Unifying Principle for Active Devices: Charge Control Principle

Transcription

1 ES 330 Electncs II Supplemental Tpc #1 (August 2015) Unfyng Pncple f Actve Devces: hage ntl Pncple Dnald Estech An actve devce s an electn devce, such as a tansst, capable f delveng pwe amplfcatn by cnvetng dc bas pwe nt tme vayng sgnal pwe. It delves a geate enegy t ts lad than f the devce wee absent. The chage cntl famewk [13] pesents a unfed undestandng f the peatn f all electn devces and smplfes the cmpasn f the seveal actve devces used n cmpund semcnduct analg and dgtal ntegated ccuts. hage Q c ntllng Electde Emttng Electde (electns) llectng Electde hage Q Tanspt Regn Fgue 1. Genec chage cntl devce cnsstng f thee electdes embedded aund a chage tanspt egn. nsde the genec electn devce shwn n Fg. 1. It cnssts f thee electdes encmpassng a chage tanspt egn. The tanspt egn s capable f supptng chage flw (the electns shwn n the fgue) between an emttng electde and a cllectng electde. A thd electde, called the cntl electde, s used t

2 establsh the electn cncentatn wthn the tanspt egn. Placng a cntl chage, Q, n the cntl electde establshes a cntlled chage, dented as Q, n the tanspt egn. The peatn f actve devces depends upn the chage cntl pncple [1]: Each chage placed upn the cntl electde can at mst ntduce an equal and ppste chage n the tanspt egn between the emttng and cllectng electde. At mst we have the elatnshp, Q = Q. Any paastc cuplng f the cntl chage t chage n the the electdes, emte pats f the devce, wll decease the cntlled chage n the tanspt egn, that s, Q < Q me geneally. F example, chage cuplng between the cntl electde and the cllectng electde fms a feedback utput capactance, say. Tme vaatn f Q leads t the mdulatn f the cuent flw between emttng and cllectng electdes. The genec stuctue n Fg. 1 culd epesent any ne f a numbe f actve devces (e.g., vacuum tubes, unpla tanssts, bpla tanssts, phtcnducts, etc.). Hence, chage cntl analyss s vey bad n scpe and t apples t all electnc tanssts. Statng wth the chage cntl pncple, we asscate tw chaactestc tme cnstants wth an actve devce, theeby, leadng t a fstde descptn f ts behav. Applcatn f a ptental dffeence between the emttng and cllectng electdes, say V, establshes an electc feld n the tanspt egn, althugh ths appled feld s nt always needed when dffusn ntenal felds fm dpng pfles ae effectve. Electns n the tanspt egn espnd t the electc feld and mve 2

3 acss ths egn wth a tanst tme. The tanst tme 1 s the fst f the tw mptant chaactestc tmes used n chage cntl mdellng. Wth chage Q n the tanst egn, the statc (dc) cuent I between emttng and cllectng electdes s I = Q/ = Q c / (1) A smple ntepetatn f s as fllws: s equal t the length l f the tanspt egn dvded by the aveage velcty f tanst (.e., = l/v). Fm ths pespectve a chage f Q (culmbs) s swept ut the cllectng electde evey secnds. v n R n ntllng Electde Emttng Electde Tanspt Regn V R L llectng Electde v ut Fgue 2. Genec chage cntl devce f Fg cnnected t nput and utput essts, R n and R L, espectvely, wth bas vltage and nput sgnal appled. nsde Fg. 2 shwng the cmmnemttng electde cnnectn f the actve devce f Fg cnnected t nput and utput (.e., lad) esstances, say R n and R L, 1 The tanst tme s best ntepeted as an aveage tanst tme pe cae (n u case the electn). We nte that 1/ s cmmn t all devces t s elated t a devce s ultmate capablty t pcess nfmatn. 3

4 espectvely. The secnd chaactestc tme f mptance can nw be defned t s the lfetme tme cnstant and we dente t by the symbl. It s a measue f hw lng a chage placed n the cntl electde wll eman n the cntl temnal. The lfetme tme cnstant s establshed n ne f seveal ways dependng upn the physcs f the actve devce and ts cnnectn envnment. The cntllng chage may leak away by (1) dschagng thugh the extenal esst R n as typcally happens wth FET devces, (2) ecmbnng wth ntemxed ppstely chaged caes wthn the devce (e.g., base ecmbnatn n a bpla tansst), (3) dschagng thugh an ntenal shunt leakage path wthn the devce. The dc cuent flwng t eplensh the lst cntl chage s I n = Q/ = Q c / (2) The statc (dc) cuent gan G I f a devce s defned as the cuent delveed t the utput dvded by the cuent eplenshng the cntl chage dung the same tme ped. Whee n secnds chage Q s bth lst and eplenshed, chage Q c tmes the at / has been suppled t the utput esst R L. In symbls, the statc cuent gan s G I = I /I n = / (3) pvded Q = Q hlds. In the dynamc case the pcess f smallsgnal amplfcatn cnssts f an ncemental vaatn f the cntl chage Q c dectly esultng n an ncemental change n the cntlled chage, Q. The esultng vaatn n utput cuent flwng n the lad esst tanslates nt a tme vayng vltage v. The chage cntl fmalsm hlds just as well f lagesgnal stuatns. In the lagesgnal case the changes n cntl chage 4

5 ae n lnge small ncemental changes. hage cntl analyss unde lage chage vaatns s less accuate due t the smplcty f the mdel, but stll vey useful f appxmate swtchng calculatns n dgtal ccuts. An mptant dynamc paamete s the nput capactance f the actve devce. apactance s a measue f the wk equed t ntduce a chage cae n the tanspt egn. apactance s gven by the change n chage Q fm a cespndng change n nput vltage v n. It s desable t maxmze n an actve devce. The tanscnductance g m s calculated fm g m I v n I Q Q v v n (4) The fst patal devatve n the ghthandsde f Eq. (2.2.4) s smply (1/ ) and the secnd patal devatve s. Hence, the tanscnductance g m s the at g m (5) A physcal ntepetatn f g m s the at f the wk equed t ntduce a chage cae t the aveage tanst tme f a chage cae n the tanspt egn. The tanscnductance s ne f the mst cmmnly used devce paametes n ccut desgn and analyss. In addtn t anthe capactance, say, s ntduced and asscated wth the cllectng electde. apactance accunts f chage n the cllectng electde cupled t ethe statc chage n the tanspt egn chage n the cntl electde. A nnze ndcates that the cuplng between the cntllng electde and the chage n tanst s less than unty (.e.,q < Q ). 5

6 F smallsgnal analyss the capactance paametes ae usually taken a fxed numbes evaluated abut the devce s bas state. When usng chage cntl n the lagesgnal case, the capactance paametes must nclude the vltage dependences. F example, the nput capactance can be stngly dependent upn the cntl electde t emttng electde and cllectng electde ptentals. Hence, dung the change n bas state wthn a devce the magntude f the capactance s tme vayng. Ths vaatn can damatcally affect the swtchng speed f the actve devce. Paametc dependences upn the nstantaneus bas state f the devce ae at the heat f accuate mdellng f lagesgnal swtchng behav f actve devces. ntllng Electde llectng Electde v y y v y f v y v Emttng Electde y = y f g m = y = y = Fgue 3. A twpt smallsgnal admttance paamete mdel f an actve devce. Ntce the fwad admttance y f s the tanscnductance f the devce. We ntduce the smallsgnal admttance chage cntl mdel shwn n Fg. 3. Ths mdel uses the emttng electde as the cmmn temnal n a twpt cnnectn. 6

7 The tanscnductance g m s the magntude f the eal pat f the fwad admttance y f and s epesented as a vltagecntlled cuent suce pstned fm cllectngtemttng electde. The nput admttance, dented by y, s equvalent t ( /), whee s the cntl chage lfetme tme cnstant. Paamete y can be expessed n the fm (g s ) whee s = j. An utput admttance, smlaly dented by y, s gven by ( / ) whee s the tanst tme and, n geneal y = (g s ) n geneal. Fnally, the utputtnput feedback admttance y s ncluded usng a vltagecntlled cuent suce at the nput. Often y s small enugh t appxmate as ze (the mdel s then sad t be unlateal). nsde the fequency dependence f the dynamc (ac) cuent gan G. The lwfequency cuent gan s ntepeted as fllws: An ncemental chage q c s ntduced n the cntl electde wth lfetme. Ths pduces a cespndng ncemental chage q n the tanspt egn. hage q s swept acss the tanspt egn evey tanst tme secnds. In tme chage q csses the tanst egn 7

8 tmes, whch s dentcally equal t the lwfequency cuent gan. v g g m v y (a) Shtccut lg G / 20 db/decade T 0 db B lg Fgue 4. cut used t calculate the smallsgnal cuent gan G f u actve devce. The lfetme asscated wth the cntl electde ases fm chage leakng ff the cntllng electde. Ths s mdeled as an R tme cnstant at the nput f the equvalent ccut shwn n Fg. 4(a) wth equal t R n. The beak fequency B asscated wth the cntl electde s (t s 3dB belw the lw fequency value) B 1 1 R n (6) When the chage n the cntl electde vaes at a ate less than B, G s equal t / because chage leaks ff the cntllng electde faste than 1/. Altenatvely, when 8

9 s geate than B, G deceases wth nceasng because the appled sgnal chage vaes me apdly than 1/. Hence, G s nvesely pptnal t G 1 T (7) whee T s the cmmnemtte unty cuent gan fequency. At T (= 2f T ) the ac cuent gan equals unty as llustated n Fg. 4(b). Nw cnsde the cuent ganbandwdth pduct G f. Puely capactve nput mpedance can t defne a bandwdth. Hweve, a fnte, eal mpedance always appeas at the nput temnal n any pactcal applcatn. Let R be the effectve nput esstance f the devce (.e., R wll be equal t (1/g ) n paallel wth the extenal nput esstance R n ). Snce the nput cuent s equal t q c / and the utput cuent s equal t q/, the cuent ganbandwdth pduct s G q / f q / 2 c (8) F B, at =1/, and assumng q c = q, G 1 T f 2 2 f T (9) f T T ) s a wdely quted paamete used t cmpae benchmak actve devces. Smetmes f T T ) s ntepeted as a measue f the maxmum speed a devce can dve a eplca f tself. It s easy t cmpute and hstcally has been easy t measue wth bdges and late usng Spaamete test equpment. Hweve, f T des have ntepetatve lmtatns because t s defned as cuent nt a shtccut utput. 9

10 Theefe, t gnes the effect f bth nput esstance and utput capactance upn actual ccut pefmance. Lkewse, vltage and pwe gan expessns can be deved. It s necessay t defne the utput mpedance befe ethe can be quantfed hweve. Let R be the effectve utput esstance at the utput temnal f the actve devce. We shall make the assumptn that nput and utput R tme cnstants ae dentcal, that s, R = R. That may nt be tue n geneal, but we must assume smethng t defne these utput paametes and t nt t fa fm ealty n many applcatns. The vltage gan G v can be expessed n tems f G, R G G G v R, (10) whee R s the paallel equvalent utput esstance fm all esstances at the utput nde. The pwe gan G p s cmputed fm the pduct f G G v alng wth the pwe ganbandwdth pduct. These esults ae lsted n Table 1 as summazed fm Jhnsn and Rse [1]. These smple expessns ae vald f all devces as ntepeted fm the chage cntl pespectve. They pvde f a fstde cmpasn, n tems f a few smple paametes, amng the actve devces cmmnly avalable. Fm an examnatn f Table 1 t s evdent that maxmzng and mnmzng leads t hghe tanscnductance, hghe paametc gans and geate fequency espnse. Ths s an mptant bsevatn n undestandng hw t mpve upn the pefmance f any actve devce. 10

11 Wheeas f T has lmtatns, the fequency at whch the maxmum pwe gan extaplates t unty, dented by max, s a me useful ndcat f the fequency lmt f the devce s actve egn. The pmay lmtatn f max s that t s vey dffcult t measue dectly and s theefe usually extaplated fm Spaamete measuements n whch the extaplatn s an appxmatn. The smple chage cntl mdel s useful because f the physcal nsght t gves n undestandng actve devces. Fst, all actve devces have ntenal capactance fm the pesence f chage n the cntllng electde and n the tanst egn. Evey actve devce expeences a 20 db/decade gan fallff because f the exstence f capactance. In a feldeffect tansst, s establshed by the cuplng f the chage n the gate electde t the chage n the channel. In cntast, n a bpla junctn tansst cnssts f bth the cntllng chage and the cntlled chage (.e., the mnty cae chage n tanst) cexstng smultaneusly n the base egn. F ths easn s geneally much geate n a bpla tansst than n a feldeffect tansst ths s the pncple easn bpla tanssts aea capable f achevng much geate tanscnductance g m than feldeffect devces. Tansst desgnes ty t maxmze as much as pssble whle stll achevng the values needed f the tansst paametes. 11

12 Refeences [1] E. O. Jhnsn and A. Rse, Smple geneal analyss f amplfe devces wth emtte, cntl, and cllect functns, Pceedngs f the IRE, 47, 407, [2] E. M. hey, and D. E. Hpe, Amplfyng Devces and LwPass Amplfe Desgn, Wley, New Yk, 1968, haptes 2 and 5. [3] R. Beaufy, and J. J. Spakes, The junctn tansst as a chagecntlled devce, ATE Junal, 13, 310, Table 1. Afte Jhnsn & Rse [1] Paamete Symbl Expessn Tanscnductance g m T uent Amplfcatn G 1 T Vltage Amplfcatn G v 1 T Pwe Amplfcatn G p = G G v uent GanBandwdth Pduct G f 1 Vltage GanBandwdth Pduct G v f 1 Pwe GanBandwdth Pduct G p f 2 1 Nte: Table assumes R = R. 2 These ntes wee taken fm D. B. Estech, mpund Semcnduct Devces f Analg and Dgtal cuts, hapte 72, n The VLSI Handbk, 2 nd edtn, edted by WaKa hen, R Pess (Tayl & Fancs Gup), Bca Ratn, FL, 2007; pages 724 t 729. ISBN T 2 T 2 T 2 T 12