Bipolar Junction Transistor

Transcription

1 Bipolar Juntion Transistor Bipolar Juntion Transistor: A bipolar juntion transistor (BJT) is widly usd in disrt iruits as wll as in IC dsign, both analog and digital. Its main appliations ar in amplifiation of small signals, and in swithing digital logi signals. In a BJT, both majority arrirs and minority arrirs play a rol in th opration of th transistor, hn th trm bipolar. Th iruit symbol of th NPN transistor with urrnt and voltag polaritis markd is shown in Figur 1. IC Colltor + Bas + VCE IB VBE IE - Emittr Figur 1. Ciruit symbol of a NPN BJT Th haratristi urvs of BJT ar not only hlpful in studying th bhavior of th transistor but also in dtrmining th rgion of opration for th transistor. As was don with a diod, w an draw a load lin on th abov urvs to dtrmin th oprating point of th transistor. Th intrstion of th load lin with th urvs givs th oprating point, rfrrd to as th Q-point. Th rgions of intrst in a transistor ar th amplifying rgion, utoff rgion and th saturation rgion. Th last two ar xtnsivly usd whn th transistor is usd in digital iruits. Ths thr rgions ar dfind as follows: CUTOFF : both th mittr and olltor juntion ar rvrs biasd Colltor voltag is at supply voltag SATURATION : both th mittr and olltor juntions ar forward biasd Colltor voltag is at almost 0V ACTIVE : mittr juntion is forward biasd, olltor juntion is rvrs biasd

2 In th ativ rgion, th olltor urrnt is indpndnt of th valu of th olltor voltag and hn th transistor bhavs as an idal urrnt sour whr th urrnt is dtrmind by V BE. Th olltor urrnt is dpndnt on th bas urrnt as, I C = β I B + ( β + 1 ) I CO V CE = ons tan t (1 ) whr β is alld th d ommon mittr urrnt gain of th transistor, dfind as β = I C I B ( 2 ) Anothr paramtr of intrst in th ativ rgion is α, th urrnt transfr ratio, or ommon bas urrnt gain, whih is dfind by α = I C I CO I E V CB = ons tan t ( 3 ) Th urrnt gain paramtrs α and β ar rlatd by: β = α 1 α ( 4 ) Whn th transistor is biasd in th ativ rgion it oprats as an amplifir. Th biasing problm is that of stablishing a onstant DC urrnt in th mittr (or th olltor) whih is insnsitiv to variations in tmpratur, valu of β and so on. This is quivalnt to dsigning th transistor iruit so that th Q-point is in th middl of th DC load lin. Changing th biasing rsistors has th fft of shifting th Q-point along th DC load lin, moving th transistor into th rgions of utoff or saturation. Th amplifiation proprty an b graphially intrprtd as sn in Figur 2. I I Q-point Output Signal tim V b v b Input Signal tim

3 Figur 2. Amplifiation of a small signal Load lin analysis Writing th output loop quation from Figur 4, w hav V CC I C R C V CE I E R E = 0 ( 5 ) I C = f( V CE,I B ) ( 6 ) For β larg, I E I C (7 ) Using quations 5 and 7, w an writ: or V CC I C ( R C + R E ) V CE = 0 (8 ) I C = V CC V CE R C + R E = 1 R C + R E V CE + V CC R C + R E ( 9 ) This is th (straight lin) quation of th load lin on a plot of I C vs V CE, whr V CC is th powr supply voltag. Th axis rossings an b found by stting I C =0 or V CE = 0. V CC R C + R E I C I CQ Q I B V CQ Q V CC Figur 3. BJT IV urvs and load lin V CE Th analysis suggsts that small sinusoidal signals, v b, suprimposd on th DC voltag V BE, will giv a sinusoidal olltor urrnt, i C, suprimposd on th DC urrnt I C at th Q- point. Dpnding upon th onfiguration of th rsistors in th olltor, th mittr, and th load, thr will b an idal Q-point for a maximum distortion-fr output signal amplitud. Dtrmining this rsistor rquirs onstruting an a load lin.

4 Coupling apaitor Th figur blow shows an a voltag sour onntd to a apaitor and a rsistor. Sin th impdan of th apaitor is invrsly proportional to th frquny th apaitor will blok DC and allow AC to pass. For th oupling rsistor to work proprly its ratan must b muh smallr than th rsistan at th smallst oprating frquny of th iruit. For xampl an audio iruit from 20Hz to 20kHz th lowst oprating frquny is 20Hz. Good oupling ours whn : X C = <0.1R This mans that th ratan should b at last 10 tims smallr than th frquny at th lowst point of opration. Whn this rul is satisfid than th apaitor boms a short iruit at a. Th bas biasd amplifir. Whn analyzing th bas biasd amplifir first of all th quisnt point must b found. This is th d oprating point of th iruit. For th iruit shown blow th d voltags ar found as follows

5 V V B B = = 1.8V V = = 1.1V E 1.1 I E = = But I = I I = V I = = = 6.04V 3 R ma ma Not that on th mittr thr is no a voltag as for a analysis all apaitors ar a shortd to ground whil for d apaitors ar opn iruits. This is th rason why a d voltag appars on th mittr. AC Bta Th urrnt gain of th iruit at d is givn by β = d I I I and I ar givn by th d urrnts found whn finding th quisnt point of th transistor. Th a urrnt gain is givn by i β a = i DC urrnt gain is also known as h FE and a urrnt gain is known as h f. AC rsistan of th Emittr diod

6 Th bas-mittr juntion an b rprsntd as a diod. Th a mittr urrnt I dpnds on th valu of V b. This juntion an b approximatd as having an intrnal rsistan r. This dos not xist in rality but it is usd to modl th transistor amplifir. Th a rsistan of th mittr diod is dfind as ' v r = i b This says that th rsistan of th mittr diod quals th a bas mittr voltag dividd by th a mittr urrnt. Th prim ( ) in r is th standard way to indiat that th rsistan is insid th transistor. For instan th figur abov shows an a bas mittr voltag of 5mv pk-pk. At th givn Q point this sts up an mittr urrnt of 100uA pk-pk. Th a rsistan is of th mittr diod is givn by ' 5mV r = = 50Ω 100uA Th a mittr rsistan always drass whn th d mittr urrnt inrass, baus v b is ssntially a onstant valu.

7 Formula for a mittr rsistan A pratial formula for th mittr rsistan is th following ' 25mV r = I This formula assums small signal opration, room tmpratur and a rtangular bas-mittr juntion. It an b applid to all transistors to stimat th valu of th bas-mittr rsistan. Th valu of r is important baus it will dtrmin th voltag gain of th transistor. Th smallr it is th largr th voltag gain. E Transistor modls A transistor an b simplifid to a modl to alulat various paramtrs. An a modl is ndd to analyz th iruit opration whn an a signal is prsnt. On of th arlist and most fftiv modls wr th Ebrs Moll modl. In this modl th mittr diod ats lik a urrnt sour i. Somtims th Ebrs Moll modl is rfrrd to as th T modl. Anothr ommon modl whih is mor widly usd is th π-modl, rfrrd to as pi-modl. Th pi-modl shows th input impdan of th transistor. Whn an a input signal drivs a transistor amplifir an a bas-mittr voltag v b is gnratd aross th juntion. This voltag sour driving th transistor has to supply a small a urrnt so that th amplifir will work orrtly. By ohm s law w an stat that th bas of th transistor has input impdan. Th diagrams blow show th onpt. Th input impdan at th bas is givn by

8 Z in( bas) = βr ' This quation tlls us that th input impdan of th bas is qual to th a urrnt gain multiplid by th a rsistan of th mittr diod. Th diagram blow visually shows th input impdan at th bas Analyzing an amplifir Whn it oms to analyzing an amplifir on has to prform a d and an a analysis. A d analysis is prformd whn all apaitors ar opnd. Thn you hav th d quivalnt iruit. Whn an a analysis is prformd, all d voltag sours and all apaitors ar shortd to ground. Th transistor is than transformd into th quivalnt T or pi-modl. Th nxt xampl will analyz a ommon transistor amplifir

9 As you an s all apaitors hav bn shortd, th d supply point has bom an a ground and th transistor has bn rplad by th pi-modl. In th bas iruit, th a input iruit th a input voltag appars aross R 1 in paralll with R 2 in paralll with βr. In th olltor iruit, th urrnt sour pumps an a urrnt of i through R in paralll with R L. This typ of amplifir is known as th ommon mittr (CE) amplifir. Th CE amplifir has its mittr at a ground AC quantitis on a datasht Th datasht givs svral important masurmnts on th a haratristis of th transistor. Som of ths paramtrs ar dsribd hr. H paramtrs wr th traditional mthods of analyzing a transistor. From ths paramtrs th valus of β,r and othr r paramtrs ar drivd. Looking at th Small signal haratristis part of th data sht th following formulas ar usd to driv th mor ommon paramtrs of a transistor. β = h f ' h r = h i f

10 Th datasht quots th minimum and maximum valus of ah paramtr so th variation an b alulatd. Othr usful paramtrs ar F t High frquny limitations of th transistor C ib,c ob Input and output apaitans of th transistor NF Nois Figur. How muh nois th transistor gnrats Th graphs on th datasht ar usd to xtrat usful information on th transistor haratristis Voltag Amplifirs Aftr analyzing th a haratristis of a ommon mittr amplifir, it is now appropriat to dtrmin th gain and input/output impdans of suh a iruit. Th gain of a ommon mittr amplifir an b summarizd as A = ( R RL) r ' Th a olltor rsistan is known as r and it is givn by R C R L. Hn it an b statd that th voltag gain of an amplifir is th a olltor rsistan dividd by th a rsistan of th mittr diod. Th loading fft of input impdan Until now w hav assumd an idal voltag sour with zro sour rsistan. Howvr th input impdan of th transistor and of th sour will intrat and rdu th voltag apparing on th mittr diod.

11 Th a voltag sour is rprsntd by V G and its intrnal rsistan R G. Th voltag that is atually applid to th bas of th transistor is th voltag aross Z in(stag). This is alulatd by : v in = R g Z in( stag) + Z in( stag) v g Voltag gain Th voltag gain is dfind as th a output voltag dividd by th a input voltag. Th a bas urrnt i b that flows through th input impdan of th bas (βr ). using ohms law on an writ : v in = i βr b '

12 Workd xampl In th iruit blow find th output voltag if β = 300, r =22.7Ω and gain = 117. Whn β = 300 Z in(bas) = (300)(22.7) = 6.8kΩ Th input impdan of th stag is Z in(stag) = 10k 2.2k 6.8k = 1.42kΩ Th input voltag an b alulatd as

13 1.42k vin = 2m= 1.41mV k Th amplifid a voltag is V out = Av in = (117)(1.41mV) = 165mV Multistag amplifirs It is not a wis ida to put on stag with a larg gain, but to hav svral stags with smallr gain. Using a larg gain with a singl stag is not a good ida sin th input and output impdan will b ngativly afftd. Th shmati blow shows a 2 stag voltag amplifir togthr with its assoiatd pi-modl. Not that th input impdan of th sond stag will load th output impdan of th first stag. Th input impdan (Z in ) of 2 nd stag is in paralll with th olltor rsistan (R C ) of th first stag. Th a olltor rsistan of th first stag is

14 First stag r =R C Z in(stag) Thus th voltag gain of th first stag is R z A = in( stag) 1 ' r Th ovrall voltag gain of th amplifir is givn by th produt of th individual gains A Total = A 1 A 2 Ngativ fdbak A voltag amplifir that dpnds only on r suffrs from hang in gain, quisnt urrnt tmpratur variations baus Bta (β) and r hang from on transistor to anothr. On mthod to stabiliz th voltag gain is th kp som of th mittr rsistan un-bypassd. This rsistor will at as ngativ fdbak and will kp th gain onstant. Th shmati is shown blow as wll with its a quivalnt modl

15 Th voltag gain of suh a iruit is A r = r r ' + If r is muh gratr than r than th gain rdus to r A = r Th input impdan at th bas is inrasd by th ation of ngativ fdbak. Th input impdan is now Z in(bas) = β(r + r ). If r is muh gratr than r than th input impdan is only βr.