Mixed-Signal IC Design Notes set 2: Fundamentals of Analog IC Design

Transcription

1 EE94J /594J not, M. odwll, copyrightd 0 Mixd-Signal Dign Not t : Fundamntal of Analog Dign Mark odwll Univrity of alifornia, Santa Barara rodwll@c.uc.du , fax

2 Tranitor ircuit Dign EE94J /594J not, M. odwll, copyrightd 0 Thi not t -rviw th aic -tart at th lvl of a firt dign cour -mov vry quickly Thi will -talih a common trminology -accommodat capal tudnt having minimal ackground in.

3 EE94J /594J not, M. odwll, copyrightd 0 D modl D ia analyi

4 arg-signal Modl For Bia Analyi EE94J /594J not, M. odwll, copyrightd 0 c - Providd that c xp(...not that c / > 0, T ) and c / β, whr kt / q i pcifid intrnal to th mittr ritanc T x Th x drop i ignificant for HBT oprating at currnt dniti nar that rquird for pak tranitor andwidth.

5 D Bia Exampl: urrnt Mirror EE94J /594J not, M. odwll, copyrightd 0 rf c Q Q x x W hav and t ln( c ( / x ), ) t ln( c / ( x ) ) Aum that β >>, & aum that A E A E ( A E i th mittr ara). Thi impli x from which w find x c /, and c /,

6 Simplr D Modl for Bia Analyi EE94J /594J not, M. odwll, copyrightd 0 c c t i oftn ufficint in ia analyi to ignor th variation of with c and intad tak, on φ., on dpnd upon currnt dnity and tchnology. Biad at currnt dniti, on φ ~ within ~ 0% of 0.9 Modrn Si/SiG HBT 0.7 or 0.9 ngaa/np HBT.4 GaA/GanP HBT pak andwidth ia,

7 Simpl D Bia Exampl EE94J /594J not, M. odwll, copyrightd 0 c Q Q - f w nglct th Approximat c c c c c ( ( 0.9 ) / drop, thn 0.9 ) / φ 0.9 (SiG). 0 olt.

8 EE94J /594J not, M. odwll, copyrightd 0 Efficintly Handling Ba urrnt n Bia Analyi f on can olv imultanou quation : c whr drop iingificant, c c c ( / β, φ ) / c Q Q Quickr : find y itration : ) olv ) olv c ( c / β 3) u thi valu of φ) / to olv c ( φ - ) / Work cau any wll - dignd circuit ha only wakly dpndnt upon β. D ia

9 Typical ircuit Biaing in Mixd-Signal EE94J /594J not, M. odwll, copyrightd 0 rf rf Biaing with currnt mirror mor prci--- oftn mor compact ut load mittr nod with ---or wor and provid path for tag-tag coupling itiv iaing--- ritivly load mittr nod---lowr D prciion

10 Prolm with urrnt Mirror Biaing EE94J /594J not, M. odwll, copyrightd 0 rf tag-tag coupling through and th hard currnt mirror rfrnc...

11 Prolm with urrnt Mirror Biaing EE94J /594J not, M. odwll, copyrightd 0 Bcau of and output impdanc Z c, th currnt ourc ( jω) vari with frquncy. ( ω) j Z c W will driv thiin latr lctur. mplication : incrad common - mod gain at high frqunci common - mod intaility

12 Avoiding Thrmal ntaility EE94J /594J not, M. odwll, copyrightd 0 Givn that...not that d Th dvic ha om thrmal ritanc dt (Klvin/Watt). < < / dt d d x c kt Fat Bipolar normally u avoid thrmal runaway.thrmal runaway can alo rult from intrnal dvic tmpratur gradint. arg ara dvic mut thrfor avoidd...u array of allating. ( k d dt / q T 3/ ln( / q)ln( c c / / ) ( kt urrnt mirror i dt dp t dp d d dt thrmallyuntal if * / q)ln( / q)( d / dt ) ~ 300m mallr dvic with (proc dpndnt)...usb HBT proc put af maximum dvic ara ~ 0 quar micron at 0 ), o at contant c ( kt θ c c, c / / dp θ to ) 5 c c Q Q A/ cm x iaing rf x

13 EE94J /594J not, M. odwll, copyrightd 0 mall-ignal aand analyi

14 Hyrid-π Bipolar Tranitor Modl EE94J /594J not, M. odwll, copyrightd 0 x β / g m B i c τ f τ τ c g m -jωτ c,diff g m τ f j x E Accurat modl, ut too dtaild for quick hand analyi

15 EE94J /594J not, M. odwll, copyrightd 0 Ovrimplifid Modl for Quick Hand Analyi B g m B g m E E n mot high-frquncy circuit, th nod impdanc i low and c i thrfor ngligil. Nglcting in high-frquncy analyi i a poor approximation ut i nvrthl common in introductory tratmnt. Th "txtook" analy which follow u thi ovrimplifid modl. Th introductory tratmnt will latr rfind.

16 ommon Emittr Stag: Baic EE94J /594J not, M. odwll, copyrightd 0 7 ) in, T δ / δ β ( r ) ) δ 5) δ δ / β c q δ q 4) δ δ / g m ) δ δ c 3) δ E δ 6) δ δ ( r ) δ β ( r ) E 8) δ out / δin δout / δb q /( r ) q /( / gm) Gain i - /( / g ) ; Tranitor i β ( r q m in E )

17 Emittr Followr Stag: Baic EE94J /594J not, M. odwll, copyrightd 0 6 ) in, T δ / δ β ( r q ) 4) δ δ / β c 3) δ δ / g m ) δ δ c ) δ q δ 5) δ δ ( r q ) δ β ( r q ) q 7) δ out / δin δout / δe q /( r q ) q /( q / gm) Gain i /( / g ) ; Tranitor i β ( r q q m in E )

18 ommon-ba Stag: Baic EE94J /594J not, M. odwll, copyrightd 0 6) δ δ ( r / β ) in ) δ out q δ ) δ / δ r / β 7 in, T B 5) δ δ / g m ) δ δ c 7) δ / δ /( r / β ) out in 4) δ δ / β q c B q 3) δ δ / β c Gain i /( r / β ) ; Tranitor i r / β q in

19 Emittr Followr Output mpdanc ommon-ba Stag: Baic EE94J /594J not, M. odwll, copyrightd 0 EE45 /8 not, M. odwll, copyrightd B out, mittr out, amp 7 in, T B ) δ / δ r / β 5) δ δ / gm ) δ δ c 6) δ δ ( r / β ) in ) δ out q δ 7) δ / δ /( r / β ) out in 4) δ δ / β q c B q 3) δ δ / β c EE Gain i /( r / β ) ; Tranitor i r / β q in E.F.output impdanc i am prolm a.b. input impdanc r / β / g / β out, mittr B m B out, amp out, mittr EE

20 ncluding Bia ircuit itanc EE94J /594J not, M. odwll, copyrightd 0 in, Amp B B int B in, T q gn in gn B Th ar (trivially) addd in paralll with th tranitor trminal impdanc to dtrmin th nt circuit impdanc. From which, / /( in gn in, amp in, amp gn ), tc.

21 Baand Analyi Of Multitag ircuit EE94J /594J not, M. odwll, copyrightd 0 For aand analyi of multi-tag circuit, imply rak into individual tag. Q Q 3 Q Q 4 oad impdanc of th Nth tag includ th input impdanc of th (N) th tag Analyi i thn trivial... in out in in3 out Q Q 4 Q Q 3 in4 out3 in3 out in3 in in out in4 out3 in4

22 EE94J /594J not, M. odwll, copyrightd 0 mall-ignal aand analyi

23 EE94J /594J not, M. odwll, copyrightd 0 High-Frquncy Analyi: Th Gnral Prolm B 49 Ω x 6.4 ff c i 6500 Ω 3.7 ff ' π 350 Ω g m ' 8 ff diff j 38 ff x 4. 3 Ω B E 49 Ω x 6.4 ff c i 6500 Ω 3.7 ff ' π 350 Ω g m ' gn Q Q 8 ff diff j 38 ff x E 4. 3 Ω Analyzing frquncy rpon i difficult: cannot parat tag-y-tag Mthod #: nodal analyi: accurat, gnral, tdiou. Mthod #: mthod of tim contant: accurat, limitd applicailty, quick & intuitiv

24 Nodal Analyi EE94J /594J not, M. odwll, copyrightd 0

25 EE94J /594J not, M. odwll, copyrightd 0 Tutorial: Tranfr Function Analyi: Nodal Analyi Simpl & vry familiar xampl : common - mittr amplifir. in out gn gn in B out gn gn E g m

26 EE94J /594J not, M. odwll, copyrightd 0 Tutorial: Tranfr Function Analyi: Nodal Analyi ducd circuit : in out ( i gn ) i gn / gn i g m Stp: Writ Nodal Equation from K G i g m G in out i 0

27 EE94J /594J not, M. odwll, copyrightd 0 Tutorial: Tranfr Function Analyi: Nodal Analyi Stp :Solv Nodal Equation : / N( ) / D( ) out in N( ) D( ) G G i i g g m m 0 G ( g m ) D( ) ( G )( G ) ( g )( ) i m Stp 3: Organiz in powr of D( ) G G i ( G i ( G i G G g m )

28 EE94J /594J not, M. odwll, copyrightd 0 Tutorial: Tranfr Function Analyi: Nodal Analyi Stp 4 : Sparat into dimnionl ratio - of - polynomial form, parating contant and gain from th tranfr function... out in out gn / GiG gn ( G N( ) D( ) i ( ( g G i m ) G G ) g m out gn ( ( g m i ) i ( ) i / i gn g m i

29 EE94J /594J not, M. odwll, copyrightd 0 Tutorial: Tranfr Function Analyi: Nodal Analyi not that o... out gn i gn in, Amp ( ( in, Amp gn ( g ) ( gn m ) ( gn i ( ( ) ) / gm) i g gn m ) i i in, Amp in, Amp ) a a gn out gn ( ) ( ) out gn mid and a a

30 EE94J /594J not, M. odwll, copyrightd 0 Tutorial: Tranfr Function Analyi: Nodal Analyi Stp 5: Find th root (pol & zro) of th polynomial out gn ( ) ( ) out gn mid and a a out gn mid and ( / )( p / p ) what ar fficint mthod of finding th pol?

31 EE94J /594J not, M. odwll, copyrightd 0 Finding Pol from Tranfr Function

32 Finding Pol and Zro EE94J /594J not, M. odwll, copyrightd 0 atio - of - Polynomial Form : out gn ( ) ( ) out gn at mid-and * m a a Pol and Zro : out gn ( ) ( ) out gn at mid-and * m ( / ( / z p )( )( / / z p )( )( / / z p )... )...

33 EE94J /594J not, M. odwll, copyrightd 0 Finding Pol: omplx Pol << d n d n gn out n n gn out gn out gn out j j k k a a k a a k a a a a a a k ω ζω ω ζω ω ω ζ... / ) / ( thn thiar complx, th root of f... at modrat frqunci and thn w can ignor th / f ζω n ω n jω d ) ( ζ ω ω n d

34 EE94J /594J not, M. odwll, copyrightd 0 Finding Pol: Sparatd Pol Approximation f th root.g. ( a out in out in / a k ) ar << ( a ) a widly paratd, thn k a a a a a / a a jω σ a i th dominant pol.

35 EE94J /594J not, M. odwll, copyrightd 0 ntroductory ircuit Dign: ummary

36 EE94J /594J not, M. odwll, copyrightd 0 Gain Stag: Elmntary Bandwidth Analyi Uing th ovrimplifid dvic modl low, with pi dnoting th um of a-mittr dpltion and diffuion capacitanc, andwidth of E/B/ tag can found. g m B E

37 E Stag: Elmntary Bandwidth Analyi EE94J /594J not, M. odwll, copyrightd 0 gn in c i i th paralll comination of gn, in, and pi q i th paralll comination of, c, and o Not in th dominant pol (a) th millr-multiplication of th collctor a capacitanc

38 Stag: Elmntary Bandwidth Analyi EE94J /594J not, M. odwll, copyrightd 0 gn in EE i i th paralll comination of gn, and in, q i th paralll comination of and Not that th frquncy rpon i a m. Givn, th tranfr function vry oftn ha complx pol, and may how trong gain paking, hnc ringing in th pul rpon.

39 B Stag: Elmntary Bandwidth Analyi EE94J /594J not, M. odwll, copyrightd 0 gn cc in, j g m τ gn gn in in in in in, gm*in cc g m ( jω) q / kt jωτ c Hr w hav a prolm. To th xtnt that th B tag i modld y a vry vry impl hyrid-pi modl (xplicitly, with zro ), w find (y vry impl analyi) vry high andwidth, with pol having tim contant qual to tau_, to tau_c, and to th product of th load ritanc tim (). Not that ) nput capacitanc i indd a notd. Do not includ ffct of tau_c ) gnoring in B tag analyi, whil appaling for implicity (.g. undrgrad cla) i quit unraonal, a oftn dominat high frquncy rolloff. Mor rgarding thi latr.

40 EE94J /594J not, M. odwll, copyrightd 0 Mthod of Tim ontant

41 EE94J /594J not, M. odwll, copyrightd 0 mak rviion for firt for MOT, giv y ummary without drivation th tandard tag xprion. thn dfin MOT, firt and cond ordr thn how a -tag Mthod Darlington diff amp, of and ay cap to ground, cap twn input and output. Tim ontant Giv xprion for cap to ground Giv xprion for cap twn in and out of gnral lock thn u thi for D tag g only thn u thi for tag only thn do for E tag only thn work th full Darlington diff amp thn how how E (with dgn) B ar am prolm thn r-how tag rlationhip

42 EE94J /594J not, M. odwll, copyrightd 0 Finding Bandwidth: Mthod of Tim ontant B 49 Ω x 6.4 ff c i 6500 Ω 3.7 ff gn Q Q diff 8 ff j 38 ff ' π 350 Ω B x E g m 4. 3 Ω ' 49 Ω x 6.4 ff c i 6500 Ω 3.7 ff ' π 350 Ω g m ' diff 8 ff j 38 ff x 4. 3 Ω E tak a gnral ntwork (no inductor or dlay tau), and parat into part, ntwork without capacitor, and th capacitor:

43 EE94J /594J not, M. odwll, copyrightd 0 MOT: Sparation into apacitor & itiv N-port Th intrnal capacitor-fr ntwork i now frquncyindpndnt. Th MOT mthod (not provn hr) rli on rult from n-port ntwork thory

44 MOT: Opn-ircuit itanc EE94J /594J not, M. odwll, copyrightd 0 work xampl to illutrat thi 0 i all othr port opn - circuitd.thi i dtrmind y applying a from thi th mall ignal ritanc maurd at port on with tt voltag (or currnt) at th port and computing th rulting currnt (or voltag)

45 MOT: th Dominant Tim ontant EE94J /594J not, M. odwll, copyrightd 0 Th MOT firt - ordr tim contant dirctly giv u th dominant tim contant condary tim contant andwidth i/ πa. of th circuit. f (and only if) th i ngligil, th 3- db W mut u th cond - ordr (hort - circuit) tim contant to dtrmin a a a.

46 MOT: Ar W Saving Any Work? EE94J /594J not, M. odwll, copyrightd 0 Ar w aving work rlativ to rut-forc nodal analyi: MOT would of only modrat valu if w had to calculat all th i' ach tim. Fortunatly, mot trm involv quantiti alrady found in midand tag analyi: input and output impdanc, load impdanc, tc. work xampl to illutrat thi

47 MOT: Short-ircuit itanc EE94J /594J not, M. odwll, copyrightd 0 i th mall ignal all othr port opn - circuitd, xcpt for port, ritanc maurd at port on with which ihortd

48 MOT: Th Scond-Ordr Tim-ontant EE94J /594J not, M. odwll, copyrightd 0

49 MOT: An Exampl EE94J /594J not, M. odwll, copyrightd 0 work xampl cond ordr trm in ithr E tag or tag.

50 MOT: Working th Efficintly EE94J /594J not, M. odwll, copyrightd 0 Bcau y 0 xx yy finding ach trm in th MOT. Th trick i to work th prolm o that a much a poil : ) trmar rlatd toinput, ouput, load impdanc ) trm ar on found arlir,in 0 xx x yy Thr ar "funny"ca, w alway hav choic in analyi. which ari o oftn that will giv thm on th nxt pag (not th ar intimatly rlatd to th wll- known Millr ffct) a

51 MOT and th Millr Effct EE94J /594J not, M. odwll, copyrightd 0 driv y xx ( A ) i v out i A v out i A v a out [ ( A ) ] τ i v out

52 EE94J /594J not, M. odwll, copyrightd 0 MOT: port impdanc twn collctor and a driv f w dcid xplicitly that comination of any xtrnal circuit ritanc and and that 0 yy x q xtrnal ritor and ( g ) m q c q x imilarly dnot th comind ffct of, thn i todnot th paralll,

53 EE94J /594J not, M. odwll, copyrightd 0 MOT: Port mpdanc Btwn Emittr & Ba

54 MOT: Multitag Exampl EE94J /594J not, M. odwll, copyrightd 0 work on th oard...

55 ommon-a tag y MOT EE94J /594J not, M. odwll, copyrightd 0 gn gn a a... r gn not that cau gn a r gn, a r r gn r input and output, th form iidntical to that of E tag. Not alo th Millr multiplication ffct with ar indpndnt of location of gn

56 What' in nxt lctur? EE94J /594J not, M. odwll, copyrightd 0 lating amplifir gain to S-paramtr acadd common-mittr amplifir, gain-andwidth and ft limit itiv fdack amplifir for highr andwidth Th hrry-hoopr (trancondcuctand-tranimpdanc) dign Darlington tag, nfit, limit, and hadach Ft-doulr tag Ditriutd amplifir (rifly) And latr: input tuning for () improving S, S and () improving andwidth...

57 End EE94J /594J not, M. odwll, copyrightd 0