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-豆柴文库

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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:
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,anddai