EE105 - Fall 005 Microelecronic Devices and Circuis ecure 9 MOS Transisor Small-Signal Model Announcemens Homework 4 due oday Homework 5 due nex week ab 3 his week Reading: Chaper 4 (4.5-4.6), 8.3 Check ou he EECS Colloquium omorrow, Wednesday 4-5pm in he Woz Room (Soda) Mike Rosenfield, IBM, on Muli-core sysems 1
ecure Maerial as lecure MOS I-V relaionship Sample and hold This lecure Sample and hold MOS amplifier example 3 Some Convenions V, I D DC values v gs, i d AC (small signal) values v, i D oal volages, currens in ime domain V gs, I d frequency (Fourier/aplace ransform) domain V, V SS supply volages (someimes currens as well) 4
Sample & Hold Funcion Goal: charge up load capacior o inpu volage rapidly when conrol volage is swiched on; hold volage on capacior when conrol is swiched off Applicaions: analog-o-digial converers vgb() + - vs() + C v() - 5 inear Model: v s small Iniial condiion: v 0 V Gae volage seps from 0 V o V.5 V i µ C ( W / )( v V v ) v D n ox DS DS Gae-source volage: v V v i D Drain-source volage: v DS v S - v µ C ( W / )( V V )]( v v ) [ n ox S 6 3
Equivalen Circui rds vs() + - C v() r DS { µ C ( W / )( V V )} 1 n ox 7 Example µ n C ox 50 µa/v, V V.5 V, V 0.5 V, 0.6 µm If we wan r DS 100 Ω, hen he MOSFET widh mus be: W r DS 0.6 [ µ ncox ( V )] 6 100[ 50 10 ()] 60µ m For an efficien layou, his ransisor wih W/ 100 should be folded see example in Chaper 4. 8 4
Example Waveform v () 50 mv 0.63(50) 31.5 mv v ( ) v τ r DS C S (1 e 50 mv / r DS C ) 9 Sampling Error Absolue error e v - v S Relaive error ε e / v S vs v ε S ε e r ( s / DS C 1 e ) vs s / r DS C, where s is he sampling ime (ime inerval where V V ) Example case: r DS 100 Ω, C 500 ff τ 50 ps For 16 bi precision, we need he relaive error ε < -16 1.5 x 10-5 15 ppm (pars per million) s τln () ε τ(11.1) 554ps 10 5
Sampling arge Volages If he source (a.k.a. inpu) volage is no small need o use he full model for he MOSFET v DS v S v > V v V v V sauraed, as long as v S > V V K µ nc i ox D ( W / ) dv i C D ( ) d ( V V v ) ( v V ) K( V V v ) dv C d v d 0 0 K ( V V v ) C dv 11 Solve for oad Volage v Cdv d 0 C C C o K( V ) K( V V v ) K( V V ) v ( V ) C( V v ) Cv K( V )( V v ) K( V )( V v ) [ K( V ) K( V ) v] Cv v [ K( V V ) C ] K( V V ) v( ) K K( V ) ( V V ) + C C 1+ [ id ( 0) ] ( 1/ C ) i D ( 0) V V 1 6
v () Sampled Volage Waveform i D () 0 1.5 V V v V v V ess han V Slope i D ( 0)/C v approaches V V 1.5 V (for v S V ) µ n C ox 50 µa/v, (W/) 100 i D ( 0) 5.6 ma 13 Improved Sample and Hold NMOS and PMOS ransisors in parallel sampled volage can be pulled up o he supply volage and pulled down o ground. φ vs() + - φ C V() 14 7
A Simple Circui: An MOS Amplifier v in Inpu signal R D V Supply Rail v O V O + v o v V + v s v s i DS I DS + i ds Oupu signal V v o 15 Sweep Inpu Volage v IN +V MOSFET is sauraed high slope v O v DS MOSFET is riode low slope V 0 (negaive supply, V SS 0) v IN v 16 8
Selecing he Oupu Bias Poin V is seleced so ha V OUT is cenered beween +V SUPPY and V SUPPY (i.e. around V /) Consrain on he DC drain curren: I DS (V - V OUT ) / R D I DS I D,SAT... verify ha MOSFET is sauraed afer finding V BIAS 17 Finding he Inpu Bias Volage Hand calculaion: use I D,SAT W µ nc I ox D, SAT ( V ) Typical numbers: W 40 µm, µm, R D 5 k Ω µ n C ox 100 µa/v, V 1 V, V 5 V I D V R SUP D, SAT 10 100 ( 1) I D V Wan V DS ~.5V: I D,SAT V /I D 0.1mA, V 1.3V 18 9
Applying he Small-Signal Volage Approach 1. Jus use v IN in he equaion for he oal drain curren i D and find v OUT v v V + v v s IN ( ) V cos( ω) sm s Resul: v OUT V R i D DS V R D W µ n C ox ( V + v V ) s 19 Solving for he Oupu Volage v OUT vout W µ ( ) 1 ncox v V + s RD V V V I DS vout v V 1+ s RDIDS V 0 10
Oupu Volage v O v DS V 0 v IN v 1 Small-Signal Case inearize he oupu volage for he s.s. case Expand (1 + x) 1 + x + x las erm can be dropped when x << 1 1+ V 1+ V vs V v s V 1+ V v s V + V vs V 11
inearized Oupu Volage For his case, he oal oupu volage is v v + s O V RDIDS 1 V vo VO + vo R ( ) DI V DS RDIDS vs V The oupu volage is he sum of he DC volage V O and he smallsignal volage v o. RDI v DS o vs Av vs V V A V V 3 Plo of Oupu Waveform (Gain!) Numbers: V / (V V T ) 5/ 0.3 16 oupu inpu mv 4 1