4. Biasing Transistor Circuits
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- Oscar Colin Arnold
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1 Lectue 5: toductio to electoic aalog cicuits iasig Tasisto icuits ugee Papeo, 2008 Ou mai aim is to aalyze the dawbacks of the bias i the elemetay tasisto cicuits ad to suggest a betteolutio fo both discete ad itegated electoic cicuits Dawbacks of the bias i the elemetay tasisto cicuits The elemetay biasig has the two followig mai dawbacks. xcessive use of static souces The fist dawback is elated to the eed to use too may static sigal souces i multi-stage electoic cicuits. The souce i ig. 1 is ot uivesal: it caot be used fo biasig othetages. Tasistos i othetages may eed a diffeet base-emitte voltage, eithe due to the diffeece i thei paametes o the diffeece i theitatic states. t is also a complex task to coect a sigle souce to a umbe of stages ad to decouple it fom idividual sigal souces i each stage. Themal istability The secod dawback of the elemetay biasig is elated to its themal istability caused by: 0.5( / / T l( / O max 0.5( O 0.5( O mi 0 i T l( / Q' Q δ 100%/5 o 2m/ o T δ %/, 2 m/ [see ig. 1 ], v δ o 100%/10 [see ig. 1 (c], whee δ deotes the elative chage, deotes the absolute chage i the coespodig vaiable, ad o is the leakage cuet due to the discotiuity of the semicoducto just beeath its suface [see ig. 1(c]. The silico atoms that ae located just beeath the suface do ot have eighbos above them. As a esult, each of them has a vacacy that ca be used by electos to tavel fom atom to atom. The typical value of the leakage cuet is below 100 pa. (t is obvious that the leakage cuet is popotioal to the voltage betwee the temials, thee is o leakage if thee is o diffeece betwee the electical potetial of the temials. To coside the leakage cuet we add i ig. 1(d a o souce to the ideal, leakage-fee tasisto. Note that we coside oly the leakage cuet of the evese biased - juctio ad do ot coside the leakage cuet of the fowad biased - juctio. This is because both the static ad dyamic impedaces of a fowad biased juctio ae elatively low, ad the coected i paallel elatively high p p o o (c (d i o ig. 1. iasig the elemetay amplifie. icuit. The depedece of o tempeatue (fo a fixed. (c The leakage cuet o due to the discotiuity of the semicoducto just beeath its suface. (d cludig the leakage cuet ito the tasisto model.
2 Lectue 5: toductio to electoic aalog cicuits leakage impedace ca be eglected iasig pactical discete cicuits Discete cicuits ae assembled fom sepaate compoets, each maufactued by special techology. Thee ae o picipal limitatios, ad the desige ca ejoy the possibility of usig the wide vaiety of compoets, thei values, ad toleaces. Howeve, the picipal disadvatage of the discete desig is the impossibility of usig idetical tasistos (see ectio 2.3. To impove the elemetay biasig the followig is usually doe i the desig of discete cicuit. To get id of the ouivesal souce, it is simply eplaced [see ig. 2] by a voltage divide 1, 2, ad the sigal souce is coected to the cicuit via a couplig capacito. (Note that othewise the souce would goud the static voltage of the tasisto base. Note also that the couplig capacito does ot let us amplify dc small sigals. t may be a seious dawback if we do have to amplify them. To icease the themal stability of the bias, a feedback esisto is coected betwee the emitte of the tasisto ad the goud. f ow the collecto cuet will ise with tasisto tempeatue, ad, hece, will ise as well. o a costat ad ealy costat, iceasig will icease, decease the voltage acoss, decease, ad hold back i this way the ise of the collecto cuet (egative feedback. ode ot to let to hold back the ac smallsigal collecto cuet, a bypass capacito is coected i paallel to. To aalyze the themal stability the sesitivity of to (T, (T, ad o (T of the cicuit i ig. 2, we fist apply the Thévei theoem to, 1, ad 2. The esult is show i ig. 2. We ow ca easily fid ' ( ' +. (1 (1 + ' + + o ( o (1 + + o + + (1 + ( ( ' o o ( o + (2. ( /( o ' o o ' ' ' ' + o ig. 2. iasig discete cicuits. A pactical cicuit ad its equivalet fo fidig the static state afte applyig the Thévei theoem to, 1, ad 2. o o o O, (4 whee,, ad ae the sesitivity factos givig the sesitivity of to (T, (T, ad o (T, espectively. 1 + ( ( ( + (1 + + (1 + 0 mi mi 1. (5 The sesitivity of to o (T, (T, ad (T ca be foud as follows: ( [ + o ( + (1 + 2 ] + mi Note that both ad i (4 ae egative, theefoe,
3 Lectue 5: toductio to electoic aalog cicuits due to is positive. The sesitivity factos i (5 should appoach thei miima to impove the bias themal stability. Oe ca see that this is obtaied whe 0 (we deote this as (, ad, (we deote this as ad. Deceasig deceases the pat of the leakage cuet icemet, o, eteig the tasisto base. ceasig ad iceases the egative feedback though. We caot use too small because this equivalet esistace ot oly shotes some pat of the leakage cuet to goud but also does the same to the iput sigal [see ig. 2]. a pactical cicuit we ca oly use tasistos with limited ad caot use too geat. The voltage dop acoss too geat educes too much the age of the output voltage (see ig. 3. A geeal compomise fo choosig ad is as follows: xample cicuits (6 ig. 3 shows a cicuit with the static state chose i accodace to ( iasig itegated cicuits tegated, solid-state cicuits compise thi-film compoets located o the substate of silico. Hece, thee ae picipal techology limitatios that estict the size of compoets, thei exteme values, ad toleaces. A impotat advatage of itegated cicuits is the possibility to use a lage umbe of idetical tasistos [see ig. 4]. (A couple of tasistos ca be ealy idetical povided they ae close each othe o the same silico substate. Moe distat tasistos ae much moe diffeet because they pass the techological pocess i substatially moe diffeet coditios. t is impossible to maitai exactly the same techological paametes acoss the etie substate suface. To simplify the techology ad educe the aea of the chip, the itegated cicuit desig is aimed at usig oly tasistos. Oly a few esistos ad capacitos, if at all, ae allowed. Theefoe, we have to fid a diffeet solutio to elimiate the dawbacks of the elemetay bias. We will see i ectio 2.4, that havig a couple of idetical tasistos, ad we do have plety o them o a chip, we ca easily build a idepedet cuet souce. Defiig the collecto cuet i a amplifie though biasig the emitte cuet by the idepedet cuet souce [see ig. 4] helps us to both get id of the o-uivesal souce ad to impove the bias stability. Moeove, we do ot also have to use eithe couplig o bypass capacitos. We simply ~75kΩ ~110µA kΩ 1 11 ~10µA 10 ~100µA 2 ig. 3. xample cicuit. 4.15kΩ o + o 1 1kΩ 10 1mA 1 0 O max 0.5( Omi 4.15 v O O 5.85 ~1mA ' 0.5( Omi ~1mA 1.7 Omi o 0.1 detical tasistos Not idetical tasistos + + tatic state mall sigal ig. 4. iasig itegated cicuits. Tasistos i a wafe. A pactical cicuit employig a cuet souce to apply. coect the sigal souce diectly to the base, without sacificig the dc gai. We do ot also suffe fom the themal sesitivity of o, because the taslatio is via α, which is almost isesitive to tempeatue (thik why?. We
4 Lectue 5: toductio to electoic aalog cicuits do ot suffe fom the amplificatio of the leakage cuet o sice α + o, ad this sets at its miimum, mi 1. uthemoe, late i the couse we will also get id of by eplacig it with a tasisto. The oly task we will have to solve is how to coect the emitte of the amplifie to goud fomall sigals [see ig. 4], icludig dc oes. (Pove that leavig this task usolved will educe to zeo the voltage gai of the amplifie. L? L L M L? L L 2.4. uet mio Let us ow desig a pactical cuet souce. Ou aim is to povide a almost costat cuet though a vaiable load L coected to a static voltage supply [see ig. 5]. (The load may epeset ot just a esisto but also a etie cicuit we would like to bias. ice cuet souces ae abset i atue, we will covet the static ito a costat, o almost costat, cuet. We will fist covet ito the costat collecto cuet of a maste tasisto ad the copy o mio it with a idetical slave tasisto coected to the load [see ig. 5]. We eed the maste tasistoice the L value ca fluctuate i a geeal case. stead of a ot ecessaily costat load, L, we use a costat efeece load (a esisto,, ad this povides us with a costat efeece cuet: ( ± >> f ( T. (7 M +2 M M M M 2 (1+2/ ( /2+1 2 L L L L Note that despite the shoteig the base ad the collecto, the tasistotill opeates i the active egio (the collecto-base juctio is ot biased i the fowad diectio ad, theefoe, M M. To copy M, we fist copy the voltage of the maste by coectig to it the base-emitte juctio of the slave. o M, the same povides, the same, collecto cuets i both the tasistos: M. To check the situatio fo > M, let us coside the gaphical solutio i ig. 5. Note that to fid the load lie of the maste tasisto i ig. 5, we apply i ig. 5 Mille's theoem fo cuets ad fid the equivalet load, (1+2/, at the collecto of the maste tasisto. om igs. 5 ad, we ca coclude that N i M Q Q M M 1/[ (1+2/ ] 1/ N 1 1/( Lmi 0 M 2 1/ L 1/ Lmax v L o 4243 M , ( o though N 1 N which is the equatio of a o-ideal (pactical cuet souce: a ideal cuet souce ad a esisto i paallel to it [see ig. 5(c]. We ca also say that (8 is the Noto equivalet of the slave tasisto with the equivalet cuet souce N ( / (2+ ad the Noto esistace N o [see ig. 5(c]. lave N 2 (c L L 2 + N o ig. 5. uet mio. Developig the cicuit. Gaphical solutio. (c quivalet cicuit.
5 Lectue 5: toductio to electoic aalog cicuits tage i tage j tage k ~ / 2 ~ ~3 / 2 uet Mio ig. 6. Multi-output cuet mio with a sigle. Thus, we get exactly what we eed: a cuet souce that keeps almost costat cuet though a vaiable load. Note that the slave ca be able to copy ot exactly the same M. o example, it is possible to copy 1/2, o 1/3, o 2/1 of M if the coss-sectioal aea of the slave base-emitte juctio, A, is 1/2, o 1/3, o 2/1 of A M. (ecall / T e that, ad A. Note also that it is possible to coect to a maste a umbe of slaves (see ig. 6 each povidig a scaled, elative to M, fo the stage it has to bias. Natually, the 2 tem i (8 should be eplaced by i 1 i, whee is the umbe of the slave tasistos. N [1] A.. eda ad K..mith, Micoelectoic cicuits.
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