1/13/12 V DS. I d V GS. C ox ( = f (V GS ,V DS ,V SB = I D. + i d + I ΔV + I ΔV BS V BS. 19 January 2012

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1 /3/ 9 January 0 Study the linear model of MOS transistor around an operating point." MOS in saturation: V GS >V th and V S >V GS -V th " VGS vi - I d = I i d VS I d = µ n ( L V V γ Φ V Φ GS th0 F SB F ) ( λv S ) I d = f (V GS,V S,V SB ) = I i d = I I d ΔV I d GS ΔV I d S ΔV BS V GS V S V BS

2 /3/ Transconductance g m! G g m I V GS I = µ n L λv S µ n ( )( V GS V t ) ( L V GS V t ) λv S << g m µ n L V V ( GS t ) µ n L I = I V sat S Vgs gmvgs Vbs B gmbvbs rds Output resistance r ds g ds r ds I V S g ds = µ n V S ( L λ V S ) V GS V t ( ) = µ n L λ ( V GS V t ) λ I Body Transconducatnce g mb! g mb I S V BS = µ n V BS L V GS V th ( ) = µ n ( ) V th = V th0 γ Φ F V BS Φ F γ g mb = g m Φ F V SB ( L V GS V th ) V th V BS G S Vgs gmvgs gmbvbs rds γ = qεn A C Ox Vbs B Example :" Υ = 0.3, " G λ n Ξ 0.05 (/V), " Φi F = 0.6V, " Vgs gmvgs gmbvbs I = ma, " V dsat = 00mV, " V SB = 00mV." S Vbs rds g m = ma/v (ms); S=Siemen" g mb = 0.8 ma/v Ξ 0% g m " r ds = 40 k." B

3 /3/ The low-frequency small signal model of a MOS transistor in the triode region is a resistance." I = µ n L V V ( GS th )V S V S S g ds r ds I = µ n V S L V GS V th V S ( ) If V S << V GS - V th, (the common case V S near to zero) " g ds = = µ n r ds L ( V GS V t ) This resistance value is controlled by V GS." r ds To complete the small-signal model of the MOSFET, the intrinsic and extrinsic capacitors have to be added. These capacitors play an important role in high frequency operation." The frequency capability of a MOS transistor is specified by finding the transition f T." i o f T is the frequency where the magnitude of the short-circuit common-source current gain falls to. " i i = s(c gs C gd )v gs Current in C gd is neglected:" v i - i i i o g m v gs i i C g d i o i o i i g m s(c gs C gd ) g m i o i i s= jω ( ) f T = π (C gs C gd ).5 µ n π L V V GS th v g s - C g s g m v g s f T can be improved by operating at high values of (V GS -V th ), and faster transistor can be made by smaller L." 3

4 /3/ Introduction The CMOS process CMOS technology processing The MOS Transistor Basic device physics Small Signal Model Basic blocks in CMOS Analog Circuits Inverter Voltage follower Current mirrors Amplifiers C analysis i = µ n ( L V V GS thn ) ( λv S ) AC analysis (small signal) Simple current mirror! "C analysis" V = V GS th I ref µ Cox( L) I OUT I ref ( L) = µ Cox( L) = I ref µ C ( L) ( L) ox Output impedance:" "r out = r ds = " λ I out ΔV = VGS Vth = I ref µ Cox( L) VGS-Vth 4

5 /3/ Cascode current mirror! "C analysis" V =Veff= V GS - V th at I =I ref Vout = Vth Veff - Veff -Vth Veff V V ΔV OUT th M3 M4 i ref i out (Vth Veff) V A Vth Veff M M Vout - VthVeff=VGS M M Vx - i x The output impedance is increased by a factor ( a v ): " Vsb - vx = R ( g r ) r i x out m ds ds g m Vgs rds g mb Vsb rds Vx VthVeff ilson current mirror! "- C analysis" I OUT ( L) = I REF ( L) M M3 M "- Output impedance" VthVeff r o = g m r ds r ds3 Super-ilson current mirror! "- C analysis" ide-swing cascode current mirror! "- C analysis" Cascode! i ref i out M3 (Vth Veff) V A M Vout M4 Vth Veff M - Veff Advantage: minimum output voltage is only Veff "" ownside: increased complexity and power consumption. " 5

6 /3/ Improved ide-swing cascode current mirror! "- C analysis" Veff Added transistor M5 equalizes the voltages at the drains of M and M3 : Channel-length modulation effects are reduced." Analyse AC (faibles signaux) vout Av = = gm ( rds R) gmr v in AC analysis (continued)! Vo Vi Vgs rds rds "Transfer function (G) = vo/vi" S g m Vgs v v = g r r Kirchhoff: 0 = ( vo / rds ) gm v ( vo / rds ) ( ) o gs m ds ds Transconductance and output impedance (g m, r ds )" g m = µ Cox ( VGS Vth ) = µ Cox I L L rds = λi G g r m ds = µ λ L I Voltage Gain (G)" "G lorsque ou L " dx λ = d "G lorsque I " L eff dv S i 6

7 /3/ The voltage follower, as suggested by its name, replicates voltage V IN at the output." C Analysis Vdd Vdd Vin Vin Vout Vout I Bias I Bias Vss Vss P-well process " N-well process" V = V th ( φ F VOUT φ F ) th0 γ Assume that the transistor is saturated:" I ( ) = I BIAS = µ Cox VIN VOUT Vth L V OUT L I BIAS = µ C V Vth IN ox If the substrate is connected to the source, then V th =V tho." AC Analysis AC Analysis (Cont d) If" In practice, this value is degraded by r ds, and g s, and has a value between 0.9 and " The output resistance is found using a test voltage source V x at the output and measuring the current flowing with v in =0" The voltage follower is useful to match impedances : It is often used to lower the output impedance of a voltage amplifier." 7

8 /3/ AC analysis AC analysis (Cont d) Ideal Op-Amp Openloop" Vp ve Vn - A ve Vo Closedloop" Vp ve Vn - A ve Vo Basic -stage Op-Amp R R NMOS inputs" Small signal open-loop gain: PMOS inputs" G oa = gm ro = gm (ro ro4) gm5 (ro5 ro8) " 8

9 /3/ A V C C Vi R g m Vi C R g m V C Vo A = aa CL=C a a C C P = - g m R C c R V C C P = g m C C g m z = C C Vi R g m Vi C R g m V C Vo z = C C RZ g m Vi gm Vi R CC C RZ gm V R C Vo P = g m C 9

10 /3/ The common-mode rejection ratio (CMRR) measures how well the amplifier can reject signals common to both inputs." The differential stage determines how well the entire opamp rejects common mode signals." The common-mode signal appearing on the drains of M3 and M4 will be identical" The most efficient manner in which to increase the CMRR of this amplifier is to increase the resistance r o5" Input common-mode range! ifferential amplifier with a current mirror load." Slew rate" I ω SR = g SR = m ( VGS Vth ) ω 0

11 /3/ ominate noises are thermal and flicker" Active region K VR ( f ) = LC oxf I R ( f ) = 4 4kTY/gm γ g m K VR ( f ) = 4kT γ LC f g ox m V ( ) n f 0-0dB/decade Root spectral density µ V 3. Hz /f noise dominates /f noise corner hite noise dominates ( Hz) 6 ( 3. 0 ) = ( ) 6 Vn ( f ) 0 f "PMOS has less flicker noise than NMOS (holes mobility is less than electron)" The gain of the input stage in a MOS op amp is usually large enough so that the input-referred noise of the overall amplifier is dominated by the noise contributions from the input-stage transistors." i = g ( v v ) g ( v v ) O m - eq eq m 3-4 i = g O m v IT eq 3 eq 4

12 /3/ For a MOS transistor the input-referred /f noise can be modeled as:" where Kf is the flicker noise coefficient" Using this model for each transistor in the input stage, the input-referred /f noise for the entire stage is" Assuming that L = L, =, L4 = L3 and 4 = 3" The input-referred thermal noise for an NMOS transistor is:"

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