

averagecurrent

of200

mA

with

ripplenotto

exceed0.5

V.Whatsize

ofsm

oothingcapacitor

isneeded?

The

AC

supplyis

at50

Hz.

[around2400

µF]H

oww

ouldyouransw

erchangeifthe

supplyw

eredesigned

forNorth

Am

ericaratherthan

Europe?

Exam

ple11.5

Design

apow

ersupply

with

atransform

er,bridgerectifier

andsm

oothingca-

pacitorto

work

fromthe

AC

mains

inE

uropeand

supply9

Vat200

mA

.Ripple

onthe

outputshould

notexceed0.5

V.Assum

ethatthe

secondaryw

indingofthe

transformerhas

aresistance

of10

.

Calculate

thevalue

ofsm

oothingcapacitor

andthe

(rms)

outputvoltageof

thetrans-

former

needed.W

hatvoltagerating

shouldbe

specifiedfor

thecapacitor,considering

bothno

loadand

fullload?E

stimate

theno-load

voltageand

regulation.[R

oughly2400

µF,12V

;17V

;40%or30

]

12

Linearregulators

Linearregulators

takein

currentatahigher,variable

voltageand

supplyitata

lower,regulated

voltage.The

differencein

voltageis

lostina

semiconductordevice

andthe

differencein

power

isdissipated

asheat.

Thus

theyare

intrinsicallyinefficient.

The

advantagesare

thatthey

aresim

ple,cheapand

electricallyquiet.

Another

disadvantageis

thatthey

requirea

DC

inputat

arelatively

lowvoltage,

which

typicallycom

esfrom

atransform

er,rectifier

andsm

oothingcapacitor.

The

transformerm

akesthe

overallsupplylarge

andheavy.

You

cansee

thisin

‘wall

warts’

orm

obilephone

chargers:older

onesthat

uselinear

regulatorsare

largerand

heavy,w

hilenew

eronesthatuse

switching

suppliesinstead

areoften

smallerthan

British

mains

plugs.L

inearregulatorsare

alsow

idelyused

within

equipmentto

deliverthevoltages

requiredby

differentcomponents.M

obilephones

mighthave

aroundten,forinstance.A

systemm

ighthaveits

main

powersupply

at5.0V

DC

,which

isreduced

to3.3

V,2.5V,1.8

Vorless

forindividualIC

s.

12.1Zener

dioderegulator

AZ

enerdiode

isa

specialtypeof

diode,which

isdesigned

tohave

asharp

reversebreakdow

ncharacteristic

ata

specifiedvoltage

VZ ,

asshow

nin

figure12.1(a)

onthe

facingpage.

This

means

thatthe

voltageacross

thediode

remains

almost

constantif

itis

reversebiassed.

Inreality

itisnotquite

constantandthe

datasheetgives

arecom

mended

valueof

currentforthe

bestperformance.R

emem

berthatZenerdiodes

areoperated

inreverse

bias!A

simple

circuitthatusesthisfeatureisshow

nin

figure12.1(b).T

hiscircuitiscalleda

shuntregulator

becausethe

diodeis

connectedacross

theload.

Itwould

bea

goodidea

toconnecta

capacitoracross

theload

asw

ell.(W

e’llnextlookatregulators

where

theactive

componentis

inseries

with

theload.)

Aresistor

Rs m

ustalways

beconnected

between

thediode

andsupply.

W

henthere

isno

loadconnected

(IL D

0),I

s DI

Z D.V

in V

Z/=

Rs .T

hiscurrentflow

sthrough

theresistorand

Zenerdiode

andallits

energyis

wasted

asheat.

N

owconnecta

loadw

itha

highresistance.T

hevoltage

Vout D

VZ

sothe

currentI

s drawn

fromthe

supplyrem

ainsthe

same.H

owever,som

eofthis

currentnowflow

sthrough

theload

asI

Land

thecurrent

IZ

throughthe

Zenerdiode

isreduced.T

huscurrentis

divertedaw

ayfrom

theZ

enerdiodeand

intothe

loadbutthe

totalcurrentremains

constant.

98

Section12.1

Zenerdiode

regulator99

I

V

VZreversebreakdow

n

load

VZ

Rs

Is

IL

IZV

in

Vout

(a)(b)

IZ

Figure12.1

(a)T

hecurrent–voltage

characteristicof

aZ

enerdiode

and(b)

asim

pleshunt

regulator.

T

hiscontinuesastheresistance

oftheload

isreduceduntilallthe

currentIsflowsthrough

theload

andthere

isnone

leftforthediode,so

IZ D

0.

T

hediode

ceasesto

functiononce

thereis

nocurrentflow

ingthrough

it,sothe

voltageV

out fallsbelow

VZ

iftheresistance

oftheload

isreduced

anyfurther.

This

circuitthereforeacts

asa

regulatorforcurrentsthrough

theload

upto

Is .T

hereis

anotherlim

itationas

well.T

hepow

erdissipatedin

theZ

enerdiode,givenby

IZV

Z ,mustnotexceed

itsrating.T

hissets

am

aximum

valuefor

IZ

andtherefore

am

inimum

valuefor

IL .

This

simple

regulatoris

adequtew

henthe

changesin

IL

aresm

allandV

indoes

notchangetoo

much.R

ealZenerdiodes

showa

smallchange

inV

Zw

ithcurrent

IZ ,w

hichcan

bereduced

byusing

oneregulatoras

thesource

voltagefora

secondregulator.

Figure12.2

shows

arough

analogyw

itha

water

tankthatm

aym

akethe

operationclearer.

The

aimis

tosupply

water

with

aconstantpressure

(head),equivalenttovoltage.

Water

flows

intoa

tankfrom

aninlet.

The

tankhas

anoverflow

,w

hichstops

thelevel

risingabove

aset

value.T

heoutlet

isat

thebottom

ofthe

tank.T

hesystem

will

work

providedthat

theflow

fromthe

outletisless

thanthatfrom

theinlet.Ifthis

isnottrue,the

levelofwaterw

illfall,theoverflow

willstop

runningand

thepressure

goesdow

n.

inlet (Is )

overflow (IZ )

outlet (IL )

Figure12.2

Aw

atertankas

ananalogy

toa

shuntregulator.

100Linear

regulatorsC

hapter12

VZ

= 5 V

Rs =

200 WIs =

25 mA

IL = 15 m

AIZ

= 10 m

AV

s

= 10 V

VL

(a)(b)

010

2030

4050

IL / mA

0 10 20 30 40 50

I / mA

IZ IsILR

L

50

VL / V

(c)

Figure12.3

Analysis

ofa

regulatorw

itha

Zener

diode.(a)

Circuitand

conditionsatspecified

operatingpoint.

(b)C

urrentsas

afunction

ofcurrentthrough

theload.

(c)Voltage

acrossload

asa

functionofcurrentthrough

it.

Zener

diodesare

nowrarely

usedfor

most

applications.T

heyhave

beenreplaced

bybandgap

references,w

hoseperform

anceis

betterin

almost

allrespects.

Astraightforw

ardbandgap

referencegives

avoltage

ofabout

1.2V.T

hisis

relatedto

anelectronic

propertyof

siliconcalled

itsbandgap,w

hichyou

willstudy

inE

lectronicD

evices2.

Integratedreferences

areavailable

forarange

ofcomm

onvoltages.T

heaccuracy

dependson

howm

uchyou

wish

topay,as

doesthe

stabilityagainsttem

perature,outputresistanceand

soon.

This

isdiscussed

insection

7.1on

page53

inconnection

with

dataconversion.

Worked

example

A5

VZ

enerdiodeisspecified

foracurrentof10

mA

andisrequired

toregulate

aload

of15m

A.

Itisfed

froma

10V

supply.C

omplete

thedesign

ofthe

circuitandanalyse

itsbehaviour

asa

functionofthe

currentthroughthe

load.C

onsiderthe

operatingpoint

first.T

hetotal

currentthrough

theload

anddiode

is25

mA

andthe

voltageacross

thediode

is5

V.The

supplyis

at10V,leaving

5V

tobe

droppedacross

theseries

resistorR

s .Thus

Rs D

.5V

/=.2

5m

A/D

200

.T

hecircuitis

shown

infigure

12.3.N

owvary

thecurrentthrough

theload

(bychanging

itsresistance).

First,supposethatthe

loadbecom

esan

opencircuit,

RL D

1,so

thatI

L D0.

Now

allthe25

mA

flows

throughthe

Zener

diode.T

hepow

erdissipated

inthe

diodeis

5V

25

mA

D125

mW

.Itshould

berated

todissipate

atleastthispow

er,which

isthe

maxim

umpossible

inthis

circuit.Increase

thecurrent

IL

throughthe

load.T

hecurrent

Is

fromthe

supplyrem

ainsthe

same

becauseitis

givenby

.Vs

VZ/=

Rs D

25

mA

.KC

Lgives

Is D

IZ C

IL

sothe

currentthrough

Section12.2

Seriestransistor

regulator101

inletoutlet

control

pressuresensor

valve

controlV

inV

out

heat(a)

(b)

Figure12.4

Aseries

regulatorina

(a)plumbing

and(b)electricalsystem

.

thediode

fallsas

thatthroughthe

loadrises.

The

Zener

diodestillacts

asa

regulatorprovided

thatsome

currentflows

throughitso

VL D

VZ D

5V

.T

hiscontinues

untilallthecurrentflow

sthrough

theload,so

IL D

Is D

25

mA

andI

Z D0.

Atthis

specialpointtheZ

enerdiode

hasjuststopped

conductingso

itnolonger

regulatesbut

thevoltage

acrossthe

loadrem

ains5

V.Increase

thecurrentthrough

theload

further.T

hecurrentdraw

nfrom

thesupply

nowex-

ceedsthe

designvalue

of25m

Aso

thevoltage

droppedacross

Rs increases,w

hichm

eansthat

thevoltage

acrossthe

loadfalls.

Infact

Rs and

RL

forma

simple

potentialdivider.N

ocurrent

flows

throughthe

Zenerdiode;itallflow

sthrough

theload,so

IL D

Is .T

hevoltage

acrossthe

loadis

givenby

VL D

Vs

Rs I

s DV

s R

s IL

:(12.1)

Thus

VL

fallsas

IL

increases.This

continuesuntilthe

loaddraw

sits

maxim

umpossible

current,w

hichm

eansthatthe

loadhas

become

ashortcircuit.In

thislim

it,V

L D0

soallof

Vs appears

acrossR

s andI

L DI

s DV

s =R

s D.1

0V

/=.2

00

/D

50

mA

.A

llthese

resultsare

plottedin

figure12.3.

The

maxim

umcurrent

thatcan

bedraw

nby

theload

beforeregulation

failsis

equalto

thetotal

currentfrom

thesupply

while

theload

isregulated.

12.2S

eriestransistor

regulatorT

hisis

them

ostcom

monly

usedtype

oflinear

regulator.I’ll

startw

itha

plumbing

analogyagain,show

nin

figure12.4(a).

This

time

theflow

isthrottled

bya

valve,which

iscontrolled

sothatthe

outletremains

ataconstantpressure

asm

easuredby

asensor.

This

isstillw

astefulbecause

theenergy

isdissipatedin

thethrottle

valvebutitisa

greatdealbetterthanthe

tankw

iththe

overflowbecause

theflow

sin

theinletand

outletareequal(unless

some

wateris

neededto

powera

hydrauliccontrolsystem

).T

heelectricalanalogy

isto

usea

controllableresistorinstead

ofthevalve

asIhave

shown

infigure

12.4(b).The

‘controllableresistor’isreally

atransistor,eithera

bipolarjunctiontransistor

(BJT

)or

am

etal–oxide–siliconfield-effecttransistor

(MO

SFET

).Itgetshotand

oftenneeds

aheatsink,w

hichw

e’llinvestigatein

section15.5

onpage

133.A

more

complete

circuitfora

traditional(high-dropout)regulator

isshow

nin

figure12.5

onthe

nextpage.

Power

issupplied

atV

inand

theregulated

outputis

deliveredat

Vout .

The

102Linear

regulatorsC

hapter12

- +V

outV

in

Vref

R1

R2

++

voltageerroram

plifier

v+

v–

Figure12.5

Simplified

circuitofa

seriesregulator

with

abipolar

junctionpass

transistorand

erroramplifier.T

hepow

ersupplyto

theam

plifierisom

itted.

usage‘3

Vregulator’

means

thatthe

outputis

at3

V.L

inearregulators

needV

in>

Vout and

thedifference

mustexceed

aparam

etercalled

thedropoutvoltage,w

hichI’lldefine

later.T

hecontrol

isperform

edby

avoltage

erroram

plifier,w

hichis

reallyjust

atype

ofoperational

amplifier.

Its

non-invertinginputis

connectedto

areference

voltage.I’veshow

nthe

previouscircuit

with

aZ

enerdiodealthough

asuperiorreference

would

beused

nowadays.

T

heinverting

inputisconnected

tothe

outputvoltage,reducedby

apotentialdivider.

T

heoutputdrives

thebase

ofa

passtransistor,w

hichcontrols

theflow

ofcurrentfrom

theinputto

theoutput.I’ve

shown

annpn

bipolartransistorbutitwould

bean

n-channelM

OSFE

Tnow

adays.

Itlooks

asthough

itis

difficultto

analysethis

circuitbut

negativefeedback

makes

iteasy.

Rem

emberthe

basicrule

ofoperationforan

operationalamplifierw

ithnegative

feedback:

T

heam

plifierdoes

whatever

itcan

tobring

itsinverting

andnoninverting

inputsto

thesam

epotential.

Here

thism

eansthatittries

toget

Vref D

R2

R1 C

R2

Vout

orV

out DR

1 CR

2

R2

Vref :

(12.2)

The

voltagedivider

isrequired

becauseotherw

isew

ew

ouldneed

Vref D

Vout ,w

hichcould

beaw

kward.Italso

givesa

way

tovary

theoutputvoltage,should

thisbe

needed.In

words,the

circuitoperatesas

follows.Suppose

thattheoutputvoltage

drops.This

causesv

todrop

attheopam

p,sovC

>v

andthe

outputoftheopam

pbecom

esm

orepositive.T

hisdrives

more

currentintothe

baseofthe

passtransistor,w

hichincreases

theoutputvoltage.T

heerroris

thereforecorrected

bynegative

feedback.

Section12.2

Seriestransistor

regulator103

0 2 4 6 8 10

02

46

810

voltage / V

input voltage / V

regulatednot regulated

headroom

dropoutvoltage

1.2 V

5.0 V

Figure12.6

Simulated

outputvoltage

asa

functionof

inputvoltage

forthe

5V

regulatorin

figure12.5

onthe

precedingpage.

Headroom

anddropoutvoltage

The

lossin

voltagein

theregulator,

Vin

Vout ,is

calledthe

input–outputvoltagedifferentialor

headroomvoltage.

The

regulatorw

illoperatecorrectly

onlyif

theheadroom

isgreater

thana

minim

umvalue

calledthe

dropoutvoltage.This

isone

ofthem

ostimportantparam

eterson

thedata

sheet.Figure

12.6show

sa

simulation

ofthe

outputandinputvoltages

forthe

simple

regulatorin

figure12.5

onthe

precedingpage

configuredfora

5V

output.ItrequiresV

in>

6:0

Vto

regulateand

hasa

dropoutvoltageof

1.2V.Y

oucan

alsosee

thatitisnota

perfectregulatorbecause

theoutputvoltage

risesnoticeably

asthe

inputisincreased

above6

V.Itgivesan

outputofonly4.8

Vw

henitstarts

toregulate.A

comm

ercialIChas

farbetterperformance

thanthis.

The

dropoutvoltageofa

realregulatorisratherhigherthan

inthis

example

becauseithas

am

oreelaborate

circuittodrive

thepass

transistor.A

traditionalregulatorm

aytherefore

havea

dropoutvoltageof2–3

V.

Power

dissipationT

hevoltage

reference,op-am

pand

outputdivider

usea

small

amount

ofpow

erbut

most

isdissipated

inthe

passtransistor.

Itis

givenby

theproduct

ofthe

currentand

theheadroom

voltage,P

diss DI

out .Vin

Vout /:

(12.3)

Inputsmoothing

capacitor,inputvoltageand

efficiencyT

heinputto

theregulatorin

am

ainssupply

comes

froma

transformer,rectifierand

smoothing

capacitor.We

sawthata

largecapacitorw

asneeded

toreduce

ripplein

asim

plesupply,w

ithout

104Linear

regulatorsC

hapter12

aregulator.H

owdoes

thischange

when

aregulatoris

used?T

hecriticalrequirem

entisthatthe

inputvoltageto

theregulatoris

always

kepthighenough

forcorrect

operation.In

otherw

ords,it

must

stayabove

theoutput

voltageplus

thedropout

voltage.Let’s

lookatan

example.

A5.0

V,100m

Apow

ersupplyusesa

regulatorwith

adropoutvoltage

of2.0V.T

hedesigner

wishes

togetaw

ayw

itha

100µF

smoothing

capacitoronthe

outputofabridge

rectifier,which

isthe

inputtothe

regulator.Whatvoltage

shouldthe

transformerproduce,assum

ingagain

thatithas

aninternalresistance

of7

?

1.T

heinputto

theregulatorm

ustremain

above5.0

+2.0

=7.0

Vforcorrectoperation.T

hisdeterm

inesthe

bottomofthe

ripplew

aveform.

2.T

heripple

voltageis

givenby

equation(11.4)

onpage

95.H

erethe

currentis100

mA

(ignoringthe

currentusedby

theregulator

itself),

t0:6

=.2f

/as

usualandw

eare

givenC

D100

µF.T

hesegive

Vripple D

6:0

V.

The

peakof

theripple

istherefore

at7.0+

6.0=

13.0V.

3.A

ddtw

odiode

dropsfrom

thebridge

rectifierasusualto

get14.6V.

4.T

hevoltage

dropin

thetransform

eristhe

same

asin

section11.4

onpage

95because

thecurrentis

thesam

e.Thatw

asabout2.1

Vso

thefinalresultis

16.7V

peak.

5.T

hisis

equivalentto11.8

Vrm

s,which

would

berounded

upto

12V

ormore

inpractice.

(Itisrounded

upbecause

thisgives

more

headroom;rounding

down

couldgive

toolow

avoltage

fortheregulatorto

operate.)

This

PSUtherefore

needs12

Vrm

sinputto

producea

5V

DC

output,which

shows

thatmost

ofthe

inputpow

eris

wasted

inthe

regulator.T

heinput

andoutput

currentsare

roughlythe

same

onaverage

andP

DV

Iso

theefficiency

isvery

roughlyV

rms;out =

Vrm

s;in D5=1

240%

,w

hichis

poor.You

cansee

why

cheappow

ersuppliesgethot.

12.3Low

dropoutregulators(LD

Os)

Atypicaldropoutvoltage

isaround

2V

forthe

conventionalregulatorthatI

describedabove.

This

lossis

notaproblem

fora

highoutputvoltage,butw

hatabouta3

Voutputfor

instance?T

heinputvoltage

would

haveto

beabove

5V

andaround

halfthe

energyw

ouldbe

dissipatedin

theregulatorratherthan

suppliedto

theload.

This

isnotacceptable,particularly

inportable

applications.Low

dropoutregulators

(LD

Os)

aretherefore

availablew

ithdropout

voltagesof

0.3V

orless.

The

circuitdiffersfrom

figure12.5

onpage

102in

onecriticalrespect:

The

transistorispnpratherthan

npnand

theoutputistaken

fromthe

collectorratherthanthe

emitter.

You

might

reasonablyask:

why

would

anybodyever

usea

highdropout

regulator?T

hereason

isthatthe

circuitinfigure

12.5has

two

desirablecharacteristics.

Itgives

alow

outputresistance,althoughthis

dependson

thecircuitas

aw

hole,notjustthe

transistor.Rem

emberthatan

idealsupplyhas

zerooutputresistance.

Ithas

goodstability,m

eaningthatitis

unlikelyto

oscillate.

Section12.4

Packagedregulators

105

Why

shouldoscillation

occur?T

hisw

illbeexplained

inC

ontrol3buthere

isa

roughpicture.

The

controlleruses

anop-am

pw

ithnegative

feedback,which

isequivalentto

aphase

changeof

180°for

asine

wave.

Other

components

inthe

circuitalsogive

phasechanges,w

hichvary

with

frequency.D

isasterstrikes

ifthese

othercom

ponentsgive

afurther

phasechange

of180°

atsome

frequency.The

totalphasechange

becomes

360°,thenegative

feedbackis

nowpositive

feedbackand

thew

holecircuitoscillates

violently.M

ostlow-dropoutregulators

needto

beprotected

againstoscillationby

conectinga

capac-itoracross

theiroutput.The

valueand

eventhe

typeofcapacitorare

specifiedin

thedata

sheetand

thisadvice

mustbe

followed.I’llsay

more

aboutthisw

henw

elook

atanexam

pleofa

datasheetforthe

LM

2931in

chapter13.M

odernregulators,

likem

ostanalogue

circuits,are

builtfrom

metal–oxide–silicon

field-effect

transistors(M

OSFE

Ts)

ratherthan

bipolartransistors.

The

passtransistor

ofan

LD

Obecom

esa

p-MO

SFET

ratherthan

apnp

bipolartransistor.

Idescribed

MO

SFET

sbriefly

inE

lectronicE

ngineering1Y

becausethey

havedom

inateddigital

electronicsfor

much

longer.T

heyhave

two

particularadvantagesforL

DO

s.

T

heequivalent

ofthe

baseof

abipolar

transistoris

thegate

ofa

MO

SFET.T

hisis

theelectrode

thatcontrolsthe

flowofcurrentbetw

eenthe

othertwo

terminals,the

sourceand

drain.The

criticalfeatureis

thatthegate

lookslike

acapacitorand

draws

nocurrentin

asteady

state,which

reducesthe

powerconsum

ption.

T

hevoltage

between

thecollector

andem

itterof

abipolar

transistorcannotfallbelow

avalue

calledthe

saturationvoltage

innorm

aloperation.T

hisw

illbeexplained

inA

na-logue

Electronics

2.Itsm

agnitudeis

determined

bythe

physicsofsilicon

anditis

hardto

make

itmuch

lowerthan

0.2V.O

nthe

otherhand,thechannelofa

MO

SFET

ism

orelike

aresistor,w

hosevalue

canbe

reducedby

design.Thus

itispossible

toreduce

thedropout

voltagefurther.

Forexam

ple,theFD

S9926AM

OSFE

Tthatw

em

ayuse

inthe

projecthas

an‘on’resistance

of40m

and

more

modern

deviceshave

evenlow

erresistance.

You

willstudy

MO

SFET

sin

Electronic

Devices

2,Power

Electronics

2and

Electronic

Circuit

Design

3.

12.4P

ackagedregulators

Itis

veryunlikely

thatyou

will

needto

builda

regulatorfrom

separatecom

ponents.A

vastrange

ofpackagedregulators

isavailable

with

thefollow

ingfeatures:

fixed

orvariableoutputvoltage

(remem

berthata‘5

Vregulator’m

eansonew

ithan

outputof5

V,notinput)

positive

ornegativesupply

conventionalorlow

dropout(LD

O)

w

idechoice

ofpowerratings

(andpackages

tosuit)

currentlim

itingand

thermalshutdow

nforsafety

106Linear

regulatorsC

hapter12

shutdow

ninputs,‘pow

ergood’outputsand

otheroptionalfeatures

The

moststraightforw

arddevices

givea

fixedoutputvoltage

andcom

ein

packagesw

ith3

pins:input,outputand

comm

on(ground).

Infactthey

lookjustlike

simple

transistorsand

youm

ayrem

emberone

likethis

onthe

noveltylights

thatyoubuiltin

Electronic

Engineering

1X.I’llgo

throughan

example

inthe

nextchapter.

12.5E

xamples

Exam

ple12.1

Azenerdiode

hasa

breakdown

voltageof4.7

Vata

currentof10m

A.D

eter-m

inea

suitableseries

resistorifitis

toregulate

aload

currentof50

mA

froma

supplyat10

V.H

owm

uchpow

erisdissipated

inthe

diode?W

hathappensifthe

loadis

removed?

[88

,47

mW

]

Exam

ple12.2

Calculate

thediode

current,outputvoltageand

whether

theregulation

isstill

effectiveif

theload

currentin

theprevious

questionchanges

to(i)

10m

Aand

(ii)70

mA

.[50

mA

,4.7V,regulation

working;0

A,3.84

V,regulationfails]

Exam

ple12.3

How

couldthe

outputvoltagebe

made

adjustable?

Exam

ple12.4

Supposethatyou

wantan

adjustablepow

ersupplyforan

undergraduateelec-

tronicslaboratory

whose

outputis

variablefrom

3V

forlogic

circuitsto

20V

foranalogue

circuits,with

am

aximum

currentof1

A.T

heinputvoltage

ischosen

tobe

25V

togive

plentyofheadroom

atalloutputvoltages.Underw

hatconditionsis

them

aximum

powerdissipated

inthe

passtransistorand

whatis

itsvalue?

[22W

]

Exam

ple12.5

The

benchPSU

sin

Rankine

709have

adjustable,bipolar,

regulatedoutputs

from0

to˙15

Vat200

mA

.Estim

atethe

maxim

umpow

erdissipated.[7.2

W]

Why

arethese

linearratherthansw

itchedregulators?

Exam

ple12.6

The

designeris

appalledby

thefigure

of40%

forthe

example

insection

12.2on

page101

andtries

toredesign

thesupply

for75%

efficiency.C

anthis

bedone

and,ifso,

how?

Ifnot,howabout50%

?

13

How

toread

adata

sheet:the

LM2931

low-dropoutregulator

Adata

‘sheet’is

availablefor

everyelectronic

component.

Ihave

putsheetinquotation

marks

becausesom

eof

themrun

tohundreds

ofpages.

Agood

datasheetdoesn’tprovide

onlythe

specificationsbutgives

plentyof

ideasfor

howto

usethe

component.

Often

youfind

theso-

lutionto

yourproblem

inthe

applicationsinform

ation.M

anufacturersw

antyou

tobuy

theircom

ponentsand

itisin

theirinteresttom

akethem

easyto

use.W

eare

luckyto

havegood

datasheets

availablefrom

mostm

anufacturersin

electronics.Inm

yexperience

itis

much

harderto

getsuchhelpfulinform

ationfor

mechanicalcom

ponents.A

lways

getthedata

sheetfromthe

manufacturer’s

web

site.M

anyotherpages

come

upif

youuse

Google

tofind

acom

ponentbuttheyare

bestavoided.Inthe

erabefore

thew

eb,datasheets

were

publishedin

booksand

we

keepa

selectionofthese

ina

smalllibrary

neartheelectronics

stores.Some

bookscontain

usefulintroductionsbutfrankly

mostofthe

materialis

obsolete.I’lluse

thedata

sheetfortheTexasInstrum

ents(formerly

NationalSem

iconductor)LM

2931low

-dropoutregulatorasan

example.

I’vechosen

thisbecause

itiskeptin

ourelectroniccom

-ponentstores

andhas

agood

datasheet.Itis

also‘autom

otivequalified’,w

hichm

akesituseful

forprojects

suchas

theForm

ulaStudent

racingcar.

Against

this,it

isnow

anold-fashioned

component.

More

modern

components

havefar

superiorperform

ancebut

generallycom

ein

tinypackages

thatwe

cannotassemble.

I’llgothrough

them

ainheadings

onthe

datasheet,w

hichvary

alittle

bym

anufacturer.

13.1G

eneraldescriptionT

hisis

onthe

frontpageand

givesa

generaldescriptionof

thedevice,as

youm

ightexpect.It

willbe

asum

mary

ofitsm

ostrelevantproperties,inevitablypresented

inthe

bestlight.

O

utputvoltage(tw

ofixed

valuesoradjustable

with

on/off).

R

angeofinputvoltage

(upto

26V,butprobably

limited

bypow

erdissipation).

D

ropoutvoltage(0.2–0.6

V,dependingon

conditions).

107

108H

owto

reada

datasheet

Chapter13

C

urrentrating(rathervague,probably

dueto

thedifferentversions

andpackages).

Q

uiescentcurrent

IQ

.T

hism

eansthe

currentconsum

edby

theregulator

itself,w

hichflow

soutof

theground

pinrather

thanthe

output.Itis

describedas

‘low’

butishigh

bym

odernstandards

ataround10%

ofI

out .This

isa

side-effectofthelow

dropoutvoltage.E

ffectivelyitis

wasted

current.(A

more

modern

devicew

itha

MO

SFET

ratherthan

abipolarpass

transistorwould

waste

much

lesscurrent.)

Packages,w

hichinclude

alarge

power

package,aconventionalsm

alltransistoroutline

(TO92)and

tinysolder-bum

psurface

mountdevice

(SMD

).

Protection

againstaw

iderange

offaults.

This

devicew

asdesigned

forautom

otiveap-

plications,which

presentanotoriously

hostileelectricalenvironm

ent.For

example,the

devicecan

withstand

transientvoltagesof˙

50

Von

itsinput.

You

coulddescribe

itasstudent-proofbutthatm

ightbegoing

abittoo

far.

This

sectionis

usefultogive

youan

imm

ediateidea

ofw

hetherthe

componentw

illmeetyour

needs.How

ever,youalw

aysneed

togo

furthertocheck

thedetails.

13.2C

onnectiondiagram

sY

ou’llneed

thesew

henyou

come

tolay

outthe

circuitif

youdo

itby

hand(although

thisinform

ationshould

bein

theO

rCA

Dlibraries).

Note

thatthe

TO-220

andTO

-263packages

havem

etaltabs,

which

areconnected

internallyto

ground.T

hisis

important

ifyou

boltthe

regulatorsto

thechassis

ofyour

equipment.

There

willbe

noproblem

ifthe

chassisis

alsoat

ground,otherwise

–bang!

This

devicecan

bebought

ina

surfacem

ountpackage.

Many

components

canonly

beboughtin

suchpackages

nowadays.B

every

carefulthatyoudo

notordersurfacem

ountpack-ages

bym

istake!Som

ecatalogues

show‘SM

D’

symbols

tohighlight

these,but

notalw

ays.Students

ordera

lotofsurface

mountdevices

inerror,w

herelarger

packagesare

availableand

would

havebeen

much

easiertouse.

13.3O

rderinginform

ationY

oudon’tnorm

allyneed

thisbecause

we

canorder

onlythe

varietieslisted

inthe

major

cata-logues

(preferablyR

SorFarnell,butalso

Rapid,C

PC,M

aplin,DigiK

ey,...).

13.4Typicalapplications

Now

we

havereached

thesingle

mostim

portantsection,where

them

anufacturertellsyou

howto

usethe

product.I’veextracted

them

ostrelevantpartinfigure

13.1on

thenextpage.Itshow

sthe

circuit,which

issim

plein

thiscase.

Followthese

instructions.It’s

fairlystraightforw

ardfor

asim

ple,3-pindevice

likethe

fixed-voltageversions

ofthe

LM

2931.H

owever,you

must

dow

hatit

says.H

ereyou

aretold

that‘C

2m

ustbe

atleast

100µF

tom

aintainstability’.

Itm

eansit!

Icanassure

youthatthe

regulatorwillnotw

orkifyou

omitthis

capacitor–plenty

ofstudents

havetested

thisoverthe

yearsand

foundthatthe

datasheetis

correct.You

arefurther

Section13.5

Absolute

maxim

umratings

109

LM

2931 Fixed

Ou

tpu

t

*Required

ifregulatorislocated

farfrompow

ersupplyfilter.

**C2

mustbe

atleast100µF

tom

aintainstability.

May

beincreased

withoutbound

tom

aintainreg-

ulationduring

transients.Locate

asclose

aspossible

tothe

regulator.This

capacitorm

ustberated

overthesam

eoperating

temperature

rangeas

theregulator.

Theequivalentseries

resistance(E

SR

)ofthis

capacitoriscritical;see

curve.

Figure13.1

Extract

from‘Typical

Applications’

ondata

sheetfor

National

Semiconductor

LM

29312.

advisedthatthe

ESR

ofthiscapacitor(equivalentseries

resistance,explainedin

section15.2

onpage

128)iscriticaland

arereferred

toa

curvelaterin

thedata

sheet.

13.5A

bsolutem

aximum

ratingsT

hism

eansw

hatitsays:exceed

theseratings

andyou

willdestroy

ordam

agethe

device.A

ninteresting

featureis

thelim

itoninternalpow

erdissipation,becausethere

isn’tone.Itis

inter-nally

limited,w

hichm

eansthatthe

deviceshuts

itselfdow

nif

itdetectsthatitis

overheating.T

hem

aximum

junctiontem

peratureis

neededto

calculatethe

sizeofa

heatsink.

13.6E

lectricalcharacteristicsT

hreesets

ofcharacteristics

aretabulated

inthis

datasheet

becausethe

LM

2931com

esin

versionsfor

fixed3.3

Vand

5.0V

outputsand

anadjustable

version.I’ll

focuson

the3.3

Vdevice.

You

willalm

ostcertainlyneed

tostudy

thissection

carefullyto

findoutw

hethera

deviceis

suitablefor

yourparticular

application.T

hisdata

sheetisa

littleunusualbecause

thereare

usuallythree

columns

ofnum

bers:m

inimum

,typical

andm

aximum

(althoughone

entryis

oftenm

issingforeach

row).H

erethere

isonly

asingle

‘Lim

it’column

insteadofm

inimum

andm

aximum

,butitsometim

eshas

two

numbers!

The

Lim

itheadingrefers

usto

Note

3,which

explainsthe

conditionsunder

which

thelim

itshold.

Let’s

lookata

fewparam

etersin

detail.T

hetherm

alresistanceis

curiouslyburied

innote

4,possiblybecause

itdependson

thepackage

ratherthanthe

outputvoltage.

Outputvoltage

Look

atthefirstrow

,foroutputvoltage.

The

typicalvalueis

3.3V,w

hichyou

would

probablyhave

guessed.T

helim

itsare

3.135and

3.465V

andare

innorm

altype,sothey

holdat25°C

110H

owto

reada

datasheet

Chapter13

junctiontem

perature.G

iventhis

rangeofparam

eters,which

shouldyou

usew

henyou

designa

circuit?

If

youare

designinga

singlepiece

ofequipm

entandcan

affordto

buya

fewextra

com-

ponents,use

the‘typical’

valueand

testthat

thecom

ponentperform

sclose

enoughto

this.

T

hisw

on’twork

ifyouare

designinga

productformass

production–

thousandsorm

ore.Soonerorlateryou

willinevitably

getacom

ponentwhose

performance

isclose

toone

ofthe

limits.In

thiscase

youm

ustdesignforthe

whole

rangeofpossible

parameters.

This

means

thatyoushould

generallydesign

forthew

orstcase.Willyourcircuitw

orkcorrectly

overthe

fullrange

of3.135–3.465

V?

It’sno

goodif

youare

usinga

microcontroller

whose

specificationfor

VD

Dis

3:3˙

0:1

V:you

willhave

tofind

anotherregulator.In

factitiseven

worse

thanthis

becausethe

range3.135–3.465

Vapplies

onlyat25°C

.Ifyou

includethe

fullspreadofoperating

conditionsthe

specificationw

idensto

2.970–3.630V.

Quiescentcurrent

This

time

we

aregiven

atypical

valueof

0.4m

Aand

asingle

limit

of1:0

mA

max

fora

small

load,I

o 10

mA

.O

bviouslythe

worst

casecorresponds

tothe

maxim

umquiescent

currentbecause

itis

wasted.

There

would

beno

pointin

givingthe

oppositelim

itof

them

inimum

current;ideallyitw

ouldbe

zero,which

norealdevice

canever

deliver.Y

oushould

designfor

thew

orstcase,which

is1.0

mA

.T

hereis

asecond

rowfor

Io D

100

mA

,which

givesa

typicalvalueof15

mA

.There

reallyoughtto

bea

maxim

umas

well(and

thereis

forthe5.0

Vversion).

Dropoutvoltage

Data

fortwo

outputcurrentsare

providedin

thiscase.T

herange

for10m

Acurrentseem

slarge.

Asusual,you

shoulddesign

forthew

orstcaseof0.2

V.Furtherinsightovertherange

ofdropoutvoltage

isgiven

inthe

plotsso

we’lllook

atthemnext.

13.7Typicalperform

ancecharacteristics

This

sectioncontains

alarge

number

ofplots

thatshow

theperform

anceof

atypical

device.(In

most

casesit

would

notbe

practicableto

showthe

limiting

casesas

well.)

You

might

besurprised

thatsom

uchdata

isprovided

forasim

plepow

erregulator!T

hefirsttw

oplots

arefor

thedropoutvoltage

andillum

inatethe

valuesin

thetable.

The

veryfirstplotshow

sthatthe

dropoutvoltagerises

with

temperature,from

0.05V

to0.10

Vin

thecase

of10

mA

load.T

hisexplains

alarge

partofthe

rangeshow

nin

thetable.

The

secondplotshow

sthe

dependenceon

currentatafixed

temperature,presum

ably25°C

.The

numbers

don’tseemquite

consistentwith

thefirstplot....

The

plotfor

‘Output

atvoltage

extremes’

showhow

thedevice

shutsdow

nif

theinput

voltagebecom

estoo

large,which

isa

goodsafety

feature.T

heplots

forthe

quiescentcurrenthelp

toexplain

theranges

listedthe

theearlier

table.T

heplots

ofpow

erdissipation

assistyouto

designa

suitableheatsink.

Section13.8

Schematic

diagram111

Finallycom

esthe

promised

plotof

the‘O

utputcapacitor

ESR

’,w

hichshow

sthe

regionw

ithinw

hichthe

deviceis

stable.Interestingly

thereis

alow

erlim

itas

well

asan

upper,so

youshouldn’t

spendtoo

much

money

ona

capacitorw

itha

verylow

ESR

!I

lookedup

theE

SRof

electrolyticcapacitors

inthe

datasheet

thatI

providedfor

them

icrophoneam

plifierin

Electronic

Engineering

1Y.Itquoted2.7

for

a100

µF,16V

Wgeneral-purpose

capacitor.T

hisdoes

notmeetthe

specificationfor

theL

M2931.

You

shouldlook

fora

capacitorthatis

speciallydesigned

forpowersupplies.(M

orem

odernL

DO

shave

lessdem

andingrequirem

entsand

some

willw

orkw

ithoutacapacitor.)

13.8S

chematic

diagramY

oudon’toften

seethis

onm

oderndata

sheets,partlybecause

oftradesecrets

butalsobecause

theyare

usuallytoo

complicated

tobe

ofm

uchpractical

useto

anybodybut

aprofessional

circuitdesigner.Still,it’s

interestingto

pickoutthe

major

components.

Can

youspotthe

passtransistor?

Severaltransistors

havetw

ocollectors,

many

with

numbers

nextto

theseparate

connections.These

givethe

relativeareas

andthe

currentsare

normally

inthe

same

ratio.

13.9A

pplicationhints

Here

againthe

manufacturerhelps

youto

usethe

deviceand

avoidcom

mon

problems.Itstarts

againw

iththe

capacitoracrossthe

output,which

isa

criticalrequirement.T

hereis

some

inter-esting

materialon

useatlow

temperatures,w

hichcan

causealum

iniumelectrolytic

capacitorsto

freezeand

losetheircapacitance!

Probablyyou

won’tbe

designingcircuits

fortemperatures

below

30°C

inthe

nearfuturebut,w

hoknow

s,youm

ighttakea

jobw

iththe

British

Antarctic

Survey.

13.10D

efinitionofterm

sT

hisis

afairly

uncomm

onfeature

butuseful

forunfam

iliarcom

ponents.Som

eanalogue-to-

digitalconvertershave

excellentsectionsthatdefine

thetechnicalterm

sused.

Note

theprecise

definitionofthe

dropoutvoltage.

13.11P

hysicaldimensions

These

isn’tofm

uchuse

inm

ostcasesbecause

thefootprints

shouldalready

bein

OrC

AD

.On

theother

hand,thedraw

ingsshow

theprecise

sizeof

thepackage

andthe

spacingof

thepins,

which

isn’talways

obvious.Itis

particularlyhelpfulfor

surface-mountpackages,w

hichcom

ein

ahuge

varietyofsizes

whose

names

arenotalw

aysstandard.

Exam

ple13.1

This

questionrefers

tothe

datasheet

forthe

LM

2931.A

ssume

thatw

eare

usinga

devicew

itha

5V

fixedoutputand

aTO

-92package.

(a)W

hatcapacitorisrequired

onthe

output?

(b)W

hatrangeofinputvoltages

shouldbe

used?

112H

owto

reada

datasheet

Chapter13

(c)W

hathappensifthe

componentis

connectedback

tofront?

(d)W

hatisthe

dropoutvoltageat100

mA

?

(e)W

hathappensifthe

inputvoltagedrops

toolow

?

(f)W

hatisthe

maxim

umoutputcurrent?

(g)Suppose

thatthedevice

supplies100

mA

atthem

aximum

recomm

endedinputvoltage.

How

much

poweris

dissipated?Is

thisacceptable?

Whatw

ouldhappen?

(h)W

hatism

eantbythe

term‘ripple

rejection’?

Exam

ple13.2

An

LM

2931is

usedto

supplya

systemw

ith100

mA

at5

V.Use

worst-case

designto

specifythe

inputthatmustbe

availableto

theregulatorto

ensurethatitcan

supplythe

loadunderallconditions

permitted.B

yhow

much

doesthe

outputvoltagechange

iftheload

isrem

oved?

14

Sw

itchingpow

ersupplies

Linearregulators

havetw

oserious

disadvantages,theirpoorefficiencyand

therequirem

entforthe

inputvoltageto

behigherthan

theoutputvoltage.Sw

itchingregulators

work

inan

entirelydifferentw

ay:theystore

theenergy

attheinputvoltage

andrelease

itattheoutputvoltage.T

heoutputvoltage

canbe

smallerthan

theinputvoltage

asin

linearregulatorsbutitcan

insteadbe

largeror

evenof

theopposite

signfor

asw

itchingregulator.

They

arevery

versatileand

cangive

much

higherefficiency

thanlinear

regulators.E

nergycan

bestored

ineither

capacitorsorinductors

andboth

areused.

Inductorsare

much

more

widely

employed

butcapacitorshave

advantagesforsom

eapplications.

14.1S

witched-capacitor,charge-pum

por

flying-capacitorconverters

These

produceoutputs

whose

voltageis

givenby

am

ultipleor

simple

fractionof

theinput

voltage,includingnegative

values.T

hesim

plestisan

inverter:V

out D

Vin .

Here

ishow

thecircuitin

figure14.1

works.

T

hetw

oleft-hand

switches

areclosed

onone

phaseof

theclock

(figure14.1(a))

andthe

capacitorC

1charges

tothe

inputvoltage.It’s‘top’plate

ispositive.

D

uringthe

otherphase

(figure14.1(b))

thetop

plateof

thecapacitor

isconnected

toground.T

hevoltage

acrossthe

capacitordoesnotchange

becauseitis

determined

bythe

C

1

C2

clock

Vin

Vout =

-Vin

C1

C2

(a)(b)

Figure14.1

Asw

itched-capacitorvoltageinverter.

113

114Sw

itchingpow

ersupplies

Chapter14

charge,which

hasnotm

oved,sothe

bottomplate

isforced

toV

in .This

isconnected

tothe

outputsoV

out D

Vin .

The

secondcapacitor

C2

isa

reservoirorsmoothing

capacitorasin

asim

plerectifier.Itsupplies

theload

while

C1

isrecharging

fromthe

input.The

activecapacitor

C1

isw

himsically

calleda

flyingcapacitor

andthe

switches

arereally

MO

SFET

s.T

hecircuitcan

easilybe

modified

toproduce

Vout D

2V

in .B

ycharging

two

capacitorsin

parallelbutdischargingthem

inseries

itispossible

toproduce

Vout D

2V

in .More

complicated

circuitsw

ithnetw

orksofcapacitors

areneeded

forV

out D32V

inand

fractionalratios.Sw

itched-capacitorconvertershavethe

advantagethatthey

aresim

ple,needingonly

thereg-

ulatorchip

andexternalcapacitors.

They

producea

littleelectrom

agneticinterference

becauseof

thesw

itchingbutit

isusually

notserious.

The

disadvantagesare

rippleon

theoutput

andpoor

regulationin

simple

converters.T

hesw

itchingfrequency

isoften

around1

MH

znow

a-days,w

hichreduces

boththe

rippleand

sizeofcapacitors

needed(w

hy?).They

arerestricted

tosim

pleratios

ofinputandoutputvoltage

ortheefficiency

suffers.The

disadvantagesare

seriousand

switched-capacitorconverters

areused

onlyin

particularniches.One

isto

generatea

nega-tive

biasso

thatasingle-supply

opamp

candrive

itsoutputallthe

way

down

tozero

(section6.2

onpage

41).Here

aretw

oothers

thatyoum

ightencounter.

RS

-232interface

driversD

igitalsystems

oftenneed

tocom

munication

with

computers

anda

serial(CO

M)portis

simple

touse.

CO

Mports

havenow

vanishedfrom

standarddesktop

computers

butrem

ainw

idelyused

incom

merce

andindustry.A

problemis

thattheC

OM

portusesan

ancientprotocolcalledR

S-232,which

employs

avoltage

between

15

and3

Vto

representa1

andC3

toC15

Vto

representa0.

The

officialvoltagelevels

usedto

be˙12

Vbutm

anysystem

snow

uselow

ervoltages,often˙

5V

.T

hisis

closertothe

voltagesused

fordigitalelectronicsbutthe

negativevoltage

isa

particularnuisance.T

hesolution

isto

usean

interfacedriver

thatincludesa

switched-capacitor

converter.T

hem

ostwell-know

nis

theM

aximM

AX

232,nowratherold,w

hichneeds

threeexternalcapacitors

toproduce

levelsof˙

2V

supplyfrom

5V.T

henew

erMA

X3232

isdesigned

for3V

suppliesand

everym

ajorcompany

offersequivalentdevices.

Drivers

forw

hiteand

blueLE

Ds

Most

modern

digitalcom

ponentsw

orkw

ithsupplies

of3

V(or

less).R

ed,yellow

orgreen

LE

Ds

areeasy

todrive

becausethey

needabout

1.8V.

White

andblue

LE

Ds

arebased

ondifferentsem

iconductorsand

needa

highervoltage,around

3to

4V,so

theycannotbe

drivendirectly.Specialdrivers

aretherefore

neededto

supplysm

allblueand

white

LE

Ds

from3

Vin

productssuch

asm

obilephones.

Dim

mable

lights,‘fun’lights

(toys,children’sshoes...)

andhigh-pow

erwhite

LE

Ds

forcamera

flashesin

mobile

phonesare

otherapplications.W

hereverthere

isa

need,them

anufacturersw

illprovidea

solution.A

wide

rangeof

LE

Ddrivers

isavailable,m

anyof

which

usesw

itchedcapacitors

tostep

upthe

voltage.T

heym

ayalso

regulatethe

currentratherthan

thevoltage,w

hichis

donebecause

brightness/current.

(Many

driversuse

inductorsrather

thancapacitors

fortheir

greaterefficiency,particularly

forhighercurrent.)

Section14.2

Switched

inductorconverters

115

14.2S

witched

inductorconverters

Most

switching

convertersuse

inductorsand

thew

ord‘inductor’

isusually

dropped–

infact

theyare

oftenjustcalled

‘switchers’.

Portablecom

putersand

evendesktop

computers

ofrea-

sonablesize

would

notbepossible

withoutsw

itchingconverters.

I’lldescribethe

basictypes,

which

convertDC

fromone

voltageto

another,andsay

alittle

aboutmains

suppliesatthe

end.Sw

itcherscom

ein

threebasic

varieties:

buck

–steps

down

voltage,same

sign

boost–

stepsup

voltage,same

sign

buck/boostorinverting

–changes

signofvoltage,can

stepup

ordown

Thus

youcan

getanym

agnitudeand

eithersign

ofoutputvoltage

(inprinciple)!

The

flybackconvertercom

binesan

invertingconverterw

ithisolation

between

inputandoutput.M

orecom

-plicated

topologiesare

oftenused

inpractice.

An

inductorstoresenergy

inits

magnetic

field,which

isproportionalto

current.The

currentm

usttherefore

riseand

fallas

theenergy

isstored

andreleased.

The

detailsfollow

fromthe

basicequation

foraninductor,

vL

.t/DL

diL

dt

:(14.1)

Avoltage

isgenerated

bya

changein

current,not

asteady

value.Y

oucan

imagine

thatthe

inductortriesto

resistchangesin

current.Here

aretw

oim

portantcases.

Ifthe

currentthroughan

inductorisconstant,there

iszero

voltageacross

it.(Zero

voltagedoes

notimply

zerocurrent!)

If

thevoltage

acrossan

inductoris

constant,thecurrentrises

orfalls

steadilydepending

onthe

signofthe

voltage.

The

traditionalway

ofanalysingA

Ccircuits

with

inductance,usingphasors

andim

pedance,isuseless

forthese

applicationsbecause

thew

aveforms

arenothing

likesine

waves.

The

circuitsm

ustbeanalysed

intim

eratherthan

frequency.T

hegeneralidea

isthatan

inductorissw

itchedso

thatenergyis

storedin

itsm

agneticfield

fromthe

inputduring

onephase

andreleased

tothe

loadduring

theother

phase.It

israther

likethe

smoothing

capacitorin

alinear

supply,which

storesand

releasescharge.

Thatcaused

itsvoltage

togo

upand

down

duringeach

cycle.In

thesam

ew

ay,the

currentthrough

theinductorram

psup

anddow

nas

energyis

storedand

released.The

confusingfeature

isthatthe

voltageacross

theinductor

changessign

between

thetw

ophases

becauseof

equation(14.1).

The

equivalentfeatureof

thestorage

capacitoris

thatitscurrentchanges

signbetw

eenstorage

andrelease,butthatseem

sfarm

orenatural.

Figure14.2

onthe

nextpageshow

sa

comparison

ofthesetw

ocom

ponents.

14.3B

asicbuck

converterT

hebuck

converterisa

step-down

supplyso

Vout

<V

in ,likethe

linearregulator.The

circuitinfigure

14.3on

page117

hastw

osw

itchesdriven

inantiphase

andan

inductorinseries

with

the

116Sw

itchingpow

ersupplies

Chapter14

Energy stored in electric field,

generated by voltageC

annot change voltage instantly

trelease

t

Equal areas: charges balance so that

average voltage remains constant.

tt

energy

Periodic storage and release of energy in a pow

er supplyA

ssume constant currents for capacitor and constant voltages for inductor

releaseenergy

Reservoir capacitor w

ith ripple voltageSw

itched inductor with ripple current

iCiL

vC

vL

store

store

store

store

iC vC

iLvL

·iC Ò = 0

vC

=qC

=1C

iC (t) dtÚ

iC=

Cdv

C

dt

Figure14.2

Com

parisonofstored

energyin

capacitorsand

inductors.Note

carefullythe

direc-tions

ofthecurrents

andvoltages.

Section14.3

Basic

buckconverter

117

clock

LIL

VL

Vout

Vin

IoutIin

load

S1

S2

Figure14.3

Circuitofa

basicbuck

converter.

load.(One

ofthesw

itchescan

bereplaced

bya

diodebutit’s

easiertoanalyse

itlikethis.)

Let’s

lookatthe

two

phasesseparately,w

herethe

inductorstoresand

releasesenergy,orcharges

anddischarges.

Tom

akelife

easyI’llassum

ethatthe

inputandoutputvoltages

remain

constant.T

hisneeds

reservoircapacitors

acrossthe

loadand

input,which

arenotshow

n.L

ettheduty

cyclebe

D,w

hichm

eansthe

fractionof

eachcycle

thatisspentin

thecharging

phase.Itlies

inthe

range0

D

1.If

theoverallperiod

isT

,theconverter

spendsD

Tin

eachcharging

phaseand

.1D

/Tin

thedischarging

phase.

Charging

orstorage

phaseIn

thestorage

phase,S

1is

closedand

S2

isopen.

The

circuitcanbe

simplified

tofigure

14.4w

iththe

inputsupply,inductorandload

inseries.T

hecurrents

areallthe

same,

iin DiL D

iout ,and

thevoltages

obeyv

in Dv

L Cv

out .Check

thesigns

carefully!T

herate

ofchangeofcurrent

isgiven

bythe

equationforan

inductor,

diL

dt

Dv

LLD

vin

vout

L>

0:

(14.2)

Thus

thecurrentincreases

steadilyprovided

thatv

in>

vout ,w

hichis

whatw

ew

antduringthe

storagephase:

Energy

isdraw

nfrom

theinputand

storedin

them

agneticfield

ofthe

inductor.

Vin

IinL

IL

Vout

Iout

load

VL

Figure14.4

Effective

circuitofabasic

buckconverterin

thecharging

orstoragephase.

118Sw

itchingpow

ersupplies

Chapter14

LIL

VL

Vout

Iout

load

Figure14.5

Effective

circuitofabasic

buckconverterin

thedischarging

orreleasephase.N

otethat

vL

<0.

The

inductorischarged

with

energy.

Release

phaseFigure

14.5show

sthe

circuitin

the‘release’

phase,w

ithS

1open

andS

2closed.

Only

theinductor

andload

areleft

inthe

circuit.T

heinput

isdisconnected

andiin D

0.T

hesum

ofthe

EM

Fsaround

thecircuitm

ustbezero

byK

irchoff’slaw

sonow

vL

D

vout .

Thus

vL

haschanged

signand

become

negative.The

rateofchange

ofcurrentisgiven

by

diL

dt

Dv

LLD

v

out

L<

0:

(14.3)

The

currentdecreasessteadily

asenergy

isreleased

fromthe

inductortothe

load.The

inductoris

beingdischarged.

Currentand

voltagew

aveforms

The

waveform

sare

plottedin

figure14.6

onthe

nextpage.

Acentral

relationbetw

eenthem

follows

fromthe

averagevalue

overeachcycle

ofthevoltage

acrossthe

inductor:

hvL iD

L diL

dt

:(14.4)

This

isjust

theaverage

ofthe

basicequation

(14.1)for

thevoltage

acrossan

inductor.T

heaverage

valueof

thecurrentrem

ainsconstantover

along

time:

itramps

upand

down

within

eachcycle

butstaysthe

same

onaverage.

Thus

theright-hand

sideis

alsozero

anditfollow

sthathv

L iD0

asw

ell.This

means

thattheaverage

voltageacross

theinductoris

zeroovereach

cycleof

operation.(T

heequivalentrelation

fora

smoothing

capacitoris

thathiC iD0

sothat

hvC i

remains

constant.)W

eknow

thevoltages

acrossthe

inductorinthe

two

phasesso

we

canw

orkoutthe

average:

0DhV

L iDT

store .Vin

Vout /C

Trelease .

Vout /D

ŒDT

.Vin

Vout /C

Œ.1D

/T.

Vout /D

.DV

in V

out /T:

(14.5)

Section14.3

Basic

buckconverter

119

releaseenergy

storeenergy

000

IL = Iout

Iin

VL

Vin – V

out

–Vout

0T

DT

(1 – D)T

ttt

Iave

store

release

Figure14.6C

urrentsandvoltage

acrosstheinductorin

abuck

regulatorwith

dutycycle

DD

14 .

This

givesthe

relationbetw

eenthe

inputandoutputvoltages,

Vout D

DV

in:

(14.6)

The

outputvoltageis

always

lessthan

theinputvoltage

andcan

becontrolled

byvarying

D.

This

isan

example

ofpulse

width

modulation

(section8.3

onpage

67).Figure

14.6show

sD

D14 .

Switch

S2

isoften

replacedby

adiode,as

shown

infigure

14.7.C

onfirmfor

yourselfthat

thisconducts

atthe

correcttim

es.A

diodeis

notalw

aysused,

althoughit

issim

plerthan

asw

itch;why

mighta

switch

bepreferred?

Sum

mary

ofbuckconverters

The

main

propertiesofbuck

convertersare:

outputvoltage

<inputvoltage

outputcurrentflow

sthroughinductor;itflow

sallthetim

eso

itisrelativelyeasy

tosm

ooth

inputcurrentis

pulsed

120Sw

itchingpow

ersupplies

Chapter14

load

PWM

control

Vin

Vout

Figure14.7

Block

diagramofa

complete

buckregulator.

The

inductorsand

capacitorscan

bem

adesm

allerif

thefrequency

isincreased

becauseless

energyneeds

tobe

storedand

releasedin

eachcycle.

Frequenciesused

tobe

inthe

kHz

rangebutnow

may

bein

MH

z.A

complete

converterneeds

afeedback

loopto

controlD

andm

aintaina

constantoutputvoltage.A

blockdiagram

isshow

nin

figure14.7.Y

oubuy

anintegrated

circuit,ofcourse,andI’ve

providedthe

datasheetfor

theL

M3100

asan

example

[40].B

uckconverters

arew

idelyused

tosupply

low-voltage

digitalsystems

(5.0,3.3,2.5and

1.8V

)from

higherD

Cvoltages,

suchas

12V

ina

caror

froma

batteryof

severalcellsin

series.T

heydo

notprovideisolation

between

theinputand

outputsothey

cannotbeused

topow

erequipmentfrom

them

ains(w

hichalso

needsa

rectifier).

14.4B

oostconverterT

hetw

osw

itchesand

theinductorform

a‘Y

’inthe

buckconverterand

thisY

canbe

arrangedin

threew

ays.The

othertwo

ways

givethe

othertwo

typesofconverter.W

e’llnextlookatthe

boostconverter,show

nin

figure14.8.

Ihave

shown

adiode

ratherthan

asecond

switch.

Itsoutputvoltage

isgiven

by

Vout D

Vin

1D

:(14.7)

The

main

characteristicsare:

O

utputvoltage>

inputvoltage,same

sign,hencethe

name.load

Vin

Vout >

Vin

Figure14.8

Circuitofa

basicboostconverter.

Section14.5

Inverting(buck/boost)converter

121

Vin

load

Vout <

0

Figure14.9

Circuitof

abasic

invertingor

buck/boostconverter.T

heoutputhas

theopposite

polarityto

theinput;note

theorientation

ofthecapacitors

anddiode.

O

utputcurrentispulsed

andneeds

goodsm

oothing.

Boost

convertersare

usefulin

equipment

thatw

orksoff

asingle

AA

cellor

thelike.

This

includesa

lotof

portableelectronics,

suchas

MP3

players.T

heyare

alsoused

togenerate

voltagesfor

LE

Ds,

oftenseveral

LE

Ds

inseries.

Forexam

ple,the

National

Semiconductor

LP5526

[41]providesallofthese

functionsforbacklights

anda

camera

flashin

am

obilephone.

Another

example

ofa

modern

boostconverter

isthe

TexasInstrum

entsT

PS61200.T

hiscan

work

froma

0.3V

input,admittedly

notwith

wonderfulefficiency.

This

lowinputvoltage

allows

ittooperate

froma

singlesolar

cell,which

typicallyproduces

about0.3–0.4V

;severalcells

inseries

areneeded

togetsufficientvoltage

tobe

usefulwithoutsuch

aregulator.

14.5Inverting

(buck/boost)converterT

hecircuitis

shown

infigure

14.9.N

otethe

orientationofthe

diodeand

electrolyticcapacitor

onthe

output.Itsoutputvoltage

isgiven

by

Vout D

D

1D

Vin

:(14.8)

The

main

characteristicsare:

O

utputvoltagehas

oppositesign

toinputvoltage

andm

aybe

largerorsmallerin

magni-

tude.

B

othinputand

outputcurrentsare

pulsed,soheavy

smoothing

isneeded.

Effectively

theinductor

is‘charged’

fromthe

inputthen

‘discharged’into

theoutput.

This

actionis

analogousto

thereservoircapacitorin

alinearpow

ersupply.The

currentrisesduring

chargingso

thevoltage

acrossthe

inductoris

positive;the

currentfallsduring

dischargingso

thevoltage

changessign.

These

convertersare

usefulwhere

aw

iderange

ofinputvoltages

mustbe

tolerated,eitherlow

eror

higherthan

theoutput.

They

areoften

usedin

modern

productspow

eredby

Li-ion

cells,whose

voltagedeclines

roughlyfrom

4V

to3

Vorbelow

asthey

discharge.Many

circuitsare

designedto

work

from3.3

Vand

thereforeneed

asupply

thatcan

stepthe

voltageup

ordow

n.Buck/boostconverters

areideal.

Buck/boostconverters

canbe

made

togive

thesam

esign

ofoutputvoltage

asthe

inputbyusing

two

switches

andtw

odiodes,butthat’s

gettingrathercom

plicated(look

atthedata

sheetforthe

LinearTechnology

LTC

3454ifyou

areinterested).

122Sw

itchingpow

ersupplies

Chapter14

Vin

load

Vout <

0

Figure14.10

Circuitof

abasic

flybackconverter.

Many

more

components

areneeded

inprac-

tice.

14.6Flyback

converterT

heinverting

convertercanbe

modified

sothatthe

inductorhastw

ow

indings,oneforthe

inputand

aseparate

onefor

theoutput.

This

iscalled

aflyback

converterfor

historicalreasons.T

hecircuitis

shown

infigure

14.10.T

heinductor

nowlooks

likea

sortof

transformer

butdoes

notw

orkin

anythinglike

thesam

ew

ayas

atraditionaltransform

erw

ithsteady

sinew

aveson

inputandoutput.

Infactitis

bettertothink

ofitasa

coupledinductor.

The

dotsshow

the‘sense’ofthe

windings,the

startsifthey

areboth

wound

ina

chosendirection.

The

circuithasthe

same

two

phasesof

operationas

theothersw

itchingconverters.

In

thestorage

phase,currentflows

fromthe

inputthroughthe

primary

winding

(onthe

left)andbuilds

upthe

magnetic

fluxand

energyin

thecore

ofthetransform

er;nocurrent

flows

inthe

secondaryw

indingbecause

ofthediode.

In

therelease

phase,them

agneticflux

decaysand

drivesa

currentthroughthe

secondaryw

inding(on

theright)and

theforw

ard-biasseddiode

intothe

load;nocurrentflow

sin

theprim

aryw

indingbecause

thesw

itchis

open.

Thus

energyis

storedin

thecore

ofthe

inductorin

onephase

andreleased

inthe

otheras

before.The

newfeature

isthatone

coilisused

tofeed

inenergy

andthe

othertoextractit.T

hisisolatesthe

outputfromthe

input,which

isessentialina

mainspow

ersupply.Furthersecondaryw

indingscan

beadded

togetm

ultipleoutputs,although

onlyone

canbe

regulatedby

thePW

Maction.

14.7C

omplete

mains

switching

power

supplyunit

The

flybackconvertercan

beused

asthe

coreofa

complete

powersupply

unittogive

alow

DC

voltagefrom

theA

Cm

ains.(M

orecom

plicatedcircuits

areused

inpractice

forhigher

power

andefficiency.)

Itisoften

calledan‘off-line’supply

becausethe

electronicsw

orksdirectly

fromthe

‘line’(A

merican

usage),not

viaa

transformer.

These

arethe

functionsof

theblocks

infigure

14.11on

thefacing

page.

T

heelectrom

agneticinterference

(EM

I)filterkeepsswitching

noisegenerated

bythe

PSUoutofthe

mains.Itshould

alsoprotectthe

systemfrom

incoming

noiseand

spikes.

Section14.8

Generalfeatures

ofswitching

converters123

EMI filter

Power factor correction

FlybackPWM driver

Rectifier and filter

Outputprotection

PWM

controlisolator

Figure14.11

Acom

pletem

ainssw

itchingpow

ersupply.

Pow

erfactor

correctionis

neededto

avoidthe

problemof

drawing

currentonly

atthe

peaksofthe

voltageand

isrequired

bythe

EU

forpowers

abovea

certainrating

(60W

?).C

orrectionis

gettingm

oredem

andingas

legislationbecom

esm

orestringent.

T

hem

ainsis

thenrectified

directly,smoothed

(notshown)and

fedto

aflyback

converter.

T

heflyback

driverswitches

thecurrentthrough

thetransform

erwinding

onand

off

T

heoutputofthe

transformeris

rectifiedand

smoothed.

A

nypracticalproductrequires

protectionagainstoverload,shortcircuitand

thelike.

T

hesupply

must

beregulated

safelyso

thefeedback

controlm

ustinclude

anisolator

between

theinputand

output.This

mightbe

optical(diodeand

detector)oratransform

er.

You

arenot

advisedto

pokeinside

oneof

these!T

heirm

ains-powered

partsreach

thepeak

voltageof

theA

Cinput

andit

isnot

pleasantto

touchone

ofthese

components.

(Yes,

I’vetried.)

14.8G

eneralfeaturesofsw

itchingconverters

Let’s

startwith

thegood

features.

E

fficient,over90%possible.

V

ersatile,wide

rangeofcurrents,inputvoltages

andoutputvoltages.

L

ightweightand

compact–

make

laptopsw

ithcom

pactchargerspracticable.

B

oostconvertersenable

operationfrom

verylow

inputvoltages,suchas

anM

P3player

froma

singleA

Acell.

B

uck/boostconverters

canprovide

3.3V

outputw

hilecom

pensatingfor

thedecline

involtage

ofaL

i-ioncellas

itdischarges.

And

nowforthe

lessattractive

issues.

124Sw

itchingpow

ersupplies

Chapter14

Vout

C1

C2

clock Vin

Figure14.12

Whatis

thefunction

ofthissw

itched-capacitorconverter?

C

reatestrong

electromagnetic

interference(E

MI),w

hichm

ustbepainstakingly

suppressed.A

naloguecircuits

areparticularly

sensitiveand

needa

quietsupply.

N

eedcareful

design,particularly

theselection

ofthe

inductorsand

thelayout

ofthe

printedcircuitboard.M

anufacturersprovide

detailedadvice

indata

sheets.

U

nreliable–

lessso

thanin

thepast,butoften

seemto

bethe

partthatbreaksin

domestic

products.The

off-linecom

ponentsare

highlystressed

andparticularly

vulnerable.

14.9W

illIneedto

designone

ofthese?Y

ouw

illalmostcertainly

haveto

designa

small,linear

supplyas

partofTeam

Design

Project3.

The

hardware

usedin

thecurrentprojectruns

froma

12V

supply,which

isneeded

todrive

two

DC

motors.H

owever,the

microcontrolleruses

3.3V

andotherparts

oftheelectronics

may

need5

Voreven˙

15

V!

You

cannotescapefrom

powersupplies

inany

practicaldesign.Itis

lesslikely

thatyouw

illhaveto

designa

switching

power

supply.H

owever,they

haveoften

beenrequired

inTeam

Project4

andseveral

studentshave

neededthem

forIndividual

Project4.Read

thedata

sheetextremely

carefullyand

followits

recomm

endationsto

theletter.

The

detailsofthe

inductor,capacitorandlayoutofthe

PCB

arecritical.

14.10E

xamples

Exam

ple14.1

Whatis

thefunction

ofthesw

itched-capacitorconverterinfigure

14.12?

Exam

ple14.2

Abuck

(step-down)

switched-m

odeconverter

operatesat

100kH

zand

pro-vides

a5

Voutputfrom

a15

Vinput.

The

averageoutputcurrentis

1A

andm

ustnotfluctuateby

more

than˙10%

duringeach

cycle.

(a)A

twhatduty

cycleD

doesthe

converteroperate?

(b)Sketch

thew

aveformsforthe

inputcurrent,outputcurrentandvoltage

acrosstheinductor,

making

thesam

esim

plificationsas

inthe

lecture.Yourplots

shouldshow

thescales.

Section14.10

Exam

ples125

(c)W

hatisthe

averageinputcurrent?

(d)W

hatvalue

ofinductor

isneeded?

This

isnot

coveredin

thenotes

butfollow

ssim

plyfrom

vL D

LdiL

=dt.

(e)Suppose

thatthesw

itchingsupply

is95%

efficient.How

doesthis

compare

with

alinear

regulatorforthesam

ejob?

Exam

ple14.3

Whatis

theoutputfrom

aboost(step-up)

converterw

ithan

inputof5

Vand

DD

12 ?W

hatwould

happenif

Dw

ereraised

to0.95?

[10V

]

Exam

ple14.4

The

inputtoan

inverting(buck/boost)converteris

10V.W

hatvaluesof

Dare

neededto

getoutputvoltagesof

5,10

and20

V?

[13 ]

Exam

ple14.5

Suggestsuitabletypes

ofpow

ersupply

forthe

following

applicationsand

ex-plain

yourchoice.Detailed

designsare

notrequired.

(a)A

mains-pow

eredhi-fi

amplifier,w

hichruns

fromsupplies

of˙30

V.

(b)A

mains-pow

eredem

beddeddigitalsystem

with

suppliesof5.0

Vand

3.3V,both

atsev-eralam

peres.

(c)T

hedisplay

ofabasic

mobile

phone,which

ispow

eredby

a3.6

Vbattery.T

hebacklight

forits

displayuses

sixgreen

LE

Ds

andcan

besw

itchedon–off,notdim

med.

You

may

connecttheL

ED

sin

anyw

aythatyou

wish.

(d)T

heprocessor

ina

digitalcamera,w

hichis

designedto

work

at2:4˙

0:1

V.

The

power

comes

fromtw

oA

Abatteries,w

hichm

aybe

ofanycom

mon

typethatyou

may

specify.Is

aregulatorrequired

atalland,ifso,whattype

shouldbe

used?

15

Passive

components,heatsinks

andprinted

circuitboards

Ishallfirstreview

some

propertiesof

comm

onpassive

components

thatyouw

illencounter–

resistors,capacitorsand

inductors.T

heyare

distinguishedfrom

activecom

ponents,which

canam

plifya

signaland

areusually

made

fromsem

iconductors.T

heim

agesare

takenfrom

theR

SC

omponents

web

site,rsww

w.com

.W

e’llthenlook

atheatsinksand

finallyprinted

circuitboards

(PCB

s).

15.1R

esistorsW

hatdoyou

needto

specifyfora

resistor?W

ellresistanceis

obvious!H

owever,itnotthe

onlyparam

eter–the

listissurprisingly

long.Here

isan

abbreviatedcatalogue.

R

esistance–

Values

comm

onlyrange

between

anohm

anda

fewm

egohms.Y

ouhave

tow

orryaboutthe

resistanceofthe

leadsand

jointsforlow

values,andleakage

aroundthe

resistorathighvalues.A

voidextrem

evalues

where

possible.

Tolerance

–N

o10

k

resistorhasa

resistanceofexactly

10k

becauseofsm

allfluctua-tions

inm

anufacturing.Mostofourresistors

havea

toleranceofs2%

but5%com

ponentsare

alsocom

mon

and1%

too.Y

oucan

getselected

valuesw

ithbetter

accuracybut

itcosts

money.

Look

fora

bettersolution,such

asusing

anintegrated

circuitthatincludesm

atchedresistors

tosetthe

gainofan

opamp,forinstance.

Pow

errating

–W

hathappensifyouput10

Vacrossa

standard10

resistorfrom

stores,w

hichis

probablyrated

forapow

erdissipationof

110

W?

Notw

hatyoum

ightwant...

C

onstruction–

Resistors

arefabricated

inm

anyw

ays.Two

comm

onm

ethodsare

touse

asolid

carboncom

positem

aterialorto

cutahelicaltrack

ina

metalfilm

onthe

surfaceof

acylindricalbody.

Wirew

oundresistors

areused

forhigh

powers

andare

constructedlike

anold-fashioned

electricalbarfire(butencapsulated).

Package

–Traditionalaxialleads,surface

mountpackages,specialcasings

todissipate

theheatproduced

byhigh-pow

erresistors...

126

Section15.1

Resistors

127

Figure15.1A

selectionofresistors:axial,surface

mount(m

uchsm

allerthanthe

others),single-in-line

(SIL)

packof

5resistors,

power

resistor,trim

mer

andpotentiom

eter(not

tothe

same

scale).

M

ore–

Temperature

coefficientof

resistance,long

termstability,

maxim

umvoltage,

noise,...

Figure15.1

shows

images

ofseveraltypesofresistor.O

ftenyou

needseveralresistors

ina

cir-cuitand

manufacturers

produceseveraltypes

ofpacksfordifferentapplications.A

fewsym

bolsfrom

Capture

areshow

nin

figure15.2

onthe

nextpage.

R

1–

The

gainofa

simple

amplifierbased

onan

opamp

issetby

theratio

oftwo

resistors.Y

oucan

buypacks

oftwo

connectedresistors

(threepins)w

hoseratio

istrim

med

tom

eeta

specificedaccuracy.

R

2–

Often

youneed

severalresistorswith

thesam

evalue,such

aswhen

youdrive

severalL

ED

sfrom

adigitalcircuit.

Ifthe

resistorscan

allbeconnected

between

theL

ED

sand

ground(or

VD

D )you

canchoose

apack

with

oneend

ofallthe

resistorsconnected

toa

comm

onpin.T

hesetypically

come

insingle-in-line

packages(SIL

orSIP).

R

N1

andR

N2

–T

heseare

differentsymbols

forpacks

ofidenticalresistors

with

inde-pendentconnections,used

where

itisnotpossible

toconnectthem

alltoa

comm

onpin.

This

isalso

comm

onw

hendriving

displays.T

heyoften

come

indual-in-line

packages(D

ILor

DIP)

asthe

symbol

forR

N2

makes

clear,butSIL

packagesare

alsoavailable.

(RN

standsforR

esistorNetw

ork.)

You

mustbe

verycarefulto

checkthatthe

numbering

ofthe

pinsin

Capture

match

thatofthe

packagew

henusing

anyofthese

multiple

resistors.Potentiom

etersare

usedw

herea

variableresistor

isneeded.

They

havea

thirdconnection

calledthe

sliderthatcan

bem

ovedfrom

oneend

oftheresistorto

theother,form

inga

potentialdivider.

Some

aredesigned

tobe

installedon

frontpanels

andturned

byknobs

butthis

isnow

old-fashioned.O

thers,often

calledtrim

mers,

arem

ountedon

aPC

Band

adjustedw

ith

128Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

R1

RE

SIS

TOR

SIP

3

R1

RE

SIS

TOR

SIP

3

123

RN

2

RE

SIS

TOR

DIP

4

RN

2

RE

SIS

TOR

DIP

4

12345 6 7 8

C R2

RE

SIS

TOR

SIP

5

C R2

RE

SIS

TOR

SIP

5

12345

RN

1

RE

SA

R_IS

_4/SM

RN

1

RE

SA

R_IS

_4/SM

1234

8765

Figure15.2

Selectionofresistorpacks

fromthe

DISC

RE

TE

libraryin

OrC

AD

Capture.

ascrew

driverto

achievethe

desiredperform

ancefrom

acircuit–

thegain

ofan

amplifier,for

instance.Any

componentw

itha

moving

partisless

reliablethan

afixed

oneso

youshould

aimto

avoidtrim

mers.A

PCB

with

alarge

numberoftrim

mers

isalm

ostalways

apoordesign.

Figure15.3(a)show

sa

simplified

diagramofan

idealisedresistor.Itis

formed

froma

pieceof

resistivem

aterialof

lengthd

andconstant

cross-sectionA

with

acontact

ateach

end.Its

resistanceis

RD

dA

;(15.1)

where

is

calledthe

resistivityof

them

aterial.T

heconductivity

is

oftenused

asw

ell:

D1=

.T

heelectrical

behaviouris

notas

straightforward

asthis

when

youlook

indetail.

Inparticular,a

resistorhas

inductanceas

wellas

resistance.T

hisbecom

essignificantathigh

frequenciesbecause

theim

pedanceofan

inductorrisesw

ithfrequency.Y

oum

ayneed

toselect

atype

ofresistorthathaslow

inductance(carbon

composition

ratherthanm

etalfilm)forhigh-

frequencycircuits.

15.2C

apacitorsT

hesecom

ein

ahuge

rangeof

valuesfrom

pFto

Fw

ithnum

erousdifferenttypes.

The

prin-ciple

isstraightforw

ard:a

capacitorhastw

om

etalplatesseparated

bya

dielectric,asshow

nin

dielectric, thickness d

metal plate, area A

lengthd

lengthd

areaA

areaA

N turns

(a) resistor(b) capacitor

(c) inductor

Figure15.3

Diagram

ofa

theoretical(a)resistor,(b)

capacitorand

(c)inductor

(asyou

might

remem

berfromschool!).

Section15.2

Capacitors

129

Figure15.4

Aselection

ofcapacitors:

ceramic

multilayer,tw

oalum

iniumelectrolytics

anda

padder.

figure15.3(b)on

thepreceding

page.The

capacitanceis

givenby

CD

0

r A

d;

(15.2)

where

Ais

thearea

ofeach

plate,d

isthe

thicknessof

thedielectric

thatseparatesthe

plates,

0 D8:8

54

10

12

Fm

1

isthe

permittivity

offreespace

and

r isthe

relativeperm

ittivityof

thedielectric

orthedielectric

constant.This

isunity

forfreespace

bydefinition,around

10for

many

plasticsand

over100forsom

eceram

ics.Alarge

valuegives

acom

pactcapacitor.T

hem

aindistinction

between

capacitorsisthetype

ofdielectric.Mostare

plastics:polyester,polypropylene,

polycarbonate,polystyrene,

teflon(rare).

Some

work

well

athigh

frequency(polystyrene,

forinstance)

butgive

largepackages,

while

othersgive

compact

capacitorsbut

arerestricted

tolow

frequency.C

eramic

capactorsare

particularlysm

allbecause

ofthe

highdielectric

constantbutthiscom

esata

price:theircapacitance

variesstrongly

with

temperature

andapplied

voltage(changes

of50%

arenotunusual;

seebelow

).I’ve

shown

afew

typesin

figure15.4.

Many

modern

devicescom

ein

surfacem

ountpackagesand

arevirtually

indistin-guishable

fromother

components

with

two

leads,suchas

resistors.T

heyare

justanonymous,

rectangular,blackpatches!

Inpractice

many

capacitorsdo

nothaveflatplates

asin

thesketch.

Often

the‘plates’

anddielectric

arew

oundinto

acylinder

likea

Swiss

rollbut

thisincreases

theseries

resistanceand

inductance(see

below).

You

may

encountera

smalladjustable

capacitorcalled

apadder,

analogousto

atrim

merresistor.O

ld-fashionedradios

were

tunedw

ithlarge,air-spaced

variablecapacitors

buttheseare

longobsolete.

No

electroniccom

ponentsare

ideal.Capacitors

havetw

oresistances

associatedw

iththem

:one

inseries

andone

inparallel

asshow

nin

figure15.5(a)

onthe

nextpage.

(They

exhibitinductance

asw

ell,which

becomes

importantathigh

frequency.)T

heparallelresistance

rep-resents

leakagebetw

eenthe

platesand

isparticularly

significantw

ithelectrolytic

capacitors(below

).T

heseries

resistancelim

itsthe

speedatw

hichthe

capacitorcan

charge–

remem

berthe

RC

time

constant?C

apacitorsthatm

ustrespondquickly,such

asthe

decouplingcapacitors

acrossdigitalIC

sorin

switching

powersupplies,m

ustbechosen

tohave

alow

valueof

Rseries .

Itisalso

known

asthe

equivalentseriesresistance

orESR

.

130Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

Rseries

RleakageC

Rseries

L

(a)(b)

Figure15.5

Simplified

equivalentcircuitofarealistic

(a)capacitorand(b)inductor.

Electrolytic

capacitorsE

lectrolyticcapacitors

arem

adein

aratherdifferentw

ayfrom

thesim

plesketch.T

heplates

areusually

aluminium

andare

separatedby

aconducting

paste,theelectrolyte.A

currentispassed

between

theplates,w

hichcauses

anoxide

layertogrow

onthe

anode.This

isthe

same

processof

anodizationthatis

usedto

givea

shiny,protectivefinish

toalum

iniumproducts.

The

oxideis

agood

insulatorandacts

asthe

dielectriclayerofthe

capacitor.Itisalso

thin,which

givesa

largecapacitance.T

huselectrolytic

capacitorsare

usedw

herea

highvalue

isneeded.

Electrolytic

capacitorsneed

aperm

anentDC

biasacross

themto

maintain

theoxide

film.

This

means

thatthey

must

beconnected

thecorrect

way

round.If

thisis

notdone

theoxide

thins,breaks

down,

allows

acurrent

topass

andthe

capacitorexplodes

with

anunpleasant

smell!

The

polarityis

always

shown

onthe

package.Tantalum

electrolyticcapactors

offersuperiorperform

anceata

highercost.T

hetolerance

ofelectrolyticcapacitorsispoor,typically˙

20%

butsometim

es50=C

100%

,w

hichis

afancy

way

ofsaying

afactor

of2!

They

leakbadly

andtheir

rangeof

temperature

isrestricted.T

heirlifetime

islim

itedand

theyare

oftenresponsible

forthedeath

ofequipment

fromold

age.A

secondparam

eterthatmustalw

aysbe

specifiedforan

electrolyticcapacitoris

itsw

orkingvoltage.

You

will

haveseen

thisas

CM

AX

inO

rCA

D.

Atypical

valueis

16V

fora

small

componentbutobviously

much

higherworking

voltagesm

ightbeneeded

forapow

ersupply.Pow

ersuppliesusually

containlarge,alum

inium,electrolytic

capacitorsforsm

oothing.The

ripplecurrentflow

sin

andoutof

thecapacitor

oneach

cycleand

causeitto

heatupbecause

ofthe

power

dissipatedin

theseries

resistanceR

series .Such

capacitorstherefore

havea

ripplecurrentrating

thatmustbe

respected.

Decoupling

capacitorsA

lldigitalICs

shouldhave

adecoupling

capacitorconnected

acrossthem

toreduce

thespread

ofnoise

fromthem

.T

hisis

becauseC

MO

Scircuits

drawa

pulseof

currentat

everyclock

transition,which

may

bevery

strongfora

largeIC

(100A

forafancy

microprocessor).

Manu-

facturersgive

detailedrecom

mendations,w

hichshould

befollow

ed.T

hisadvice

istaken

fromthe

datasheetfor

theFreescale

MC

9S08QG

8,asm

all8-bitmicrocontroller,and

youw

illfindsom

ethingsim

ilarinevery

datasheet.

Typically,applicationsystem

shave

two

separatecapacitors

acrossthe

powerpins:

abulk

electrolyticcapacitor,

suchas

a10

µFtantalum

capacitor,to

providebulk

chargestorage

forthe

overallsystem

,and

abypass

capacitor,such

asa

0.1µF

Section15.2

Capacitors

131

Figure15.6

Capacitance

asa

functionof

voltagefor

a1

µF,10

V,X

5Rm

ultilayerceram

iccapacitor[29].

ceramic

capacitor,locatedas

nearto

theM

CU

power

pinsas

practicaltosuppress

high-frequencynoise.

Itseems

strangeto

puta0.1

µFcapacitor

inparallelw

itha

10µF

capacitor.W

hybother,w

henthe

smaller

onem

akesa

tinycontribution

tothe

overallcapacitance?

The

differenceis

theE

SR.

Electrolytic

capacitorshave

relativelyhigh

resistances,w

hichgives

thema

longtim

e-constant

DR

series C.

This

means

thattheycannotcharge

anddischarge

quickly.T

hesm

allercapacitoris

usuallyspecified

asa

multilayerceram

iccom

ponent,which

hasa

verylow

ESR

.Itcan

thereforerespond

quicklyto

thespikes

ofcurrentdrawn

bythe

microcontroller.T

helarger

capacitoractsas

areservoirforslow

erchanges.D

ecouplingcapacitors

shouldalso

beused

foranaloguecom

ponents,suchas

op-amps,in

am

ixedsignalsystem

.Inthis

casethe

purposeis

tokeep

noiseoutofthe

IC.

Low

-dropoutpow

ersupplies

needa

capacitoron

theiroutput

forstability

andthese

areusually

specifiedas

multilayer

ceramic

typesfor

modern

ICs.

Ceram

iccapacitors

of1

µFare

nowreadily

obtainablealthough

theyw

ereunfeasibly

largein

thepast.T

hecom

pactsizecom

esat

apenalty,

mentioned

above.To

make

thisclear,

figure15.6

shows

thecapacitance

ofa

nominally

1µF,10

Vm

ultilayerceramic

capacitorasafunction

ofvoltage[29].T

hecapacitance

fallsrapidly

asa

functionofvoltage

andis

down

toabout25%

ofitsnom

inalvalueatthe

ratedvoltage.

These

components

donot

obeyQ

DC

V!

The

propertiesdepend

stronglyon

thespecific

ceramic

usedas

thedielectric.

These

aredenoted

with

codessuch

asX

5R,w

hichw

asused

forthefigure.T

hecapacitance

may

alsovary

stronglyw

ithtem

perature.T

hesecapacitors

haveother

interestingproperties.

The

dielectricsare

piezoelectric,which

meansthata

mechanicalstressproducesan

electricfield.In

otherwords,the

capacitorgeneratesa

voltageif

youdrop

it.T

hiscan

beputto

gooduse

forenergy

harvestingif

thecapacitor

is

132Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

Figure15.7

Aselection

ofinductors:

axial,toroidal,ferritebeads

andtransform

erkit.

These

arenotto

scaleand

thekiton

therightis

much

largerthanthe

others.

subjecttoregularvibration.O

nthe

otherhand,itwould

behopeless

touse

sucha

capacitorona

wire

carryinga

weak

signal.

15.3Inductors

These

areused

lessfrequently

butare

unavoidablein

power

suppliesand

forkeeping

high-frequency

noiseoutof

circuits.T

heyare

usuallym

adeby

winding

turnsof

wire

ona

coreas

shown

ratherbadly

infigure

15.3(c)on

page128.

The

valueof

inductanceL

isgiven

roughlyby

LD

0

r N2A

d(15.3)

where

0 D

4

10

7H

m

1is

theperm

eabilityoffree

space,

r isthe

relativeperm

eabilityofthe

materialofthe

core(unity

forair),N

isthe

numberofturns,

Ais

thecross-sectionalarea

ofthecore

andd

isthe

lengthofthe

coil.The

valuesrange

fromµH

forhigh-frequencychokes

toH

forlargeinductors

inlow

-frequencypow

ersupplies.Figure15.7

shows

some

examples.

The

corem

aybe

airfor

smallvalues,ferrite

dustforhigh

frequenciesor

laminations

(thin,insulated

layers)ofsoftironforlow

frequencies.The

corem

ustbean

insulatortoavoid

lossesby

eddycurrent,

which

isw

hylam

inationsor

particlesare

usedrather

thana

solidblock

ofm

aterial(Engineering

Electrom

agnetics2).

The

shapevaries:

inductorsare

oftenaxial

(likeresistors).

Toroidal(doughnut-shaped)

inductorshave

theadvantage

thatm

agneticflux

doesnot

leak.L

ow-frequency

transformers

havelam

inatedcores

made

ofEand

I-shapedstam

pings.The

wire

ofthew

indingm

ustbethick

enoughto

carrythe

specifiedcurrent.

This

wire

hasresistance,w

hichm

akesrealinductors

farfrom

ideal.This

isone

reasonw

hythey

areavoided

where

possible.Ihavedraw

nthe

simplest

equivalentcircuit

infigure

15.5(b)on

page130.

Really

thereis

capacitanceas

well,

which

causesresonance

–inductors

canbe

nasty.H

owever,they

areessentialforsw

itch-mode

power

suppliesand

detailedrecom

mendations

arem

adein

theapplication

sheetforICs.Follow

themcarefully!

Smallinductors

calledchokes

areused

tosuppress

high-frequencynoise

inm

anysystem

s.O

ftenthe

inductanceis

smallenough

thataferrite

coreor

beadcan

beplaced

aroundthe

wire

ratherthanvice

versa.You

willfind

theseallovercom

putersystems–

onthe

leadto

them

onitorand

USB

cables,forinstance,oftenincorporated

intothe

connector.

Section15.4

Standardvalues

ofcomponents

133

Table15.1

Standardvalues

ofcom

ponents.T

herow

forE

24show

sthe

extravalues

beyondE

12.E

310

2247

E6

1015

2233

4768

E12

1012

1518

2227

3339

4756

6882

E24

1113

1620

2430

3643

5162

7591

Transformers

These

areinductors

with

two

ormore

windings

asIm

entionedin

section11.1

onpage

90.They

areused

tochange

thevoltage

forA

Cand

forisolation.

Obviously

bothfeatures

areused

inpow

ersupplies.Criticalspecifications

arethe

voltageson

primary

andsecondary

andthe

power

thatcanbe

transferred,measured

inV

A.(W

hynotw

atts?T

hedifference

ispartly

toem

phasizethatthe

tranformertransm

itsthis

powerratherthan

dissipatingit,and

partlybecause

thecurrent

andvoltage

may

notbein

phase.You’llencounterthe

issuesin

PowerE

ngineering3.)

Isolationtransform

ersare

widely

usedin

networks

toprotectthe

systemin

caseof

faults.T

hisincludes

ethernetandthe

publictelephone

system;specialized

devicesare

availableforeach

application.Y

oum

ayoccasionally

encounteradjustable

transformers,often

calledV

ariacs.U

suallythe

secondary‘w

inding’is

justatap

(aninterm

ediateconnection)

onthe

primary

winding,w

hichm

eansthatthey

donotprovide

isolation.T

hisarrangem

entiscalled

anautotransform

er(fig-

ure11.1

onpage

91)and

savesw

ire.Fixed

autotransformers

arew

idelyused

forconverting

230V

to110

Vorvice

versa.

15.4S

tandardvalues

ofcomponents

Com

ponentscome

ina

restrictedrange

ofvalues.Thisisparticularly

trueforcapacitorsbecause

theycover

sucha

wide

rangeand

come

inso

many

varieties.T

hestandard

valuesare

givenin

table15.1

andm

aybe

multiplied

bya

powerof10.T

hereason

fortheapparently

strangechoice

ofnum

bersis

thattheygive

roughlyequalratios

between

values.(In

otherw

ords,theirloga-

rithms

areequally

spaced.)R

esistorsare

readilyobtainable

inE

12and

E24

values,sometim

esm

ore.M

anycapacitors

areavailable

onlyin

E3

values,oftenE

6butonly

afew

typesoffer

aw

iderchoiceofvalues.

15.5H

eatsinksT

heheatgenerated

inany

componentm

ustbedissipated

topreventthe

componentgetting

toohot.H

eatisdissipated

by

radiation

convection

tothe

airsurroundingthe

device

conduction

toanother

body,either

aheatsink

orthe

PCB

tow

hichthe

component

ism

ounted

134Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

V1

V2

I =V

1 -V

2

R

T1

T2

P =

T1 -

T2

q

(b) Heat flow

, P [W

](a) C

harge flow, I [A

]

Figure15.8

Flowof

chargethrough

anelectrical

resistanceR

compared

with

flowof

heatthrough

atherm

alresistance.

The

smallsize

ofmostcom

ponentsm

eansthatspecialm

easureshave

tobe

takento

remove

theheatif

thepow

erdissipation

isabove

about14

W.

The

mostcom

mon

problemarises

inpow

ertransistors,as

inthe

seriesregulator.

The

temperature

limitfor

thesem

iconductorjunction

istypically

125–150°C.T

heheat

generatedflow

sfrom

thesem

iconductorto

thecase

andthen

tothe

surroundingair.

This

flowis

limited

bythe

thermal

resistance

(ghastlynotation

butstandard),m

easuredin

unitsof°C

/Wor°C

W

1.The

flowofheatin

watts

(P)depends

onthe

temperature

differenceand

thetherm

alresistance,sothat

PD

.T1

T2 /=

or

.T1

T2 /D

P.

This

isjustlike

Ohm

’slaw

,ID

.V1

V2 /=

Ror

.V1

V2 /D

IR

,andthe

same

rulesapply

forcom

biningresistances.Figure

15.8illustrates

theanalogy.

Ifthe

ambienttem

perature(thatof

thesurroundings)

isT

a ,thejunction

temperature

isT

jand

thecase

temperature

isT

c ,thenT

j DT

a CP

.jc C

ca /

where

jc

isthe

resistancebetw

eenjunction

andcase

and

cais

theresistance

between

caseand

thesurrounding

air.T

hetw

oresistances

arein

seriesand

thereforeadd,as

shown

infigure

15.9.L

et

jc D1:5°C

=Wand

ca D

100°C

=W,

which

aretypical

valuesfor

asm

alldevice.

Todissipate

20W

with

anam

bienttemperature

of40°C

would

givea

junctiontem

peratureof

40C

20.1

:5C100/D

2070°C

.T

hedevice

would

notlastlong!(N

orm

ightyoureyes

ifyou

were

notwearing

safetygoggles.)

The

valueof

ca

canbe

reducedby

attachinga

heatsink.

This

isa

pieceof

metal

thatim

provesthe

transferof

heatfromthe

deviceto

theair.

Figure15.10

onthe

nextpageshow

sa

coupleofexam

ples.Som

etimes

thecase

oftheequipm

entcanbe

used;powertransistors

areoften

mounted

ona

metalrearpanel.

Ta

Tc

qjc

qca

casejunction

ambient

ambient

case

junction

Tj

Tj

Tc

Ta

qjc

qca

[b]

Figure15.9

Flowof

heatoutofa

transistorfrom

thejunction

tothe

case,with

resistance

jc ,and

fromthe

caseto

theam

bient,with

resistance

ca .T

hisis

likecurrentthrough

resistorsin

series.

Section15.5

Heatsinks

135

Figure15.10

Heatsinks

with

thermalresistances

of50°C/W

and0.4°C

/W.

When

aheatsink

isattached,

ca

forthe

nakeddevice

isreplaced

bythe

valuefor

theheat

sink,

hs .T

hisis

illustratedin

figure15.11

onthe

following

page.D

onotadd

theresistance

ofthe

heatsinkto

ca

orthe

resistancew

illgoup,notdow

n!A

thirdresistance

isoften

addedto

modelthe

flowfrom

thecase

tothe

heatsink,

ch ,butI’llassume

thatthishas

beenincluded

in

hs .Com

mon

heatsinkshave

valuesof

hs ranging

from50°C

/Wfora

smallheatsink

tobelow

1°C/W

fora

largeone.

Ifa

simple

heatsink

isnot

sufficientthen

thecom

ponentm

ayhave

toforce

cooledw

itha

fanto

blowair

acrossit,as

inm

ostPCs.

Liquid

coolingis

requiredin

extreme

cases,oftenbecause

ofinsufficientspaceforairto

flow.

Supposethat

thedevice

inthe

example

abovew

erem

ountedon

aheat

sinkw

ith

ca D4°C

=W.T

henT

j D40C

20.1

:5C4/D

150°C

,which

isjustperm

issible.Itmightnotbe

goodforreliability,though,so

alargerheatsink

(smaller

ca )w

ouldbe

preferable.O

ftenthe

metal

caseor

tabon

thepackage

ofa

transistor,w

hichis

usedto

boltit

tothe

heatsink,isalso

connectedto

oneofthe

terminals

ofthetransistoritself–

usuallythe

drainor

collector,becausethis

isw

herem

ostenergyis

dissipated.A

ninsulating

washer

mustbe

usedbetw

eenthe

transistorandheatsink

ifthisconnection

would

causea

shortcircuit.Surface-m

ountdevices

(section15.7)

areoften

designedto

usean

areaof

copperon

theprinted

circuitboardas

theirheat-sink.

The

datasheetshow

sthe

shaperequired

tocarry

away

theheat.

Forexam

ple,inthe

projectw

em

ayuse

theFairchild

FDS9926A

dualn-M

OSFE

T,w

hichsom

esin

aSO

IC-8

package.Its

datasheet

shows

threeexam

plesof

PCB

layoutw

ithdifferenttherm

alresistance,reproducedin

figure15.12

onthe

nextpage.A

catchis

thattheserequire

‘2oz

copper’,which

isthickerthan

usual(typically1

oz).Many

surface-mountdevices

havelarge

padsunderthe

middle

ofthepackage

toprovide

goodtherm

alcontacttothe

heatsinkon

thePC

B.T

hisw

orksw

ellbutsuchpackages

arealm

ostimpossible

toassem

bleby

hand.

Power

dissipationderating

curveSom

em

anufacturersspecify

thevalue

of

jcbut

itis

alsocom

mon

togive

aderating

curveinstead.

This

specifiesthe

power

dissipationas

afunction

ofcase

temperature

(notam

bienttem

perature).Figure

15.13on

page137

shows

anexam

ple.A

lternativelythe

datais

givenin

theform

ofanequivalentstatem

ent:

136Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

Ta

Tc

case

junction

heat sink

Tj

Tj

Tc

Ta

qjc

qhs

[b!]

Figure15.11

Flowof

heatoutofa

transistorfrom

thejunction

tothe

case,with

resistance

jc ,and

fromthe

caseto

aheatsink

with

resistance

hs .

Totaldissipation

at25°Ccase

temperature

=3

W.

D

erateat20

mW

/°Cforhighertem

peratures.

Toconvertthis

information

toa

thermalresistance,go

backto

thegeneralequation

forheatflowbetw

eenthe

junctionand

ambientfora

baredevice,

PD

Tj

Tc

jc

(15.4)

The

maxim

umpow

erdissipation

occursw

henthe

junctionreaches

itsm

aximum

temperature,

soP

max D

Tj;m

ax T

c

jc

DT

j;max

jc

T

c

jc

(15.5)

Ifthis

isconsidered

asa

functionP

max .T

c /,it

isa

straightline

with

slope1=

jc ,w

hichis

negative.This

isthe

same

asthe

deratingfigure

apartfromthe

sign.Turningthe

expressionfor

theslope

around,thetherm

alresistanceis

theinverse

ofthenegative

slopeofthe

graph.In

thisexam

plethe

permitted

dissipationis

3W

ata

casetem

peratureof

25°C,falling

tozero

at175°C.T

hederating

figureis

therefore.3

0/=

.175

25/D

3=1

50D

0:0

2W

=°CD

20

mW

=°C.Taking

thereciprocalgives

atherm

alresistanceof

jc D

.175

25/=

3D50°C

=W.

a)78°/W

when

mounted on a 0.5in

2

pad of 2 oz copper

b)125°/W

when

mounted on a 0.02

in2

pad of 2 ozcopper

c)135°/W

when m

ounted on am

inimum

pad.

Scale 1 : 1 on letter size paper

Figure15.12

Shapeof

copperon

PCB

forFairchild

FDS9926A

dualn-M

OSFE

Tto

obtaindifferentvalues

ofthermalresistance,taken

fromthe

datasheet.

Section15.6

Printed

circuitboards137

power / W

3025

175case tem

perature / °C

Figure15.13

Atypical

deratingcurve

fora

small

power

transistor,show

ingthe

maxim

umperm

itteddissipation

asa

functionofthe

temperature

ofthecase.

These

calculationsare

allfora

steadystate.

The

heatsinkcan

betreated

asa

capacitorfor

briefpulses

ofpow

erand

theheatflow

shouldbe

analysedin

thesam

ew

ayas

anR

Ccircuit.

SeePow

erElectronics

2.H

ereare

some

approximate

expressionsforthe

powerdissipated

incom

mon

components.

Field-effecttransistor:

Vds

Id .

B

ipolartransistor:V

ce I

c .

Z

enerdiode:V

Z I

Z .

L

inearregulator:.V

in V

out /I

out .

Of

courseyou

haveto

analysethe

circuitto

findthe

voltagesand

currentsneeded

forthese

expressions.

15.6P

rintedcircuitboards

Most

circuitsare

builton

printedcircuit

boardsor

PCB

s.O

thersystem

s,such

asstripboard

(veroboard)aresom

etimes

usedforconstructing

prototypes,butthesecan

bem

oretrouble

thanthey

arew

orth.(Butbreadboards

areeven

worse!)

Electricalconnections

between

components

areprovided

bycopper

trackson

thePC

B.T

hisis

calledetch

inPC

BD

esignerbecause

ofa

comm

onm

anufacturingprocess.

1.T

heboard

startsw

itha

complete

layerofcoppercoatedw

itha

light-sensitivelayercalled

photoresist.

2.T

heboard

isexposed

tolightthrough

am

askthatcovers

thearea

where

thecoppershould

remain.

3.A

developingsolution

removes

theexposed

photoresist,revealingthe

copperunderneath.

4.T

heboard

isplaced

inan

etchingsolution,

traditionallyferric

chloride(FeC

l3 )w

itha

littlehydrochloric

acid,which

stripsthe

exposedcopperto

leaveonly

thedesired

regions.

138Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

Double-sided

boardsare

made

inm

uchthe

same

way

with

two

exposuresbutm

orecom

plicatedprocesses

areneeded

tom

akeboards

with

internallayers.A

furtherstep

isalso

neededto

addplating

throughthe

holesin

mostcom

mercialboards.

Read

Maxfield’s

book[9]to

learnm

ore.B

oardsproduced

inthe

departmentdo

nothaveplated-through

holes,sovias

mustbe

installedby

solderingw

iresthrough

thehole.

Inthe

distantpastthelayoutw

asdone

byhand

andphotoreduced

ontothe

board.N

owthe

layoutisdone

byC

AD

tools,asyou

know.

Severallayersm

ustbespecified

inaddition

tothe

tracksthem

selves.

Silkscreen

–m

ainlytext

tohelp

theuser

ofthe

board,particularly

bythe

connectors;often

onlyon

thetop

A

ssembly

outlines–

identifieseach

componentforassem

bly

Solder

mask

–restricts

soldertojoints

andprevents

itspreadingoverallcoppered

areas

Solder

paste–

neededto

attachsurface-m

ountcomponents

Afurtherdrillfile

specifiesthe

coordinatesand

diameters

ofholes

form

ountingcom

ponentsand

theboard

itself.A

tthe

endyou

normally

senda

setof

filesthat

specifyall

thelayers

anddrillholes

toa

manufacturer.

These

arecom

monly

calledG

erbersaftera

comm

onform

at.Prototype

boardscan

bem

adefor

lessthan

£25and

thecost

fallsrapidly

with

quantity.T

hem

anufacturingprocess

inthe

department’s

electronicw

orkshopis

more

basic.Y

oum

ustprintthe

masks

forthetop

andbottom

oftheboard,there

isno

silkscreen.Holes

aredrilled

byhand

forone-offboardsbutan

automatic

drillisused

forproductionruns.

The

conductingtracks

arem

adeofcopper,w

hosethickness

isspecified

inounces

persquarefoot(sorry

–the

USA

dominates).T

hethicknessof‘1

oz’copperisabout35µm

,which

isusefulto

calculatethe

resistanceofa

track.T

hem

aterialofthe

boarditself

musthave

goodelectricalproperties

(insulatorand

dielec-tric),be

mechanically

strongand

heat-resistant.M

ostprofessionalboardsare

made

ofa

greenfibreglass–epoxy

laminate

calledFR

-4.T

hedepartm

entuses

acheaper,

lightbrow

nm

aterialforless

demanding

applications,designatedFR

-16.The

‘FR’stands

for‘fireresistance’,w

hichseem

sa

curiousw

ayto

classifyPC

Bs.

Boards

arem

adew

ithdifferentnum

bersoflayers,as

yousaw

inthe

laboratory.

Single

layer–

adequateforsim

pledesigns

butrapidlybecom

ehard

toroute.

D

oublelayer

–w

idelyused

forless

demanding

applications;much

easierto

routethan

singlelayer.T

hedepartm

entcanproduce

singleand

double-sidedboards.

Fourlayer

–typically

thesignalsrun

onthe

outertwo

layerswhile

theinneronesare

usedforpow

erandground

planes.T

hisgives

much

betterelectricalperformance.

The

planesgive

lowim

pedanceand

helpto

screensignals

inthe

tracksfrom

oneanother(you’lllearn

aboutthisin

Electrom

agneticC

ompatibility

3).Itiseasy

toprobe

theboard

ifthesignals

areon

theoutside.

Six

layer–

usuallyhave

signalson

theoutsides,then

powerand

groundplanes,w

ithtw

ofurther

layersof

signalsin

them

iddle.T

hem

iddlelayers

areparticularly

wellscreened

buthardto

probe,sotestpoints

mustbe

added.

Section15.7

Com

ponentpackages139

103

PCB

Pad

Com

ponent

Plated-through

hole

Top

Bottom

Tw

o free vias

Connector

covers topof joint

Wire soldered top and bottom

Via form

ed by pin of com

ponent soldered top and bottom

No connection

between top and bottom

Cannotsolderto top

Figure15.14

Cross-section

ofa

double-sidedprinted

circuitboard

(PCB

)show

ingfree

viasform

edby

aplated-through

holeand

aw

irethrough

anon-plated

holesoldered

topand

bottom.

Avia

canalso

beform

edusing

apin-through-hole

componentbutnotata

connectorbecauseit

coversthe

toppad.

E

ightlayersorm

ore–

complicated!

(And

expensive.)

Ina

comm

erciallyproduced,

multi-layer

boardthe

copperplating

extendsthrough

theholes,

joiningthe

padson

thetw

osides

oftheboard.A

plated-throughhole

thatisused

purelyto

move

atrack

fromone

sideof

theboard

tothe

otheris

calleda

via.See

thesketch

infigure

15.14.U

nfortunatelyw

ecannot

produceplated-through

holesin

thedepartm

ent,w

hichis

why

youhad

toinsertw

iresforvias

andsoldersom

ecom

ponentstop

andbottom

onthe

noveltylights

inE

lectronicE

ngineering1X

.This

isa

nuisance,sotry

toavoid

viasw

henyou

layoutyour

own

PCB

s.If

viasare

unavoidable,putthemsom

ewhere

convenient–notunder

components,for

instance.Followthe

tipsin

theinstructions

onPC

BD

esigner.W

hena

PCB

islaid

out,theC

AD

software

needsto

knowthe

widths

oftracks,spacing

oftracks,size

ofvias

andsim

ilarinform

ation.T

heseconstitute

thedesign

rulesand

theinform

a-tion

mustbe

enteredby

handorread

froma

technology(ortech)file

inPC

BD

esigner.Solderused

toconsistofa

lead–tinalloy

butmostlarge-scale

productionm

ustnowuse

lead-free

components

andassem

bly.T

heE

uropeanU

nion’sR

estrictionof

Hazardous

Substances(R

oHS)

legislationhas

outlawed

many

otherchem

icalsthat

were

formerly

usedand

similar

restrictionsare

beingim

posedin

otherpartsofthe

world.W

estilluse

solderthatcontainslead

inthe

laboratorybecause

lead-freesolder

ism

uchharder

touse

inm

anualassem

bly,but

we

expecttobe

forcedto

changein

afew

years.

15.7C

omponentpackages

The

packagesin

which

components

areencapsulated

havechanged

dramatically

inthe

lasttwo

decades.T

hetw

ogeneralstyles

areshow

nin

figure15.15

onthe

following

pagefor

an8-pin

integratedcircuit.

O

ldercom

ponentsare

designedto

bem

ountedon

thetop

ofthe

board(usually).

Their

pinspoke

throughholes

tothe

oppositeside

oftheboard,w

herethey

aresoldered

topads

onthe

tracks.These

arepin-through-hole

orPTH

components.T

hepins

areusually

laidouton

a0:1 00grid,w

hichm

akesthem

easyto

solderbyhand.

140Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

Figure15.15Pin-through-hole

andsurface-m

ount(gullwing)integrated

circuits.Some

surface-m

ountpackageshave

solderpadsunderneath

them,usually

forheatsinks.There

may

alsobe

anadhesive

padto

mountthe

componentuntilithas

beensoldered.

M

ostmodern

components

aredesigned

tobe

mounted

onthe

same

sideof

theboard

astheir

tracks.T

heseare

surface-mountdevices

orSM

Ds.

They

donotneed

holesdrilled

throughthe

boardforpins,w

hichallow

sthe

leadsto

bem

uchclosertogether.

An

increasingnum

berofcomponents

haveno

pinsorleads

atall.They

justhavesolderbum

psorm

etalpadson

theirboundariesto

make

theconnections.T

heseneed

specializedassem

bly.T

hestandard

packagesforalmostallcom

ponentsarenow

surface-mount,w

iththe

exceptionof

largeitem

ssuch

assockets

thatneedthe

securityof

pinsthrough

theboard.

Unfortunately

therange

ofsurface-m

ountpackages

isvast

soI

haveprovided

aguide

tothe

more

comm

ontypes

ofpackagein

figure15.16

onthe

nextpage.

D

ualinline

package(D

IP)–

sometim

esD

IL,

orPD

IPfor

plasticD

IP.T

hisw

asthe

standardpin-through-hole

packagefor

integratedcircuits

form

anyyears.

Pinsare

0:1 00

apartw

ithrow

sare

separatedby

0:3 00.

Wider

packagesw

ereused

forlarger

ICs

with

many

pinsbutare

nowrare.H

owever,m

odulessuch

asthe

mbed

havethe

same

pinoutsothatthey

canbe

usedeasily

with

veroboardand

breadboards(prototyping

boards).

Sm

alloutlineintegrated

circuit(SOIC

)–

sometim

esjustSO

.These

were

theearliest

surface-mountpackages.T

heirpadsare

0:0

5 00apartwith

rows

about0:2 00apart.Y

oum

ayuse

anopam

por

adualM

OSFE

Tin

aSO

IC-8

packagein

theproject.

They

areone

ofthe

fewtypes

ofSMD

thatisrelatively

easyto

solderbyhand.

T

hinshrink

smalloutline

package(T

SSOP)

–‘thin’

refersto

thevertical

dimension

and‘shrink’

tothe

separationof

thepins.

They

areroughly

twice

asclose

asin

aSO

ICbut

dimensions

were

changingfrom

imperial

tom

etricat

thetim

eso

theseparation

isofficially

0.65m

m.(Itjusthappens

thatthisis

closeto

0:0

25 00.)

Q

uadflat

pack(Q

FP)–

havepins

onall

fouredges,

unlikethe

packagesdescribed

previously.The

pitch(separation

between

centresofpins)isoften0.65

or0.50m

m,w

hichm

akesthem

‘challenging’to

solder.M

icrocontrollerstypically

come

inthese

packages.Plenty

ofvariationsare

offered,suchas

LQ

FPforlow

profileQ

FP.

Q

uadflat-pack

no-lead(Q

FN)–

oneofthe

mostpopularpackages

atpresent.Ithasno

leadsatall,justm

etalpatcheson

theunderside

ofthepackage.M

ostdevicesalso

havea

largecentralpad,typically

usedforground

orasa

heatsink.They

areextrem

elydifficult

tosolderby

handand

thecentralpad

isclose

toim

possible.Pleaseavoid

them.

Section15.7

Com

ponentpackages141

0.1≤ divisions

1206

0805

0603

1 mm

divisions

Resistors andcapacitors

SOT

23-3

SOIC

-8(0.05≤ pitch)

DIP-8

(0.1≤ pitch)

QFN

-16(pads underneath:

no leads)

QFP-32

(0.5 mm

pitch)

QFP-24

(0.65 mm

pitch)

TSSO

P-8(0.65 m

m pitch)

PTH

resistor(0.4≤)

Figure15.16

Outlines

ofa

selectionof

surface-mount

packagesw

itha

conventionalresistor

andD

IP-8IC

forcomparison.

The

suffixon

thesem

iconductorpackagesshow

sthe

numberof

pinsand

thebackground

gridhas

0:1 00spacing.

B

allgridarray

(BG

A)

–no

pins,just

atw

o-dimensional

arrayof

solderballs

onthe

underside.V

italfor

fancydigital

processorsw

ithhundreds

ofpins

butdefinitely

forautom

aticassem

bly.Pingrid

arrayis

similar

butwith

through-holepins

ona

0:1 00grid

andis

nowrare

becausethe

packageis

som

uchlarger.

Plastic

leadedchip

carrier(PL

CC

)–

anearly

SMD

,oftenused

form

icrocontrollers.H

asJ-leads

thatcurl

underthe

bodyrather

thangull-w

ingthat

stickout.

The

pitchis

typically0:0

5 00andspecialsockets

areused.

Sm

alloutlinetransistor

(SOT

)–

many

varieties,ofw

hichSO

T23

isnow

comm

onfor

discretetransistors.Itis

about2

mm

3

mm

.The

packageis

notrestrictedto

transistorsdespite

itsnam

e:O

p-amps

oftencom

ein

SOT

23-5packages,w

hichare

thesam

esize

asSO

T23-3

fortransistorsbutw

ith5

leadsinstead

of3.

Passivecom

ponentsare

availablein

surface-mountpackages

tom

atchsem

iconductorsbutthe

geometry

issim

plebecause

theyhave

onlytw

oleads.

The

sizeis

quotedas

two

double-digitfigures

suchas

1206,which

means

0:1

2 000:0

6 00.T

hisparticular

sizeis

nottooaw

kward

tohandle

butyou

must

notbreathe

tooheavily

onan

0603package

orit

will

flyaw

ay!E

vensm

aller0402packages

arenow

inuse

forportableelectronic

productsw

herea

compactPC

Bis

essential.

142Passive

components,heatsinks

andprinted

circuitboardsC

hapter15

15.8E

xamples

Exam

ple15.1

Whatisthe

maxim

umcontinuousvoltage

thatcansafely

beapplied

toa

120

,quarter-w

attresistor?

Would

thisbe

aproblem

ina

circuitw

itha

5V

supply?W

hatis

them

aximum

safecurrent?

[5.5V,46

mA

]

Exam

ple15.2

Old-fashioned

radiosw

eretuned

with

air-spacedvariable

capacitorsw

itha

maxim

umvalue

ofaround

300pF.

What

totalarea

isrequired,

assuming

thatthe

platesare

0.5m

mapart?

Exam

ple15.3

Atypical

valuefor

adecoupling

capacitorfor

adigital

integratedcircuit

is100

nF.Supposethatthe

ICruns

at10M

Hz.W

hatvalueofequivalentseries

resistance(E

SR)is

neededto

ensurethatthe

capacitordecouples

digitalswitching

noiseeffectively?

Isthis

likelyto

bea

problemin

practice?O

nlya

roughestim

ateis

needed.Whatw

ouldhappen

iftheIC

ranat1

GH

zinstead?

Exam

ple15.4

Acoil

is25

mm

longw

ith25

turnsw

oundon

acore

of5

mm

diameter

andrelative

permeability

1000.E

stimate

itsinductance.

Estim

atealso

itsresistance

assuming

thatthe

wire

iscopperw

ithdiam

eter0.5m

m.

[0.6m

H,0.04

]

Exam

ple15.5

Aperverse

bureaucratdecreesthatthere

shouldbe

only10

standardvalues

ofresistor

perdecade

insteadof

thetraditional12.

Whatshould

theybe?

(Inother

words,w

hatreplaces

thecurrentvalues

of10,12,15,18...?)

Rem

ember

thattheyare

separatedby

equalratios.

Exam

ple15.6

Atransistor

dissipates2

Wand

hasa

thermal

resistanceof

5°C/W

between

junctionand

case.C

alculatethe

junctiontem

peraturew

henthe

ambient

temperature

is50°C

with

aheatsink

ofthermalresistance

(i)50°C/W

and(ii)10°C

/W.

[80°C,160°C

]

Exam

ple15.7

AT

IP120transistoris

requiredto

dissipate40

Win

anam

bienttemperature

of30°C

.Determ

inethe

thermalresistance

oftheheatsink

requiredto

keepthe

junctiontem

peraturebelow

150°C.T

hereis

aninsulating

washer

oftherm

alresistance

0.5°C/W

between

thecase

andthe

heatsink.T

hetransistor

isspecified

fora

dissipationof

65W

below25°C

,deratedat

0.5W

/°Cathighertem

peratures.[0.5°C

/W]

What

sizeof

heatsinkw

ouldbe

neededif

aT

IP3055w

ereused

instead?T

hisis

alarger

transistorwith

am

aximum

dissipationof90

Wderated

at0.7W

/°C.

Exam

ple15.8

Whatis

theresistance

ofa‘typical’track

ona

PCB

?Take

ittobe

20m

mlong,

0.5m

mw

ideand

made

of‘1

oz’copper.

Takethe

resistivityof

copperto

be2

10

8

m.

Whatw

ouldhappen

iftheboard

were

made

with

half-ouncecopperinstead?

[Very

roughly0.02

]

Furtherreading

This

isa

ratherunsystem

aticcollection

ofbooks,

articlesand

applicationnotes

thatm

aybe

usefulforthis

courseand

particularlyin

subsequentprojects.A

llmanufacturers

provideA

p-plication

Notes

tohelp

youuse

(andtherefore

encourageyou

tobuy)

theircom

ponents.B

oththese

andthe

datasheets

containa

wealth

ofinformation.T

hecircuitthatyou

needis

probablyin

oneofthese

documents

unlessyou

aretackling

agenuinely

newproblem

.

Books

[1]B

onnieB

aker.AB

aker’sD

ozen:R

ealAnalog

Solutionsfor

DigitalD

esigners.New

nes,2005.(ISB

N0750678194)

This

isclose

tobeing

the‘book

ofthe

course’for

thefirst

half.It

isaim

edat

digitalengineers

who

needto

handlethe

interfaceto

analogueelectronics.M

uchofthe

bookis

onA

DC

sand

DA

Cs

andtreats

issuessuch

asnoise.T

heauthoris

nowatTexas

Instruments,

havingbeen

formerly

atMicrochip

Technologyand

Burr–B

rown,so

sheknow

sw

hatsheis

writing

about!T

hem

athematics

isoccasionally

alittle

flakyand

sheuses

‘differentiate’w

hereI

would

write

‘subtract’(the

usagecom

esfrom

theterm

‘differentialam

plifier’,w

hichsubtracts

ratherthandifferentiates).

[2]John

H.D

avies.MSP

430M

icrocontrollerB

asics.New

nes,2008.(ISBN

9780750682763)See

userweb.elec.gla.ac.uk/j/jdavies/m

spbookforerrata

anddow

nloads.

Naturally

Irecomm

endm

yow

nbook!

Itcoversa

differentmicrocontrollerbutthe

generalaspects

ofembedded

systems

areequally

applicableto

them

bed.You

mightfind

some

ofthe

materialfam

iliar.

[3]D

Fitzpatrick.Analog

Design

andSim

ulationusing

OrC

AD

Capture

andP

Spice.New

nes,2011.(ISB

N9780080970950)

[4]PaulH

orowitz

andW

infieldH

ill.TheA

rtofElectronics.Second

edition,Cam

bridgeU

ni-versity

Press,1989.(ISBN

0521370957)

No

electronicengineer

shouldbe

withoutthis

book,with

itslucid

coverageof

allaspectsofelectronics.M

anydetails

arenow

outofdatebutthe

principlesare

astrue

asever.T

heonly

problemis

thatitistoo

easyto

read,sothatthe

readertends

tofly

throughthe

texttoo

fasttoabsorb

it!

143

144F

urtherreading

[5]W

altKester(editor),A

nalogD

evices.Data

Conversion

Handbook.N

ewnes,2004.(ISB

N0750678410)

Nearly

1000pages

onall

aspectsof

dataconversion

fromtheir

historyto

thedesign

ofPC

Bs.Itgoes

intothe

theorym

oredeeply

thanB

aker’sbook

butisless

coherentbecauseofits

editednature.T

heauthors

arefrom

Analog

Devices

andthe

examples

aretaken

fromtheirrange

ofproducts.

[6]W

altKester(editor),A

nalogD

evices.Mixed-signaland

DSP

Design

Techniques.New

nes,2002.(ISB

N0750676116)

[7]W

altK

ester(editor),

Analog

Devices.O

pA

mp

Applications

Handbook.N

ewnes,

2004.(ISB

N0750678445)

[8]R

onM

ancini(editor),TexasInstrum

ents.Op

Am

psfor

Everyone.T

hirdedition,N

ewnes,

2009.(ISBN

9780750677011)

Despite

thedifferenttitle,this

coversm

uchthe

same

materialas

Baker’s

bookalthough

thereis

ratherm

oreaboutop-am

ps,asyou

mightexpect.T

hisis

agood

placeto

lookfor

information

onsingle-supply

op-amps.Itsuffers

alittle

fromhaving

aneditorratherthan

singleauthor

butisreasonably

coherent.An

earlierversion

canbe

downloaded

fromthe

TI

web

siteas

applicationnote

SLO

D006b

butitisnearly

500pages

longso

theprinted

versionm

ightbew

orththe

cost.

[9]C

liveM

axfield.B

ebopto

theB

ooleanB

oogie:A

nunconventional

guideto

electronics.T

hirdedition,

New

nes,2009.

(ISBN

9781856175074)See

alsow

ww

.maxm

on.com/booginfo.htm

.

Thisbook

fullylivesup

toitssubtitle:Itisnothing

likea

conventionaltextbookand

coversa

broaderspectrum

ofelectronics

thanyou

would

guessfrom

thetitle.It

startsw

iththe

relationbetw

eenanalog

anddigitalsignals

andthe

main

bodyofthe

bookconcludes

with

usefulmaterialon

components

andconstruction.T

heappendices

coversom

efascinating

topicsfollow

edby

acom

prehensiveglossary

ofterms

comm

onlyused

inelectronics

(andm

anym

orethatare

not).Studycarefully

thesection

onH

owto

become

famous.

[10]K

raigM

itzner.Com

pleteP

CB

Design

usingO

rCA

DC

aptureand

PC

BE

ditor.New

nes,2009.(ISB

N9780750689717)

An

excellentbookon

OrC

AD

PCB

Designer.Itgoes

farbeyond

yourintroduction

atthebeginning

oftheyearand

explainsnum

eroustechniques.H

ighlyrecom

mended.T

heonly

drawback

isthatitconcentrates

onPC

Bs

form

odern,comm

ercialproductionrather

thanourold-fashioned,in-house

process.

[11]John

Watkinson.

TheA

rtof

Digital

Audio.T

hirdedition,

FocalPress,

2000.(ISB

N9780240515878)

An

excellentbookon

many

aspectsofanalogue-to-digitaland

digital-to-analogueconver-

sionw

ithem

phasison

audioapplications

(asyou

would

expectfromthe

title).The

same

authorhas

written

anIntroduction

toD

igitalAudio,

secondedition,

FocalPress,

2002(ISB

N9780240516431).

Further

reading145

[12]R

Toulsonand

TimW

ilmshurst.Fastand

Effective

Em

beddedSystem

sD

esign:A

pplyingthe

AR

Mm

bed.New

nes,2012(ISB

N9780080977683)

[13]Joseph

Yiu.The

Definitive

Guide

toA

RM

Cortex-M

3and

Cortex-M

4P

rocessors.3rdE

di-tion,N

ewnes,2013.(ISB

N9780124080829)

Application

noteson

AD

Cs

andD

AC

s[14]

Nicholas

Gray.A

BC

sofA

DC

s.NationalSem

iconductor,2004.Application

note.

[15]Freescale

(formerly

Motorola)M

68HC

11R

eferenceM

anualMotorola,2002.A

vailableon

thew

ebatw

ww

.freescale.com/files/m

icrocontrollers/doc/ref_manual/M

68HC

11RM

.pdf

Section12

providesa

gooddescription

ofthe

operationof

asuccessive-approxim

ationA

DC

.

[16]T

homas

Kugelstadt.The

operationofthe

SAR

–AD

Cbased

oncharge

redistribution.TexasInstrum

ents,2005.Application

noteSLY

T176.

[17]A

Simple

AD

CC

omparison

Matrix.T

hisleads

intoa

setofmore

detailedapplication

noteson

individualtypesofA

DC

.Maxim

IntegratedProducts,2003.A

pplicationnote

AN

2094.

[18]B

onnieB

aker.Glossary

ofanalog-to-digitalspecificationsand

performance

characteris-tics.Texas

Instruments,2006.A

pplicationreportSB

AA

147.

[19]R

onM

ancini,Texas

Instruments.Sensor

toA

DC

—analog

interfacedesign.A

pplicationnote

slyt173(2000).

Explains

howto

match

thespan

ofa

sensor’soutputvoltage

tothe

inputofan

analog-to-digitalconverter(A

DC

).

Application

Notes

onA

mplifiers

(mostly

single-supply)[20]

Ron

Mancini,Texas

Instruments.Single-supply

opam

pdesign.A

pplicationnote

slyt189(1999).

[21]B

ruceC

arter,TexasInstrum

ents.ASingle-Supply

Op-A

mp

CircuitC

ollection.Application

notesloa058

(2000).

[22]B

ruceC

arter,TexasInstrum

ents.Designing

Gain

andO

ffsetinThirty

Seconds.Applica-

tionnote

sloa097(2002).

[23]K

itchin,C

harles.Avoid

comm

onproblem

sw

hendesigning

amplifier

circuits.A

nalogD

ialogue,volum

e41,

issue08,

pages1–4,

2007A

ugust.A

vailableon

thew

ebat

ww

w.analog.com

/library/analogDialogue/archives/41-08/am

plifier_circuits.pdf

This

isan

excellentandconcise

summ

aryof

comm

onproblem

s,much

ofw

hichapplies

tosingle-supply

circuits.There

isan

earlierarticleon

Dem

ystifyingsingle-supply

op-amp

designin

Electronic

Design

New

s,2002M

arch21,pages

83–90.

146F

urtherreading

[24]R

onM

ancini,Texas

Instruments.

How

toread

asem

iconductordata

sheet.E

lectronicD

esignN

ews,2005

April14.w

ww

.edn.com/article/C

A514964.htm

l.

This

focusseson

op-amps

butthe

principlesare

more

general–

designingfor

thew

orstcase

ofeachparam

eter,forinstance.

Application

Notes

onPow

erS

upplies[25]

National

Semiconductor.

Introductionto

Power

Supplies.A

pplicationN

oteA

N-556

(2002).

[26]C

hesterSim

pson,NationalSem

iconductor.LinearR

egulators:Theory

ofOperation

andC

ompensation.A

pplicationN

oteA

N-1148

(2000).

Com

ponents[27]

Ron

Mancini,Texas

Instruments.U

nderstandingbasic

analog–

passivedevices.A

pplica-tion

reportSLO

A027

[28]R

onM

ancini,TexasInstrum

ents.Understanding

basicanalog

–active

devices.Applica-

tionreportSL

OA

026A

[29]G

lennM

orita,Analog

Devices.Low

dropoutregulators—W

hythe

choiceofbypass

capac-itor

matters.A

nalogD

ialogue45–01

Back

Burner,January

2011.

Magazines

andarticles

[30]C

ircuitCellar

isam

onthlyelectronicsm

agazine.ItssubtitleisThe

magazine

forcom

puterapplications

butthecom

putersare

almostalw

aysem

beddedratherthan

ona

desktop.Itispublished

inthe

USA

andthe

postagem

akesthe

printedversion

expensivein

Britain

butthe

onlineedition

atww

w.circuitcellar.com

isaffordable.A

goodread.

Data

sheetsprovided

Ihave

attacheda

selectionof

datasheets

asexam

plesof

therange

ofcom

ponentsavailable.

Most

areonly

extractsto

savepaper.

Dow

nloadthe

fullsheet

fromthe

manufacturer’s

web

siteif

youneed

it;the

onlineversion

ofthese

notescontains

hyperlinksto

thecom

ponentsor

documentitself.

[31]A

nalogD

evicesA

D7788,a

16-bitsigma–delta

AD

C.

[32]ST

Microelectronics

TS951

low-pow

erop-amp.

[33]Texas

Instruments

RE

F29xxvoltage

reference.

[34]E

nergizeralkaline–manganese

dioxideL

R03

cell(2012).

[35]E

nergizerCR

2032lithium

coincell(2009).

[36]C

omparison

ofbattery

chemistries

fromB

uchmann

batteryuniversity

(mainly

onsec-

ondarycells),w

ww

.batteryuniversity.com(2005).

[37]D

uracellnickel–metalhydride

rechargablecells

(1997).

[38]Panasonic

Li-ion

CG

R18650E

cell(2007).

[39]N

ationalSemiconductorL

M2931

low-dropoutregulator(2006).

[40]N

ationalSemiconductorL

M3100

bucksw

itchingregulator(2006).

[41]N

ationalSemiconductor

LP5526

lightingm

anagementunitw

ithhigh

voltageboostcon-

verter(2006).

147

Low Power, 16-/24-Bit,Sigm

a-Delta ADCs

AD7788/AD7789

Rev. B

Inform

ation furnished by Analog D

evices is believed to be accurate and reliable. How

ever, no responsibility is assum

ed by Analog D

evices for its use, nor for any infringements of patents or other

rights of third parties that may result from

its use. Specifications subject to change without notice. N

o license is granted by im

plication or otherwise under any patent or patent rights of A

nalog Devices.

Trademarks and registered tradem

arks are the property of their respective owners.

O

ne Tech

no

log

y Way, P

.O. B

ox 9106, N

orw

oo

d, M

A 02062-9106, U

.S.A.

Tel: 781.329.4700 w

ww

.analo

g.com

Fax: 781.461.3113

©2006 A

nalo

g D

evices, Inc. A

ll righ

ts reserved.

FEATU

RES

AD

7788: 16-bit reso

lutio

n

AD

7789: 24-bit reso

lutio

n

Power

Sup

ply: 2.5 V

to 5.25 V

op

eration

N

orm

al: 75 µA

maxim

um

Pow

er-do

wn

: 1 µA

maxim

um

R

MS n

oise: 1.5 µ

V

AD

7788: 16-bit p

-p reso

lutio

n

AD

7789: 19-bit p

-p reso

lutio

n (21.5 b

its effective) In

tegral n

on

linearity: 3.5 p

pm

typical

Simu

ltaneo

us 50 H

z and

60 Hz rejectio

n

Intern

al clock o

scillator

VD

D mo

nito

r chan

nel

10-lead M

SOP

INTER

FAC

E 3-w

ire serial SP

I®-, QSP

I™-, M

ICR

OW

IRE™

-, and

DSP

-com

patib

le Sch

mitt trig

ger o

n SC

LK

AP

PLIC

ATIO

NS

Smart tran

smitters

Battery ap

plicatio

ns

Portab

le instru

men

tation

Sen

sor m

easurem

ent

Temp

erature m

easurem

ent

Pressure m

easurem

ent

Weig

h scales

4 to 20 m

A lo

op

s

FUN

CTIO

NA

L BLO

CK

DIA

GR

AM

03539-001

SERIA

LIN

TERFA

CE

AN

DC

ON

TRO

LLO

GIC

CLO

CK

*AD

7788: 16-BIT A

DC

AD

7789: 24-BIT A

DC

AIN

(+)

AIN

(–)

GN

D

-A

DC

*

AD

7788/A

D7789

REFIN

(+)R

EFIN(–)

VD

D

DO

UT/R

DY

DIN

SCLK

CS

Figure 1.

GEN

ERA

L DESC

RIP

TION

Th

e AD

77

88

/AD

77

89

are low

po

wer, lo

w n

oise, an

alog fro

nt

end

s for lo

w freq

uen

cy measu

remen

t app

lication

s. Th

e AD

77

89

con

tains a lo

w n

oise, 2

4-b

it, ∑-∆

AD

C w

ith o

ne d

ifferential

inp

ut. T

he A

D7

78

8 is a 1

6-b

it version

of th

e AD

77

89

.

Th

e devices o

perate fro

m an

intern

al clock

. Th

erefore, th

e

user d

oes n

ot h

ave to su

pp

ly a clock

sou

rce to th

e devices.

Th

e ou

tpu

t data rate is 1

6.6

Hz, w

hich

gives sim

ultan

eou

s

50

Hz/6

0 H

z rejection

.

Th

e parts o

perate w

ith a sin

gle p

ow

er sup

ply fro

m 2

.5 V

to

5.2

5 V

. Wh

en o

peratin

g from

a 3 V

sup

ply, th

e po

wer d

issi-

patio

n fo

r the p

art is 22

5 µ

W m

axim

um

. Th

e AD

77

88

/AD

77

89

are available in

a 10

-lead M

SO

P.

AD7788/AD7789

Rev. B | Page 3 of 20

SPECIFICATIONS A

D7789

VD

D = 2

.5 V

to 5

.25

V; R

EF

IN(+

) = 2

.5 V

; RE

FIN

(−) =

GN

D; G

ND

= 0

V; all sp

ecification

s TM

IN to T

MA

X , un

less oth

erwise n

oted

.

Table 1.

Parameter

1 A

D7789B

U

nit

Test Con

ditio

ns/Co

mm

ents

AD

C C

HA

NN

EL SPECIFIC

ATION

Outp

ut Up

date Rate 16.6

Hz nom

AD

C C

HA

NN

EL

No M

issing Codes

224

Bits min

Resolution

19 Bits p

-p

O

utput N

oise 1.5

µV rms typ

Integral Nonlinearity

±15

pp

m of FSR m

ax

Offset Error

±3

µV typ

O

ffset Error Drift vs. Tem

perature

±10

nV/°C typ

Full-Scale Error3

±10

µV typ

G

ain Drift vs. Tem

perature

±0.5

pp

m/°C

typ

Pow

er Supp

ly Rejection 90

dB min

100 dB typ, AIN

= 1 V

AN

ALO

G IN

PUTS

D

ifferential Input Voltage Ranges

±REFIN

V nom

REFIN

= REFIN

(+) −

REFIN(−

) A

bsolute A

IN Voltage Lim

its2

GN

D −

30 mV

V min

VD

D + 30 m

V V m

ax

Analog Inp

ut Current

Input current varies w

ith input voltage

Average Inp

ut Current 2

±400

nA/V typ

Average Inp

ut Current D

rift ±

50 p

A/V/°C

typ

N

ormal-M

ode Rejection2

@

50 Hz, 60 H

z 65

dB min

50 Hz ±

1 Hz, 60 H

z ± 1 H

z C

omm

on-Mode Rejection

AIN

= 1 V

@ D

C

90 dB m

in 100 dB typ

@

50 Hz, 60 H

z2

100 dB m

in 50 H

z ± 1 H

z, 60 Hz ±

1 Hz

REFERENC

E INPU

T

REFIN Voltage

2.5 V nom

REFIN

= REFIN

(+) −

REFIN(−

) Reference Voltage Range

20.1

V min

VD

D V m

ax

Ab

solute REFIN Voltage Lim

its2

GN

D −

30 mV

V min

VD

D + 30 m

V V m

ax

Average Reference Inp

ut Current

0.5 µA

/V typ

A

verage Reference Input C

urrent Drift

±0.03

nA/V/°C

typ

N

ormal-M

ode Rejection2

@

50 Hz, 60 H

z 65

dB min

50 Hz ±

1 Hz, 60 H

z ± 1 H

z C

omm

on-Mode Rejection

AIN

= 1 V

@ D

C

110 dB typ

@ 50 H

z, 60 Hz

110 dB typ

50 H

z ± 1 H

z, 60 Hz ±

1 Hz

1 Temp

erature range: −40°C

to +105°C

. 2 Sp

ecification is not production tested b

ut is supp

orted by characterization d

ata at initial prod

uct release. 3 Full-scale error ap

plies to b

oth positive and negative full scale and ap

plies at the factory calib

ration conditions (VD

D = 4 V).

AD7788/AD7789

Rev. B | Page 9 of 20

PIN CONFIGURATION AND FUNCTION DESCRIPTIONS

03539-005

AD

7788/A

D7789

TOP VIEW

(Not to Scale)

SCLK

1

CS

2

AIN

(+)3

AIN

(–)4

REFIN

(+)5

DIN

DO

UT/R

DY

VD

D

GN

DR

EFIN(–)

109876

Figure 5. Pin Configuration

Table 6. Pin Function D

escriptions Pin

No.

Mn

emo

nic

Descrip

tion

1

SCLK

Serial Clock Inp

ut for Data Transfers to and from

the AD

C. The SC

LK has a Schmitt-triggered inp

ut, making the

interface suitable for op

to-isolated app

lications. The serial clock can be continuous, w

ith all data transm

itted in a continuous train of p

ulses. Alternatively, it can b

e a noncontinuous clock with the inform

ation being trans-

mitted to or from

the AD

C in sm

aller batches of data.

2 C

SC

hip Select Inp

ut. This is an active low logic inp

ut used to select the AD

C. C

S can be used to select the A

DC

in system

s with m

ore than one device on the serial bus or as a fram

e synchronization signal in comm

unicating w

ith the device. CS can b

e hardwired low

, allowing

the AD

C to op

erate in 3-wire m

ode with SC

LK, DIN

, and D

OU

T/RDY used to interface w

ith the device.

3 A

IN(+

) A

nalog Input. A

IN(+

) is the positive term

inal of the fully differential analog input.

4 A

IN(−

) A

nalog Input. A

IN(–) is the negative term

inal of the fully differential analog input.

5 REFIN

(+)

Positive Reference Input. REFIN

(+) can lie anyw

here betw

een VD

D and GN

D +

0.1 V. The nominal reference

voltage (REFIN(+

) − REFIN

(−)) is 2.5 V, b

ut the part functions w

ith a reference from 0.1 V to V

DD .

6 REFIN

(−)

Negative Reference Inp

ut. This reference input can lie anyw

here betw

een GN

D and V

DD −

0.1 V. 7

GN

D

Ground Reference Point.

8 V

DD

Supp

ly Voltage. 3 V or 5 V nominal.

9 D

OU

T/RDY

The DO

UT/RD

Y falling edge can be used as an interrup

t to a processor, indicating that valid data is availab

le. W

ith an external serial clock, the data can be read using the D

OU

T/ RDY p

in. With C

S low, the data/control w

ord

information is p

laced on the DO

UT/RD

Y pin on the SC

LK falling edge and is valid on the SCLK rising edge.

The end of a conversion is also indicated by the RDY b

it in the status register. When C

S is high, the DO

UT/RD

Y p

in is three-stated, but the RD

Y bit rem

ains active.

10 D

IN

Serial Data Inp

ut to the Input Shift Register on the A

DC

. Data in this shift register is transferred to the control

registers within the A

DC

; the register selection bits of the com

munications register identify the ap

prop

riate register.

AD7788/AD7789

Rev. B | Page 10 of 20

TYPICAL PERFORMANCE CHARACTERISTICS

03539-007

–120

–110

–100

–90

–80

–70

–60

–50

–40

–30

–20

–10

040

8020

60100

120140

dB

160

0

FREQ

UEN

CY (H

z)

Figure 6. Frequency Response with 16.6 H

z Update Rate

03539-008

0 10 20 30 40 50 60 70

8388591

OCCURENCE

8388625C

OD

E

VD

D = 3VV

REF = 2.048V

TA = 25°C

RM

S NO

ISE = 1.25µV

Figure 7. AD

7789 Noise H

istogram

03539-009

83885910

200400

600800

CODE

1000

8388625

REA

D N

O.

VD

D = 3V, VR

EF = 2.048V,T

A = 25°C, R

MS N

OISE = 1.25µV

Figure 8. A

D7789 N

oise Plot

03539-013

0

0.5

1.0

1.5

00.5

1.01.5

2.02.5

3.03.5

4.04.5

RMS NOISE (µV)

5.0

3.0

2.5

2.0

VR

EF (V)

VD

D = 5VU

PDA

TE RA

TE = 16.6Hz

TA = 25°C

Figure 9. AD

7788/AD

7789 Noise vs. V

REF

Rev 3

July 20051/16

16

TS

951-TS

952-TS

954

Input/Output R

ail-to-Rail Low

Pow

er Operational A

mplifier

R

ail-to

-rail input com

mon-m

ode voltage range

R

ail-to

-rail outp

ut voltage swing

O

perating from 2.7

V to

12V

H

igh-speed (3MH

z, 1V/µ

s)

Lo

w consum

ption (0.9mA

@ 3V

)

S

upply voltage rejection ratio: 80d

B

La

tch-up imm

unity

A

vailable in SO

T2

3-5 micropackage

Descrip

tion

The

TS

95x

family

are

rail-to

-rail B

iCM

OS

operationa

l am

plifiers

optim

ized and

fullyspecified

for 3V and 5V

operation.

The T

S95

1 is housed in the sp

ace-saving 5 pinsS

OT

23

packag

e that

make

s it

well

suited

for

battery-pow

ered system

s. T

his m

icropackage

simplifies the P

C boa

rd design b

ecause of it’sab

ility to

be p

laced in

tight spaces

(outsid

edim

ensions a

re: 2.8m

m x 2.9m

m)

Ap

plicatio

ns

S

et-top boxes

La

ptop/no

tebook com

puters

T

ransform

er/line drivers

P

ersonal entertainm

ents (CD

players)

P

ortable comm

unication (cell phones, pa

gers)

Instrum

entation & sensoring

D

igital to analog conve

rter buffers

P

ortable headphone speaker drivers

TS

951ILT

TS

951ID

TS

952IN-T

S952ID

-TS

952IP

T

TS

954IN

-TS

954ID-T

S954IP

T

ww

w.st.com

TS

951-TS

952-TS

954A

bso

lute M

aximu

m R

ating

s

3/16

1 A

bso

lute M

aximu

m R

ating

s

Table 1.

Key p

arameters an

d th

eir abso

lute m

aximu

m ratin

gs

Table 2.

Op

erating

con

ditio

ns

Sym

bo

lP

arameter

Value

Un

it

VC

CS

upply voltage (1)

1.A

ll voltage values, except differential voltage are with respect to netw

ork ground terminal.

14V

Vid

Differential Input V

oltage (2)

2.D

ifferential voltages are the non-inverting input terminal w

ith respect to the inverting input terminal. If V

id > ±1V,

the maxim

um input current m

ust not exceed ±1m

A. In this case (V

id > ±1V) an input serie resistor m

ust be added to lim

it input current.

±1

V

Vin

Input Voltage (3)

3.D

o not exceed 14V.

VD

D-0.3 to V

CC

+0.3

V

Tstg

Storage Tem

perature Range

-65 to +150

Tj

Maxim

um Junction Tem

perature150

°C

Rthja

Therm

al Resistance Junction to A

mbient (4)

SO

T23-5

SO

8S

O14

TS

SO

P8

TS

SO

P14

4.S

hort-circuits can cause excessive heating and destructive dissipation.

250125103120100

°C/W

ES

D

HB

M: H

uman B

ody Model (5)

TS

951T

S952

TS

954

5.H

uman body m

odel, 100pF discharged through a 1.5kΩ

resistor into pin of device. 123

kV

MM

: Machine M

odel (6)

6.M

achine model E

SD

, a 200pF cap is charged to the specified voltage, then discharged directly into the IC

with

no external series resistor (internal resistor < 5Ω

), into pin to pin of device.

100V

CD

M: C

harged Device M

odel1.5

kV

Latch-up Imm

unity200

mA

Lead Temperature (soldering, 10sec)

260°C

Sym

bo

lP

arameter

Valu

eU

nit

VC

CS

upply voltage2.7 to 12

V

Vicm

Com

mon M

ode Input Voltage R

angeV

DD -0.2 to V

CC +

0.2V

Toper

Operating Free A

ir Temperature R

ange-40 to +

125°C

Electrical C

haracteristics

TS

951-TS

952-TS

954

4/16

2 E

lectrical Ch

aracteristics

Table 3.

VC

C = +3V, VD

D = 0V, R

L con

nected

to V

cc /2, Tam

b = 25°C (u

nless o

therw

ise sp

ecified)

Sym

bo

lP

arameter

Min

.Typ

.M

ax.U

nit

Vio

Input Offset V

oltage T

min

≤ Tam

b≤ T

max

68m

V

DV

ioInput O

ffset Voltage D

rift2

µV/°C

IioInput O

ffset Current

Tm

in≤ T

amb

≤ Tm

ax

13080

nA

Iib

Input Bias C

urrent V

icm =

Vcc/2

Tm

in≤ T

amb

≤ Tm

ax

35100200

nA

CM

RC

omm

on Mode R

ejection Ratio

5080

dB

SV

RS

upply Voltage R

ejection Ratio

Vcc =

2.7V to 3.3V

6080

dB

Avd

Large Signal V

oltage Gain

Vo =

2Vpk-pk R

L = 600Ω

80dB

VO

HH

igh Level Output V

oltage RL = 600Ω

2.82.9

V

VO

LLow

Level Output V

oltage RL =

600Ω80

250m

V

IscO

utput Short C

ircuit Current

10m

A

IccS

upply Current (per A

mplifier)

No load, V

icm = V

cc/20.9

1.3m

A

GB

PG

ain Bandw

idth Product R

L = 2kΩ

3M

Hz

SR

Slew

Rate

1V

/µs

∅m

Phase M

argin at Unit G

ain RL =

600Ω, C

L=

100pF60

Degree

s

Gm

Gain M

argin RL =

600Ω, C

L=

100pF10

dB

en

Equivalent Input N

oise Voltage

f = 1kH

z25

TH

DTotal H

armonic D

istortionV

out = 4Vpk-pk, F

= 10kH

z, Av =

2, RL =

10kΩ0.01

% nVHz

------------

TS

951-TS

952-TS

954E

lectrical Ch

aracteristics

7/16

Fig

ure 1.

Su

pp

ly curren

t vs. sup

ply vo

ltage

Fig

ure 2.

Ou

tpu

t sho

rt circuit cu

rrent vs.

ou

tpu

t voltag

e

Fig

ure 3.

Voltag

e gain

and

ph

ase vs. freq

uen

cyF

igu

re 4.S

up

ply cu

rrent vs. tem

peratu

re

Fig

ure 5.

Ou

tpu

t sho

rt circuit cu

rrent vs.

temp

erature

Fig

ure 6.

Slew

rate vs. temp

erature

RE

F2912

RE

F2920

RE

F2925

RE

F2930

RE

F2933

RE

F2940

SB

VS

033B – JU

NE

2002 – RE

VIS

ED

FE

BR

UA

RY

2008

ww

w.ti.co

m DE

SC

RIP

TIO

NT

he RE

F29xx is a precision, low

-power, low

-voltage dropoutvoltage reference fam

ily available in a tiny SO

T23-3.

The R

EF

29xx small size and low

power consum

ption (50µAm

ax) make it ideal for portable and battery-pow

ered applica-tions. T

he RE

F29xx does not require a load capacitor, but is

stable with any capacitive load.

Unloaded, the R

EF

29xx can be operated with supplies w

ithin1m

V of output voltage. A

ll models are specified for the w

idetem

perature range, –40°C to +

125°C.

FE

AT

UR

ES

M

icroS

IZE

PA

CK

AG

E: S

OT

23-3

L

OW

DR

OP

OU

T: 1m

V

H

IGH

OU

TP

UT

CU

RR

EN

T: 25m

A

L

OW

TE

MP

ER

AT

UR

E D

RIF

T: 100p

pm

/°C m

ax

H

IGH

AC

CU

RA

CY

: 2%

L

OW

IQ : 50µA m

ax

PRODUCTIO

N DATA information is current as of publication date.

Products conform to specifications per the term

s of Texas Instruments

standard warranty. Production processing does not necessarily include

testing of all parameters.

Copyright ©

2002-2008, Texas Instrum

ents Incorporated

100pp

m/°C

, 50µA in

SO

T23-3

CM

OS

VO

LTAG

E R

EF

ER

EN

CE

AP

PL

ICA

TIO

NS

P

OR

TA

BL

E, B

AT

TE

RY

-PO

WE

RE

D E

QU

IPM

EN

T

D

AT

A A

CQ

UIS

ITIO

N S

YS

TE

MS

M

ED

ICA

L E

QU

IPM

EN

T

H

AN

D-H

EL

D T

ES

T E

QU

IPM

EN

T

PR

OD

UC

TV

OL

TA

GE

(V)

RE

F2912

1.25

RE

F2920

2.048

RE

F2925

2.5

RE

F2930

3.0

RE

F2933

3.3

RE

F2940

4.096

1IN

2O

UT

3G

ND

RE

F2912

RE

F2920

RE

F2925

RE

F2930

RE

F2933

RE

F2940

SO

T23-3

DR

OP

OU

T V

OLT

AG

E vs LO

AD

CU

RR

EN

T350

300

250

200

150

100500

Dropout Voltage (mV)

05

1015

2025

30

Load Current (m

A)

www.ti.c

om

Please be aw

are that an important notice concerning availability, standard w

arranty, and use in critical applications ofT

exas Instruments sem

iconductor products and disclaimers thereto appears at the end of this data sheet.

All tradem

arks are the property of their respective owners.

RE

F2912, 2920, 2925, 2930, 2933, 29403

SB

VS

033Bw

ww

.ti.com

EL

EC

TR

ICA

L C

HA

RA

CT

ER

IST

ICS

(Co

nt.)

Bo

ldface

limits apply over the specified tem

perature range, TA = –40°C

to +125°C

.A

t TA =

+25°C

, ILOA

D = 0m

A, V

IN = 5V

, unless otherwise noted.

RE

F29xx

PA

RA

ME

TE

RC

ON

DIT

ION

SM

INT

YP

MA

XU

NIT

S

RE

F2930

OU

TP

UT

VO

LT

AG

EV

OU

T2.940

3.03.06

VInitial A

ccuracy2

%

NO

ISE

Output V

oltage Noise

f = 0.1H

z to 10Hz

33µV

PP

Voltage N

oisef =

10Hz to 10kH

z94

µV

rms

LIN

E R

EG

UL

AT

ION

VR

EF

+ 50m

V ≤ V

IN≤ 5.5V

120375

µV

/V

RE

F2933

OU

TP

UT

VO

LT

AG

EV

OU

T3.234

3.303.366

VInitial A

ccuracy2

%

NO

ISE

Output V

oltage Noise

f = 0.1H

z to 10Hz

36µV

PP

Voltage N

oisef =

10Hz to 10kH

z105

µV

rms

LIN

E R

EG

UL

AT

ION

VR

EF

+ 50m

V ≤ V

IN≤ 5.5V

130400

µV

/V

RE

F2940

OU

TP

UT

VO

LT

AG

EV

OU

T4.014

4.0964.178

VInitial A

ccuracy2

%

NO

ISE

Output V

oltage Noise

f = 0.1H

z to 10Hz

45µV

PP

Voltage N

oisef =

10Hz to 10kH

z128

µV

rms

LIN

E R

EG

UL

AT

ION

VR

EF

+ 50m

V ≤ V

IN≤ 5.5V

160410

µV

/V

RE

F2912, R

EF

2920, RE

F2925, R

EF

2930, RE

F2933, R

EF

2940

OU

TPU

T VO

LTAG

E TE

MP

DR

IFT(2)

dVO

UT /dT

–40 °C≤ T

A≤ +125°C

35100

pp

m/°C

OU

TP

UT

CU

RR

EN

TILO

AD

25m

A

LO

NG

-TE

RM

ST

AB

ILIT

Y0-1000

H24

ppm1000-2000

H15

ppm

LO

AD

RE

GU

LA

TIO

N(3)

dVO

UT /dILO

AD

0mA

< ILO

AD

< 25m

A,

3100

µV/m

AV

IN = V

RE

F + 500m

V(1)

TH

ER

MA

L H

YS

TE

RE

SIS

(4)dT

25100

ppm

DR

OP

OU

T V

OL

TA

GE

VIN

– VO

UT

150

mV

SH

OR

T-C

IRC

UIT

CU

RR

EN

TIS

C45

mA

TU

RN

-ON

SE

TT

LIN

G T

IME

to 0.1% at V

IN=

5V w

ith CL

= 0

120µ

s

PO

WE

R S

UP

PL

YV

oltageV

SIL

= 0

VR

EF

+ 0.001(5)

5.5V

Over T

emp

erature

–40°C≤ T

A≤ +125°C

VR

EF

+ 0.055.5

VQ

uiescent Current

IQ42

50µA

Over T

emp

erature

–40 °C≤ T

A≤ +125°C

59µA

TE

MP

ER

AT

UR

E R

AN

GE

Specified R

ange–40

+125

°CO

perating Range

–40+

125°C

Storage R

ange–65

+150

°CT

hermal R

esistanceS

OT

23-3 Surface-M

ountθ

JC110

°C/W

θJA

336°C

/W

NO

TE

S: (1) M

inimum

supply voltage for RE

F2912 is 1.8V

. (2) Box M

ethod used to determine over tem

perature drift. (3) Typical value of load regulation reflects

measurem

ents using a force and sense contacts, see text “Load Regulation”. (4) T

hermal hysteresis procedure is explained in m

ore detail in Applications Inform

ationsection of data sheet. (5) F

or IL > 0, see Typical C

haracteristic curves.

RE

F2912, 2920, 2925, 2930, 2933, 29404

SB

VS

033Bw

ww

.ti.com

TY

PIC

AL

CH

AR

AC

TE

RIS

TIC

SA

t TA =

+25°C

, VIN =

+5V

power supply, R

EF

2925 is used for typical characteristics, unless otherwise noted.

QU

IES

CE

NT

CU

RR

EN

T vs T

EM

PE

RA

TU

RE

6050403020100

IQ (µA)

Tem

perature (°C)

–40–20

020

6040

80100

120140

TE

MP

ER

AT

UR

E D

RIF

T (0°C

to +70°C

)50454035302520151050

Number of Units

510

1520

2530

4035

4550

5565

60

Drift (ppm

/°C)

TE

MP

ER

AT

UR

E D

RIF

T (–40°C

to +125°C

)1009080706050403020100

Number of Units

510

1520

2530

4035

4550

5565

60

Drift (ppm

/°C)

LOA

D R

EG

ULA

TIO

N vs T

EM

PE

RA

TU

RE

6543210

Load Regulation (µV/mA)

Tem

perature (°C)

–40–20

020

6040

80100

120140

OU

TP

UT

VO

LTA

GE

vs TE

MP

ER

AT

UR

E2.502

2.500

2.498

2.496

2.494

2.492

2.490

Output Voltage (V)

–40–20

020

6040

80100

120140

Tem

perature (°C)

MA

XIM

UM

LOA

D C

UR

RE

NT

vs TE

MP

ER

AT

UR

E3530252015105

Maximum Load Current (mA)

–40–20

020

6040

80100

120140

Tem

perature (°C)

RE

F2912, 2920, 2925, 2930, 2933, 29405

SB

VS

033Bw

ww

.ti.com

TY

PIC

AL

CH

AR

AC

TE

RIS

TIC

S (C

on

t.)A

t TA =

+25°C

, VIN =

+5V

power supply, R

EF

2925 is used for typical characteristics, unless otherwise noted.O

UT

PU

T IM

PE

DA

NC

E vs F

RE

QU

EN

CY

100101

0.1

0.01

Output Impedance (dB)

110

1001k

10k100k

Frequency (H

z)

PO

WE

R-S

UP

PLY

RE

JEC

TIO

N R

AT

IO vs F

RE

QU

EN

CY

9080706050403020100

PSRR (dB)

110

1001k

10k100k

Frequency (H

z)

OU

TP

UT

VO

LTA

GE

vs SU

PP

LY V

OLT

AG

E (ILO

AD =

25mA

)2.5008

2.5000

2.4992

2.4984

2.4976

2.4968

2.4967

2.4952

2.4944

2.4936

Output Voltage (V)

2.53

3.54

4.55

5.56

Supply (V

)

OU

TP

UT

VO

LTA

GE

vs LOA

D C

UR

RE

NT

2.50152

2.50000

2.49848

2.49696

2.49544

2.49392

2.49824

2.49088

2.48936

Output Voltage (V)

05

1015

2025

30

Load Current (m

A)

LINE

RE

GU

LAT

ION

vs TE

MP

ER

AT

UR

E200

150

100500

–50

Line Regulation (µV/V)

Tem

perature (°C)

–40–20

020

6040

80100

120140

OU

TP

UT

VO

LTA

GE

vs SU

PP

LY V

OLT

AG

E (N

o Load)2.50138

2.50000

2.49862

2.49724

2.49586

2.49448

2.49310

2.49172

2.49034

2.48896

Output Voltage (V)

2.53

3.54

4.55

5.56

Supply (V

)

AA

Classification:Alkaline

Chemical System:Zinc-Manganese Dioxide (Zn/MnO2)

Designation:IEC-LR6

Nominal Voltage:1.5 volts

Nominal IR:150 to 300 milliohms (fresh)

Operating Temp:-18°C to 55°C

Typical Weight:23.0 grams

Typical Volume:8.1 cubic centimeters

Jacket:Plastic Label

Shelf Life:10 years at 21°C

Terminal:Flat Contact

©Energizer Holdings, Inc. - Contents herein do not constitute a warranty.

Important NoticeThis datasheet contains typical information specific to products manufactured at the time of its publication.

Battery Selection Indicator

High Drain

Devices

Moderate Drain

Devices

Continuous discharge to 0.8 volts at 21°C

Industry Standard Testing (21°C):

Low Drain

Devices

Ultra+ (LR6)Specifications

(millimeters)

No added mercury or cadmium

Industry Standard Dimensions

Milliamp-Hours Capacity

PRODUCT DATASHEET

Engineering Data

1-800-383-7323 / USA 1-800-383-7323 / CANADA

Western European Region + 44 1494 556111 www.energizer.eu

Engineering Data

0.8

1.0

1.2

1.4

1.6

020406080100

Vo

ltag

e (C

CV

)

Service (hours)

RADIO 43 ohm 4 hrs/day

REMOTE 24 ohm 15 sec/min 8 hrs/day

REMOTE

RADIO

0.8

1.0

1.2

1.4

1.6

04812162024

Vo

ltag

e (C

CV

)

Service (hours)

TAPE PLAYER 10 ohm 1 hr/day

TOY 3.9 ohm 1 hr/day

TOY

TAPE PLAYER

0

1000

2000

3000

25100250500

Ca

pa

city

(mA

h)

Discharge (mA)

14.50

13.50

1.00

Minimum

49.20

50.50

7.00

Minimum

0.10

Typical

5.50

Maximum

Form No. EBC - 8808EU-BPage 1 of 1

Ni-MH Rechargeable Batteries

5.1 General CharacteristicsThe discharge characteristics of the nickel-m

etalhydride cell are very sim

ilar to those of the nickel-cadm

ium cell. The charged open circuit voltage

of bothsystem

s ranges from 1.25 to 1.35 volts per cell. O

ndischarge, the nom

inal voltageis 1.2 volts per cell and

the typical end voltageis 1.0 volt per cell.

Figure 5.1.1illustrates the discharge character-

istics of nickel-metal hydride and nickel-cadm

iumrechargeable cells of the sam

e size. As shown, the volt-

age profile of both types of cells is flat throughout most

of the discharge. The midpoint voltage

can range from1.25 to 1.1 volts per cell, depending on the dischargeload.

Figure 5.1.1can also be used to com

pare thecapacity of the tw

o rechargeable types. Note that the

capacity of the nickel-metal hydride cell is typically up to

40 percent higher than that of a nickel-cadmium

cell ofequivalent size.

5.2 Discharge Characteristics: Effect of Discharge Rate and Tem

peratureTypical discharge curves for D

UR

ACELL nickel-m

etal hydride batteries under constant current loads atvarious tem

peratures are shown in Figures 5.2.1

to5.2.3.

Discharge voltage is

dependent on dischargecurrent and discharge tem

perature.

FIGURE 5.1.11.5

1.4

1.3

1.2

1.1

1.0.9

Voltage (V)

Ampere-Hour Capacity (%

)

Comparison of discharge voltage and capacity of

same-size N

i-MH and N

i-Cd cells. [Conditions: Charge: C/3 for 5 hours, Tem

perature: 21°C (70°F)]

0 20 40 60 80 100 120 140 160 N

i-MH

C/5C/5

Ni-Cd

5 5Perform

ance Characteristics

FIGURE 5.2.1

Voltage (V)Discharge Capacity (Ah)

FIGURE 5.2.2

Discharge Capacity (Ah)

Voltage (V)

C (2.4A)

Voltage (V)

Discharge Capacity (Ah)

8.5

8.0

7.5

7.0

6.5

6.0

5.50 0.5 1.0 1.5 2.0 2.5

C/5 (0.48A)

C (2.4A)

C (2.4A)

FIGURE 5.2.3

Voltage and capacity of DURACELL DR30 Ni-M

H batteries at various discharge tem

peratures and rates.[Conditions: Charge: 1C to -∆V = 60m

V@

21°C (70°F)]

Temperature: -20°C (-4°F)

8.5

8.0

7.5

7.0

6.5

6.0

5.50 0.5 1.0 1.5 2.0 2.5

C/5 (0.48A)

C (2.4A)

Temperature: 45°C (113°F)

8.5

8.0

7.5

7.0

6.5

6.0

5.5

C/5 (0.48A)

C (2.4A)

0 0.5 1.0 1.5 2.0 2.5

Temperature: 21°C (70°F)

C/5 (0.48A)

Temperature: 0°C (32°F)

6

Classification:"Lithium

Coin"Chem

ical System:

Lithium / M

anganese Dioxide (Li/MnO

2 )D

esignation:ANSI / NEDA-5004LC, IEC-CR2032

Nom

inal Voltage:3.0 Volts

Typical Capacity:240 m

Ah (to 2.0 volts)(Rated at 15K ohm

s at 21°C)Typical W

eight:3.0 gram

s (0.10 oz.)Typical Volum

e:1.0 cubic centim

eters (0.06 cubic inch)M

ax Rev Charge:

1 microam

pereEnergy D

ensity:198 m

illiwatt hr/g, 653 m

illiwatt hr/cc

Typical Li Content:0.109

grams (0.0038 oz.)

UL Listed:

MH12454

Shipping:For com

plete details, please reference:Special Provision A45 of the InternationalAir Transport Association DangerousGoods Regulations49 CFR 173.185

LoadC

utoff2.0V

(ohms)

(hours)

15,0001,263

Bkgnd D

rain:Continuous15K ohm

s0.19 m

A @2.9V

Pulse Drain:

2 seconds X 12 times/day

400 ohms

6.8 mA @

2.7V

©Energizer H

oldings, Inc. - Contents herein do not constitute a warranty.

Typical Drains:

at 2.9V (m

A)

0.19

Pulse Test at 21°C (70°F)

Typical Discharge Characteristics

Internal Resistance Characteristics

Important N

oticeThis datasheet contains typical inform

ation specific to products manufactured at the tim

e of its publication.

ENERGIZER CR2032

Schedule:

Simulated A

pplication testTypical Perform

ance at 21°C (70°F)

Continuous

Lithium Coin

Specifications

mm

(inches)

Cross Section

Industry Standard Dim

ensions

United States:

Global (except US):

PROD

UCT DATASH

EET

1.82.02.22.42.62.83.03.2

0300

600900

12001500

Voltage, CCV

Service, Hours

Load: 15K ohm

s -Continuous

Typical Drain @

2.9V: 0.19 m

A

0 20 40 60 80 100

120

1.82.02.22.42.62.83.03.2

025

5075

100125

150200

225250

IR, ohms

Voltage, CCV

Capacity, mA

h

IR

Pulse

Bkgnd

1-800-383-7323 USA/CANw

ww

.energizer.com

3.20 (0

.126)

2.90 (0

.114)

17.70

(0.697

)M

aximum

20.0

0 (0.78

7)

19.70

(0.776

)

0.20 (0.0

08) M

aximum

Ref.

Permissib

le deflection from a flat.

0.10 (0

.004) M

inim

um R

ef.(A

pplies to top edge of g

asket ored

ge of crimp, w

hichever is h

igher.)

This B

attery has U

nderw

riters Lab

oratories component R

ecognition

Form No. EBC - 4120J

Page 1 of 1

Se

co

nd

ary

Ba

tterie

s

Recharg

eable

batte

ries p

lay a

n im

porta

nt ro

le in

our life

and m

any d

aily

chore

s w

ould

be u

nth

inkable

with

out th

e

ability

to re

charg

e a

n e

mpty

batte

ry. Poin

ts o

f inte

rest a

re s

pecific

energ

y, years

of s

erv

ice life

, load c

hara

cte

ristic

s,

safe

ty, pric

e, s

elf-d

ischarg

e, e

nviro

nm

enta

l issues, m

ain

tenance re

quire

ments

, and d

isposal.

Lead

Acid

— O

ne o

f the o

ldest re

charg

eable

batte

ry s

yste

ms; is

rugged, fo

rgiv

ing if a

bused a

nd e

conom

ical in

pric

e; h

as a

low

specific

energ

y a

nd lim

ited c

ycle

life. L

ead a

cid

is u

sed fo

r wheelc

hairs

, golf c

ars

, pers

onnel

carrie

rs, e

merg

ency lig

htin

g a

nd u

nin

terru

ptib

le p

ow

er s

upply

(UP

S).

Nic

kel-c

ad

miu

m (N

iCd) —

Matu

re a

nd w

ell u

nders

tood; is

used w

here

long s

erv

ice life

, hig

h d

ischarg

e c

urre

nt,

extre

me te

mpera

ture

s a

nd e

conom

ical p

rice a

re o

f importa

nce. D

ue to

enviro

nm

enta

l concern

s, N

iCd is

bein

g

repla

ced w

ith o

ther c

hem

istrie

s. M

ain

applic

atio

ns a

re p

ow

er to

ols

, two-w

ay ra

dio

s, a

ircra

ft and U

PS

.

Nic

kel-m

eta

l-hyd

ride (N

iMH

) — A

pra

ctic

al re

pla

cem

ent fo

r NiC

d; h

as h

igher s

pecific

energ

y w

ith fe

wer to

xic

meta

ls. N

iMH

is u

sed fo

r medic

al in

stru

ments

, hybrid

cars

and in

dustria

l applic

atio

ns. N

iMH

is a

vaila

ble

in A

A a

nd

AA

A c

ells

for c

onsum

er u

se.

Lith

ium

-ion

(Li!io

n) —

Most p

rom

isin

g b

atte

ry s

yste

ms; is

used fo

r porta

ble

consum

er p

roducts

as w

ell a

s e

lectric

pow

ertra

ins fo

r vehic

les; is

more

expensiv

e th

an n

ickel- a

nd le

ad a

cid

syste

ms a

nd n

eeds p

rote

ctio

n c

ircuit fo

r

safe

ty.

The lith

ium

-ion fa

mily

is d

ivid

ed in

to th

ree m

ajo

r batte

ry ty

pes, s

o n

am

ed b

y th

eir c

ath

ode o

xid

es, w

hic

h a

re c

obalt,

manganese a

nd p

hosphate

. The c

hara

cte

ristic

s o

f these L

i-ion s

yste

ms a

re a

s fo

llow

s.

Lith

ium

-ion

-co

balt o

r lithium-cobalt (L

iCoO

2): H

as h

igh s

pecific

energ

y w

ith m

odera

te lo

ad c

apabilitie

s a

nd

modest s

erv

ice life

. Applic

atio

ns in

clu

de c

ell p

hones, la

pto

ps, d

igita

l cam

era

s a

nd w

eara

ble

pro

ducts

.

Lith

ium

-ion

-man

gan

ese o

r lithium-manganese (L

iMn2O

4): Is

capable

of h

igh c

harg

e a

nd d

ischarg

e c

urre

nts

but

has lo

w s

pecific

energ

y a

nd m

odest s

erv

ice life

; used fo

r pow

er to

ols

, medic

al in

stru

ments

and e

lectric

pow

ertra

ins.

Lith

ium

-ion

-ph

osp

hate

or lith

ium-phosphate

(LiF

eP

O4): Is

sim

ilar to

lithiu

m-m

anganese; n

om

inal v

olta

ge is

3.3

V/c

ell; o

ffers

long c

ycle

life, h

as a

good s

afe

record

but e

xhib

its h

igher s

elf-d

ischarg

e th

an o

ther L

i-ion s

yste

ms.

There

are

many o

ther lith

ium

-ion b

ased b

atte

ries, s

om

e o

f whic

h a

re d

escrib

ed fu

rther o

n th

is w

ebsite

. Mis

sin

g in

the lis

t is a

lso th

e p

opula

r lithiu

m-io

n-p

oly

mer, o

r Li-polymer. W

hile

Li-io

n s

yste

ms g

et th

eir n

am

e fro

m th

eir u

niq

ue

cath

ode m

ate

rials

, Li-p

oly

mer d

iffers

by h

avin

g a

dis

tinct a

rchite

ctu

re. N

or is

the re

charg

eable

lithiu

m-m

eta

l

mentio

ned. T

his

batte

ry re

quire

s fu

rther d

evelo

pm

ent to

contro

l dendrite

gro

wth

, whic

h c

an c

om

pro

mis

e s

afe

ty.

Once s

olv

ed, L

i-meta

l will b

ecom

e a

n a

ltern

ativ

e b

atte

ry c

hoic

e w

ith e

xtra

ord

inary

hig

h s

pecific

energ

y a

nd g

ood

specific

pow

er.

Table

1 c

om

pare

s th

e c

hara

cte

ristic

s o

f four c

om

monly

used re

charg

eable

batte

ry s

yste

ms s

how

ing a

vera

ge

Seco

nd

ary (R

echarg

eable) B

atteries – B

attery U

niv

ersityhttp

://battery

un

iversity.co

m/learn

/article/secondary

_b

atteries

1 o

f 308/0

9/2

011

15

:50

perfo

rmance ra

tings a

t time o

f public

atio

n.

Tab

le 1

: Ch

ara

cte

ristic

s o

f co

mm

on

ly u

sed

rech

arg

eab

le b

atte

ries

The fig

ure

s a

re b

ased o

n a

vera

ge ra

tings o

f com

merc

ial b

atte

ries a

t time o

f public

atio

n; e

xperim

enta

l batte

ries w

ith

above-a

vera

ge ra

tings a

re e

xclu

ded.

1 Inte

rnal re

sis

tance o

f a b

atte

ry p

ack v

arie

s w

ith m

illiam

pere

-hour (m

Ah) ra

ting, w

iring a

nd n

um

ber o

f cells

.

Pro

tectio

n c

ircuit o

f lithiu

m-io

n a

dds a

bout 1

00m

W.

2 Based o

n 1

8650 c

ell s

ize. C

ell s

ize a

nd d

esig

n d

ete

rmin

es in

tern

al re

sis

tance.

3 Cycle

life is

based o

n b

atte

ry re

ceiv

ing re

gula

r main

tenance.

4 Cycle

life is

based o

n th

e d

epth

of d

ischarg

e (D

oD

). Shallo

w D

oD

impro

ves c

ycle

life.

5 Self-d

ischarg

e is

hig

hest im

media

tely

afte

r charg

e. N

iCd lo

ses 1

0%

in th

e firs

t 24 h

ours

, then d

eclin

es to

10%

every

30 d

ays. H

igh te

mpera

ture

incre

ases s

elf-d

ischarg

e.

6 Inte

rnal p

rote

ctio

n c

ircuits

typic

ally

consum

e 3

% o

f the s

tore

d e

nerg

y p

er m

onth

.7 T

he tra

ditio

nal v

olta

ge is

1.2

5V

; 1.2

V is

more

com

monly

used.

8 Low

inte

rnal re

sis

tance re

duces th

e v

olta

ge d

rop u

nder lo

ad a

nd L

i-ion is

ofte

n ra

ted h

igher th

an 3

.6V

/cell.

Cells

mark

ed 3

.7V

and 3

.8V

are

fully

com

patib

le w

ith 3

.6V

.

Seco

ndary

(Rech

argeab

le) Batteries –

Battery

Un

iversity

http

://battery

univ

ersity.com

/learn/article/seco

nd

ary_

batteries

2 o

f 30

8/0

9/2

011 1

5:5

0

June 2005

LM

2931S

eries Lo

w D

rop

ou

t Reg

ulato

rsG

eneral D

escriptio

nT

he LM2931 positive voltage regulator features a very low

quiescent current of 1mA

or less when supplying 10m

A loads.

This unique characteristic and the extrem

ely low input-output

differential required for proper regulation (0.2V for output cur-

rents of 10mA

) make the LM

2931 the ideal regulator forstandby pow

er systems. A

pplications include mem

ory stand-by circuits, C

MO

S and other low

power processor pow

ersupplies as w

ell as systems dem

anding as much as 100m

Aof output current.D

esigned originally for automotive applications, the LM

2931and all regulated circuitry are protected from

reverse batteryinstallations or 2 battery jum

ps. During line transients, such

as a load dump (60V

) when the input voltage to the regulator

can mom

entarily exceed the specified maxim

um operating

voltage, the regulator will autom

atically shut down to protect

both internal circuits and the load. The LM

2931 cannot beharm

ed by temporary m

irror-image insertion. F

amiliar regu-

lator features such as short circuit and thermal overload pro-

tection are also provided.T

he LM2931 fam

ily includes a fixed 5V output (±

3.8% toler-

ance for A grade) or an adjustable output w

ith ON

/OF

F pin.

Both versions are available in a T

O-220 pow

er package,T

O-263 surface m

ount package, and an 8-lead surface mount

package. The fixed output version is also available in the

TO

-92 plastic and 6-Bum

p micro S

MD

packages.

Featu

resV

ery low quiescent current

Output current in excess of 100 m

A

Input-output differential less than 0.6V

Reverse battery protection

60V load dum

p protection

−50V

reverse transient protection

Short circuit protection

Internal thermal overload protection

Mirror-im

age insertion protection

Available in T

O-220, T

O-92, T

O-263, S

O-8 or 6-B

ump m

i-cro S

MD

packagesA

vailable as adjustable with T

TL com

patible switch

See A

N-1112 for m

icro SM

D considerations

Co

nn

ection

Diag

rams

FIX

ED

VO

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AG

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525406

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TO

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525411

To

p V

iew

525412

Sid

e View

8-Pin

Su

rface Mo

un

t

525407

*NC

= N

ot internally connected. Must be electrically isolated from

the rest ofthe circuit for the m

icro SM

D package.

To

p V

iew

TO

-92 Plastic P

ackage

525408

Bo

ttom

View

© 2006 N

ational Sem

iconductor Corporation

5254w

ww

.national.com

LM2931 Series Low Dropout Regulators

6-Bu

mp

micro

SM

D

525438

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p V

iew(B

um

p S

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n)

micro

SM

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525439

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PU

T V

OL

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GE

TO

-220 5-Lead

Po

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525409

Fro

nt V

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TO

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urface-M

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ackage

525413

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525414

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in TO

-220LM

2931T-5.0

LM2931T

-5.0R

ailsT

03B

LM2931A

T-5.0

LM2931A

T-5.0

Rails

3-Pin T

O-263

LM2931S

-5.0LM

2931S-5.0

Rails

TS

3B

LM2931A

S-5.0

LM2931A

S-5.0

Rails

TO

-92LM

2931Z-5.0

LM2931Z

-51.8k U

nits per Box

Z03A

LM2931A

Z-5.0

LM2931A

Z1.8k U

nits per Box

8-Pin

SO

ICLM

2931M-5.0

2931M-5.0

Rails

M08A

LM2931A

M-5.0

2931AM

-5.0R

ails

* 6-Bum

pm

icro SM

DLM

2931IBP

X-5.0

Tape and R

eelB

PA

06HT

A

Adjustable,

3V to 24V

5-Pin T

O-220

LM2931C

TLM

2931CT

Rails

T05A

5-Pin T

O-263

LM2931C

SLM

2931CS

Rails

TS

5B

8-Pin

SO

ICLM

2931CM

LM2931C

MR

ailsM

08A

3.3V* 6-B

ump

micro S

MD

LM2931IB

PX

-3.3T

ape and Reel

BP

A06H

TB

No

te:T

he micro S

MD

package marking is a single digit

manufacturing D

ate Code O

nly.

3w

ww

.national.com

LM2931

Typ

ical Ap

plicatio

ns

LM

2931 Fixed

Ou

tpu

t

525404

*Required if regulator is located far from

power supply filter.

**C2 m

ust be at least 100 F

to maintain stability. M

ay be increased without bound to m

aintain regulation during transients. Locate as close as possible to theregulator. T

his capacitor must be rated over the sam

e operating temperature range as the regulator. T

he equivalent series resistance (ES

R) of this capacitor is

critical; see curve.

LM

2931 Ad

justab

le Ou

tpu

t

525405

No

te: Using 27k for R

1 will autom

atically compensate for errors in V

OU

T due to the input bias current of the AD

J pin (approximately 1

A).

ww

w.national.com

4

LM2931

Ab

solu

te Maxim

um

Ratin

gs (N

ote 1)

If Military/A

erosp

ace specified

devices are req

uired

,p

lease con

tact the N

ation

al Sem

icon

du

ctor S

ales Office/

Distrib

uto

rs for availab

ility and

specificatio

ns.

Input Voltage

Operating R

ange26V

Overvoltage P

rotection

LM2931A

, LM2931C

(Adjustable)

60V

LM2931

50VInternal P

ower D

issipation

(Notes 2, 4)

Internally Limited

Operating A

mbient T

emperature

Range

−40°C

to +85°C

Maxim

um Junction T

emperature

125°CS

torage Tem

perature Range

−65°C

to +150°C

Lead Tem

p. (Soldering, 10 seconds)

230°CE

SD

Tolerance (N

ote 5)2000V

Electrical C

haracteristics fo

r Fixed

3.3V V

ersion

VIN =

14V, IO =

10mA

, TJ =

25°C, C

2F

(unless otherwise specified) (N

ote 2)

Param

eterC

on

ditio

ns

LM

2931-3.3U

nits

Typ

Lim

it(N

ote 3)

Output V

oltage3.3

3.4653.135

VM

AX

VM

IN

4V V

IN 26V

, IO = 100 m

A

−40°C

TJ

125°C

3.6302.970

VM

AX

VM

IN

Line Regulation

4V V

IN 26V

433

mV

MA

X

Load Regulation

5mA

IO 100m

A10

50m

VM

AX

Output Im

pedance100m

AD

C and 10mA

rms ,

100Hz - 10kH

z

200m

Quiescent C

urrentIO

10mA

, 4V

VIN

26V0.4

1.0m

AM

AX

−40°C

TJ

125°C

IO = 100m

A, V

IN = 14V

, TJ =

25°C15

mA

Output N

oise Voltage

10Hz -100kH

z, CO

UT

F330

Vrm

s

Long Term

Stability

13m

V/1000 hr

Ripple R

ejectionfO =

120Hz

80dB

Dropout V

oltageIO =

10mA

IO = 100m

A

0.050.30

0.20.6

VM

AX

Maxim

um O

perational InputV

oltage33

26V

MIN

Maxim

um Line T

ransientR

L, V

O 5.5V

,

T =

1ms,

100ms

7050

VM

IN

Reverse P

olarity Input Voltage, D

CV

O −

0.3V, R

L−

30−

15V

MIN

Reverse P

olarity Input Voltage,

Transient

T =

1ms,

100ms, R

L−

80−

50V

MIN

5w

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.national.com

LM2931

Electrical C

haracteristics fo

r Fixed

5V V

ersion

VIN =

14V, IO =

10mA

, TJ =

25°C, C

2 = 100

F (unless otherw

ise specified) (Note 2)

Param

eterC

on

ditio

ns

LM

2931A-5.0

LM

2931-5.0U

nits

Typ

Lim

it(N

ote 3)T

ypL

imit

(Note 3)

Output V

oltage5

5.194.81

55.254.75

VM

AX

VM

IN

6.0V V

IN 26V

, IO = 100m

A

−40°C

TJ

125°C

5.254.75

5.54.5

VM

AX

VM

IN

Line Regulation

9V V

IN 16V

6V V

IN 26V

241030

241030

mV

MA

X

Load Regulation

5 mA

IO

100mA

1450

1450

mV

MA

X

Output Im

pedance100m

AD

C and 10mA

rms ,

100Hz -10kH

z

200200

m

Quiescent C

urrentIO

10mA

, 6V

VIN

26V0.4

1.00.4

1.0m

AM

AX

−40°C

TJ

125°C

IO = 100m

A, V

IN = 14V

, TJ =

25°C15

30515

mA

MA

X

mA

MIN

Output N

oise Voltage

10Hz -100kH

z, CO

UT

F500

500V

rms

Long Term

Stability

2020

mV

/1000hr

Ripple R

ejectionfO =

120 Hz

8055

80dB

MIN

Dropout V

oltageIO =

10mA

IO = 100m

A

0.050.3

0.20.6

0.050.3

0.20.6

VM

AX

Maxim

um O

perational InputV

oltage33

2633

26V

MIN

Maxim

um Line T

ransientR

L, V

O 5.5V

,

T =

1ms,

100ms

7060

7050

VM

IN

Reverse P

olarity Input Voltage,

DC

VO

−0.3V

, RL

−30

−15

−30

−15

VM

IN

Reverse P

olarity Input Voltage,

Transient

T =

1ms,

100ms, R

L−

80−

50−

80−

50V

MIN

No

te 1:A

bsolute Maxim

um R

atings indicate limits beyond w

hich damage to the device m

ay occur. Electrical specifications do not apply w

hen operating the devicebeyond its rated operating conditions.

No

te 2:S

ee circuit in Typical A

pplications. To ensure constant junction tem

perature, low duty cycle pulse testing is used.

No

te 3:A

ll limits are guaranteed for T

J = 25°C

(standard type face) or over the full operating junction temperature range of −

40°C to +

125°C (bold type face).

No

te 4:T

he maxim

um pow

er dissipation is a function of maxim

um junction tem

perature TJm

ax , total thermal resistance

JA , and ambient tem

perature TA . T

hem

aximum

allowable pow

er dissipation at any ambient tem

perature is PD =

(TJm

ax − T

AJA . If this dissipation is exceeded, the die tem

perature will rise above

150°C and the LM

2931 will go into therm

al shutdown. F

or the LM2931 in the T

O-92 package,

JA is 195°C/W

; in the SO

-8 package, JA is 160°C

/W, and in the

TO

-220 package, JA is 50°C

/W; in the T

O-263 package,

JA is 73°C/W

; and in the 6-Bum

p micro S

MD

package JA is 290°C

/W. If the T

O-220 package is used

with a heat sink,

JA is the sum of the package therm

al resistance junction-to-case of 3°C/W

and the thermal resistance added by the heat sink and therm

alinterface.

If the TO

-263 package is used, the thermal resistance can be reduced by increasing the P

.C. board copper area therm

ally connected to the package: Using 0.5

square inches of copper area, JA is 50°C

/W; w

ith 1 square inch of copper area, JA is 37°C

/W; and w

ith 1.6 or more square inches of copper area,

JA is 32°C/

W.

ww

w.national.com

6

LM2931

No

te 5:H

uman body m

odel, 100 pF discharged through 1.5 k

Electrical C

haracteristics fo

r Ad

justab

le Versio

nV

IN = 14V

, VO

UT =

3V, IO =

10 mA

, TJ =

25°C, R

1 = 27k, C

2 = 100

F (unless otherw

ise specified) (Note 2)

Param

eterC

on

ditio

ns

Typ

Lim

itU

nits

Lim

it

Reference V

oltage1.20

1.26V

MA

X

1.14V

MIN

IO 100 m

A, −

40°C

Tj

125°C, R

1 = 27k

1.32V

MA

X

Measured from

VO

UT to A

djust Pin

1.08V

MIN

Output V

oltage Range

24V

MA

X

3V

MIN

Line Regulation

VO

UT +

0.6V

VIN

26V0.2

1.5m

V/V

MA

X

Load Regulation

5 mA

IO

100 mA

0.31

%M

AX

Output Im

pedance100 m

AD

C and 10 mA

rms , 100 H

z–10 kHz

40m

/V

Quiescent C

urrentIO =

10 mA

0.41

mA

MA

X

IO = 100 m

A15

mA

During S

hutdown R

L0.8

1m

AM

AX

Output N

oise Voltage

10 Hz–100 kH

z100

Vrm

s /V

Long Term

Stability

0.4%

/1000 hr

Ripple R

ejectionfO =

120 Hz

0.02%

/V

Dropout V

oltageIO

10 mA

0.050.2

VM

AX

IO = 100 m

A0.3

0.6V

MA

X

Maxim

um O

perational Input

Voltage

3326

VM

IN

Maxim

um Line T

ransientIO =

10 mA

, Reference V

oltage 1.5V

7060

VM

IN

T =

1 ms,

100 ms

Reverse P

olarity InputV

O −

0.3V, R

L

Voltage, D

C−

30−

15V

MIN

Reverse P

olarity InputT

= 1 m

s, 100 m

s, RL

Voltage, T

ransient−

80−

50V

MIN

On/O

ff Threshold V

oltageV

O =3V

On

2.01.2

VM

AX

Off

2.23.25

VM

IN

On/O

ff Threshold C

urrent20

50A

MA

X

7w

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LM2931

Typ

ical Perfo

rman

ce Ch

aracteristics

Dro

po

ut V

oltag

e

525416

Dro

po

ut V

oltag

e

525417

Lo

w V

oltag

e Beh

avior

525418

Ou

tpu

t at Vo

ltage E

xtremes

525419

Lin

e Tran

sient R

espo

nse

525420

Lo

ad T

ransien

t Resp

on

se

525421

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8

LM2931

Peak O

utp

ut C

urren

t

525422

Qu

iescent C

urren

t

525423

Qu

iescent C

urren

t

525424

Qu

iescent C

urren

t

525425

Rip

ple R

ejection

525426

Rip

ple R

ejection

525427

9w

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LM2931

Ou

tpu

t Imp

edan

ce

525428

Op

eration

Du

ring

Lo

adD

um

p

525429

Referen

ce Vo

ltage

525430

Maxim

um

Po

wer D

issipatio

n(S

O-8)

525431

Maxim

um

Po

wer D

issipatio

n(T

O-220)

525432

Maxim

um

Po

wer D

issipatio

n(T

O-92)

525433

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10

LM2931

Maxim

um

Po

wer D

issipatio

n(T

O-263)

(Note 4)

525434

On

/Off T

hresh

old

525435

Ou

tpu

t Cap

acitor E

SR

525436

11w

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LM2931

Sch

ematic D

iagram

525401

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12

LM2931

Ap

plicatio

n H

ints

One of the distinguishing factors of the LM

2931 series regu-lators is the requirem

ent of an output capacitor for devicestability. T

he value required varies greatly depending uponthe application circuit and other factors. T

hus some com

-m

ents on the characteristics of both capacitors and the reg-ulator are in order.H

igh frequency characteristics of electrolytic capacitors de-pend greatly on the type and even the m

anufacturer. As a

result, a value of capacitance that works w

ell with the LM

2931for one brand or type m

ay not necessary be sufficient with an

electrolytic of different origin. Som

etimes actual bench test-

ing, as described later, will be the only m

eans to determine

the proper capacitor type and value. Experience has show

nthat, as a rule of thum

b, the more expensive and higher quality

electrolytics generally allow a sm

aller value for regulator sta-bility. A

s an example, w

hile a high-quality 100 F

aluminum

electrolytic covers all general application circuits, similar sta-

bility can be obtained with a tantalum

electrolytic of only47

F. T

his factor of two can generally be applied to any spe-

cial application circuit also.A

nother critical characteristic of electrolytics is their perfor-m

ance over temperature. W

hile the LM2931 is designed to

operate to −40°C

, the same is not alw

ays true with all elec-

trolytics (hot is generally not a problem). T

he electrolyte inm

any aluminum

types will freeze around −

30°C, reducing

their effective value to zero. Since the capacitance is needed

for regulator stability, the natural result is oscillation (and lotsof it) at the regulator output. F

or all application circuits where

cold operation is necessary, the output capacitor must be rat-

ed to operate at the minim

um tem

perature. By coincidence,

worst-case stability for the LM

2931 also occurs at minim

umtem

peratures. As a result, in applications w

here the regulatorjunction tem

perature will never be less than 25°C

, the outputcapacitor can be reduced approxim

ately by a factor of two

over the value needed for the entire temperature range. T

ocontinue our exam

ple with the tantalum

electrolytic, a valueof only 22

F w

ould probably thus suffice. For high-quality alu-

minum

, 47F

would be adequate in such an application.

Another regulator characteristic that is notew

orthy is that sta-bility decreases w

ith higher output currents. This sensible fact

has im

portant connotations.

In m

any applications,

theLM

2931 is operated at only a few m

illiamps of output current

or less. In such a circuit, the output capacitor can be furtherreduced in value. A

s a rough estimation, a circuit that is re-

quired to deliver a maxim

um of 10m

A of output current from

the regulator would need an output capacitor of only half the

value compared to the sam

e regulator required to deliver thefull output current of 100m

A. If the exam

ple of the tantalumcapacitor in the circuit rated at 25°C

junction temperature and

above were continued to include a m

aximum

of 10mA

of out-put current, then the 22

F output capacitor could be reduced

to only 10F

.In the case of the LM

2931CT

adjustable regulator, the mini-

mum

value of output capacitance is a function of the outputvoltage. A

s a general rule, the value decreases with higher

output voltages, since internal loop gain is reduced.

At this point, the procedure for bench testing the m

inimum

value of an output capacitor in a special application circuitshould be clear. S

ince worst-case occurs at m

inimum

oper-ating tem

peratures and maxim

um operating currents, the

entire circuit, including the electrolytic, should be cooled to them

inimum

temperature. T

he input voltage to the regulatorshould be m

aintained at 0.6V above the output to keep inter-

nal power dissipation and die heating to a m

inimum

. Worst-

case occurs just after input power is applied and before the

die has had a chance to heat up. Once the m

inimum

value ofcapacitance has been found for the brand and type of elec-trolytic in question, the value should be doubled for actual useto account for production variations both in the capacitor andthe regulator. (A

ll the values in this section and the remainder

of the data sheet were determ

ined in this fashion.)L

M2931 m

icro S

MD

Lig

ht S

ensitivity

When the LM

2931 micro S

MD

package is exposed to brightsunlight, norm

al office fluorescent light, and other LED

's, itoperates w

ithin the guaranteed limits specified in the electri-

cal characteristic table.

Defin

ition

of T

erms

Dro

po

ut V

oltag

e: The input-output voltage differential at

which the circuit ceases to regulate against further reduction

in input voltage. Measured w

hen the output voltage hasdropped 100 m

V from

the nominal value obtained at 14V

in-put, dropout voltage is dependent upon load current andjunction tem

perature.In

pu

t Vo

ltage: T

he DC

voltage applied to the input terminals

with respect to ground.

Inp

ut-O

utp

ut D

ifferential: T

he voltage difference between

the unregulated input voltage and the regulated output volt-age for w

hich the regulator will operate.

Lin

e Reg

ulatio

n: T

he change in output voltage for a changein the input voltage. T

he measurem

ent is made under condi-

tions of low dissipation or by using pulse techniques such that

the average chip temperature is not significantly affected.

Lo

ad R

egu

lation

: The change in output voltage for a change

in load current at constant chip temperature.

Lo

ng

Term

Stab

ility: Output voltage stability under accel-

erated life-test conditions after 1000 hours with m

aximum

rated voltage and junction temperature.

Ou

tpu

t No

ise Vo

ltage: T

he rms A

C voltage at the output,

with constant load and no input ripple, m

easured over a spec-ified frequency range.Q

uiescen

t Cu

rrent: T

hat part of the positive input currentthat does not contribute to the positive load current. T

he reg-ulator ground lead current.R

ipp

le Rejectio

n: T

he ratio of the peak-to-peak input ripplevoltage to the peak-to-peak output ripple voltage at a speci-fied frequency.T

emp

erature S

tability o

f VO :

The percentage change in

output voltage for a thermal variation from

room tem

peratureto either tem

perature extreme.

13w

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LM2931

Ph

ysical Dim

ensio

ns inches (m

illimeters) unless otherw

ise noted

8-Lead

Su

rface Mo

un

t Packag

e (M)

NS

Packag

e Nu

mb

er M08A

3-Lead

TO

-220 Plastic P

ackage (T

)N

S P

ackage N

um

ber T

03B

ww

w.national.com

14

LM2931

LM

3100S

IMP

LE

SW

ITC

HE

R®

Syn

chro

no

us

1MH

z1.5A

Step

-Do

wn

Voltag

eR

egu

lator

Gen

eralD

escriptio

nT

heLM

3100S

ynchronouslyR

ectifiedB

uckC

onverterfea-

turesall

functionsneeded

toim

plement

ahighly

efficient,cost

effectivebuck

regulatorcapable

ofsupplying

1.5Ato

loadsw

ithvoltages

aslow

as0.8V.

Dual

40VN

-Channel

synchronousM

OS

FE

Tsw

itchesallow

forlow

externalcom-

ponentthus

reducingcom

plexityand

minim

izingboard

space.T

heLM

3100is

designedto

work

exceptionallyw

ellw

ithceram

icand

othervery

lowE

SR

outputcapacitors.The

Constant

ON

-Time

(CO

T)

regulationschem

erequires

noloop

compensation,

resultsin

fastload

transientresponse,

andsim

plifiescircuit

implem

entation.T

hroughthe

useof

aunique

designthe

regulatordoesnotrely

onoutputcapacitor

ES

Rfor

stability,as

dom

ostother

CO

Tregulators.

The

operatingfrequency

remains

nearlyconstant

with

lineand

loadvariations

dueto

theinverse

relationshipbetw

eenthe

inputvoltage

andthe

on-time.

The

opratingfrequency

canbe

externallyprogram

med

upto

1MH

z.P

rotectionfeatures

includeV

CC

under-voltagelockout,

thermal

shutdown

andgate

driveunder-voltage

lockout.T

hepart

isavailable

ina

thermally

enhancedeT

SS

OP

-20package

Featu

resn

Inputvoltage

range4.5V

-36V

n1.5A

outputcurrent

n0.8V,

±1.5%

referencen

Integrated40V,

dualN-C

hannelbucksynchronous

switches

nLow

component

countand

smallsolution

sizen

No

loopcom

pensationrequired

nU

ltra-fasttransient

responsen

Stable

with

ceramic

andother

lowE

SR

capacitorsn

Program

mable

switching

frequencyup

to1M

Hz

nM

ax.duty

cyclelim

itedduring

start-upn

Valley

currentlim

itn

Precision

InternalReference

foradjustable

outputvoltage

down

to0.8V

nT

hermalshutdow

nn

Therm

allyenhanced

eTS

SO

P-20

package

Typ

icalA

pp

lication

sn

5VD

C,

12VD

C,

24VD

C,

12VA

C,

and24V

AC

systems

nE

mbedded

System

sn

IndustrialControls

nA

utomotive

Telematics

andB

odyE

lectronicsn

Point

ofLoad

Regulators

nS

torageS

ystems

nB

roadbandInfrastructure

nD

irectC

onversionfrom

2/3/4C

ellLithiumB

atteriesS

ystems

Typ

icalA

pp

lication

20174702

SIM

PLE

SW

ITC

HE

R®

isa

registeredtradem

arkof

NationalS

emiconductor

Corporation

February

2006

LM3100SIMPLESWITCHER®Synchronous1MHz1.5AStep-DownVoltageRegulator

©2006

NationalS

emiconductor

Corporation

DS

201747w

ww

.national.com

Ab

solu

teM

aximu

mR

ating

s(N

ote1)

IfM

ilitary/Aero

space

specified

devices

arereq

uired

,p

leaseco

ntactth

eN

ation

alSem

icon

du

ctor

Sales

Office/

Distrib

uto

rsfo

ravailab

ilityan

dsp

ecification

s.

VIN

,R

ON

toG

ND

-0.3Vto

40V

SW

toG

ND

-0.3Vto

40V

SW

toG

ND

(Transient)-2V

( <100ns)

VIN

toS

W-0.3V

to40V

BS

Tto

SW

-0.3Vto

7V

AllO

therInputs

toG

ND

-0.3Vto

7V

ES

DR

ating(N

ote2)

Hum

anB

odyM

odel±

2kV

Storage

Temperature

Range

-65˚Cto

+150˚C

JunctionTem

perature(T

J )150˚C

Op

erating

Ratin

gs

(Note

1)

Supply

Voltage

Range

(VIN

)4.5V

to36V

JunctionT

emperature

Range

(TJ )

−40˚C

to+

125˚C

Therm

alResistance

(θJC )

(Note

3)6.5˚C

/W

ElectricalC

harateristics

Specifications

with

standardtype

arefor

TJ

=25˚C

only;lim

itsin

boldfacetype

ap-ply

overthe

fullOperating

JunctionT

emperature

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2

Tuesday 27 N

ovember 2012

1005 – 1055

Continued overleaf

Page 1 of 2

University of G

lasgowD

egrees of M.E

ng., B

.En

g. and B

.Sc. (Hon

s) in E

ngin

eering

EL

EC

TR

ON

IC D

ESIG

N P

RO

JEC

T 2

First C

lass Test

Attem

pt AL

L questions. T

otal 50 marks. T

ime 50 m

inutes

The num

bers in square brackets in the right-hand margin indicate the m

arks allotted to thepart of the question against w

hich the mark is show

n. These m

arks are for guidance only.

An electronic calculator m

ay be used provided that it does not have a facility for eithertextual storage or display, or for graphical display.

Q1

(a)D

efine the quantity LSB

for an analogue-to-digital converter (AD

C) and explain

its significance. Write dow

n an equation for the input–output characteristic of anA

DC

, defining all terms that you use.

[4]

(b)D

raw a clearly labelled sketch of the input–output characteristic for a 3-bit A

DC

with L

SB

= 0.2 V

. Pay particular attention to the labels, scales and units of the

axes.[5]

(c)A

n 8-bit AD

C has an input range of 0 – 5.120 V

. What outputs does it produce for

inputs of (i) 10 mV

, (ii) 1234 mV

and (iii) 5114 mV

?[3]

(d)W

hat can you say about the input if the output is 180 (decimal)?

[2]

Q2

The output of a tem

perature sensor is a voltage proportional to absolute temperature

with a scale of 10 m

V K

–1. It is required to work over the range –40°C

to +75°C

. [Take

0°C =

273 K.] T

he output is connected directly to an AD

C, w

hose full-scale voltage isset by the single pow

er supply at 5.0 V.

(a)W

hat range of voltages must be converted by the A

DC

?[2]

(b)T

he system is required to resolve 0.5°C

or better. How

many bits of output m

ustthe A

DC

produce?[3]

(c)T

he digital system chosen for this application has only an 8-bit A

DC

. Is itpossible to m

eet the specification of the system by including som

e type ofam

plifying circuit? If so, explain what type of circuit should be used and give its

specification but do not design the circuit in detail.[4]

(d)A

reviewer suggests that it w

ould be better to use an AD

C w

ith a separatereference voltage, rather than a reference derived from

the power supply. E

xplainw

hether this is good advice or not.[2]

(e)T

he designer accepts the advice and chooses a reference with a voltage drift of

100ppm/°C

. Explain w

hether this is a good choice or not.[2]

End of question paper

Page 2 of 2

Q3

(a)Sketch the circuit of a 2-bit flash A

DC

. [3]

(b)W

hat are the general characteristics of a flash AD

C and for w

hat type ofapplication w

ould it be used?[3]

Q4

The m

ain feature of interest in the output of a‘knock’ detector in a car is a signal around7 kH

z but other components of the output have frequencies up to 40 kH

z. The signal is

fed to an AD

C, w

hich requires 10-bit resolution.

(a)W

hat is the minim

um frequency at w

hich samples should be taken to ensure a

faithful representation of the input?[2]

(b)E

xplain what w

ould happen if a lower sam

pling frequency were used. D

efine anyspecialised term

s that you use.[2]

(c)T

his would traditionally be seen as an application for a successive-approxim

ationA

DC

but why m

ight a sigma–delta A

DC

be preferred?[2]

(d)Sigm

a–delta AD

Cs w

ere more expensive than successive-approxim

ation AD

Cs in

the past but this is now changing. W

hy?[2]

Q5

(a)A

resistive sensor can be modelled as the potential divider show

n on the left ofFigure Q

5. Obtain the T

hévenin equivalent circuit of the sensor.[3]

(b)T

his sensor is connected to a 12-bit AD

C w

ith input characteristics of Rin =

10 kWand C

in = 10 pF

and a fixed charging time of 1 µs. W

ill the system suffer from

errors due to incomplete charging?

[6]

VC

C = 3.0 V

20 k W

10 kW

AD

CV

inFigure Q

5.

Tuesday 19 M

arch 20131005 – 1055

Continued overleaf

Page 1 of 2

University of G

lasgowD

egrees of M.E

ng., B

.En

g. and B

.Sc. (Hon

s) in E

ngin

eering

EL

EC

TR

ON

IC D

ESIG

N P

RO

JEC

T 2

Second Class T

est

Attem

pt AL

L questions. T

otal 50 marks. T

ime 50 m

inutes

The num

bers in square brackets in the right-hand margin indicate the m

arks allotted to thepart of the question against w

hich the mark is show

n. These m

arks are for guidance only.

An electronic calculator m

ay be used provided that it does not have a facility for eithertextual storage or display, or for graphical display.

Q1

A pow

er supply is found to deliver 3.3 V into a 100 W

load and 3.0 V into a 50 W

load.Y

ou may assum

e that it can be modelled by a N

orton or Thévenin equivalent circuit.

(a)C

alculate the open-circuit voltage, short-circuit current and output resistance ofthe supply.

[6]

(b)W

hat current and voltage would the supply deliver to a 200 W

load?[2]

(c)W

hat load dissipates the maxim

um pow

er from this supply and w

hat is thism

aximum

power?

[4]

Q2

A m

obile phone is powered by a L

i-ion battery with an open-circuit voltage of 3.6 V

,an internal resistance of 0.1 W

and a capacity of 2000 mA

h. Part of the phone is a

radio-frequency power am

plifier that draws 6 A

in pulses of 1 ms and requires a supply

voltage between 3.3 V

and 3.6 V. T

he other parts of the phone draw a m

uch lower

current and can be neglected for parts (a)–(c).

(a)S

how that the phone w

ill not work correctly if the pow

er amplifier is connected

directly to the battery.[1]

(b)A

capacitor is connected across the power am

plifier to maintain the voltage w

hilethe am

plifier is operating. You m

ay assume that the capacitor is ideal. E

stimate

the value of capacitance needed to ensure correct operation of the power

amplifier. O

nly an estimate is required, not an exact calculation.

[6]

(c)T

he capacitor has an equivalent series resistance (ES

R) of 0.2 W

. Is there enoughtim

e for the capacitor to recharge between pulses of the pow

er amplifier if it

operates every 20 ms?

[3]

(d)E

stimate the lifetim

e of the battery assuming that the pow

er amplifier operates as

described in part (c) and that the other components of the phone draw

a steady100 m

A.

[3]

(e)T

he phone has an LE

D that draw

s 3.0 mA

and drops 1.6 V to show

that it isturned on. D

esign and draw a suitable circuit.

[2]

End of question paper

Page 2 of 2

Q3

A sw

itch-mode pow

er supply can be modelled by the circuit show

n in Figure Q

3,w

hich also shows a plot of the current through the inductor as a function of tim

e for asingle, com

plete period of switching. T

he switch alternates betw

een positions (a) and(b) w

ith corresponding labels on the plot.

(a)W

rite down the general relation betw

een current and voltage as a function of time

for (i) a capacitor and (ii) an inductor.[2]

(b)W

hat are the input and output voltages of this converter?[4]

(c)H

ow can the output voltage of this converter be varied and w

hat range of outputvoltages can be produced?

[2]

iL (t)

load

10 m

H

02

46

t / ms

10 2 3

iL / A

(a)(b)

(a)(b)

Figure Q

3.

Q4

A 5.0 V

linear regulator has a dropout voltage of 1.2 V.

(a)W

hat is the minim

um input voltage required for correct operation of this

regulator?[1]

(b)S

ketch an annotated plot of the output voltage as a function of the input voltagefrom

zero to 10 V.

[5]

(c)H

ow m

uch power is dissipated in this regulator w

hen the input is at 9.0 V and the

load draws 200 m

A?

[2]

(d)W

hat is the (power) efficiency of the regulator under these conditions?

[2]

Q5

A transistor has therm

al resistances qjc =

2∞C/W

and qca =

80∞C/W

, and a maxim

umjunction tem

perature of 125∞C.

(a)D

etermine the m

aximum

permitted pow

er dissipation in an ambient tem

peratureof 25∞C

.[3]

(b)Specify the heatsink required if the transistor is to dissipate 3

W safely in the sam

eam

bient temperature.

[2]