外文翻译AT89CX051微控制器的模拟数字变换器应用文档格式.docx

外文翻译AT89CX051微控制器的模拟数字变换器应用文档格式.docx

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RCAnalog-to-DigitalConverter

Thisconversionmethodoffers.Anextremelylowcomponentcountattheexpenseofaccuracyandconversiontime.Intheexamplepresentedbelow,resolutionisbetterthan50millivolts,accuracyissomewhatlessthanatenthofaVoltandconversiontimeissevenmillisecondsorless.

AsshowninFigure1,theRCanalog-todigital.conversionmethodrequiresonlytworesistorsandacapacitorinadditiontotheAT89CX051microcontroller.Amicrocontrolleroutput（pin11）,whichswingsfromapproximatelygroundtoVCC,alternatelychargesanddischargesthecapacitorconnectedtothe

non-invertinginputoftheinternalcomparator（pin12）.Themicrocontroller

measuresthetimerequiredforthevoltageonthecapacitortomatchtheunknownvoltageappliedtotheinvertinginputoftheinternalcomparator（pin13）.Theunknownvoltageisafunctionofthemeasuredtime.

TheHP5082-7300LEDdisplaysshowninFigure1arenotrequiredfortheconversion,butareutilizedbythesoftwaretoimplementasimpletwo-digitvoltmeter.Theresultoftheanalog-to-digitalconversionisdisplayedinvoltsandtenthsofavoltonthetwodisplays.ThevoltmeterapplicationdoesnotutilizethefullresolutionoftheRCconversionsoftware,butservestodemonstratethemethodaswellasprovidingatoolfordebug.

Thewaveformforatypicalcapacitorcharge/dischargecycleisshowninFigure2.ThedischargeportionofthecurveisidenticaltothechargeportionrotatedaboutthelineVC=VCC/2.Theequationsanddiscussionbelowapplytothechargeportionofthecycle,exceptwhereindicated.

Thevoltageonthecapacitorasafunctionoftimeisgivenbytheexponentialequation:

VC=VCC（1-e-t/RC）

（1）

whereVCisthevoltageonthecapacitorattimet,VCCisthesupplyvoltageandRCistheproductofthevaluesoftheresistorandcapacitor.NotethatvoltageisexpressedinVolts,timeinseconds,resistanceinOhmsandcapacitanceinFarads.TheproductRCisalsoknownasthe“timeconstant”ofthenetworkandaffectstheshapeofthewaveform.Thewaveformissteepestwhencapacitorchargingordischargingbeginsandflattenswithtime.

ThefirstproblemwiththeRCconversionmethodisthedifficultyofsolvingtheexponentialequationwithoututilizingfloatingpointcalculationsandtranscendentalfunctions.Onacompressedtimescale,theexponentialcurveappearsstraightovermuchofitslength,suggestingthatitmightbeapproximatedbyaline.Thisschemefailsduetothecontinuousvariationinslopeoverthelengthofthecurve,whichproducessignificanterror.ItalsodoesnotaddresstheproblemwherethecurverollsoffseverelyneartheasymptoteatVCC.

Themicrocontrollerneednotsolvetheexponentialequationinrealtimeifalookuptableisusedtomappre-calculatedvaluestoeachsampledtimeinterval.Thisschemeallowsthedatatobeencodedandformattedasrequiredbytheapplicationwhilesimplifyingtheconversionsoftware.Symmetriesinthedatamaybeexploitedtoreducethesizeofthetable.

ThesecondproblemwiththeRCconversionmethodisthesubstantialerrorwhichresultsfromvariationsincomponentvalues.Figure3showsanexaggeratedviewofthevariationinthevoltageonthecapacitorduetovariationsinthevaluesoftheresistorandcapacitor.Asshowninthefigure,thevariationinthevoltageonthecapacitordecreasesasthevoltageonthecapacitordecreases.

Thesymmetryofthecapacitorcharge/dischargecyclecanbeexploitedtoreducetheeffectofvariationsincomponentvaluesonconversionaccuracy.ThisisdonebyutilizingthechargeportionofthecycletomeasurevoltageslessthanVCC/2andthedischargeportiontomeasurevoltagesgreaterthanVCC/2.TheworstcaseerrorisreducedtotheerroratVCC/2.

Beforecomponentvaluescanbeassigned,thetimeintervalatwhichthecomparatoroutputistobesampledmustbedetermined.Thesampleintervalshouldbeasshortaspossibletomaximizeconverterresolutionandminimizeconversiontime.Thesampleintervalislimitedbythetimerequiredtoexecutetherequisitecode,whichisdeterminedbytheclockrateofthemicrocontroller.Inthevoltmeterapplication,themicrocontrolleroperateswitha12-MHzclock,resultinginasampleintervaloffivemicroseconds.

Thetimeconstant（RC）affectstheshapeofthecapacitorcharge/dischargewaveform.Thevalueofthetimeconstantmustbechosensothatthesteepestpartsofthewaveformareresolvabletothedesiredresolution.Thesteepestpartofthechargeportionofthewaveformoccursneartheorigin,whilethesteepestpartofthedischargeportionoccursnearVCC.Duetothesymmetryofthewaveform,thesametimeconstantmaybeusedformeasurementsmadeoneitherportionofthewaveform.

Figure4showsanexpandedviewoftherelationshipbetweenvoltageandsampletimeneartheorigin.Inthefigure,Visthedesiredvoltageresolutionoftheconverterandtisthesampleintervaldeterminedpreviously.Thecurvelabeled’VC’representsthevoltageonthecapacitor,

whichappearslinearatthisscale.Inthefigure,theslopeofthecurveisideal,causingsamplingtooccurnearthecenterofthevoltageintervals.Theslopeofthecurvemaybelessthanshown,butmaynotbegreater,orresolutionwillbelost.Notethatthefirstsampleisoffsetfromtheoriginby1/2

tocenterthesampleinthefirstvoltageinterval.Toobtaintheminimumvalueofthetimeconstantwhichwillproducetherequiredslopeatthefirstsample,solveEquation1forRC：

RC=-t/1n（1-VC/VCC）

（2）

Thenset

totheminimumdesiredresolution（0.05-volt）,

tothesampleintervaldeterminedpreviously（fivemicroseconds）,andcalculateRCatthefirstsamplepoint,where

VC=1/2

andt=1/2

:

TheproductofthevaluesofRandCmustnotbelessthanthecalculatedminimumtimeconstant.Utilizingaresistorwithaonepercenttoleranceandacapacitorwithafivepercenttolerance

（Rnorm-1%）（Cnorm-5%）>

4.99*10-4

Inthevoltmeterapplication,theselectedvaluesofRandCare267kilohmsand2nanofarads,respectively,yieldingaminimumtimeconstantofapproximately5.02•10-4.AnadditionalconstraintisplacedonthevalueofR.ReferringagaintoFigure1,notethe5.1kilohmpullupresistor

connectedtopin11ofthemicrocontroller.Thisresistorispresenttosupplementthemicrocontroller’sweakinternalpullup,buthasthedetrimentaleffectofchangingthetimeconstantoftheRCnetworkduringthechargeportionofthecapacitorcharge/dischargecycle.Thisproducesanasymmetryinthecharge/dischargewaveform,whichcontributestoconversionerror.Tominimizetheeffectofdifferencesinthecapacitorchargeanddischargepaths,thevalueofRshouldbechosentobemuchgreaterthanthevalueofthepullupresistor.Inthevoltmeterapplication,theselectedvalueofRis267kilohms,whichexceedsthevalueofthepullupresistorbymorethananorderofmagnitude.

Thetimeconstant（RC）,whichisafunctionofthedesiredconverterresolution,determinesthedurationofthecapacitorcharge/dischargecycle.Themoretimerequiredforthecapacitortochargeanddischarge,thegreaterthenumberofsamplesrequiredinthemeasurementloopandthegreaterthenumberofentriesinthelookuptable.

Figure1.TypicalCapacitorCharge/DIschargeCycle

Figure2.CapacitorVoltageVariationasaFunctionofRCVariation

Figure1.Figure2

Ctothesymmetryofthecapacitorcharge/dischargewaveform,thedeterminedsamplecountmaybeusedformeasurementsmadeduringeitherportionofthecycle.

FromEquation3:

tmax=-RmaxCmax•ln（1-（1/2）VCC/VCC）

=-（Rnom+1%）（Cnom+5%）ln（1/2）

=-（1.01）（267•103）（1.05）（2•10-9）ln（1/2）

=393s.

Theminimumnumberofsamplesforhalfthecycleis:

tmax/t=（393•10-6）/（5•10-6）=79

Tomaximizeaccuracy,voltagesfromzerotoVCC/2aremeasuredduringthechargeportionofthecapacitorcharge/dischargecycleandvoltagesfromVCCtoVCC/2aremeasuredduringthedischargeportionofthecycle.Asaresult,thetotalnumberofentriesinthetableistwicethenumberofsamplescalculatedpreviouslyforeachhalfcycle.Thelookuptablecontainsapplication-specificvaluescorrespondingtothecalculatedvoltageateachsample.Foreachhalfcycle,theNthentryinthetablecorrespondstothevoltageatt=（N-1）t,wheretisthesampleintervaldeterminedpreviously.Forthechargehalfcycle,thevoltageateachsampleiscalculatedbysolvingEquation1forthetimeelapsedsincethecapacitorbegantocharge.Forthedischargehalfcycle,thevoltageateachsampleiscalculatedbysolvingthefollowingequationforthetimeelapsedsincethecapacitorbegantodischarge:

VC=VCC•e-t/RC（3）

Thesizeandcontentsofthetablemayvaryfromapplicationtoapplicationdependingonthesampleintervalandconversionresolution.Astheresolutionincreases,thenumberofentriesinthetablegrows.

Inthevoltmeterapplication,withresolutionequalto0.05Volt,thelookuptablecontains158entries,whichistwicethenumberofsamplesperhalfcyclecalculatedabove.

Voltagescorrespondingtosamplestakenduringthechargehalfcyclearecalculatedbyreplacing’t’with’Nt’inEquation1,whereNrepresentsthesamplenumber（0-78）.Bysettingtequaltothesampleintervalof5microseconds,Rto267kilohms,Cto2