GBM830 Dispositifs Médicaux Intelligents Microelectronics Part : Basic analog CMOS circuits Mohamad Sawan et al. Laboratoire de neurotechnologies Polystim!! http://www.cours.polymtl.ca/gbm830/! mohamad.sawan@polymtl.ca! M548 February 0 Outline Main CMOS circuits design rules Introduction The CMOS process CMOS technology processing The MOS Transistor Basic device physics Small Signal Model Basic analog CMOS circuits Inverter Voltage follower Current mirrors Amplifiers and Op-Amps GBM830 - Dispositifs Médicaux Intelligents
Small-Signal Models of MOS Transistors I d = I D i d Study the linear model of MOS transistor around an operating point.! MOS in saturation: V GS >V th and V DS >V GS -V th! V GS v i- V DS I d = µ n C ox ( L V V γ Φ V Φ GS th0 F SB F ) ( λv DS ) I d = f (V GS,V DS,V SB ) " = I D i d = I D I % d $ ' # & ΔV " I d % GS $ ' # & ΔV " I % d DS $ ' # & ΔV BS V GS V DS V BS GBM830 - Dispositifs Médicaux Intelligents 3 Small-Signal Models of MOS Transistors Transconductance g m! G D g m I D V GS I D = µ n C ox µ n C ox L λv DS ( )( V GS V t ) ( L V V GS t ) λv DS << g m µ n C ox L V ( GS V t ) µ n C ox L I D = I D V Dsat S Vgs gmvgs Vbs B gmbvbs rds Output resistance r ds g ds r ds I D V DS g ds = µ n C ox ( V DS L λ V DS )( V GS V t ) = µ C n ox L λ ( V V GS t ) λ I D GBM830 - Dispositifs Médicaux Intelligents 4
Small-Signal Models of MOS Transistors Body Transconducatnce g mb! g mb I DS V BS = µ n C ox ( V BS L V V GS th ) = µ C n ox ( L V V GS th ) V th V BS ( ) V th = V th0 γ Φ F V BS Φ F G D γ g mb = g m Φ F V SB S Vgs gmvgs gmbvbs rds γ = qεn A C Ox Vbs B GBM830 - Dispositifs Médicaux Intelligents 5 Small-Signal Models of MOS Transistors Example :! Υ = 0.3,! G D λ n Ξ 0.05 (/V),! Φi F = 0.6V,! V gs g m v gs g mb v bs I D = ma,! V dsat = 00mV,! V SB = 00mV.! S V bs r ds g m = ma/v (ms); S=Siemen! g mb = 0.8 ma/v Ξ 0% g m! r ds = 40 k.! B GBM830 - Dispositifs Médicaux Intelligents 6 3
Small-Signal Models of MOS Transistors The low-frequency small signal model of a MOS transistor in the triode region is a resistance.! I D = µ n C ox L V V " # ( GS th )V DS V DS $ % g ds r ds I D $ ' = µ n C ox V DS % & L ( ) V GS V th V DS S ( ) r ds D If V DS << V GS - V th, (the common case V DS near to zero)! g ds = = µ n C ox r ds L ( V GS V t ) This resistance value is controlled by V GS.! GBM830 - Dispositifs Médicaux Intelligents 7 Parasitic capacitors in MOS Transistors 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.! GBM830 - Dispositifs Médicaux Intelligents 8 4
Transition frequency 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.! GBM830 - Dispositifs Médicaux Intelligents 9 Outline 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 GBM830 - Dispositifs Médicaux Intelligents 0 5
Diode connected MOS DC analysis i D = µ n C ox ( L V V GS thn ) ( λv DS ) AC analysis (small signal) GBM830 - Dispositifs Médicaux Intelligents Current Mirror Small signal model simplifications!!!!all current sources è Open circuit!!all voltage source è Short circuit!!all power supplies è Ground! Open circuit M iref iout M Vout - No current in this part of the circuit Gate Vx g m Vgs g mb Vsb rds g m Vgs g mb Vsb rds GBM830 - Dispositifs Médicaux Intelligents 6
Current Mirror Simple current mirror!!dc analysis! I V GS OUT = V th = µ C ox µ C I ox ref ( L) ( L) µ C I ox ref ( L) = ( L) I ref ( L) M iref iout M Vout - Output impedance:!!!r out = r ds =! λ I out ΔV = V GS V = th µ C I ox ref ( L) VGS-Vth GBM830 - Dispositifs Médicaux Intelligents 3 Current Mirror Cascode current mirror!!dc analysis! V =Veff= V GS - V th at I D =I ref Vout = Vth Veff - Veff -Vth Veff V V ΔV OUT th i ref i out M3 M (Vth Veff) V A Vout M4 Vth Veff M - VthVeff=VGS M M Vx - i x The output impedance is increased by a factor ( a v ):! v i x x ( ) Vsb - = R g r r out m ds ds g m Vgs rds g mb Vsb rds Vx VthVeff GBM830 - Dispositifs Médicaux Intelligents 4 7
Current Mirror ilson current mirror!!- DC analysis! I OUT = ( L) I REF ( L) M M3 M!- Output impedance! VthVeff r o = g m r ds r ds3 Iref Iout Super-ilson current mirror!!- DC analysis! M3 M4 VA M Vout M - GBM830 - Dispositifs Médicaux Intelligents 5 Current Mirror ide-swing cascode current mirror!!- DC analysis! Cascode! i ref i out M3 M (Vth Veff) V A Vout M4 Vth Veff M - Veff Advantage: minimum output voltage is only Veff!! Downside: increased complexity and power consumption.! GBM830 - Dispositifs Médicaux Intelligents 6 8
Current Mirror Improved ide-swing cascode current mirror!!- DC analysis! Veff Added transistor M5 equalizes the voltages at the drains of M and M3 : Channel-length modulation effects are reduced.! GBM830 - Dispositifs Médicaux Intelligents 7 Analog CMOS Inverter l Analyse AC (faibles signaux) v A = = g r R g R ( ) out v m ds m vin GBM830 - Dispositifs Médicaux Intelligents 8 9
Analog CMOS Inverter AC analysis (continued)! Vo Vi Vgs rds rds!transfer function (G) = vo/vi! S g m Vgs = ( vo rds ) gm vgs ( vo r o ds ) ( ) Kirchhoff: 0 / / Transconductance and output impedance (g m, r ds )! g m = µ Cox µ L λi L ( VGS Vth ) = Cox I D v v = g r r i m ds ds rds = G g r m ds = µ C ox λ L I Voltage Gain (G)! D D!G lorsque ou L! dx λ = d!g lorsque I D! L eff dv DS GBM830 - Dispositifs Médicaux Intelligents 9 Voltage Follower The voltage follower, as suggested by its name, replicates voltage V IN at the output.! DC Analysis Vdd Vdd Vin Vin Vout Vout I Bias I Bias Vss Vss P-well process! N-well process! V th = V ( φ V φ ) th0 F OUT γ F I V Assume that the transistor is saturated:! D = I = µ C OUT BIAS = ox L L I BIAS µ C ox ( V V V ) IN V IN OUT V th th If the substrate is connected to the source, then V th =V tho.! GBM830 - Dispositifs Médicaux Intelligents 0 0
Voltage Follower AC Analysis GBM830 - Dispositifs Médicaux Intelligents Voltage Follower 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 0.95.! 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.! GBM830 - Dispositifs Médicaux Intelligents
Common Gate Amplifier AC analysis GBM830 - Dispositifs Médicaux Intelligents 3 Common Gate Amplifier AC analysis (Cont d) GBM830 - Dispositifs Médicaux Intelligents 4
Operational amplifiers Ideal Op-Amp Openloop! Vp ve Vn - A ve Vo Closedloop! Vp ve Vn - A ve Vo Basic -stage Op-Amp R R M3 M4 Vdd M5 M6 M7 Vdd M8 Iref V M M V- Vout Cout V Iref M M V- Vout Cout M6 M7 Vss M8 M3 M4 Vss M5 NMOS inputs! Small signal open-loop gain: PMOS inputs! G oa = gm ro = gm (ro ro4) gm5 (ro5 ro8)! GBM830 - Dispositifs Médicaux Intelligents 5 Operational amplifiers : Stability GBM830 - Dispositifs Médicaux Intelligents 6 3
Operational amplifiers : Stability A V C C Vi R g m Vi C R g m V C Vo A = aa CL=C a a C C IAI (db) P# P# 0 0 f (Hz) Phase -90-80 GBM830 - Dispositifs Médicaux Intelligents 7 Operational amplifiers : Stability P = - R C c R g m V C C g m P = C C z = g m C C Vi R g m Vi C R g m V C Vo z = & C $ C % g m R Z #! " Vi gm Vi R CC C RZ gm V R C Vo P = g m C GBM830 - Dispositifs Médicaux Intelligents 8 4
Operational amplifiers : CMRR 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.! GBM830 - Dispositifs Médicaux Intelligents 9 Operational amplifiers : CMRR 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! GBM830 - Dispositifs Médicaux Intelligents 30 5
Operational amplifiers : Input common-mode range Input common-mode range! Differential amplifier with a current mirror load.!!!! Slew rate! I Dω SR = g SR = m ( VGS Vth ) ω GBM830 - Dispositifs Médicaux Intelligents 3 Operational amplifiers : Noise Dominate noises are thermal and flicker! Active region V R ( f ) K = LC f ox I R ( f ) = 4 4kTY/gm γ g m K R = 4 γ ( ) V f kt LC f g ox m V ( ) n f 0 µ V Hz 0 0. 3. /f noise dominates -0dB/decade 0 Root spectral density /f noise corner hite noise dominates ( Hz) 6 ( 3. 0 ) ( ) V ( f ) = 0 f 6 n!pmos has less flicker noise than NMOS (holes mobility is less than electron)! g m = µ Cox µ L L ( VGS Vth ) = Cox I D GBM830 - Dispositifs Médicaux Intelligents 3 6
Operational amplifiers : Noise GBM830 - Dispositifs Médicaux Intelligents 33 Operational amplifiers : Noise 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 O i = g m vit eq 3 eq 4 GBM830 - Dispositifs Médicaux Intelligents 34 7
Operational amplifiers : /f NOISE 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! GBM830 - Dispositifs Médicaux Intelligents 35 Operational amplifiers : Thermal NOISE The input-referred thermal noise for an NMOS transistor is:! GBM830 - Dispositifs Médicaux Intelligents 36 8