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文档格式.docx
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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.
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.
Thepeak-to-peakvalueofthesinusoidalfunctionis16mV+2mV=18mV.Thepeakamplitudeofthesinusoidalwaveformis,therefore,18mV/2=9mV.Countingdown9mVfrom2mV(or9mVupfrom-16mV)resultsinanaverageordclevelof-7mV,asnotedbythedashedlineofFig.13.47.
EXAMPLE13.17DeterminetheaveragevalueofthewaveformofFig.13.48.
EXAMPLE13.18ForthewaveformofFig.13.49,determinewhethertheaveragevalueispositiveornegative,anddetermineitsapproximatevalue.
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,