英文版模拟有源滤波器MATLAB实现

个人资料整理 仅限学习使用DesignandrelizationofanlogactivefilterbasedonMATLABSchoolofautomation,ChongqinguniversityEmail:sdu@ABSTRACTThispaperdescribesthebasicconceptsoffiltersintroducedanalogactivefilter designprinciplesandapproximation theory.Including Butterworth approximation, ChebyshevtypeIapproximation, ChebyshevⅡtypeapproximation, elliptic function approximation andBezierapproximation.Thefirstauthorstudiedtheanalogactivefilterdesignprocessandperformancetesting.Combinesthetraditionalhardwaredesignmethodsandsoftwareprogrammingtechniques ，theMATLAB simulationofavarietyoffilterapproximation techniqueofamplitude-frequencycharacteristiccurveandanillustrativeexample.Butterworthfilterinstanceonsimulationstudies,bytheprogramtoquickly gettheminimum orderandthecutoff frequency,replacingthetraditionalcomplexcalculations。convenientlyachievedbytheanaloglow-passfiltertothehigh-pass,low-passandband-stopfilter theconversion。complexonquadopampcircuit designsimulation,throughitsdifferentpointsstrikeoutputtransferfunctiontosimulatethesecond-orderlow-pass,highpass,bandpassandband-stopfilterfrequencycharacteristiccurveandgetbettersimulationresults.Keywords:Analog and Active Filter。Theory of Approximation,Amplitude-frequencycharacteristics，MATLABprogramdesignI、INTRODUCTION1、ResearchbackgroundFilteringisabasicandimportanttechnologyinsignalprocessing,usingfilterwecanextractthedesiredsignalandsuppressunwantedparts.Theso-calledfilterisacertainsignalprocessingmeansthatwithtransmissioncharacteristics.Accordingtothedifferentprocessedsignaloffilter,thefiltercanbedividedintotwotypes:analoganddigitalfilters.Analogfilterisacommon

conversiondeviceinthetestsystemoradedicatedinstrumentation.Forexample:aband-passfilterforspectrumanalyzerfrequencyselectiondevice。low-passfilterfordigitalsignalanalysissystemintheanti-aliasingfilterfrequency。high-passfilterisusedforacousticemissiondetectortoexcludelow-frequencyinterferencenoise。bandstopfilterisusedineddycurrentvibrometernotchfilter,andsoon.2、Mainworkcontent个人资料整理 仅限学习使用Atthewholedesignprocess,threemainstepsweredone.Thefirstone,Familiarwiththeprincipleofanalogactivefilter.second,designthehardwarecircuitofanalogactivefilter.Thelastoneisthesimulationdebuggingofsoftwareandhardware(basedontheMATLAB>.、MaterialsandMethodsA、ThebasicconceptsofanlogactivefilterFig.2 Chebyshev I filter prototypeAccordingtothetraditionalclassification,amplitude-frequencydiagramthefiltercanbedividedintofourtypes:low-pass,high pass,bandpassandband-stopfilter.According to the"bestapproximationproperties"standardtoclassifyfliter,flitercanbe divided into the butterworth filter,chebyshevfilter, Besselfilter andEllipticfilter.Sincetheidealthingsthataredifficulttoachieve,sowedesigneditallanalogactivefilter using approximation methods. Thefollowing arethefourapproximation modelimages.Fig.3Ellipticfilteramplitude-frequencydiagramFig.1 Butterworth filter prototypeamplitude-frequencydiagramFig.4 Besselfilter amplitude-frequencydiagramIntheaboveofthesefilter prototypes,个人资料整理 仅限学习使用Wecangetthefollowingconclusions:Butterworthfilterpass-bandandstop-bandhaveasmoothmonotonicfeatures,butatthesametransitionbandwidthconditions,thefilterrequiredthelargestnumberoforder.ChebyshevIandIIorapass-bandfilterhavingastop-bandripple,butthesametransitionbandwidthconditions,theorderofthefilterarerequiredtobelessthantheButterworthfilter.Ellipticfilterpass-bandandstop-bandhaveripplesoccur,butinthesametransitionbandwidthconditions,thefilterorderoftherequiredminimum.Besselfilterhasthewidesttransition,butwithoptimallinearphasefrequencycharacteristics.Therefore,thereisnoabsolute"good"filter,accordingtothedifferentoptionstosolvetheproblemofdifferentfilters,soeachfilterdesignmethodwehavemastered.2、ApplicationofMATLABOurresearchisdesignandrelizationofanlogactivefilterbasedonMATLAB.SoatthistimeweintroductionMATLABfunction.[b,a]=butter(n,wn[,'ftype'],'s'>[z,p,k]=butter(n,wn[,'ftype'],'s'>[b,a]=cheby1(n,Rp,wn[,'ftype'],'s'>[z,p,k]=cheby1(n,Rp,wn[,'ftype'],'s'>[b,a]=cheby2(n,Rs,wn[,'ftype'],'s'>[z,p,k]=cheby2(n,Rs,wn[,'ftype'],'s'>[b,a]=ellip(n,Rp,Rs,wn[,'ftype'],'s'>[z,p,k]=cheby2(n,Rp,Rs,wn[,'ftype'],'s'>[b,a]=besself(n,wn[,'ftype'],'s'>[z,p,k]=besself(n,wn[,'ftype'],'s'>Intheaboveinvocation,‘n’isthefilterorder,‘wn’isthefiltercutofffrequency。's'oftheanalogfilter,thedigitalfilterdefault.'Ftype'typeoffilter'High' high-passfilter cutoff frequencywn.'stop'band-stopfilterwithacutofffrequencywn=[w1,w2](w<w2>.'ftype' default, low-pass or band-passfilter.Whendesigningtheband-passfilter,the

cutofffrequencyofwn=[w1,w2](w1<w2>.a,brespectively,thefiltertransferfunctionnumeratoranddenominatorpolynomialcoefficientvector。z,p,karethefilterzero,poleandgain.Rp,Rsweredesignedpass-bandrippleandstop-bandattenuation,inunitsofdB.Minimumorderselectionfunctionrad/s。[n,wc]=buttord(wp,ws,Rp,Rs,'s'>。Butterworthfilter[n,wc]=cheb1ord(wp,ws,Rp,Rs,'s'>。ChebyshevIfilter[n,wc] =cheb2ord(wp, ws,Rp,Rs,'s'>。ChebyshevIIfilters[n,wc]=ellipord(wp,ws,Rp,Rs,'s'> 。EllipticfilterWhere, wp is the pass-band edgefrequency, isthestop-bandedgefrequency,inunitsof . , ,respectivelypass-bandrippleandstop-bandattenuation,inunitsofdB.Bothwithinthepassband,respectively,themaximumallowableamplitudelossanddecreaseindBstop-band.'s'indicatesthattheanalogfilter(bydefault,thefunctionforthedigitalfilter>。functionreturnsthesmallestnistheorderoftheanalogfilter。 oftheanalogfiltercutofffrequencyin .BDesignExampleBiquadcircuitdesignWeknowbiquadcircuitcanconstituteavarietyoffilters,asmanyexistingsecondop-ampcircuit,herewewilldiscussthefollowingcircuitsimulation.个人资料整理 仅限学习使用Fig.5kensecondOrdermultioperationalamplifiercircuitWe analyzed the main circuit is The above-described H (s> are thecomposedofaaddersA1,andtwointegrators generalbiquadfunction,weusethefunctionA2, A3composition, canbeseenfromthe denominator polefrequencyandthequalityabove,theoutputofthefirstamplifierA1: factorvalueequivalenttosaidstandardformwillberewrittenas:<1）Theoutputofthesecondamplifierandtheoutputofthethirdamplifierisinvertingintegrator,thevoltagebetweenthemis:

<5）ThedeformationofthetransferfunctioncanbederivedforeachequivalentqualityfactorQandcutofffrequency:中 ：Formulacanbeobtainedfromtheabovethree中：<2）<3）中：<4）个人资料整理 仅限学习使用180/pi>% useof semi-logarithmic plot thephaseresponsegridon。xlabel('Angularfrequency'>。ylabel('Phase/degrees'>。GraphshowninFigure6:Different parameters will result indifferent frequency characteristics, forsimplicity,wemayassumethattheresistance25 and capacitance. There are transferfunctionis:； =1；； ；； ；ThesimulationprogramofthetransferfunctionbasedonMATLAB:b=[001]。a=[111]。%denominatorpolynomialcoefficientsofthefiltertransferfunctionfigure(1>,freqs(b,a>。%Thefirstmethod[h,w]=freqs(b,a>。%calculatedcomplexfrequencyresponseofthefiltermag=abs(h>。pha=angle(h>。%getthefilterfrequencyandphasefrequencyresponsefigure(2>,subplot(2,1,1>,loglog(w,mag>。%doublelogarithmiccoordinatesplottedamplitudefrequencyresponsegridon。xlabel('Angularfrequency'>。ylabel('Magnitude'>。subplot(2,1,2>,semilogx(w,pha*

Fig.6V3-endedoutputlow-passfilterphasefrequencycharacteristicsModifytheprogramas:b=[0-10]。%numeratorpolynomialcoefficientsofthefiltertransferfunction.ItsgraphicsshowninFigure7Fig.7V2-endedoutputlow-passfilterphasefrequencycharacteristicsModifytheprogramas:b=[100]。%numeratorpolynomialcoefficientsofthefiltertransferfunctionItsgraphicsshowninFigure8个人资料整理 仅限学习使用Fig.8V1-endedoutputlow-passfilterphasefrequencycharacteristicsWecandrawaconclusionfromfigure6-8,theoutputfromthedifferenceplace,thedifferenttypestransferfunctioncanbeobtained,totaketheoutputobtainedfromthefirststagewegetthehigh-passfunction。theoutputfromthesecondstageisband-passfunction,theoutputfromthethirdstageislow-passfunction.Abovetheseexamplewecangetthatthelow-passandhigh-passtandemcantogetband-passfilter.III.AcknowledgmentsMydeepestgratitudegoesfirstandforemosttoProfessorCao,forhisconstantencouragementandguidance.hehaswalkedmethroughallthestagesofthewritingofthisthesis.Withouthjisconsistentandilluminatinginstruction,thisthesiscouldnothavereacheditspresentform.Second,IamgreatlyindebtedtotheprofessorsandteachersattheDepart