Amplifiers, Source followers & Cascodes Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgium willy.sansen@esat.kuleuven.be Willy Sansen 0-05 02
Operational amplifier Differential pair v- : B v + Current mirror v OUT Current mirror Singletransistor amplifier Willy Sansen 0-05 022
Table of contents Single-transistor amplifiers Source followers Cascodes Willy Sansen 0-05 023
Single-transistor amplifier - I L + + + - v GS - gm v GS r DS - A v = g m r DS = 2 I DS V E L = 2 V E L V GS -V T I DS V GS -V T A v 00 if V E L 0 V and V GS -V T 0.2 V Willy Sansen 0-05 024
Single-transistor amplifier - 2 High gain? Low V GS -V T and large L!!! Willy Sansen 0-05 025
MOST or bipolar amplifier? MOST A v = V E L (V GS -V T )/2 A v 00 if V E L 0 V and V GS -V T 0.2 V Bipolar A v = V E kt/q 3 vs 2 stages for 0 6 A v 000 if V E 26 V since kt/q = 26 mv Willy Sansen 0-05 026
Gain, Bandwidth and Gain-bandwidth I L + - C L A v0 = g m r DS BW = 2π r DS C L For all single-stage Operational amplifiers g m GBW = 2π CL Willy Sansen 0-05 027
Gain A v, BW and GBW A v A v0 BW -20 db/decade A v0 = g m r DS GBW g m GBW = 2π CL A v0 φ (A v ) 0 o f φ (A v ) = - 45 o -90 o at BW Willy Sansen 0-05 028
Single-transistor amplifier : Exercise GBW = 00 MHz for C L = 3 pf Techno.: K n 50 µa/v 2 L min = 0.5 µm I DS? L? W? GBW.C L? I DS Willy Sansen 0-05 029
Gain, Bandwidth and Gain-bandwidth I L A v0 = g m r DS R S + - BW = 2π R S C GS C GS g m GBW = 2π CGS r DS R S = f T r DS RS ~ WC ox V GS -V T W? L? V GS -V T? Willy Sansen 0-05 020
Gain, Bandwidth and Gain-bandwidth R S C F I L + A v0 = g m r DS - BW = 2π RS A v0 C F GBW = 2π RS C F Willy Sansen 0-05 02
Miller effect I L C F R + S R S C FM I L + - - A v0 = g m r DS C FM =(+A v0 ) C F Miller, Dependence of the input impedance of a three-electrode vacuum tube upon the load in the plate circuit, Scient. Papers Bur. Standards, 920, 367-385. Willy Sansen 0-05 022
Miller capacitance feedback effects R S C F I L + A v A v0 BW - j f/f A z v = A v0 + j f/f p + g m R S g m f z = 2π CF - φ (A v ) 0 o f p GBW f z f For phase, a positive zero is like a negative pole!!! -90 o - 80 o Willy Sansen 0-05 023
Amplifier with local R- (series) feedback g mr = g m C inr i out ~ RS R outr + g m R S RS R outr = r DS (+ g m R S ) (g m r DS ) R S C GS C inr = + gm R S But R S gives extra noise! Willy Sansen 0-05 024
Amplifier with local L- feedback Z inl i out R outl g ml = g m + g m L S s R outl = r DS (+ g m L S s) L S L S Z inl = g m CGS + + L S C GS s 2 s C GS No extra noise! Z inl = L S ω T + L S s+ s CGS Willy Sansen 0-05 025
Amplifier with local MOST-R- Feedback M M2 i out V DS2 = V GS2 -V GS 0.2 V r DS2 = KP W 2 /L 2 (V GS2 -V T ) R outr = r DS (+ g m r DS2 ) C inr = C GS +C GS2 + gm r DS2 Willy Sansen 0-05 026
Diode-connected MOST : parallel Feedback I DS I DS V DS = V GS -V T V DS = V GS G = D + V DS = V GS - saturation V GS I DS = K W n (V DS -V T ) L 2 0 V T V DS Willy Sansen 0-05 027
Diode-connected MOST: small-signal I DS i DS + + - G = D V DS = V GS - v GS g m v GS r DS r ds = /g m // r DS /g m Willy Sansen 0-05 028
Diode-connected MOST at high frequencies I DS i DS + v GS + G = D DS = V GS -V C GS - g m v GS r DS BW = g m C DS 2π (C GS +C DS ) f T 2 Willy Sansen 0-05 029
Wideband amplifier M2 V DD V OUT = V DD -V GS2 (V OUT ) M A v0 = g m (W/L) g m2 = (W/L) 2 V GS2 -V T = VGS -V T R OUT = /g m2 Willy Sansen 0-05 0220
Linear wideband amplifier 2I B V DD V OUT = V GS2 M M2 A v0 = g m (W/L) g m2 = (W/L) 2 V GS2 -V T = VGS -V T R OUT = /g m2 Current mirror with only nmosts Same V OUTDC as V INDC No body bias effect Good PSRR Double power consumption Willy Sansen 0-05 022
Wideband amplifiers 2I B 2I B M M2 M M2 A v0 = g m (W/L) g m2 = (W/L) 2 V GS2 -V T = VGS -V T A v0 = g m R out R out = /g m2 R out = r DS //r DS2 Willy Sansen 0-05 0222
Class A versus class AB amplifier + i out M2 i out M2 M C L M C L = A v = A v Class A stage Class AB stage Willy Sansen 0-05 0223
CMOS inverter-amplifier V DD V DD 0 M2 0 M2 M M C L C L Digital invertor Analog amplifier Willy Sansen 0-05 0224
Operating points nmost & pmost V DD I DS M2 I DS nmost M 4 M2 pmost M C L V DD = V DSn + V DSp V DSn = V OUT V DSp = V DD -V OUT = V GSn + V GSp V GSn = V IN V GSp = V DD -V IN 6 7 0 5 3 2 V OUT Willy Sansen 0-05 0225
Transfer characteristic V DD i DS M2 M C L V DD V DD 2 0 i DS I DSA 0 2 3 4 = 0 = 5 V DD 2 Analog amplifier = = 0 6 7 V DD 0 Willy Sansen 0-05 0226
Analog amplifier : DC V DD i DSA V in = V DD V out = 2 V DD 2 M2 I DSn = K n (V in -V T ) 2 v L in n C L M W n W p I DSp = K p (V DD -V in -V T ) 2 L p W n W n K I DS = K n ( -V T ) 2 n = K p 2 L n W p L p L n V DD Willy Sansen 0-05 0227
Analog amplifier : AC model V DD i DSA M2 M + C L - r DSn r DSp C L g mn v iv g mp v iv For the same I DS en V GS -V T : g mn = g mp = g m Willy Sansen 0-05 0228
Analog amplifier: AC gain Av V DD i DSA If V En L n =V Ep L p = V E M2 M C L g DSn = g DSp = g DS (g DS = /r DS ) 2g A v0 = - m = - 2g DS V DD 2 2V E -V T Willy Sansen 0-05 0229
Analog amplifier : BW & GBW V DD i DSA M2 M C L A v0 = 2g m R out R out = r DS 2 BW = 2π Rout C L 2g m GBW = 2π CL Willy Sansen 0-05 0230
Analog amplifier: poles due to CGS V DD A v0 = 2g m R out R S M2 2g m C GS M C L GBW = 2π CL C GSt = C GS + C GS2 But if R S C GSt > r DS C L : GBW = f T r DS R S Willy Sansen 0-05 023
Analog amplifier: poles due to CDG V DD C DG f d f nd R S C DG M2 C L g m R S f z M CL 2π R out C L A v0 ( - sc DGt /g m ) = + s (R out C L + A v0 R S C DGt ) + s 2 R S R out C DGt C L f Willy Sansen 0-05 0232
Analog amplifier: other poles V DD A v0 = 2g m R out C DG R S M2 GBW = M C L 2g m 2π C L C DGt = C DG + C DG2 But if R S C DGt > 2π GBW : GBW = 2π RS C DGt Willy Sansen 0-05 0233
Class AB operation V DD i C M2 i C2 I C2 I C i L i C C L I DSA i L M 0 i L = i C2 -i C V DD 2 VDD Willy Sansen 0-05 0234
Table of contents Single-transistor amplifiers Source followers Cascodes Willy Sansen 0-05 0235
Single-transistor stages Common source Common drain Common gate i out v vin out v Rout in V B I V B B + i out R in i in I B i out = g m = i out = i in R out /g m R in /g m Amplifier Source follower Cascode Voltage buffer Current buffer Willy Sansen 0-05 0236
Source follower with V BS = 0 (p-well) R S Z OUT = gm V GS = V T0 + I B K W/L V GS = ct if I B = ct V B I B R B C L V OUT = V IN -V GS V OUT = V IN A v = Willy Sansen 0-05 0237
Source follower with V BS 0 (n-well) R S Z OUT < gm V GS = V T + V GS ct I B K W/L VB I B R B C L V OUT = V IN -V GS A v = V T = V T0 + γ [ 2Φ F +V OUT - 2Φ F ] n Willy Sansen 0-05 0238
Source follower non-linearity R S V OUT γ = 0 slope VB I B C L γ = 0.8 V /2 slope /n 0 V T V IN Willy Sansen 0-05 0239
Emitter follower R S R OUT R S R IN VB I B C L V B R E R S +r B A v = R OUT = + g m β+ Limited isolation! R IN = r π +r B + (β+)r E Willy Sansen 0-05 0240
Source follower with C L load g m 0mS g mr f d f nd f z A v = ( + s C GS /g m ) + s B + s 2 C 2 R S /g m ms 0.mS A v 0. f d M G Hz g mr f B = R S C DG + C DS g m C GS g m R S + (+ ) r DS 0.0 C 2 = C DS C DG + 0.00 f C DS C GS + C DG C GS C DS = C L + C DS M G Hz Willy Sansen 0-05 024
Source follower with C L load g m 0mS ms 0.mS A v 0. 0.0 f d f g nd mr f g z mr g mr = R S g mu f d M G Hz g mr f g mr = C DGt C DG C DGt = C L + C DS + C GS C DG C DS C GS C DS + C GS 0.00 M G Hz f g mu = R S Willy Sansen 0-05 0242
Source follower : Output impedance g m 0mS g mr f z f d f nd g mr = C GS + C DS R S C DG ms g mu 0.mS Z out 0kΩ k g mu f d f nd M G Hz f g mu f z = C GS + C DS R S C GS + C DG 00 0 g mr M Inductive G Hz f 2π R S C GS f d,higm = 2π R S C DG Willy Sansen 0-05 0243
Emitter follower : Output impedance g m 0mS ms 0.mS Z out 0kΩ k 00 0 f d f nd C π + C CE g f mr z g mr = R S C π + C µ g mu g mu g mr f d M G Hz M f nd Inductive G L = R S ω T Hz f f g mu f z = C je + C CE R S C je + C µ 2π R S //r π (C π +C µ ) Willy Sansen 0-05 0244
Source follower as active L V B R S C GS I B Z OUT C L g m g m Z OUT L R S f Z OUT ( + R g S C GS s) m L R S 2π f T f T g m R S f T g m up to f T = 2π CGS Willy Sansen 0-05 0245
Source follower as active L R S L L L I B I B I B2 I B I B2 L R S 2π f T L /g mp 2π f Tn L /g mp 2π f Tn V DSn = V GSn V DSn = V GSn + V GSp V DSn = V GSp Willy Sansen 0-05 0246
Floating inductor with parallel C R tune R tune L = R tune ω T2 T 2 V out+ V out- V out+ V out- V in- T C V in+ C I B A v = g m g m2 with HF peaking! Willy Sansen 0-05 0247
Table of contents Single-transistor amplifiers Source followers Cascodes Willy Sansen 0-05 0248
Single-transistor stages Common source Common drain Common gate i out v vin out v Rout in V B I V B B + i out R in i in I B i out = g m = i out = i in R out /g m R in /g m Amplifier Source follower Cascode Voltage buffer Current buffer Willy Sansen 0-05 0249
Cascode with resistive load A R? R L A R = R L + i DS R in? i in I B g m r DS R Lc R L A R = R i in = in iin Willy Sansen 0-05 0250
Cascode with resistive load R L i L g m R B i ds i in + i ds r DS i L i in I B R B i in R Lc = g m r DS R B R Lc R L Willy Sansen 0-05 025
Cascode with active load A R i B R Lc + i DS r DS A R R in R B i in I B R B g m r DS R Lc R L A R = R in = iin iin R Lc = g m r DS R B 00 R B Willy Sansen 0-05 0252
Cascode versus single-transistor I B I B + M2 M M A v = (g m r DS ) R out = r DS A v = (g m r DS ) (g m r DS ) 2 R out = r DS (g mr DS ) 2 Willy Sansen 0-05 0253
Cascode versus single-transistor I B I B + M2 M C L M C L BW = 2π R out C L g m GBW = for both! 2π C L Willy Sansen 0-05 0254
Cascode versus single-transistor I B A v + M I B M2 C L A v2 = g m2 r DS2 A v = g m r DS Single transistor GBW M C L Cascode : High gain At low freq. f g m GBW = 2π CL Willy Sansen 0-05 0255
Miller effect in cascode? A v2 = g m2 r o2 A v = g m r o I B R S A v R S C M f nd r o2 C L R S C M + M2 v m C L R St f d R S C M M A v2 r o C L f g m GBW = 2π CL C L No Miller if R S < R St = r o2 CM g m2 g m Willy Sansen 0-05 0256
Cascode with capacitance Cm at middle point A v2 = g m2 r o2 A v = g m r o2 I B C m r o C m f nd r o2 C L R S + M2 v m C L C mt f d C m /g m2 M C m A v2 r o C L g m GBW = 2π CL C mt = g m2 r o2 C L = A v2 C L f Willy Sansen 0-05 0257
Telescopic Cascode +3 M4 A v = g m R out +2 + M3 M2 I B R out R out = r DS g m2 r DS2 2 M C L BW = 2π Rout C L g m GBW = 2π CL Willy Sansen 0-05 0258
Folded Cascode I B A v = g m R out M2 + R out = r DS g m2 r DS2 M i ds BW = 2π Rout C L I B2 C L g m GBW = 2π CL I DS = I B -I B2 I B / 2 Willy Sansen 0-05 0259
Cascode versus cascade I B I B I B2 + M2 M M M2 A v = (g m r DS ) (g m r DS ) 2 A v = (g m r DS ) (g m r DS ) 2 Willy Sansen 0-05 0260
Cascode versus cascade I B Two-stage Miller amplifier + M2 I B C c I B2 C L M M M2 CL g m GBW = 2π CL g m GBW = 2π Cc Willy Sansen 0-05 026
Regulated cascode or gain boosting I B I B I B2 M2 + M2 M M M3 A v = (g m r DS ) (g m r DS ) 2 A v = (g m r DS ) (g m r DS ) 2 (g m r DS ) 3 Hosticka, JSSC Dec.79, pp. -4; Sackinger, JSSC Febr.90, pp. 289-298; Bult JSSC Dec.90, pp. 379-384 Willy Sansen 0-05 0262
Regulated cascode, Cascode & single-transistor A v Reg.cascode A v = g m r DS I B I B2 A v3 A v2 = g m2 r DS2 A v3 = g m3 r DS3 C L M2 A v2 Cascode M M3 A v Single trans. GBW GBW = g m 2π CL f Willy Sansen 0-05 0263
Gain boosting +V B A gb I B A A gb BW gb M2 C L M A casc A v = A gb (g m r DS ) (g m r DS ) 2 GBW gb f z = GBW g m 2π C L Willy Sansen 0-05 0264 f
Pole-zero doublet and settling time A v V OUT A v0 V IN τ GBW τ pz f pz BW f pz GBW f t t V OUT = V IN [ - exp (- ) - exp (- )] 0 τ GBW Kamath, etal, JSSC Dec.74, pp. 347-352 f pz GBW τ pz f pz = GBW = t 2π τ pz 2π τ GBW Willy Sansen 0-05 0265
Single-transistor stages i out vin + i out i in V B V B I B I B i out = g m = i out = i in Z out /g Z m in /g m Amplifier Source follower Cascode Willy Sansen 0-05 0266
MOST amplifier & follower i out i out R S R out R out + + + - - - R B R S R out I B + - R out R B R B > /g m R B > /g m A G A V g m /R B R in R out r o g m R B r o /g m /g m Willy Sansen 0-05 0267
Bipolar transistor (β >> ) R in R in i out i out R S R out R out + + + - - - R B R S R out I B + - R out R B R B > /g m R B > /g m A G A V g m /R B R in r B +r π r B +r π +βr B r B +r π +βr o r B +r π +βr B R out r o g m R B r o /g m + R S /β /g m + R S /β Willy Sansen 0-05 0268
In- & output resistances MOST cascode R L R out R L R out R out R out R in R in R in R in R B i in I B i in R B i in I B i in R B > /g m R B > /g m A R R in R L R L g m r o R B - /g m /g m R B R out g m r o R B g m r o R B Willy Sansen 0-05 0269
In- & output resistances Bipolar trans. cascode R L R L R out R out R out R out R in R in R in R in R B i in I B i in R B i in I B i in R B > /g m R B > /g m A R R L R L g m r o R B - R in /g m /g m R B //(r B +r π ) r B +r π R out g m r o R B g m r o (R B //(r B +r π )) βr o βr o Willy Sansen 0-05 0270
Calculation of AR for a MOST cascode R out R in + v - g m v r o g m v + R B i in R B i in i in - R B > /g m v = - A R = g m r o R B = -g m vr o = - R B yields = - R B i in ( + g m r o ) and g m r o >> Willy Sansen 0-05 027
Table of contents Single-transistor amplifiers Source followers Cascodes Willy Sansen 0-05 0272