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Introduction to Tube Amplifier Theory: 10.02.15Featuring the AX84 P1-eXtreme Amplifier
byDavidSorlien,revisedandupdatedbyStephenKeller
TheP1eXamplifierisasimplethreestagevacuumtubeelectricguitaramplifier.AsoutlinedinFig.1,itconsistsoftwopreampstagesdrivingapowerampstage.Dependingonthechoiceofoutputtube,thisampiscandeliverbetween7and15wattsintoa4,8,or16ohmload.
Fig.1:P1eXblockdiagram
Placedbetweenthetwopreampstagesisapreampvolumecontrol.Inasimilarmanner,thebass,middle,andtrebletonecontrolsandamastervolumecontrolareplacedbetweenthepreampandthefinalpowerampstage.Theguitaramplifierperformstwoprimaryfunctions:One,itamplifiesthesmallvoltagesandcurrentsproducedbytheguitarpickupintoasignalpowerfulenoughtodriveaspeaker.Two,itshapesthefrequencyresponse,tonality,anddistortioncharacteristicsoftherawguitarsignalintoaformpleasingtothemusician.
Tobettergrasphowaguitaramplifieraccomplishesthesefunctions,let'stakeawalkthroughtheinnerworkingsoftheAX84P1eXtremeamp(P1eX).Forreference,thereiscopyofrevision06.03.16oftheschematicprovidedinAppendix1attheendofthisdocument.Tofullyunderstandhowaguitarampworks,evenasimpleoneliketheP1eX,youmustknowhowtoreadschematicdiagrams,andunderstandwhatthingslikeresistorsandcapacitorsare.Youalsoneedsomeknowledgeofbasicalgebraandelectronictheory.
HOWTHEHECKDOTUBESWORKANYWAY?
Soyouruntothebookstoreandbuyabookonbasicelectronics.Hnm...,notubechapter.Evensomegoodtubeampbooksfailtoexplainhowtubeswork.Manydifferenttypesoftubeshavebeendevelopedovertheyears,butguitarampsgenerallyuseonlythreetypes:diodes,triodesandpentodes.
P1eXTheory 1
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VACUUMDIODES
Let'sstartwiththevacuumdiode,becauseitisthesimplesttypeofvacuumtube.Insidetheglassbottle,thereareafewmetalparts:thefilament,thecathode,andtheplate.Thefilamentissometimescalledtheheater,becausethatisexactlywhatitdoesitheatsthecathode.Likethefilamentinalightbulb,thetubefilamentisathinlengthofwirethatgetshotwhenelectricityflowsthroughit.
Asthefilamentheatsthecathode,itemitselectronsfromitssurfaceinaprocesscalledthermionicemission.Withthecathodewarmedup,acloudofelectronsgathersaroundthecathode,asshowninFig.2(b).Theelectronsrepresentedinthisdrawinghavenoplacetogobecausetheplateisnegativelychargedwithrespecttothecathode.Inmattersofelectricity,likechargedobjectsrepeleachother,sothenegativelychargedelectronsjusthangaroundthecathodelikefarmboysdreamingofbigcitylights!ButconsiderFig.2(c).Thingschangewhentheplateismadepositivewithrespecttothecathode.Nowtheelectronsstreamofffromthecathodetotheplate,causingcurrenttoflow1intheplatecathodecircuit.Ifyouthinkaboutthisbehavior,youseethatthevacuumdiodefunctionsasaonewayvalvethatallowscurrenttoflowinonlyonedirection.Itisthisfunctionthatmakesitusefulforconvertingalternatingcurrent(AC)intodirectcurrent(DC).
Invacuumtubeamplifiers,vacuumdiodesareoftenusedtorectifytheAClinevoltageintoaDCvoltagesuitableforpoweringtheplatesofothertubesinthecircuit.TypicalexamplesincludetheEZ80andthe5U4types.Solidstatesilicondiodesbehaveinasimilarmannerandareoftenusedinplaceofvacuumdiodesintubeampsbecauseoftheirlowercostandimprovedreliability.Yet,therearesomesonicgainstobehadfromusingavacuumrectifierinpushpullpoweramplifiersduetothegreateroverallloaddependentvoltagedropintroducedbytherectifier.Thisissometimescalledsag.Singleendedamplifiers,suchastheP1eX,presentroughlythesameloadtothepowersupplywhethertheyareatidleorrunningflatout,sothevoltagesagfromthetuberectifierdoesnotoccur.Consequently,avacuumtuberectifieraddscostandcomplexity,butlittlesonicvalue,toampsliketheP1eX.WhilesomesomeearlyversionsoftheP1ampusedtuberectifiersintheirpowersupplies,theP1eXreliesonsolidstatediodesformainsrectification.Besidestheirfunctionasrectifiersinpowersupplies,diodesalsoareusedinmanyothertypesofcircuits,includingautomaticvolumecontrols,compressor/expandercircuits,andradiosignaldetectors.Wewon'tspendanymoretimeonvacuumtubediodes,thoughwewilldiscusstheP1eXpowersupplylateron.
1 Anoteonconventionalelectriccurrentvs.electronflow:Conventionalelectriccurrentisdefinedastheflowofpositivechargeinacircuit.Thisisbecausetheconventionaldefinitionofelectriccurrentwasdevelopedbeforethediscoveryoftheelectronanditsnegativecharge.Backintheearlydays,electronicsexperimentersknewthatinvisiblebitsofchargeflowedthroughthewireinacircuit,buthadnowayofdeterminingthedirectionthebitstraveled.Theytooktheirbestguess.Bzzzzt!Wrong!Bythetimethenotsoancientsrealizedthemistake,itwastoolate.Byconvention,mostelectronicstextsrefertoelectriccurrentandmeanthenegativeflowofelectroncurrent.Thereareexceptionsinelectronicstextsaswellasintextsfromotherfields.Sometreatcurrentasflowingfrompositivetonegativeandsomeasflowingfromnegativetopositive.Additionally,somematerialsallowcurrentflowsinbothdirectionsbutcarriedbydifferentparticles.Donotletthissituationconfuseyou.Fromtheperspectiveofvacuumtubedesign,thedirectionofthecurrentflowrarelymatters,aslongasyoutreatitconsistently.Theimportantthingtorememberisthatcurrentisameasureofthevolumeofelectronsflowingpastaparticularpointinacircuit.Thegreaterthevolume,themoreusefulwork(ordamage)youcandowithit.
P1eXTheory 2
Fig.2:Thediode,forwardand
reversedbiased
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VACUUMTRIODES
Thingsgetmuchmoreinterestingwhenyouaddanelectrodebetweenthecathodeandplateofavacuumdiode,creatingatriode(Fig.3).The12AX7commonlyfoundinguitaramplifierscontainstwotriodesinsideitsglassenvelope.Thisnewelectrodeiscalledthecontrolgrid(orgrid,forshort)andisusuallyconstructedofameshofthinwirespositionedbetweentheplateandcathodeveryclosetothecathode.Ifyouweretoconnectthegridtothecathode,thetubewouldbehavemuchlikeadiode.Mostoftheelectronswouldflowrightpastthegridontheirwaytotheplate.Donottrythis.Mosttriodesarenotdesignedtobeoperatedinthismanner.
Whenchargeonthegridismademorenegativewithrespecttothecathode,theelectronflowfromcathodetoplatestartstogetpinchedoff.Fig.4illustratesthisproperty.Thedeviceinthisdrawingisconceptual,sodon'tgohuntingforarealtriodethatproducestheseresults.InFig.4(a)thegridvoltageis1V,soitisnotveryrepulsivetoelectronsandmanyofthemsuccessfullytraveltotheplate,whichallowstheplatecircuittodraw10mA.Asthegridvoltagebecomesmorenegativewithrespecttothecathode,asshowninFig.4(b),moreoftheelectronsarerepelledbythegrowingnegativechargeonthegrid,andthenumberofelectronsthatpassthroughthegridisreduced.Inthisexample,thecurrentintheplatecircuitfallsto5mA.Asthegridvoltageisdrivenevenmorenegativethanthecathode,theelectronflowisreducedfurtheruntilatsomenegativevoltagethecurrentcutsoffcompletely,asillustratedinFig.4(c).Whenthetriodeiscutofflikethis,nocurrentcanflowintheplatecircuit,andincreasinghownegativethegridiswithrespecttothecathodebeyondthispointhaslittleeffectonthebehaviorofthetriode.
EveryACsignalcyclesupanddownwithrespecttosomelevelofDCbiasvoltage.Ifyourhouseislikemine,themainACvoltageisabout125VRMS(rootmeansquare),meaningthevoltagecyclesbackandforthinasinewavefromapositivepeakof+177Vto0Vtoanegativepeakof177V.ThatzeroinmiddleindicatesithasaDCbiasvoltageof0V(oritshouldhaveifyourwiringiscorrect).Inasimilarmanner,thesignalonthegridhasaDCbiasvoltage.Itcouldbe0V,likeyourhousemains,oritcouldbesomepositiveornegativeDCvoltage.ThatDCbiasvoltage,whenappliedtothegrid,iscalledgridbias.ItisalsosometimesreferredtoasthezerosignalgridvoltagebecauseitisthevoltagethegridsitsatwhenthesignalisreducedtozeroACvolts.AnegativeDCbiasvoltagesufficienttoreduceplatecurrenttozeroiscalledthecutoffbias.
Whenthegridvoltagebecomesthesameasthecathodevoltage,thegridbiasissaidtobeat0V,andtheonsetofgridconductionoccurs.Gridconductionmeansthatcurrentflowsinthegridcircuitaswellasintheplatecircuit.Althoughmostsmallsignaltriodesdonottoleratesustainedoperationinthe
P1eXTheory 3
Fig.4:Currentfallsasgridvoltagegoesmorenegativewith
respecttocathode
Fig.3:VacuumTriode
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gridconductionregion,manypowertriodesandothersortsoftubesaredesignedforit.Continuedincreasesingridbiasvoltageallowevenmorecurrenttoflowintheplateandgridcircuits,uptoalimit.Thepointwhereplateandgridcurrentsnolongerincrease,regardlessofincreasesingridbiasvoltage,iscalledthesaturationpoint.Thesaturationpointisdeterminedbythecathode'sabilitytoemitelectronsatagivenoperatingtemperature,whichisgovernedbythecathode'smaterialandconstruction.
Betweenthecutoffpointandtheonsetofgridconduction,atriodebehavesasaroughlylineardevice.Smallsignaltriodesaretypicallydesignedtooperateinthislinearregion.Betweengridconductionandsaturation,atriode'sbehaviorbecomesverynonlinearbecausethegridisdrawingoffprogressivelymoreofthecurrentflow.Foragiventriodestage,weensureoperationinthislinearrangebysettingthezerosignalgridbiasabouthalfwaybetweenthecutoffpointandtheonsetofgridconduction.Sowhatdoesitmeantosetthebiasvoltageofastageandhowdowedothat?Theanswertothatquestionisinthenextsection.
BIASINGA12AX7GAINSTAGE
Beforewebeginthediscussionofsettingthezerosignalbiasvoltage,let'sestablishthreecommonabbreviationsthatwillappearintheequationsbelow:
E, meaningelectromotiveforcemeasuredinvolts.
I, meaningelectriccurrentmeasuredinamperes.R, meaningelectricalresistancemeasuredinohms.
TherelationshipamongthesethreeelectricalpropertiesisdefinedbyOhm'slaw:
E= IR whichcanalsobeexpressedas I=ERorR=
EI
Don'tletthemaththrowyou.Ohm'slawbasicallysaysthatthecurrentthroughagivencircuitelementtimestheresistancepresentedbythatelementgivesthevoltagedropacrossthatelement.ThecoolthingaboutOhm'slawisthatifyouhavetwoofthevalues,youcanfigureouttheremainingvalue.Supposeyoumeasuredthevoltagewithrespecttothecircuitgroundjustbeforeandjustaftera1Kohmresistorandobserveda12voltdifferencebetweenthetwo.Theresistorissaidtodrop12volts.YoucanplugthevoltageandresistancevaluesthatyouknowintoOhm'slaw,asfollows:
I=ER=
121000
=.012 A=12mA
Youcanseethat12mAflowsthroughtheresistor.Thatmeansthatthecircuitfollowingtheresistanceisdrawing12mA.Ohm'slawisapowerfultoolthatwillhelpusanalyzehowtheP1eXamplifierfunctions.
P1eXTheory 4
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TakealookatFig.5.ItshowsthefirstpreampstagefromtheP1eXschematic.Thisisanexampleofaresistancecapacitancecoupled,groundedcathodevoltageamplifier.Itoperatessuchthatthevoltageacrossplateloadresistor(R22)isanamplifiedandinvertedcopyofthegridsignalvoltageatpin7.ThesignalenterstheamplifierviaJ2,whereyouplugintheguitar.R25providesaloadacrosswhichthesignalfromthepickupscanform.ThegroundedcirclearoundtheleadfromtheinputjacktoR24indicatesshieldedwireintendedtopreventelectromagneticfield(EMF)interferencefrommixingwiththesignal.R24isagridstopperresistoranditspurposeistorolloffhighfrequenciestofurtherlimitEMFinterference.Typically,itismounteddirectlyonthetubesockettofurtherreducethechanceofEMFnoise.SomedesignersprefertoreducethevalueofR24becauseofitseffectonthehighfrequencyresponseofthepreamp.Othersremoveitalltogether.Insuchcases,itisimportantthatthegroundattheinputjackservesasthesignalgroundtochassisgroundtiepoint.Otherwise,theleadfromtheinputjacktothefirstpreampgridcanactasaradioantenna.
Let'sthinkaboutwhatishappeninginthatcircuit.FirsttakealookattheIpEpgraphfromthe12AX7datasheet,showninFig.6.Itlooksconfusingatfirst,butthisgraphcantellyouallsortsofthingsaboutthetube'sbehaviorinacircuitonceyoulearnhowtounpackit.Thecurvedlinesthatslopeupwardtotherightarecalledplatecurves.Eachonerepresentsthebehaviorofthetriodewhenthegridisataspecificbiasvoltage(0V,0.5V,1Vandsoforth).RecallinFig.4,thatasthegridvoltagebecamemorenegative,theplatecurrentdropped.Youcanseethatbehaviorinthe12AX7triode.Ataconstant150Vontheplate,theplatecurrentisabout3.2mAwhenthegridisat0V,about1.2mAwhenthegridisat1V,andabout0.2mAwhenthegridisat2V.Ataconstant150Vplatevolts,thetriodecutsoffwithagridbiasvoltagesomewherebetween2Vand2.5V.
P1eXTheory 5
Fig.6:12AX7IpEpgraph
Fig.5:StageoneoftheP1eXpreampisa12AX7gainstage
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ThesignalcomingintothegridofthetriodeisanACsignal.ItsvoltageisswingingupanddownaroundtheDCbiasvoltageatthefrequencyofthenotesbeingplayed.It'sgoingpositivewithrespecttothebiasvoltageandthennegativewithperhapsa1Vto2Vpeaktopeakswing.Ifthisgridsignalswingssufficientlynegativetocausethecurrentintheplatecircuittocutoff,thentherewouldbenovoltagedropinR22(rememberOhm'slawE=R*I),andthevoltageattheplatewouldequalthepowersupplyvoltage,whichis274VforstageoneoftheP1eXpreamp.Youcanseethatagridvoltageofapproximately3.6Visnecessarytocausethetriodetocutoffwhentheplateisat275V.Gridconductionoccurswhenthegridvoltageis0V,sowewantabiaspointaboutmidwaybetweenthesetwopoints;somewherebetween1Vand2Vwouldbefine.
Whennosignalispresentattheinput,thegridofV4BisconnectedtogroundthroughresistorsR24andR25,sotheDCvoltage(Eg)atV4B'sgridis0V.Theproblemishowtomakethegridvoltagenegative.WecoulduseafixednegativeDCsourcelikeabatteryoraseparatepowersupply.Butwedon'thavetoresorttothosemeans.Remember,thegridonlyhastobenegativewithrespecttothecathode.IfwecanraiseV4B'scathodevoltagetoabout1.4V,wecanaccomplishthesamethingasloweringthetriode'sgridfrom0Vdownto1.4V.
Oneconvenientwaytodothisistoplacearesistorbetweenthecathodeandground.Thisraisesthecathodeabovegroundbythevoltagedroppedacrossthecathoderesistor.Thistechniqueforsettingthebiasvoltageiscalledselfbiasorcathodebias.LookbackattheschematicinFig.5.ThevoltageacrossR22is:
ER22
=274V181V=93V
UsingOhm'slaw,thecurrentthroughR22is:
I R22=E R22R22
=93V
100K=0.93mA
So,0.93mAflowsintheplatecircuitofV4B.Thecurrentinthecathodecircuitofatriodeisthesumofthecurrentsintheplateandgridcircuits.Becauseourtriodeisoperatingbelowtheonsetofgridconduction,nearlyzerocurrentflowsinthegridcircuit.Forpracticalpurposes,thecurrentflowinginthecathodecircuitisequivalenttothecurrentintheplatecircuit.Therefore,usingOhm'slawagain,wecanmultiplyIR22timesthecathoderesistance(Rk)todetermineV4B'scathodevoltage.RkintheschematicisidentifiedasR23andhasavalueof1.5Kohms:
Ek V4B= I R22RkV4B =0.93mA1.5K=1.40V
Rememberthatthebiasisthegridvoltagereferencedtothecathodevoltage.WecaneasilycalculatethebiasvoltageofV4BbysubtractingcathodevoltageofV4Bfromitsgridvoltage.Recallabovethatatzerosignalthegridvoltageis0V,sothatgives:
EgridbiasV4B=E gV4BEk V4B=01.4=1.40V
That'sgood;1.40Visrightwherewewantittobe.
P1eXTheory 6
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Wasn'titconvenientthatweknewwhattheplatevoltagewas?Ifyouweredesigningyourownpreampstagefromscratch,youwouldhavetocalculatethezerosignalplatevoltageandcorrespondingbiasvoltage.Thereareafewwaystodothis.SomeusecomputerstomodelthecircuitinPSPICE(modelsforpopulartubesareavailableonDuncanMunro'swebsite).Otherspreferthechallengeofdoingthemathbyhand(ouch!).I'mavisualsortofengineerandlikedrawing,soI'llshowyouhowtodrawaloadline.
Aloadlineissimplyagraphicalrepresentationofthecircuitthatshowstherelationshipbetweentheplateloadresistor(R22)andthetriode(V4B)inthecontextoftheIpEpgraphfromthedatasheet.SupposeyouhadalreadydecidedthatyourB+wastobe275VandyourloadresistorR22wastobe100K.BecauseR22isafixedresistance,itwillplotasastraightline.Oneendofthat100KloadlinewouldbeatthecutoffpointwhereplatecurrentiszeroandplatevoltageequalsB+(275V,0.0mA).Tofindtheotherendofthe100Kloadline,useOhm'sLawtodivideB+(275V)bythevalueoftheplateloadresistor(100K).Thisgivestheplatecurrentof2.75mA,suchasitwouldbewhenthetheloadresistorisdroppingtheentireB+voltageandtheplateisat0V(0V,2.75mA).Fig.7showsthislineinredonthe12AX7IpEpgraph.Itsupperleftterminalpointisat(0V,2.75mA)onthegraph,anditslowerrightterminalpointisat(275V,0mA)onthegraph.YoucandothiswithanyvalueofloadresistorandB+voltage.
Nowlet'sassumewewantagridbiasvoltageof1.4V.Howdowefigurethatout?ThereisnoplatecurveontheIpEpgraphforagridvoltageof1.4V.It'seasy:Weextrapolatethevalue.Imaginethattherewereplatecurvesfor1.1V,1.2V,1.3V,and1.4Vonthegraph.Becausethedeviceislinearinthisregion,thosecurveswouldbemoreorlessevenlyspacedbetweenthe1Vand1.5Vplatecurves.Thatmeansthatthe1.4VplatecurvewouldintersecttheR22loadlineupfromthe1.5Vintersectionatabout1/5thedistancebetweenthe1Vand1.5Vplatecurves.I'vedrawnadotthereandlabeleditBiasPoint.Thebiaspointisatapproximately(180V,0.93mA)onthegraph.Thismeansthatthezerosignalplatevoltagewillbeabout180V,withaidlecurrentofabout0.93mA.Weknowwewantthecathodetobeabout1.4Vabovegroundandweknowtheidlecurrent;therefore,wecancalculatethedesiredcathoderesistanceusingOhm'slaw:
R=EI=
1.4V0.00093
=1505
P1eXTheory 7
Fig.7:A100Kloadlinewithanoperatingpointat1.4Vgridbias
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Afteranampisbuilt,ofcourse,itiseasytomeasuretheactualplateandcathodevoltagesandcalculatethecurrentfromthosevalues.Butifyouaredesigningastagefromscratch,thenyoucangettherefromaloadline.Supposeyouwantedtousea75KohmloadresistorwithaB+of250Vandthegridbiassetat1.2V.Tryworkingthatoutonthe12AX7IpEpgraph.Istheloadlinegoingtobesteeperorflatterthanthe100Kloadline?Ifyousaidsteeper,youareontherighttrack.Seeifyoucandeterminewhatcathoderesistancewouldbenecessarytoachievethatbiasvoltage.Whatwouldthequiescentplatevoltagebeatthatbiaspoint?Don'tlookbeforeyoutrytoworkthisout,butthereisagraphofthatloadlineandoperatingpointinAppendix2atthebackofthisdocument.
Thechoiceofbiaspointaffectsthetonalanddistortioncharacteristicsofagivenpreampstage.Youmaywanttotuneyourampfordifferenttonalqualitiesbymodifyingthebiaspointofeitherthefirstorsecondpreampstages.Ingeneral,makingthebiaslessnegativewithrespecttothecathode(increasingthecurrentthroughthetriode)makesforawarmertonebutaffordslesscleanheadroom.Alternatively,makingthebiasmorenegativewithrespecttothecathodemakesforacoolertone.Tastesvary,soasyouadvancefrombuildinganexistingdesignliketheP1eXtocreatingyourowndesigns,youmaywishtoexperimentwithdifferentoperatingpoints.Youcaneventweakanexistingdesignwithloadchangesandoperatingpointchanges.Note,however,thatyoucanonlypushtheoperatingpointsofarineitherdirectionbeforeyouhavetostartrethinkingtheoveralldesignofthestageandperhapstheentireamp.
AMPLIFYINGTHEINPUTSIGNAL
Wesetthebiaspointtokeepthetubeoperatinginthelinearpartofthecurve.InplainEnglish,thismeansthetubecircuitisdesignedsothataninputsignalthatdoesn'ttrytopushthegridintoconductionorpastthecutoffvoltagewillgetamplifiedwithminimaldistortion.Thereisalwaysaslightamountofdistortionbecauseavacuumtubeisnotaperfectlylineardevice.Wewon'tworryaboutthishere;itwouldbetoocomplicatedtoaddthisnonlinearityintothecalculationsbelow.
ThetwopreampstagesintheP1eXcircuitamplifytheinputsignalinseriesbeforeitisdeliveredtotheoutputstageorpoweramp(V1).Sothequestionis,howmuchamplificationoccursinthepreamp?Nowthatweknowtheoperatingpointofthefirsttriodestage,wecandetermineitsvoltagegain.Todothis,weneedtounderstandthreeoperationalparametersthatapplytotriodes:theamplificationfactor,transconductance,andplateresistance.
Theamplificationfactorisameasureofhowwellthetriodeamplifiesthegridvoltage;itistheratioofthechangeinplatevoltagetothechangeingridvoltage.Ontubedatasheetsitisusuallydenotedbythesymbol
=changeinplatevoltagechangeingridvoltage
(platecurrentheldconstant),ormoreformally=E p Eg
, I p const
Ofthethreetriodeparameters,itisthemostconstantacrossvariousoperatingpoints.Somuchsothatwegenerallytreatitasaconstantandtakethevaluegiveninthedatasheet.Becauseitisaratiooftwovoltages,ithasnounitofmeasurement.
Transconductance(ormutualconductance)istheratioofchangeinplatecurrenttothechangeingridvoltage.Inthelinearoperatingregion,itisroughlyconstant,butfluctuatesconsiderablyastheoperating
P1eXTheory 8
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pointmovesoutofthisregion.Thisratioislooselyameasureofhowefficientlythegridcontrolstheplatecurrent.Itisusuallydenotedintubedatasheetsbythegm:
gm=changeinplatecurrentchangeingridvoltage
plate voltageheld constant ormoreformally gm= I pEg
,E p const
TheunitoftransconductanceiscalledaSiemens,orintheoldertextsthemho.WhileSiemensisnowtheinternationalstandardnamefortheunitofconductance,itwasnotwidelyusedattheheightoftubedesign.BecausemanyofthetubedatasheetsavailableontheInternetusethetermmho,sowillwe.
Thethirdprimaryoperatingparameterofinterestisplateresistance(rp,sometextsrefertothisasra.)ortheratioofthechangeplatevoltagetothechangeplatecurrent.Ithelpstothinkofatriodeasavariableresistor.Whenthegridvoltageismademorepositive,morecurrentflowsthroughthetube.Thismeanstheeffectiveresistancebetweentheplateandcathodedecreases.Makethegridvoltagemorenegative,andthisresistanceincreases.Plateresistance,likeanyotherresistance,ismeasuredinohms:
r p=changeinplatevoltagechangeinplatecurrent
grid voltage held constant ormoreformally r p=E p I p
,E gconst
Lookingatthesimilarityoftheseparameterswithrespecttoeachother,youmightwonderiftheyaresomehowrelated.Theyare,infact,mathematicallyrelated,andwewilltakeadvantageofthatlater.First,however,let'sexaminethetriodeparametersinabitmoredetail.
The,gm,andrpvaluesforaparticulartubeareusuallyspecifiedatacoupleofdifferentplatevoltagesinthetube'sdatasheet.Forinstance,a12AX7datasheetIhaveindicates:
PlateVoltage 100 250 VOLTSAmplificationFactor()alsocalledmu 100 100Transconductance(gm) 1250 1600 MHOsPlateResistance(rp) 80K 62.5K OHMS
Whiletheamplificationfactorofmosttriodescanusuallybeconsideredaconstantregardlessoftheoperatingpoint,thesameisnottruefortransconductanceandplateresistance.Becausetheplatevoltageatouroperatingpoint(181V)isneither100Vor250V,wehavetodeterminethetransconductanceandplateresistanceforourquiescentoperatingpoint.Thereareavarietyofwaystoestimatethesevaluesforagivenoperatingpoint,buttoreallyseewhattheymeanforthetube,it'sagoodexercisetoplotthemontheplatecurves.
Considertheenlargedviewofthe12AX7IpEpplatecurvesaroundouroperatingpointthatisshowninFig.8.Thefirstthingwedoisdrawaverticallinethroughtheoperatingpoint,makingsureitintersectsboththe1Vand2Vgridvoltagecurves.Thisrepresentstheconstantplatevoltageneededforcalculatingthetransconductancevalue.Next,weplothorizontallinesfromtheintersectionsatthe1Vand2Vgridcurvestoobtaintheplatecurrentsatthosegridvoltages.ThesearemarkedIaandIdonthedrawing.
P1eXTheory 9
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AtEg1(1V),theplatecurrentIais1.73mAandatEg2(2V),theplatecurrentIdis0.30mA.Pluggingthosevaluesintothetransconductanceformulagives:
gm= I pE g
=I a I d
Eg1Eg2=1.73mA.31mA1V2V
=1420mho
Calculatingplateresistancetakesasimilarapproach.First,plotagridcurvethroughtheoperatingpointthatisroughlyparalleltothenearestspecifiedgridcurve.Thisrepresentsthe1.4Vgridvoltagethatmuststayconstantfortheplateresistancecalculation.Nextchoosetwovoltagesaroundtheoperatingpoint,say175Vand185V.ThosearemarkedasVaandVbonthegraph.Nextdrawverticallinesfromthosevoltagestointersectour1.4VgridcurveandobtaintheassociatedplatecurrentsatIbandIc.
AtVa(175V)onthe1.4Vgridcurve,theplatecurrentIcis0.88mAandatVb(185V)onthe1.4Vgridcurve,theplatecurrentIbis1.03mA.Pluggingthosevaluesintotheplateresistanceformulagives:
r p=E p I p
=V bV aI bI c
=187V173V
1.05mA0.86mA=73.6K
Asyoucansee,itisrelativelyeasytoplotthetransconductanceofatubeontheplatecurves.Allittakesisdrawingaverticallinethroughyourquiescentoperatingpoint.Accuratelyplottingaplatecurvethroughanarbitraryoperatingpointismuchmoredifficultandgenerallynotworththetroublebecause,asmentionedearlier,thethreeparametersareinterrelated.Specifically,theamplificationfactorofatriodeistheproductofitstransconductanceanditsplateresistance.Mathematically,thisisexpressedas:
=gmr p whichisalsoequivalenttogm=r por r p=
gm
Recallthattheamplificationfactor()ofatriodeisrelativelyconstantoveralargerangeofoperatingconditions.Therefore,ifyouknoweitheroneoftheotheroperatingparameters,itissimpletocalculatethemissingparameter.Sincetransconductanceiseasiertoplotaccurately,wetypicallyplotitforthedesiredoperatingpointandthenplugitandthetriode'samplificationfactorintotheaboveformulaandsolvefortheplateresistance.
r p=gm=
100.001420
=70422 (Wewillroundthisto70Kohms.)
P1eXTheory 10
Fig.8:CalculatingtransconductanceandplateresistanceontheIpEpgraph
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Oncewehavetheplateresistanceandthetransconductance,wecalculatethevoltagegainforthissortofcircuitusingthisformula:
Gain=r pRlRg1gmRk
where:
gm isthetransconductanceofthetrioderp istheplateresistanceofthetriodeRl istheplateloadresistance(note:somedocumentsrefertothisasRaorRp)Rg isfollowinggridresistanceRk istheunbypassedresistanceinthecathodecircuit
Thesymbol||isshorthandtoindicateresistancesinparallel.Theplateloadresistanceissimplythevalueoftheplateresistor(R22ofthepreampstageone).Thefollowinggridresistanceisthetotalresistanceofthecircuitconnectedtotheplateofthetube,notincludingtheplateloadresistor.Thecathoderesistanceistheunbypassedpartofthecathodecircuit.
SincewearetalkingaboutACsignals,let'sjustimaginethatC15hasnoresistanceatalltotheACoutputsignal(inactualpractice,itsresistancevarieswithfrequency).TheonlyreasonC15isinthecircuitistoblockthe181VDCpresentattheplateofV4B,andpassonlytheACsignal.Thatsaid,thefollowinggridresistanceseenbyV4Bisequalto1.2Mohms(R21+VR6).
Thecathodebypasscapacitor,C16,allowsapathforACsignalstobypassR23.ConsiderwhathappensifC16isnotpresent.WhenanACvoltageisappliedtothegrid,itcausesthecurrentflowingthroughthetubetochange.WithoutC16,thevaryingcurrentthroughthetubewouldcausethevoltagedropacrossR23tovary,whichwouldcausethegridbiasvoltagewouldvarywiththesignal.Suchdegenerativefeedbackfromcathodetogridreducesthegainofthestage.ThepresenceofC16preventsthatfeedbackforsignalsaboveacertainfrequency.Thoughwewon'tdiscusshowtocalculateitjustyet,the1FvalueofC16causesthefirststagetohaveaneffectivecathoderesistanceof0ohmstoallACvoltagesabove200Hz.Pluggingthesevaluesintothegainformulagives:
Gain=70K100K1.2M
11400MHOS
0=55.7
SoanACsignalof100mVwithafrequencyabove200HzonthegridofV4Bproducesa5.57VACsignalontheplate.AtthejunctionofR21andthetopofVR6themaximumsignalstrengthisabout4.3VAC.Signalsbelow200Hzaresomewhatattenuatedbecauseofthechangesingridbiaswejustmentioned.
ThevalueofC16hasamarkedeffectonthestage'slowfrequencyresponse.Forexample,doublingC16to2Fcausesthestagetobefullybypassedatallfrequenciesabove100Hz.DoublingC16againto4F
P1eXTheory 11
-
lowersthebypassfrequencydownto50Hz.GoingtheotherwayandhalvingthevalueofC16to0.5Fbypassesthecathodeonlyforfrequenciesabove400Hz.ThisisanotherplaceintheP1eXwhereyoumaywanttoexperimentwithdifferentcomponentvalues.Generallywithaguitaramplifier,youwantsomebasscutinordertokeepthelowfrequenciesfrombecomingmuddywhentheampisdrivenhard.
COUPLINGCAPACITORS
Inthelastsection,weassumedthatC15presentsinfiniteresistancetoDC,andzeroresistancetoAC.HighDCresistanceisveryimportantwhenacapacitorcouplesampstages.
ConsiderwhathappensifsomeoftheDCvoltagemakesitswaythroughC15intothenextstage.Stagetwoofthepreampisdesignedsothegridisat0.7Vpotential(withrespecttothecathode)whennoinputsignalisapplied.IfapositiveDCvoltagewereappliedtothegrid,itwouldalterthebiasandwouldrequireadjustingthecathoderesistortomaintainthedesiredbias.So,ifsomeoftheDCvoltagepresentattheplateofV4BweretogetpastC15,itwouldcomplicatethedesignofstagetwo.Whilesomedesignsoperatewithdirectcouplingbetweenthestages,wewon'texplorethosehere.
Thus,C15needstoblockDCvoltagesbutlettheaudiosignalthrough.Usedinthisway,acapacitorissometimescalledaDCblockingcapacitorandmorefrequentlycalledacouplingcapacitorbecauseitcouplestheoutputfromoneamplifierstagetotheinputofanotherstage.
ThecombinationofC15andVR6createsahighpassfilter.Lowerfrequencysignalsencountermoreresistancethanhigherfrequencysignals.IntheP1eX,C15isselectedsuchthatthecutofffrequencyofthishighpassfilterisbelowthefrequencyrangeofaguitar.IfyousubstituteasmallervaluecapacitorforC15,youdecreasethebassresponseoftheamp.IncreasingthevalueofC15givesincreasedbassresponsethatis,lowerfrequenciesarelessattenuatedbythecouplingcapacitor.
VOLUMECONTROL
R21andthepotentiometerVR6formavariablevoltagedividerinthecircuit,theoutputofwhichfeedstheinputgridofthesecondstage.AtthelowestsettingofVR6,thegridofV4Aisconnecteddirectlytogroundandallofthesignalfromthefirststageofthepreampisshuntedtoground.Atthehighestsetting,theACvoltageappliedtothegridofV4Aisabout78percentoftheACvoltagepresentatV4B'splate.
R21limitsthestageonegainbeforefeedingittostagetwo.Butwaitaminute!Isn'tgaingood?Uptoapoint,yes.Buttoomuchgaincandrivethenextstageintoaparticularlynastysoundingformofdistortioncalledblockingdistortionaverynonmusicalsoundthatissometimescalledfartingout.
P1eXTheory 12
Fig.9:Couplingcapacitors
-
I'llleaveittoyoutoguesswhatthissoundslike.R21attenuatesthesignalalittletopreventthisfromhappening.Thegreatertheattenuation,themorenoticeableitappearsathigherfrequencies,C14isaddedtoallowagreaterproportionofthesignal'shighfrequencyenergyintostagetwo.Thishelpsbrightenthestageandkeepitfromsoundingmuddy.
GAINMANGEMENT
BesidestheapproachusedintheP1eX,therearevariousotherwaystomanagegainbetweenstages.Youcaninsertavoltagedividerafterthevolumepotentiometer,asshowninFig.10.Withsuchanarrangement,thebrightcapbypassesthetophalfofthedivider.Thisexampleshowsthe50percentdividerusedintheP1andHOprojects.
Asecondapproachtogainmanagementistouseasplitloadplateresistor.Thistechnique,showninFig.11,placesthedividerintheplateload.Themainadvantageofasplitloadisthatitattenuatesthesignalwithoutchangingitstoneasmuchasotherdividermethods,thusreducingtheneedforbrightcaps.RefertoSteveAhola'sarticle,SplitLoadPlateResistorsformoreinformation.
Athirdapproachistoeliminatetheinterstageattenuationandemployalowergaintube,suchasa12AU7.Thedisadvantageofapproachisthatitreducesthegainofbothstages,whichmaynotbedesirable.Therearealsodissimilartriodesavailable,suchasthe12DW7,thatcontainalowgainandahighgaintriodeinthesameenvelope.Thesepresentadditionalopportunitiesforexperimentation.
P1eXTheory 13
Fig.11:Splitloadplateresistors
Fig.10:Voltagedivider
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PREAMPSTAGETWO
Usingthesametechniquesdescribedearlier,wecaneasilydeterminethebiascurrentandvoltageforV4A.Sincetheschematicshowsthevoltages,Iwillnotbotherwiththemath.Feelfreetotryyourhandatthecalculationsandseeifyoucomeupwiththesamevoltagesasshownintheschematic.Fig.12showsaloadlineforstagetwowithaloadresistanceof120Kohmsandaquiescentoperatingpointat136Vontheplateand0.7Vonthegrid.
Therearetwosignificantdifferencesbetweenthisloadlineandthatofthefirststage.Thefirstisthatitislesssteepthanthe100Kohmloadinthefirststage.Thisresultsinslightlygreatervoltagegainforthestage,whichovercomessomeofthelossesintroducedbythetonestackthatfollowsthisstage.
Theseconddifferenceisthatthequiescentoperatingpointisclosertotheonsetofgridconduction.Ratherthansettingthequiescentplatevoltageabouthalfwaybetweentheplatevoltageatthecutoffpointandtheplatevoltageatgridconduction,thebiasonthesecondstagesetsthequiescentplatevoltageaboutonethirdthewaybetweentheplatevoltageatthecutoffpointandtheplatevoltageattheonsetofgridconduction.Thismeansthatlargesignalstendtocompressduetogridclampingbeforetheybegintoclipduetothesignaltryingtopushbeyondthecutoffvoltage.Thisproducesasmootherformofdistortionwhencomparedtoclippingthatmanyconsiderpleasingtotheear.Tounderstandwhythisisso,let'stakealookatwhathappensinthestageasthegridsignalswinggrowslargerthan0.7Vpeaktopeak.Inotherwords,itspeakvoltageisgreaterthanthegridbiasvoltage,asshownininFig.13:
ThecurvesinFig.13representtheoriginalinputsignalvoltage(ein),thelevelinvoltsthatthecathodeisliftedabovethecircuitground(ek)andtheresultantclippedsignalvoltagethatappearsatthegridofV4A(eg).1Asyoucansee,thenegativegoingswingofegtrackscloselywiththeinputsignal.Onthepositivegoingportionofeg,however,thingsgetinteresting.Asthegridvoltageapproachesandpassesthecathodevoltage(thatis,asthegridbecomespositivewithrespecttothecathode),thegridmustdrawdirect
1 WaveformsinFig.13andFig.14courtesyofMerlinBlencowe.
P1eXTheory 14
Fig.12:120Kloadlinewiththeoperatingpointat136V/1.158mA
Fig.13:Gridclippingduetoanoverdrivensignal.
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currenttotrackwiththepositivegoingswingoftheinputsignal.Whilethereareplentyofelectronsflowingoutofthecathodethatcouldgointothegrid,recallthattheDCcircuitthroughwhichthoseelectronsmustflowincludesa1Mohmvolumepotentiometerattheinputofthestagestage.Thisresistancelimitsthetotalcurrentthatcanflowthroughthegridtoafractionofamilliampere.Becauseofthisgridcurrentlimitation,thepositivegoingswingoftheegisclipped.Suchgridclippingoftheinputsignalisinvertedandamplifiedontheplateload,asshowninFig.14b:
Whilethenegativeswingoftheinputsignaltoanresistivelyloadedstageisnotlimitedbythegrid,theinvertedpositiveswingoftheoutputsignalislimitedbythemaximumpowersupplyvoltageavailabletothetube.Ifthegridvoltageswingsfarenoughnegativewithrespecttothecathode,thenplatecurrentcutsoffandtheoutputsignalclipsasshowninFig.14b.
NoticeinFig.14a,andsimilarlyinFig.14b,howthedownwardswingoftheplatesignalfrom136Vatthebiaspointto75Visshorterinamplitudethantheupwardswingfrom136Vtoabout210V(or275VinFig.14b?Thisiscalledcompressionandistheresultofthecombinationofthenonlinearbehaviorofthetubeandchoiceofoperatingpoint.
Allthreeformsofdistortiongridclipping,plateclippingandcompressionhavetheirplaceinguitaramplificationandeachcontributesdifferentharmoniccharacteristicstothesignal.Thus,theselectionofoperatingpointsandsupplyvoltagesdeterminesanamplifier'scharacteristictonalqualities.Whendesigningapreamplifieritmaybedesirable,asisdoneintheP1eXdesign,tobiassomestageswarmlybyreducingthecathoderesistance.Inothercases,adesignermightchoosetobiasastagecoldlywithmuchlargercathoderesistancestopushtheoperatingpointmuchclosertothecutoffpoint.Asyouprogressbeyondasimpletwostagepreamplifier,youwillfindplentyofroomforexperimentation.
P1eXTheory 15
Fig.14:Relationshipbetweengridinputandplateoutputsignals
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Let'smoveontocalculatingthegainofthesecondstage.Aswiththefirststage,wedeterminethetransconductanceandplateresistanceattheoperatingpoint.Recallthevaluesfromthedatasheet:
PlateVoltage 100 250 VOLTS
Transconductance(gm) 1250 1600 MHOS
PlateResistance 80K 62.5K OHMS
Aswithstageone,theplatevoltageofV4Afallsbetween100Vand250V,sowemustestimateagain.Todothatweusethesamegraphingtechniqueusedforthefirststage,butwitha120Kohmloadlineandanoperatingpointat136Vontheplateand0.7Vonthegrid.Thisgivesatransconductancevalueof1600andplateresistanceof62.5K.
StagetwooftheP1eXpreamp(showninFig.15)differsfromstageoneinthatithasatonestackinparallelwiththeplateload.Itseemslikeitwouldbedifficulttodeterminetheeffectiveresistanceofthiscircuit.Well,itis,andthatmakescalculatingthegainofthisstageabitmorecumbersome,especiallyifwewanttoconsiderhowthestagegainchangesatdifferentfrequencies.However,wecanapproximateitseffectonthegainofthestageifwemakesomeassumptions.
Remembertheformulaforgain:
Gain=r p [RlRg]
1gmRk
Hey!Thereareacoupleofparenthesestherethatweren'ttherebefore.That'sdeliberate.Wearegoingtopullthattermoutandcalculateitseparately.Hereistheterm:
RlRg
ThistermrepresentstheeffectiveresistanceofthecircuitattachedtotheplateofV4A.Oncewehavetheeffectiveloadresistance,weplugitintotheformulaabove.Hereishowtocalculatetheeffectiveload:
Reffective=R17Rg
P1eXTheory 16
Fig.15:P1eXstagetwoofthepreampisfollowedbythetonestack.
-
PluginthevalueforR17:
Reffective=120KRg
Nowtakealeapoffaith.Justignorethegridresistanceofthefollowingstage,asifthetonestackdoesnotexistandtheoutputimpedanceisinfinite.Then,theequationabovereducesto:
Reffective=120K
Plugthenumbersintotheformulaforgain:
Gain=65.2 K120K
11600MHOS
Rk
The1Fofbypasscapacitance(C12)setsthehalfboostfrequencyatabout283Hz(seethenextsectionfordetailsabouthowwedeterminethehalfboostfrequency),soforaudiofrequenciessignificantlyabovethehalfboostfrequencywegetagainof:
Gain=65.2K120 K
11600MHOS
=67
Asthefrequencyfallssignificantlybelowthehalfboostfrequencythegaingraduallydropstoaminimumof34,whichyoucalculatebyassumingthecathodeisnotbypassed:
Gain=65.2K120K
11600MHOS
604=34
Atthehalfboostfrequency,thestagegainisabout50;andaroundthehalfboostfrequencythegainshiftsfromtheminimumtothemaximum.Afullybypassedgainof67isconsiderablygreaterthantheactualgainofstage.Toseewhy,we'llhavetoaddintheeffectofthetonestackonthestage.Beforewelookatthetonestacklet'sseehowtocalculatethehalfboostfrequency.Themathinthenextsectionmaybemoredifficultthanyouarewillingtotakeonrightnow.Ifyouwanttoskipitandmovedirectlytothetonestackdiscussion,youcandosowithoutworry.Thereisnothinginthetonestacksectionthatdependsonknowinghowtocalculatethehalfboostfrequency.
P1eXTheory 17
Fig.16:Stagetwotreatedasifthe
outputloadwasaninfiniteimpedance.
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CALCULATINGTHEHALFBOOSTFREQUENCY
Asmentionedearlier,itisoftendesirabletoapplysomebasscuttoguitaramplifiers.Byusingarelativelysmallcathodebypasscapacitorweonlypartiallybypassthecathode,leavingthelowerfrequenciesunbypassedandthereforeattenuatedorshelvedtoalowerlevel.Thetechnicalnameforthisisalowshelffilter.Itissonamedbecausethefrequencyresponsegraph(Fig.17)looksalittlelikeashelf.
MerlinBlencowe(MerlinontheAX84bulletinboard)andDavidIvanJameshavepublishedahandyformulafordeterminingthehalfboostfrequencyofaplateloadedtriodegainstage.Givenvaluesfortheplateresistance,theloadresistance,thecathoderesistance,cathodebypasscapacitance,andtheamplificationfactorofthetube,youcancalculatethefrequencyatwhichthegainishalfwaybetweentheunbypassedgainandthefullybypassedgain.Thisformulais:
f halfboost=1 Rk 12 RLr p12 Rk 1
2RkC k
where:
istheamplificationfactorofthetrioderp isplateresistanceofthetriodeRp istheplateloadresistanceortheeffectiveloadresistance(Rp||Rg)Rk isthecathoderesistanceCk isthecathodebypasscapacitance
Donotlettheapparentcomplexityofthisformulathrowyou.Givenwhatwealreadyknowabouttheseamplifierstages,itisasimplesubstitutionproblemtosolveforthehalfboostfrequency.Let'sworkthroughitusingthestagetwodatafromthepreviouspages.Fromthedatasheet,weknowthe
P1eXTheory 18
Fig.17:Eachstageformsalowshelffilterwiththehalfboostfrequencyaround200300Hz
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amplificationfactorofthe12AX7triodeis100.Wecalculatedthe12AX7plateresistanceatthestagetwooperatingpointtobe65.2K.Theplateloadresistoris120Kandthecathoderesistoris604ohms.Thecathodebypasscapacitanceis1F.Pluggingthesevaluesintotheformulagives:
f halfboost=1 Rk 12 RLr p12 Rk 1
2RkC k=1
6041001
2120K62.5K126041001
2604.000001
Simplifyingthesevalues,weget:
f halfboost=1 6100436500030502
0.0038=1.1542
0.0038=282.72Hz
Forthosereaderswhoaremathematicallyinclinedandwishtoknowhowtoderivethisformula,pleaserefertoBlencowe,M.andJames,D.I.ChoosingCathodeBypassCapacitors,AudioXpress,August2008,pp.1920.
YoumightwanttoexperimentwithdifferentvaluesofCkinthisformulaandseehowtheyaffectagivengainstage'shalfboostfrequency.Itisalsoaninterestingexercisetostudythecathodebypassvaluesofvariousproductionamplifiersandseehowtheycompare.Modifyingsuccessivestagecathodebypasscapacitancesisoftenusedtoshapetheoverallfrequencyresponseofanamplifier.
P1eXTheory 19
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INCLUDINGTHETONESTACKRESISTANCEINGAINCALCULATIONS
Whathappenstothegainofthisstageifwedonotignorethetonestackcircuit?
ThesimplestapproximationofthetonestackistoimaginethatC8,C9,andC10behaveasshortcircuitstoACvoltages,effectivelyremovingthebasscontrol(VR3)andtophalfofthemiddlecontrol(VR4)fromthecircuit.Thecapacitorsinthetonestackdonotactuallybehavethatway.Instead,thefrequencyofthesignalplaysalargeroleinthetotalimpedanceofthestack,butthissimplificationgivesanacceptableapproximation.Supposealsothatthetonecontrolsaresetattheirmidpoints.ApplyingtheseassumptionsgivestheequivalentcircuitshownatthebottomofFig.18.
ThetotalACresistanceofthisapproximatecircuitis:
Rtonestack=R11VR2VR42
Now,pluginthevalues:
Rtonestack=100K250K 252=100K250K 12.5=83.9K
Theeffectiveresistanceontheplateturnsouttobe:
Reffective=120K83.9K=49.4K
Plugthenumbersintothebypassedandunbypassedgainformulastoobtain:
Gainbypassed=65.2K49.4K
11600MHOS
=28.1K
625=44.9
andGainunbypassed=
65.2K49.4K1
1600MHOS604
=28.1K1229
=22.9
Asyoucansee,thisisasignificantdifferencefromthegainnumbersweobtainedwithoutconsideringthetonestack.Additionally,thechangeineffectiveloadmovesthehalfboostfrequencyupalittleto297Hz.Recall,however,thatthisisonlyanapproximation.CapacitorsdonotactasdeadshortstoACvoltages,butratherasfrequencydependentimpedances.Sotheattenuationfromthetonestackisnotquitesopronounced.
Therearesomequestionsyoumightwanttothinkabout:Whatistheeffectongainifthecontrolsaresetattheirlowestpoints?Orthehighestpoints?WhatistheeffectofraisingorloweringthevalueoftheR11?
P1eXTheory 20
Fig.18:AmodelofthetonestackthatassumesC9andC10behaveasACshortsandeach
controliscentered
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TONESTACK(THELONGCOMPLICATEDEXPLANATION)
Ifyouhavereadmanyschematicsoftubeguitaramps,thetonecontrolcircuitryshouldlookfamiliarbecausemanyampcompanieshaveusedthisarrangementofcomponentsfortheirtonecontrols.ThetubeampguruscallthiscircuitaFMVtonestack,whichstandsforFender/Marshall/Vox.TheFMVtonestackhasbeenduplicatedinhundredsofguitarampsinthelasthalfcentury.
Technicallyspeaking,thetonestackisasetofpassivefilters,eachwithitsown3dbpoint.Anotherwaytothinkofthetonestackistocallitapassivenetworkwithfrequencydependentinsertionloss.Whenasignalisinsertedintothiscircuit,somefrequenciesareattenuatedmorethanothers.
Let'sfirstdiscusstwotypesofpassiveRCfiltershighpassandlowpass.
Firstthehighpassfilter:Imagineyouhaveinputandoutputconnectionswhosesignalssharethesameground.Wireacapacitorbetweentheinputandoutputconnections,andputaresistorbetweentheoutputconnectionandground.ThiscreatesanRChighpassfilterthathasa3dbcutofffrequencyof:
F cutoff=1
2RC
The3dbpointreferstothefrequencyatwhichtheoutputsignalis3dblowerthantheinputsignal.Inahighpassfilter,lowerfrequenciesareattenuatedmore.
Alowpassfilterissimplytheoppositeofahighpass.Again,imagineyouhaveinputandoutputconnectionswithacommonground.Wirearesistorbetweentheinputandoutputandplaceacapacitancebetweentheoutputandground.ThiscreatesanRClowpassfilterthathasa3dbcutofffrequencyof:
F cutoff=1
2RC
Yes,thisisexactlythesameformulaasabove.Convenient,huh?
Ifyoufeedtheoutputofahighpassfilterintotheinputofalowpassfilter,yougetabandpassfilter.
P1eXTheory 21
Fig.19:Filters
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Now,let'sdissecttheP1eXtonestack,startingwiththetreblecontrol.
ImaginethatR11,C9,andC10areremovedfromthecircuit.Youareleftwithonecapacitorbetweentheinputandoutput(C8),andasetofpotentiometersacrosstheoutputandground(VR2,VR3,andVR4).Theresistancesofthepotentiometersaddupandcanbethoughtofasasingleresistor.Soweareleftwiththesimple,highpassRCfiltershowninFig.20.
NowconsiderwhatisgoingonatVR2.Signalswithafrequencygreaterthanthe3dbcutofffrequencypassrightthroughthecapacitortothetopterminalofVR2.Frequencieslowerthanthe3dbcutofffrequencyarenoticeablyattenuated.Rememberhowthevolumecontrolworks?Itisaresistivevoltagedivider.ThesamethinghappenswithVR2(thetreblecontrol).WhenthewiperisclosertothetopofVR2,thesignalthatjustmadeitswaythroughthehighpassfilterisattenuatedless.MovingthewipertowardthebottomlegofVR2causesmoreattenuationofthehighpassfilteroutput.
TakeacloselookatVR3(thebasscontrol).Asthewipermovestowardthebottomlegofthepotentiometer,theresistanceofVR3isreduced.Thiscausesthe3dbcutofffrequencytoincreaseasVR3rotatescounterclockwise(movingthewiperclosertothebottomleg).
ImaginethatC8,C10,andVR2areremovedfromthetonestackcircuit,asshowninFig.21.Whatremainsisactuallytwofiltersinseries.R11andC9formalowpassfilter,andC9andthecombinationofVR3andVR4formahighpassfilter.Hereagain,the3dbcutofffrequencyofthehighpassfilterdependsonthesettingofVR3.Atthehighestbasscontrolsettings,the3dbcutofffrequencyofthehighpassfiltercreatedbyC9,VR3,andVR4iswellbelowthefrequencyoftheguitar'slowEstring.Lowersettingsofthebasscontrolraisethe3dbcutofffrequency,attenuatingthebass.
MovingontoVR4(themiddlecontrol),wehaveacircuitalmostidenticaltothebasscontrol.ImaginethatC8,C9,VR2,andVR3areremovedfromthecircuit,asshowninFig.22.R11andC10formalowpassfilter,justlikethebasscontrolcircuit.C10andVR4createahighpassfilter,butwithamuchhigher3dbcutofffrequencythanthehighpasselementinthebasscontrolcircuitry.Thedifferencehereiswhathappenstotheoutputofthiscombinationoffilters.Thinkofitthisway:TheoutputofthefiltersthatmakeupthemidcontrolispresentatthewiperofVR4.MovethewiperofVR4towardsthetopleg(midcontrolup),andlessofthisoutputisshuntedtogroundthroughVR4.Turningdownthemid
P1eXTheory 22
Fig.20:Thetreblecontrolinisolation
Fig.21:Thebasscontrolinisolation
-
controlshuntsmorefilteredsignaltoground,attenuatingthemidfrequencies.
Notonlydoesthemidcontrolattenuatemidfrequencies,italsoattenuatestheoverallleveloftheoutputsignal.ConsiderwhathappenswhenVR4isturnedallthewaydown,essentiallyshortingonesideofC10toground.Inthissetting,C10effectivelyshuntsmostofthesignalpresentatthelowerlegofR11toground.Andforpracticalpurposes,thelowerlegofVR2isalsoshuntedtogroundthroughthecombinationofC9andC10,atleastforACsignals.Thus,themidcontrolaffectstheoveralloutputofthetonestack.
Wemadeahugeassumptionherewhenweignoredsomeofthetonestackcomponentstoanalyzethehigh,mid,andbasscontrolcircuitsseparately.Doingthismadeiteasiertoseehoweachsectionworked,butweignoredthefactthatthefiltersinteractwitheachother.Thisinteractionisfartoocomplextoexplainhere.Ifyouarecuriousaboutit,youcanfindamorethoroughanalysisoftheFenderstyletonestackinRichardKuehnel'sexcellentbookCircuitAnalysisofaLegendaryTubeAmplifier:TheFenderBassman5F6A.ExcerptsfromthisbookareavailableatthePentodePresswebsite:
www.pentodepress.com.
TONESTACK(THESHORTSUMMARY)
TrebleControl(VR2):ThispotentiometeractsasabalancecontrolbetweentheoutputofahighpassfilterformedbyC8andthethreepotentiometers,andtheoutputofthecomplexfiltercreatedbyR11,C9,C10,VR3,andVR4.
BassControl(VR3):Thispotentiometersetsthelower3dbcutofffrequencyofabandpassfilterformedbyR11,C9,VR3,andVR4.Italsoaffectsthe3dbcutofffrequencyofthetreblecontrolcircuit.
MidControl(VR4):ThispotentiometercontrolstheattenuationofthebandpassfilterformedbyR11,C10,andVR4.Italsoactsasavariableattenuatorforthetonestackoutput.
P1eXTheory 23
Fig.22:Themiddlecontrolinisolation.
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VACUUMPENTODES
Adiscussionaboutpentodetubeshastostartwithanexaminationofthelimitationsoftriodetubes.Inthetalkabouttriodes,welearnedthatinsideatriodethereareafewmetalpieces,separatedfromeachotherbyavacuum.Now,considerthatacapacitorismadebyseparatingtwoconductivesurfacesbyaninsulatingdielectric.Avacuumisasortofdielectric.Soinsidethetriode,thereareacoupleofvirtualcapacitors,onebetweentheplateandgrid,andonebetweenthegridandcathode.Theseinternalcapacitancesarecalledinterelectrodecapacitances.
Lookingatthe12AX7datasheet,wecanfindtheinterelectrodecapacitancespecifications:
TriodeUnit1 TriodeUnit2
GridtoPlate 1.7 1.7 pf
GridtoCathode 1.6 1.6 pf
PlatetoCathode 0.46 0.34 pf
Theabilityofatriodetoaccuratelyamplifyhighfrequencysignalsislimitedbythiscapacitance.Wedonothavetoworrymuchaboutthis,sinceaguitaramplifierisnotdesignedtoamplifyradiofrequencies,butthedesiretobuildradioamplifiersintheVHF,UHFandhigherfrequencybandsledresearcherstolookforwaystoreduceinterelectrodecapacitances.
Anotherlimitationoftriodesisthatplatecurrentdependsnotonlyongridvoltage,butalsoonplatevoltage.Forexample,supposeyoulowerthegridvoltageinatriodecircuit.Aswelearnedabove,loweringthegridvoltageresultsinanincreaseinplatecurrent.AndOhm'slawdictatesthatthevoltageacrosstheloadresistormustincreaseascurrentthroughitincreases.Now,thesupplyvoltageisaconstant,sotheplatevoltagemustdecreaseasthevoltageacrosstheloadresistorincreases(thetwovoltagesmustadduptothesupplyvoltage).Loweringtheplatevoltageresultsinreducedplatecurrent;gainislimitedinatriodebecauseofthis.Inapreampstage,reducedgainpresentsnoproblembecausewehavetodiscardsomeofthegainbetweenstagestopreventblockingdistortion.However,inanoutputstage,interactionbetweenplatevoltageandplatecurrentisnotgooditonlyreducesthemaximumoutputpoweroftheamp.Whatwasneededwasawaytodecoupletheoutputpowerfromtheplatevoltage.
Theeffortstoreduceinterelectrodecapacitanceandtoincreaseoutputpowerledtothedevelopmentofthetetrode.Atetrodehasanextraelementcalledthescreengridfixedbetweenthegridandplate.Thescreengridsolvesbothproblemswiththetriode.Addinganelementbetweenthegridandplatereducesthedistancebetweenelectrodesinsidethetubewhich,inturn,reducetheinterelectrodecapacitance.Thisallowsthetetrodetosuccessfullyamplifymuchhigherfrequencies.
Furthermore,thescreengridallowstheplatecurrenttooperateindependentlyfromtheplatevoltage.Howdoesitdothis?Rememberourdiscussionofdiodesandtriodes.Theelectronsstreamingoffthecathodeareattractedtotheplate,becausetheplatehasapositivevoltagepotentialcomparedtothe
P1eXTheory 24
-
cathode.Youcouldsaythattheplateexertsapullingforceontheelectrons.Inatetrode,thescreengridisoperatedatavoltagethatisslightlylessthantheplatevoltage.Now,becausethescreengridisphysicallyclosertothecathodethantheplate,thescreengridexertsmorepullontheelectronsthantheplate.Someoftheelectronsactuallyhitthescreengrid,butmostpassrightthroughonthewaytotheplate.Thus,platevoltagehasverylittleeffectonelectronflowinatetrode.Thesteadyvoltageofthescreengridprovidesanearlyconstantpullingforceontheelectrons.Asaresult,thegridhasalmostcompletecontroloverplatecurrent,regardlessofchangesinplatevoltage.
Whilewearetalkingaboutelectronswhizzingaroundinsideatube,nowisaperfecttimetodiscussthemainlimitationofatetrode.Imaginewhathappenstoanelectroninsideatetrodetube.Itgetsknockedoutofthecathodebecauseoftheheatingeffectofthefilament.Then,thepullofthescreengridmakesitspeedawayfromthecathode.Itacceleratespastthegridandthescreengrid.Theshorttripisoverwhenitsmashesintotheplate.Thisimpactactuallycausessomeelectronstobeknockedoutoftheatomicstructureoftheplate.Foreveryelectronthatsmashesintotheplate,twoorthreeelectronsareknockedoutoftheplate.
We'retalkingaboutparticlephysicshere!Impressyourfriends:Tellthemthatsmallparticleacceleratorspoweryouramp.
Thisphenomenoniscalledsecondaryemission.Triodesdonotsuffermuchfromsecondaryemission.Electronvelocitiesintriodesarelowerandthereistypicallylittleelsethatispositivelychargedtoattractthosestrayelectrons,sotheyquicklyfallbacktotheplateelectrode.Inatetrode,however,thescreenispositivelycharged,soittendstoattractthoseelectronsaswell.Thisisparticularlytruewhenalargegridsignalcausestheplatevoltagetotemporarilydropbelowthescreenvoltage.Undersuchconditions,theslowmovingelectronsfromsecondaryemissionareattractedtothescreengridanddonotmaketheirwaybacktotheplate.Thisreducesplatecurrentandincreasesscreengridcurrent,reducinggainandclippingthepeakoftheamplifiedsignal.
Toaddressthisproblem,researchersatPhilipsplacedanadditionalelementcalledasuppressorgridbetweenthescreenandplateandlocatedveryclosetotheplate,creatingthepentode.Thesuppressorgridisusuallyconnectedtothecathode,ofteninternally,whichputsitatavoltagepotentialmuchlowerthantheplate.Itdoesnotinterferewiththeflowofelectronsfromthecathode,becausethoseelectronsaretravelingatsuchahighvelocitythattheypassrightthrough.Theslowermovingsecondaryemissionelectrons,however,areeasilyrepelledbythesuppressorgridstraightbacktotheplate.Theeffecthandilyeliminatestheproblemsassociatedwithsecondaryemission.
OUTPUTSTAGE
TheoutputstageoftheP1eXemploysandEL34powerpentodeasacathodebiased,singleended,transformerloadedpoweramplifier.Wehavealreadydiscussedcathodebiasing.Singleendeddescribesanoutputconfigurationwhereatubes(orasetoftubesinparallel)isconnectedtotheoneterminalofaloadandtheotherterminaloftheloadconnectstoground(oftenviathepowersupply).
P1eXTheory 25
Fig.23:Thepentode
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InthecaseoftheP1eX,theloadconsistsoftheoutputtransformer(T2)andwhateverspeakeryouhaveconnectedtotheoutput.
R9ontheschematicisagridstopperresistorthatreducestheblockingdistortionthatoccurswhenoverdrivingtheEL34grid.
AttachedtothecathodeofV1isacircuitalmostidenticaltothecathodecircuitofthepreampstages.R10isthecathoderesistor,chosentosettheproperbiascurrent.C7isthecathodebypasscapacitor.
Calculatingthegainoftheoutputstageisnotreallynecessary.Thedesigngoalisnottoprovideacertainamountofgain,buttodeliverthemaximumpossiblepowerintotheloadwithoutburningupthetube.Muchlikethepreampstages,thisgoalisaccomplishedbysettingthebiascorrectly.BecausetheP1eXisasingleendedamp,theoutputtubemustbebiasedapproximatelymidwaybetweenthecutoffpointandtheonsetofgridconduction.Justaswiththetriode,apentodeiscutoffbymakingthegridvoltagesufficientlynegativewithrespecttothecathodesuchthattheplatenolongerconductscurrent.Gridcurrentflowstartstoflowasthegridvoltagebecomesequaltothecathodevoltage.
Keepingthetubefromburningoutisthemostimportantissuetoaddresswhendesigninganoutputstage.Setthebiastoofarpositive,andthetubewillfailasitattemptstodissipatemorepowerthanitcanhandle.Rememberyourbasicelectronictheory:P=I*E(powerequalscurrenttimesvoltage).ItisverysimpletodeterminethepowerdissipatedinacathodebiasedtubestagesuchastheP1eXoutput
P1eXTheory 26
Fig.24:TheP1eXpoweramplifiertakesthehighvoltage,lowcurrentsignalfromthepreampandconvertsittoalowvoltage,highcurrentsignalsuitablefordrivingaspeaker.
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stage.Becauseallthecurrentinthetubemustflowthroughthecathoderesistor,dividingthecathodevoltagebythecathoderesistorvaluedeterminesthecathodecurrent.CathodecurrentintubeV1equalsplatecurrentplusscreengridcurrent.Lookingatthevoltagesontheschematic,youcanseethatourscreencurrentisabout10mA(a10Vdropacrossthe1KresistorR8).
Theplatecurrentisthecathodecurrentminusthescreengridcurrent,asfollows:
I p=I k I g2
Ohm'slawtellsusthatthecathodecurrentisequivalenttothevoltagedropacrossthecathoderesistordividedbythevalueofthecathoderesistor:
I k=EkRk
Substitutingthislastformulaintotheplatecurrentformulashowninthepreviousformulagives:
I p=E kRk I g2
Todeterminethescreencurrent,youmeasurethevoltagedropacrossthescreenresistorR8anddividethatvoltagebythevalueofR8.Usingthemeasurementsshownontheschematic,weseethereisa10VdropacrossR8.Thatmeans10mAofcurrentareflowingthroughthescreengrid.Pluggingthevoltageacrossthecathoderesistor,thevalueofthatresistorandthescreencurrentintothepreviousformulagivestheplatecurrent:
I p=27.2380
.010=.062=62.0mA
Todeterminetheplatedissipationinwatts,youthensubtractthecathodevoltage(Ek)fromtheplatevoltage(Ep)andmultiplytheresultbytheplatecurrent:
Plate Dissipation=E pE kI p=38627.2 .062=22.2W
ThedatasheetindicatesthatthemaximumplatedissipationforanEL34is25W.Assumingthevoltagesontheschematicarethevoltagesmeasuredintheactualcircuit,theplatedissipationisabout22W.Atthesevoltages,theampisrunningatapproximately88percentofthemaximumplatedissipation.Inprinciple,youcanrunasingleendedoutputstageat100percentofitsmaximumplatedissipationbecausethisoutputstructurehasarelativelyconstantcurrentdrawfromzerosignaltomaximumsignal.Inpractice,you'llwanttobackitdownabitbecausetubesaren'tperfectlylinear.ThissettingisfinefortheEL34.
Donotassumethatyourampwillbehaveexactlylikethis.Itisveryimportantthatyoumeasuretheactualvoltagesanddothemath.Productiontubeswanderconsiderablyfromthepublishedspecifications,soitisimportanttocheckatubeincircuitandmeasureitsdissipation.Forexample,anEL34withahighergainthanthepublishedspecificationswilldrawmoreplatecurrentforagivengridvoltage.Itcouldbedamagedifplatedissipationexceeds25W.Tocorrectforsuchasituation,you
P1eXTheory 27
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increasethevalueofthecathoderesistortodecreasetheplatecurrent.Differentpowerdissipationinanoutputstageproducesdifferenttonalresponses.Ultimately,youmaywishtobiasbyeartoobtainthetoneyouprefer.Thisisfineaslongasyoudon'tviolatethetubespecifications.Bearinmindthathighercurrentsgenerallyresultinshorterlifespansforoutputtubes.
OUTPUTTRANSFORMER
Theoutputtransformerisoneoftheleastunderstoodcomponentsinatubeamp.Theconstructionisfairlysimple:twocoilsofwirewoundaroundamagneticcore.Thecoilontheinputsideiscalledtheprimary.Thecoilontheoutputsideiscalledthesecondary.
Thenametransformerisdescriptiveofitsfunctionitperformsatransformationofthevoltageandcurrentfromtheinputtotheoutput.Forinstance,intheP1eX,theoutputtransformerconvertsthehighvoltage,lowcurrentoutputfromtheoutputtubeintoalowvoltage,highcurrentsignalsuitabletodrivealoudspeaker.Somebasictransformerformulasfollow.Asyoucansee,theturnsratioisequivalenttothevoltageandcurrentratios.
EACPrimaryEACSeconary
=N TurnsPrimaryN TurnsSecondary
andIACSecondaryIACPrimary
=N TurnsPrimaryN TurnsSecondary
Theformulasaboveassumeanidealtransformerwithnolosses,buttheyarecloseenoughforourpurposeshere.
Inatubeamp,themostimportantjoboftheoutputtransformeristoreflectthelowspeakerimpedanceintothehighimpedanceloadneededbytheoutputtube.Atransformeralonehasnoprimaryorsecondaryimpedance;ithasanimpedanceratio.Ifyoulookinatubeamppartscatalog,youwillseetheprimaryandsecondaryimpedancesspecifiedasratiosaccordingtothisformula:
Z PrimaryZ Secondary
= NTurnsPrimaryNTurnsSecondary 2
orN TurnsPrimaryN TurnsSecondary
= Z PrimaryZ SecondarySupposeyoubuyatransformerwitha5Kohmsto8ohmsimpedanceratio.Theturnsratiois:
N TurnsPrimaryN TurnsSecondary
= 50008 =625=25Ifyouweretouseaspeakeranimpedanceof4ohms,theimpedancereflectedbackontheprimarywouldbe2.5Kohms.
N TurnsPrimaryN TurnsSecondary
= 25004 =625=25P1eXTheory 28
Fig.25:Atransformer
Fig.26:Theoutputtransformerwiring.
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TheoutputtransformershownintheP1eXschematichasa16ohmssecondarywithadditionaltapsat8and4ohms.Assumingyouconnectyourspeakertotheappropriatetap,thereflectedprimaryimpedanceis5Kohms.Thisprimaryimpedancewasnotchosenbyaccident.RatherthevalueistakenfromtypicaldesignexamplesinEL34datasheetforoperatingpointssimilartothatusedintheP1eXoutputstage.
POWERSUPPLY
ThepowersupplyintheP1eXisanexampleofafullwaverectifiersupply.Thepowertransformerhasthreesecondarywindings.TheredwindingiscentertappedandprovidesahighvoltagesourcefortheB+powertothepreampandoutputstage.Thegreen6.3VACwindingprovidesthefilamentsupply.Theyellow5VACwindingisintendedtoheatavacuumtuberectifier.ThestockP1eXdesignhasnotuberectifieranddoesnotusetheyellowwinding.
Fig.27:TheP1eXpowersupplycircuitfrommainstoplateincludingfilamentsupplies
First,let'slookattheB+supply.Thecentertapofthepowertransformer'shighvoltagesecondarywindingisconnectedtoground.Thisgroundconnectionreferencesthesecondarysignaltozerovolts,soitisalternatingcurrentaroundthecircuit'szerovoltagepoint.InthecaseoftheP1eX,thevoltageswingsfrom0Vto+400V,backdownto0V,thento400V,andbackto0V.IntheUS,eachcycletakes1/60ofasecond.Perhapsyouarequestioningthevalueof400V,becausetheHammondtransformerspecificationssaythesecondaryvoltageis275VAC.TransformersecondariesaregenerallyspecifiedbytheirRMSACoutputvoltage.RMSisameasureofvoltagedeliveredintoaloadovertimeratherthanameasurementofaninstantaneouspeakvoltage.TogetthepeakvoltageyoumustmultiplytheRMSvoltagetimesthesquarerootof2(approximately,1.414):
V peak=V RMS2=2752=389V
Hmm...389V.Sowhataccountsfortheextra11V?Fortheirclassicseriesoftransformers,Hammondassumesalinevoltageof115VAC,whichwasaUSstandardbackintheday.Sincethen,USwall
P1eXTheory 29
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voltagehasclimbedtoabout120VAC.That5VRMSdifferenceontheprimarysideaccountsforahigherpeakvoltageofabout405Vonthesecondaryside.SubtractacoupleofvoltsforthedropacrossthediodesandafewmorevoltsforDClossesinthesecondarywinding,andyouhaveaB+valueofabout400VDC.You'llalsofindthesameproportionalvoltageincreaseintheothersecondarywindings.
Eachsideofthehighvoltagesecondarywindingconnectstotheanodeofaseriesstringoftwo1N4007siliconrectifierdiodes.Thecapacitorsacrosseachdiodesetsnuboutsomeofthehighfrequencyswitchingnoisethatthediodesintroduceintothepowersignal.Thecathodesofthesetwodiodestringsaretiedtogethertoformafullwaverectifier.Arrangedthisway,thediodesformasortofonewayvalvesoonlythepositivevoltageswingsareallowedthrough.ThetwooutofphaseACvoltagesareturnedintoonebouncingDCvoltage.Whatdoesthatmeanexactly?Considerthefollowingdiagram:
Fig.28:RectifyingACintopulsatingDC
Thelinevoltageisconnectedtotheprimary.Thetransformerstepsituptoabout287VAC.Noticehoweachsideofthesecondarywindingisoutofphasewiththeothersuchthatwhenonehalfofthewindingisswingingpositive,theotherisswingingnegative.Eachdiodeallowsonlythepositiveswinginghalfthrough,sowhentheycombineafterthediodes,thesignalformsapulsatingDCvoltage.
ThestandbyswitchimmediatelyfollowingthediodesallowsyoutodelayturningontheB+totheplatesuntilafterthefilamentshavewarmedup.Considerwhathappenswhenatubeampisturnedonwiththe
P1eXTheory 30
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standbyswitchclosed.Thefilamentsinsidethepreampandpowertubesarecold,sonocurrentflowsfromtheplatetocathode.Withsilicondiodesastherectifier,theB+voltagejumpstofullvaluealmostinstantlywhenpowerisapplied.Rememberwhenwedeterminedthevoltagespresentontheplatesofthepreamptubesbymultiplyingcurrentbythevalueoftheplateloadresistor.Well,whennocurrentisflowingthroughthetube,thereisnovoltagedropacrosstheplateloadresistor.So,shortlyafterthepowerswitchisthrown,thevoltageattheplatesrisetofullpowersupplyvalue.ThecouplingcapacitorsaresubjectedtothefullB+value,whichiswhyallcouplingcapsinatubeampshouldbeabletowithstandthefullB+voltage.Additionally,biasvoltagesareat0V,becausenocurrentthroughthetubesmeansnocurrentthroughthecathoderesistor.
Oncethecathodeheatsupenough,currentwillbegintoflowthroughthetube.Whentheampisfirstturnedon,however,thereisfullB+ontheplate,andnearlyzerobiasvoltage.Thisquicklysettlesasthetubeswarmup,butforashortperiodoftimetheyarestressedbeyondtheirspecifiedlimits.Thestandbyswitchisintendedtoaddresstheseissues,butitbringsitsownsetofissuestothedesign.OneoftheproblemsisthattoggleswitchesarerarelyratedforDCoperationattypicalB+values,whichmeanstheswitchitselfwillbeoperatedbeyonditsspecifications.Anotherissueisthatrunningatubeamplifierforlongperiodswithoutanyvoltageontheplatesisalsoharmfultothetubes.TheRadiotronDesigners Handbook,4thEd.recommendsnomorethan15secondsonstandby.Forthisreasonthe330KresistorR1wasadded.Thereismuchdebateaboutwhetherthestandbyswitchaddsanyvaluetothedesign.
Thebouncingoutputvoltageatthecathodesofthosetwodiodesaddsatremendousamountof120HzhumtotheB+.Thishummustbefilteredout.C3servesasthefirststepinthatfilteringprocess.Capacitorsusedforthispurposearecalledfiltercapacitors.
R4,whichiswiredtoparallelC3,isthebleederresistor.Itisasafetydevicethatquicklydrainsthecurrentstoredinthefiltercapacitorswhentheampisswitchedoff.Someamplifiersalsouseableederresistortoprovideaslightvoltageregulationeffectbyensuringthereisalwayssomeloadonthepowersupply.R4doesnotprovidemuchregulatoryeffectbecauseitscurrentdrawisverysmall.
Afterthefirstfiltercap,thereisanRClowpassfilterbuiltfromR5andC4.ThesetwocomponentssmooththeB+voltageevenmore,anddropthevoltageslightly.TheoutputofthisfiltersuppliesthemainB+totheoutputstage.DownstreamfromthisfirstlowpassfilterisanotherRCfilterbuiltfromR6andC5.R6lowersthevoltageatad,andC5smoothsthevoltage.TheoutputofhisfiltersuppliespowertothescreengridoftheEL34.Finally,anotherRCfilterisbuiltfromR7andC6.Theoutputofthisfiltersuppliespowertothepreampsection.
Therearetwoprimaryreasonswhythepowersupplyisdesignedwithsuccessivestagesoffiltering.Thefirstisthatyouwantthepreamppowersupplytobeveryquiet.Inordertofunctionproperly,thefirststageofanelectricguitarpreampmustbesensitivetoverysmallsignals.Itdoesn'tcarewhetherthesourceofthosesignalsisaguitarpickuporthepowersupply.Anynoiseorhumonthepowersupplyendsupbeinggreatlyamplified.Thesecondreasonformultiplestagesoffilteringistodecouplethepowerstagesfromeachother.Withoutthisdecoupling,alowfrequencyfeedbackpathexistsfromthepowerstagetothepreampstages.Lowfrequencyoscillationcanstartviathispathandcausetheamplifiertomakeaputtputtputtingsoundknownasmotorboating.
P1eXTheory 31
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FILAMENTSUPPLY
The6.3VACwindingofpowertransformersuppliespowertothetubefilaments.Whendesigninganamp,itisimportanttoselectapowertransformerthatcanprovidethecurrentrequiredbyallthefilaments.TheHammond270DXcansupplymorethanenoughcurrentforthislittleamp.
Ifyouhaveexaminedschematicsofvarioustubeamps,youmayhavenoticed100ohmresistorsconnectedbetweeneachsideofthefilamentsupplyandground.Theseresistorsprovideagroundreferenceforthefilamentvoltage.Itisimportanttoprovideareferencepointforthefilamentsupply,butthereisaproblemwhenthisreferenceisthesameastheamplifier'sgroundreference.
Tounderstandthis,wehavetoreviewsometubetheory.Rememberthataheatedcathodeemitselectrons.Infact,thecathodehasacoatingofmaterialthatisverygoodatspewingoffelectronswhenheated.Eventhoughthefilamentdoesnothavethissamecoating,itdoesemitafieldofelectronsduringnormaloperation.Becausethefilamentisconnectedto6.3VAC,thisfieldhasa60Hzsignature.Foratleastpartofeach60Hzcycle,ithasapotentialthatislessthanthevoltagepresentonthecathodeinour12AX7stages.Duringthistime,thecathodeattractssomeelectronsfromthefieldaroundtheheater,whichinturnaremixedintothesignalthegridandpassedontotheplate.Theendresultisthatpowersupplyhumisintroducedintothepreampstages.
TheP1eXdesignusesaclevertechniquetoavoidthisproblem.Insteadofhavingthefilamentsupplyreferencedtoground,itisreferencedtoapositivevoltagetakenfromthetopofthecathoderesistorontheEL34,whichisapproximately25V.Thiselevates(orbiases)theheatervoltagesufficientlyabovethepreamptube'scathodevoltagetopreventheaternoisefromenteringthepreamp.AnalternatewaytoelevatetheheatersistousetwoseriesresistorsacrossC4toformavoltagedividerwithataptoobtain1050VDCheaterreference.
Thatconcludesourdiscussionofthepowersupply.
Fig.29:TheP1eXpowersupplyrevisited
P1eXTheory 32
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AFEWFINALWORDS
Buildingyourownamplifierisanexitingandrewardingproject.Nothingquitecomparestothesatisfactionfeltthefirsttimeyoupowerupyourampanditworks.ThisdocumenthasofferedabasicoverviewoftheinsandoutsoftheP1eXdesigninthehopesthatitwilldemystifywhatgoesoninsideourfavoritehouseholdparticleaccelerator.
Anoteaboutsafety:Thevoltagesinsideanelectricguitaramplifierarepotentiallydeadly.Pleasetaketimetoreaduponhowtoworksafelybeforeattemptingtobuildanyelectronicsprojects.Manygoodresourcesonthistopiccanbefoundforfreeonline.TwosourcesofnotearetheDrifterAmpsguide,foundathttp://www.drifteramps.com/safety.htmlandAikenAmp'ssafetyguidelinesathttp://www.aikenamps.com/Safety/Tips.html.Thisinformationcouldsaveyourlife.Readit!
Thisoverviewhasprovidedjustatasteofthevacuumtubeamplifierdesignprocess.Itisnottheendofthestory.Therearemanyotherdesignaspectstobeexplored:pentodestages,directcoupledstages,pushpulloutputstages,transformercoupledstages,cathodefollowers,alternatepassivetonecontrols,activetonecontrols,feedbackamplifiers,multichannelamplifiers,switchingtechniques,effectsloops,variousonboardeffectssuchasreverb,tremoloandvibrato,andhostofothertopics.Wearen'tgoingtotrytocoverthoseatall.Wehopethatthisbriefdocumenthasgivenyouasolidbaselineknowledgeabouttubeamplifiertheory.Youwillfindthatthemoreyoulearnaboutthetopic,themorethereistolearn.Thatisagoodthing.Thereisawideuniverseofcircuitvariationstotryandthetonalpossibilitiesarenearlylimitless.
Asyoustudyotheramplifierdesigns,remembertheconceptsyoulearnedhere:howtoconstructloadlines,howtoanalyzethegainandfrequencyresponseofeachstageinanamplifier,andhowthecouplingbetweenstagescausesthemtointeract.Thosearepowerfultoolsforunderstandinganyvacuumtubeamplifier.Youareembarkingonathoroughlyenjoyablequest.Neverstoplearning,besafe,havefun.
P1eXTheory 33
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Appendix1:P1eXREV06.03.16CompleteSchematic
P1eXTheory 34
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Appendix2:12AX7WITHA75KOHMLOADAT250V
Aspromised,hereistheloadlinefora12AX7witha75KohmloadandaB+of250V.
The75Kohmloadissteeperthana100Kohmload.WithaB+of250Vandabiaspointat1.2Vonthegrid,thezerosignalplatevoltageisabout170Vat1.1mA.Gainissomewhatreducedbythischangebecausethelowerplateresistancedoesnotallowforaslargeanoutputsignalswing.Toverifythis,simplyreplacetheplateloadandcathoderesistancesinthegaincalculations:
Gainfullybypassed=70K75K1.2M
11400MHOS
0=49.2 andGainunbypassed=
70K75 K1.2M1
1400MHOS1.1K
=19.4
Additionally,thesteeperloadlinewithagridbiasalittlecloserto0Vlowersthehalfboostfrequencyfrom199.4Hzforthestockstageonepreamp,downtoabout192.4Hz:
f halfboost=1 Rk 12 RLr p 12 Rk 1
2RkC k = 1
11001001
270.6K70K 1211001001
21100.000001 = 192.4Hz
P1eXTheory 35
Fig.30:Asteeploadlineresultsinreducedgainatgenerallyhighercurrents
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Appendix3:AbbreviationsandSymbols
Symbol Meaning
E Electromotiveforcemeasuredinvolts(V)
I Electriccurrentmeasuredinamperes(A)
R Electricalresistancemeasuredinohms()
mA Milliampere,aunitofelectricalcurrentequivalentto1/1000ofanampere
Theamplificationfactorofanvacuumtubeelectrode
gm Mutualconductancebetweenthegridandplateofatriode
rp(ra) Dynamicplate(anode)resistance
RL(Ra) DCplate(anode)loadresistance
Rk DCcathodeloadresistance
Rg DCgridresistance
G Gainofanamplifier;thatis,theratioofoutputvoltagetoinputvoltage
V Volt,theunitofelectromotiveforce
Ohm,theunitofresistance
P1eXTheory 36
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CREDITS(DaveSorlien)
Thisdocumentcontainsmaterialfromvariouspostsfromrec.audio.tubesandalt.guitar.ampsbythefollowingauthors:DuncanMunro,NedCarlson,Anonymous.
Thankstothefollowingindividualsfortheirassistance:RandallAiken,Carl,Nuke,Stephen,andespeciallyChrisHurley,withoutwhomtherewouldnotbeanAX84project.
CREDITS(StephenKeller)
InadditiontothefineworkthatDaveSorliendidwiththefirstversionofthisdocument,IwouldliketoacknowledgeandthankMerlinBlencowe,CliffChappell,ChrisHurley,Kyle,EvanLudeman,DannyNoordzy,andMilesO'Neil(akaHarrisonFordPrefect)andJeffSpenserwhoread,encouraged,andcommentedonearlydrafts.Theirmanyinsightshavemadethisamuchbetterdocument.AlsothankstoHalReichartandJoeVallinawhosevalianteffortsascopyeditorswerehelpfulbeyondcalculation.
Whilemanypeoplehavecontributedtothedevelopmentofthisamplifier,itisfittingtomentionandthankPhilRowley(akaZaphod),whodesignedtheoriginalAX84P1eXtreme.
REFERENCES
Bench,S.SimpleTubeGainCalculationshttp://www.triodeel.com/gaincalc.htm(lastupdated02/23/2008;downloaded9/13/2009).
Blencowe,M.DesigningTubePreampsforGuitarandBass,Leeds:MerlinBlencowePublisher,2009.
Kuehnel,R.CircuitAnalysisofaLegendaryTubeAmplifier:TheFenderBassman5F6A,2ndEd.,Seattle:PentodePress,2005.
LangfordSmith,F.ed.,RadiotronDesigner'sHandbook,4thEd.,Sydney:TheWirelessPressforAmalgamatedWirelessValveCo.,1953.
M.I.T.Staff,PrinciplesofElectricalEngineeringSeries,AppliedElectronics,NY:JohnWiley&Sons,Inc.,1943.
Schwartz,M.,AmecoAmateurRadioTheoryCourse,Mineola,NY:AmecoPublishingGroup,1963.
P1eXTheory 37
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LEGALSTUFF
Copyright1998DavidSorlien,newmaterialcopyright2009byStephenKeller
THISDOCUMENTATIONISPROVIDEDFREEOFCHARGEFORNONPROFITRELATEDPURPOSESSUCHASEDUCATIONALORHOBBYUSE.REPRODUCTIONOFTHISDOCUMENTFORCOMMERCIALUSEISSTRICTLYPROHIBITEDUNLESSWRITTENPERMISSIONHASBEENPROVIDEDBYTHECOPYRIGHTHOLDERS.
NOLIABILITYCANBEACCEPTEDFORERRORSINTHISDOCUMENTATION.FURTHERMORE,NOLIABILITYCANBEACCEPTEDFORLOSSESINCURREDDIRECTLYORINDIRECTLYARISINGOUTOFTHEUSEOFINFORMATIONINTHISDOCUMENTATION.
ALLTRADEMARKSACKNOWLEDGED.
P1eXTheory 38
Fig. 1: P1-eX block diagramFig. 2: The diode, forward and reversed biasedFig. 3: Vacuum TriodeFig. 4: Current falls as grid voltage goes more negative with respect to cathodeFig. 5: Stage one of the P1-eX preamp is a 12AX7 gain stageFig. 6: 12AX7 Ip-Ep graphFig. 7: A 100K load line with an operating point at -1.4V grid biasFig. 8: Calculating transconductance andplate resistance on the Ip-Ep graphFig. 9: Coupling capacitorsFig. 10: Voltage dividerFig. 11: Split-load plate resistorsFig. 12: 120K load line with the operating point at 136V/1.158mAFig. 13: Grid clipping due to an overdriven signal.Fig. 14: Relationship between grid input and plate output signalsFig. 15: P1-eX stage two of the preamp is followed by the tone stack.Fig. 16: Stage two treated as if the output load was an infinite impedance.Fig. 17: Each stage forms a low-shelf filter with the half-boost frequency around 200-300 HzFig. 18: A model of the tone stack that assumes C9 and C10 behave as AC shorts and each control is centeredFig. 19: FiltersFig. 20: The treble control in isolationFig. 21: The bass control in isolationFig. 22: The middle control in isolation.Fig. 23: The pentodeFig. 24: The P1-eX power amplifier takes the high-voltage, low-current signal from the preamp and converts it to a low-voltage, high-current signal suitable for driving a speaker.Fig. 25: A transformerFig. 26: The output transformer wiring.Fig. 27: The P1-eX power supply circuit from mains to plate including filament suppliesFig. 28: Rectifying AC into pulsating DCFig. 29: The P1-eX power supply revisitedFig. 30: A steep load line results in reduced gain at generally higher currentsIntroduction to Tube Amplifier Theory: 10.02.15Featuring the AX84 P1-eXtreme Amplifier