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

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

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

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

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

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

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

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

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

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

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

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.

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

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.

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

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

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

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

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.

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

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.

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

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.

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

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

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

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

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

Appendix1:P1eXREV06.03.16CompleteSchematic

P1eXTheory 34

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

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

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

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