LC Filter Design (Rev. A) - Texas Instruments

1 1 SLAA701A October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesignAll trademarksare the propertyof October2016 RevisedNovember2016LC FilterDesignABSTRACTIn higher-powerclass-Damplifiers,generallya bove10 W of outputpower,a filteron the outputof theamplifieris filteris passivein natureand usesbothan inductorand a capacitoron ,it is referredto as an LC the LC filteriscriticalto meetthe desiredaudioperformance,efficiency,EMC/E MIrequirements,and costfor the a guideto aid in the sectionof LC filtercomponentsforclass-Damplifiersto meettarget-designgoalsof the end (BTL).. (PBTL).. (SE).. (Traditional) OutputLC AD ModulationWithType-1or Resistance(DCR).. of Figures1 Stereo(Two-Channel)BTL (Traditional) October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesign6 Effectof Q on AD FilterResponseWithCBTL= F and LBTL= 10 BD or AD FilterResponseWithCg= F and LBTL= 10 AD FilterResponseWithCBTL= F, Cg= F, and LBTL= 10 ModulationFilterConvertedto +Nvs OutputPower,4.

2 1922 TPA3251 EVMTHD+Nvs SignalFrequency,20 W, 4 ..1923 PVDD/ 2 30 V, 600 kHz,2 BTL,4 ..2328 TPA3251 THD+Nvs OutputPowerfor VariousInductors600 kHz,36 V, 4 ..2629 TPA3251 THD+Nvs Frequencyfor VariousInductors20 W, 600 kHz,36 V, 4 ..2630 Class-DSE Filter - AD of BD VoltageRatingless than85 VoltageRatingbetween85 C and 105 CapacitanceChangevs DC of Tables1 Class-DFilterTypesand TheirSE RBTL= 8 ..173 FilterComponents RBTL= 6 ..174 FilterComponents RBTL= 4 ..175 AverageChangein Inductancefor 10 , DissipationFactor,and Idle PowerMeasuredfor 10 AOut BOut COut October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC Descriptionsfor SelectingMetalizedFilm class-Daudioamplifierssupportmultipleout putconfigurationsin a allowsfora high levelof flexibilityfor the end (BTL)Bridge-tiedload (BTL)is the mostcommonoutputconfigurationfor a BTLconfigurationconsistsof one amplifierdrivingone side of a load and anotheramplifier,with an invertedsignalfromthe first amplifier ,drivingthe otherside of the resultsin 2 morevoltageswingacrossthe load for a givensupplyvoltagewhencomparedto a single -endedconfigurationwhereone sideof the load is tied to the amplifieroutputand the otherside to voltageswingacrosstheload equatesto a 4 powerincreasebecauseP = V2/ R.

3 So, a BTL load configurationoffers4 morepowerto the load thana single -endedconfigurationfromthe of the load is driven,the load is not ,the voltageacrossthe load mustbe measureddifferentiallyrelativeto Stereo(Two-Channel) (PBTL)Parallelbridged-tiedload (PBTL)is an outputconfigurationthat takesa stereoBTL amplifierand connectsthe outputsin parallelfor a maximumoutputvoltageswingis the samefor a BTL outputconfiguration,the maximumcurrenthas beenincreasedbecauseeachoutputsharesthel oad oftenallowsfor lower-impedanceloadsto be drivenwith higheroutputpowerwhencomparedto BTL with the amplifiercurrentlimit has doubledcomparedto AOut BOut COut DClass-DAmplifierOut AOut BOut COut October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesignFigure2. (SE)In a single -ended(SE)configuration,only one outputis usedto drivethe load ratherthana pair of outputsoperatingout of phase,as foundin BTL and this reason,only half of the Signalswingis availablecomparedto BTL or a quarterof the total configurationcanallowfor four channelswith a singlestereoBTL amplifieras shownin Figure3.

4 Someamplifiersalso allowa combinationof 1 BTL and 2 SE channelsfor supportof audiosystemswith a to the PWMmodulationof a class-Damplifier,a DC voltageof PVDD/ 2 or half of the supplyvoltageis presentafterthe LC SE mode,becausethe speakeris now ground-referenced,eithera DCblockingcapacitoror someothermeansof referencingthe speakerto PVDD/ 2 is necessaryso that noDC voltageappearsacrossthe October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesign2 Class-DModulationSchemesThis sectiondescribeshow analogsignalsare convertedto PWMsignalsto drivethe MOSFETsin be classifiedas usingone of two modulationtechniques,AD(traditional)or BD (Traditional)ModulationThe traditionalswitchingtechnique(AD modulation)modulatesthe duty cycleof a rectangularwaveform,suchthat its averagecontentcorrespondsto the BTL outputs(seeFigure4) arethe inverseof modulationhas no significantcommon-modeswitchingcontentin its ,thereis a common-modeDC voltagedue to the averagevalueof the the load see this DC voltagelevel,it doesnot contributeto DC voltageis equalto PVDD/ 2, or half of the TPA312xD2familyemploysAD TASmodulatorscan be configuredfor AD AD (Traditional)ModulationBecausethe switchingwaveformis nearlyentirelydifferential,a BTL-connectedload acrossthe A-legandB-legseesthe full idle, the amplifierswitchesat the nominalPWMfrequencywitha 50%duty cycleacrossthe causessignificantcurrentflow and powerdissipationinto the LC Filter is necessaryto reducethe currentto a smallresidualripplefor ,the lowerthe ripplecurrentfor an AD modulationclass-Damplifier,the betterthe efficiencydueto reducedload dissipationand reducedI2R loss acrossRDS(on)

5 Of the October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC ModulationThe BD modulationswitchingtechniquemodulatesthe duty cycleof the differenceof the outputsignalssuchthat its averagecontentcorrespondsto the BTL outputs(seeFigure5) arenot the inverseof modulationhas significantcommon-modecontentin its be also be configuredfor BD BD Filter7 SLAA701A October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesign3 Class-DOutputLC FilterFrequencyResponsePropertiesThe frequencyresponseof the second-orderclass-DLC outputfilter is criticalwhenselectingthecomponentvaluesf or the inductorand LC Filter responsealso varieswith load impedancedeterminesthe dampingratioof the outputLC Filter and is classifiedasoverdamped,criticallydamped, or is also importantto understandthe speakerloadimpedancevariationsfor the applicationand selectthe L and C valuesthat suit the ,the LC Filter valueis selectedfor a criticallydamped,flat passband.

6 And considerationswhenselectingcomponentsfor the second-orderlow-passfilter is the cut-off frequencyand Q factoror Effectof Q on FrequencyResponseTI recommendsusinga second-orderButterworthlow-passfilter becauseof its flat pass-bandand doesnot recommendthe use of LC filtersthat peakexcessively,like the underdampedfilterresponseshownin Figure6. At high frequency,the peaksare generallyharshto the humanear and canalso triggerthe protectioncircuitry,suchas overcurrent,of ,overdampedfiltersresultin attenuationof high-frequencyaudiocontentin the = CgVin+_Vout+_RL = RBTL/2C = 2x CBTL + CgVin+_Vout+_RL = RBTL/2 LBTLLBTLC = 2x CBTLRL = RBTL/2 Vin+_Vout+_RBTLVout+LBTLVout -CgCgLBTLCBTLRBTLVout+LBTLVout -CgCgLBTLLBTLCBTLRBTLVout+LBTLVout -Class-DOutputLC October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterTopologiesFor class-Damplifiers,thereare primarilytwo Filter typesuseddependingon the is a differentialfilter usedfor AD Type-2filter is a common-modefilter primarilyusedfor BD showseachfilter type and the associatedsingle-endedequivalentthat is usedlaterin this sectionfor frequencyresponseand single -endedequivalentis usedto makethecomputationsfor eachfilter type Class-DFilterTypesand TheirSE EquivalentCircuitsClass-DBTLF ilterTypesType-1 Type-2 HybridType-1 single -EndedEquivalentType-2 single -EndedEquivalentHybridSingle-Ended EquivalentClass-DModulation:ADClass-DMod ulation:BD or AD( )Class-DModulation:ADFilterType:Differen tialFilterType:CommonModeFilterType.

7 HybridCBTL= Differentialbridgedtied load capacitorCg= single -endedcapacitorto groundRBTL= Differentialload impedanceLBTL= Seriesinductor0 LCCapacitor valueforcriticallydampedButterworthfilte 12rR=w 0 LLInductor value for critically dampedButterworth fi terR2l =wLCRL11 Damping Ratio2Q2z == LCQRQ uality Factor QL=002 Conversion between radians and frequency in hertzw = pf001 Cutoff frequency of single ended LC filter22 L Cw==-pp fLCRLVoutVin+_+ Filter9 SLAA701A October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC goal is to use the single -endedequivalentof eachfilter type for easyanalysis,the frequencyresponseof the single -endedfilter mustbe single -EndedLC FilterThe equationsfor the single -endedLC Filter shownin Figure7 follow:(1)(2)(3)(4)As previouslymentioned,it is usuallydesirableto designa Filter that is criticallydampedwith a this type of Filter ,Q = 1 / 2.

8 By substitutingQ = 1 / 2 into equationsforCut-offFrequencyandQualityFa ctorpreviouslylisted,L and C valuescan be derivedfor a criticallydampedsystemassumingthe desiredcut-offfrequency, o, is known.(5)(6)LBTL2x CBTLRBTL/2 Vout+LBTLVout -2x CBTLRBTL/2 Vout+_Vout+_LBTLCBTLRBTLVout+LBTLVout -Vout+_Class-DOutputLC October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC Type-1filter is a differentialfilter designedfor AD modulationhasno significantcommon-modecontenton its outputs,thus only the differentialmodeis neededfor differentialBTL components,CBTLand RBTLof the AD modulationLC Filter shownin Figure8, can besimplifiedto a Type-1 Filterfor AD ModulationFrominspection,the Type-1filter can be split into an equivalentcommon-modefilter as shownin scaledby a factorof 2 sincein the common-modemodel,the capacitorsappearin Type-1 FilterEquivalentCircuit010 Peaking( ) 20log Q dB== -w066 BTLBTL11143156 Hz2 L C 2 L2 C2 (10 10 ) ( 10 )

9 --====p p p f6 BTLBTLL6 BTLR2 10Q 10-- ==== BTLBTLLBTL0000 BTL00 BTLLLLL 10 HRCwhere R, R4 ,2 , a1R211nd40 FR2 40000 F F2R222==m===W w = p=w ====mw p p ==m mfffBTLLBTL0000 BTLL0 RLwhere R, R4 ,2 , andR2240 H222 40000===W w = p=w===mpp fffLBTLC = 2x CBTLRL = RBTL/2 Vin+_Vout+ Filter11 SLAA701A October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesignNowthe single -endedequivalentcan be drawnas shownin Figure10. The differencebetweenthe originalfilter and single -endedequivalentis that CBTLhas beenmultipliedby a factorof two and RBTLhas beendividedby a factorof single -endedequivalentcircuitto find the Filter componentvalues,CBTL= C / equationsoutlinedin , a Filter is designedwith a targeted40-kHzbandwidthand 4- L and C valuescan be calculatedas follows:The neareststandardinductorvalueis 10 standardcapacitorvalueis standardinductorand capacitorvaluesfromthe previouscalculations,the Q factorfor 4 is:(7)Withthe targetedQ of 1 / 2 the cut-offfrequencyis:The peakingat cut-offfrequencyin dB is:RBTLVout+LBTLVout -CgCgLBTLVout+_Frequency (Hz)Gain (dB)-40-30-20-1001020101001k10k100k1MD00 12 :3 :4 :6 :8.

10 OUTDiffBTL2 INBTLBTLV (s)1H ( )LV (s)1 s2 Cs2sR==+ +Class-DOutputLC October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesignUsingthe transferfunction(Equation8), the frequencyresponseof the selectedLC Filter can be plottedfordifferentspeakerloadsto providea completevisualevaluationof the LC Filter responsewith variousspeakerloads.(8)Figure11. Type-1LC FilterResponseWithCBTL= F and LBTL= 10 Type-2class-Dfilter is a common-modefilter designedfor BD or AD is commonmode,it can be easilyconvertedinto its componentsCgand differentialload RBTLof the LC Filter shownin Figure12, can besimplifiedto a Type-2 Filterfor BD or AD ModulationBTLBTLLBTL0000 LLBTL00gLL 10 HRCwhere R, R4 ,2 , and40 40000 222C C F ==m===W w = p=w ====mw p p ==m mfffBTLLBTL0000 BTLL0 RLwhere R, R4 ,2 , andR2240 H222 40000===W w = p=w===mpp fffLBTLC = CgVin+_Vout+_RL = RBTL/2 LBTLCgRBTL/2 Vout+LBTLVout -RBTL/2 Vout+_Vout+ Filter13 SLAA701A October2016 RevisedNovember2016 SubmitDocumentationFeedbackCopyright 2016,TexasInstrumentsIncorporatedLC FilterDesignFrominspection.