4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 1/18 Graphcal Analyss of a BJT Amplfer onsder agan ths smple BJT amplfer: ( t) = + ( t) O O o B + We note that for ths amplfer, the output oltage s equal to the collector-to-emtter oltage ( () t = () t ). O E + ( t ) + E Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 2/18 y = m x + b f we apply KL to the collector-emtter leg, we fnd: = E 0 We can rearrange ths to get an expresson for the collector current n terms of oltage E (.e., = f ( E ) ): = + 1 E Note ths s an equaton of a lne! = + 1 E y = m x + b Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 3/18 The load lne Ths equaton s referred to as the amplfer s load lne, whch we can graphcally represent as: y = b = m = 1 x = E The load lne prodes the crcut relatonshp (a KL) between and E. The alue of and E must le somewhere along the load lne! Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 4/18 s E for a BJT Exactly where on the load lne depends on the dece (BJT) relatonshp between and E. ecall that ths relatonshp s: acte saturaton E The alue of and E must also le somewhere along ths dece cure! Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 5/18 Sort of lke the Grandew trangle Q: How can the alues for and E smultaneously be a pont on the load lne, and a pont on the dece (BJT) cure? A: Easy! the alues for and E le at the pont where the two cures ntersect!, E E Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 6/18 But t all depends on the nput! Of course, the alues of and E depend on the nput to the amplfer: ( t) = + ( t) As the oltage ( t ) changes, so wll the alues and E. Note, howeer, that the load lne wll not change the slope 1 and y- ntercept are ndependent of oltage ( t ). What does change s the BJT relatonshp between and E. For example, n acte mode, the collector current s ndependent of E (we re gnorng the Early effect)! Howeer, the collector current of a BJT s dependent on the oltage base-toemtter BE. Thus, as ( t ) changes, so does BE, resultng n a new BJT relatonshp (cure) between and E. Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 7/18 c changes as the nput changes Graphcally, we can represent ths as: ( ) = t 1 1 ( ) = t 3 3 ( ) = t 2 2 E where 1, 2, 3 are three dfferent nput oltages such that 1 < 2 < 3. Thus, as the nput oltage ( t ) changes wth tme, the BJT ersus E cure wll change, and ts ntersecton wth the amplfer load lne wll change and wll lkewse be a functon of tme! E Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 8/18 The operatng pont Say that the small-sgnal nput oltage s zero ( o ( t ) = 0). n ths case, the nput oltage s smply a constant bas oltage ( ( t) = ). The collector current and oltage collector-to-emtter are lkewse D bas alues ( and ). E The ntersecton of the two cures n ths case defne the operatng pont (bas pont, Q pont) of the amplfer. Q po nt = E E Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 9/18 What happens f you make B too large Q: see! We know that a large D collector current results n a large transconductance g m a result that s typcally requred for large oltage gan. t appears that we should make (and thus ) as large as possble, rght? A: NO! There s a bg problem wth makng the bas oltage too large BJT saturaton wll result! We can graphcally show ths unfortunate occurrence: = (large!) saturaton E E 0.2 Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 10/18 There s stll a problem A BJT n saturaton makes a poor amplfer! Q: Oh see! We need to set bas oltage to be large, but not so large that we push the BJT nto saturaton, rght? acte = (large) E > E 0.7 A: NO!! There s a bg problem wth ths strategy as well! emember, t s the total nput oltage that wll determne the BJT cure. f we D bas the amplfer so that t s nearly n saturaton, then een a small oltage can push the BJT nto saturaton mode. Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 11/18 A lttle more than bas; then a lttle less than bas For example, recall that the small sgnal nput ( t ) s an A sgnal. n other words ts tme aeraged (.e., D ) alue s zero, meanng that the alue of ( t ) wll effectely be negate half of the tme and poste the other half. Say then that the magntude of the small sgnal nput s lmted to a alue Δ : So that: ( t) Δ Δ ( t) Δ for all tme t and thus: Δ ( t) +Δ for all tme t Let s now look at three scenaros for the small-sgnal nput oltage : 1) = Δ 2) = 0 3) = +Δ Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 12/18 We re httng the floor The resultng output oltage wll of course be dfferent for each case: = +Δ = = Δ E 0.2 E = Δ E E o Look what happened here! f the nput small-sgnal s large and poste, the total nput oltage ( and thus total BE ) wll be too large, and thus push the BJT nto saturaton. Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 13/18 Dstorton!!!!!!!! The output oltage n ths case (when = +Δ ) wll smply be equal to: as opposed to the deal alue: ( ) 0.2 O t (BJT saturated) () t = +Δ (BJT acte) O E o where Δ o = Ao Δ. Note for ths amplfer, the small-sgnal oltage gan A o s negate, so that the alue Δ o s also negate: Δ = A Δ < o o 0 Snce the BJT s n saturaton durng some porton of ( ) t, the amplfer output sgnal wll not look lke the nput sgnal dstorton wll result! Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 14/18 neer sad ths was easy Q: Now get t! We need to make small, so that the BJT does not enter saturaton, and the output sgnal s not dstorted! A: NO!! There s a problem wth ths too! We can agan graphcally examne what happens f we make the bas oltage too small. = +Δ = = Δ = +Δ E E o E E E = Look what happened here! Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 15/18 Now we re httng the celng f the nput small-sgnal s large and negate, the total nput oltage ( and thus total BE ) wll be too small, and thus push the BJT nto cutoff. Note the collector current wll be zero ( = 0) when the BJT s n cutoff! The output oltage n ths case (.e., when = Δ ) wll smply be equal to: E ( t) = (BJT cutoff) O as opposed to the deal alue: ( t) = Δ (BJT acte) O E o where Δ o = Ao Δ. Note for ths amplfer, the small-sgnal oltage gan s negate, so that the alue Δ o s poste. Snce the BJT s n cutoff durng some porton of ( ) t, the amplfer output sgnal wll not look lke the nput sgnal dstorton wll result! Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 16/18 What do we do? Q: Ykes! s there nothng we can do to aod sgnal dstorton? A: To get allow for the largest possble (dstorton-free) output sgnal o ( t ), we typcally need to bas our BJT such that we are about half way between basng the BJT n saturaton and basng the BJT n cutoff. Note f the BJT s n saturaton: E 0.2 (BJT saturaton) Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 17/18 Whereas, f t s n cutoff: Bas n the mddle E = 0 = (BJT cutoff) t s edent that for ths partcular amplfer, basng half-way between saturaton and cutoff means basng such that: E 2 or equalently: 2 Jm Stles The Un. of Kansas Dept. of EES
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 18/18 The output s maxmzed Q po nt = +Δ 2 = = Δ = + Δ E E o = E 2 = Δ E E o E The bas soluton aboe s optmal for ths partcular amplfer desgn. Other amplfer desgns wll result n other optmal bas desgns t s up to you determne what they are. emember, the total oltage ( t ) E must be larger than 0.7 for all tme; otherwse saturaton (and thus sgnal dstorton wll result). Lkewse, the total collector current ( t ) must be greater than zero for all tme; other wse cutoff (and thus sgnal dstorton) wll result. Jm Stles The Un. of Kansas Dept. of EES