MODELINGMEASUREMENTSYSTEMS
USINGVOLTAGEDIVIDERS
LAB2INTRO:MEASURINGPROPERTIESOFVOLTAGEDIVIDERS,DEVELOPINGMODELSOF
MEASUREMENTDEVICES(DMM,SCOPE),BUILDINGAVARIABLEVOLTAGESOURCE
GOALS
Inthislab,youwillgainexperienceworkingwiththeprototypingboard,whichwillbethemainplatformfor
buildingcircuitsfortherestofthesemester.Youwillalsolearnhowtorefineyoumodelofacircuittoincludethe
measurementprobes.Finally,youwilluseapplyyourknowledgeofvoltagedividerstobuildadimmerswitch.
Proficiencywithnewequipment:
o
o
Prototypingboard:
! Setpowerrailsontheboard
! Determinetheconnectionlayoutontheproto-boards
! Beabletoassembleresistivecircuitsandmeasurementtestpointsontheboards
Potentiometers
! Determinetheconnectionsona10-turnpot.
! Useapottocontinuouslycontrolanoutputvoltage.
Modelingmeasurementsystems:
o
o
Developmathematicalandschematicmodelsofvoltagedividers.
Refinethevoltagedividermodelstoincludetheeffectofthemeasurementprobes.
Applications:
o
Buildadimmerswitchforalightbulb.
DEFINITIONS
Potentiometer(pot)–athreeterminalresistivedevicethatprovidesavariableresistancebetweentheendsand
thewiperconnection.
READINGS
DiefenderferandHoltonChapter1.
Additionallyoralternatively,youmightlookatFisher/CrippsSections2.1-2.3and/orHorowitz&HillSection1.03
1
LABPREPACTIVITIES
Answerthefollowingtwoquestionsinyourlabbook.ScantherelevantlabbookpagesandturninthepdftoD2L
bymidnightthedaybeforeyourlabsectionmeets.Hint:ifyoureadthroughtheentirelabguidebeforeyoucome
tolabyouwill1)bebetterpreparedtoaskquestions/conducttheexperiment,2)seehowthelabpreprelatesto
themorechallengingpartsofthelablater.Forexample,completingthelabprepthisweekwillallowyouto
constructthenecessarymodelsofvoltagedividersandmeasuringprobesveryquicklyduringyourlabsession.
Question1
ResistiveVoltageDividers(idealpowersupply)
Anidealvoltagesource(nointernalresistance)drivescurrentaroundtheloopofresistorsshown
inFigure1(a).
a.
b.
c.
Deriveaformulaforthecurrent,I,andtheoutputvoltage,Vout.
WhatisVoutifV=10V,R1=2kΩ,andR2=1kΩ?
CalculatethevoltageVoutforthemodifiedcircuitshowninFigure1(b)withR3=10kΩ
andtheothercomponentsunchanged.
Question2
ResistiveVoltageDividers(non-idealpowersupply)
Anon-idealvoltagesourcehasanoutputimpedance(resistance).Firstconsiderasupplywithan
outputimpedance500Ω.
a.
DrawamodifiedcircuitdiagramofFigure1(a)tomodelthenon-idealvoltagesourceas
I
anidealsourcewithaseriesresistor.
b. Deriveaformulaforthecurrent,I,andtheoutputvoltage,Voutofthecircuityoudrew
forPart(a)ofQuestion2.
R1
+
c. WhatisVoutifV=10V,R1=2kΩ,andR2=1kΩ?
d. AnadditionalloadisconnectedbetweenV
3
V outandgroundintheformoftheresistorR
Vout
asshowninFigure1(b).CalculatethevoltageVoutforthiscircuit(withthenon--ideal
powersupply)andwithR(a)
3=10kΩ. œ
R2
Labactivities
a. Readthroughallofthelabstepsandidentifythestep(orsub-step)thatyouthinkwill
0V
bethemostchallenging.
b. Listatleastonequestionyouhaveaboutthelabactivity.
Question3
I
I
R1
+
V
(a)
Vout
œ
R1
+
(b)
V
œ
R2
Vout
R2
R3
0V
0V
Figure1)VoltageDividers
I
2
(b)
Figure 2.4 Voltage dividers
R1
+
V
Vout
REVIEWINGLABWRITEUPS
Step0
ReviewApproachandExpectationstoLaboratoryNotebookwrite-ups:
Lab1Notebookshavebeenreturnedtoyou.Theseweregradedlenientlyandfuturelabswillbe
morestrictlyreviewedforcompletenessandcorrectness.
a.
b.
c.
Reviewthelabnotebookwrite-upguidelinesonthecoursewebsite.
Compareyourwrite-upforLab1withtheExemplarLab1Write-upSharedinLab.
Identify3specificitems/approachesthatyouwilleitherkeeporchangefor
laboratory2(e.g.Iwillmakesuretolabelmygraphsandplotusingthe
Mathematicaguidelinesprovided).
SETTINGUPYOURPROTOTYPINGBOARD
Mostcircuitdesignsarefirsttestedusingprototypingboardstoallowforeasychangesofcomponents.Oncethe
circuitworksandmeetsthedesiredspecifications,thecircuitwilloftenbebuiltusingmorepermanentmethods
suchassolderingtoaVectorboardortoaprintedcircuitboard.Presenttechnologyallowsforanyonetocheaply
design,layout,andhaveprofessionalcircuitboardsprinted.Forexample:http://www.expresspcb.com/
Step1
3
Testyourprototypingboard.
a. Yourinstructorwillgiveyourteamaprototypingboardtouseforbuildingyourprojects.
Writeyourteammember’snamesonit.Yourteamwillusethesameboardall
semester.Anincompleteexperimentcanbeleftontheboardandfinishedlater.Store
theboardontheshelflabeledforyoursection.
b. Onthefrontpanel,youwillfind:
• BNCcablejacksthatcarryelectricsignalsbetweenyourcircuitontheboardandthe
functiongeneratorandoscilloscope.
• Coloredbananajackstobringindcpowerfortransistorsorchipsfromanexternalpower
supply.
• Aprecision10kΩten-turnpotentiometerandseveralswitches.
• Awireorcomponentontheboardmightbebroken,ormightbreakduringthesemester.
Don’tworry–youwillbeabletorepairtheboardasyougo.
c. Thecircuitboardcontainsarraysofholes,interconnectedbyburiedconductors,into
whichcomponentsarepluggedtobuildyourcircuit.Ingeneral,youcanneverbesure
thatanytwocontactsarereallyconnected,oranywireisreallycontinuous,unlessyou
testityourself,sogetintothehabitoftestingthings.
d. DeterminewhichholesonyourprotoboardareconnectedbyusingtheDMM.Drawa
diagraminyourlabbookoftheconnections.Youcanreferbacktothisdiagram
throughoutthesemesterasyoubuildnewcircuits.
Step2
Makingpowerconnectionstoyourprotoboard.
a. For essentially all circuits, you will need power connections (+15 V, -15V, ground).
Connectthepowersupplytothepanelusingbananacables.
b. USE A COLOR CODE FOR THE POWER CONNECTIONS! Typically black = ground, red =
+15V,andblue=-15V.Usingaconsistentcolorcodewillallowyouandotherstomore
quicklydebugyourcircuits.Youarealsolesslikelytoplugsomethinginincorrectlyand
burnupacomponent.Writedownyourcolorcodeinyourlabbook.
c. Onceyouhavepowerconnectedtothefrontpanel,usethewiressolderedontheback
of the connectors to make connections to the board (+15, -15, and 0V). The long rails
that run the length of the board are best for distributing power to all of your
components.Usetheseforonlypowerorground.
d. Goodelectricalcontactisessentialwhenyouplugincomponentsorwires.Useonly22
or 24 gauge solid wire, not stranded wire. 22/24 gauge wire should make a good
connection with the conductors inside the board without slipping out easily. Push in
eachwireuntilyoufeelthecontactsgrip.
e. Reliablegroundconnections(0V),readilyaccessiblefromanypointontheboard,are
essentialtothegoodfunctioningofmostcircuits.Thefrontpanelisthegroundforyour
circuit board since the outside of the BNC connector connects the front panel of your
circuitboardtothegroundofotherinstrumentsinyourexperiment.
Step3
Supplyingpowertotheprotoboard.
a. TurnonyourDCpowersupplysuchthatitproduces+15Vand-15V.Setthecurrent
limit to about 100 mA. This will reduce the amount of smoke released from your
componentswhenyouhappentopluginthepowerincorrectly.Describetheprocedure
youfollowedtosetthecurrentlimit.
b. MeasurethevoltageonyourprotoboardrailsusingaDMM.Youmayneedtouseawire
toprobethevoltageifyourDMMprobesdonotfitintheholes.Alwaysrememberto
measurevoltageswithrespecttoground.Recordthevoltagesinyourlabbook.
BUILDINGANDTESTINGVOLTAGEDIVIDERS
Step4
Fixed-valuevoltagedivider-1kΩ
Components(resistors,capacitors,transistors,etc.)areavailablefromthecommunitystock.
Takewhatcomponentsyouneedfortheexperiment.
a. BuildavoltagedividersimilartotheoneshowninFig.1(a)usingresistorsofaround
1kΩ.Drawadiagramofthecircuitinyourlabbook.Makesuretolabeltheresistors
andrecordallmeasuredcomponentvaluesandvoltages.
b. MeasureeachresistorwithyourDMMbeforeinsertingitintoyourcircuitandrecord
thevalue.Whyshouldyoumeasurecomponentvaluesbeforeplacingtheminthe
circuit?
c. Predicttheoutputvoltageyoushouldmeasurebasedonyourinputvoltageand
resistancemeasurements.Includeyourcalculationsandnumericalpredictionsinyour
labbook.
d. Now,applyaDCvoltagetotheinputandmeasuretheoutputvoltageofyourdivider,
firstusingfirstyourDMMandsecondusingyouroscilloscopewiththeminigrabbers.
Recordyourmeasurements.(DonothavetheDMMandtheoscilloscopeconnectedat
4
thesametimebecauseeachmayperturbthemeasurementdifferently.)
Comparethevoltagesyoupredictedtothevoltagesyoumeasured.Doesyourmodelof
thevoltagedivideragreewitheachofyourmeasurements?Explicitlyrecordwhat
criteriayouusedtodeterminewhetherornotthemodelandmeasurementsagreed.
f. Completethissteponlyifyourmodelandmeasurementsdidnotagree.Ifyourmodel
andmeasurementsdidnotagree,youwillhavetoeitherrefineyourmodeloryour
experiment.Let’sstartbyrefiningyourmodel.Considertheinputresistanceofyour
measurementdevice.Drawacircuitdiagramthatincludesthatresistance.HINT:You
alreadyworkedwiththiscircuitmodelinyourprelab.Deriveanexpressionforthe
outputvoltagenowincludingtheunknownmeasurementdeviceresistance.Usethis
newmodeltodeterminetheinputresistanceofmeasurementdevice.
Fixed-valuevoltagedivider–1MΩ and10MΩ
a. Completestepsa-fofQuestion4fortwoadditionalvoltagedividers,oneusingresistors
~1MΩandonewithresistors~10MΩ.
b. Usingyourrefinedmodel,youhavedeterminedtheinputresistanceofboththeDMM
andscope.Specificationorspec.sheetsordatasheetscanalsobeusedtorefineyour
model.
c. LookuptheinputresistanceofyourDMMusingthespec.sheetsonthecoursewebsite.
Doesthemeasuredinputresistanceagreewiththeinstrumentspecs?Explicitlyrecord
whatcriteriayouusedtodeterminewhetherornottheresistancesagree.
d. Thereisaneasywaytodeterminethespecifiedinputimpedanceofthescope.Where
canyoufindthatinformation?Doesthemeasuredinputresistanceagreewiththe
instrumentspecs?Explicitlyrecordwhatcriteriayouusedtodeterminewhetherornot
theresistancesagree.
e.
Step5
APPLICATIONEXPERIMENT:BUILDACONTROLLABLEVOLTAGESOURCE(DIMMERSWITCH)
Youwillnowuseyourskillswithbuildingandtestingvoltagedividerstobuildacontrollablevoltagesourceusinga
potentiometer.
Step6
Step7
5
a.
Determiningtheoperationofapotentiometer.
a. Thepotentiometeronthecircuitboardpanelhasthreeconnections.Twoofthe
connectionsareatoppositeendofaresistor.Thethirdconnectionisconnectedtoa
sliding“wiper.”UsetheDMMtomeasuretheresistancebetweenallpossiblepairsof
connectionswhileturningtheknoboveritscompleterange.
b. Drawadiagramofthepotincludingamodeloftheinternalcomponentsandexternal
connectionsusingtheresistanceobservations.
Buildavariablevoltagesource/Usingapottolightalightbulb(LightbulbDimmer)
a. Drawacircuitdiagramthatusesonepottocreateavariablevoltagedivider.
b. Deriveanexpressionfortheoutputvoltagebasedontheinputvoltageandthetwo
resistances.Arebothresistancesvariableorisonefixed?
c. Constructyourvoltagedivideranduseascopetomeasuretheoutputvoltage.Doyou
needtoincludethescopeinputresistanceinyourmodel?Explainwhyorwhynot.
d. Predictthemaximumandminimumoutputvoltage(whenthewiperisatoneendand
thentheother).
e. Testyourmodelbymakingmeasurementsonthescope.Makesuretoincludethelimits
ofthevoltagesource.Doyourmeasurementsagreewithyourpredictions?Explicitly
recordwhatcriteriayouusedtodeterminewhetherornotthemodeland
measurementsagree.
f.
g.
6
Nowconnectalowvoltagelightbulbtotheoutput.Youmayneedtoincreasethe
currentlimitonthepowersupplytoseevisiblelight(Donotexceed500mAoryourpot
mayburnout).Describequalitativelythebrightnessofthebulbasthepotknobis
adjusted.Whatistheminimumvoltageneededtoseethelightbulbturnon?
Bonusquestion:Agoodvoltagesourcehasverylittle(afewohms)outputresistance
andthusverylittlepowerisdissipatedinthesupply.Whatistheoutputresistanceof
thecircuit(includingyourpowersupplyandexternalcomponents)ifitproduces10V?
Wouldthiscircuitbegoodforcreatingavariablevoltagesourceintherangeof5-10V?
HINT:Considerthepowerdissipatedinthesource.Explainusingyourdiagram,model,
andvaluesofresistance.