Convertidores A/D para señales de sensores

Transcripción

1 Convrtdors A/D ara sñals d snsors Ingnro n Elctrónca, º Curso Frnando Mdro Dto. Elctrónca Elctromagntsmo Escula Suror d Ingnros Unvrsdad d Svlla Insttuto d Mcrolctrónca d Svlla CNM, CSIC Unvrsdad d Svlla Convrtdors ara snsors d 3 F. Mdro Convrtdors A/D ara snsors Analog sgnal DR (bt) Amlfcaton Ssmolog DC Instrum & snsor ntrfacs. Intrfac A/D K Fltrng K K M A/D Thrmal nos lmt M dgtal sgnal Radar Sch ADSL Vdo HDTV Dsk Drvrs Prsonal Comm. [Nshmura Ph.D. 993] Intgratng ADC Incrmntal ADC Σ ADC Audo db(.33bt)/ar Algorthmc M Flash, Pln, Introlatv Amltud (dbv) G log(frq.) Hz Outut sctrum Rsoluton (DR) Sd Frqunc (Hz) Σ modulaton-basd convrtrs sutabl for a larg numbr of alcatons Convrtdors ara snsors d 3 F. Mdro

2 Convrsón Sgma-Dlta Prncos báscos Antalasng fltr a Ovrsamlng Modulator sh S/H Nos-shang Gross quantzaton n Dgtal fltr Dcmator f Dgtal rocssng Downsamlng d N a () t, sh () t n ( ) f ( n) d ( n) t n... n... n Xf () antalasng fltr surous f b X sh () f quantzaton rror wth nos-shang Y() f Y f ( f ) dgtal fltr... Y d ( f) f b f b f b f b Convrtdors ara snsors 3 d 3 F. Mdro Convrsón Sgma-Dlta Ruído d cuantzacón sobrmustro P Q S E () f g q mn mn g q ma ma Quantzaton rror dtrmnstc functon of th nut, howvr [Bnn48] If vars randoml from saml to saml S E () f ( Constant) f If th numbr of quantzaton lvls s larg S quantzaton nos Total quantzaton nos owr ntgratd n th sgnal band (In-band nos) M ovrsamlng rato f f S f f M S M / Convrtdors ara snsors 4 d 3 F. Mdro

3 Convrsón Sgma-Dlta El modulador Sgma-Dlta S/H Σ Modulator n bt g q Quantzr modl Frst-ordr Σ Modulator [Inos, Tran. S. Elct. & Tl.96] Z-doman rlatonshs Yz ( ) STFXz ( ) NTFEz ( ) Yz ( ) Xz ( ) Ez ( ) STF ct NTF for z ( low-frqunc) for z z z Convrtdors ara snsors 5 d 3 F. Mdro Convrsón Sgma-Dlta Modulador Sgma-Dlta d r ordn z z f-doman rlatonshs: S Q () E () f jπ f - P Q z Z-doman rlatonshs: Yz ( ) jπ f Xz ( ) Ez ( ) Yz ( ) z Xz ( ) ( z )Ez ( ) Dla S E () f 4 sn π f - S Q () f π M -» ; f 3M 3 d f b NTF f Frst-ordr nos-shang Nos Shang () dgtal fltr nos S E () f Dcras n P Q b ncrasng M 9dB/octav (3dB/octav for a sngl quantzr) f b Convrtdors ara snsors 6 d 3 F. Mdro

4 Convrsón Sgma-Dlta Caractrzacón dnámca Sgnal-to-nos rato (SNR): " Sgnal owr In-band nos owr Oftn gvn n db. For a snusodal nut of amltud A: A SNR( db) log P Q " at th modulator outut SNR(dB) Ovrloadng Sgnal-to-(nosdstorton) rato (TSNR) Amltud (dbv) Dnamc rang (DR): " " at th modulator outut Full-scal nut rang outut rang of th n-loo convrtr For sngl-bt quantzaton, DR( db).76 b( bt) [ DR 3 6. ( b ) ].5bts/3dB DR (b) / (M).5bt/octav (st-ordr Σ M) or.5bt/octav (quantzr) Effctv rsoluton (b): Full-scal sgnal owr In-band nos owr A FS DR( db) log ( ) P Q Convrtdors ara snsors 7 d 3 F. Mdro Convrsón Sgma-Dlta Arqutcturas-I st-ordr Σ Modulator How to ncras rsoluton? Incrasng M; f f b > Incrasng th ordr of NTF(z) Incrasng th numbr of quantzr lvls P Q π 3M 3 For th sam M smallr nos owr nd-ordr Σ Modulator [Cand, Trans. Comm. 985] g g frqunc-doman rlatonshs: S Q () E () f jπ f - 4 P Q g g S Q () f π4 5M 5 Z-doman rlatonshs: Yz ( ) z Xz ( ) ( z ) Ez ( ) Dla S E () f 6 sn4 π f - NTF ( f ) (DR) vs. M 5dB/octav (.5bt/octav) nd-ordr nos-shang st-ordr nd-ordr f Convrtdors ara snsors 8 d 3 F. Mdro

5 Convrsón Sgma-Dlta Arqutcturas-II Sngl-loo Lth-ordr Σ Modulator L ntgrators g g g L g L Z-doman rlatonshs: Yz ( ) z L Xz ( ) ( z ) L Ez ( ) frqunc-doman rlatonshs: S Q () f S E () f L sn L π f - P Q π L ( L )M ( L ) (DR) vs. M 3(L)dB/octav (L/bt/octav) Problms: Hgh-ordr modulators (L>) ar not uncondtonall stabl Instablt occurs for som nut lvls and ntal condtons that cannot b rdctd analtcall Tchnqus to stablz hgh-ordr loos caus a sgnfcant loss of rsoluton rsct to th dal cas Convrtdors ara snsors 9 d 3 F. Mdro Convrsón Sgma-Dlta Arqutcturas-III B L. B B [L & Sodn, ISCAS 987]. A A A L A NTF Z-doman rlatonshs: Yz ( ) STFXz ( ) NTFEz ( ) STF ( z ) L B ( z ) L L L L A ( z ) N z ( z ) L B ( z ) L A ( z ) L L z ( z ) L B ( z ) L A ( z ) L L L Goods: Rducd NTF(f) out of th band > ncras stablt All B > all zros at DC (Buthrworth or Chbchv) Othrws, zros n th sto-band > mamz fltr slctvt (Invrs Chb. or Elltc) Problms: Incrasd hardwar comlt Otmum coffcnts ml larg caactors n SC mlmntatons Incrasd occuaton ara Incrasd owr consumton Convrtdors ara snsors d 3 F. Mdro

6 Convrsón Sgma-Dlta Arqutcturas-IV Σ N L Σ 3 L Σ N L N L N Z-doman rlatonshs: CANCELLATION LOGIC Y STFXz ( ) NTF ( z )E ( z ) NTF E NTF 3 ( z )E 3 ( z ) STF z 4 NTF, NTF NTF 3 ( z ) 4 -- Cascad 4th-ordr Σ Modulator g g 3 ( g g H z g g 3 ( g g ( z ) g 4 g g g 3 g 3 [Yn & Sansn, JSSC94] g 3 g 4 g 4 g 4 g 3 g g 3 g g g H g 3 g 4 3 z E E E 3 d 3 Cancllaton logc H (z) H g 4 ( g g 3 g 4 ( z ) d d H 3 d 3 H 4 Yz ( ) z 4 Xz ( ) d 3 ( z ) 4 E 3 Convrtdors ara snsors d 3 F. Mdro Convrsón Sgma-Dlta Cuantzacón multbt Mult-bt Σ Modulator S/H B bts Goods: Rducd quantzaton nos Imrovd stablt -. Non-lnart S E () f Bnar nut / outut Analog outut q q Full scal B ( rsoluton) 3.3lo ( B ) -. q Analog nut Bttr fttng to aromat analss Problms! Modulator lnart lmtd b that of th Nd of corrcton tchnqus or ror archtcturs Convrtdors ara snsors d 3 F. Mdro

7 Convrsón Sgma-Dlta Otros mcansmos d rror Dfctv sttlng rrors Wght msmatch SNR (db) Comarator hstrss Fnt DC-gan Inut Lvl Clock Jttr P T P Q P St P Th... non-lnart Non-lnar DC-gan Thrmal nos AO A v (db) A v o (V) FOLDED BACK NOISE Frq Lnart rror -. DI Convrtdors ara snsors 3 d 3 F. Mdro Convrsón Sgma-Dlta Gananca fnta z z Imls nfnt DC-gan! Yz ( ) z Xz ( ) ( z )Ez ( ) Not ossbl n ractc C C v S (φ) S (φ) C C S (φ) S (φ) v v o - A V v In ractc: Loss ntgrator A V» z ( µ )z µ A V Yz ( ) z Xz ( ) ( z µz )Ez ( ) frqunc-doman: S Q () f P Q ( µ ) µ f 4 sn π f - S f S π µ M 3M 3 NTF ( f ) Loss µ Idal f for Lth-ordr sngl-loo Σ M: P Q ( µ ) µ π L ( L )M L π L ( L )M L domnant tra trm ~ /M L- Convrtdors ara snsors 4 d 3 F. Mdro

8 Convrsón Sgma-Dlta Dsaaramnto d condnsadors Σ N L Σ 3 L Σ N L N L N Z-doman rlatonshs: CANCELLATION LOGIC Y STFXz ( ) NTF ( z )E ( z ) NTF E NTF 3 ( z )E 3 ( z ) STF z 4 NTF, NTF NTF 3 ( z ) 4 -- Cascad 4th-ordr Σ Modulator g g 3 ( g g H z g g 3 ( g g ( z ) g 4 g g g 3 g 3 g 3 g 4 g 4 g 4 g 3 g g 3 g g g H g 3 g 4 3 z E E E 3 d 3 Cancllaton logc H (z) H g 4 ( g g 3 g 4 ( z ) d d H 3 d 3 H 4 Yz ( ) z 4 Xz ( ) d 3 ( z ) 4 E 3 Convrtdors ara snsors 5 d 3 F. Mdro Convrsón Sgma-Dlta Establcmnto ncomlto SC Intgrator Intgratng confguraton v o (t) Outut voltag v (φ) S S (φ) φ C S (φ) S (φ) OTA v o g C C C v a OTA v of v o g v v o C l v of v o [ nt S T S ] SR t ε( T S ) t φ Modllng... C Equvalnt to... gnl ( v ) v a C I o I o t g m v a v v o o ( T S ) g C o l g ( β) ; v v L v on g β v v ( L ); v > v L nt S -T S / C v on, v C C C g ς T m S o C C q v o f v I o ( g m ς) C, v C - C I osgn( v ) g m f v > I o ( g m ς) C β - g ς T m S C g C q v L I o g m ς v L ς lnal rang C nt S C q C q C t g g m T m I v - o S t q C C C q C C C l gnl ( v ) v L C l - v C l Convrtdors ara snsors 6 d 3 F. Mdro

9 Convrsón Sgma-Dlta Rudo térmco Thrmal nos (swtchs, OTA) flckr nos (OTA) (t) v v S (φ ) S (φ ) S 3 (φ ) S 4 (φ ) Clk(t) C C C S (φ ) S (φ ) C (φ ) S 3 S 4 (φ ) Foldd-back nos n a SH crcut S () f f «- S φ φ - (t) v o Clk τ SH τ T T S -BW n / s () f τ SH τ SH ; f T S T S S BW n BW n τ SH S ; f < BW f T S S S n S BW n / f S f q, C Calculaton tchnqu: For ach thrmal nos contrbuton calculat quvalnt BWn and al SH quaton () τ SH C T kt C S C kt C C C C τ T ktg m R T S C on C C P th kt C MC C kt ktg m R on MC MC Nos PSD (db/hz) C Foldd nos Inut lvl Calculatd HSPICE Frq Convrtdors ara snsors 7 d 3 F. Mdro Convrsón Sgma-Dlta No lnaldad jttr v Caactor non-lnart Cv ( ) ( α v β v ) v C( v) ( αv) S (φ) S (φ) v v φ φ C C C C S (φ) S (φ) v φ v α v n --- v n C α v --- v α v n --- v n v n v n v α --- v α v α v n ( v v ) --- g ( v v ) For snusodal nuts v A sn ( πf b nt S ) α v v π ( f b ) v n v n v --- v v Oam DC-gan non-lnart A V v ( A v n V )v n v ( v ± V r ) A V A V γ, γ «v v n v n v n v v γ v v n γ v v v n n n A A A A H, - α A 4 A V A ( γ v γ v ) 8 DC-gan (db) Usng harmonc analss γ γ A H, V A o V V o A H, V 4 A o V V o γ V π f b T s A «V o A A H, g A A A H 75 7 Outut voltag (V) γ, g 3 4A A 3 Clock Jttr v ( nt δ) v ( nt ) π f b Aδcos ( πf b nt S ) samlng tm rror (gaussan, σ t ) S J ( f ) ( ) A πf b σ t A P f J S ( π fbσt ) M Convrtdors ara snsors 8 d 3 F. Mdro

10 Convrsón Sgma-Dlta Errors n l cuantzador Q Quantzrs: sngl-bt (comarator) Offst Attnuatd b th ntgrator DC-gan Hstrss h Mult-bt convrtr d [Bosr88] P h 4h π L ( L )M ( L ) SNR (db) Man roblm: Non-lnart Gan rror Offst rror INL Error (LSBs) modl b Idal ε Φ ( a ) ( ε ) a a A 7 ε b INLA ( b )q a Non-lnar block Φ w a γ a off σ D - ( INL LSBs ) q Convrtdors ara snsors 9 d 3 F. Mdro Convrtdors A/D ncrmntals Prnco d funconamnto V n Rst Comarador V o Y Fltro D g Dgtal Intgrador Tras un cclo d rloj... Tras dos cclos V o Tras cclos... V o, V n V rf Y V n V rf V rf V o, V n Y V rf, V n ( Y Y ) V rf V o, V rf En, V o s comara otra vz con V, lo cual quval a comarar V con V rf Y ara j Convrtdors ara snsors d 3 F. Mdro Y Y nvls dscrtos valors Saracón ntr nvls V LSB ( V rf ) S lo gualamos al LSB d un convrtdor A/D dal d B bts: B log bt rqur 496 cclos; 6bt rqur cclos; tc.

11 Convrtdors A/D ncrmntals V n g g g g Rst Rst - ADC V rf V rf V rf Y Y Rst Dgtal Post-Procssng Dgtal d sgundo ordn Sgundo ordn n Cascada Ralmntacón adconal ara lmtar l rango d salda ncsaro n los ntgrators > ncsaro n baja tnsón Códgo d salda LSB ntrno V rf D g ( )Y ( g Y g Y ) V LSB V rf g ( ) B log [ g ( ) ] > sólo 9 cclos ara bt 36 ara 6 bts > la vlocdad ud aumntar Gananca n vlocdad: B B B Convrtdors ara snsors d 3 F. Mdro Convrtdors A/D ncrmntals d trcr ordn Rst -- ADC Rst V n g g g g g 3 g 3 g 3 Rst Rst Y V rf V rf V rf V rf V rf Y Y 3 Dgtal Post-Procssng Dgtal Trcr ordn n Cascada B log - ( ) > sólo 3 6 cclos ara bt 74 ara 6 bts > la vlocdad ud aumntar Inconvnnts: Maor snsbldad a la ganaca fnta Problmas d dsaaramnto ntr rocsado analógco dgtal Maor comljdad dl fltro dgtal V LSB, ff V rf V rf ( ) ( ) Convrtdors ara snsors d 3 F. Mdro

12 Convrtdors ntgradors ( dual-ram ) Prnco d funconamnto Start End CLK V n,dc -V rf g Intgrator Pud sr d tmo dscrto o d tmo contnuo... τ RC R - C Comarator V o Robusto: nsnsbl a mrcsons n constant d tmo τ frcunca d rloj Mínmo contndo analógco Rudos ródcos (como or jmlo ntrfrncas a 5Hz) son lmnados s T s multlo ntro dl rodo dl rudo Mu lnto: ( N ) rodos ara N bts ha d sr mu rcso stabl V rf Y f r D<N:> Start CLK f r Y V o Control logc Countr V n Intgratng V n T T N rods D <N:> rods V n < V n V n V o ( T ) V o ( T T ) V o ( T ) τ τ - T V d t V n T n RC Intgratng V rf τ - ( T T ) V d t T rf V n T V rf T T RC RC D <N:> constant slo V T n V rf N V n D <N:> V n V rf V rf N Convrtdors ara snsors 3 d 3 F. Mdro