Lecture 28: Single Stage Frequency response. Context

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1 Lecure 28: Single Sage Frequency response Prof J. S. Sih Conex In oday s lecure, we will coninue o look a he frequency response of single sage aplifiers, saring wih a ore coplee discussion of he CS aplifier, and hen looking a he frequency response of CG and he CD connecions. Nex: Muli-sae aplifiers

2 Reading Reading: We are discussing he frequency response of single sage aplifiers, which isn reaed in he ex unil afer uli-sae aplifiers (beginning of chaper 0). I feel ha i is iporan o ge wared back up on linear circui analysis for siple circuis before juping ino uli-sage aplifiers. We will be saring on chaper 9, uli-sae aplifiers, laer his week. Lecure Ouline Frequency response of he CS as volage ap The Miller approxiaion Frequency Response of a Volage Buffer Frequency Response of Curren Buffer 2

3 Las Tie: CS Ap wih Curren Inpu Calculae he shor circui curren gain of device (BJT or MOS) CS Shor-Circui Curren Gain MOS Case MOS BJT 0 db ωt ωz ( ω / ) g j C g g Ai ( jω) = jω( C + C ) jω( C + C ) gs gs Noe: Zero occurs when all of g curren flows ino C: g v = v jωc gs gs 3

4 Inpu ipedance Look a how Z affecs he ransfer funcion: find Z in C Inpu Ipedance Z in (jω) I = ( V V ) / Z A pu node: V = ( g V I ) R g V R Why? I = ( V A V ) / Z vc Z in = V / I Z = A vc 4

5 Miller Capaciance C M Effecive inpu capaciance: Z in = jωc M = A vc jωc = jω [( A ) C ] vc C x + V in A V,Cx + V + (-A v,cx )C x A V,Cx + V (-/A v,cx )C x Soe Exaples Coon source (eier) aplifier: AvC = Negaive, large nuber (-00) C = A, C 00C Miller Muliplied Cap has Derienal Ipac on bandwidh Coon drain (collecor) aplifier: A = Slighly less han vc gs M M ( V C ) ( AV, C ) Cgs Cgs C = 0 gs Boosrapped cap has negligible ipac on bandwidh! 5

6 CE Aplifier using Miller Approx. Use Miller o ransfor C + vgs Cgs g v gs CM = C ( + gr ) Analysis is sraighforward now single pole! Coparison Miller resul (calculae RC ie consan of inpu pole): ω { C + + g R C } p = s bs ( R ) If we hadn ade he Miller approxiaion, he resul would have been: ω { Cbs + ( + gr C } + R C p = Rs ) 6

7 Mehod of Open Circui Tie Consans Here is a echnique o find he doinan pole of a circui (only valid if here really is a doinan pole!) For each capacior in he circui you calculae an equivalen resisor seen by capacior and for a ie consan τ i =R i C i The doinan pole hen is he su of hese ie consans in he circui ω p, do = τ + τ +L 2 Equivalen Resisance Seen by Capacior For each sall capacior in he circui: Open-circui all oher sall capaciors Shor circui all big capaciors Turn off all independen sources Replace cap under quesion wih curren or volage source Find equivalen inpu ipedance seen by cap For RC ie consan This procedure is bes illusraed wih an exaple 7

8 Exaple Calculaion: CE inpu ipedance Consider he inpu capaciance C = C + C π M Open all oher sall caps (ge rid of pu cap) Turn off all independen sources Inser a curren source in place of cap and find ipedance seen by source R = r R ( ) ( ) M { } τ = RS r C + + gr C π π µ π S Coon-Drain Aplifier W ( ) 2 I DS = µ Cox VGS VT L 2 V GS = V + T 2I DS W µcox L Weak I DS dependence 8

9 CD Volage Gain v g v g + g in b CD Oupu Resisance Su currens a pu (source) node: v R ro roc i = i = gv + gbv R g + g b 9

10 CD Oupu Resisance (Con.) r o r oc is uch larger han he inverses of he ransconducances ignore R g + g b Funcion: a volage buffer High Inpu Ipedance Low Oupu Ipedance Add capaciors Procedure: Sar wih sall-signal wo-por odel Add device (and oher) capaciors C gs v v in + C 0

11 Coon-Collecor Aplifier Two-Por CC Model wih Capaciors Gain ~ Find Miller capacior for C π -- noe ha he base-eier capacior is beween he inpu and pu

12 Volage Gain A vcπ Across C π Aν C π R ( R + R ) / g R >> Noe: his volage gain is neiher he wo-por gain nor he loaded volage gain Cin = Cµ + CM = Cµ + ( AvC ) C π π L Cin = C + C + g R µ π L Cin C µ L R = g Bandwidh of CC Aplifier Inpu low-pass filer s 3 db frequency: ω C ( R ) S Rin Cµ + + grl p = π Subsiue favorable values of R S, R L : R / S g R >> / g L ω p C + BIG π ( / g ) Cµ + Cµ / g ω p g / C µ > ωt Model no valid a hese high frequencies 2

13 Coon Gae Aplifier DC bias: ISUP = IBIAS = IDS CG Curren buffer i = id = i A = i 3

14 CG Inpu Resisance v gs = v We found he approxiaion: R in g + g b CG Oupu Resisance R roc [ ro + gro RS ] = roc [ ro ( + grs )] 4

15 CG Two-Por Model ( r g r R ) + roc 0 0 S Cgs C The funcion of he CG ap was a curren buffer: Low inpu ipedance High pu ipedance No Miller-ransfored capacior! The only parasiic capaciances are direcly across he Inpu and pu: frequency response can be direcly deerined CB Curren Buffer Bandwidh Sae procedure: sar wih wo-por odel and capaciors 5

16 Two-Por CB Model wih Capaciors No Miller-ransfored capacior! Uniy-gain frequency is on he order of ω T for sall R L Suaion of Single-Sage Ap Frequency Response CS, CE: suffer fro Miller-agnified capacior for high-gain case CD, CC: Miller ransforaion nulled capacior wideband sage CG, CB: no Millerized capacior wideband sage (for low load resisance) 6

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