Part II Lectures 8-14 Bipolar Junction Transistors (BJTs) and Circuits

Size: px

Start display at page:

Download "Part II Lectures 8-14 Bipolar Junction Transistors (BJTs) and Circuits"

Allyson Lawrence
5 years ago
Views:

1 Pat ctus 8-4 pla Junctn Tanssts (JTs and cuts

2 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn pla Junctn Tanssts (JTs asc nstuctn: T tansst s a t-lay smcnduct dvc cnsstng f t tw n- and n p-typ lays f matal tw p- and n n-typ lays f matal T fm s calld an npn tansst, wl t latt s calld a pnp tansst t (wt symls a swn n Fg 8- T mddl gn f ac tansst typ s calld t as ( f t tansst Of t manng tw gns, n s calld mtt ( and t t s calld t cllct ( f t tansst F ac tansst typ, a junctn s catd at ac f t tw undas w t matal cangs fm n typ t t t Tf, t a tw junctns: mtt-as (- junctn and cllct-as (- junctn T ut lays f t tansst a avly dpd smcnduct matals avng wdts muc gat tan ts f t sandwcd p- n-typ matal T dpng f t sandwcd lay s als cnsdaly lss tan tat f t ut lays (typcally 0: lss Ts lw dpng lvl dcass t cnductvty (ncass t sstanc f ts matal y lmtng t num f "f" cas (mtt n p n (llct p n p - junctn (as - junctn Fg 8- T dc asng s ncssay t stals t pp gn f patn f ac amplfcatn swtcng pupss Tal 8- sws t tansst patn gns and t pups wt spct t t asng f t - and - junctns Tal 8- Junctns asng Opatn gn Pups - junctn as - junctn as Actv gn Amplfcatn Fwad-asd vs-asd 2 utff gn vs-asd vs-asd Swtcng 3 Satuatn gn Fwad-asd Fwad-asd T avatn JT, fm pla junctn tansst, s ftn appld t ts t-tmnal dvc T tm pla flcts t fact tat ls and lctns patcpat n t njctn pcss nt t ppstly plazd matal f nly n ca s mplyd (lctn l, t s cnsdd a unpla dvc Suc a dvc s t fld-ffct tansst (FT

3 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 2 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn Actv gn Opatn: T asc patn f t tansst wll nw dscd usng t pnp tansst f Fg 8-2 T patn f t npn tansst s xactly t sam f t ls playd y t lctn and l a ntcangd Wn t - junctn s fwad-asd, a lag num f majty cas wll dffus acss t fwad-asd p-n junctn nt t n-typ matal (as Snc t as s vy tn and as a lw cnductvty (lgtly dpng, a vy small num f ts cas wll tak ts pat f g sstanc t t as tmnal T lag num f ts majty cas wll dffus acss t vs-asd - junctn nt t p-typ matal (cllct T asn f t latv as wt wc t majty cas can css t vs-asd - junctn s asly undstd f w cnsd tat f t vs-asd dd t njctd majty cas wll appa as mnty cas n t n-typ as gn matal mnng ts wt t fact tat all t mnty cas n t dpltn gn wll css t vs-asd junctn f a dd accunts f t flw ndcatd n Fg 8-2 Fg 8-2 Applyng Kcff's cunt law t t tansst f Fg 8-2, w tan [8] T cllct cunt, wv, s cmpsd f tw cmpnnts: t majty and mnty cas as ndcatd n Fg 8-2 T mnty-cunt cmpnnt s calld t lakag cunt and s gvn t syml O ( cunt wt mtt tmnal Opn T cllct cunt, tf, s dtmnd n ttal y q [82] majty O mnty [82]

Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 3 f 8 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn mmn-as ( nfguatn: T cmmn-as cnfguatn wt npn and pnp tanssts a ndcatd

4 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 3 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn mmn-as ( nfguatn: T cmmn-as cnfguatn wt npn and pnp tanssts a ndcatd n Fg 8-3 T cmmn-as tmnlgy s dvd fm t fact tat t as s cmmn t t nput and utput sds f t cnfguatn n addtn, t as s usually tmnal clsst t, at, t gund ptntal Fg 8-3 n t dc md t lvls f and du t t majty cas a latd y a quantty calld alpa (α dc and dfnd y t fllwng quatn: α dc [83] W and a t lvls f cunt at t pnt f patn and α dc, f pactcal dvcs: 0900 α dc 0998 Snc alpa s dfnd slly f t majty cas and fm Fg 8-4, q [82] cms α [84] O T nput (mtt caactstcs f a cnfguatn a a plt f t mtt (nput cunt ( vsus t as-t-mtt (nput vltag ( f a ag f valus f t cllctt-as (utput vltag ( as swn n Fg 8-5 Snc, t xact sap f ts - cav wll dpnd n t vs-asng utput vltag, T asn f ts dpndncy s tat t gat t valu f, t m adly mnty cas n t as a swpt tug t - junctn T ncas n mtt-t-cllct cunt sultng fm an ncas n mans t mtt cunt wll gat f a gvn valu f as-t-mtt vltag ( Fg 8-4 Fg 8-5

Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 4 f 8 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn T utput (cllct caactstcs f cnfguatn wll a plt f t cllct (utput cunt

5 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 4 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn T utput (cllct caactstcs f cnfguatn wll a plt f t cllct (utput cunt ( vsus cllct-t-as (utput vltag ( f a ang f valus f mtt (nput cunt ( as swn n Fg 8-6 T cllct caactstcs av t asc gn f ntst, as ndcatd n Fg 8-6, t actv, cutff, and satuatn gns Actv gn: > 0 and α utff gn: 0 and O Satuatn gn: Fg 8-6 < 0 and ( sat ( sat F ac stuatns w t pnt f patn mvs n t caactstc cav, an ac alpa (α ac s dfnd y Δ α ac [85] Δ cnst T ac alpa s fmally calld t cmmn-as, st-ccut, amplfcatn fact, and f mst stuatns t magntuds f α ac and α dc a qut cls, pmttng t us f t magntud f n f t Fg 8-7 sws w t cmmn-as utput caactstcs appa wn t ffcts f akdwn a ncludd Nt t suddn upwad swng f ac cuv at a lag valu f T cllct-t-as akdwn vltag wn 0 (mtt pn s dsgnd O Fg 8-7 Tansst Amplfcatn Actn: T asc vltag-amplfyng actn f t cnfguatn can nw dscd usng t ccut f Fg 8-8 T dc asng ds nt appa n t fgu snc u ntst wll lmtd t t ac spns F t cnfguatn, t nput sstanc twn t mtt and t as f a tansst wll typcally vay fm 0 t 00 Ω, wl t utput sstanc may vay fm 00 kω t MΩ T dffnc n sstanc s du t t fwad-asd junctn at t nput (as t mtt and t vs-asd junctn at t utput (as t cllct Usng ffctv valus and a cmmn valu f 20 Ω f t nput sstanc, w fnd tat

6 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 5 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn / 200m / 20Ω 0mA f w assum f t mmnt tat α ac ( c, 0mA and ( 0mA(5kΩ 50 T vltag amplfcatn s Fg 8-8 Av / 50 / 200m 250 Typcal valus f vltag amplfcatn f t cmmn-as cnfguatn vay fm 50 t 300 T cunt amplfcatn ( / s always lss tan f t cnfguatn Ts latt caactstc suld vus snc α and α s always lss tan T asc amplfyng actn was pducd y tansfng a cunt fm a lw-t a g-sstanc ccut T cmnatn f t tw tms n talcs sults n t lal tansst; tat s, tansf sst tansst mmn-mtt ( nfguatn: T cmmn-mtt cnfguatn wt npn and pnp tanssts a ndcatd n Fg 8-9 T xtnal vltag suc s usd t fwad as t - junctn and t xtnal vltag suc s usd t vs as - junctn T magntud f must gat tan t nsu t - junctn mans vs asd, snc, as can sn n t Fg 8-9, Fg 8-9 Fm qs [8] and [84], w tan α ( O aangng ylds α O [86] α α Fm Fg 8-0, q [86] cms O O α 0 [87] Fg 8-0

7 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 6 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn n t dc md t lvls f and a latd y a quantty calld ta ( dc and dfnd y t fllwng quatn: dc [88] W and a t lvls f cunt at t pnt f patn F pactcal dvcs t lvls f dc typcally angs fm aut 50 t v 500, wt mst n t md ang On spcfcatn sts dc s usually ncludd as F wt dvd fm an ac yd quvalnt ccut F ac stuatn an ac ta ( ac as n dfnd as fllws: Δ ac [89] Δ cnst T fmal nam f ac s cmmn-mtt, fwad-cunt, amplfcatn fact and n spcfcatn sts ac s usually ncludd as f A latnsp can dvlpd twn and α usng t asc latnsps ntducd tus fa Usng / w av /, and fm α / w av / α Susttutng nt w av / α / and dvdng t sds f t quatn y wll sult n / α / α α ( α s tat α α [80] α n addtn, call tat O O /( α ut usng an quvalnc f /( α dvd fm t av, w fnd tat O ( O [8] O O ta s patculaly mptant paamt caus t pvds a dct lnk twn cunt lvls f t nput and utput ccuts f cnfguatn Tat s, and snc [82] O w av ( [83]

Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 7 f 8 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn T nput (as caactstcs f t cnfguatn a a plt f t as (nput cunt ( vsus t

as small Wn t as s small, t a fw cmnatns f njctd mnty cas and t s a cspndng ductn n as cunt ( Fg 8- Fg 8-2 T utput (cllct caactstcs f cnfguatn a a plt f t cllct (utput cunt ( vsus cllct-t-mtt (utput

8 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 7 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn T nput (as caactstcs f t cnfguatn a a plt f t as (nput cunt ( vsus t as-t-mtt (nput vltag ( f a ang f valus f cllct-t-mtt (utput vltag ( as swn n Fg 8- Nt tat ncass as dcass, f a fxd valu f A lag valu f sults n a lag vs as f t - junctn, wc wdns t dpltn gn and maks t as small Wn t as s small, t a fw cmnatns f njctd mnty cas and t s a cspndng ductn n as cunt ( Fg 8- Fg 8-2 T utput (cllct caactstcs f cnfguatn a a plt f t cllct (utput cunt ( vsus cllct-t-mtt (utput vltag ( f a ang f valus f as (nput cunt ( as swn n Fg 8-2 T cllct caactstcs av t asc gn f ntst, as ndcatd n Fg 8-2, t actv, cutff, and satuatn gns Actv gn: > 0 and utff gn: 0 and O Satuatn gn: 0 and / mmn-llct ( nfguatn: ( sat ( sat T td and fnal tansst cnfguatn s t cmmn-cllct cnfguatn, swn n Fg 8-3 wt npn and pnp tanssts T cnfguatn s usd pmaly f mpdanc-matcng pupss snc t as a g nput mpdanc and lw utput mpdanc, ppst t tat wc s tu f t cmmn-as and cmmn-mtt cnfguatns Fm a dsgn vwpnt, t s n nd f a st f cmmn-cllct caactstcs t cs t ccut paamts T ccut can dsgnd usng t cmmn-mtt caactstcs F all pactcal pupss, t utput caactstcs f t cnfguatn a t sam as f t cnfguatn F t cnfguatn t utput caactstcs a a plt f mtt (utput cunt ( vsus cllct-t-mtt (utput vltag (, f a ang f valus f as (nput

9 Unvsty f Tcnlgy pla Junctn Tanssts lctcal and lctnc ngnng Dpatmnt ctu gt - Pag 8 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn cunt ( T utput cunt, tf, s t sam f t t cmmn-mtt and cmmn-cllct caactstcs T s an almst unntcal cang n t vtcal scal f f t cmmn-mtt caactstcs f s placd y f t cmmn-cllct caactstcs (snc α, Fg 8-3 Tansst asng and Tmnal dntfcatn: Wnv pssl, t tansst casng wll av sm makng t ndcat wc lads a cnnctd t t mtt, cllct, as f a tansst A fw f t mtds cmmnly usd a ndcatd n Fg 8-4 xcss: Fg 8-4 Gvn an α dc f 0998, dtmn f 4 ma 2 Dtmn α dc f 28 ma and 20 µa 3 Fnd f 40 µa and α dc s Gvn tat α dc 0987, dtmn t cspndng valu f 5 Gvn dc 20, dtmn t cspndng valu f α 6 Gvn tat dc 80 and 20 ma, fnd and 7 A tansst as O 48 na and α 0992 Fnd and O Fnd ts (xact cllct cunt ( wn 30 μa Fnd t appxmat cllct cunt, nglctng lakag cunt

Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag f 0 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn D asng cuts f JTs asc ncpts: T analyss dsgn f a tansst

utput ac pw lvl s t sult f a tansf f ngy fm t appld dc suppls T analyss dsgn f any lctnc amplf tf as tw cmpnnts: t dc ptn and t ac ptn Ftunatly, t suppstn tm s applcal and t nvstgatn f

lctu s an all-nclusv tm f t applcatn f dc vltags t stals a fxd lvl f cunt and vltag F tansst amplfs t sultng dc cunt and vltag stals an patng pnt n t caactstcs tat dfn t gn tat wll

caactstc wt fu patng pnts ndcatd T asng ccut can dsgnd t st t dvc patn at any f ts pnts ts wtn t actv gn T maxmum atngs a ndcatd n t caactstcs f Fg 9- y a zntal ln f t maxmum cllct

10 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn D asng cuts f JTs asc ncpts: T analyss dsgn f a tansst amplf qus a knwldg f t t dc and ac spns f t systm T ftn t s assumd tat t tansst s a magcal dvc tat can as t lvl f t appld ac nput wtut t assstanc f an xtnal ngy suc n actualty, t mpvd utput ac pw lvl s t sult f a tansf f ngy fm t appld dc suppls T analyss dsgn f any lctnc amplf tf as tw cmpnnts: t dc ptn and t ac ptn Ftunatly, t suppstn tm s applcal and t nvstgatn f t dc cndtns can ttally spaatd fm t ac spns Hwv, n must kp n mnd tat dung t dsgn syntss stag t cc f paamts f t qud dc lvls wll affct t ac spns, and vc vsa T tm asng appang n t ttl f ts lctu s an all-nclusv tm f t applcatn f dc vltags t stals a fxd lvl f cunt and vltag F tansst amplfs t sultng dc cunt and vltag stals an patng pnt n t caactstcs tat dfn t gn tat wll mplyd f amplfcatn f t appld sgnal Snc t patng pnt s a fxd pnt n t caactstcs, t s als calld t quscnt pnt (avatd Q-pnt y dfntn, quscnt mans qut, stll, nactv Fg 9- sws a gnal utput dvc caactstc wt fu patng pnts ndcatd T asng ccut can dsgnd t st t dvc patn at any f ts pnts ts wtn t actv gn T maxmum atngs a ndcatd n t caactstcs f Fg 9- y a zntal ln f t maxmum cllct cunt max and a vtcal ln at t maxmum cllct-t-mtt vltag max T maxmum pw cnstant s dfnd y t cuv P max n t sam fgu At t lw nd f t scals a t cutff gn, dfnd y 0 μa, and t satuatn gn, dfnd y (sat Fg 9-

Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 2 f 0 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn Standad asng cuts: Fxd-as cut: Fg 9-2a sws a fxd-as ccut Analyss: F t

11 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 2 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn Standad asng cuts: Fxd-as cut: Fg 9-2a sws a fxd-as ccut Analyss: F t nput (as-mtt ccut lp as swn n Fg 9-2: 0 [9a] F t utput (cllct-mtt ccut (a lp as swn n Fg 9-2c: 0 [9] F t tansst tmnal vltags: 0 [9c] ( ad-n Analyss: Fm q [9] and Fg 9-3: Fg 9-2 At cutff gn: [92a] 0 At satuatn gn: [92] 0 Q (c Dsgn: F an ptmum dsgn: Q 2 Q ( sat 2 2 [9-3] Fg 9-3 Q

Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 3 f 0 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn 2 mtt-stalzd as cut: Fg 9-4a sws an mtt-stalzd as ccut Analyss: F t

12 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 3 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn 2 mtt-stalzd as cut: Fg 9-4a sws an mtt-stalzd as ccut Analyss: F t nput (as-mtt ccut lp as swn n Fg 9-4: 0 ( [94a] ( F t utput (cllct-mtt ccut (a lp as swn n Fg 9-4c: 0 ( [94] F t tansst tmnal vltags: [94c] ( ad-n Analyss: Fm q [94] and Fg 9-5: Fg 9-4 At cutff gn: [95a] 0 At satuatn gn: [95] 0 (c Dsgn: F an ptmum dsgn: Q 2 Q ( sat 2 2( 0 Q Q [9-6] Fg 9-5

13 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 4 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn 3 ltag-dvd as cut: Fg 9-6a sws a vltag-dvd as ccut Analyss: F t nput (as-mtt ccut lp: xact Analyss: Fm Fg 9-6: T 2 [97a] Fm Fg 9-6c: 2 T 2 2 [97] Fm Fg 9-6d: (a T T 0 ( T T ( [97c] Appxmat Analyss: ( (c Fm Fg 9-6: f >> 2 > 2 >> Snc 0 > 2 Tus n ss wt 2 Tat s, 2 2 [98a] (d Snc ( t cndtn tat wll dfn wt t appxmatn appac can appld wll t fllwng: 0 2 [98] and [98c] ( F t utput (cllct-mtt ccut lp: Fg 9-6 ( [99]

14 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 5 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn ad-n Analyss: T smlats wt t utput ccut f t mtt-asd cnfguatn sult n t sam ntsctns f t lad ln f t vltag-dvd cnfguatn T lad ln wll tf av t sam appaanc as tat f Fg 9-5 T lvl f s f cus dtmnd y a dffnt quatn f t vltag-dvd as and t mtt-as cnfguatn Dsgn: F an ptmum dsgn: Q 2 Q ( sat 2 2( [90] xampl 9-: Dtmn t dc as vltag and t cunt f t vltag-dvd cnfguatn f Fg 9-6a wt t fllwng paamts: 22, 40, 39 kω, 2 39 kω, 0 kω, and 5 kω Slutn: xact: T 2 39k 39k 3 55Ω 2 (39k(22 T k 39k T T ( μA 355k (4(5k ( 40(605μ 0 ma Q 85 Q ( 22 (085m(0k 5k 223 Appxmat: Tstng: 02 ( 40(5k 0(39k 20 kω > 39kΩ (satsfd 2 (39k( k 39k Q 0 867mA 5k Q ( 22 (0867m(0k 5k 203

15 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 6 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn 4 ltag-fdack as cut: Fg 9-7a sws a vltag-fdack as ccut Analyss: F t nput (as-mtt ccut lp as swn n Fg 9-7: 0 0 [9a] ( F t utput (cllct-mtt ccut lp as swn n Fg 9-7c: 0 ( [9] ad-n Analyss: ntnung wt t appxmatn wll sult n t sam lad ln dfnd f t vltag-dvd and mtt-asd cnfguatns T lvls f Q wll dfnd y t csn as cnfguatn Dsgn: F an ptmum dsgn: Q 2 Q ( sat 2 2( 0 ( [9-2] (a ( (c Fg 9-7

Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 7 f 0 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn Ot

83μ (00k 8 3 xampl 9-3: (Tw Suppls Dtmn and f t ccut f Fg 9-9a Slutn: Fm Fg 9-9: T 2 82k 22k 73kΩ 20 20 3 85mA (a 2 82k 22k T 2

16 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 7 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn Ot asng cuts: xampl 9-2: (Ngatv Supply Dtmn and f t ccut f Fg 9-8 Slutn: 0 (K μA 00k ( 45(83μ 3 735mA ( 3735m(2k 4 48 Fg 9-8 ( 83μ (00k 8 3 xampl 9-3: (Tw Suppls Dtmn and f t ccut f Fg 9-9a Slutn: Fm Fg 9-9: T 2 82k 22k 73kΩ mA (a 2 82k 22k T 2 (385m(22k Fm Fg 9-9c: T T 0 (K ( T ( T ( μA 73k (2(8k ( 20(3539μ 4 25mA 20 (425m(27k 8 53 T T ( 53 (3539μ(73k 59 (c Fg 9-9

17 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 8 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn xampl 9-4: (mmn-as Dtmn and f t cmmn-as cnfguatn f Fg 9-0 Slutn: Applyng K t t nput ccut: mA 2k Applyng K t t utput ccut: 0 wt 0 (275m(24k 3 4 Fg m 458μA 60 xampl 9-5: (mmn-llct Dtmn and f t cmmn-cllct (mtt-fllw cnfguatn f Fg 9- Slutn: Applyng K t t nput ccut: 0 ( ( μA 240k (9(2k ( (9(4573μ 4 6mA Fg 9- Applyng K t t utput ccut: 0 20 (46m(2k 68

Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 9 f 0 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn xampl 9-6: (PNP Tansst Dtmn f t vltag-dvd as cnfguatn f Fg 9-2 Slutn:

18 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 9 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn xampl 9-6: (PNP Tansst Dtmn f t vltag-dvd as cnfguatn f Fg 9-2 Slutn: Tstng: 02 ( 20(k 0(0k 32kΩ 00kΩ( satsfd 2 (0k( k 0k 36 ( mA k 0 (K ( Fg (224m(24k k 0 6 xcss: F t fxd-asd cnfguatn f Fg 9-2a wt t fllwng paamts: 2, 50, 240 kω, and 22 kω, dtmn: Q, Q, Q,,, and 2 Gvn t dvc caactstcs f Fg 9-3a, dtmn,, and f t fxd-as cnfguatn f Fg 9-3 (a ( Fg 9-3

19 Unvsty f Tcnlgy D asng cts f JTs lctcal and lctnc ngnng Dpatmnt ctu Nn - Pag 0 f 0 Scnd Ya, lctncs, D Amd Saadn zzulddn 3 F t mtt as ccut f Fg 9-4a wt t fllwng paamts: 20, 50, 430 kω, 2 kω, and kω, dtmn:,,,,, and 4 Dsgn an mtt-stalzd ccut (Fg 9-4a at Q 2 ma Us 20 and an npn tansst wt 50 5 Dtmn t dc as vltag and t cunt f t vltag-dvd cnfguatn f Fg 9-6a wt t fllwng paamts: 8, 50, 82 kω, 2 22 kω, 56 kω, and 2 kω 6 Dsgn a ta-ndpndnt (vltag-dvd ccut t pat at Q 8 and Q 0 ma Us a supply f 20 and an npn tansst wt 80 7 Dtmn t quscnt lvls f Q and Q f t vltag-fdack ccut f Fg 9-7a wt t fllwng paamts: 0, 90, 250 kω, 47 kω, and 2 kω 8 Pv tat ( s t qud cndtn f an ptmum dsgn f t vltag-fdack ccut 9 Pv matmatcally tat Q f t vltag-fdack as ccut s appxmatly ndpndnt f t valu f ta 0 Fg 9-4 sws a t-stag ccut wt a supply f 20 GND stands f gund f all tanssts av a f 00, wat a t and f ac stag? 20 0μF 2kΩ 3kΩ v 0μF 0μF 50kΩ 0μF v 00kΩ 056kΩ 8kΩ 3kΩ 068kΩ GND Fg 9-4

20 Unvsty f Tcnlgy as Stalzatn lctcal and lctnc ngnng Dpatmnt ctu Tn - Pag f 5 Scnd Ya, lctncs, D Amd Saadn zzulddn asc Dfntns: as Stalzatn T stalty f systm s a masu f snstvty f a ccut t vaatns n ts paamts n any amplf mplyng a tansst t cllct cunt s snstv t ac f t fllwng paamts: O (vs satuatn cunt: duls n valu f vy 0 ncas n tmpatu (as-t-mtt vltag: dcas aut 75 m p ncas n tmpatu (fwad cunt gan: ncas wt ncas n tmpatu Any all f ts facts can caus t as pnt t dft fm t dsgn pnt f patn Stalty Facts, S(O, S(, and S(: A stalty fact, S, s dfnd f ac f t paamts affctng as stalty as lstd lw: S( O Δ Δ O O, cnst [0a] S( Δ Δ O, cnst [0] S( Δ Δ [0c] O, cnst Gnally, ntwks tat a qut stal and latvly nsnstv t tmpatu vaatns av lw stalty facts n sm ways t wuld sm m apppat t cnsd t quantts dfnd y qs [0a - 0c] t snstvty facts caus: t g t stalty fact, t m snstv t ntwk t vaatns n tat paamt T ttal ffct n t cllct cunt can dtmnd usng t fllwng quatn: Δ S( O ΔO S( Δ S( Δ [02]

21 Unvsty f Tcnlgy as Stalzatn lctcal and lctnc ngnng Dpatmnt ctu Tn - Pag 2 f 5 Scnd Ya, lctncs, D Amd Saadn zzulddn Dvatn f Stalty Facts f Standad as cuts: F t vltag-dvd as ccut, t xact analyss (usng Tvnn tm f t nput (as-mtt lp wll sult n: T T 0, and > ( T and ( O, O > T, ( ( ( T T O T [03] T patal dvatn f t q [03] wt spct t O wll sult: O ( T ( ( T 0 S( O ( ( ( T T [04a] Als, t patal dvatn f t q [03] wt spct t wll sult: ( T 0 S( ( T [04] T matmatcal dvlpmnt f t last stalty fact S( s m cmplx tan ncuntd f S( O and S( Tus, S( s suggstd y t fllwng quatn: ( / ( T S( [04c] ( 2 T

22 Unvsty f Tcnlgy as Stalzatn lctcal and lctnc ngnng Dpatmnt ctu Tn - Pag 3 f 5 Scnd Ya, lctncs, D Amd Saadn zzulddn F t mtt-stalzd as ccut, t stalty facts a t sam as ts tand av f t vltag-dvd as ccut xcpt tat T wll placd y Ts a: S( O ( ( ( [05a] S( ( [05] ( / ( S( [05c] ( 2 F t fxd-as ccut, f w plug n 0 t fllwng quatn wll sult: S ( [06a] O S( [06] S ( [06c] Fnally, f t cas f t vltag-fdack as ccut, t fllwng quatn wll sult: S( O ( ( ( ( [07a] S( ( ( [07] ( / ( S( [07c] ( ( 2

23 Unvsty f Tcnlgy as Stalzatn lctcal and lctnc ngnng Dpatmnt ctu Tn - Pag 4 f 5 Scnd Ya, lctncs, D Amd Saadn zzulddn xampl 0-: Dsgn a vltag-dvd as ccut usng a supply f 8, and an npn slcn tansst wt f 80 s 5, and st at ma and t stalty fact S( O at 38 2 F t ccut dsgnd n pat (, dtmn t cang n f a cang n patng cndtns sults n O ncasng fm 02 t 0 μa, dps fm 07 t 05, and ncass 25% 3 alculat t cang n fm 25 t 75 f t sam ccut dsgnd n pat (, f O 02 μa and 07 Slutn: Pat : / 2 8/ 2 9 (, 5 > 36kΩ 9 8 (m (5 > 5kΩ 5 (5k 7 5kΩ v ma, ( m(5k kΩ > [08a] ( ( T S( O > Fg 0- ( T (8(5k T 3 8 > T 4 4kΩ (8(5k T k T > T [08] 2 2 Fm qs [08a] and [08]: 44k 22 > 36kΩ 8 Fm q [08a]: 2 22 > 2 5kΩ 36k 2 8 Fg 0- sws t fnal ccut 8 75kΩ 80 5kΩ v

24 Unvsty f Tcnlgy as Stalzatn lctcal and lctnc ngnng Dpatmnt ctu Tn - Pag 5 f 5 Scnd Ya, lctncs, D Amd Saadn zzulddn Pat 2: S ( O 38, Δ O 0 μ 02μ 9 8μA 80 S( 0 ms ( T (8(5k 44k 635, Δ ( 25 / (80 00, ( / ( T (m / 80(5k 44k S( 0 473μA, ( 2 T (0(5k 44k Δ Δ S( O ΔO S( Δ S( Δ ( 38(98μ ( 0635m( 02 (0473μ( mA Pat 3: Snc O, duls n valu f vy 0 ncas n tmpatu Δ Tus T N 5 N 5, O (75 2 O (25 (2 (02μ 6 4μA 0 0 Δ O 6 4μ 02μ 6 2μA Snc, dcass aut 75 m p ncas n tmpatu Tus Δ T , ( 25 0 > 7 ( (75m Δ S( O ΔO S( Δ ( 38(62μ ( 0635m( mA xcss: Dv a matmatcal xpssn t dtmn t stalty fact S( Δ Δ f t mtt-stalzd as ccut 2 Dscuss and cmpa (y quatns twn t latv lvls f stalty f t fllwng asng ccuts: t fxd-as ccut, t mtt-stalzd as ccut, t vltag-dvd as ccut, and v t vltag-fdack ccut

25 Unvsty f Tcnlgy JT Swtcng cuts lctcal and lctnc ngnng Dpatmnt ctu lvn - Pag f 3 Scnd Ya, lctncs, D Amd Saadn zzulddn JT Swtcng cuts asc ncpts: T applcatn f tanssts s nt lmtd slly t t amplfcatn f sgnals Tug pp dsgn t can usd as a swtc f cmput and cntl applcatns T ccut f Fg -a can mplyd as an nvt n cmput lgc ccuty Nt tat t utput vltag s ppst t tat appld t t as nput tmnal n addtn, nt t asnc f a dc supply cnnctd t t as ccut T nly dc suc s cnnctd t t cllct utput sd and f cmput applcatns s typcally qual t t magntud f t "g" sd f t appld sgnal-n ts cas (a 5 0 Fg - ( Pp dsgn f t nvsn pcss qus tat t patng pnt swtc fm cutff t satuatn alng t lad ln dpctd n Fg - F u pupss w wll assum tat O 0 ma wn 0 μa (an xcllnt appxmatn n lgt f mpvng cnstuctn tcnqus, as swn n Fg - n addtn, w wll assum tat ( sat 0 at tan t typcal 0 t 03 lvl Wn 5, t tansst wll "n" and t dsgn must nsu tat t ccut s avly satuatd y a lvl f gat tan tat asscatd wt t cuv appang na t satuatn lvl T as cunt f t ccut f Fg -a s dtmnd y [] T satuatn lvl f cllct cunt (sat f t sam ccut s dfnd y ( sat [2] T lvl f n t actv gn just f satuatn sults can appxmatd y t fllwng quatn: ( sat (max [3] F t satuatn lvl w must tf nsu tat t fllwng s satsfd: > [4] (max

26 Unvsty f Tcnlgy JT Swtcng cuts lctcal and lctnc ngnng Dpatmnt ctu lvn - Pag 2 f 3 Scnd Ya, lctncs, D Amd Saadn zzulddn xampl -: fy tat t ccut swn n Fg -2 avs lk an nvt wn t nput swtcs twn 0 and 0 Assum tat t tansst s slcn and tat 50 Slutn: t s nly ncssay t vfy tat t tansst s satuatd wn μA 220k ( sat 0 (max 323μA (50(62k Tus, w av > (max, tf t tansst s 220kΩ satuatd, and t ccut s nvt Fg -2 xampl -2: 0 62kΩ 50 fy tat t ccut swn n Fg -3 s an nvt wn t nput swtcs twn 0 and -5 Wat mnmum valu f s qud? Assum tat t tansst s slcn Slutn: (4(5k Wn 0, 0 8, nc t 20k 5k tansst s at cutff, s tat D and D 2 a n and Wn 5, T 5 k 20k 4kΩ, 4 ( 4(5k ( 5(20k T 3 2, 5kΩ 20k 5k 20k 5k 2 20kΩ T μA k 4 T 4 W assum t tansst s at satuatn, 0, Fg -3 s tat D and D 2 a ff and 20 ( sat 2 5mA, 6k (max ( sat / 25mA/ F t tansst t n satuatn, ( sat 25m > (max > > μ D D2 S G 20 6kΩ

27 Unvsty f Tcnlgy JT Swtcng cuts lctcal and lctnc ngnng Dpatmnt ctu lvn - Pag 3 f 3 Scnd Ya, lctncs, D Amd Saadn zzulddn xcs: Dsgn t tansst nvt f Fg -4 t pat wt a satuatn cunt f 8 ma usng a tansst wt a ta f 00 Us a lvl f qual t 20% f (max and standad sst valus t Fg -4 2 fy tat t ccut swn n Fg -5 s a pstv NAND wn t nput swtcs twn 0 and 2 Nglct suc mpdanc and junctn satuatn vltags and dd vltags n fwad dctn Fnd t mnmum valu f kΩ D 5kΩ 2 A D 2 5kΩ 3 00kΩ 2 Fg -5

Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag f 9 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn JT Mdlng and A quvalnt cut asc ncpts: T ky t t tansst

gapcal syml f t dvc can placd n t scmatc y ts ccut and t asc mtds f ac ccut analyss (ms analyss, ndal analyss, and Tvnn's tm can appld t dtmn t spns f t ccut T a tw scls f tugt n pmnnc tday gadng t

28 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn JT Mdlng and A quvalnt cut asc ncpts: T ky t t tansst small-sgnal analyss s t us f ac quvalnt ccuts mdls A mdl s t cmnatn f ccut lmnts, pply csn, tat st appxmats t actual av f a smcnduct dvc (JT und spcfc patng cndtns Onc t ac quvalnt ccut as n dtmnd, t gapcal syml f t dvc can placd n t scmatc y ts ccut and t asc mtds f ac ccut analyss (ms analyss, ndal analyss, and Tvnn's tm can appld t dtmn t spns f t ccut T a tw scls f tugt n pmnnc tday gadng t quvalnt ccut t susttutd f t tansst: yd and mdl n summay, t ac quvalnt ccut f t JT amplf s tand y (s Fg 2-: Sttng all dc sucs t z and placng tm y a st-ccut quvalnt 2 placng all capacts y a st-ccut quvalnt 3 mvng all lmnts ypassd y t st-ccut quvalnts ntducd y staps and 2 4 dawng t ccut n a m cnvnnt and lgcal fm 5 Us t yd quvalnt ccut f t JT t cmplt t quvalnt ccut f t amplf 6 Fnally, t fllwng paamts a dtmnd f t amplf: a nput mpdanc (Z Output mpdanc (Z c ltag gan (A v d unt gan (A Pas latnsp (θ (a ( (c Fg 2-

Ω, st-ccut nput mpdanc paamt 0 2 ( untlss, pn-ccut vs tansf vltag at paamt 0 2 f ( untlss, st-ccut fwad tansf cunt at

29 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 2 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn T Hyd (-paamts quvalnt Mdl: F t gnal yd tw-pt systm f Fg 2-2: [2a] [2] Fg 2-2 w ( Ω, st-ccut nput mpdanc paamt 0 2 ( untlss, pn-ccut vs tansf vltag at paamt 0 2 f ( untlss, st-ccut fwad tansf cunt at paamt 0 22 ( S, pn-ccut utput admttanc paamt 0 Fm t JT yd quvalnt ccut f Fg 2-3, qs [2a] and [2] cms: f [22a] [22] Fg 2-3

30 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 3 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn S S f / Z Z Gan and mpdanc mputatn f t mplt Hyd quvalnt cut: F t ccut f Fg 2-4, Fg 2-4 t vltag gan (A v / ;,, and f > f f v A ( [23a] t cunt gan (A / ; f f > f A [23] t nput mpdanc (Z / ;, and > A > f Z [23c] t utput mpdanc (Z / wn S 0 ; 0 ( S S > S, and f > S f > S f Z [23d]

Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 4 f 9 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn Typs f Hyd Paamts: Snc t a t typs f JT cnfguatn (,, and, t

31 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 4 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn Typs f Hyd Paamts: Snc t a t typs f JT cnfguatn (,, and, t a t dffnt ways tat t nput and utput can dfnd and tf t cspndng sts f -paamts as swn n Tal 2- f all f t -paamts valus n n cnfguatn a knwn, tn t valus cspndng t any t cnfguatn can dtmnd T cmmn-mtt valus f t -paamts a t ns mst ftn gvn Tal 2- JT cnfguatn -paamts sts mmn-mtt, f,, 2 mmn-llct c, fc, c, c 3 mmn-as, f,, T yd quvalnt ccuts f t and tansst cnfguatn a swn n Fg 2-5 (a and ( spctvly (a ( Fg 2-5

32 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 5 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn Tal 2-2 lsts typcal paamt valus n ac f t t tansst cnfguatns (,, and f t ad ang f tanssts avalal tday Tal 2-2 -paamts kω kω 20kΩ f μs 25 μs 05 μs / 40 kω 40 kω 2 MΩ Gapcal Dtmnatn f t Hyd Paamts: T paamts and a dtmnd fm t nput as caactstcs, wl t paamts f and a tand fm t utput cllct caactstcs as swn n Fg 2-6 Δv Δ cnst 5kΩ Δv Δv c cnst Δc Δc f 00 33μS Δ Δv cnst Fg 2-6 c cnst

Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 6 f 9 Scnd Ya, lctncs, 2009-200 D Amd Saadn zzulddn F t tansst ws caactstcs av appad n Fg 2-6, t sultng yd

33 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 6 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn F t tansst ws caactstcs av appad n Fg 2-6, t sultng yd small-sgnal quvalnt ccut s swn n Fg 2-7 Fg 2-7 T typcal valus f -paamts f tansst cnfguatn a swn n Tal 2-3 Tal 2-3 x paamts Mn Max Unt nput mpdanc kω ltag fdack at Small-sgnal cunt gan f Output admttanc 0 30 μs Appxmat Hyd quvalnt Mdl: Snc s nmally a latvly small quantty, ts mval s appxmatd y 0 and c 0, sultng n a st-ccut quvalnt f t fdack lmnt T sstanc dtmnd y / s ftn lag nug t gnd n cmpasn t a paalll lad pmttng ts placmnt y an pn-ccut quvalnt f t mdl as swn n Fg 2-8 Z f c Z c Z Fg 2-8 F t ccut f Fg 2-8, Z, and Z c Z f, and Av f A Z c A

Ya, lctncs, 2009-200 D Amd Saadn zzulddn T quvalnt

mtt f tansst cnfguatn (dynamc sstanc f t fwad dd

(dynamc sstanc f t vs dd s: als; Z, and Z ( c α,

34 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 7 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn T quvalnt Mdl: Tansst nfguatn: Fm Fg 2-9, t nput mpdanc at t mtt f tansst cnfguatn (dynamc sstanc f t fwad dd can d dtmnd y: 26m [24] t utput mpdanc at t cllct (dynamc sstanc f t vs dd s: als; Z, and Z ( c α, and Z > α Av c c α, and A > A α (a ( (c (d ( Fg 2-9

35 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 8 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn Tansst nfguatn: Fm Fg 2-0; c, c (, and Z Z c, v A c A (a ( (c (d ( (g Fg 2-0

2- Appxmat nvsn Fmulas f Hyd and Mdls: T appxmat cnvsn fmulas f yd and mdls f and cnfguatns a lstd n Tal 2-4 Tal 2-4

36 Unvsty f Tcnlgy JT Mdlng and A quvalnt cut lctcal and lctnc ngnng Dpatmnt ctu Twlv - Pag 9 f 9 Scnd Ya, lctncs, D Amd Saadn zzulddn Hyd sus Mdl: T yd vsus mdl f and tansst cnfguatns a swn n Fgs 2- (a and ( spctvly (a ( Fg 2- Appxmat nvsn Fmulas f Hyd and Mdls: T appxmat cnvsn fmulas f yd and mdls f and cnfguatns a lstd n Tal 2-4 Tal 2-4 nfguatn nfguatn ( f c ( f c f f ( f α fc ( f / ( f c xcs: Gvn 3 ma, 00, and 40 kω, sktc: T and yd quvalnt mdls 2 T and quvalnt mdls

37 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn mmn-mtt nfguatn: JT Small-Sgnal Analyss T vltag dvd ccut f Fg 3- ncluds an mtt sst ( tat may may nt ypassd y an mtt capact ( n t ac dman S s S Z Z 2 Z Z Z n Fg 3- ypassd (asnc f : F t ac quvalnt ccut f Fg 3-2, c c S s Z Z f / Z Z Z n Fg 3-2 Usng quvalnt mdl: nput mpdanc: 2 Z Z Z Z Z n S S (

38 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 2 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Output mpdanc: Appxmat (nglctng ; xact (ncludng ; Z Z Z Z Z ltag gan: Appxmat (nglctng ; xact (ncludng ; ( c Z v A Z v A S v s s v Z Z A A s unt gan: Appxmat (nglctng ; xact (ncludng ; c c A ( ]( ( [ A Z ( ( S S s s Z A A s As an ptn: v Z A Z Z A v Z A Z Z A Pas latnsp: T ngatv sgn n t sultng quatn f A v vals tat a 80 pas sft ccus twn t nput and utput vltag sgnals

39 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 3 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Usng yd quvalnt mdl: Appxmat (nglctng ; xact (ncludng ; Z f ( Av f A ( ( A v f A [/ ( ( / f / ]( ( Unypassd (nclud f : F t appxmat ac quvalnt ccut ( / Ω f Fg 3-3, c c S s Z Z f Z Z Fg 3-3 Usng quvalnt mdl: nput mpdanc: [ ( ] Z ( ( Z Z [ ( ] ( Output mpdanc: Z Z Z ltag gan: Z c Z ( (

40 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 4 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn A v unt gan: c A c Z ( [ ( ] ( ( Pas latnsp: and a ut-f-pas y 80 Usng yd quvalnt mdl: Z ( f f f f ( Av f f f A ( ( f ( ( f mmn-as nfguatn: T cmmn-as cnfguatn f Fg 3-4 s caactzd as avng a latvly lw nput and a g utput mpdanc and a cunt gan lss tan T vltag gan, wv, can qut lag S S s Z Z Z Z Fg 3-4

41 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 5 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Usng quvalnt mdl: F t appxmat ac quvalnt ccut ( Ω f Fg 3-5, nput mpdanc: Z Z [lw] Output mpdanc: Z [g] Z ltag gan: cz / A v α( α S s ( Z [g] Z Fg 3-5 c α c Z Z unt gan: c A α c α [lss tan ] ( ( Pas latnsp: and a n-pas Usng yd quvalnt mdl: F t appxmat ac quvalnt ccut ( / Ω f Fg 3-6, Z Z Z Z S f( A s v f A ( ( Fg 3-6 [ f : -v quantty] c f c Z Z

42 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 6 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn mmn-llct (mtt-fllw] nfguatn: Wn t utput s takn fm t mtt tmnal f t tansst, an amplf ccut s fd t as mtt-fllw as swn n Fg 3-7 T mtt-fllw cnfguatn s fquntly usd f mpdanc-matcng pupss t psnts a g mpdanc at t nput and a lw mpdanc at t utput Als, t utput vltag s always slgtly lss tan t nput sgnal wt an n-pas latnsp twn tm S S s Z Z Z Z Fg 3-7 Usng quvalnt mdl: F t ac quvalnt ccut f Fg 3-8, c c S s Z Z f Z Fg 3-8 nput mpdanc: [ ( ] Z / ( ( [g] Z Z

43 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 7 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Output mpdanc: s S 0 [K] F t ccut f Fg 3-9a, S s T S, and T s S Tvnn w >> S > T S, T s, and (a s S ( 0 / S s S ( / S / f f ( s s ( S ( s ( S / Fg 3-9 Dawng t ccut t "ft" t av last quatn wll sult n t cnfguatn f Fg 3-9 Tus Z Z Z / [lw] Z ( S Z ltag gan: Av ( [lss tan ] A v s s s / unt gan: A ( [g] ( ( Pas latnsp: and a n-pas Z

44 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 8 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Usng yd quvalnt mdl: Z ( f f Z ( / A v S / f A v s ( s / f A ( ( f f f xampl 3-: F t JT amplf ccut f Fg 3-0 wt t fllwng paamts: 07, f 250, and / Ω, dtmn: (a, and dc utput vltag ( (, Z, Z, Z, and Z (c A v /, and A / (d A s /, and ac utput vltag ( v s 20 S s 750Ω S Z 2 25m 9kΩ Z 0kΩ 2 3kΩ Z 80Ω 820Ω Z 2kΩ Fg 3-0

45 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 9 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Slutn: Tstng: 02, 2 08k 082k kω, 250(k 0(0k, 250 k > 00k Satsfd, 2 20(0k , 28mA, 2 0k 9k k 26m 26m 20 3Ω, 28mA, and 28m 20 28m(3k ( kΩ, Z ( f 5 075k 25 (08k 50 26kΩ, 2 9k 0k 9 0kΩ, Z Z 9 0k 5026k 7 64kΩ, Z 3 kω, and Z 2 k 3k 2 4kΩ fz 250(24k Z 94(764k Av 94, and A Av 76 Z 5026k 2k Z 94(764k Av s Av Av 087, and s Z S 764k 075k A 087(25m 2775m v s s xampl 3-2: Dsgn t JT amplf ccut swn n Fg 3- t av a vltag gan magntud f 4, Z 337 kω, Z 3 kω, and Z 2kΩ Assum tat t tansst s slcn wt 00, kω, / Ω, and >02 20 S s S Z Z 2 Z Z Fg 3-

46 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 0 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Slutn: Z 3 kω, Z 2 k 3k 6kΩ Z 2 Av 4 0 5kΩ 26m 26m k 00 0Ω, 0 2 6mA 2 6m(05k 3, Q > [a] Z ( k 0(05k 5 5kΩ Z Z 3 37k 55k 3 kω 6 36k [] 2 2 Fm qs [a] and []: Fm q [a]: xampl 3-3: 36k 36k 0 36kΩ 0 4kΩ mplt t dsgn f t JT amplf ccut swn n Fg 3-2 f a vltag gan f 25, Z 24 kω, Z 2 kω Assum tat α 0 985, 07, and / Ω alculat, and A vs 9 S S Z Z s 20Ω 0m Z 4 Fg 3-2

47 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn Slutn: Z 2 4kΩ Z 2 k 24k 2kΩ αz 0985(2k Av Ω 26m 26m mA kΩ 65m Z 576 2k 5 64Ω Z 25(564 Av s Av 55 Z s A 55 (0m 550m v s s xcss: F ac n f t ccuts swn n Fg 3-3, wt a matmatcal xpssn t dtmn ac f t fllwng paamts y usng yd quvalnt mdl (a Z and Z ( Z and Z (c A and A v S s S Z F F 2 F Z Z Z S s S Z Z 2 Z Z (a ( Fg 3-3

48 Unvsty f Tcnlgy JT Small-Sgnal Analyss lctcal and lctnc ngnng Dpatmnt ctu Ttn - Pag 2 f 2 Scnd Ya, lctncs, D Amd Saadn zzulddn 2 F t cmmn-as amplf f Fg 3-4, dtmn t fllwng paamts usng t cmplt yd quvalnt mdl and cmpa t sults t ts tand usng t appxmat mdl (a Z and Z ( Z and Z (c A and A vs (d A and A s S 6kΩ f 0 20μS S s kω Z Z 3kΩ Z 3kΩ 6 2 Z 82kΩ Fg mplt t dsgn f t JT amplf ccut swn n Fg 3-5 f a vltag gan magntud f 205, Z 5k Ω, and Z 32 kω Assum tat 00, 07, F / F2 95, and / Ω Sktc t t sam tm scal as s 0 F F 2 s S S kω 2Snwt m Z F Z Z Z Fg 3-5

49 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn Fquncy spns f JT Amplfs w-fquncy spns f JT Amplfs: F t g-pass flt ccut f Fg 4-a, t utput and t nput vltags a latd y t vltag-dvd ul n t fllwng mann:, X wt t magntud f dtmnd y 2 2 X F spcal cas w X,, and 2 A v X 2 n "dcl" (d: G( d 20lg Av 20lg0 3d 0 2 A v, G( d,0d 0707, 3d f (Hz (a Fg 4- f ( At t fquncy f wtc X, t utput wll 707 % f t nput (a 3 d dp n gan, s Fg 4- f t ccut T fquncy (f at wtc ts ccus s dtmnd fm: X ω 2πf > f f : t lw-cutff fquncy 2π

50 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag 2 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn T apacts S,, and wll dtmn t lw-cutff fquncy (f f t ladd vltag dvd JT as cnfguatn swn n Fg 4-2, ut t sults can appld t any JT cnfguatn F t amplf ccut f Fg 4-2: T cutff-fquncy f S, w f S 2 π ( S, and 2 T cutff-fquncy f, S S s S 2 Fg 4-2 π f 2 ( w / T cutff-fquncy f, f 2π w f S S S, and T lw-cutff fquncy, f Max[ f S, f, f ]

51 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag 3 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn Mll's Tm and ts Dual: F t ccut f Fg 4-3a, Av ( Av,, and 2 Z Z F Z F Z F Z F /( Av 2 > > Z Z F /( Av Z Z F /( Av F wn Z F F >, w M Z M Av As swn n Fg 4-3, X F wn Z F X F >, w X > M Z X M Av ω( Av F ( A M v F 2 Z F F Z A v Z M A v M (a Fg 4-3 ( n a smla way, F > M Z Z F /( / Av, and / Av X F X M / Av ( / Av > ω F ( / A M v F T av sws us tat: F any nvtng amplf (pas sft f 80 twn nput and utput sultng n a ngatv valu f A v, t nput and utput capactanc wll ncasd y a Mll ffct capactanc snstv t t gan f t amplf and t ntlctd capactanc cnnctd twn t nput and utput tmnals f t actv dvc

52 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag 4 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn Hg-Fquncy spns f JT Amplfs: A fquncy spns f t lw-pass flt ccut f Fg 4-4a s gvn y Fg 4-4, w t g-cutff fquncy s dtmnd fm: f H f H : t g-cutff fquncy 2π,0d 0707, 3d A v, G( d f (Hz (a Fg 4-4 f H ( At t g-fquncy nd, t a tw facts tat wll dfn t -3 d pnt: t ccut capactanc (paastc and ntducd and t fquncy dpndnc f f cut (apactancs Paamts: n g-fquncy gn t capactv lmnts f t mptanc a t nt-lctd (twn tmnals capactancs ntnal t t actv dvc and t wng capactanc twn lads f t ccut n Fg 4-5, t vaus paastc capactancs (, c, and c f t tansst av n ncludd wt t wng capactancs ( and ntducd dung cnstuctn W W c S c S W 2 s W Fg 4-5

53 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag 5 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn T g-fquncy quvalnt mdl f t amplf ccut f Fg 4-5 appas n Fg 4-6 Nt t asnc f t capacts S,, and, wc a all assumd t n t st ccut stat at ts fquncs S s T T W M T W c M T T T Fg 4-6 F t ccut f Fg 4-6: T nput g cutff fquncy, f H 2π T w T S, and 2 W M ( A W v c T utput g cutff fquncy, f H 2π T w T, and / ( / A W c M W c v c T g-cutff fquncy, f Mn[ f H, f H H ]

54 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag 6 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn f ( aatn: T ta cutff fquncy (f s ant mptant tansst cutff fquncy T f, t fquncy w t f t tansst dp t 0707 f ts lw-fquncy valu, s gvn y f 2 π ( c f t fquncy f patn s ncasd av t f f t tansst, t wll cntnu t dcas vntually, w fnd a fquncy w t ; ts fquncy s calld t f T f t tansst T f T f a tansst s muc g tan t f T latn twn ts tw fquncs s f T f W f T : t gan-andwdt pduct fquncy f Fnally, n data st, t g-fquncy paamts at tan paamts a ftn spcfd f a tansst T fllwng quatn pmts a dct cnvsn f dtmnng f f f α and α a spcfd f fα ( α xampl 4-: F t JT amplf ccut swn n Fg 4-7, wt t fllwng paamts: 36 pf, c 4 pf, c pf, W 6 pf, W 8 pf, and / Ω Dtmn f, f H, W, f, and f T 2 Sktc t fquncy spns 20 40kΩ 4kΩ S s S 0μF kω 2 0kΩ μf 00 2kΩ 20μF 22kΩ Fg 4-7

55 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag 7 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn Slutn: Tstng: 02, 00(2k 0(0k, 200 kω > 00kΩ Satsfd 2 20(0k , 65mA 2 40k 0k 2k 26m 26m 5 76Ω, 00(576 58kΩ 65m 22k 4k Av md k 0k 58k 32kΩ, f Hz S 2π ( S S 2π (k 32k(0μ 7 / kω, 4 f Hz 2π ( 2π (22k 4k(μ 26 S S 2 k 40k 0k 0 89kΩ, S 089k [ ] 2k [ 576] 24 35Ω 00 f Hz π 2π (2435(20μ T lw-cutff fquncy, f Max[ f, f, f ] f f k 32k 0 kω T S 57 H W 2π T M W S Max[ 7,26,327] 327Hz ( A 6 p 36 p ( 90(4 p 406 pf kHz 2π (057k(406 p 2 2k 4k kω T 42 H W 2π T c M W c 8622MHz 2π (42k(3p T g-cutff fquncy, f Mn[ f, f ] H v c ( / A 8p p ( /90(4 p 3pF v c H H Mn[ k,8622M ] kHz T andwdt, W f H f k kHz

56 Unvsty f Tcnlgy Fquncy spns f JT Amplfs lctcal and lctnc ngnng Dpatmnt ctu Futn - Pag 8 f 8 Scnd Ya, lctncs, D Amd Saadn zzulddn T ta cutff fquncy, f 2 π ( c 252MHz 2 π (00(576(36 p 4 p T gan-andwdt pduct, f T f 00 (252M 252MHz T fquncy spns f t lw- and g-fquncy gns, andwdt, ta cutff fquncy, and gan-andwdt pduct fquncy a swn n Fg 4-8 Av Av md d f S f f f H f f T - 3 d k 0k 00k M 0M f W f H f H 00M f (lg scal - 5 Fg 4-8 xcs: F t JT amplf ccut f Fg 4-9, dtmn t lw- and g-cutff fquncs S c c 8pF 24 pf 2 pf 80 W W 8 pf 0pF S s 0μF 0kΩ 2kΩ 33kΩ 4 6 0μF 47kΩ Fg 4-9

Unit 3: Transistor at Low Frequencies

Unit 3: Transistor at Low Frequencies Unt 3: Tansst at Lw Fquncs JT Tansst Mdlng mdl s an qualnt ccut that psnts th chaactstcs f th tansst. mdl uss ccut lmnts that appxmat th ha f th tansst. Th a tw mdls cmmnly usd n small sgnal analyss f