WHAT IS Q.docx
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WHAT IS Q.docx
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WHATISQ
WHATISQ
Q=Fc/BD中心频率/带宽
通俗地说,Q值就是决定该频率点增益变动时对两边频段的影响程度,Q值越大,对该点以外的影响越小,Q值越小,影响越大
比如,用一个WAVES的8段EQ进行举例.在一个频率点4088上提升7db,Q值为100时,曲线如下,基本只对该频点提升了,对周围影响很小
频率点和增益不变,Q值调到0.5,这时该频率点的增益提升,影响的频段很宽.
另外,该均衡器的频率点从16-21357HZ连续可调,Q值0.5-100连续可调,增益-18到+18db连续可调.要是用模拟电路来搭这个均衡器,不知道电路有多复杂了,还要考虑做好指标,就更难了.在数字音频时代,大力推荐使用数字效果器
问:
Q值和衰减斜率有什么区别呢?
貌似斜率越高Q值越大?
答:
Q越大斜率就越陡
WhatisQ
byDickPiercefromapostingofhisonthenewsgrouprec.audio.tech,14Nov1995
compiledbysanford1@
"Q"isoneofthosedimensionlessnumbersthatcausesnosmallamountofconsternationamongstthosewhodon't
understandwhatitmeans,aswellasamongthosethatTHINKtheydo!
However,theprinciplebehindQ,whenusedinthecontextofloudspeakers,isVERYsimple.
1)Itissimplytheratiobetweenenergystoringandenergydissipativemechanismsatresonance.
2)Inelectricalterms,itistheratioofthereactancetotheresistance.
AhighQindicatesthatfortheamountofenergystoredinaresonantsystem,themechanismsthatdissipatethatenergy
aresmall.Soahigh-Qsystemwilltendtohavearesonancethatdecaysslowly,becausetheamountofresistance
availabletodissipatetheenergyissmallcomparedtotheamountofenergystored.
Alow-Qsystemwilltendtodampentheresonantmotionquickly,becausetheenergyisdissipatedquicklyandremovedfromtheresonantsystem.
Thereareprimarily2energydissipatingmechanismsavailableinaloudspeakerdriver:
mechanicalandelectrical(thereis
another,acoustical,butitisVERYsmallwhencomparedtotheothermechanisms).
Themechanicaldissipativemechanismsareprimarilythefrictionallossesinthedriver'ssuspension,and,toalesserextent,acousticabsorption.
Thereare,essentially,twoelectricalmechanismsforenergydissipation:
theDCresistancetothevoicecoilandtheoutputresistanceoftheamplifier.Inalmostallcases,theDCresistanceofthevoicecoilcompletelydominates.
Thesetwomechanisms,mechanicalandelectrical,determine,respectively,themechanicalQ(Qms)andtheelectricalQ
(Qes)oftheloudspeakerdriver.TheirparallelcombinationdeterminesthetotalQ(Qts)oftheloudspeakerdriver."Amen.
WhenwemountaloudspeakerdriverontoabafflesystemwealsohavetotakeintoaccounttheQofthebafflesystem
toarriveatthetotalsystemQ.ToworkoutthetotalQofthedriverandbafflesystemyousimplymultiplythebaffle
systemQwiththetotalQoftheloudspeakerdriver.
Closedboxesstoreenergythatinteractswiththeloudspeakerdriverincomplexways,especiallyinventedenclosures.Boxesthemselvesalsohaveresonances.
Normallyahigh-Qclosedboxiscombinedwithlow-QloudspeakerdrivertogiveadesirabletotalsystemQ.
Butwhenwemountaloudspeakerdriveronanopenbafflethissituationisreversed.Anopenbafflestoresnoenergyandhasalow-Qof0.2andCarverchosetouseahigh-QwooferwithatotalQof3+toarriveatadesirabletotalsystemQ.
Carver'shigh-Qwooferwasalsochosenforanothergoodreasontodowithmountingawooferonanopenbaffle.
Aswedecreaseinfrequencyorincreaseinwavelength,thesysteminitiallybehavesasaninfinitebaffle.Whenthewavelengths
arelongenoughtobeaquarterofthebaffledimensions,thewavesbegintocanceleachotheraroundtheedgesofthe
dipolebaffle.
Thewavetravelsouttotheedge(1/4)andbacktotheoppositesideofthevibratingspeakercone,whereitisexactlyoutofphaseandcancelsout.
Quarterwavecancellationonanopenbaffleisafirstorderphenomenon-theroll-offoccursat6dBperoctave.Whenwereachthefree-airresonancepointofthehigh-Qwooferweaddtothisthesecond-ordersub-resonancefall-offofthehigh-Qwoofertoendupwithathird-orderor18dbperoctavefall-offbelowthefree-airresonancepointofthehigh-Qwoofer(thismakesagoodrumblefilterintheCarvercase).
Inloudspeakerliteraturewecanlookatthefamilyofcurvesforthefrequencyresponseofaloudspeakerdriveronan
infinitebaffleaswedecreasethefrequency.
Startingwiththerolled-offcurve
whenQ=0.5(criticallydamped),thenthe
ButterworthgraphwithQ=0.71(maximallyflat),thena
littlerippleatQ=1,thenclearlya
bumped-upgraphatQ=1.4.
未命名1.jpg
WhentheQishigherthananyyoucanusuallyfindinloudspeakerdrivercataloguesyoustarttogetboostingabovethe
resonancepointoftheloudspeakerdriver,andasufficientlyhigh-Qwillresultinaslopeofabout6dBperoctaveabove
thefree-airresonancepointoftheloudspeakerdriver.
Thisincreaseof6dBperoctaveofthehigh-Qloudspeakerdrivercanbeusedtocounteractthe6dBperoctavequarterwavecancellationtogiveaflatfrequencyresponserightdowntothefree-airresonantfrequencyoftheloudspeakerdriver.ThisisamuchmoreelegantsolutiontotheproblemofquarterwavecancellationonanopenbaffletothatusedbyCelestion,etcofusingaconventionallow-Qwooferwithelectronic
equalizationsinceitdoesnotinvolveadditionalamplifierpowerandthenecessityofelectronicequalizationequipment.
High-Qwoofersarerelativelyeasytodesign/make.Bothwaysofovercomingquarterwavecancellationonabaffleentail
theuseoflongthrowwoofersforthesafeoperationofthewoofer.
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再来一段:
二阶低通的
SecondOrderPassiveResonantFilters
lcr_circuits_2nd_order_low_pass_filter.gif
Figure2-BasicLCRsecondorderlowpassresonantfilter.
NowAVcontainstwofrequencydependantimpedanceswhichmeansthatitisinverselyproportionaltoω2
AV=ZC/(R+ZL+ZC)
Equation3LCRSecondOrderLowPass
Givinganabsolutevalueof:
|AV|=1/√((1-ω2LC)2+(ωRC)2)
Equation4LCRSecondOrderLowPass
I'llletyoudothesubstitutionshere,rememberaswiththefirstorderfiltersyouneedtotreateachphaseindividuallytogetatrueabsolutevalue,drawaphasediagramifyouthinkitwillhelpyou.YoushouldalsoconsiderwhatAVwouldlooklikeifVoutweretakenacrosstheresistorinductorcombinationinstead.
Sincethegainisnowinverselyproportionaltothesquareofthefrequencytheroll-offofthefilterwillbetwiceassteepasthefirstorderfilter(rememberwe'reworkinginthelogdomainwhenmeasuringthegainvsfrequency)makingitmoreprecise,thisisshowninfigure3.Sowhereasthefirstorderfilterdropsby6dBeverytimethefrequencydoublesthesecondorderfilterdropsby12dB.Infactforannthorderfiltertherolloffwillben*6dBperoctave.
lcr_circuits_2nd_order_low_pass_respopnse.gif
Figure3-Frequencyresponseofasecondorderlowpassfilterwithf0=5kHz.(clicktoenlarge)
ResonantFrequency
Theresonantfrequency(ω0orf0)isthepointatwhichtheimpedanceofthecapacitorandinductorareequal,itisatthispointthatthebreakhappensinthegainofthefilter(seefigure3).ForasimpleRLCcirucititisdefinedas:
ω0=2πf0=1/√(LC)
Equation5ResonantfrequencyofanLCRcircuit
YoucanverifythisyourselfbymakingZC=ZLandre-arrangingtosolveforω.
QFactor
TheQfactorisdeterminedbytheresistorinserieswiththeinductorandcapacitor,itdescribesthesharpnessoftheresonancepeakorkneethatthefilterwillhave.Theeffectthatthishasisshowninfigure4,notehowasQincreasesthepeakbecomesgreater.Thiscouldcauseproblemsifyoudon'twanttoamplifyyoursignal.
Qiscalculatedusingthefollowingformula:
Q=ω0L/R=1/ω0CR
Equation6QfactorforanLCRcircuit.
lcr_circuits_effect_of_q.gif
Figure4-EffectsofQonthe'knee'ofthefilterfrequencyresponse.
Phase
Thephaseoftheoutputdiffersfromthatoftheinputby:
&angAV=tan-1(ωRC/ω2LC-1)
Equation7PhasedifferencebetweeninputandoutputofanLCRcircuit.
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2010-8-0120:
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再来两张图:
贝塞尔滤波器、巴特沃思滤波器、切比雪夫滤波器的特性。
可以看出他们的Q值是不一样的。
F_3_11.gif
F_3_13.gif
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