Microelectronics Main CMOS design rules & basic circuits

GBM8320 Dispositifs médicaux intelligents Microelectronics Main CMOS design rules & basic circuits Mohamad Sawan et al. Laboratoire de neurotechnologies Polystim mohamad.sawan@polymtl.ca M5418 6 & 7 September 2018

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 Diode, Inverter Current mirrors Voltage follower Amplifiers and Opamps. Low-Power Circuit Techniques Themes, mixed-signal & future of low-power designs. GBM5320 - Dispositifs Médicaux Intelligents 2

CMOS technology for medical implants integration Low power consumption is crucial for medical implant devices A single-chip must allow very-low-power operation while containing amplifiers, filters, ADCs, battery management system, voltage multipliers, high voltage pulse generators, programmable logic and timing control Recent CMOS processes are suitable for pure analog integration with high operating speed CMOS is suitable to VLSI of both high-density digital circuits (e.g. DSP, memory, etc.) and analog circuits (amplifiers, ADC, DAC, etc.) CMOS digital circuits feature 0 static power consumption. High performance MOS switches à CMOS technology suitable for high accuracy sample-data circuits. GBM5320 - Dispositifs Médicaux Intelligents 3

Mixed signal design overview Newer CMOS technologies with smaller feature sizes can operate at increasingly high speed, comparable to some bipolar technologies. CMOS technologies become mainstream technologies for mixed-signal integration due to the advantages of low-cost and high-integration density. Digital circuitries cost decreases by 29% each year in CMOS technology thanks to device downscaling; To benefit from this, analog ICs have to be integrated on the same chip with the digital circuits in mixed-signal integration; e are in SoC (System on a Chip) era, which favors CMOS technology; System on Chip: mixed-signal integrated circuits that contains analog, memory, logic, and embedded processor. GBM5320 - Dispositifs Médicaux Intelligents 4

Mixed-signal circuit design overview MOSFET f t frequency is continuously increasing over time. The minimum channel length of MOS transistors dropped from 25 mm in 1960s to less than 15 nm in the year 2014. Benefit of much higher complexity, smaller volume, less power consumption and higher frequency performance. GBM5320 - Dispositifs Médicaux Intelligents 5

CMOS technology processing CMOS technologies have penetrated application areas, which is used to be the exclusive domain of bipolar or BiCMOS technology. Out of seven integrated RF transceivers introduced in 2003, four are realized in a CMOS process technology. GBM5320 - Dispositifs Médicaux Intelligents 7

CMOS technology processing Four terminals: gate, source, drain, body Source Gate Drain Polysilicon Gate oxide body stack looks like a capacitor Gate and body are conductors SiO 2 (oxide) is a very good insulator. Called Metal-oxide-semiconductor (MOS) Even though gate is no longer made of metal. Silicon Run Video n+ n+ S D p Bulk Si SiO 2 https://www.youtube.com/watch?v=kclmr_tqcy8 GBM5320 - Dispositifs Médicaux Intelligents 8 G B

CMOS technology processing Lithography process similar to printing press On each step, different materials are deposited or etched. In Typically use p-type substrate for nmos transistors Requires n-well for body of pmos transistors. Vss In Out V SS V DD Out V DD SiO 2 n+ n+ p+ p substrate n well p+ n+ diffusion p+ diffusion polysilicon metal1 nmos transistor pmos transistor GBM5320 - Dispositifs Médicaux Intelligents 9

CMOS technology processing Substrate are tied to V SS and n-well to V DD Metal to lightly-doped semiconductor forms poor connection. Use heavily doped well and substrate contacts / taps. In V SS In Out V DD V SS Out V DD p+ n+ n+ p+ p+ n+ p substrate n well substrate tap well tap GBM5320 - Dispositifs Médicaux Intelligents 10

CMOS technology processing Transistors and wires are defined by masks. p+ V SS In Out n+ n+ p+ p+ V DD n+ Cross-section taken along dashed line. substrate tap p substrate n well well tap In AIn V SS V DD Out Out V SS V DD substrate tap nmos transistor pmos transistor well tap GBM5320 - Dispositifs Médicaux Intelligents 11

CMOS technology processing Six masks n-well Polysilicon n+ diffusion p+ diffusion Contact Metal n well Polysilicon n+ Diffusion p+ Diffusion AIn Contact Out V SS substrate tap nmos transistor pmos transistor well tap V DD Metal GBM5320 - Dispositifs Médicaux Intelligents 12

CMOS technology processing 0.35_m µm 200nm p+ n+ n+ p+ p substrate 1.25 1.25_m µm n well p+ n+ 600_m µm Cross section of 0.35um CMOS technology 6.5nm GBM5320 - Dispositifs Médicaux Intelligents 13

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 Diode, Inverter Current mirrors Voltage follower Amplifiers and Op-Amps. Low-Power Circuit Techniques Themes, Mixed-signal & future of low-power designs. GBM5320 - Dispositifs Médicaux Intelligents 14

MOSFET Structure The NMOS transistor is on p- substrate (bulk or body). L Two n+ regions form S (source) and D (drain) terminals. MOS transistor is symmetric. S has lower potential than D for NMOS. p- substrate is connected to the most negative voltage. L drawn is the channel length drawn in the layout L is the effective channel length. t ox is the gate oxide thickness (40Å in 0.18 µm and 22Å in 0.13 µm) GBM5320 - Dispositifs Médicaux Intelligents 15

MOS Characteristics If V GS > 0, the electrical field will repel holes and attracts electrons. S V G >>0 + + + + + + + + + + + + + + D hen V GS reaches n+ a value called the threshold voltage (V th ), channel Depletion region under the gate becomes inverted. It changes from p-type to n-type semiconductor. - - - - - - - - - - - - - - - - - p - substrate B n+ Channel n-type channel exists between the source and drain that allows carriers to flow. GBM5320 - Dispositifs Médicaux Intelligents 16

I D MOS Characteristics ID I = µ C V V 2L ( ) 2 D n ox GS th I-V characteristics If V GS > V th the channel is inverted. Conductivity is controlled by V GS - V th. hen V DS > 0 current I D flows from drain to source. The drain current : I D = dq dt dq is the channel charge in dy at a distance y from the source, and dt is the time required for this charge to cross the length dy. V S = 0 n+ Triode region I = µ C ( V V ) V L D n ox GS th DS - + V(y) V DS =V dsat y V G S >V th y+dy Active region B y V DS > 0 n+ I D V DS GBM5320 - Dispositifs Médicaux Intelligents 17

MOS Characteristics I-V characteristics (Cont d) dq = Q I dy Q I is the induced electron charge in unit area of the channel. The gate-to-channel voltage at a distance y from the source is V GS -V(y). Assume this voltage exceeds V th we can write: Q I = C ox dt = dy v d ( y) V GS V ( y) V th v d (y) is the electron velocity at y. v d (y) = µ n E (y), E (y) = - C ox = ε ox t ox = K ox ε 0 t ox E(y) is horizontal electrical field and µ n is the average electron mobility. dv dy I D = dq dt I D = C ox V GS V ( y) V th µ n dv dy GBM5320 - Dispositifs Médicaux Intelligents 18

MOS Characteristics I-V characteristics (Cont d) L V I D dy = C 0 DS ox V GS V ( y) V 0 th µ n dv I D = µ n C ox 2L 2 ( V V 2 GS th )V DS V DS If V DS << 2(V GS - V th ), I D is proportional to V DS. I D = µ n C ( ox L V V GS th )V DS I D Triode region I = µ C V V 2L Active region ( ) 2 D n ox GS th I = µ C ( V V ) V L D n ox GS th DS V DS =V dsat V DS GBM5320 - Dispositifs Médicaux Intelligents 19

MOS Characteristics I-V characteristics (Cont d) I D I < µ C ( V V ) V L D n ox GS th DS VS = 0 V G S >>V th V D > 0 I D n+ n+ I = µ C ( V V ) V L D n ox GS th DS B V DS As V DS increases, I D increases until the drain end of the channel becomes pinch off. Pinch off occurs when V GD <= V th the channel is not inverted near the drain (Q I =0). V GD V th V DS V GS V th GBM5320 - Dispositifs Médicaux Intelligents 20

MOS Characteristics I-V characteristics (Cont d) I D V S = 0 V G S >>V th V GD <V th, V DS >V GS -V th I = µ C V V 2L ( ) 2 D n ox GS th I D Active region n+ n+ Triode region Pinch -off I D = µ n C ox 2L 2 V V GS th = µ n C ox ( 2L V V GS th ) 2 2 ( )V DS V DS V DS =V GS V th =V Dsat I = µ C ( V V ) V L D n ox GS th DS V DS =V dsat For V DS > V GS -V th I D stays constant by ignoring the second order effects. V DS GBM5320 - Dispositifs Médicaux Intelligents 21

MOS Characteristics Channel length modulation I D increases slightly with increasing V DS due to the increasing of the depletion region width X d with V DS VS = 0 n+ L eff VB = 0 V G S >>V th X d V DS >V GS -V th n+ I D I D = µ n C ox 2L eff ( V GS V th ) 2, L eff = L X d di D = µ dv n C ox V 2 DS 2L GS V th eff ( ) 2 dl eff dv DS = I D L eff dx d dv DS = λi D GBM5320 - Dispositifs Médicaux Intelligents 22

MOS Characteristics Channel length modulation (cont d) I D = µ n C ox ( 2L V V GS th ) 2 ( 1+ λv DS ) Therefore, a good approximation to the influence of V DS on I D is I D Triode region Active or pinch -off region V DS = V GS -V th Actual I D I ( D λ = 0) + di D V dv DS DS Ideal V GS Increases = I ( D λ = 0) ( 1+ λv ) DS V GS <=V th I D = µ n C ox ( 2L V V GS th ) 2 ( 1+ λv DS ) I D = µ n C ox ( L V V GS th )V DS V DS GBM5320 - Dispositifs Médicaux Intelligents 23

MOS Characteristics Body effect V S > 0 V G S V DS If V SB increases, the effective threshold voltage increases. ID V SB increases, the depletion region between the channel and the substrate becomes wider à Q B k. n+ V B = 0 n+ Q B qn A x d = 2qε Si N A 2Φ F 2qε Si N A (2Φ F +V SB ) V th = V th0 + ΔV th, V th0 = V th (V SB = 0) V th = V th0 + γ ( V SB + 2Φ F 2Φ F ), γ = 2qN K ε A Si 0 C ox γ is the body effect constant GBM5320 - Dispositifs Médicaux Intelligents 24

PMOS equations µ p C ox I D = 2L 2 ( V V 2 SG thp )V SD V SD, V > V andv > V SG thp DG thp µ p C ( ox 2L V V ) 2 1+ λv SG thp ( SD ), V SG > V thp andv DG < V thp I D Triode region Active or pinch -off region V SD = V SG - V thp Actual Ideal V SG Increases V SG <= V thp VSD GBM5320 - Dispositifs Médicaux Intelligents 25

MOS symbols D B G S NMOS PMOS The B symbol is used for substrate to avoid confusion with source. Drain in NMOS is positioned on top while the source is positioned on top for PMOS. Symbol with B connection is used when the source and the substrate have different voltages Symbols w/o arrow are used for digital circuit. GBM5320 - Dispositifs Médicaux Intelligents 26

Device model summary Linear / triode region V DS < V GS - Vth Saturation region V DS >= V GS - Vth eak inversion V GS < Vth V GS nv T I = I e 1 e D S 0 L V GS V DS V T I e, V >> V L nv T S 0 DS T kt 0 V = 26 mv at T = 300 K T q Strong inversion V GS > Vth 2 V DS I = µ C ( ) D ox V V V GS th DS L 2 µ C ( V V ) V, V << V L ox GS th DS DS dsat 1 I = µ C V V + λv 2 L 2 ( ) ( 1 ) D ox GS th DS GBM5320 - Dispositifs Médicaux Intelligents 27

Equations : NMOS I D Triode region Active or pinch -off region In V DS = V GS -V th Actual Ideal V GS Increases V SS V DD Out V GS <=V th I D = µ n C ox ( L V V GS thn )V DS, V GS > V thn andv GD > V thn (V DS < V GS V thn ) µ n C ox ( 2L V V GS thn ) 2 ( 1+ λv DS ), V GS > V thn and V GD < V thn (V DS > V GS V thn ) V DS V thn = V thn0 + γ ( V SB + 2Φ F 2Φ F ), γ = 2qN K ε D Si 0 C ox λ = dx d L eff dv DS GBM5320 - Dispositifs Médicaux Intelligents 28

Equations : PMOS ID Triode region Active or pinch -off region In V SD = V SG - V thp Actual Ideal V SG Increases V SS V DD Out V SG <= V thp VSD I D = µ p C ox ( L V V SG thp )V SD, V SG > V thp andv DG > V thp (V SD < V SG V thp ) µ p C ox ( 2L V V SG thp ) 2 ( 1+ λv SD ), V SG > V thp andv DG < V thp (V SD > V SG V thp ) V thp = V thp0 + γ ( V BS + 2Φ F 2Φ F ), γ = 2qN K ε A Si 0 C ox λ = dx d L eff dv SD GBM5320 - Dispositifs Médicaux Intelligents 29

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 GS + v i - V DS V DS >V GS -V th I d = µ n C ( ox 2L V V γ 2Φ +V 2Φ ) 2 ( 1+ λv ) GS th0 F SB F DS I d = f (V GS,V DS,V SB ) = I D + i d = I D + I d V GS ΔV + GS I d V DS ΔV + DS I d V BS ΔV BS GBM5320 - Dispositifs Médicaux Intelligents 31

Small-Signal Models of MOS Transistors Transconductance g m G D g m I D V GS I D = µ n C ox 2 µ n C ox 2 ( )( V GS V t ) 2 L 1 + λv DS L V V GS t ( ) 2 λv DS << 1 g m µ n C ox L V ( GS V t ) 2µ n C ox L I D = 2I D V Dsat S V gs g m v gs V bs B g mb v bs r ds Output resistance r ds g ds r ds 1 I D V DS g ds = µ n C ox V DS 2 ( )( V GS V t ) 2 = µ nc ox L 1+ λ V DS 2 ( ) 2 λ I D L λ V GS V t GBM5320 - Dispositifs Médicaux Intelligents 32

Small-Signal Models of MOS Transistors Body Transconducatnce g mb g mb I DS V BS = µ n C ox V BS 2 ( ) 2 = µ n C ox L V GS V th 2 ( ) V th L V GS V th V BS V th = V th0 + γ ( 2Φ F + V BS 2Φ ) F G D g mb = g m γ 2 2Φ F + V SB S V gs g m v gs g mb v bs r ds γ = 2qεN A V bs C Ox B GBM5320 - Dispositifs Médicaux Intelligents 33

Small-Signal Models of MOS Transistors Example : γ = 0.3, G D λ n Ξ 0.025 (1/V), 2Φi F = 0.6V, I D = 1 ma, S V gs g m v gs g mb v bs r ds V dsat = 200 mv, V bs V SB = 100 mv. g m = 1 ma/v (ms); S = Siemen B g mb = 0.18 ma/v Ξ 20% g m r ds = 40 k. GBM5320 - Dispositifs Médicaux Intelligents 34

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 2L 2 ( V V 2 GS th )V DS V DS g ds r ds 1 I D V DS = µ n C ox L S ( V GS V th V DS ) r ds D If V DS << V GS - V th, (the common case V DS near to zero) g ds = 1 = µ n C ox r ds L ( V V GS t ) This resistance value is controlled by V GS. GBM5320 - Dispositifs Médicaux Intelligents 35

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. GBM5320 - Dispositifs Médicaux Intelligents 36

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 1. 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 o i i g m s(c gs + C gd ) f T = 1 2π i o i i g m (C gs + C gd ) 1.5 µ n 2π L 2 s= jω 1 ( V V GS th ) + v gs - i i C gs C gd g m v gs f T can be improved by operating at high values of (V GS -V th ), and faster transistor can be made by smaller L. GBM5320 - Dispositifs Médicaux Intelligents 37 i o

Diode connected MOS DC analysis i D = µ n C ox ( 2L V V GS thn ) 2 ( 1+ λv DS ) AC analysis (small signal) GBM5320 - Dispositifs Médicaux Intelligents 39

Analog CMOS Inverter l Analyse AC (faibles signaux) v A = = g r R g R ( ) out v m ds m vin GBM5320 - Dispositifs Médicaux Intelligents 40

Analog CMOS Inverter AC analysis (continued) Vo Transfer function (G) = vo/vi Vi Vgs S gm1 Vgs rds1 rds2 = ( vo rds 1) gm 1vgs1 ( vo r o ds2 ) ( ) Kirchhoff: 0 / / Transconductance and output impedance (g m, r ds ) g m = µ Cox 2µ L r ds λ = 1 λi L ( VGS Vth ) = Cox I D v v = g r r i m1 ds1 ds2 = G 1 1 g r m ds = 2 µ C ox λ L I Voltage Gain (G) D D G lorsque ou L dx d L eff dv DS G lorsque I D GBM5320 - Dispositifs Médicaux Intelligents 41

Current Mirror Simple current mirror I DC analysis V GS OUT = V = th + 1 µ C 2 ox µ C 2I ox ref ( L) ( L) 1 2 µ C 2I ox ref ( L) I D = µ n C ox ( 2L V V GS th ) 2 ( 1+ λv DS ) 1 = ( L) 2 I ref ( L) 1 M1 iref iout + M2 Vout - Output impedance: r out = r ds2 = 1 λ I out λ = dx d L eff dv DS ΔV = V GS V th = µ C 2I ox ref ( L) 1 VGS-Vth GBM5320 - Dispositifs Médicaux Intelligents 43

Current Mirror Cascode current mirror DC analysis V =Veff= V GS - V th at I D =I ref Vth+Veff=VGS Vout = 2Vth+ 2Veff - Veff -Vth + Veff V V + 2ΔV OUT th -VGS M3 M4 iref 2(Vth +Veff) Vth +Veff iout M2 VA + + Veff - Vout M1 - M2 M1 + Vx - ix The output impedance is increased by a factor (1 + a v2 ): + Vsb2 - gm2 Vgs2 rds1 gmb2 Vsb2 rds2 Vx v i x x ( 1 ) = R + g r r out m2 ds1 ds2 Vth+2Veff GBM5320 - Dispositifs Médicaux Intelligents 44

Current Mirror ilson current mirror - DC analysis I OUT = ( L) 2 I REF ( L) 1 Ids1 M1 M3 M2 Io + Vo - Output impedance - Vth+2Veff Vo Io Ids1 Vds1 r o = g m1 r ds1 r ds3 Iref Iout Super-ilson current mirror - DC analysis M3 M4 VA M2 M1 + Vout - GBM5320 - Dispositifs Médicaux Intelligents 45

Current Mirror ide-swing cascode current mirror - DC analysis Cascode iref iout M3 2(Vth +Veff) VA M2 + Vout M4 Vth +Veff M1-2Veff Advantage: minimum output voltage is only 2 Veff Downside: increased complexity and power consumption. Vth+2Veff GBM5320 - Dispositifs Médicaux Intelligents 46

Current Mirror Improved ide-swing cascode current mirror - DC analysis 2Veff Added transistor M5 equalizes the voltages at the drains of M1 and M3 : Channel-length modulation effects are reduced. GBM5320 - Dispositifs Médicaux Intelligents 47

Voltage Follower The voltage follower, as suggested by its name, replicates voltage V in at the output. DC Analysis Vdd Vdd Vin I Bias Vout Vin I Bias Vout I Assume that the transistor is saturated: D = I = µ C BIAS ox 2L ( V V V ) 2 IN OUT th Vss P-well process Vss N-well process V OUT = 2 L I BIAS µ C ox + V IN V th V th = V ( 2φ + V φ ) th0 + F OUT γ 2 F If the substrate is connected to the source, then V th =V tho. GBM5320 - Dispositifs Médicaux Intelligents 49

Voltage Follower AC Analysis Av = g m1 g m1 + g s1 + g ds1 + g ds2 GBM5320 - Dispositifs Médicaux Intelligents 50

Voltage Follower AC Analysis (Cont d) If g m1 Av = g m1 + g s1 + g ds1 + g ds2 g m1 g s1 + g ds1 + g ds2 Av " 1 In practice, this value is degraded by r ds1,2 and g s1, 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. i x = ( g ds1 + g ds2 + g mb + g m1 )v x R out = 1 g ds1 + g ds2 + g mb + g m1! 1 g m1 GBM5320 - Dispositifs Médicaux Intelligents 51

Common Gate Amplifier AC analysis V out V s1 = g m1 + g s1 + g ds1 G L + g ds1! g m1 G L + g ds1 Y in = i s = g + g + g m1 s1 ds1! g m1 V s1 1+ g ds1 G L 1+ g ds1 G L r in = 1 g m1 1+ R L r ds1 GBM5320 - Dispositifs Médicaux Intelligents 52

Common Gate Amplifier AC analysis (Cont d) r in = 1 g m1 1+ R L r ds1 R L = r ds r in = 2 g m1 V s1 V in = r in r in + R s = 2 g m1 2 g m1 + R s = 2 2 + g m1 R s V out V in = V out V s1 V s1 V in V out V s1 = g m1 r ds1 + r ds2 GBM5320 - Dispositifs Médicaux Intelligents 53

Operational amplifiers Ideal Op-Amp Openloop Vp + ve Vn - + A ve Vo Closedloop Vp + ve Vn - + A ve Vo Basic 2-stage Op-Amp R1 R2 M3 M4 Vdd M5 M6 M7 Vdd M8 Iref V+ M1 M2 V- Vout Cout V+ Iref M1 M2 V- Vout Cout M6 M7 Vss M8 M3 M4 Vss M5 NMOS inputs PMOS inputs Small signal open-loop gain: G oa = gm ro = gm1 (ro2 ro4) gm5 (ro5 ro8) GBM5320 - Dispositifs Médicaux Intelligents 55

Operational amplifiers : Stability GBM5320 - Dispositifs Médicaux Intelligents 56

Operational amplifiers : Stability A V2 C C Vi R1 R2 gm1 Vi C 1 gm2 V2 C 2 Vo A = a1a2 CL=C2 a1 a2 C1 C2 IAI (db) P#1 P#2 0 0 f (Hz) Phase -90-180 GBM5320 - Dispositifs Médicaux Intelligents 57

Vi Operational amplifiers : Stability V o V i = gm1 Vi R1 V2 C 1 C c R2 gm2 V2 C 2 g m1 g m2 R 1 R 2 (1 C c Vo s g m2 ) = -1 R 2 C c R 1 P2 = C 1 +C 2 1+ s[(c 2 + C c )R 2 + (C 1 + C c )R 1 + g m2 R 1 R 2 C c ]+ s 2 R 1 R 2 (C 1 C 2 + C c C 1 + C c C 2 ) P1 g m 2 g m 2 z = g m 2 C C z = C C 1 g 1 m2 R Z Vi gm1 Vi R1 CC C1 RZ gm2 V2 R2 C2 Vo P 2 = g m 2 C 2 GBM5320 - Dispositifs Médicaux Intelligents 58

Operational amplifiers: Voltage offset Ideal Op-Amp Vp + + M3 M4 Vdd M5 Vn ve - A ve Vo Iref V+ M1 M2 V- Vout Cout Small signal open-loop gain: G oa = gm1 (ro2 ro4) gm5 (ro5 ro8) Mismatch between input transistors V os = ΔV T (1 2) + ΔV T (3 4) g m3 g m1 + M6 ( V GS V T )( 1 2 ) 2 Mismatch between loads after attenuation by Gms M7 Δ L ( 1 2) L ( 1 2) Vss Δ L GBM5320 - Dispositifs Médicaux Intelligents 59 L M8 ( 3 4) ( 3 4) Mismatch between /L of input trs and loads when operate at weak biaising voltage.

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. GBM5320 - Dispositifs Médicaux Intelligents 60

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 GBM5320 - Dispositifs Médicaux Intelligents 61

Operational amplifiers : Input common-mode range Input common-mode range Differential amplifier with a current mirror load. Slew rate SR SR = = 2I D1 g ω m1 2 ( V ) GS Vth ω 2 1 GBM5320 - Dispositifs Médicaux Intelligents 62

Operational amplifiers : Noise Dominate noises are thermal and flicker Active region V 2 R ( f ) K = LC ox f 2 R ( ) I f = 4kT γ g m 2 K 1 R = + 4 γ ( ) V f kt LC f g ox m V ( ) n f 10 µ V Hz 1 0 0.1 3.2 1 1/f noise dominates -10dB/decade 10 Root spectral density 1/f noise corner hite noise dominates Vn ( Hz) 6 2 ( 3.2 10 ) 2 ( ) ( f ) = + 1 10 f 2 6 PMOS has less flicker noise than NMOS (holes mobility is less than electrons) g m = µ Cox 2µ L L ( VGS Vth ) = Cox I D GBM5320 - Dispositifs Médicaux Intelligents 63

Operational amplifiers : Noise GBM5320 - Dispositifs Médicaux Intelligents 64

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. 2 2 2 2 i = g ( v + v ) 2 2 2 + g ( v + v ) O m1-2 eq1 eq2 m3-4 eq3 eq4 i 2 O = g 2 m1 2 v 2 IT GBM5320 - Dispositifs Médicaux Intelligents 65

Operational amplifiers : 1/f NOISE For a MOS transistor the input-referred 1/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 1/f noise for the entire stage is g = µ C V V = 2µ C L Assuming that L2 = L1, 2 = 1, L4 = L3 and 4 = 3; m ox ( GS th ) ox D L I GBM5320 - Dispositifs Médicaux Intelligents 66

Operational amplifiers : Thermal NOISE The input-referred thermal noise for an NMOS transistor is: γ = 2qεN A C Ox GBM5320 - Dispositifs Médicaux Intelligents 67

Mixed-signal Low-power Circuit Techniques - Power consumption in microelectronics systems - Analog-digital SNR crossover curves (Power, Area vs SNR) - Feedback and calibration (Analog & Digital techniques) - Ultra-low-power systems of the future (Analog & Digital techniques) - Five determinants of low-power techniques - Task, Technology, Topology, Speed and Precision - Optimum point for digitization - Traditional vs Energy efficient mixed-signal architecture - Themes in low-power mixed-signal circuit design - Slow and parallel operation - Noise and offset management - Compressive functions (AGC) - Pipelined designs - High-speed Technology (high gm/c) - Symmetric designs (less offset) - Gating circuit techniques. GBM5320 - Dispositifs Médicaux Intelligents 69

Principles of Mixed-signal Low-power Designs - Themes in low-power mixed-signal circuit design (Cont d) - Passive systems with high Q - Adaptive biasing - Efficient encoding of the needed computation. - Evolution of low-power designs - Subthreshold operation maximizing energy efficiency - Optimize analog preprocessing before digitization - Balance computation and communication cost - Exploit collective analog or hybrid computation - Reduce the amount of information to be processed - Use feedback and feed forward architectures (robustness and efficiency) - Separate speed and precision - Operate slowly and adiabatically. GBM5320 - Dispositifs Médicaux Intelligents 70