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ANOTHER IEWOF

RobertR.CordellIn recent years he use of large amounts of negative feed-

back in audio amplifiers has become controversial.Severalpeople have examined the time-responsepropertiesof feed-back ampl i f ie rsand have conc luded tha t ampl i f ie rswh ichemploy large amounts of negative feedback are prone to aform of high-frequency distortion called "transient intermo-du la t iond is to r t ion" T lM) [1-4 ] .S implyput , th is d is to r t ion ssa id o occur when a s igna lchanges oo qu ick ly fo r the am-plifier to follow it properly.The observation hat a large amount of negative eedbackcauses IM tends o run counter o the convent iona lw isdomthat increasednegative eedback generally mproves a givenamplifier 's performance,so long as adequate stabil i ty is pre-served. Severalother researchershave recently questionedthese ind ingsand conc lude hat la rgeamounts o f negat ivefeedbackdo not inc rease he poss ib i l i ty f T IM and can infac t improve ampl i f ie rper fo rmanceas long as the ampl i f ie rhasan adequateslew rate [5,6].T IM is thus a popu lar sub jec t sur rounded by a cer ta inamount of controversy. t has also become a frequently citedreason or degradedsound. Advertisements ndicate that sev-era l manufac turers ave been in f luencedby the d iscuss ionsas wel l , some proud ly po in t ing out tha t they use very l i t t lenegative eedback.Much of the misunders tand ingand d isagreementsur -round ing he sub jec tseems o s tem rom inadequate ons id -eration of the trade-offs and constraints nvolved in the ao-plication of negative eedback, especiallyas t relates o con-temporary , ea l -wor ldampl i f ie r c i rcu i ts .Th is is par t icu la r lytrue of feedback compensation. For this reason,we will takethe t ime to rev iew impor tan t negat ive eedback pr inc ip leswhere necessary.Given a good understanding of negativefeedbackas t is app l ied o aud io ampl i f ie rs , ome o f t he TIMissues hould become easier o resolve.Beforeproceed ing , e shou ld po in t ou t tha t T lM, wh ich isassociatedwith negative feedback and its compensation, ison ly one form of h igh- f requency n termodu la t ion is to r t ion .The term "dynamic in termodu la t iond is to r t ion" (D lM) hasbeen used to describe the general class of intermodulationd is to r t ionswhich depend on f requencyaswel l as ampl i tude.TIM is hus one fo rm o f D lM. S ince he produc t o f f requencyand ampl i tude mpl ies ra te-o f -change, nd s ince the max i -mum rate-o f -changehat an ampl i f ie rcan fo l low is ca l led tss lew ra te , he te rm "s lew induced d is to r t ion" (S lD) has a lsobeen usedas a labe l o r D lM. Thesed is t inc t ions re ,howev-er, relatively weak and unimportant, referr ing more to themechanism han to the measuredor audible effect. Becauseit is the source of most of the controversy,we wil l concen-t ra te on TIM; however ,our d iscuss ionwi l l cons ider o thersourcesof DIM as well, some of which may in practice bemoreser ious .Transientntermodulation istortionFirst,et's ake lookat hepopular IMargumentso ge tsome background.What follows is a sort of composite para-phras ing f manyof the argumentswhich haveappeared.

Feedback mpl i f ie rsopera te on the pr inc ip le hat a la rgepor t ion of the input s igna l s cance l ledby feedback rom theampl i f ie r ou tput , leav ing a smal l s igna l -p lus -er rorwh ichdr ives he ampl i f ie r so as to produce he des i redoutput . Inampl i f ie rsw i th la rgeamounts o f negat ive eedback , h is s ig -na l -p lus -er rors fo rced to be very smal l and thus , n theory ,low d is to r t ion resu l ts .Under these cond i t ions , he net ga inw i th feedback c losed- loop a in ) dependsa lmos texc lus ive lyon how much o f the output s igna l s fed back ; .e . , f one-ten th of i t i s ed back, he ga in wi l l be 10 .The arge eedbackfac tor ( ra t ioo f ga in w i thout feedback o ga in wi th feedback)is ob ta ined by put t ing a la rgeamount o f ga in n the forward-path or open- loop ampl i f ie r .The open- loop ampl i f ie r s thusvery sens i t ive nd wi l l over load f the er ror , o r some reason,getsa t a l l apprec iab le .A l l ampl i f ie rshave a f in i te de lay rom input to output . l f afeedbackampl i f ie r s d r iven w i th a s igna l hav ing a very fas tr ise ime ( l ike the lead ingedge o f a squarewave) , herewi l lbe a br ie f n terva ldur ing which the open- loop ampl i f ie rseesthe fu l l input s igna l , und imin ished by negat ive eedbackwhich hasn ' tye t go t ten back o the input . Over loadwi l l thusoccur and d is to r t ionwi l l resu l t .The more sens i t i ve nputs o fampl i f ie rsw i th h igh feedback fac tors a re tha t much moreprone o such an over load.

S ince h is fo rm o f d is to r t ion s b rought about by fas t ran-s ien ts n the input s igna land because n over loadcond i t ioncauses ntermodu la t ion d is to r t ion , he phenomenon ts re -fe r red o as rans ien t n te rmodu la t ion is to r t ion TlM) .Return ing o the or ig ins o f T lM, the s i tua t ion is fu r theraggravatedby the add i t iona l s lownessof response ntro-duced in the open- loop ampl i f ie r by necessary eedbackcompensat ion .Each s tage n a mul t i - s tageampl i f ie r in t ro -duces phase sh i f t tha t inc reaseswi th f requency . Feedbackcompensat ion o l ls o f f the open- loop response o tha t thefeedback actor falls below unity before enough excessphasesh i f t accumula tes o cause ins tab i l i ty or peak ing in thec losed- loop response.The frequency where the feedbackfac tor a l ls o un i ty is ca l led he ga in c rossoverrequency . norder to achieve a stable gain crossover requency, the 6 dB /octave compensation roll-off must begin at some lower fre-quency. Amplifiers with large feedback factors (at low fre-quenc ies )have more ga in to "ge t r id o f " and mus t s tar t he i rcompensat ion o l l -o f f a t a lower f requency , resu l t ing n asmal le ropen- loop bandwid th . An ampl i f ie r w i th 20 dB o ffeedbackneedn ' t s ta r t ts ro l l -o f f un t i l 100 kHz fo r a 1-MHzga in c rossover , h i le one wi th 60 dB o f feedbackmust s ta r ta t 1 kHz . The a t te rampl i f ie r ,w i th heav ier eedback ompen-

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FREQUENCY-HzFig. -Post-RIAA spectraldistr ibution for phonographrecords.sa t ionand a long open- loop t ime cons tant , s thus s lower nrespond ing o input s igna ls .In respond ing o a fas t nput s igna l e .g . , squarewave) ,ala rge nterna lvo l tageor cur ren t overshootw i l l be producedin order to qu ick ly charge he compensat ing apac i to randovercome he ef fec t o f the long t ime cons tant t in t roduces .The largeovershoot s produced during the interval betweenthe fas t input change and the t ime when the feedbackcatchesup w i th the input , when a la rged i f fe renceor er rors igna l s app l ied o the open- loopampl i f ie r .In some cases h is overshoot may be 10 to 100 t imes aslargeas he nomina l s igna l eve lsa t tha t po in t . Unfor tunate_ly , the s tages r io r to the compensat ion o in t cannot a lwayshand le such.a la rges igna l w i thout non l inear i tyor ou t r igh tc l ipp ing . f the overshootcauses heses tages o c l ip or gen-era te d is to r t ion , TIM resu l ts .When these overshootsarec l ipped, he ampl i f ie r s n to the we l l - known phenomenonofs lew- ra te imi t ing .I t can be shown mathemat ica l ly hat i f the input s igna l sband l imi ted to a f requency less than the open- roopbandwid th o f the ampl i f ie r ,no overshoot an occur ,euen fthe input s igna l s a band l imi ted squarewave. Thus , w ideopen- loop bandwid th e l iminates the poss ib i l i ty o f TIMcausedby overshoots . av ingwide open- loop bandwid th , nturn , p lacesa l imi t on the feedback ac tor fo r a g iven ga incrossover requency. Forexample, f we choosean open-loopbandwidth ol 2O kHz and a gain crossover requency of 1MHz, then we are imi ted o a feedback ac toro f on ly 34dg.The aboveexp lanat ionof IM seemsplaus ib le nough,andi t has appeared n var ious orms in many p laces . t i s theor ig in o f the popu lar be l ie f tha t smal l eedback ac torsandwide open- loop bandwid th are necessary or min imiz ingTlM. A l though i t may at f i r s t g lance seem conv inc ing , hi iexp lanat ion is somewhat overs impl i f ied and mis lead ing .Whi le some of the issues ave been ana lyzed n greatdeta i lin techn ica l papers , o ther more impor tan t cons idera t ionshave been ignored. In several espects,the roblem seems ol ie w i th not see ing he fo res t or the t rees .A few more recenrpapershave, however ,done a very good job in lend ing n_s igh t and perspec t iveo some of the more impor tan t ssuesIs,6j.The approach aken here wi l l invo lve essdeta i l and morescope and perspective.For example, we.l l attempt to deter_mine jus t how fas t aud io program s igna ls ea l ly are . Thelength of the unavo idab le ime de lay n the ampl i f ie r andhow i t i s a f fec tedby feedbackcompensat ion s another m-por tan t area n need of d iscuss ion .We wi l l a lsoexamine hecond i t ions .govern ingver loadof an ampl i f ie r ,sn terna ls tag_es . Th is w i l l be done in the contex t o f a prac t ica lampl i f ie r

topo logy wi th rea l is t ic ombinat ionsof feedback ac tor andopen- loop bandwid th . Recogn iz inghat in add i t ion o l imi tson ampl i . tude, mpl i f ie rs re imi ted o prov id inga max imumrate-o f -change t the i r ou tput , much at ten t ionwl l l be oa id oampl i f ie r s lew- ra teper fo rmanceand i ts re la t ionsh ip o TlM.F ina l ly , echn iques or measur ing mpl i f ie rTIM per fo rmancewi l l be d iscussed.Program Characteristics

lus t as a l l rea l ampl i f ie rsare band l imi ted ,so are a l l rea lp rogram sources .No program source wi l l ever produce asquarewave wi th razor -sharp dges . n fac t , no t on ly areprogramsourcesband l imi ted n the smal l_s igna lense,butthey are more ser ious ly imi ted in la rge-s ignaf andwid th , orpower bandwid th .As an example , f ine t ipe mach inemightbe f la t o 20k1z at low leve ls , u t i t typ ica l iy annot produceanywherenear fu l l ou tpu t a t 20 kHz. Such res t r ic t ions reusua l lydue to equa l iza t ionwhich pre-emphas izeshe h ighf requenc ies o hat the subsequent e-emphas is t the rep[_duc ing end wi l l reduceh igh- f requency o ise .H igh f requen_c ies w i l l , there fore , ver load he medium more read i ly hanlow f requenc ies . uch equa l iza t ioncharac ter is t tcsre com_mon to a tmos tevery ype of programsource, nc lud ingpho_nograph,FM, and tape. As a resu l t , he max imum hi [L r_ f re -quency output o f each program source is cons t ra ined ora therwe l l -de f ined imi ts .S inces igna lsw i th a la rge ate-o f -change r , , t ime der iva-t ive" are genera l ly he cause of T lM, we need a way ofcharacterizing he tendency of a given program source toproduce hem. Such a measure hou ld not be abso lu te , i ket ime der iva t ive , u t ra thershou ld be re la t ive o that i t can beapp l iedequa l lywe l l a t d i f fe ren t po in ts n the sys tem egard_lessof s igna l eve l .We w i l l there foreuse the ra t io o f oeakt ime der iva t ive o peak ampl i tude expressed n , ,vo l ts :Der_mic rosecond er vo l t " (V / t ts l /V , and ca l l i t the normal izedt ime der iva t ive . he inverse f th is quant i ty is s imi la r o , bu tnot qu i te the same as large-s igna l ise t ime. Knowing thenormal ized ime der iva t ive ,we can go to any po in t in thesys temand, g iven the max imum ampl i tude at tha t po in t ,de termine he commensura temax imum ime der iva t ive .Wi th the except ionof a mic rophone, he bes t sourceof

fas t program s igna ls n the home is probab lv the ohono-graph.However , ts per fo rmance s wei l -cons t ia ined y me_chan ica lp rocessesuch as t rack ing .The per fo rmance s a lsowel l charac ter ized.n F ig . 1 , the dots are a scat te rp lo t ofmax imumobserved utput leve ls t var ious requenc ies oma survey of many records.These data were taken from the{11 l ia r rackab i l i ty iagramwide ly pub l ishedby ShureBros .[7 ] Whi le the usua lpresenta t ions n termsof grooveve loc i_ty , h is n format ionhasbeen RIAAequa l izedand normal izedto 25 cm,/S t 1 kHz and 1 V peak . t showswhat ac tua l lv anbe expec ted t the outputo f one,sphono preamp (asshown,the data are no t usefu l o r po in ts n the sys tempr ror o RIAAequa l iza t ion , uch as the phono preamp input) . The datarepresentedby the X's are spectral data for a single cymbalc rash and were presentedby Toml inson Holman t8 l . Thecrash is one from a Sheffield Lab direct-to-disc recordingwhich is noted or i ts rack ing i f f i cu l ty .Wi th re ferenceo Fig . '1 , e see hat the h ighes tampl i tudeoccursa t 4 kHz and is 1 .35V peak ,wh i le the h ighes t imeder iva t ive ccursa t 10 kHz and is 0 .035V/ uS. Th is resu l ts na normal ized ime der iva t iveof on ly 0 .026 V / pS) /V . Thus ,in a sys temsub lec ted o a w ide var ie tyo f mater ia lsuch asrepresented y the dots o f F ig .1, a po in t in the sys temwhichmust hand le an ampl i tude of 1 V peak wi th low d is to r t ionmust hand le a t ime der iva t iveof 0 .026V/ pS wi th equa l lylow d is to r t ion .Beforeproceeding urther, we should take note of the facttha t an advanced reb lecontro l w i l l tend to inc reasehe nor_

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mal ized ime der iva t iveof the program,but not as much asone might a t f i r s t th ink . The reason or th is is found uoonfur ther examinat ionof F ig . 1 . The peak t ime der iva t ivewi l linc rease n propor t ion to the greaterampl i tude of the h igh-f requency s igna ls .However , mos t t reb le contro l ac t ion oc-curs be tween 2 kHz and-10 kHz, mean ing that the overa l lpeak ampl i tude (occur r ingat 4 to 5 kHz in F ig . 1) w i l l in -c reasesomewhat as we l l . Basedon these observa t ions , ecan conc lude hat 6 dB of t reb le boos t w i l l inc rease ne nor_mal ized ime der iva t ive y perhaps50 percent .Whi le the cymbalc rashexh ib i tssubs tant ia l l t rason ic on-ten t , i ts ampl i tude genera l ly ies be low the enve lope o f theother po in ts .Not ice hat i ts mid-band record ing eve l s ac tu-a l ly ra ther ow in compar ison.Taken a lone, he normal izedt ime der iva t ive or the cymbal c rashmight be fa i r ly h igh , bu tthe ra t io o f in te res tmus t be basedupon the peak ampl i tudefor a l l the mus ic .Even f the three h ighes t po in ts on F ig .1 are ignored,anovera l lpower bandwid th o f less han 10 kHz is obta ined,anda max imum normal ized ime der iva t ive f approx imate ly .05(V/ LtS) /V results. By comparison, a 2O-kHz sinusoid ha s anormal ized ime der iva t ive f 0 .126 V t tS) V.Mus ic , o f course , produces many s imul taneous po in tswhose ampl i tudesand t ime der iva t ives dd in some fash ionto produce a to ta l ampl i tude and a to ta l t ime der iva t ive orthe comple te spec t rum.We can ga in fur ther ins igh t by rec -ognizing that for mid-band frequencies between about 50 0Hz and 2 kHz, post-RIAA amplitude is directly related to re-corded velocity. Above 2 kHz, post-RIAA time derivative an drecorded velocity are directly related, .e.,a 50-cm/S, 10-kHzcomponent produces he same ime der iva t ive t the outputof the phono preamp as a 50-cm,/S, O-kHzcomponent. Thisla t te r e la t ionsh ips due to the in tegra t ing f fec to f the 2-kHzRIAA h igh- f requency o l l -o f f . Knowing th is , we can get agood idea o f the normal ized t ime der iva t ive by assumingrea l is t ic a lues or the max imum tota l mid-band ve loc i tyandthe max imum tota l h igh- f requencyve loc i ty . Not ice tha t asmal le r assumpt ion for the max imum mid-band ve loc i tyy ie ldsa la rgernormal ized ime der iva t ive .Keep n mind thatthe mid-band and h igh- f requencymax ima need not occurs imul taneous ly .

As an example , f we assume max imum mid-band ve loc i -ty o f 25 cm,/Sand a la rgemax imum h igh- f requency e loc i tyof 150 cmlS (probably impossible to track), we arr ive at afigure of 0.076 (V/pS) /V. Based on this figure, a 100-wattampl i f ie r wh ich can de l iver 4O V peak wi th an B-ohm loadmust c lean ly reproduce igna lsw i th 3 V / p 5 t ime der iva t ives .

Fig.2-{ompensated and uncompensatedpower amplifieropen-loop gain vs. requency.

Th is f igure may seem very smal l to some peop le , bu t theterm "c lean ly " is the key here .We are cer ta in lynot ta lk ingabout the u l t imate s lew- ra te capab i l i ty o f the ampl i f ie r ,wh ich genera l ly occurs under non l inear opera t ing cond i -t ions . .C lear lyhe ampl i f ie rmus t have someopera t ingmarg inin order to sa t is fy he "c lean ly " requ i rement .As we sha l l eela ter , n some cases h is requ i reds lew ingmarg incan be sub-s tan ia l .A l though i t i s very un l ike ly hat any mater ia lw i l l approachthe 0.076 (V/ lrS) /Y, figure, we can be even more conserva-t ive i f we w ish and s imply say that a fu l l -ampl i tude 20-kHzsinusoid, 0.125 (V/ lr S) ,/V, must be handled with adequates lew ingmarg in .Requ i r ing hat a squarewave band l imi ted o2O kHz ,0 .25 (V / p S) /V , be hand led c lean ly wou ld add yetanother ac toro f two in conserva t ism.Basedon these observa t ions , e may conc lude that rea laud io s igna lsare no t near ly as fas t as some would l ike tobe l ieve .However , h is is no t cause or complacencywi th re-spec t o T lM. l t mere ly g ives us a more rea l is t ic e rspec t ivefor dea l ingwi th the prob lem.Low-Pass FilteringI t has o f ten been sugges ted hat a low-pass i l te r (LpF)bep laced ahead of the power ampl i f ie r o assure hat the pro-gram bandwid th does not exceed he open- loop bandwid tho f t h e a m p l i f i e r n o r d e r o m i n i m i z eT I M [ 1 - 3 1 . l t h o u g hw ewi l l see a ter hat such a precaut ionhas no bear ingon TtUsuscept ib i l i ty ,t i s wor th not ing tha t the LPFwi l l p lacea l imi ton the power bandwid th , and thus the t ime der iva t ive ,o fs igna ls pp l ied to the power ampl i f ie r . n th is la t te r espec t ,the LPFcou ld prevent TIM i f such a l imi ta t ion were neces-sary .However ,our ear l ie rd iscuss ions howed that the powerbandwid th o f rea l aud io s igna ls s cons iderab ly ess han 20kHz. Assuming hat an LPF uto f f o f less han 4Ok1z is unac-ceptab le due to f requency- response r ror ( -1 d8 at 20 kHzassuming i rs t -o rder u to f f ) , t i s qu i te sa fe o say hat such af i l te r w i l l have no ef fec t on TIM produced by program s ig-n a l s .Ticks, pops, and mistracking may, however, produce con-s iderab ly a rgernormal ized ime der iva t ives han program,a tleas t n the casewhere w ideband mov ing-co i lcar t r idges re

employed. Va lues as h igh as 0.1 to O.2 (V / l ts l /V may beencountered.However ,even a s tep nput w i l l on ly be l imi tedto 0 .25 (V /1 tS) /Y by a4O-kHz LPF. he f i l te r w i l l thus haveon ly a l imi ted ef fec t on the smal le rnormal ized ime der iva-t ive o f the t icks ,pops ,and mis t rack ing .One a lsohas o won-der how impor tan t TIM- f ree reproduc t ionof theseannoy ings igna ls ea l ly s . t i s probab lysu f f ic ien t ha t s lew- ra te imi t ingnot be encountered n the sys temunder hesecond i t ions .The on ly sens ib le eason or an LPF eems o be improvedimmuni ty to r . f . n te r fe rence,f th is s requ i red .Feedback ompensationAs ment ioned ear l ie r , eedbackopera teson the pr inc ip leo f feed inga por t ion of the ou tput back o the input fo r com-par isonwi th the input s igna l .The loop so fo rmed may beuns tab le f the phase of the s igna l is incor rec t .Feedbackcompensat ion s employed to assure tab i l i tyby contro l l ingthe net ga in and phasesh i f t a s igna lseesas i t goes aroundthe comple te oop.S ince he ro le p layed by feedbackcompensat ion s c ruc ia lto the TIM dis tor t ion mechan ism,and s ince in many TIMdiscuss ionst is no t adequate ly ons idered, t i s appropr ia tea t th is po in t to take a look at feedback ompensat ion .Because l l rea l ampl i f ie rshave in i te bandwid th , he ga inand thus the feedback ac tor mus t beg in to ro l l o f f a t somef requency . n a mul t i - s tage mpl i f ie r ,eachs tageusua l ly on-tr ibutes one or more "poles" (6 dB/octave roll-offs) and ac -company ingphasesh i f t . f a t some high f requencywe have

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Fig.' l Simplified schematicof a popular power amplifierdesign.a prob lem,we mus t cons ider he t ime i t takesa rea lprograms igna l o r ise ,what the de lay ime rea l ly s ( i t i s no t the open-loop r ise t ime as some have impl ied) , and the over loadmechan ism f open- loopampl i f ie rga in s tages .The open- loop ampl i f ie r can be mode led as a b lock ofga in , a dominant f i r s t -o rdercompensat ion ro l l -o f f , and apure de lay as shown in F ig .5 . E f fec ts f the o ther nondomi-nant po les are lumped in w i th the de lay w i th l i t t le loss o faccuracy . t i s we l l - known that , fo l low ing a s tep change atthe nput o f a f i r s t -o rderRC ow-pass i l te r , he output beg insto change mmedia te ly ,no mat te r how long the RC t imecons tant ;on ly the ra te o f change w i l l depend on the t imecons tant . hus ,a f te r a suddenchangeat the ampl i f ie r nput ,the ou tput w i l l beg in to change af te r the above-ment ionedpure de lay .Th is s the propagat ionde lay t ime of the ampl i -f ie r and is the de lay t ime dur ing which we mus t be con-cernedabout over load ing he ampl i f ie r n order to dea l w i ththe issue aisedabove.The propagationdelay t ime can be estimated by consider-,ing the phasemarg in o f the feedback oop. l f an ampl i f ie rhasa phasemarg ino f 45 degrees t a 1 -MHz ga in c rossover ,then the to ta l fo rward path de lay (assumning f a t feedbackpath) must be 135degrees, f which about 90 degrees s f romthe compensat ion o le and 45 degrees s f rom the propaga-t ion de lay .Th is works out to 125 nS. Mos t power ampl i f ie rsw i l l havecons iderab lyess ropagat ion e lay han th is .I t should be pointed out that it is incorrect to say that theampl i f ie r is w i thout feedback dur ing th is in te rva l . Thec losed- loop mpl i f ie r s a l inear sys temso long as the ga in ,ro l l -o f f ,and de lay e lementso f the mode l are inear . t i s a lsoFig.5-A simple model of the open-loop amplifier showingtime response o a step input. In practice, gain and delay aiedistr ibuted throughout the amplif er.

OUT

a continuous ystem n spite of the delay,and feedback spresent100 percentof the time as long as no stages reclipped.The feedback s, however,continuously out ofdate" by a time equal o the delay.Fortunately,he feedbackequationseadily ake his nto account n both the frequen-cy and imedomains.Cana ful l -ampl i tudenput signal , uchas a bandl imi tedsquare ave, ise arenough n 125nS o cause nyampl i f ierstageso becomenonlinear r to overload? he integratingactionof the compensation il l preventstages eyond hecompensationrom overloading,ypically eavingonly theinputstage efore t to worryabout seeFig. ).Consider sa worstcase 2-V peaksquarewavebandlim-i ted o 20kHz. t wi l l r ise bout63mV n 125nS, nd h is senough o dr ivesome nputstagesnto nonl inear i ty.h is sparticularlyrueof the differential airwithout emitter esis-tors (local eedback ften calledemitterdegeneration), sshown n the designof Fig.4. With a 63-mVerror signaldr iv ing t , i ts smal l -s ignala in s less han hal f ts nominalvalue.This nonlinearitywould result n ,,soft, 'TIM underthese onditions.However,most high-quality mplif ierde -signshaveenough ocal eedback f one sortor anotheratthe nputstage o al lowgood inear i tyn handl ing uchanerror signal.As we will see momentarily, uch eedback susual ly lsoan importantngredientn achieving ighslewrate.Feedbackactorand open-loopbandwidthareclearlyno trelevant ere,sincedesignswith differentvalues or theseparametersould easilyhave he same nput stagedesignand propagation elay.The importantcriterionhere is tohavean input stage hat can handle argeinputs ignals, tleast nder ransient ondit ions.

Slew RateReal oweramplif iers re not only l imited n termsof out-put amplitude;hey arealso imitedwith respecto the rate-of -changer t imeder ivat ivef the output .Whenan ampl i -f ier s asked o del ivermore han ts maximum mpl i tude,tclipsandproduces constant mplitude ndependent f theinputs ignal . imi lar ly,f anampl i f ierscal led pon o del ivera greaterime derivativehan tsslew ate, he amplif ierwil lgo into slew-rate imiting and producean output rate-of-changendependentf the nputs ignal . swi th ampl i tude-induced istor t ion, lew- inducedistor t ion SlD), r (T lM),hasa gradual nset. t is non-zero elow he slew-rateimitand rises s he slew-rateimit sapproached.Havingdiscussed mplif ierbehavior uring the propaga-t iondelayntervalo l lowing suddennputchange, e mustnow determinef the ampl i f ier an keepup wi th the t imeder ivat iveal led or by he nputs ignal i thoutbeing r iveninto nonlinearity y internalerrorsignals i.e.,overshoots).This s basically question f marginagainst lew-rateimit-ing,since lewing s the resultwhen the internalovershootsareso big they areclipped.Recall hat theseovershoots regeneral lyhe resul tof the ci rcui t at tempt ing o quicklycharge apacitances,articularlyhe compensatingapacitor.

At th ispoint t is importanto emphasizehat i t is themagnitude f theseovershoots hich is important, ot per-centage;manypapersn the literature aveerred n empha-siz ing he lat ter 1,2] . l t shouldbe c lear hat good marginagainst lew-rateimitingguaranteeshat he overshoots il lnotbe arge nough o cause onl inear i tynd husTlM.How does eedba ckactoraffect lew ate?By tself,not atall. Forexample, mplif iers ith high eedbackactors sual-ly have he extraopen-loopgain afterthepoint of compen-sation.The most commonexample s the use of a currentsource ollectoroadon the predriver tage, s n Fig. . Sup-pose or the moment hat the predriver tagehas a shuntcapacitor t its nput (base)or compensationunlikeFig. ).I J. ENOEAGATIONELAYAUDIOo February980


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INPUTG) _,-- LOW EEDBACKWIDEOPEN-LOOPBANDWIDTHMODERATEEEDBACKMODERATEPEN_LOOPBANDWIDTHLARGE EEDBACKSMALLOPEN-LOOPBANDWIDTH

--r-

rtutig. LA model of the feedback amplifier showing the errortime response o a bandlimited step input for variouscombinations of feedback actor and open-loop bandwidth.Closed-loop bandwidth is held constant, and feedback isvaried by changing only A2. Input level s assumed o be zeroprior to the step.l f we doub le the ga in a f te r the compensat ion by somemeans ,we mus t doub le the va lue of the compensat ing a-pac i to r o res tore he ga in c rossover requency o i ts o r ig ina lva lue . However , he added ga in means that we now needon ly ha l f the t ime der iva t ive n the capac i to r o ach ieve hesameoutput t ime der iva t ive , o the magn i tudeof the cur ren tovershoot harg ing he larger ompensat ing apac i to r s un-changed.The percentage vershoot s approx imate lydou-bfed, however, becauseof the smaller final value as a resulto f t h e d o u b l e d d . c . g a i n .T h i s s i l l u s t r a t e dn F i g . 6 . E v enthough the open- loop ro l l -o f f s ta r tsone oc tave lower , theinput s tagedoesn ' t have to work any harder to ach ieve ag ivens lew a te .The s i tua t ion s the same or ampl i f ie rsus ing Mi l le r -e f fec tcompensat ion s n F ig .4 . Here ,even the capac i to rva lue isunchanged as the feedback factor is raised or lowered byvary ing he load impedanceof the predr iver Q3) . Th is s sobecause he feedback ac t ion of C3 contro ls the h igh- f re -quencyga in ra ther han the load res is tance. mpl i f ie rswh icharede l ibera te ly es ignedwi th low feedback ac tors yp ica l lyach ieve h is by p lac ing a phys ica l oad res is tancerom theco l lec tor f the predr iver o ground [9 ] .l f we assume hat a l l o f the s igna lcur ren t f rom the inputs tage an f low in to C3, hen the s lew ra te or the ampl i f ie r nF ig . is about (0 .5mA/84 pF) 6 V pS. ln prac t ice , t w i l l besomewhat ess ecause f somecur ren t low in to R2and Q3.An improvedampl i f er s shown in F ig .7and is an exampleof an ampl i f ie rw i th a very h igh feedback ac tor . n add i t ion

Fig. 7-Simplified schematic of an improved power amplifier.

to us ing a h igh-qua l i ty ur ren t source oad fo r the predr iver ,t r ip le Dar l ing tonsare u t i l i zed in the output s tage or ex t racur ren tga in and hencea l igh ter oad on the predr iver o l lec -to r node. Add i t ion of the pa i r o f do t ted predr iver oad res is -(o rs , R15and R16,w i l l conver t i t to a low- feedbackdes ignwi th a 20-kHzopen- loop bandwid th . The requ i redcompen-sat ing apac i tanceemains nchanged.The open- loop ga in for the h igh- and low- feedbackver -s ionsof F ig .7 s shown in F ig .B.The ga in c rossoverrequencyfor bo th des igns s the same,and the on ly d i f fe rence s in -c reased oop ga in a t f requenc ies e low 20 kHz fo r the h igh-feedbackdes ign .The s lew ra te or both des igns s the samefor a s tep input s ta r t ingat zero vo l ts .Th is fu r ther i l lus t ra testhe fac t tha t feedback ac tor and open- loop bandwid th haveno effect on slew rate.What does affect slew rate s the design of the input stage.For a g iven s izecompensat ing apac i to r , n input s tagewi tha h igher output cur ren t capab i l i tyw i l l p rov ide an inc reaseds lew ra te . However , mere ly inc reas ing he ta i l cur ren t o f as imple d i f fe ren t ia lpa i r s tage,as in F ig .4 , w i l l no t work be-cause hat w i l l inc reasehe s tagega in ( t ransconduc tance)ythe same ac tor .Th iswou ld then necess i ta te propor t ionate-ly la rger ompensat ing apac i to r o res tore he ga in-c rossoverfrequency, and the slew rate would be back to where it wasbefore .One popu lar so lu t ion s to use emi t te r degenera t ion .Forexample ,we can keep the ta i l cur ren t he same,use em-i t te r degenera t ion o reduce he ga in ,and then use a smal le rcompensat ingcapac i to r .Th is approach is used in F ig . 7 ,where R2 and R3 reduce the ga in by a fac tor o f 10 . Th ispermi tsa dramat ic nc reasen s lew ra te .Loca lemi t te rdegen-era t ion is a lso des i rab le because t inc reases he overa l ll inear i tyo f the s tageand permi ts l inear opera t ion up to ala rger ercentage f the u l t imates lew ingcapab i l i ty .I t i s mpor tan t o rea l ize hat the ex t raga in in mos t ampl i -f ie rs w i th h igh feedback ac tors s not ach ieved by add ingmore vo l tage-ga in tages , h ich wou ld tend to inc rease on-l inear i tyand propagat ionde lay . As can be seen rom Fig .7 ,the on ly e lementswhich need to be added to ach ieveveryh igh ga in are emi t te r - fo l lowers . hese s tagesare prac t ica l lyde lay less nd ac tua l ly end to improve inear i tyby iso la t ingdr iv ings tages rom the input non l inear i t ies f the nex t s tage.Non l inear i t ies esu l t ing rom trans is to r e ta dependenceonco l lec torvo l tage (Ear ly f fec t ) and cur ren t and junc t ion ca-pac i tance ependence n vo l tageare educed n th is way .I t was ment ioned ear l ie r ha t a 1OO-wat t mol i f ie r wou ldhave o c lean lyhand le t ime der iva t ives p to about 3 V /pSfor wors t -case rogram mater ia l .How much marg in aga ins ts lew- ra te imi t ing is requ i red or c lean, ow-T lM opera t ion?Th isdependsvery much on the par t icu la r mpl i f ie rdes ign .Agood des ignwi th p len ty of loca l eedbackand a l inearopen-loop responsemay requ i re a marg in o f less han-1 .5 o 1,wh i le a rea l lypoor des ignwi th grossopen- loop non l inear i tycou ld requ i reas much as 10 to -1 . However ,even the of ten-c r i t i c ized 741 opera t iona l ampl i f ie r , when opera ted underreasonab le ond i t ions , equ i res ess han a marg ino f 5 to 1 .A marg ino f 4 t o 1 shou ld be more than adequate or pow-er ampl i f ie rs f reasonab le es ign o guarantee hat T IM pro-duced by in terna l overshootsw i l l be comple te ly naud ib le .Based n t h is and the prev ious lyd iscussed rogramcharac-te r is t ics ,he 100-wat t mpl i f ie rshou ld prov ide a s lew ra teo fat least 12 V/ 1tS.This also gives us a 50 percent marginaga ins t lew ing n the presence f a 0 .2 (V / p lS) /V u l l -ampl i -tude pop or t ick .Not ice tha t we 've pa id very l i t t le a t ten t ion to what hap-pens when out r igh t s lew- ra te imi t ing occurs ; a ther ,we 'veout l ined the cond i t ions requi red to s tay in a ra ther l inearreg ion of opera t ion where , a t mos t , the non l inear i t ies resof t . Th is s main ly becauseTIM w i l l become aud ib le be fores lew- ra te imi t ing occurs . However , t i s wor th no t ing tha t

8

AUDIO e Februarv 980


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@,Izae 4 0

loo tk tok took tMFREQUENCY-Hz

Fig.L-Open-loop gain comparison of amplifiers with highand low feedback actorsand equal gain crossoverfrequency.The maior difference s the greater eedback nthe audio band for the former case.recovery rom a s lew ing cond i t ion fo r mos t contemporaryampl i f ie r topo log ies s no t a f fec ted by the open- loop t imecons tant .Th iswas not necessar i lyhe case n some veryear lyt rans is to r mpl i f ie rdes igns n which a t rans is to r ou ld satu-ra te dur ing s lew ing and charge he compensat ing apac i to rto an abnormalvo l tage.Recoveryn modern ampl i f e rs s no t

s ign i f i can t ly onger han the t ime i t takes he output to s lewto the new s igna l a lue .A t th is po in t , i t shou ld be c lear ha t s lew ra te s the mos timpor tan t s ing le parameter govern ing TIM per formance,wh i le feedback fac tor and open- loop bandwid th have nobear ingon T lM. In Par t l , we ' l l con t inue by look ing at o thercauses f h igh- f requency r dynamic n termodu la t ion is to r -t ion (D lM) , why a la rge eedback ac tor is good ins teadofbad,and techn iques va i lab le or measur ing IM in the lab .7 f lReferences1. Ota la , M., "Transient Distor t ion n Transistor ized udio power Ampl i f ie rs, , ,IEEE fransactions on Audio and Erectro-.coustics, Vol. AU-18, pp. 234-239,Sept. ,1970.2 . Ota la , M., and E. e inonen, "The Theory of Transient n termodula t ion Dis-tortion," IEEE fnnsactions on Acoustics. Speech end Signal processing, Vol.ASSP-25, o . 1 , pp. 2-8 , Fet : . ,1977.3. Leach,W. M., "Transient M Distor t ion n Power Ampl i f e rs, ' ,Aud io , pp.34-4'1,Feb., 1975.4. Cre iner , R.A., "Amp Design and Over load," Audio ,pp.5O-62,Nov.,1977.5. Iung, W. C. , M. L . Stephens,and C. C. Todd,, ,S lewing Induced Distor t ionand l ts Ef fecton Audio Ampl i f ie r Per formanc+With Corre la tedMeasurementL isten ing Resu l ts ,"AES Prepr in t No.1252 presented at the 57th AtS Conven-t ion, LosAngeles,May, 19776. Carde, P., Transient Distor t ion in FeedbackAmpl i f ie rs," lour . o f the AudioEngineering Sociely, Y ol. )6, No. 5, pp. 31 4-321,M ay, 1978.7 . Kogen, ., B. iacobs, and F. Kar lov, "Trackab i l i ty-1973," Audio , pp.- t6-22,Aug.,-1978. Ho lman, T. , L)ynamic RangeRequi rements f phonograph ic preampl i fie rs, , ,Audio, pp. 72-79, uly, 19779. Leach, W. M., "Bu i ld a Low TIM Ampl i f e r ," Aud io , pp.3O-46,Feb.,1976.1O. Le inonen, E. , M. Ota la , and l. Cur l , "A Method for Measur ing Transientfntermodufation Distortion (IlMl," tour. of the Audio Engineering Society,Vo l . 25, pp. ' l7O-177,Apr i l ,197711. Corde l l , R. R. , 4 Fu l ly In -Band Mul t i tone Test or Transient n termodula-t ion Distor t ion ," AIS Prepr in t No. 1519presentedat the f f th AESConvent ion,New York. Nov. . 1979. 49

LOWFEEDBACK

GAINCROSSOVERFREQUENCY

Ihe ltrneable Tonealrrn'JUltracruft.It always happens.You put together your dream tonearm/cartridge combina-tion. And along comes a new "super" cartridge with parameters that iustwon't work with your arm. Unlessyou own a tuneable Ultracraft-so adiust-able you get the utmost performance from any cartridge.The UltracraftAC-30,AC-3OOMK-II and AC-3OOO C all use our uniqueADJUSTABTE AMPING SYSTEM,with a control that lets youregulate clearance between the damping bowl and oilcup for perfect tracking and customizedfrequency response.Our famed jewel-bearingUNIPIVOT DESIGNassuresstylus freedom so you hearevery nuance of every re-cording. AC-3000 MC an dAC-3O0 MK-II accept interchangeable PLUG-INARM STEMS n straight andS-shapes, f different diameters and materials,with integral or separateheadshells.Ultracraft's uniquely precise lateral balancing device, and anti-skating system(never before used on a single-point suspensionarm), plus features ike a 650gram stabilizer, special itz wires and a 3-step counterbalance, cleady makeUltracraft the ultimate tonearm. Let your Osawa dealer tune one up for you.OSAWA CO. (USA) lnc., 521Fifth Avenue, New York,New York lOOlTDistributed in Canadaby Intersound Elecffonics, Montreal, Quebec

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