FilterPro™ User's Guide - Texas Instruments

1 User's GuideSBFA001C June1991 RevisedFebruary2011 filterpro User's , designedtoaidinthedesignofactivefiltersi mplementedwiththemultiplefeedback(MFB) ' (Four-Pole), (Five-Pole),3dBRippleChebyshevFilterShow ingCutoffat (Unity-Gain,First-OrderButterworth;f 3dB= 1/2 R1 C1).. (Gain= R2/R1)..1013 Sallen-KeyComplexPole-PairSection,Unity- Gain(Gain= 1)..1014 Sallen-KeyComplexPole-PairSection(Gain= 1 + R4/R3).. a ,Windows, June1991 RevisedFebruary2011 filterpro User's GuideSubmitDocumentationFeedback 1991 2011, , DesignReportThroughthePrinterIconin ,Chebyshev,andBesselUnity-GainMFBLow-Pas sFilters, ,Chebyshev,andBesselUnity-GainMFBLow-Pas sFilters, , , , User's GuideSBFA001C June1991 RevisedFebruary2011 SubmitDocumentationFeedback 1991 2011,TexasInstrumentsIncorporatedStop bandIdealresponsebrick wallf definesLP applicationswherea specificamplitudeversusfrequencybehavior isrequiredfroma specificphaseshift,ortimedelay,needstobe incorporatedin a circuitanda filtermaybeusedin programmakesit easytodesignlow-pass,high-pass,bandpass, bandreject, setcutofffrequency,fc; refertoFigure1.

2 Thisregionwherethefrequenciesreadilypass throughthefilteris calledthepassband, andfcis reached,thefilterbeginstoattenuateanyfre quencyhigherthanfc. Theregionabovefcis calledthestopband. Mostoftentheattenuationincreases,orrolls off, ,non-idealoperationalamplifierlimitation s, June1991 RevisedFebruary2011 filterpro User's GuideSubmitDocumentationFeedback 1991 2011,TexasInstrumentsIncorporatedStop bandIdealresponsebrick wallf ,asshownin Figure2, hasa passbandwhereallfrequenciesabovethecutof ffrequency(fc) , withinthefilter'sstop-band, User's GuideSBFA001C June1991 RevisedFebruary2011 SubmitDocumentationFeedback 1991 2011,TexasInstrumentsIncorporatedStop bandStop bandBandwidthIdealresponsebrick wallf cutofffrequencyLf cutofffrequencyHBandwidth = (f - ) passbandthatallowsa selectbandoffrequenciesthatfallwithinthe passbandtopasswithlittle,orno,attenuatio n;refertoFigure3.

3 Anupper(fH) andlower(fL) cutofffrequencydefinethebandwidthofthefi lter(fHtofL). Frequenciesbeyondthepassbandliein thetwostopbandsandreceivegreaterattenuat ionasthefrequencymovesfurtherawayfromthe passbandin June1991 RevisedFebruary2011 filterpro User's GuideSubmitDocumentationFeedback 1991 2011,TexasInstrumentsIncorporatedStop bandf cutofffrequencyLf cutofffrequencyHBandwidth = (f - ) ,orband-rejectfilter,is sometimesreferredtoasanotchfilterduetoit snotch-likegainversusfrequencystopbandch aracteristic,whichis illustratedin Figure4. Thepurposeofthisfiltertypeistoattenuate, orreject, (oratleastwithintheintendedpassband)with a ,anall-passfiltercanbedesignedwitha specified 45 ,a simplefirst-order, mindthatthephaseshiftwillbedifferentfrom 45 particulartimedelay;forexample,159 s ata foundby: = tD/tP(360 ) = (159 s/1ms)(360 ) = Where:tD= delaytimeandtP= User's GuideSBFA001C June1991 RevisedFebruary2011 SubmitDocumentationFeedback 1991 2011,TexasInstrumentsIncorporatedFILTER RESPONSE vs FREQUENCYN ormalized FrequencyFilter Response (dB)+10010-----20304050f /100cf /10cfc10fc5-Pole Chebyshev3dB RippleRippleFILTER RESPONSE vs FREQUENCYN ormalized FrequencyFilter Response (dB)4-Pole Chebyshev3dB RippleRipple+10010-----20304050f /100cf ,andperfectlypasssignalsbelowthecutoff(i nthepassband).

4 Thisideal,brick-wallresponseis shownin Figure1 throughFigure4. Inrealfilters, thepassband;sometradeoffgainvariation(ri pple)in thepassbandforsteeperroll-off;stillother stradeoffbothflatnessandrateofroll-offin :Butterworth,Chebyshev,Bessel,Gaussian, (MaximallyFlatMagnitude) a moderatelysteep betterthanChebyshev,anditsrateofattenuat ionis (EqualRippleMagnitude) 'snameis alsotransliteratedTschebychev,Tschebysch eff, (ripple)in ,whichhave3dBattenuationatthecutofffrequ ency,theChebyshevcutofffrequencyis ,allrippleisabovethe0dB-gaindcresponse,s ocutoffis at0dB(asFigure5 shows).Forodd-orderfilters,allrippleisbe lowthe0dB-gaindcresponse,socutoffis at (ripple)dB,asFigure6 givennumberofpoles,a (Five-Pole),3dBRippleChebyshevFilterShow ing(Four-Pole),3dBRippleChebyshevFilterS howingCutoffat 3dBCutoffat0dB7 SBFA001C June1991 RevisedFebruary2011 filterpro User's GuideSubmitDocumentationFeedback 1991 2011, (MaximallyFlatTimeDelay)AlsocalledtheTho msonfilter,thisfilterhasexcellentpulsere sponse(thatis,minimalovershootandringing ) ,thuspreservingthewaveshapeoffilteredsig nalsin givennumberofpoles,itsmagnituderesponsei s notasflat,noris itsattenuationbeyondthe takesa higher-orderBesselfiltertogivea magnituderesponsewhichapproachesthatofa givenButterworthfilter,thepulseresponsef idelityoftheBesselfiltermaymaketheaddedc omplexity(becauseoftheneedforadditionalf iltersections)

5 (MinimumGroupDelay)Thistypeoffilterhasan impulseresponsethatis a (Equi-RippleDelay)SimilartotheBesselresp onse,thisfilterresponsehasa phaseresponsethatis a maximally-flattimedelay,thesefiltersappr oximatelinearphasetowithina givenripple( ).Theyhavea sharpermagnituderesponsethantheBesselfil ter,sometimesallowingfora lower-orderfiltertobeusedtoachievea ,butsomeconfigurationsarebetterwiththere al-polesectionfollowing(seeFigure16). TheprogramautomaticallyplaceslowerQ stagesaheadofhigherQ ,high-pass, (evenorder)Figure10 Fiveormorepoles(oddpoles)Figure118 filterpro User's GuideSBFA001C June1991 RevisedFebruary2011 SubmitDocumentationFeedback 1991 2011,TexasInstrumentsIncorporatedOptiona l BufferComplexPole-PairSection AVINA1 VOOptional BufferReal Pole SectionVINVOA1R1C1A2 Optional BufferReal Pole SectionComplexPole-PairSection AVINVOA1R1C1A2 Optional BufferComplexPole-PairSection AComplexPole-PairSection NVINVOA1 Optional BufferReal Pole SectionComplexPole-PairSection AComplexPole-PairSection (Unity-Gain.)

6 F 3dB= 1/2 R1 C1) June1991 RevisedFebruary2011 filterpro User's GuideSubmitDocumentationFeedback 1991 2011, : MultipleFeedback(MFB),illustratedin Figure12 Sallen-Key,shownin ,(Gain= R2/R1)Unity-Gain(Gain= 1) (Gain= 1 + R4/R3) (sometimescalledInfiniteGainorRauch) is ,theoutputpolaritywillbethesameastheinpu t; sixth-orderfilterconsistingofthreeMFBsta geswouldinvertthreetimes,resultingin ,ormaynot,bea concernin , User's GuideSBFA001C June1991 RevisedFebruary2011 SubmitDocumentationFeedback 1991 2011, a a noninvertingcircuit,whichmaymakeit preferableovertheMFB,butthisis ruleofthumb,theSallen-Keytopologyis important, unity-gainfilteris used, is low(forexample,Q < 3)Atunity-gain, becausetheopampis usedasa ,gainis determinedbytheR2 , ,thevaluerequiredforC1in ,useFilterProtodefinethecomponentvalueso fthesamedesignusingbothcircuittypes, ,manage.

7 1 GHzprocessororfaster 2 GBRAM orgreater Atleast250 MBoffreehard-diskspace Minimum1024x 768display Microsoft Windows is helpful,butnotrequired,tohavea printeravailable,eitherlocallyorona , June1991 RevisedFebruary2011 filterpro User's GuideSubmitDocumentationFeedback 1991 2011, ,youarepresentedwiththeFilterDesignWizar d,asshownin :Thisareashowsyouwhereyouarein :Thisareais :ClickBackorNexttowalkthroughyourdesignb eforefinalizingit. Ifthereis noneedtousetheDesignWizard, theDesignWizardis closed,youcancreateadesignbyaccessingthe Filemenuin User's GuideSBFA001C June1991 RevisedFebruary2011 SubmitDocumentationFeedback 1991 2011, (TimeDelay)Oncetheappropriatefilteris selected, : Low-pass: Gain(A0):Entertheoverallgainrequiredfort hefilterin voltspervolt(V/V)ordecibels(dB).Thegainv alueis automaticallyconvertedtotheotherunitif youdidnotenterit.

8 Forexample,if youenter'1'in theV/Vbox,thevalue'0dB'is automaticallyenteredbytheapplication,and vice-versa. PassbandFrequency(fc):Enterthepassbandfr equencyofthefiltertypechosenin hertz(Hz) AllowablePassbandRipple(RP):Enterthemaxi mumallowablepassbandripplein decibels(dB),in therangeof0 to3dB. StopbandFrequency(Fs):Enterthestopbandfr equencyofthefiltertypechosenin hertz(Hz). StopbandAttenuation(ASB):Enterthestopban dattenuationofthefiltertypechosenin decibels(dB). FilterOrder:ChecktheSetFixedbuttonif youwanttoforcetheorder(upto10)ofthefilte r13 SBFA001C June1991 RevisedFebruary2011 filterpro User's GuideSubmitDocumentationFeedback 1991 2011, High-pass: Gain(A0):Entertheoverallgainrequiredfort hefilterin voltspervolt(V/V)ordecibels(dB).Thegainv alueis automaticallyconvertedtotheotherunitif youdidnotenterit. Forexample,if youenter'1'in theV/Vbox,thevalue'0dB'is automaticallyenteredbytheapplication,and vice-versa.

9 PassbandFrequency(fc):Enterthepassbandfr equencyofthefiltertypechosenin hertz(Hz). AllowablePassbandRipple(RP):Enterthemaxi mumallowablepassbandripplein decibels(dB),in therangeof0 to3dB. StopbandFrequency(Fs):Enterthestopbandfr equencyofthefiltertypechosenin hertz(Hz). StopbandAttenuation(ASB):Enterthestopban dattenuationofthefiltertypechosenin decibels(dB). FilterOrder:ChecktheSetFixedbuttonif youwanttoforcetheorder(upto10)ofthefilte r. Bandpass: Gain(A0):Entertheoverallgainrequiredfort hefilterin voltspervolt(V/V)ordecibels(dB).Thegainv alueis automaticallyconvertedtotheotherunitif youdidnotenterit. Forexample,if youenter'1'in theV/Vbox,thevalue'0dB'is automaticallyenteredbytheapplication,and vice-versa. CenterFrequency(fo) AllowablePassbandRipple(RP):Enterthemaxi mumallowablepassbandripplein decibels(dB),in therangeof0 to3dB.

10 PassbandBandwidth(BWP):Enterthepassbandb andwidthofthefiltertypechosen. StopbandBandwidth(BWS):Enterthestopbandb andwidthofthefiltertypechosen. StopbandAttenuation(ASB):Enterthestopban dattenuationofthefiltertypechosenin decibels(dB). FilterOrder:ChecktheSetFixedbuttonif youwanttoforcetheorder(upto10)ofthefilte r. Bandstop/Notch: Gain(A0):Entertheoverallgainrequiredfort hefilterin voltspervolt(V/V)ordecibels(dB).Thegainv alueis automaticallyconvertedtotheotherunitif youdidnotenterit. Forexample,if youenter'1'in theV/Vbox,thevalue'0dB'is automaticallyenteredbytheapplication,and vice-versa. CenterFrequency(fo):Enterthecenterfreque ncyofthefiltertypechosen AllowablePassbandRipple(RP):Enterthemaxi mumallowablepassbandripplein decibels(dB),in therangeof0 to3dB. PassbandBandwidth(BWP):Enterthepassbandb andwidthofthefiltertypechosen.