Circuits with Transistors

Transcription

1 ircuits with Transistors ontnts 1 Transistors 1 2 Amplifirs h paramtrs Bipolar Junction Transistor (BJT) BJT as a switch Small signal BJT amplifirs r paramtrs ommon Emittr Amplifir ommon ollctor Amplifir ommon Bas Amplifir Fild Effct Transistors (FET) Small signal FET amplifirs Powr amplifirs lass A powr amplifirs Voltag and powr gain Powr gain Efficincy lass B and class AB powr amplifirs Efficincy lass powr amplifirs Diffrntial amplifir Two inputs and two ouputs On input and two ouputs Two inputs and on ouputs On input and on ouput Darlington and Sziklai connctions 17 1 Transistors Transistors ar thr trminal smicounductor amplifying dvic that rgulats currnt or voltag. A small chang in th currnt or voltag at an innr smiconductor layr (which acts as th control lctrod) producs a larg, rapid chang in th currnt passing through th ntir componnt. Th componnt can thus act as a switch, opning and closing an lctronic gat. A transistor is a activ dvic that can amplify, producing an output signal with mor powr in it than th input signal E. ortina Pag 1

2 S v s i i v i O Av i i v o L Input sourc Amplifir Load Figur 1: Thvnin s quivalnt of an amplifir with signal sourc connctd to input and a load impdanc connctd to th ouput Thr ar two kind of transistors, th bipolar transistor (also calld th junction transistor), and th fild ffct transistor (FET). Invntd in 1947 at Bll Labs, transistors hav bcom th ky ingrdint of all digital circuits, including computrs. Prior to th invntion of transistors, digital circuits wr composd of vacuum tubs, which had many disadvantags: thy wr much largr, rquird mor nrgy, dissipatd mor hat, and wr mor pron to failurs. For a good introduction about vacuum tubs and how to us thm visit th wb pag 2 Amplifirs An amplifir is a dvic that taks an input signal and magnifis it by a factor A whr v out = Av in. Ths gain is th so calld opn-loop gain. In ordr to study how an idal amplifir looks lik, an amplifir has bn sktchd in figur 1. In this figur th amplifir has bn rplacd by a Thvnin s quivalnt and an input sourc and output load hav bn addd. In ths conditions th ral amplification factor (A r ) can b xprssd as: A r = v o v s = i o L v s = Av i o L L v s taking into account that th input sourc quivalnt circuit w can stat and substituting in th uppr xprssion i v i = v s s + i i L A r = A s + i o + L Looking that xprssion w can asily ss that th ral gain is smallr than th opn-loop gain. For an idal amplifir w can xprss that: a) i, so th ntir sourc voltag v s is dvlopd across i. In othr words all v s is placd across th amplifir input and th input sourc v s dos not hav to dvlop any powr (i i = 0 whn i = ) b) o 0 so all th availab voltag is dvlopd across L and non of it is lost intrnally. c) A for obvious rasons. d) A should b constant with frquncy, that is, amplify all frquncis qually. E. ortina Pag 2

3 i 1 i 2 h 11 v 1 v 2 h 12 v 2 h 21 i 1 h 22 Figur 2: h paramtrs dfinition 2.1 h paramtrs An amplifir can b sn as a quadrupol. h paramtrs cams from a dirct application of Thvnin thorm to th input dipol and Norton thorm to th output dipol. S figur 2. Th Kirchoff quations for this modl ar: v 1 = h 11 i 1 + h 12 v 2 If th output is short-circuitd v 2 = 0 thn If th input is opn i 1 = 0 i 2 = h 21 i 1 + h 22 v 2 h 11 = v 1 i1 = h i input impdanc h 21 = i 2 i1 = h f currnt gain h 12 = v 1 v 2 = h r invrs voltag gain h 22 = i 2 v2 = h o output admitanc Ths four last rlations givs th maning of th h paramtrs. Bwar, that th maning is with th conditions imposd up, that is, output short-circuit (no load) and opn input (no input). Typical valus of ths paramtrs ar: h 11 = 3.5kΩ h 12 = h 21 = 120 h 22 = 8.5µS 3 Bipolar Junction Transistor (BJT) A bipolar junction transistor is a dvic basd in thr ara smiconductor matrial with two diod junction. Thr ar two typs of BJT, th so calld npn and pnp transistors, dpndig obviously on doping of ach ara. It is calld bipolar bcaus both lctrons and hols ar involvd in its opration. Th trh rgions ar calld mitr, bas and collctor. In figur 3 ar shown both typs of BJT and th majority currnt flow. In ordr to show th transistor ffct, th diod polarization should b corrct, that is, th mittr-bas is in forward bias and th bas-collctor in rvrs bias. In a NPN transistor: E. ortina Pag 3

4 forward biasd rvrs bias n+ p n + p n p mitr bas collctor mitr bas collctor V EE V V EE V I I = αi c I I = αi c Ι = (1 α ) Ι b Ι = (1 α ) Ι b c c b b Figur 3: a) Elctrons ar majoritary carrirs in th mittrs, so thy can pass with no problms to th bas. As th mittr is intndd to provid th charg carrirs will b havly dopd. b) Th bas is slightly dopd and mad vry thin. This allows that th rcombination currnt, that will xit by th bas is small and that th diffussion lngth is longr than th bas lngth and consquntly almost all lctrons from mittr will pass to th collctor c) Onc in th collctor, th lctrons will xit by th lad. For PNP transistors th xplanation is xactly th sam just changing lctrons for hols and invrsing th currnts. In ordr to study th transistor w ar going to mount th so calld common mittr configuration. In figur 4 is shown how this configuration. Th paramtrs α cc and β cc, dfind for dirct currnt ar: α cc = I I E 0.99 β cc = I I B 100 I E = I B + I β cc = 1 α cc In th right sid of th figur 4 hav bn plottd a family of charactrisic courbs of a transistor. For a fixd valu of V BB, that fix I B, w can incras V from 0V. For lowr valus of V both diods ar forward bias so V E will incras accordingly, this rgion is calld saturation. With V high nough will ntr in th activ or linar rgion, whr th bas-collctor jounction is rvrs bias. At this momnt I bcams stabl (or almost) and α cc E. ortina Pag 4

5 c b V B + v s V BE V E V + V BB Brakdown rgion I I B8 I B7 I B6 Saturation rgion I B5 I B4 I B3 I B2 I B1 I = 0 B Blockag rgion Figur 4: Transistor charactrsitic curvs I B1 < I B2 < I B3,tc V E E. ortina Pag 5

6 I I c A I b I Q Q I BQ B V EQ V E V c Figur 5: Q point. Variations inducd in collctor currnt I and V E by a variation of th bas currnt I B dos not chang with V E. In fact, I incras just a bit du to th largr dpltion rgion in th bas-collctor junction. So in this rgion th valu of I is controlld by I B in such a way that I = β I B. With V E larg nough th bas-collctor junction brakdown incrasing I quickly. Not that if I B = 0 thn I = 0 so th transistor dos not conduct. In this situation thtransistor is in th so calld blockag stat. Applying dirctly Kirchoff s laws to th circuit w can find dirctly in th output circuit that th summation of voltags around th loop givs V I V E = 0 I = V 1 V E this is th quation of a straight lin, known as load lin. Suprimposing th load lin on th output charactristics in ffct givs us a graphical solution to two simultanous quations: on quation, blonging to th transistor, non-linar quation givn by th family of I V E graphs, and th othr th load lin. Th intrsction points show th possibl valus that may xist in th circuit. In absnc of th any input signal, v s = 0, th oprational point is calld Q-point. In cas of an input signal provoqus th variation of th V E valu, modifiyng consquntly th oprational point. In figur 5 is shown how th oprational point movs in th transistor charactristic-plot. 3.1 BJT as a switch On of main utilitis of BJT ar as lctronic switchs. If th transistor is in blockag, thn th transistor can b sn as an opn circuit. On th othr hand, if th transistor is in saturation, thn th transistor can b sn as a closd circuit. 3.2 Small signal BJT amplifirs W can found thr typs of small signal BJT amplifir configurations as shown in figur 7: E. ortina Pag 6

7 +V +V +V +V B I = 0 sat I B 0 V I = 0 B E +V BB I B E Figur 6: Transistor viw as an lctronic switch ommon Emittr. From A point of viw th mittr is connctd to th ground. Input signal is in th bas and output in th collctor ommon ollctor. From A point of viw th collctor is connctd to th ground. Input signal is in bas and output in th mittr. ommon bas. From A point of viw th bas is connctd to th ground. Input signal is in th mittr and output in th collctor. +V +V 1 3 V out 1 S V in 1 s V in 1 load 2 V out v s 2 2 v s 2 load +V V out s 1 load v s V in 2 Figur 7: Th thr amplifir configurations. On th lft th common mittr amplifir, in th cntr th common collctor amplifir and on th lft th common bas amplifir In figur 8 ar shown th dfinition of h paramtrs for ths thr configurations. In tabl 1 ar shown th ratios for th thr configurations. E. ortina Pag 7

8 ommon Emmitr ommon Bas ommon ollctor h i = V b /I b h ib = V /I b h ic = V b /I b h r = V b /V c h rb = V /V c h rc = V b /V h f = I c /I b h fb = I c /I b h fc = I /I b h o = I c /V c h ob = I c /V c h oc = I /V Tabl 1: h paramtrs ratios for th thr amplifir configurations Bas h i ollctor Bas h ic Emittr i b h v h i h r c f b o i b h v h i h rc fc b oc Emittr ollctor ommon Emittr ommon ollctor Emittr i h ib h v h i h rb c fb ob ollctor Bas ommon Bas Figur 8: h paramtrs dfinition E. ortina Pag 8

9 3.2.1 r paramtrs It is much mor asy to work with rsistancs than with h-paramtrs. This is why has bn dfind a scond st of paramtrs, calld r-paramtrs. Thir dfinitions ar: α ca Alpha A (I c /I ) β ca Alpha A (I c /I b ) r r b r c A rsistanc at mittr A rsistanc at bas A rsistanc at collctor Th rlationship btwn both st of paramtrs is ommon Emittr Amplifir α ca = h fb β ca = h f r = h r h o 25mV I E r c = h r + 1 h o r b = h i h r h o (1 + h f ) Th input is at bas and th output is at collctor Thr is a phas invrsion btwn input and output 1 and 3 ar coupling capacitors for input and output signals 2 is th so calld drivation capacitor allows th maximum gain at th stup. Th ractanc of all capacitors should b ngligabl at oprational frquncy. Emittr is connctd to ground from A point of viw. Dirct currnt rlations ( 2 β V B = β ) V V E = V B V BE I E = V E Altrnativ currnt rlations V = V I r = 25mV I E E. ortina Pag 9

10 in = β ca r out A v = r A v = V b V out A v A i = I I inp A p = A va i ommon ollctor Amplifir Input is at bas and output at th mittr. Thr is no phas invrsion btwn input and output Input rsistanc is high and output rsistanc is low Maximal gain in voltag is 1. Th collctor is connctd to ground from th A point of viw. Th capacitor ractanc must b ngligabl at th oprating frquncy Dirct currnt rlations ( 2 β V B = β ) V V E = V B V BE I E = V E Altrnativ currnt rlations V = V r = 25mV I E = charg in = β ca (r + ) ( ) s out = β ca A v = r + A i = I I inp A p = A i E. ortina Pag 10

11 3.2.4 ommon Bas Amplifir Input is at mittr and output at collctor Thr is no phas invrsion btwn input and output Input rsistanc is low and output rsistanc is high Maximal currnt gain is 1. Bas is connctd to A ground Dirct currnt rlations ( 2 β V B = β ) V V E = V B V BE I E = V E Altrnativ currnt rlations V = V I r = 25mV I E in r out c = charg A v c r A i 1 A p A v 4 Fild Effct Transistors (FET) 4.1 Small signal FET amplifirs 5 Powr amplifirs Up to now w hav studid singl stag amplifirs, but a practical amplifir consists of svral stags which ar cascadd to produc a gain high nough in ordr to driv a signal. Typically input signals (from a microphon, a radio station or a particl dtctor), ar on th ordr of µv, whras usabl signals should b in th volt rang. Onc th signal is in this rang, it can b considrd inmun from intrfrnc by nois or othr disturbing signals. Firsts stags of th amplifir ar voltag gain amplifirs as th ons w hav sn prviously coupld ithr dirctly or via a capacitor or a transformr. Usually th last stag of an amplifir is a powr amplifir. This sction dos not contribut to voltag gain, it is basically E. ortina Pag 11

12 a currnt amplifir. Anothr way of looking at it is that th voltag sction is a signal amplifir with no significant powr an its output. It is th task of th powr amplifir to produc substantial powr at th output, which it dos by amplifying th currnts. Powr amplifirs should b fd by larg nois-fr voltag signals. Thr ar four diffrnt powr amplifirs, calld of class A, class B, class AB and class. This classification is dtrmind by th prcntag of input cycl that th amplifir works in th linar rgion. 5.1 lass A powr amplifirs A class A amplifir is an amplifir polorizd in such a way that it works in th linar rgion for th whol cycl (360 o ). In this mod th transistor nvr ntrs in th blockag or saturation rgion so th output signal is an amplifid copy of th input on. A class A amplifir is qual as any of th small signal amplifir prsntd bfor. As an xampl w will us a common mittr amplifir in th sam configuration as in figur 7. As w ar daling with big signals th optimal oprational Q-point is th on that is cntrd in th load lin. In cas of asymmtry th output signal will b limitd by th closst point of blockag or saturation. Th condition ndd to cntr th Q-point in th cas of an common mittr amplifir is: V EQ = I Q c Voltag and powr gain Voltag and powr gain ar th sam as in small signal amplifirs, A v = c r A i = β th only diffrnc is that th formul r 25mV/I E is not longr valid bcaus th big oscillations of th signals almost covrs th transconductanc curv I vs V BE, as is shown in figur 9. As r = V BE / I th valu is biggr in th lowr part of th curv than in th uppr part. This bhaviour can produc som distorsions du to th diffrnt gain. Th only way to rduc this distorsion is to work in th most linar rgion Powr gain Th gain in powr is: ( ) A p = A i A v = β A v = β r Efficincy Efficincy (η) is givn by th ratio of A signal powr to D powr supplid. η = P A P D = = 0.25 E. ortina Pag 12

13 I I 2 Q I 1 V BE V BE Figur 9: Variation of r ovr th transconductanc curv V cc v in v out v in v out Figur 10: lass B amplifir in common collctor whr P A = 1 2 V EQ 1 2 I Q = 0.5V EQ I Q P = 2V EQ I Q 5.2 lass B and class AB powr amplifirs A class B powr amplifir is an amplifir in which th transistor is polarizd at th blockag point, in such a way that will oprat in th linar rgion only half of th cycl (180 o ). Th advantag of this kind of stups is that th fficincy is biggr than in a class A amplifir, on th othr hand, if w nd to amplify th whol cycl w nd to build a st up with two transistors in th so calld push-pull amplifir. In figur 10 is shown how it works a class B common collctor a mplifir. As it has bn said th oprational Q-point is at blockag, so whil th signal is in th positiv rgion th transistor will b in th linar ragion, but onc th signal is lowr nough to mak V BE < 0.7V thn th transistor is in blockag and will not conduct. Du to this th output signal is not a copy of th input signal. In ordr to amplify th whol cycl, w hav to build th push-pull stup, composd by two followr mittrs, onc mad with a npn and th otr with a pnp. In figur 11 is shown th principl of this stup. Th principl is th sam as xplaind bfor for th npn. Th pnp will hav th sam bhavour but whn th signals polaritis changd. As it has bn said E. ortina Pag 13

14 V cc V cc Q 1 Q 1 v out v out v in Q v in 2 L Q 2 L V cc V cc v in v out Figur 11: In th uppr plot is shown how a class push-pull works. In th lowr plot is shown th distorsion in th push-pull amplifir. Th transistors only ar proporly polarizd in th shadowd rgions. around a bas polarisation rgion around 0V non of th transistors will conduct, bcaus both bas-mittr junctions will not b proprly polarizd, what producs a gap in th output, known as crossovr distorsion. In ordr to avoid this gap, both transistors should b slightly polarizd bfor th blocakg point. This variation is calld as class AB amplifir. In th cas of th push-pull stupt this polarization can b don ithr by a rsistor dividr or with a coupl of diods. This last configuration is prfrd bcaus its bhaviour with th tmpratur is much stabl. In figur 12 ar shown both stups Efficincy whr η = P A P D = 0.25π = 0.79 P A = 1 2 V EQ 1 2 I Q = 0.5V I sat For ach transistor, output is a half-wav signal, so th currnt man valu is P = V I sat π E. ortina Pag 14

15 V cc V cc Q 1 3 Q 1 3 v out D 1 v out v in 2 v in D 2 Q 2 Q 2 L L Figur 12: Push-pull polarization in class AB in ordr to avoid th crossovr distorsion 5.3 lass powr amplifirs lass amplifirs ar polarizd in ordr to allow conduction in lss that half cycl. Th fficincy is much highr that th rst of powr amplifirs, but th wav form is svrly distortd. Thy ar usd usually for radio frquncy rsonanc amplifirs. 6 Diffrntial amplifir Is a configuration usd to amplify th diffrnc voltag btwn two input signals. In th idal cas th output is ntrly indpndnt of th individual signals lvls (only diffrnc mattrs). Whn both inputs chang lvls togthrs that s a common-mod input chang. A diffrntial chang is calld normal-mod. With discrt componnts on can imagin four configurations, show in figur 13, rgarding th numbr of input and outputs possibls. Th output tnsion in all cass can b xprssd in th form: v o = A diff (v 1 v 2 ) Th input that is in phas with th output (v 1 ) is calld non-invrting input, whil th othr (v 2 ), that has opposit phas with th output is calld invrting output. Th gain A diff will chang for ach configuration. This gain is calld diffrntial gain. 6.1 Two inputs and two ouputs This amplifir is sktchd in figur 13-a. This is th most gnral diffrntial amplifir. Th output is takn btwn both collctors. Idally th circuit is symtric, that is both transistors and rsistors ar idntical vrywhr. In this cas, if v 1 = v 2 th output will b 0. Th gain is calculatd as: A diff = ( r ) E. ortina Pag 15

16 +V +V v o v o v 1 v 2 v V EE V EE a) b) +V +V v o v o v 1 v 2 v V EE V EE c) d) Figur 13: Diffrntial amplifirs: a) Two inputs, two outputs. b) On input, two outputs. c) Two inputs, on output. d) On input, on output E. ortina Pag 16

17 6.2 On input and two ouputs In cas that on of th inputs it is not usd, this should b connctd to th ground. This amplifir is sktchd in figur 13-b. Th gain is also A diff = /( r ). Th applications of two outputs diffrntial amplifirs ar quit rar bcaus thy nd a floating charg, that should b connctd btwn both collctors, whil usual chargs has on nd connctd to th ground. 6.3 Two inputs and on ouputs This amplifir, sktchd in figur 13-c is by far th most usful. Plas not that th amplifir is not symtric anymor, and th non-invrting input is clarly dfind. Usually on popl talk about oprational amplifir is talking about this configuration. Th gain is calculatd as: A diff = 2( + r ). Th factor 2 cams from th fact that thr is only on. Th input impdanc (for any of both inputs) is: r i = 2βr. Th common mod input gain is xprssd as: A M = r An important paramtr is th so calld ommon Mod jction atio (M), that xprss, usually in db, th ratio of rsponso of normal mod signal to th rspons for a common-mod signal of th sam amplitud. M is dfind thn as: M = A diff A M = r 2( + r ) For usual configurations 1 >> + r so M 1 + r Th discussion about diffrntial amplifirs in Princips d Elctroniqu by P. Malvino is xcllnt. 6.4 On input and on ouput Sktchd in figur 13-d. On of th inputs is not usd so it is connctd to ground. Th gain is A diff = /2( + r ). 7 Darlington and Sziklai connctions E. ortina Pag 17