General Prerequisites Preamble - Virginia TechLiaB/EDPS 2/Electronic Desgin Project 2... ·...
-
Upload
nguyenxuyen -
Category
Documents
-
view
215 -
download
0
Transcript of General Prerequisites Preamble - Virginia TechLiaB/EDPS 2/Electronic Desgin Project 2... ·...
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
..
..
..
..
..
..
..
..
..
.6
2.2R
esolution,precisionand
accuracy.
..
..
..
..
..
..
..
..
..
..
..
.9
2.3Sum
mary
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.10
2.4E
xamples
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.10
3B
asictypesofanalogue-to-digitalconverter
123.1
Introduction.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.12
3.2C
omparators
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
143.3
Flashconverters
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
163.4
Pipelineconverters
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
183.5
Successive-approximation
(SAR
)converters.
..
..
..
..
..
..
..
..
..
203.6
Practicalissuesw
ithSA
RA
DC
s.
..
..
..
..
..
..
..
..
..
..
..
..
233.7
Integratingconverters
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.26
3.8Sum
mary
ofclassicalAD
Cs
..
..
..
..
..
..
..
..
..
..
..
..
..
.29
3.9E
xamples
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.30
4Sam
pling,oversampling
andsigm
a–deltaconverters
314.1
Sampling
rateand
theN
yquistfrequency.
..
..
..
..
..
..
..
..
..
..
314.2
Sigma–delta
converters.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.33
4.3Practicalissues
with
sigma–delta
converters.
..
..
..
..
..
..
..
..
..
344.4
Summ
aryofsigm
a–deltaconverters
..
..
..
..
..
..
..
..
..
..
..
.35
4.5R
eflectionon
AD
Cs
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
364.6
Exam
ples.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
36
5Sum
mary:Selection
ofanA
DC
37
vii
viiiC
ontents
6Signalconditioning
396.1
Am
plification.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
396.2
Single-supplyop-am
ps.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.41
6.3C
ircuitsw
ithsingle-supply
op-amps
..
..
..
..
..
..
..
..
..
..
..
.43
6.4Filters
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.46
6.5C
omparators
andSchm
itttriggers.
..
..
..
..
..
..
..
..
..
..
..
.47
6.6Sam
ple-and-holdcircuit.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.50
6.7Sum
mary
ofsignalconditioning.
..
..
..
..
..
..
..
..
..
..
..
..
516.8
Exam
ples.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
51
7C
omplete
systemsw
ithA
DC
s53
7.1Voltage
reference.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
537.2
Ratiom
etricm
easurements
..
..
..
..
..
..
..
..
..
..
..
..
..
..
557.3
Measurem
entofabsolutevoltages
with
asim
pleA
DC
..
..
..
..
..
..
..
557.4
Worked
example:Tem
peraturesensorw
ithL
M35
and8-bitA
DC
..
..
..
..
567.5
Worked
example:M
easurementoftem
peratureusing
atherm
istor.
..
..
..
587.6
Worked
example:sensorw
ithgiven
rangeofvoltages.
..
..
..
..
..
..
.61
7.7W
orkedexam
ple:Sensorforaw
eighingm
achine.
..
..
..
..
..
..
..
.62
7.8E
xamples
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.64
8D
igital-to-analogueconverters
668.1
Introduction.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.66
8.2G
eneralfeaturesofdigitalto
analogueconverters
..
..
..
..
..
..
..
..
668.3
Pulsew
idthm
odulation.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.67
8.4Types
ofdigitaltoanalogue
converter.
..
..
..
..
..
..
..
..
..
..
.69
8.5Sum
mary
ofDA
Cs
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
768.6
Exam
ples.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
77
IIPow
ersuppliesand
passivecom
ponents78
9Pow
ersupplies
799.1
Introduction.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.79
10B
atteries82
10.1Introduction
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
8210.2
Capacity
ofbatteries.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
8310.3
How
shouldyou
choosea
battery?.
..
..
..
..
..
..
..
..
..
..
..
.85
10.4Forw
hatvoltageshould
youdesign
abattery-pow
eredcircuit?
..
..
..
..
.86
10.5Supercapacitors
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
8710.6
Worked
example:pulsed
currentdrawn
froma
coincell
..
..
..
..
..
..
.87
10.7E
xamples
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.89
Contents
ix
11R
ectifiers90
11.1Transform
ers.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
9011.2
Rectifiers
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.91
11.3Sm
oothing.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
9211.4
Calculation
ofinputvoltage.
..
..
..
..
..
..
..
..
..
..
..
..
..
.95
11.5C
onclusion.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.96
11.6E
xamples
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.96
12L
inearregulators
9812.1
Zenerdiode
regulator.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
9812.2
Seriestransistorregulator
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.101
12.3L
owdropoutregulators
(LD
Os)
..
..
..
..
..
..
..
..
..
..
..
..
.104
12.4Packaged
regulators.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.105
12.5E
xamples
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.106
13H
owto
reada
datasheet
10713.1
Generaldescription
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
10713.2
Connection
diagrams
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.108
13.3O
rderinginform
ation.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
10813.4
Typicalapplications.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.108
13.5A
bsolutem
aximum
ratings.
..
..
..
..
..
..
..
..
..
..
..
..
..
.109
13.6E
lectricalcharacteristics.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
10913.7
Typicalperformance
characteristics.
..
..
..
..
..
..
..
..
..
..
..
11013.8
Schematic
diagram.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.111
13.9A
pplicationhints
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.111
13.10Definition
ofterms
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
11113.11Physicaldim
ensions.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.111
14Sw
itchingpow
ersupplies
11314.1
Switched-capacitor,charge-pum
porflying-capacitorconverters
..
..
..
..
11314.2
Switched
inductorconverters.
..
..
..
..
..
..
..
..
..
..
..
..
..
11514.3
Basic
buckconverter
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.115
14.4B
oostconverter.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.120
14.5Inverting
(buck/boost)converter.
..
..
..
..
..
..
..
..
..
..
..
..
12114.6
Flybackconverter
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.122
14.7C
omplete
mains
switching
powersupply
unit.
..
..
..
..
..
..
..
..
.122
14.8G
eneralfeaturesofsw
itchingconverters
..
..
..
..
..
..
..
..
..
..
.123
14.9W
illIneedto
designone
ofthese?.
..
..
..
..
..
..
..
..
..
..
..
.124
14.10Exam
ples.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
124
15Passive
components,heatsinksand
printedcircuitboards
12615.1
Resistors
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
12615.2
Capacitors
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.128
15.3Inductors
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.132
15.4Standard
valuesofcom
ponents.
..
..
..
..
..
..
..
..
..
..
..
..
.133
xC
ontents
15.5H
eatsinks.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
13315.6
Printedcircuitboards
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.137
15.7C
omponentpackages
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.139
15.8E
xamples
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.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
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
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
LT
AG
E O
UT
PU
T
TO
-220 3-Lead
Po
wer P
ackage
525406
Fro
nt V
iew
TO
-263 Su
rface-Mo
un
t Packag
e
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
To
p V
iew(B
um
p S
ide D
ow
n)
micro
SM
D L
aser Mark
525439
AD
JUS
TA
BL
E O
UT
PU
T V
OL
TA
GE
TO
-220 5-Lead
Po
wer P
ackage
525409
Fro
nt V
iew
TO
-2635-L
ead S
urface-M
ou
nt P
ackage
525413
To
p V
iew
525414
Sid
e View
8-Pin
Su
rface Mo
un
t
525410
To
p V
iew
ww
w.national.com
2
LM2931
Ord
ering
Info
rmatio
nO
utp
ut
Nu
mb
erP
ackage
Part N
um
ber
Packag
e Markin
gT
ransp
ort M
edia
NS
C D
rawin
g
5V3-P
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
ww
.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
ww
.national.com
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
ww
w.national.com
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
ww
.national.com
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
ww
w.national.com
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
ww
.national.com
LM2931
Sch
ematic D
iagram
525401
ww
w.national.com
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
ww
.national.com
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
(TJ )
range.M
inimum
andM
aximum
limits
areguaranteed
throughtest,
de-sign,
orstatisticalcorrelation.
Typicalvalues
representthe
most
likelyparam
etricnorm
atT
J=
25˚C,
andare
providedfor
ref-erence
purposesonly.
Unless
otherwise
statedthe
following
conditionsapply:
VIN
=18V
,V
OU
T=
3.3V.
Sym
bo
lP
arameter
Co
nd
ition
sM
inT
ypM
axU
nits
Start-U
pR
egu
lator,
VC
C
VC
CV
CC
outputvoltage
CC
C=
680nF,
noload
5.06.0
7.2V
VIN
-V
CC
VIN
-V
CC
dropoutvoltage
ICC
=2m
A50
140m
V
ICC
=20m
A350
570
IVC
CL
VC
Ccurrent
limit
(Note
4)V
CC
=0V
4065
mA
VC
C-U
VLO
VC
Cunder-voltage
lockoutthreshold
(UV
LO)
VIN
increasing3.6
3.753.85
V
VC
C-U
VLO
-HY
SV
CC
UV
LOhysteresis
VIN
decreasing130
mV
tVC
C-U
VLO
-DV
CC
UV
LOfilter
delay3
µs
IINIIN
operatingcurrent
No
switching,
VF
B=
1V0.7
1m
A
IIN-S
DIIN
operatingcurrent,
Device
shutdown
VE
N=
0V17
30µA
Sw
itchin
gC
haracteristics
RD
S-U
P-O
NM
ainM
OS
FE
TR
ds(on)0.18
0.35Ω
RD
S-
DN
-ON
Syn.
MO
SF
ET
Rds(on)
0.110.2
ΩV
G-U
VLO
Gate
drivevoltage
UV
LOV
BS
T-
VS
Wincreasing
3.34
V
So
ft-startISS
SS
pinsource
currentV
SS
=0.5V
68
9.8µA
Cu
rrent
Lim
it
ICL
Syn.
MO
SF
ET
currentlim
itthreshold
1.9A
ON
/OF
FT
imer
tON
ON
timer
pulsew
idthV
IN=
10V,
RO
N=
100kΩ
1.38µs
VIN
=30V
,R
ON
=100
kΩ0.47
tON
-MIN
ON
timer
minim
umpulse
width
200ns
tOF
FO
FF
timer
pulsew
idth260
ns
En
able
Inp
ut
VE
NE
NP
ininput
thresholdV
EN
rising1.236
1.261.285
V
VE
N-H
YS
Enable
thresholdhysteresis
VE
Nfalling
90m
V
Reg
ulatio
nan
dO
ver-Vo
ltage
Co
mp
arator
VF
BIn-regulation
feedbackvoltage
VS
S≥
0.8VT
J=
−40˚C
to+
125˚C0.784
0.80.816
V
VS
S≥
0.8VT
J=
0˚Cto
+125˚C
0.7880.812
VF
B-O
VF
eedbackover-voltage
threshold0.894
0.9200.940
V
IFB
5100
nA
Th
ermal
Sh
utd
ow
n
TS
DT
hermalshutdow
ntem
peratureT
Jrising
165˚C
LM3100
ww
w.national.com
4
LP
5526L
igh
ting
Man
agem
ent
Un
itw
ithH
igh
Voltag
eB
oo
stC
on
verterw
ithu
pto
150mA
Serial
FL
AS
HL
ED
Driver
Gen
eralD
escriptio
nLP
5526is
aLighting
Managem
entU
nitfor
portableapplica-
tions.It
isused
todrive
displaybacklights,
keypadLE
Ds,
RG
BLE
Ds
andcam
eraflash
LED
s.LP
5526can
drive2
separatelyconnected
stringsof
LED
sw
ithhigh
voltageboost
converter.T
heR
GB
driverallow
sdriving
eitherindi-
vidualcolorLE
Ds
orR
GB
LED
fromseparate
supplypow
er,or
itcan
beused
todrive
seriesconnecter
flashLE
Ds
fromhigh
voltageboost
converter.
The
backlightdrivers
(MA
INand
SU
Bpins)
areboth
highresolution
constantcurrent
mode
drivers.T
heflash
outputscan
driveseries
connectedflash
LED
with
upto
150mA
ofcurrent.E
xternalPW
Mcontrolcan
beused
fordim
ming
anyselected
LED
outputsor
itcan
beused
totrigger
theflash.
The
flashhas
also1-second
safetytim
er.
The
deviceis
controlledthrough
2-wire
lowvoltage
I 2Ccom
patibleinterface
thatreduces
thenum
berof
requiredconnections.
Featu
resn
High
efficiencyboost
converterw
ithprogram
mable
outputvoltage
upto
20Vn
2individualdrivers
forserialdisplay
backlightLE
Ds
nA
utomatic
dimm
ingcontroller
nS
tandalone
RG
Bcontroller
nD
edicatedflash
functionn
Safety
functionto
avoidprolonged
flashn
3generalpurpose
IOpins
n25-bum
pm
icroS
MD
Package:
(2.54mm
x2.54m
mx
0.6mm
)
Ap
plicatio
ns
nC
ellularP
honesand
PD
As
nM
P3
Players
nD
igitalCam
eras
Typ
icalA
pp
lication
20179770
March
2006
LP5526LightingManagementUnitwithHighVoltageBoostConverterwithupto150mASerialFLASHLEDDriver
©2006
NationalS
emiconductor
Corporation
DS
201797w
ww
.national.com
Typ
icalA
pp
lication
(Continued)
20179701
Co
nn
ection
Diag
rams
25-Bu
mp
Th
inM
icroS
MD
Packag
e,L
arge
Bu
mp
NS
Packag
eN
um
ber
TL
A25C
CA
20179771
To
pV
iew20179772
Bo
ttom
View
LP5526
ww
w.national.com
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]