HAPER 4 POLAR JUNON RANSSORS (Js) haptr Outln 4.1 Dc Structur and Physcal Opraton 4.2 urrnt oltag haractrstcs 4.3 J rcuts at D 4.4 Applyng th J n Amplfr Dsgn 4.5 Small Sgnal Opraton and Modls 4.6 asc J Amplfr onfguratons 4.7 asng n J Amplfr rcuts 4.8 Dscrt rcut J Amplfrs NUEE Elctroncs L. H. Lu 4 1
4.1 Dc Structur and Physcal Opraton Physcal structur of bpolar juncton transstor (J) oth lctrons and hols partcpat n th conducton procss for bpolar dcs J conssts of two pn junctons constructd n a spcal way and connctd n srs, back to back h transstor s a thr trmnal dc wth mttr, bas and collctor trmnals From th physcal structur, Js can b ddd nto two groups: npn and pnp transstors Mods of opraton h two junctons of J can b thr forward or rrs basd h J can oprat n dffrnt mods dpndng on th juncton bas h J oprats n act mod for amplfr crcuts Swtchng applcatons utlz both th cutoff and saturaton mods Mod EJ J utoff Rrs Rrs Act Forward Rrs Saturaton Forward Forward NUEE Elctroncs L. H. Lu 4 2
Opraton of th npn transstor n th act mod Elctrons n mttr rgons ar njctd nto bas du to th forward bas at EJ Most of th njctd lctrons rach th dg of J bfor bng rcombnd f th bas s narrow Elctrons at th dg of J wll b swpt nto collctor du to th rrs bas at J Emttr njcton ffcncy ( ) = En /( En + Ep ) as transport factor ( ) = n / En ommon bas currnt gan () = n / E = < 1 rmnal currnts of J n act mod: E (mttr currnt) = En (lctron njcton from E to ) + Ep (hol njcton from to E) (collctor currnt) = n (lctron drft) + O (J rrs saturaton currnt wth mttr opn) (bas currnt) = 1 (hol njcton from to E) + 2 (rcombnaton n bas rgon) NUEE Elctroncs L. H. Lu 4 3
rmnal currnts: ollctor currnt: n AE qdndn x) / dx AE qdnn as currnt: Hol njcton nto mttr du to forward bas: Elctron hol rcombnaton n bas: otal bas currnt: Emttr currnt: E 1 A qd n N W E n E / ( (0) / W D N S 2 E / Q W n 1 AE qdpedpe x) / / n AE q 2 pe 1 2 S ( ) Dn NE LpE 2 Dn n 1 W E 1 2 / 2 ( dx n (0) W / n S A E E N / E qd L AE qwn 2N n pe pe 2 n 2 E / E / NUEE Elctroncs L. H. Lu 4 4
Larg sgnal modl and currnt gan for J n act rgon ommon mttr currnt gan ommon bas currnt gan (1) (+1) E E ommon mttr currnt gan: ommon bas currnt gan: h structur of actual transstors D ( D 2 W ) D /(1 ) n modrn procss tchnologs, th J utlzs a rtcal structur ypcally, s smallr and clos to unty whl s larg /( 1) pe n N N E W L pe 1 2 1 n n 1 1 NUEE Elctroncs L. H. Lu 4 5
Opraton of th npn transstor n th saturaton mod Saturaton mod: both EJ and J ar forward basd arrr njcton from both mttr and collctor nto bas as mnorty carrr concntraton chang accordngly ladng to rducd slop as ncrass ollctor currnt drops from th alu n act mod for ngat For a gn E, drops sharply to zro at around 0.5 and E around 0.2 J n saturaton: Esat = 0.2 urrnt gan rducs (from to forcd ): forcd saturaton n p0 xp( E / ) n p0 xp( / ) ncrass n p0 NUEE Elctroncs L. H. Lu 4 6
Ebrs Moll modl n EM modl, th EJ and J ar rprsntd by two back to back dods DE and D urrnt transportd from on juncton to th othr s prsntd by F (forward) and R (rrs) EM modl can b usd to dscrb th J n any of ts possbl mods of opraton EM modl s usd for mor dtald dc analyss / h dod currnts: ( E / DE SE 1) ( D S 1) F SE R S S h trmnal currnts: E DE RD D FDE E Applcaton of th EM modl h forward act mod: E 1 E / S S 1 R S E / 1 1 S F F R S E / 1 S 1 F F h saturaton mod: E S SE SE E / E / S S / / E / ( 1 ) (1 F S R ) / E DE R D D F DE NUEE Elctroncs L. H. Lu 4 7
h cutoff mod O (J rrs currnt wth mttr opn crcutd) O = (1 R F ) S oth EJ and J ar rrs basd n ral cas, rrs currnt dpnds on EO (J rrs currnt wth bas opn crcutd) EO = O /(1 F ) F s always smallr than unty such that EO > O J currnt flows from ( to ) so J s rrs basd EJ currnt flows from (E to ) so EJ s slghtly forward basd + (3) DE = 0 S (1) (3) R S S (1) E E E E = 0 (2) R S F DE (4) (2) R S R F S (4) + = O = (1 R F ) S (5) = ( R 1) S +(1 F ) DE = 0 DE = S (1 R )/(1 F ) (5) = S + F DE = S (1 R F )/(1 F ) EO = O /(1 F ) (6) NUEE Elctroncs L. H. Lu 4 8
h pnp transstor ransstor structur: mttr and collctor ar p typ bas s n typ Opraton of pnp s smlar to that of npn Opraton of pnp n th act mod ollctor currnt: as currnt: Emttr currnt: / E S E / Larg sgnal modl and currnt gan for J n act rgon ommon mttr currnt gan ommon bas currnt gan (1) (+1) E E 1 1 Exrcs 4.1 (xtbook) Exrcs 4.3 (xtbook) NUEE Elctroncs L. H. Lu 4 9
4.2 urrnt oltag haractrstcs rcut symbols, oltag polarts and currnt flow rmnal currnts ar dfnd n th drcton as currnt flow n act mod Ngat alus of currnt or oltag man n oppost polarty (drcton) Summary of th J currnt oltag rlatonshps n th act mod h trmnal currnts for a J n act mod solly dpnd on th juncton oltag of EJ h ratos of th trmnal currnts for a J n act mod ar constant h currnt drctons for npn and pnp transstors ar oppost E npn transstor E / S S S E / E / E pnp transstor E / S S S E / E / E 1 1 NUEE Elctroncs L. H. Lu 4 10
urrnt oltag charactrstcs of J h charactrstcs h E charactrstcs h Early ffct As J rrs bas ncrass, th ffct bas wdth W ff rducs du to th ncrasng dplton For a constant juncton oltag E : h slop of n (x) ncrass ncrass n (0) harg storag Q n rducs dcrass urrnt gan and ncrass Y Early oltag ( A ) s usd for th lnar approxmaton of Early Effct X E / Lnar dpndnc of on E : (1 / ) Exhbt fnt output rsstanc: S E A 1 ro E constant E A NUEE Elctroncs L. H. Lu 4 11 n 0 0 W X W Y W Z Z
ommon bas output charactrstcs Early ffct brakdown rsus plot wth arous E as paramtr s known as common bas output charactrstcs h slop ndcats that dpnds to a small xtnt on Early ffct ncrass rapdly at hgh brakdown J s slghtly forward basd for 0.4 < < 0 No sgnfcant chang s obsrd n h J stll xhbts charactrstcs as n th act mod J turns on strongly and th starts to dcras for < 0.4 charactrstcs n th saturaton mod and Esat s consdrd a constant ( 0.2 ) urrnt gan (): larg sgnal / E and small sgnal (ncrmntal) / E NUEE Elctroncs L. H. Lu 4 12
ommon mttr output charactrstcs () rsus E plot wth arous E as paramtr ommon mttr currnt gan s dfnd as = / h J turns on wth a post at low E J oprats n saturaton mod h cur has a fnt slop du to Early ffct h charactrstcs lns mt at E = A A s calld th Early oltag (~ 50 to 100 ) ommon mttr output charactrstcs () Plot of rsus E wth arous as paramtr J n act rgon acts as a currnt sourc wth hgh (but fnt) output rsstanc h cutoff mod n common mttr confguraton s dfnd as = 0 urrnt gan: larg sgnal b dc / and b ac / Early ffct brakdown NUEE Elctroncs L. H. Lu 4 13
Saturaton of common mttr confguraton n saturaton rgon, t bhas as a closd swtch wth a small rsstanc R Esat h saturaton cur can b approxmatd by a straght ln ntrsctng th E axs at Eoff h saturaton oltag Esat Eoff + sat R Esat Esat s normally tratd as a constant of 0.2 for smplcty rgardlss th alu of ncrmntal n saturaton s lowr than that n act rgon: forcd sat / < Ordr factor / forcd NUEE Elctroncs L. H. Lu 4 14
ransstor brakdown ransstor brakdown mchansm: Aalanch brakdown: aalanch multplcaton mchansm taks plac at J or EJ as punch through ffct: th bas wdth rducs to zro at hgh J rrs bas n confguraton, O s dfnd at E = 0 h brakdown oltag s smallr than O for E > 0 n E confguraton, EO s dfnd at =0 h brakdown oltag s smallr than EO for > 0 ypcally, EO s about half of O rakdown of th J s not dstruct as long as th powr dsspaton s kpt wthn saf lmts rakdown of th EJ s dstruct bcaus t wll caus prmannt dgradaton of NUEE Elctroncs L. H. Lu 4 15
Exrcs 4.13 (xtbook) Exrcs 4.14 (xtbook) Exampl 4.3 (xtbook) Exrcs 4.21 (xtbook) NUEE Elctroncs L. H. Lu 4 16
4.3 J rcuts at D J opraton mods h J opraton mod dpnds on th oltags at EJ and J h charactrstcs ar strongly nonlnar Smplfd modls and classfcatons ar ndd to spd up th hand calculaton analyss Mod EJ J npn transstor pnp transstor Act Forward Rrs utoff Rrs Rrs nrs Mod E < 0, 0 Saturaton Mod E 0, 0 nrs Mod E < 0, 0 Saturaton Mod E 0, 0 Saturaton Forward Forward nrs Rrs Forward utoff Mod E < 0, < 0 Act Mod E 0, 0 E utoff Mod E < 0, < 0 Act Mod E 0, 0 E Smplfd modls and classfcatons for th opraton of th npn J ut off mod: E = = = 0 E < 0.5 and < 0.4 Act mod: E = 0.7 and : : E = 1: : (1+) E > 0.3 Saturaton mod: E = 0.7 and E = 0.2 / = forcd < NUEE Elctroncs L. H. Lu 4 17
Equalnt crcut modls NUEE Elctroncs L. H. Lu 4 18
D analyss of J crcuts Stp 1: assum th opraton mod Stp 2: us th condtons or modl for crcut analyss Stp 3: rfy th soluton Stp 4: rpat th abo stps wth anothr assumpton f ncssary Exampl 4.4 = 100 Exampl 4.5 NUEE Elctroncs L. H. Lu 4 19
Exampl 4.9 (xtbook) Exampl 4.11 (xtbook) NUEE Elctroncs L. H. Lu 4 20
Exrcs 4.22 (xtbook) Exrcs 4.23 (xtbook) Exrcs 4.24 (xtbook) Exrcs 4.25 (xtbook) Exrcs 4.28 (xtbook) Exampl 4.12 (xtbook) NUEE Elctroncs L. H. Lu 4 21
4.4 Applyng th J n Amplfr Dsgn J oltag amplfr A J crcut wth a collctor rsstor R can b usd as a smpl oltag amplfr as trmnal s usd th amplfr nput and th collctor s consdrd th amplfr output h oltag transfr charactrstc () s obtand by solng th crcut from low to hgh E utoff mod: 0 E < 0.5 and = 0 O = E = Act mod: E > 0.5 and = S xp( E / ) O = R = R S xp( E / ) Saturaton: E furthr ncrass E = Esat = 0.2 O = 0.2 NUEE Elctroncs L. H. Lu 4 22
asng th crcut to obtan lnar amplfcaton h slop n th ndcats oltag gan J n act mod can b usd as oltag amplfcaton Pont Q s known as bas pont or dc opratng pont = S xp( E / ) h sgnal to b amplfd s suprmposd on E E (t) = E + b (t) h tm aryng part n E (t) s th amplfd sgnal h crcut can b usd as a lnar amplfr f: A propr bas pont s chosn for gan h nput sgnal s small n ampltud h small sgnal oltag gan h amplfr gan s th slop at Q: A d d E E E E oltag gan dpnds on and R Maxmum oltag gan of th amplfr A R E R A max NUEE Elctroncs L. H. Lu 4 23
Dtrmnng th by graphcal analyss Prods mor nsght nto th crcut opraton Load ln: th straght ln rprsnts n ffct th load = ( E )/R h opratng pont s th ntrscton pont Locatng th bas pont Q h bas pont (ntrscton) s dtrmnd by proprly choosng th load ln h output oltag s boundd by (uppr bound) and Esat (lowr bound) h load ln dtrmns th oltag gan h bas pont dtrmns th hadroom or maxmum uppr/lowr oltag swng of th amplfr NUEE Elctroncs L. H. Lu 4 24
4.5 Small Sgnal Opraton and Modls h collctor currnt and th transconductanc h total quantts (ac + dc) of th collctor currnt: Small sgnal approxmaton: b << h transconductanc ndcats th ncrmntal chang of rsus chang of E h transconductanc g m s dtrmnd by ts dc collctor currnt Gnral, Js ha rlatly hgh transconductanc compard wth FEs at th sam currnt ll h bas currnt and th nput rsstanc at th bas h total quantts (ac + dc) of th bas currnt: Small sgnal approxmaton: Rsstanc r s th small sgnal nput rsstanc btwn bas and mttr (lookng nto th bas) NUEE Elctroncs L. H. Lu 4 25 b b E E S S b E E / / / / ) ( b b c 1 E m g b b E E S S / / / / b b b 1 m b b g r
h mttr currnt and th nput rsstanc at th mttr h total quantts (ac + dc) of th mttr currnt: Small sgnal approxmaton: Rlaton btwn r and r : Output rsstanc accountng for Early ffct Us th collctor currnt quaton wth lnar E dpndnc: h output rsstanc r o s ncludd to rprsnt Early Effct of th J h rsultng r o s typcally a larg rsstanc and can b nglctd to smplfy th analyss NUEE Elctroncs L. H. Lu 4 26 c E E m m E b g g r 1 b E b b m c g r )r 1 ( m m g r g r A E S E 1 / A constant E o r E 1
J small sgnal modls wo modls ar xchangabl and dos not affct th analyss rsult h hybrd modl ypcally usd as th mttr s groundd Nglct r o h modl ypcally usd as th mttr s not groundd Nglct r o NUEE Elctroncs L. H. Lu 4 27
hr basc confguratons 4.6 asc J Amplfr onfguraton ommon Emttr (E) ommon as () ommon ollctor () haractrzng amplfrs h J crcuts can b charactrzd by a oltag amplfr modl (unlatral modl) h lctrcal proprts of th amplfr s rprsntd by R n, R o and A o h analyss s basd on th small sgnal or lnar qualnt crcut (dc componnts not ncludd) oltag gan: A Orall oltag gan: o RL Ao RL Ro o G R sg n Rn R sg A R n Rn R sg RL R R L so A o NUEE Elctroncs L. H. Lu 4 28
h common mttr (E) amplfr haractrstc paramtrs of th E amplfr nput rsstanc: Output rsstanc: Opn crcut oltag gan: oltag gan: A R n r Orall oltag gan: E amplfr can prod hgh oltag gan R g m o R r nput and output ar out of phas du to ngat gan Lowr ncrass R n at th cost of oltag gan Output rsstanc s modrat to hgh Small R rducs R o at th cost of oltag gan o A R o g ( R r ) g m o ( R RL ro ) gm( R RL ) r r G gm( R RL ro ) gm ( R RL) r R r R sg m R sg NUEE Elctroncs L. H. Lu 4 29
h common mttr (E) wth an mttr rsstanc haractrstc paramtrs (by nglctng r o ) nput rsstanc: R n ( 1 )( r R ) r (1 ) R Output rsstanc: Ro R Opn crcut oltag gan: A o gmr 1 R / r oltag gan: A Orall oltag gan: G gmr 1 g R r r m gmr 1 g R RL R R L g R m Emttr dgnraton rsstanc R s adoptd nput rsstanc s ncrasd by addng (1+)R Gan s rducd by th factor (1+g m R ) h orall gan s lss dpndnt on t s consdrd a ngat fdback of th amplfr gm( R RL) 1 g R R m m L Rsg 1 gmr RL R r r R sg gm( R RL) 1 g R m NUEE Elctroncs L. H. Lu 4 30
h common bas () amplfr haractrstc paramtrs of th E amplfr (by nglctng r o ) nput rsstanc: Rn r Output rsstanc: Ro R Opn crcut oltag gan: Ao gmr oltag gan: A g R R ) Orall oltag gan: m( L r G r R ( R RL ) E amplfr can prod hgh oltag gan nput and output ar n phas du to post gan nput rsstanc s ry low A sngl stag s not sutabl for oltag amplfcaton Output rsstanc s modrat to hgh Small R rducs R o at th cost of oltag gan h amplfr s no longr unlatral f r o s ncludd sg g m NUEE Elctroncs L. H. Lu 4 31
h common collctor () amplfr haractrstc paramtrs of th amplfr (by nglctng r o ) nput rsstanc: Rn ( 1 )( r RL) Output rsstanc: Ro r Rsg / Opn crcut oltag gan: Ao RL /( RL r ) 1 Rn RL ( 1) RL Orall oltag gan: G R 1)( R r ) R amplfr s also calld mttr followr. nput rsstanc s ry hgh Output rsstanc s ry low h oltag gan s lss than but can b clos to 1 amplfr can b usd as oltag buffr t s notd that, n th analyss, th amplfr s not unlatral R n sg R L r ( L sg 1 NUEE Elctroncs L. H. Lu 4 32
D bas for J amplfr 4.7 asng n J Amplfr rcuts h amplfrs ar opratng at a propr dc bas pont Lnar sgnal amplfcaton s prodd basd on small sgnal crcut opraton h D bas crcut s to nsur th J n act mod wth a propr collctor currnt h classcal dscrt crcut bas arrangmnt A sngl powr supply and rsstors ar ndd hnn qualnt crcut: = R 2 /(R 1 +R 2 ) R = R 1 R 2 J opratng pont: R E / R (1 1/ ) E R s chosn to nsur th J n act ( E > Esat ) A two powr supply rson of th classcal bas arrangmnt wo powr suppls ar ndd Smlar dc analyss J opratng pont: R EE E / R (1 1/ ) E NUEE Elctroncs L. H. Lu 4 33
asng usng a collctor to bas fdback rsstor A sngl powr supply s ndd R nsurs th J n act ( E > E 0.7 ) J opratng pont: E / R (1 1/ ) h alu of th fdback rsstor R affcts th small sgnal gan asng usng a constant currnt sourc h J can b basd wth a constant currnt sourc h rsstor R s chosn to oprat th J n act mod h currnt sourc s typcally mplmntd by a J currnt mrror urrnt mrror crcut: oth J transstors Q 1 and Q 2 ar n act mod Assum currnt gan s ry hgh: REF R EE E R Whn applyng to th amplfr crcut, th oltag has to b hgh nough to nsur Q 2 n act Exrcs 6.35 (xtbook) Exrcs 6.36(xtbook) NUEE Elctroncs L. H. Lu 4 34
4.8 Dscrt rcut J Amplfrs rcut analyss: D analyss: Rmo all ac sourcs (short for oltag sourc and opn for currnt sourc) All capactors ar consdrd opn crcut D analyss of J crcuts for all nodal oltags and branch currnts Fnd th dc currnt and mak sur th J s n act mod A analyss: Rmo all dc sourcs (short for oltag sourc and opn for currnt sourc) All larg capactors ar consdrd short crcut Rplac th J wth ts small sgnal modl for ac analyss h crcut paramtrs n th small sgnal modl ar obtand basd on th alu of omplt amplfr crcut D qualnt crcut A qualnt crcut NUEE Elctroncs L. H. Lu 4 35
h common mttr (E) amplfr h common mttr amplfr wth an mttr rsstanc NUEE Elctroncs L. H. Lu 4 36
h common bas () amplfr h common collctor () amplfr NUEE Elctroncs L. H. Lu 4 37
h amplfr frquncy rspons h gan falls off at low frquncy band du to th ffcts of th couplng and by pass capactors h gan falls off at hgh frquncy band du to th ntrnal capact ffcts n th Js Mdband: All couplng and by pass capactors (larg capactanc) ar consdrd short crcut All ntrnal capact ffcts (small capactanc) ar consdrd opn crcut Mdband gan s narly constant and s aluatd by small sgnal analyss h bandwdth s dfnd as W = f H f L A fgur of mrt for th amplfr s ts gan bandwdth product dfnd as G = A M W NUEE Elctroncs L. H. Lu 4 38
Exrcs 6.40 (xtbook) Exrcs 6.41 (xtbook) Exrcs 6.43 (xtbook) Exrcs 6.44 (xtbook) NUEE Elctroncs L. H. Lu 4 39