单片机外文翻译外文文献英文文献基于单片机的超声波测距系统的研究与设计.docx

单片机外文翻译外文文献英文文献基于单片机的超声波测距系统的研究与设计.docx

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单片机外文翻译外文文献英文文献基于单片机的超声波测距系统的研究与设计

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外文翻译

theequivalentdcvalue.Intheanalysisofelectroniccircuitstobeconsideredinalatercourse,bothdcandacsourcesofvoltagewillbeappliedtothesamenetwork.Itwillthenbenecessarytoknowordeterminethedc（oraveragevalue）andaccomponentsofthevoltageorcurrentinvariouspartsofthesystem.

EXAMPLE13.13DeterminetheaveragevalueofthewaveformsofFig.13.37.

FIG.13.37

Example13.13.

Solutions:

a.Byinspection,theareaabovetheaxisequalstheareabelowoveronecycle,resultinginanaveragevalueofzerovolts.

b.UsingEq.（13.26）:

asshowninFig.13.38.

Inreality,thewaveformofFig.13.37（b）issimplythesquarewaveofFig.13.37（a）withadcshiftof4V;thatisv2=v1+4V

EXAMPLE13.14Findtheaveragevaluesofthefollowingwaveformsoveronefullcycle:

a.Fig.13.39.

b.Fig.13.40.

Solutions:

Wefoundtheareasunderthecurvesintheprecedingexamplebyusingasimplegeometricformula.Ifweshouldencounterasinewaveoranyotherunusualshape,however,wemustfindtheareabysomeothermeans.Wecanobtainagoodapproximationoftheareabyattemptingtoreproducetheoriginalwaveshapeusinganumberofsmallrectanglesorotherfamiliarshapes,theareaofwhichwealreadyknowthroughsimplegeometricformulas.Forexample,

theareaofthepositive（ornegative）pulseofasinewaveis2Am.

Approximatingthiswaveformbytwotriangles（Fig.13.43）,weobtain（usingarea1/2baseheightfortheareaofatriangle）aroughideaoftheactualarea:

Acloserapproximationmightbearectanglewithtwosimilartriangles（Fig.13.44）:

whichiscertainlyclosetotheactualarea.Ifaninfinitenumberofformswereused,anexactanswerof2Amcouldbeobtained.Forirregularwaveforms,thismethodcanbeespeciallyusefulifdatasuchastheaveragevaluearedesired.Theprocedureofcalculusthatgivestheexactsolution2Amisknownasintegration.Integrationispresentedhereonlytomakethemethodrecognizabletothereader;itisnotnecessarytobeproficientinitsusetocontinuewiththistext.Itisausefulmathematicaltool,however,andshouldbelearned.Findingtheareaunderthepositivepulseofasinewaveusingintegration,wehave

where∫isthesignofintegration,0andparethelimitsofintegration,Amsinaisthefunctiontobeintegrated,anddaindicatesthatweareintegratingwithrespecttoa.Integrating,weobtain

Sinceweknowtheareaunderthepositive（ornegative）pulse,wecaneasilydeterminetheaveragevalueofthepositive（ornegative）regionofasinewavepulsebyapplyingEq.（13.26）:

ForthewaveformofFig.13.45,

EXAMPLE13.15DeterminetheaveragevalueofthesinusoidalwaveformofFig.13.46.

Solution:

Byinspectionitisfairlyobviousthat

theaveragevalueofapuresinusoidalwaveformoveronefullcycleis

zero.

EXAMPLE13.16DeterminetheaveragevalueofthewaveformofFig.13.47.

Solution:

Thepeak-to-peakvalueofthesinusoidalfunctionis16mV+2mV=18mV.Thepeakamplitudeofthesinusoidalwaveformis,therefore,18mV/2=9mV.Countingdown9mVfrom2mV（or9mVupfrom-16mV）resultsinanaverageordclevelof-7mV,asnotedbythedashedlineofFig.13.47.

EXAMPLE13.17DeterminetheaveragevalueofthewaveformofFig.13.48.

Solution:

EXAMPLE13.18ForthewaveformofFig.13.49,determinewhethertheaveragevalueispositiveornegative,anddetermineitsapproximatevalue.

Solution:

Fromtheappearanceofthewaveform,theaveragevalueispositiveandinthevicinityof2mV.Occasionally,judgmentsofthistypewillhavetobemade.

Instrumentation

Thedcleveloraveragevalueofanywaveformcanbefoundusingadigitalmultimeter（DMM）oranoscilloscope.Forpurelydccircuits,simplysettheDMMondc,andreadthevoltageorcurrentlevels.Oscilloscopesarelimitedtovoltagelevelsusingthesequenceofstepslistedbelow:

1.FirstchooseGNDfromtheDC-GND-ACoptionlistassociatedwitheachverticalchannel.TheGNDoptionblocksanysignaltowhichtheoscilloscopeprobemaybeconnectedfromenteringtheoscilloscopeandrespondswithjustahorizontalline.Settheresultinglineinthemiddleoftheverticalaxisonthehorizontalaxis,asshowninFig.13.50（a）.

2.Applytheoscilloscopeprobetothevoltagetobemeasured（ifnotalreadyconnected）,andswitchtotheDCoption.Ifadcvoltageispresent,thehorizontallinewillshiftupordown,asdemonstratedinFig.13.50（b）.Multiplyingtheshiftbytheverticalsensitivitywillresultinthedcvoltage.Anupwardshiftisapositivevoltage（higherpotentialattheredorpositiveleadoftheoscilloscope）,whileadownwardshiftisanegativevoltage（lowerpotentialattheredorpositiveleadoftheoscilloscope）.Ingeneral,

1.UsingtheGNDoption,resetthehorizontallinetothemiddleofthescreen.

2.SwitchtoAC（alldccomponentsofthesignaltowhichtheprobeisconnectedwillbeblockedfromenteringtheoscilloscope—onlythealternating,orchanging,componentswillbedisplayed）.

Notethelocationofsomedefinitivepointonthewaveform,suchasthebottomofthehalf-waverectifiedwaveformofFig.13.51（a）;thatis,noteitspositionontheverticalscale.Forthefuture,wheneveryouusetheACoption,keepinmindthatthecomputerwilldistributethewaveformaboveandbelowthehorizontalaxissuchthattheaveragevalueiszero;thatis,theareaabovetheaxiswillequaltheareabelow.

3.ThenswitchtoDC（topermitboththedcandtheaccomponentsofthewaveformtoentertheoscilloscope）,andnotetheshiftinthechosenlevelofpart2,asshowninFig.13.51（b）.Equation

（13.29）canthenbeusedtodeterminethedcoraveragevalueofthewaveform.ForthewaveformofFig.13.51（b）,theaveragevalueisabout

TheprocedureoutlinedabovecanbeappliedtoanyalternatingwaveformsuchastheoneinFig.13.49.InsomecasestheaveragevaluemayrequiremovingthestartingpositionofthewaveformundertheACoptiontoadifferentregionofthescreenorchoosingahighervoltagescale.DMMscanreadtheaverageordclevelofanywaveformbysimplychoosingtheappropriatescale.

13.7EFFECTIVE（rms）VALUES

Thissectionwillbegintorelatedcandacquantitieswithrespecttothepowerdeliveredtoaload.Itwillhelpusdeterminetheamplitudeofasinusoidalaccurrentrequiredtodeliverthesamepowerasaparticulardccurrent.Thequestionfrequentlyarises,Howisitpossibleforasinusoidalacquantitytodeliveranetpowerif,overafullcycle,thenetcurrentinanyonedirectioniszero（averagevalue0）?

Itwouldalmostappearthatthepowerdeliveredduringthepositiveportionofthesinusoidalwaveformiswithdrawnduringthenegativeportion,andsincethetwoareequalinmagnitude,thenetpowerdeliverediszero.However,understandthatirrespectiveofdirection,currentofanymagnitudethrougharesistorwilldeliverpowertothatresistor.Inotherwords,duringthepositiveornegativeportionsofasinusoidalaccurrent,powerisbeingdeliveredateach

instantoftimetotheresistor.Thepowerdeliveredateachinstantwill,ofcourse,varywiththemagnitudeofthesinusoidalaccurrent,buttherewillbeanetflowduringeitherthepositiveorthenegativepulseswithanetflowoverthefullcycle.Thenetpowerflowwillequaltwicethatdeliveredbyeitherthepositiveorthenegativeregionsofsinusoidalquantity.AfixedrelationshipbetweenacanddcvoltagesandcurrentscanbederivedfromtheexperimentalsetupshowninFig.13.52.Aresistorinawaterbathisconnectedbyswitchestoadcandanacsupply.Ifswitch1isclosed,adccurrentI,determinedbytheresistanceRandbatteryvoltageE,willbeestablishedthroughtheresistorR.Thetemperaturereachedbythewaterisdeterminedbythedcpowerdissipatedintheformofheatbytheresistor.

Ifswitch2isclosedandswitch1leftopen,theaccurrentthroughtheresistorwillhaveapeakvalueofIm.Thetemperaturereachedbythewaterisnowdeterminedbytheacpowerdissipatedintheformofheatbytheresistor.Theacinputisvarieduntilthetemperatureisthesameasthatreachedwiththedcinput.Whenthisisaccomplished,theaverageelectricalpowerdeliveredtotheresistorRbytheacsourceisthesameasthatdeliveredbythedcsource.Thepowerdeliveredbytheacsupplyatanyinstantoftimeis

Theaveragepowerdeliveredbytheacsourceisjustthefirstterm,sincetheaveragevalueofacosinewaveiszeroeventhoughthewavemayhavetwicethefrequencyoftheoriginalinputcurrentwaveform.Equatingtheaveragepowerdeliveredbytheacgeneratortothatdeliveredbythedcsource,

which,inwords,statesthat

theequivalentdcvalueofasinusoidalcurrentorvoltageis1/2or0.707ofitsmaximumvalue.

Theequivalentdcvalueiscalledtheeffectivevalueofthesinusoidalquantity.

Insummary,

Asasimplenumericalexample,itwouldrequireanaccurrentwithapeakvalueof2（10）14.14AtodeliverthesamepowertotheresistorinFig.13.52asadccurrentof10A.Theeffectivevalueofanyquantityplottedasafunctionoftimecanbefoundbyusingthefollowingequationderivedfromtheexperimentjustdescribed:

which,inwords,statesthattofindtheeffectivevalue,thefunctioni（t）mustfirstbesquared.Afteri（t）issquared,theareaunderthecurveisfoundbyintegration.ItisthendividedbyT,thelengthofthecycleortheperiodofthewaveform,toobtaintheaverageormeanvalueofthesquaredwaveform.Thefinalstepistotakethesquarerootofthemeanvalue.Thisproceduregivesusanotherdesignationfortheeffectiveva