TVE 13 027 Juni
Examensarbete 15 hp Juni 2013
Design of amplifiers in LTspice Aspects on the usage of spice-ware in the work of designing an electron tube amplifier Per Normann
Abstract
Abstract Design av förstärkare i LTspice Design of amplifiers in LTspice Teknisk- naturvetenskaplig fakultet UTH-enheten
Besöksadress: Ångströmlaboratoriet Ångströmlaboratoriet Lägerhyddsvägen Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00
Per Normann
Among users of guitar amplifiers there is a tendency of being enthusiastic about the usage of electron tubes in amplifiers. Further to shy away from the usage of transistors as gain devices. This to the extent that new technology is generally avoided. In this paper however a software tool called LTspice is used as an aid in the design process of an guitar amplifier. Electron tube spice models are examined and used in the process. The amplifier being designed in this paper has two types of electron tubes, 4 EL84 in the power section and 2 ECC83 in the pre-amplifier. The output of the amplifier is 30 to 35 W.
Hemsida: http://www.teknat.uu.se/student
Handledare: Kjell Staffas Ämnesgranskare: Martin Sjödin Examinator: Martin Sjödin ISSN: 1401-5757, UPTEC F13 027
Table of Contents
Table of Contents 1 Introduction.................................................................................................4 1.1 History of amplification............... amplification........................ .................. .................. ......................................4 .............................4 1.2 Why electron tubes...............................................................................5 1.3 ld technolo!y - ne" tools .................. ........................... .................. .................. .................. .....................5 ............5 2 #heory..........................................................................................................5 2.1 $lectron tubes.......................................................................................5 2.2 #he !rounded cathode !ain sta!e......................... sta!e.................................. .................. ...................... .............% % 2.3 &ouplin! capacitor..............................................................................11 2.4 'hase in(erter................. in(erter.......................... .................. .................. .................. .................. ................................11 .......................11 2.5 'o"er sta!e.........................................................................................12 2.) #one control................... control............................ .................. .................. .................. .........................................13 ................................13 3 *imulation and desi!n................. desi!n.......................... .................. .................. .................. .................. ..........................15 .................15 3.1 $lectron tubes in +#spice.................. +#spice........................... .................. .................. ...............................15 ......................15 3.2 #he !rounded cathode !ain sta!e................. sta!e.......................... .................. ............................1% ...................1% 3.3 're amplifier.......................................................................................1, 3.4 'o"er section................ section......................... .................. .................. .................. .................. .................................1, ........................1, 3.5 Amplifier.............................................................................................1 3.) &alibratin! the tone stac................. stac.......................... .................. .................. ...............................1 ......................1 4 /esults........................................................................................................1 5 0esi!n soft"are.........................................................................................2 5.1 #one *tac &alculator 1.3....................... 1.3................................ ...........................................2 ..................................2 5.2 +oad+ine'lotter................. +oad+ine'lotter.......................... .................. .................. .................. .................. .................. ...................2 ..........2 5.3 +#spice I................. I.......................... .................. .................. .................. .................. .................. ............................2 ...................2 ) Acno"led!ement....... Acno"led!ement................ .................. .................. .................. .................. ..........................................21 .................................21 % +iterature list.................. list........................... .................. .................. .................. ................................................21 .......................................21 , Appendi............... Appendi........................ .................. .................. .................. .................. .................. .......................................22 ..............................22 ,.1 A Anode characteristics dia!rams....................... dia!rams................................ .................. ..................22 .........22 ,.2 Fre6uency responses.................. responses........................... .................. .......................................2 ..............................2 ,.3 & &ircuitry................... &ircuitry............................ .................. .................. .................. ........................................3 ...............................3 ,.4 0.........................................................................................................33
3
Sammanfattning land an(7ndare a( !itarrf8rst7rare finns en tendens att (ara entusiastis 8(er eletronr8r. fta till den !rad att ny teni und(is !enerellt i sambamd med !itarrf8rst7rare. I den h7r uppsatsen unders8s m89li!heterna att an(7nda spice-m9u(ara som h97lp i desi!narbetet. I an(7ndandet a( spice-m9u(aran an(7nds s: allade spice-modeller f8r att emulera (erli!a eletronr8r. Hur bra dessa spicemodeller :ter!er (issa e!ensaper a( eletronr8r unders8s ocs:. $n l7sare b8r ha !rundl7!!ande unsap inom eletroni;; ele troni;; dataan(7ndande; dataan(7ndande; (iss erfarenhet erf arenhet a( spice-m9u(ara underl7ttar ocs: l7sandet. Allt an(7ndande a( spice-m9u(ara ser i pro!rammet +#spice som 7r ett s: allat free"are; d(s. det finns att till!: fritt p: internet.
1 Introduction 1.1 History of amplification In 1, Alesandro olta presents a !al(anic element. With this in(ention it is possible to create electrical (olta!e. #hree 6uarters of a centery later =a"ell; >.& put for"ard ?1@ "hich is commonly no"n as =a"ells e6uations. =a"ells e6uations theoretically describes electroma!netic "a(es and thus pa(es pa(es the "ay for ne" ad(ances in the the field of electricity. In ?2@ HertB; H (erifies =a"ells theories in a series of eperiments. When the ei!hteenth century dra"s to to an end the Italian in(entor in(entor =arconi; C constructs the first si!nal transmitter ?3@ by utiliBin! the theoretical achie(ements done by =a"ell and HertB. When the electron tube ?4@ is in(ented in(ented by Forest; 0 in 1% the the transmitted si!nal can be amplified on the recei(in! end. 12 the refinement of the electron tube maes it possible to amplify the si!nal bein! sent. At the middle middle half of the 2th century the electron tube tube is the main component in !ain sta!es in electronic de(ices. A theoretical transistor ?5@ is presented in 14, by a !roup of scientists at at the ell +aboratories. $i!ht years later; in 15); the same !roup presents a "orin! transistor and reci(es the Dobel price price for this. #he transistors ad(anta!es o(er the electron tube leads to a rapid decline in the usa!e of electron tubes. y the end of the 2Eth century the usa!e of electron tubes is almost non-eistent. #here is ho"e(er one field in "hich electron tubes still are used fre6uently. In HiFi-amplifiers and !uitar amplifiers the electron tube is still popularly used. #he electron tube has some features that maes it popular to use in amplification of sound. 4
1.2 Why electron tubes From the emer!in! of the transistor till present days the de(elopment of transistors in inte!rated circuit has been etensi(e. It is no" possible to emulate electron tube lie amplifiers by the help of soft"are tools in computers. #his is ho"e(er a sub9ect of stron! opinions. #hrou!hout the !uitar amplifier community the fact "hether an emulated e mulated electron tube is on par "ith or e(en close to the real thin! seems to be a bi! no no. #he interested reader is encoura!ed to 9oin an on-line forum or 9ust read comments re!ardin! this sub9ect. While this tet is "ritten; 213-5-2); the Coo!le search transistor vs. tube renders tube renders o(er 22 million hits. #he idea that the electron tube is irreplaceable has a hu!e affect on amplifier maret. 0esi!ners and (endors of amplifiers ha(e to comply "ith this supply and demand situation. With a maret cra(in! for electron tube amplifiers; ne" in(entions is not liely to be profitable in years to come. In the race of cuttin! costs to raise profit many amplifier producers manufacture transistor amplifiers. #hese transistor amplifiers are often presented as a lo" cost alternati(e to electron tube amplifiers. In addition to this misleadin! maretin! of these de(ices is often used. Cuitar amplifiers "ith transistor techni6ue are often labelled in such a "ay that the user is lead to belie(e that the amplifier is a electron tube amplifier. al(estate; #ubetrans; al(etroni are 9ust a fe" of these these some"hat misleadin! names; note that in ritish $n!lish electron elec tron tubes are commonly no"n as (al(es.
1.3 Old technology ne! tools ther aspects of !uitar amplifiers should ho"e(er be able to benefit from ne" technolo!y. Do mater if a computer emulated electron tube amplifier is a far cry from the real thin! or not soft"are tools can be of aid in the desi!n of a tube amplifier. In this paper the underlyin! techni6ue of electron tube amplification is in(esti!ated to !i(e an insi!ht in ho" a common electron tube amplifier "ors. #his no"led!e is then used to desi!n an electron tube amplifier in the soft"are tool +#spice.
2 Theory In this section a sur(ey of the components in an electron tube amplifier is presented. #he sur(ey is meant to !i(e the reader a fair idea of ho" each part of ho" a standars electron tube amplifier "ors. #he tet is also meant to display and eplain customary construction solution. A reader of this section should ha(e basic no"led!e of alternatin! current electronics.
2.1 "lectron tubes 2.1.1 The triode asura; *. et. al. sur(eys al. sur(eys the historical usa!e and de(elopment of electron 5
tubes ?)@. An in depth eamination of the triode is presented. A common "ay of constructin! and (end contemporary triodes is in pairs mounted in (acuum tubes. ne of the predominant electron tubes is the $&&,3 "hich "hich is t"o $&1 triodes paca!e in one (acuum tube. 0ue to the "ide spread usa!e in Hi-Fi and !uitar amplifiers the $&&,3 is one of fe" types of electron tubes still bein! produced in lar!e numbers. #o !et a triode to amplify a si!nal the triode is connected to the si!nal "ire; to !round and to "ires that supply heater current. #he basic structure of the triode sta!e is presented in Illustration 1. In a triode the amplification is obtained by inducin! and controllin! an electric field bet"een the anode and the cathode. #he cathode is heated to lo"er the threshold for the cathode to emit electrons. $lectrons are prone to stream from the ne!ati(e cathode to the positi(e anode. #he electric stream from the cathode to the anode in the triode induces a Illustration 1: The in-signal in-signal is received current. y controllin! the electric at the grid connection 1. The anode field the current throu!h the triode connection 2 sends the amplified out is indirectly controlled. #he control signal. The cathode connection 3 is mechanism is achie(ed by applyin! grounded over a resistor. a ne!ati(e (olta!e at the !ird bet"een the anode and the the cathode. #he "ay the anode; cathode and !rid (olta!es are balanced is often referred to as bias. +o" ne!ati(e bias (olta!e at the !rid maes it easy for electrons to flo" from the anode to the cathode. &on(ersely; a hi!h ne!ati(e bias (olta!e at the !rid pre(ents the electrons flo" from the anode to the cathode. #his beha(iour allo"s for (ariations in the !rid (olta!e to appear at the anode. y superimposin! an electric e lectric si!nal on the bias (olta!e at the !rid the si!nal si!nal is transferred from the !rid to the anode. In !ain sta!es a triode amplifies the si!nal appearin! at the anode. #he $&1 triodes amplification factor is 1. 2.1.2 The beam po!er pentode #he beam po"er pentode is similar to the triode in many "ays. In a po"er pentode there are three !rids instead of the triodes sin!le !rid. In order from the cathode to the anode the first !rid is the control !rid; it functions lie the !rid in the triode. #he second !rid is the screen !rid that focus the electron beam so that more of o f the 9umpin! electrons mae it to the anode. #he third is suppressor !rid that hinders electrons to 9ump bac to the screen !rid. #his is necessary because the screen !rid is often ept at )
positi(e (olta!es. In this paper the $+,4 is used in the po"er section of the amplifier. #he $l,4 is a "idely spread pentode that is still bein! manufactured because of the popularity in Hi-Fi and !uitar amplifiers.
2.2 The grounded cathode gain stage #he !rounded cathode !ain sta!e is a fundamental buildin! bloc in electron tube amplifiers; it is characterised by the triode and the topolo!y of the sta!e. In Illustration 2 the schematics of a !rounded cathode !ain sta!e is outlined. #he main idea of the !rounded cathode sta!e is to amplify a small input si!nal into a lar!er output si!nal. An ideal !ain sta!e amplifies the in-si!nal "ith a linear fre6uency response and no distortion. Ho"e(er; in !uitar amplifiers a Illustration 2. A grounded grounded cathode gain stage. !ain sta!e is often deliberately desi!ned to distort the amplified si!nal and alter the fre6uency response. 2.2.1 Triode characteristics A data sheet displayin! the the static anode characteristics is often often used "hen a triode !ain sta!e is desi!ned. #here seem to be many different names used for this dia!ram; in this paper the dia!ram "ill be called static anode characteristics dia!ram. An anode characteristics dia!ram holdin! the data of the $&&,3 electron tube is displayed in Appendi A1. #he dia!ram displays the current I a and (olta!e drop U a from the anode to the cathode. #he cur(ed lines sho"s the (olta!e drop U gc gc from the !rid to the cathode. #hese lines are often referred to as !rid cur(es. #hese entities are central "hile settin! up a common cathode !ain sta!e. 2.2.2 The anode load line In a !rounded cathode !ain sta!es there is a resistor R resistor Ra connected to the anode of the triode. With a (olta!e applied on R on Ra; the triode and R and Ra are in series. If there is no current flo"in! throu!h the triode there can be no (olta!e drop o(er the R the Ra; conse6uentially by hms la"; all the (olta!e drop is o(er the triode. Assumin! that a point A point A can can be defined in the static anode characteristics dia!ram at A at A GU GU aU ma ma ; I a1 a1; Appendi A2. U ma ma is commonly no"n as plate (olta!e. If all a(ailable current flo"s throu!h %
the triode all the (olta!e drop "ill be o(er R o(er Ra. y applyin! hms la" it is possible to calculate I calculate I a! a! I a =
U a R a
.
G1
With no current flo"in! throu!h the triode a point " point " GU GU a; I ; I aU a Ra can be defined in the anode characteristics dia!ram; Appendi A2. Althou!h these t"o etreme points are are not seen in any functionin! triode triode sta!e they are useful "hen a triode sta!e is desi!n. *ince hms la" is linear a strai!ht line can be interpolated bet"een these points. y mer!in! these ideas a function G2 can be put to!ether for calculations of the anode load line in a !rounded cathode !ain sta!e. I a (U )=
U a− U R a
G2
#he dashed line in Appendi A2 forms an eemplified load line of a $&&,3 triode !rounded cathode !ain sta!e. #he load line is central in the analysis of a electron tube circuit and hence the triode sta!e. As seen in G2 the anode load line of a triode sta!e can be ad9usted simply by alterin! Ra or U a. #he load line and the !rid cur(es intersects; see Appendi A2. #hese intersections sho"s "hat U a and I and I a "ill be for different U gc gc. 2.2.3 The cathode load line +ie R +ie Ra on the anode side of the triode there is a cathode resistor Rc connected on the cathode side. *imilar to the anode load line it is possible to dra" a load line for the cathode. If all current is flo"in! throu!h Rc the (olta!e drop from the !rid to the the cathode in the triode can be calculated calculated by hms la" G1. Ad9ustin! the cathode load line is usually done after the set up of the anode load line. #his is assumed here; hence I hence I a is assumed to be no"n. A point # G U G U gc gc - I a Rc ; I aU a Ra can no" be mared in the static anode characteristics dia!ram in Appendi A2. #he cathode load line has a linear part; but it is not linear close to . #he !rid cur(es in the anode characteristics dia!ram ha(e a "obbly beha(iour at to 5 ; anode (olta!e. #his su!!ests that that it is not possible to interpolate interpolate a strai!ht cathode load line in this inter(al. hms la" is used to calculate a second point $ point $ in in the static anode characteristics dia!ram di a!ram in Appendi A2 "ith (alues chosen outside the lo" anode (olta!e (olta!e ran!e; $ ran!e; $ GU GU gc gc - I a Rc; I a.5. y puttin! to!ether these ideas a "ay of describin! the cathode load line can be defined;
,
U gc =−
U a R c R a
.
G 3
Craphically the same can be done by interpolatin! a line bet"een point & and 0 in the anode characretistics dia!ram. An interpolation bet"een # and $ and $ forms forms the cathode load line. #he blue dashed dotted line in Appendi A2 eemplifies a cathode cathode load line. #he intersection bet"een the anode and the cathode loadlines is the bias point. 2.2.# $ias point #he bias point is the operation point po int of the triode. When the operatin! point is set in an !rounded cathode !ain sta!e it is possible to determine amplification and other features of the sta!e. y shiftin! the bias point it is possible to induce more or less !ain. Dote that the bias point of the !rounded cathode !ain sta!e is determined by the (alues of U a Ra and R and Rc. 2.2.% Stationary amplification amplification i9ls e6uation states that; μ =r a g m ;
G4
"here % "here % is is the amplification factor; ra is the inner anode resistance and gm is the transconductance of the triode. i9ls e6uation is con(enient because it states a dependency that mae it possible to calculate ra. If ra is no"n the amplification of the !rounded cathode !ain sta!e can be calculated. % is % is listed in most electron tube specifications. It can also be deri(ed from a statis anode characteristics dia!ram; μ =
∂ U a ∂ U gc
∣
.
G5
I I a
#he transconductance gm is an entity that models the triodes ability to con(ert a (olta!e chan!e into a current chan!e. m is to indicate the maimum achi(able !ain of the !ain sta!e. If U a is ept constant gm is; g m=
∂ I a ∂ U gc
∣
G)
U a
#he inner resistance ra is deri(en by eepin! U gc gc constant;
r a =
∂ U a ∂ I a
∣
.
G%
U gc
It should be mentioned that these three entities (ary sli!htly dependin! on the triodes bias point. A readin! from the static anode characteristics dia!ram is often a better choise than usin! (alues listed in tube specifications. As mentioned these three entities; % entities; %;; ra and gm are readable in the static anode characteristics dia!ram. An eample; the amplification factor is read by checin! "hat &U "hat &U a is "hen &U "hen &U gc gc 1. #he amplification of a !rounded cathode !ain sta!e can be deri(ed by assumin! that the triode is a perfect amplifier "ith the !ain factor %. %. If the amplifier leads a si!nal current do"n do "n throu!h any impedance present in the !ain sta!e; all these impedances forms a (olta!e di(ider. #he out si!nal in a !rounded cathode sta!e is taen across R across Ra. #o properly calculate the amplification A amplification A all all impedances do"n to !round has to be considered ?%@; A=− μ R a ∑ i =0
1
R i
.
G,
*ince the difference bet"een the !rid and the cathode are amplified any impedance placed in series on the cathode side "ill appear to be amplified; impedanceK Ra; ra; and R and Rc. %J %J Rc. #hree more impedances forms the total impedanceK R #he amplification of the !rounded cathode sta!e is A=
− μ R a R a + r a + μ∗ R c + Rc
G
#he minus si!n is a result of the fact that an increased !rid (olta!e "ill lo"er the anode (olta!e. In practice this means that the !rounded cathode !ain sta!e not only amplifies the in-si!nal; the in-si!nal is also in(erted. It is possible to calculate the stationary amplification A amplification A by by usin! G4 and G. 2.2.& 'rid lea( resistor When a triode is operatin! the !rid is indirectly heated by the heated cathode. #he heat leads to emission of electrons from the !rid. #his loss of electrons maes the !rid sli!htly more positi(e char!ed. /educed ne!ati(e !rid (olta!e lo"ers the threshold for electrons to 9ump from anode to cathode. #his results in more current flo"in! from the anode to the cathode; hence "orsen the heat problem e(en more. #o maintain the !rid (olta!e at a controlled le(el electrons must be be replenished in the !rid. A !rid lea resistor R resistor Rgl connected connected bet"een !round and !rid "ill pro(ide a leaa!e path for electrons from the cathode into the !rid. With a !rid lea resistor in place the bias point "ill be maintained despite heat induced 1
electron emission from the !rid. Rgl has has to be lar!e enou!h to hinder the si!nal to be dumped do"n to !round. =ost electron tube ha(e a maimum listed siBe of R of Rgl . Accordin! to >ones; D. to lar!e R lar!e Rgl "ill "ill induce noise into the triode circuit and is not desirable ?%@. In !uitar tube amplifiers the predominant (alue is R is Rgl 1=L. 2.2.) $ypassed cathode A superimposed si!nal on the !rid maes maes the !rid (olta!e U gc gc (ariable. If a positi(e !oin! si!nal enters the !rid the current throu!h the triode "ill increase. #his current increases the current throu!h the cathode resistor Rc; "hich in turn increases the (olta!e drop o(er R o(er Rc. An increase of current throu!h the triode maes the cathode (olta!e hi!her. #his combination of increased (olta!e at the cathode and lo"ered (olta!e at the plate decreases the electrostatic attraction across the triode. #he result is a reduction of !ain. A superimposed si!nal of ne!ati(e direction on the other hand decreases the conduction throu!h the triode. #he current throu!h the cathode resistor R resistor Rc decreases; hence the (olta!e drop o(er R o(er Rc "ill also decrease; accordin! to hms la". #his causes the cathode to become sli!htly more ne!ati(e "hich in turn increases the conducti(ity throu!h the triode; "hich also reduces the !ain. Dot only does these phenomenons reduce the feedbac of the !rounded cathode !ain sta!e; it also reduces distortion and increases the output impedance. Done of these three features are sou!ht for in an !uitar amplifier and lucily there is an easy "ay of cancellin! them out. A capacitor # c at the cathode in parallel "ith the cathode resistor R resistor Rc "ill inhibit these phenomenons. # c has the affect that it holds the !rid (olta!e at constant le(el.
2.3 Coupling capacitor In electron tube amplifiers many parts of the amplifier are po"ered by hi!h (olta!es. ther parts operates at lo" (olta!es. #his means that a "ay of shieldin! 0& (olta!es is needed. &apacitors filters 0& (olta!es and passes A& (olta!es by pre(entin! current flo" throu!h them. A& (olta!es are transmitted by the oscillatin! electroma!netic field induced o(er the capacitor. y addin! a capacitor bet"een t"o (olta!e potentials no 0& (olta!e "ill drift by an induced current. Added to to the shieldin! of 0& (olta!es the capacitors impedance impedance is fre6uency dependent. 0ifferent fre6uencies of the si!nal "ill be attenuated differently. In tube amplifiers each sta!e is normally separated this "ay; by addin! capacitors bet"een sta!es. &apacitors used in this "ay are normally referred to as couplin! capacitors.
2.# *hase in+erter A phase in(erter splits the si!nal si!nal into t"o si!nals. ne of these these si!nals is then phase shifted. #he result is t"o indentical si!nals that are out of 11
phase. #he phase in(erter chosen for this pro9ect is the lon! tailed phase in(erter. It is a common phase in(erter in electron tube !uitar amplifiers. #he topolo!y of the ton! tailed phase in(erter is basically t"o !rounded cathode !ain sta!es mirrored a!ainst each other. o ther.
2.% *o!er stage In amplifiers "ith multiple !ain sta!es the sta!e that deli(ers the hi!hest amplitude attenuation is often referred to as the po"er sta!e. #his sta!e is also used to deli(er the amplified si!nal to the speaers. #here are different inds of po"er sta!es. In !uitar amplifiers a hi!h amplification rate is often desired and for this purpose a push-pull po"er sta!es is suitable. In this paper the electron tube in the po"er sta!e is set up (ery similar to the triodes !rounded cathode !ain sta!e. #he po"er sta!e differes in the "ay that the !rids are used. Instead Instead of one !rid three !rids are a(aliable a(aliable in a pentode. #he !rid closest the cathode is used as control !rid. #he (olta!e ran!e of the !rid is !enerally on the ne!ati(e side; "ith peas up in the positi(e (olta!e ran!e. Det !rid is the screen !rid; it is focusin! the electron beam from the cathode in a "ay that more electrons e lectrons 9umps to the anode. #he (olta!e at the screen !rid is sli!htly lo"er than the anode (olta!e. #his is to hinder electron from 9umpin! bac to the focusin! !rid from the anode. #he !rid closest to the anode is connected to the control !rid. #he ne!ati(e to lo" positi(e (olta!e ran!e is pre(entin! electrons from bein! emitted from the anode. 2.%.1 *ushpull class ,$ In a class A amplifier a !ain de(ice amplifies a si!nal o(er the entire period. y addin! a mirrored !ain de(ice the amplification of the si!nal can be de(ided bet"een the t"o !ain de(ices. ne de(ice amplifies to upper part and the other amplifies the lo"er part of a si!nal. #his is no"n as a push pull set up. In a push pull confi!uration it is possible to push amplification de(ices more. 0ue to the partition of the amplification "or; each !ain de(ice only ha(e to be acti(e durin! the desi!nated part of the si!nal. y pushin! each !ain de(ice so that they amplifie a little more than half of the si!nal amplitude the amplification is in class A mode. Dote that class A is a combination of class c lass A and . &lass is "hen an amplification de(ice amplifies stricly the upper or lo"er half of a si!nal. #he splittin! of the si!nals is done in the phase in(erter; see the section 'hase inverter for inverter for further details. #he metaphoric term pull describes the situation "hen the electrical potential of the t"o si!nals are furdest apart. *imilarly push describes the situation "hen they are close to each other. In a class A set up "ith t"o si!nals out of phase the potential effect increases by raisin! the maimum (olta!e s"in! !oin! !o in! to the output transformer.
12
2.%.2 Output transformer t ransformer In electron tube amplifiers the si!nal is of hi!h (olta!e and lo" current in a hi!h impedance en(iroment. #his is due to the functionallity of the electron tube; see the section The triode for triode for details. +oud speaers are lo" inpedance de(ices not suitable for hi!h (olta!e lo" current si!nals. A "oraround to this mismatch is the output transformer. An output output transformer steps do"n the (olta!e to more reasonable le(els. Dormal (alues in electron tube circuits are in the realms realms of 3 to 5 (olta!es. olta!es as hi!h as this this is not suitable for speaers "ith "ith lo" internal impedance; normal (alues (alues are 4 to 1) L. &onnectin! an out si!nal from a electron tube strai!ht into a speaer leads to (ery hi!h currents trou!h the speaer. Accordin! to hms la"; I =
U 400V =example = = 50 A . R 8Ω
G1
In a push pull po"er section the output transformer has !ot t"o si!nal connections. $ach si!nal connection should ha(e e6ual e6u al impedances to the a (olta!e connection. A hi!h (olta!e connection is used to raise the (olta!e potential of the circuit. #he fact that the t"o si!nals are out of o f phase !i(es an etra potential difference in the output o utput transformer. Hence the ma!nitude of the transformers ma!netic field is proportionally to the electric potential in the pulsatin! (olta!e in the inducin! coil.
2.& Tone control 2.&.1 -reuency span of guitars Cuitar tunin! has altered throu!hout history. #he last hundreds of years the most popular tunin! is; $; A; 0; C; ; e. #his tunin! is simply no"n as standard tunin!. #he lo" end of the fre6uency span in standard tunin! is the $ strin! "ith a fre6uency of ,2 HB. #he hi!hest number of frets on standard !uitars is 25. #he tone of the hi!h e strin! at the 25Eth fret is approimately 1.4 HB. Apart from standard tunin! there are many different "ays of tunin! !uitars. Ho"e(er; most alternati(e tunin!s render approimately the same fre6uency span as standard tunin!. #here are !uitars "ith an etra lo" b-strin!. #his strin! is about ) HB; "hen played open. It should be mentioned that there are o(ertones created by !uitars. #his is due to the fact that some (ibrations in the strin!s ha(e nodes that are pi(oted alon! the len!th of the strin!. With o(ertones taen into account the span in focus should !o up at least a couple of HB o(er the hi!hest tone on the fret board of the a !uitar. #he hi!hest fre6uency audiable by a human ear is ho"e(er approimately 22HB. #his "ould imply that a !uitar amplifier "ith a band pass inter(al of G5; 22 HB "ould amplify all possible fre6uencies that mi!ht mi!ht be desirable. #he aim of this paper is to present a circuit suitable for a electric !uitars. 13
#he characteristics of the amplifier "ill be fitted to this; solely. ut as it happens; most of the commonly used instruments in the "orld "o rld has (irtually the same fre6uency span as !uitars. #his "ould imply that in spite of the intention of constructin! a !uitar amplifier "ith suitable distortion and fre6uency response. #he amplifier "ill be suitable for amplifyin! other instruments to; althou!h; in a !uitarish "ay. Amon! different inds of !uitars !uitars there are a "ide tonal ran!e; often referred to as (oicin! of the amplifier; or "hich tonal ran!e different !uitars emphasiBes. If the user of an amplifier is able to chan!e the tonal response of the amplifier it is possible to emphasiBe or suppress tonal ran!es. ne "ay of controllin! the (oicin! of the amplifier is to incorporate filters for different fre6uency ran!es. #hese filters are often ad9usted so they o(erlap each other in a "ay that they to!ether co(er the normal fre6uencies of !uitars. 2.&.2 Tone stac(s #he Fender; =arshall and M tone stacs; commonly no"n as the F= tone stacs are often referred to as the most "idely spread tone stac. Do statistics ha(e been found pro(in! this assertion; but many tone stac are are unar!uably spin-offs or plain copies of these. #he F= tone stacs in turn are spin-offs or deri(ati(es of the Williamson; 0. #. D. tone stac ?,@. #he Fender A%)3 tone stac in the Illustration 3 consists of t"o main thin!s. #hree capacitors "orin! as couplin! capacitors and passi(e filters formed by the potentiometers and the capacitors. #echnically speain! these three filters are passi(e filters; made up by resistors and capacitors. #he basic buildin! Illustration 3. The A"()3 A"()3 *ender tone blocs are the hi!hpass and and the stac+. A refined version of the ,illiamson! $.T.. tone stac+. stac+. lo"pass filters. Hi!hpass filters attenuates lo" fre6uency si!nals and (ice (ersa a lo"pass attenuates hi!h fre6uency fre6ue ncy si!nals. #he limit "here a filter suppresses 3 d of the si!nal is called cut-off; or cut-off fre6euncy. y combinin! these t"o filter types a band-pass filter can be constructed. #he fre6uency span bet"een the lo"- and hi!h-cut fre6uencies is called band "idth. oth lo"pass and hi!hpass cut-off fre6uencies are calculated in the same 14
"ay e(en thou!h the topolo!y differs; accordin! accordin! to 'hysics Handboo; f =
1 2 π R C
G11
2.&.3 Treble #he capacitor &2 and the potentiometer '1 in Illustration 3 isolated forms a hi!h-pass filter. *i!nals "ith fre6uencies lo"er than the cut-off fre6uency are suppressed by &2. '1 forms a (ariable resistor bet"een &2 an ut. y alterin! the settin! of '1 the fre6uencies !oin! throu!h &2 are attenuated. If &2 is chosen in such a "ay that the cut-off fre6uency is in the hi!her part of the amplifiers ran!e; '1 !i(es the user a "ay to ad9ust le(el of the hi!h fre6uency ran!e of the amplifier. A side effect of the fact that '1 (aries the resistance resistance in the hi!h-pass filter filter is that the cut-off fre6uency is sli!htly altered. Althou!h this effect is reduced si!nificantly by '2 and '3. #hese t"o potentiometers form a resistance to !round in the #reble lo"-pass filter. If the hole tone stac circuit is considered; '1 forms a blender for hi!h fre6uencies and middle; bass fre6uencies. In fact raisin! the le(el of the '1 potentiometer "ill reduce the =iddle and ass le(els sli!htly. 2.&.# $ass nce a!ain the circuitry in Illustration 3 is analysed by isolation some components. #he resistor /5 and the capacitor &4 forms a lo"-pass filter at the node bet"een them. At this node the potentiometer '2 and the capacitor &3 forms a hi!h-pass filter. It is this lo"-pass filter that maes it possible for the user to control the fre6uencies in the bass span. #he hi!hpass filter &3 and '2 is not used to alter the fre6uency response of the tone stac. #he main purpose of &3 is to shield 0& (olta!es from leain! le ain! throu!h the tone stac. 2.&.% /iddle #he potentiometer '3 in Illustration 3 is a shunt to !round. #his implies that the =iddle control needs bass and treble fre6uencies to be able to alter the middle fre6uency response of the tone stac. An analo!y could be to ima!ine bass and treble as t"o hills. #he =iddle potentiometer can only fill the "ally; not build a hill of its o"n.
3 Simulation and design 3.1 "lectron tubes in 0Tspice In this paper three different libraries of electron tube spice models is tested. All can be found on internet; the /ydel; 0uncan and Noren electron 15
tube spice models. For the interested reader; search for spice electron tube models in models in some search en!ine to find them. #he #+spice user adds a reference to the search path to the do"nloaded library so that +#spice can access the library. #hen the propper component symbol is added by the user of the circuit editor. With these t"o steps the models are ready to be used. A "ide ran!e of different analysis can be made "hen a simulation is done. #o assess the 6uality of the electron tube models used in this paper the anode characteristic is eamined. y incrementin! the anode and !rid (olta!e in the same inter(als inter(als as those presented in a static static anode characteristics dia!ram the anode characteristics of the spice models is determined. #he three models clippin! beha(ior is eaminde by settin! up a test "here they are pushed into clippin!. #he electron tube models are also tested by settin! them up in a test "here a "a( file is created from the out si!nal. #his output file is used as a audio reference to a real electron tube. In the audio tests the main focus is to establish "hether the electron tube models are able to mimic the clippin! in a real electron tube. Done of these audio tests can be presented in this paper; ob(ious reasons. 3.1.1 Tests of the "CC3 tube t ube models #he electron tube chosen for the !rounded cathode !ain sta!es is the $&&,3. A "ide ran!e of $&&,3 models are initially tested; each electron tube model library contains se(eral spice models of each electron tube type. #he tested models are assessed and three candidates are chosen for further studies. #he anode characteristics of the three tested models are presented in Appendi A4. #he data of the real $&&,3s static anode characteristics dia!ram from al(eWiBards +oad+ine'lotter. #he clippin! beha(iour of the $&&,3 is tested and and presented in Appendi A5. In this paper the /ydel; &. $&&,3 model is chosen for the desi!n "or in +#spice. #he reason for this is that the /ydel models anode characteristic is considered closest to the real $&&,3. #his assessment is done by !raphically eamine the plot in Appendi A4. Further; the clippin! beha(iour is considered to be the closest one to a real $&&,3 electron tube. If these three electron tube models are to be raned the net best after /ydels model "ould be the 0uncan model. >ud!in! by Appendi A4 and A5 the "orst of the three is the the Noren model. oth /ydels and 0uncans 0uncans electron tube model are fairly close approimities in the anode characteristics. /ydels spice model is a closer approimation than 0uncans in terms of clippin! beha(iour. Althou!h the $&&,3 models clearly differ in the obtaind obtaind data it is not not possible to distin!uish them from each other by listenin! to audio simulations. #his disco(ery lo"ers the epectations e pectations that a !ood simulation can be made of a electron electro n tube amplifier. Cood in the sense that the simulated amplifier "ill reproduce all the properties in a credible "ay. In spite of this lac of di(er!ence and "eaness in clippin! situations the "or of desi!nin! a tube amplifier amplifier in +#spice is far from "asted. #he 1)
performance in linear situations still pro(ides a (ast insi!ht in the circuitry and the feature of it. 3.1.2 Tests of the "0# tube models $+,4 electron tubes are used for the po"er section of the simulated amplifier. $+,4 is a pentode "ith a different ind of anode characteristics than the $&&,3 electron tube. As for the $&&,3 electron tube the anode characteristic is plotted by the aid of +#spice analysis tools. For this assessment no di!ital (ersion of the measured anode characteristics from a real $+,4 is used; the reason bein! that no di!itiBed (ersion is found. Done of the electron tube models found differed in the anode characteristics assessment. In Appendi A3 the anode caracteristic for the /yden $+,4 model is presented. #he $+,4 model used differs from the characteristics of a real $+,4 in the sense that the anode characteristics of a real $+,4 is a bit indistinct; or "obbly in the the lo" anode (olta!e ran!e; to 1 1 . Done of the models tested in this paper emulates this beha(iour.
3.2 The grounded cathode gain stage A !rounded cathode !ain sta!e is set up in +#spice accordin! to the the section The grounded cathode gain stage. stage. With initial (alues of R of Ra; Rc; Rgl and and # c the circuit is tested. After testin! and tinerin! in +#spice a stabile (ersion is set up. #he fre6uency response of the !ain sta!e is monitored to determine "hether a linear fre6uency response is achie(ed. #he final (alues of the !rounded cathode !ain !ain sta!e is presented in #able 1. #able 1. #he components in the !rounded cathode !ain sta!e
U a
33
Rgl
1 =L
Ra
22 L
Rc
1.5 L
# c
4.% OF
All (alues are chosen so that they they are from the standard ran!e ran!e of electric components. #he anode (olta!e is set to 33 due to the fact that a lon! term !oal of this "or is to actually build the amplifier simulated in this paper. It happens to be that I ha(e a transformer that !i(es approimately 33 after rectification. #he fre6uency response of the modeled !rounded cathode !ain sta!e is presented in Appendi 1. Dote the plateau bet"een P1 to P5 HB. #he fre6uenies of interest; see section *reuenc/ section *reuenc/ span of guitars; guitars; are satisfactory amplified. In Appendi A) the loadlines of the +#spice simulation of the !rounded cathode sta!e is presented. #he circuit of the modeled !rounded cathode !ain sta!e is outline in Appendi &1.
1%
3.3 *re amplifier #he pre-amplifier is constructed by addin! a tone stac inbet"een t"o !rounded cathode !ain sta!es; see Appendi &2 for details. In the set up of the tone stac the free"are #one *tac &alculator is used to set up initial (alues of the tone stac. #hese initial (alues are chosen in a "ay that a; some"hat; linear fre6uency response of the tone stac is obtained. With the tone stac settin!s from the #one *tac &alculator & alculator the pre amplifiers fre6uency response is monitored. In Appendi 2 the fre6uency response of the pre amplifier is presented. Dote that the fre6uency response of the pre amplifier is not linear; rather it has !ot t"o distinct humps. #his is not alarmin! as the po"er section can be balanced in a "ay that that e(ens out this.
3.# *o!er section A po"er section is constructed by mer!in! the in(erter; in(erter; the set up of the po"er electron tubes and the transformer. #his time +#spice "as used in a more acti(e "ay than in the desi!nin! of the pre amplifier. Instead of predetermine the (alues based on charts etc. all "or is done +#spice. All parts are monitored durin! the desi!n process by the aid of tools a(aliable in +#spice. #he circuit of po"er section of the amplifier in this paper is presented in Appendi &3. 3.#.1 *hase in+erter #he phase in(erter in the desi!ned electron tube amplifier is a re(ised (ersion of the lon! tail phase in(erter in(erter commonly used in Fender amplifier. #he Fender lon! tail phase in(erter is in turn a (ersion of the *chmitt phase in(erter. #he main difference bet"een the desi!ned phase in(erter and the Fender lon! tailed phase in(erter is the triode used to dri(e it. Fender uses a $&&,1 triode to dri(e the phase in(erter; here a $&&,3 is used. #he components & also differs; see Appendi &3 for details. #he & capacitor is a shunt capacitor used to suppress hi!h fre6uencies ?@. >ud!in! by the plot in Appendi 1 the cut-off fre6uency in the preamplifier (ery hi!h; much hi!her than "hat is audible by a human ear. *uppressin! fre6uencies out of the audible ran!e is a "ay of pre(ent undetectable hi!h fre6uencies oscillation. 3.#.2 Output section #he output transformer of this amplifier is set up by mer!in! three coil components; 01 components; 01;; 02 and 0 in the +#spice circuit; see Appendi &3 for 02 and 0 in details. #he impedances of these components are arbitarly set to; 01 to; 01 02 02 1 4 L and 0 0 , L modeled after a A&3 amplifier. Dormally an output transformer has more than one output impedance connection; not 9ust one as in this eample. #he impedance of a normal no rmal speaer is 4; , or o r 1) L "hich has to be matched matched a!ainst the out impedance impedance of the output 1
1,
A&3 is a o electro electron n tube tube amplifi amplifier er "ith "ith 4 $+,4 in the the po"er po"er section. section.
transformer. #he primary ad9ustment of the output section is done by usin! a "a( file as input si!nal and assess the result; or sound of the amplifier. When the output "a(-file is 9ude!ed to be "ell balanced; in other "ords the sub9ecti(e assessed to sound !ood; an anode characteristic analysis is done. In Appendi A% the anode characteristics for the po"er tube set up is displayed. 3.#.3 *o!er tubes #he set up of the po"er tube is (ery similar to a !rounded cathode !ain sta!e. #he pentodes; $+,4; are biased ne!ati(ely by superimposin! a ne!ati(e (olta!e at the control !rid. In Appendi &3 2 pro(ides ne!ati(e bias (olta!e.
3.% ,mplifier In the mer!in! of the different parts of the amplifier etensi(e testin! is made. *e(eral fre6uency s"eeps are made "ith different tone stac settin!s. #he fre6uecy response of these s"eeps are presented in Appendi 3. #he (olume control is constant throu!h this analysis. #he simulations sho"s that the tone stac is able to alter the fre6uency respons. #o ad9ust the tone stac to the final (ersion (er sion of the amplifier a calibration is made.
3.& Calibrating the tone stac( In an attempt to mae each tone control co ntrol affect the amplification of the correspondin! fre6uency ran!e e6ually much the ran!e of the controls "ere matched. #he "ay of achie(in! this is to plot the amplification amplification in the bass; middle and treble ran!e ran!e for the correspondin! control. #he matched plot is presented in Appendi 01. #he lo!arithmic pro!ression of the cur(es are due to the lo!arithmic potentiometers used in the tone controls in the +#spice simulation.
# esults An electron tube amplifier "as desi!ned in the the soft"are +#spice. #he amplifier has 4 $+,4 electron tubes in po"er section and 2 $&&,3 electron tubes in the pre amplifier. #he simulated amplifier is balanced to !i(e a minor brea up and a linear fre6uency response. respo nse. #he maimum output is 3 to 35 W.
1
% esign soft!are %.1 Tone Stac( Calculator 1.3 #one *tac calculator is a soft"are that simulates some of the most common tone stacs found in electron tube !uitar amplifiers. #he topolo!y of each tone stac is presented alon! "ith the possibility to alter the (alues of components in each circuit. #he user can alter the control potentiometers and see the result instantaneously. &ompared to de(elopin! and testin! tone stacs in +#spice the #one *tac &alculators approach is much faster. It is ho"e(er not possible to alter the topolo!y in #one *tac &alculator. #he user is confined to the tone stacs a(ailable in the soft"are. #one *tac &alculator is de(eloped by 0uncan Amplification. It is a free"are and can be found and do"nloaded on the internetE httpE""".duncanamps.comtscdo"nload.html. httpE""".duncanamps.com tscdo"nload.html. #he only dra"bac is that it is confined to Windo"s.
%.2 0oad0ine*lotter #he +oad+ine'lotter is a spreadsheet holdin! data of electron tubes. #his data is presented in static anode characteristics dia!rams. #he user can insert (alues of anode; cathode resistors and anode (olta!e. y doin! this the anode and cathode loadlines are presented in the static anode characteristics dia!ram. #he +oad+ineplotter is constructed by the al(eWiBard; and can be do"nloaded at; httpE""".(al(e"iBard.co.u.
%.3 0Tspice I4 In this paper most simulations of circuitry are done in the soft"are +#spice. +#spice offers many different analysis tools to be used on simulated circuitry. #he user inserts a circuit "ith "ith electronic components and sets up the premisses for the simulation. When an simulation is done data can be obtained by usin! +#spice etract tool. too l. In this paper all data from the simulations is inserted direct into a chart editor in the "ord processor used to "rite this paper. 'ictures of circuitry is etracted by usin! +#spices bitmap format etractor. #he etracted bitmaps are sli!htly edited in a ima!e editor before thay are pasted into this document. &ircuitry is inserted by the usa!e of the +#spice circuit editor; components are dra!!ed and dropped in place. ne of the a(aliable analysis tools is fre6uency s"eeps. y settin! up start and end fre6uency etc. the user can one clic to !et a ode plot of a circuit Gone clic; in the sense that the user left clics on a point in the of interest and !ets a ode plot. #his tool is used on se(eral parts of the circuit in this paper. #he phase plot is ho"e(er left out in most of the plots since shifts in phase is not audible. Audio tests are made by usin! an other feature of +#spice. +#spice can tae "a( files as input and create "a( output files. #his feature !i(es the user the ability to create simulations of ho" the circuit; for instance an amplifier; mi!ht 2
sound. A third feature of +#spice is that it is possible to monitor (olta!es and currents in circuitry. #his feature is used to render anode characteristics dia!rams of the electron tube models. +#spice is a free-"are and can be do"nloaded from +inear #echnolo!ies. #here are no opted (ersions for usa!e on +inu or mac. +inu and =ac users ha(e to run +#spice in "ine. #he curious reader is encoura!ed to test the free"are. It can be found and do"nloaded fromE httpE""".linear.comdesi!ntoolssoft"are
& ,c(no!ledgement I lie to than N9ell *taffas for embarin! on an epedition bac in time "ith me. A time "hen there "ere no the transistors. transistors. A bi! hu! to my parents for all the fun and !ames "ith my ids "hen I "rote this paper. A bi! thans to my family family for lettin! me see "hat really matters matters in life.
) 0iterature list ?1@ =a"ell; >.&. G1,%3 A #reatise on $lectricity and =a!netism ?2@ HertB; H. G1,,% $lectric "a(esE bein! researches on the propa!ation of electric action "ith finite (elocity throu!h space ?3@ =arconi; C. G1,5 In(ented and demonstrated a transmitter Do publication ?4@ Forest; 0. G1% #he Audion; a De" /ecei(er for Wireless #ele!raphy ?5@ ell +abs. G14, 'ress conference ?)@ asura; *. et. al. G14 History of o f electron tubes ?%@ >ones; =. G212 al(e Amplifiers ?,@ Williamson; 0. #. D. G14 0esi!n of #one &ontrols Q Auiliary Cramophone &ircuits ?@ >ones; =. G24 uildin! al(e amplifiers
21
,ppendi5 .1 , 6 ,node characteristics ch aracteristics diagrams diagrams .1.1 ,1 A di!ital (ersion of a static anode anode characteristics dia!ram.
$&&,3 Anode charact char acteristics eristics dia !ram !ra m 5
4 -1
3 -2 A m a I
2
1
5
1
15
2
2 5
3
35
The anode characteristics characteristics diagram of the "#1 triode! one of the t4o triodes in an ##53 electron tube.
22
.1.2 ,2 $amplified loadlines of a $&&,3 !rounded cathode !ain sta!e.
$&&,3 12AM% Anode chara cteristics cteristic s dia!ram dia! ram 5
4 -1
3
-2
A m a I
& 2
1
0 A
5
1
15
2
2 5
3
35
The dashed red line is a anode loadline and thr dashed dotted line is an eemplified a cathode load line of a "#1 triode.
23
.1.3 ,3 #he $+,4s static anode characteristics dia!ram is rendered in +#spice by the use of /ydels $+,4 model. $+,4 Anode charact char acteristics eristics for f or the $+,4 spice sp ice model
;3
;25
;2
A m a I
;15
;1
;5
2
4
)
,
1
12
14
1)
1,
2
The anode characteristics characteristics for the R/del 05 model used in this paper. The curved lines are the control grid voltage for different bias levels on the control grid.
24
.1.# ,# *tatic anode characteristics for the $&&,3 spice models tested. $&&,3 models Anode charactr charactristi istics cs for electron electron tube models
5
Noren; D. /ydel; &. 0uncan
4
3 A m a I
2
1
5
1
15
2
2 5
3
35
The anode characteristics for the ##53 models tested in this paper compared 4ith the dashed lines from the static anode characteristic diagram. diagram. The tested electron tube6s grid voltage is incremented b/ -1 to prevent the plot from being to bloated.
25
.1.% ,% &lippin! in spice electron tube models.
$&&,3 models #he clippin! of different spice $&&,3 models ) Noren; D; /ydel; & 0uncan /eference 4
2 e d u t i l p m A
2
;2
-2 #ime s
The ##53 spice models are pushed into clipping. otice ho4 the tube models mimic+ clipping in real electron tubes. #lipping in real electron tubes are soft! e.i. no hard edges in the out signal.
2)
.1.& ,& +oadlines for the modeled !rounded cathode !ain sta!e. $&&,3 model Anode character characteristi istics cs of $&&,3 model 5
4
3 A m a I
2
1
5
1
15
2
2 5
3
35
The anode and cathode loadlines sho4s 4here the bias point of the modeled grounded cathode gain stage is.
2%
.1.) ,) #he loadlines for the po"er tubes in the output section.
$+,4 &haracterisctics &haracterisctics of the pushpull pushpu ll sta!e ;5 ;4 ;3 ;2 ;1 A a I
1
2
3
4
5
)
-;1 -;2 -;3 -;4 -;5
The anode characteristics characteristics of a pushpull po4er stage 4it h 05 pentodes. The blue bold lines are the loadlines of each side of the po4er stage.
2,
.2 $ 6 -reuency responses .2.1 $1 #he fre6uency response of the !rounded cathode !ain sta!e modeled in +#spice. Fre6uency respose Fre6uency response response of the !rounded cathode c athode !ain sta!e sta! e 3, 3% 5 d e d u t i l p m A
3) 35 34 33 32 1
1
1
1
Fre6uency Fre6uency HB
The freuenc/ response of the simulated grounded cathode gain stage.
.2.2 $2 #he fre6uency response of the pre-amplifier modeled in +#spice. 're amplifier #he fre6uency response of the pre amplifier )5 5 d e d u t i l p m A
) 55 5 45 2
2
2
2
Fre6uency Fre6uency HB
The freuenv/ response of the pre amplifier. The freenc/ response reveals t4o bumps! one in the bass range and one in the treble range of the spectrum.
2
.2.3 $3 #he fre6uency response for the amplifier "ith different tone stac settin!s. Fre6uency response Fre6uency s"eeps s"eeps "ith diff erent $6ualiBer settin!s % ) 5 d e d u t i l p m A
5 4 3 2 1 1
1
1
1
Fre6uency HB
*reuenc/ response response of the amplifier. amplifier. $ifferent tone tone stac+ settings is used used to chec+ that the attenuation of different freuenc/ intervals are some4hat similar. The volume control is set to 5 in all s4eeps.
.3 C 6 Circuitry .3.1 C1 #he !rounded cathode !ain sta!e as it is modeled in +#spice.
The grounded cathode gain stage set up from the 0Tspice simulation.
3
.3.2 C2 're-amplifier modeled in +#spice.
31
.3.3 C3 'o"er section modeled in +#spice
32
.# .#.1 1 #he calibration of the tone controls in the tone stac.
&alibration &alibration &alibration of the tone stac controls %5 ass %
=iddle #reble
)5
5 d n ) o i t a c i f i l 55 p m A 5
45
4
1
2
3
4
5
)
%
,
1
*ettin! of tone potentiometer potentiometer The calibration of the tone stac+. The amplitude interval of all three f reuenc/ bands are of the same magnitude! 7 to (7 d". The potentiometers potentiometers for this set up is! bass 8 297 +! middle897 + and treble8177 +.
33
