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!lash A() Converter 1ntrod3ction

!! All the 'eference ,e-el. /!T1i3 are a-ailable

!! The inp7t .i8nal i. compared to each 'eference ,e-el.

!! The inp7t .i8nal and the reference le-el ma< be

!!C7rrent.

!!>olta8e.

!! Dependin8 on implementation i..7e.

!!The @orld i. t<picall< -olta8eAmode

!! The o7tp7t i. a thermometric code

!!A thermometricAtoAbinar< tran.lation i. needed

ADCFull Scale

C C b1414

C C b1515

C C b1212

C C b1313

C C b1010

C C b1111

C C b8

C C b9

C C b6

C C b7

C C b4

C C b5

C C b2

C C b3

C C b1

Input SignalInput SignalSinin

Out

put T

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LTH1TH1

LTH3TH3

LTH4TH4

LTH5TH5

LTH6TH6

LTH7TH7

LTH8TH8

LTH9TH9

LTH10TH10

LTH11TH11

LTH12TH12

LTH13TH13

LTH14TH14

LTH15TH15

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$

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Rd

Rd

Rd

Rd/2

Rd/2

(1)

(2)

(2N-1)

(2N-2)

(2N-3)

b0

b1

b2

bN-1bN-2bN-3

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!

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!! !adder impedance is position-dependent

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!eference (adder +ic-.ac- /oise

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!la$h ADC Comparator operation

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!lash A(C Comparator operation

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!lash '(C Comparator operation

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!

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!lash A() Converter 1par3le Codes

! A #parkle code may be due to2

! Static problem

! 5ff#et

! Dynamic problem

! Samplin9 in#tant error

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!lash '/) Con-erter Spar3le Codes

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!lash '() *on-erter 1eta-3ta4ilit6

! " comparator does not reach a clear output

! 1i33erent 4ates read metasta5le output 6 di33erentl7

! Correct output9 :;;; or ;:::

! <rroneous output9 ::::

! Solutions9

o >atches ?hi4h powerA

o Bra7 encodin4

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!nter&'lati'n Advantage0

! !"e e%ui(alent resolution of a 1las" stage can 4e increased 4y 7inter8olating 4et9een t"e 8rea:8lifier out8uts

! ;dditional latc"es detect t"e 8olarity of t"e difference

4et9een single-ended out8uts of t9o ad=acent 8rea:8lifiers

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! !nterpolation red-ced the 0lash preampli3ier n-m4er

! 5ach preampli3ier e6hi4its a 3inite 7ain

! A non9:ero linear inp-t ran7e centered at ;ri

! <he di33erence 4et=een ;in and ;ri can 4e >-anti:ed at the preampli3ier o-tp-t

! Case @

;A@ B ;C@ i3 ;inB;r@

;AD B ;CD i3 ;inB;rD

! Case D

;AD B ;C@ i3 ;inB;mBE;r@F;rDGHD

! <he polaritI o3 E;ADJ;C@G is the same o3 E;inJ;mG

;AD B ;CD i3 ;inB;rD

! <he e>-ivalent resol-tion o3 a 0lash sta7e can 4e increased 4I Linterpolatin7 4et=een the preampli3ier o-tp-ts

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Inter&olation ,d.antages

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!nterpolation Advanta/es

! "he n&m(er o+ preampli+iers is halved

! "he n&m(er o+ latch is the same

! 5nterpolation red&ces

! 5np&t capacitance

! 6o7er dissipation

! Area

! 9o latenc:; all the o&tp&t si<nals re=&ire one cloc> phase to reach the o&tp&t

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!lash '() *on-erter *ircuit solution

! !he used comparator is the cascade of C23S in6erters 7ith auto8ero

!a#

! p

! !he auto8ero c9cle of the comparators ;i6es rise to char;e pumpin; in the resistor strin; net7or<

! =e9 limitation: offset? components matchin;? loadin;

! @erformance: Aer9 Bi;h speed CDEFB8G H lo7 accurac9 C! I JitG

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Two$step * +ipeline * Sub$ranging 5lgorithm

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! A-C/ 0Coarse A-C2 di4iti5es the inp7t si4nal

! 8he 97anti5ation error 0:esid7al2 is eval7ated

! A-C< 0=ine A-C2 di4iti5es the :esid7al

! i.e. the di??erence AetBeen the inp7t

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This concept is valid for an< kind of 5DC

– CDampleF =lash <AG<A

! A-C/ " H comparators

! A-C< " H comparators

! :esid7al calc7lator " /-AC G /Opamp

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! =7ll KA =lash " /L comparators

1

1

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0

0

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ADCADC2

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!wo-step *ubranging 234 Con6erters 7las9 implementation

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ADCADC2

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1

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o!"he re>;irements for the comparators of 8?@0 are relaAed

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!

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V in (nT) ADC +

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1 2 K-1 K

b j-1 ,…,b 1 , b 0 Sample (n-K-1)

b 2j-1 ,…,b j+1 , b j Sample (n-K-2)

b (k-1)j-1 ,…,b (k-2)j+1 , b (k-2)j Sample (n-1)

j j j j

b kj-1 ,…,b (k-1)j+1 , b (k-1)j Sample n

res res res

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!" $%&'()*+,,+ – !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <9= +> 9;8

!ipeline A/* Converter Switched-capacitor implementation

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!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <96 += 9;8

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! !n# co'(arator offset /i1es a con1ersion error

o i2e2 a 345 reduction

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A" Baschirotto - Analog-to-Digital Data Converters 6714707 247 of 471

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! !f#$in#3#$(i)#

! !#$*+si)u+.20$in2#

A" $aschir+tt+ - Anal+g-t+-Digital Data C+n4erters 67897:; <9= +f 9;8

!ipeline A)* Converter 0hreshold error

!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=: +> 9;8

!ipeline ()* +on-erter 0o *i1ital 3rror +orrection

! !"#$"%&%'(&)'"*+,-'"5ithout".&-&+,("/011'/+&0)"

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!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=8 +> 9;8

!i#eline ()D +on-erter 0o Di1ital 3rror +orrection

! !nput&output trans,er cur/es 0ith circuit imper,ections

!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=< +> 9;8

!"#$%"&$'()*'+,&-$./$.'01.$21,%3'-,%/45$'$..,.'

! !"res"old voltage error can 0e eliminated postponing t"e decision

'

'o ! Digital correction

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!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=> +? 9;8

!ipeline ()* +on-erter 21it-sta5e operation

! !" $%n ' $()mp,

! ! $-e/=22$%n,$-e"34

! !" $%n 5 $()mp3

! ! $-e/=22$%n,$-e",4

! !" $()mp,5$%n5$()mp3

! ! $-e/ = 22$%n4

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <=9 o> 9;8

!i#eline'A)*')igital'*orre0tion1'2#eration'

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!" $a&'(i*+,,+ - !nal+g1,+12igi,al 2a,a 3+n4e*,e*& 67897:; <== +> 9;8

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!

– "#!$%&'('#'!

o !")%*+,-'%).#(%&!'#/0-'!

o 1-)/2!-)-3-&#'!'2&$4,%&(5(&0!#4-!'#/0-!%.#6.#'!

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A. Baschirotto – Analog-to-Digital Data Converters 671470; <=; of 4;1

!"p$l"n$ ()* +,$rall r$solut"on

! "#e total )esolution ! o. a pipeline 01C 3it# m di..e)ent stage )esolutions $% 6 &% units o. eac#6 is gi8en b:

o 3#e)e $& is t#e )esolution o. t#e last stage;

o "#e e..ecti8e stage )esolution is t:picall: in t#e )ange o. <=> bits;

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!"#$%"&$ ()* (+,-".$,./+$ 0 1"&2%$ 3.42$

!

! "#$%!s'#()!$o+,-is)s!

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! I# o%&'()io#+ &(,- .)(/&

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!" $aschirotto - !nalog-to-2igital 2ata Converters 67897:; <6: of 9;8

!"#$%"&$ ()* (+,-".$,./+$ 0 1"&2%$ 3.42$ 5#$+4."5&

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!" $aschirotto - !nalog1to1Digital Data 3onverters 67897:; <68 of 9;8

!ipeline A)C A+,-ite,t/+e 0 Single stage ope+ation

!

!

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o &#$!31+%&!%&'($!)*$+'&$%!)-!&#$!2)%&!+$,$-&!%'2*/$!

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o Di ! =5>?@#i5AB9 4>?@#i 5ABC 7*)# . &)$6 -0 ? >-+(3 -11 D.('$&B 0-% r E F .+1 A 0-% r E A

! "#$ -)#$% )$%G& Gi .+1 Vin*i .+1 )#$ .11*)*-+ .%$ 6%-D*1$1 /3 )#$ H;:<

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!"#$%"&$ ()* +$,-&,.&/ 0"1& )"1"/ *2,"&1 3+0)4

! ! digital correction algorithm 012D4 coding,

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! it allows to relax the ?uanti@ation accuracy specifications in sub-!DCs

!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <69 += 9;8

!ipeline A)C +edundant 0ign )igit Coding 3+0)4

! Addi$g a redu$da$t bit mea$s i$creasi$g the stage resolutio$ b3 o$e bit mi$us o$e 4ua$ti5atio$ level7

! Thus9 the amou$t of redu$da$c3 is commo$l3 referred as ;7< bits7

=i>?9 r>; ! ?b =i>?9 r>@ ! ?7<b =i>A9 r>; ! Ab

Threshold Levels > C Threshold Levels > D Threshold Levels > E

Fi > C Fi > C Fi > G

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!"#$%"&$'()*'+$,-&,.&/'0"1&')"1"/'*2,"&1'3+0)4''

– !"anti'ation errors e--ects

! /he lo23resol"tion A5C "ses comparators 2ith

threshold voltages e<"al to the <"anti'ation step locations

– An= o--set in the comparator threshold level is translated

into a <"anti'ation error and appears as a shi-t in the location o- the <"anti'ation step >!os?

– @3Ait stage >dashed line?,

! the comparator o--set ca"ses an over-lo2 o- the

stage o"tp"t sat"rating the neCt stage and res"lting in an erroneo"s <"anti'ation.

– @.E3Ait stage >solid line?,

! the comparator o--set res"lts in a stage o"tp"t greater than !re& F@ A"t smaller than !re&

! " no in-ormation loss

! " correct <"anti'ation reconstr"ction "sing the digital o"tp"t o- the neCt stage

– A comparator o--set o- Go--set H IGre- FJ can Ae tolerated >the stage o"tp"t sta=s 2ithin !re&?

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! !he !" %its of stage " are resolved

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! r !#

Bi =9 : r=; ! 9% resolution 9 !hreshold level

Bi =9 : r=9 ! 9<=% resolution 2 !hreshold levels

Bi =2 : r=; ! 2% resolution 3 !hreshold levels

Bi =2 : r=9 ! 2<=% resolution 6 !hreshold levels

Bi =3 : r=; ! 3% resolution A !hreshold levels

! !he locations of these 4uanti5ation steps relative to the reference voltage $r&' C which corresponds to the fullEscale input amplitude are

o where ( is an integer for which (! 2 F;C (m*+GC with !!!!""#$ ! 2#$"%!1! % !1

! !he num%er of stage output codes is !!!!"# =$# "1= #%#"& ! &

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!ipeline (D* +edundant 0ign Digit *oding 3+0D4

! !"am%le ca*e a +-bit *tage 1ith and 1ithout redundancy

"i9 + : ; "i9 +<= : >

bi9 + : ?

@AA9 AB9 BA9 and BBC

bi9 +9= : D

@AAA9 AAB9 ABA9 ABB9 BAA9 BAB9 and BBAC

! Ehe tolerable oFF*et For *tage i i* in general @r G AC

Ehe tolerable oFF*et &osHi : @S%acing bet1een t1o JuantiKation *te%* &ref+nC L +

! Ehe accuracy oF the *ub-JuantiKation i*M

o relatiNe to the *tage re*olution

o inde%endent oF the total re*olution oF the ODQ<

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <6= o> 9;8

!ipeline ()C +edundant Sign )igit Coding 3+S)4

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A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <;: o= 9;8

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! !""#$%&'#(#)) +#,-()%./%&-(0 %1- )#.&/2 345&% )%/6#)

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!ipeline A)C +.-.it0per0sta4e .ased str6ct6re

A. Baschirotto - Analo01to12i0ital 2ata Converters 6/14/07 <74 o= 471

!ipeline ()* +,-.it-per-2ta4e .a2ed 2tructure

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!

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A. $as'(irotto - Analog1to12igital 2ata 3on4erters 67197:; 2;6 of 9;1

!"#$%"&$'()*'+,-."/0#$10s/34$'.3s$5's/167/61$

! "he last sta)e is not-di)itall/ corrected and it is 2s2all/ a t3o-4it 5lash

'

A" $asc()rotto - Analo01to1D)0)tal Data Converters 6/89/:; <;; o= 9;8

!ipeline ADC +.-bit-per-stage based structure!

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– -*/01&2+!05*),!

o C206'!<&!&)!*001&,:!'3!'5,!&206'!3=!)6%(78.!!

o <&!&)!*001&,:!'3!)*/01&2+!D*0*D&'39)!.)!*2:!.=!

o 7'!'5,!,2:!3=!'5,!=&9)'!D13DE!05*),!

! <&!&)!)*/01,:!*D93))!.)!*2:!.=!

! '5,!36'06'!3=!'5,!)6%(78.!&)!1*'D5,:#!!

A. Baschirotto - Analog1to1Digital Data Converters 67897:; <;= o> 9;8

!"#$%"&$ ()* +,-."/0#$102/34$ .32$5 2/167/61$

! !"aluation phase

o C" closes a negati"e feed3ac4 loop around the opamp

o 7he top plate of Cs is switched to the 9:; output<

! 7he stage residue is present at =o<

! 7he su3-:9; output selects the 9:;

output "oltage ?$dac@ through an analog multipleAor<

! $dac is capaciti"elB su3tracted from the residue such thatC

!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <;= +> 9;8

!"#el"ne ()* +,-."t-#er-2ta4e .a2ed 2tru7ture

!! !"#$%"%&'(')*& ),-%,

!!Cs.Cf ), /0*,%& '* 1)2% ( 1()& *3 '4* )& '0% '5(&,3%5 3-&/')*&6

!! 70% 89: $%2%$, /(& ;% 1%&%5('%< 35*" ( ,)&1$% <)33%5%&')($ 5%3%5%&'%

!! '0% &%1(')2% 5%3%5%&/% ! -,)&1 '0% 5%2%5,% #*$(5)'=

!!<)33%5%&')($ >%5* ! ,0*5')&1 '0% *-'#-',

!! 9 #5%/),)*& )&'%5,'(1% 1()& ), &%%<%< '* (/0)%2% '0% <%,)5%< 98: $)&%(5)'=6

!!/(#(/)'*5 5(')* Cs.Cf <%'%5")&%, '0), )&'%5,'(1% 1()& ! /(#(/)'*5 "('/0)&1 ), /5)')/($

!!8: *#("# 1()& "-,' ;% ,-33)/)%&'$= $(51% ?@ AB <CD '* 5%<-/% 3)&)'% 1()& %55*5

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"! E#("# ,%''$)&1 ')"% '0(' $)")', '0% *2%5($$ #)#%$)&% '05*-10#-'

A. $aschirotto - Analog-to-2igital 2ata Converters 67897:; <=: of 9;8

!"#$%"&$'()*'+%,-.'/"01203',4'0'$i5r67"8'4%09:'(;)'-,&<$28$2'

!

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <=8 o> 9;8

!"#$%"&$'()*'+$&$,"-'./%0"#%1"&2')"2"03%4054(&3%52'*5&6$,0$,'7.)(*8''

! !"#$%&%'(#))*+ #( -./0 %1 %23)424(&4$ 51%(6 &74 18%&974$ 9#3#9%&'" &497(%:54

! / 64(4"#) 5(%& 9#3#9%&'" -./0 '; # !i<r=>%& 3%34)%(4 1&#64

! ?!i 5(%& 9#3#9%&'"1 @%&+A BCC%&+n=D+ %(E

! 18%&9741 &7#& '34"#&4 %( &74 1#23)4 @;)E '"

7')$ @;*E 37#14

! #( '34"#&%'(#) #23)%;%4"C

! .5"%(6 &74 1#23)4 37#14 ;)+

! &74 >'&&'2 3)#&41 '; #)) &74 5(%& 9#3#9%&'"1

@%&+A BCC%&+n=D+ %( E #"4 9'((49&4$ &' &74 1&#64 %(35& F')&#64 +inG

! &74 &'3 3)#&41 '; &74 9#3#9%&'"1 #"4 6"'5($4$ &7"'567 '(4 18%&97C

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!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=< +> 9;8

!ipeline (D* +ultiplying Digital-to-(nalog *onverter (+D(*)

! "#$%&' ()* )+,- .)/0* 1!2

o ()* 3+((+4 .,/(* +1 ()* 1**-3/56 5/./5%(+$ "# %0 5+&&*5(*- (+ ()* +./4. +#(.#(

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o ?)* 0(/'* +#(.#( @+,(/'* +./0A1 %0B

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! 23 ! D9(2G43 <1)2 ;(2G43 <1)J

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!

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <=9 o> 9;8

!ipeline A)* Converter 2.2 bit4per4stage

! ! #$%&'( )*$g,-*. /&0&/$-$1* 23!4

!" $%s'()ro,,o - !n%/o01,o1D)0),%/ D%,% 3on45r,5rs 67897:; <=> o? 9;8

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!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=6 +> 9;8

!ipeline A)C +on-idealities

! 2he 456 operation, )5A conversion, s;<traction, and ampli>ication o> the resid;e have

to >;l>ill an acc;rac? re@;irement e@;al to the resol;tion o> the remaininA pipeline staAes!

o ! #$% &%'()*#+(, (- . /+/%)+,% 012 3(,4%&#%& +' )+5+#%6 78 #$% .33*&.38 (- #$% 920:

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! <*7=02: ,(,=+6%.)+#+%'

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o .57+#+(*' '#.;%' 5.8 (33*& +, #$% 3(5/.&.#(&'

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <=; o> 9;8

!"#$%"&$ ()* +,&-".$/%"0"$1

! "nit ca(acitor +D-. non-idealities

! t4e am(li6ier (arasitics7

! 6inite transconductance g"

! ma9imal out(ut current #"ax

! out(ut resistance ro

! (arasitic in(ut ca(acitance ()ar

! o66set voltage *os.

! t4e ca(acitor mismatc4es D(s= ,

and D(f >

! re6erence voltage mismatc4 D/r0 f >

! timing error in t4e sam(ling cloc? D6S>

! c4arge in@ection 6rom t4e sAitc4es

!.#$%&'()*+,,+#-#!.%/+01,+12)0),%/#2%,%#3+.45*,5*&# 67847:;# 288#+>#4;8#

!"#$%"&$'()*'+,&-".$/%"0"$12'*,3#/4/0,4',551$0'

! !om$arator offset ,oltage

o /n offset ,oltage shifts the

decision le,el of the com$arator

introducing a 6uanti7ation error to the !" 8$9bit out$ut of the stage.

! The com$arator offset ,oltage is originated from se,eral sources

o =e,ice mismatch

o >eference ,oltage le,els de,iation (!%$&'( ) )

!"#$%&'()*+,,+#-#!.%/+01,+12)0),%/#2%,%#3+.45*,5*&# 67897:;# <=>#+?#9;8#

!"#$%"&$ ()* +,&-".$/%"0"$12 *,3#/4/0,4 ,551$0

! !itho&t red&ndanc.

o /he error in the o&tp&t volta3e o4 each sta3e m&st 7e less than hal4 o4 the 89B re4erred to the resol&tion o4 the remainin3 7ac;<end pipeline A>C

o ! /he ma@imal error alloAed in the o&tp&t o4 the !"#$sta3e is

! Ahere %&'$B CD%()*$$is the 4&ll<scale o&tp&t volta3e

o ! Ee4erred to the sta3e inp&t, the ma@imal alloAed comparator inp&t re4erred o44set is

! !ith red&ndanc.

o independent on the order o4 the sta3e

!"#$%&'()*+,,+#-#!.%/+01,+12)0),%/#2%,%#3+.45*,5*&# 67897:;# <=:#+>#9;8#

!"#$%"&$ ()* +,&-".$/%"0"$12 3#/4# !$56,54/&7$

! Opamp per(ormance a((ects .oth the

static and d2namic linearit2 o( 4hole A6C.

o 9he ampli(ier o:tp:t o( an ;6AC

m:st settle to the acc:rac2 o( the

remainin< pipeline A=6 converter 4ithin hal( o( a cloc? c2cle.

! 9he ma@or opamp nonAidealities

o o((set

o limited <ain .and4idth

o sle4 rate

o (inite open loop 6CA<ain.

! nonAlinear 6CA<ain

!" $aschirotto - !nalog-to-2igital 2ata 3on4erters 67197:; 2=1 o> 9;1

!"#$%"&$'()*'+,&-".$/%"0"$12'3#/4#',551$0

!! "#$ %&&'$( )!"#$*+ '$,*$' -*(# (#$ %./0. *+1$,(*+2 *+.3(4 *' '3.$,*0.%'$5 (% 6*+

!!73,*+2 (#$ '/0.8$ .#/'$ !%

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!!73,*+2 (#$ #%85 .#/'$ !)

!! (#$ '/0.8*+2 '-*(:# *' %.$+$5 /+5 (#$ /0.8*&*$, %&&'$( 1%8(/2$ !"#$/..$/,' /:,%'' (#$ '/0.8*+2 :/./:*(%,' &#;'

!! (#$ (%. .8/($ %& &( *' /( !"#$/+5 (#$ <%((%0 .8/($ /( (#$ %3(.3( 1%8(/2$ 8$1$8

!!9#/,2$ .,$'$,1/(*%+ " (#$ %./0. %&&'$( $&&$:( /( (#$ %3(.3( V"#?i$*'

!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=< +> 9;8

!"#el"ne ()* +on-"deal"t"e12 3#am# o551et

! "#$ %&'(& %))*$+ ,%-+'.$ /0+1%234$* ' 4%0*+'0+

$11%1 %) !os5i5 6#/4# /* 2/1$4+-7 +1'0*-'+$2 +% '0 $83'-5 4%0*+'0+ *#/)+ %) +#$ %3+&3+ ,%-+'.$ !out5i

! "#$ *#/)+ 4'0 4'3*$ +#$ *+'.$ %3+&3+ +% %,$1)-%6 '02 *'+31'+$ +#$ 1$('/0/0. &/&$-/0$ *+'.$*9

o "#$ $))$4+ %) +#/* %))*$+ ,%-+'.$ 4'0 :$

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!. $as'(irotto - !nalog-to-2igital 2ata 3onverters 67897:; 2=> o? 9;8

!"#$%"&$'()*'+,&-".$/%"0"$12'3#/4#'5"&"0$'3#$&'6,,#')*-7/"&'

! !"#"$%&'(()(*&('*+,"&-().&

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.);'&!&

&

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&

!" $as'hirotto - !nalog-to-2igital 2ata 3onverters 67897:; 2=9 of 9;8

!"#$%"&$'()*'+,&-".$/%"0"$12'3#/4#'5"&"0$'3#$&'6,,#')*-7/"&'

!"eal !

'()(*e +pamp .a() e//e0*s !

! 23e e44+4 ()*4+"50e" 67 *3e ampl(/(e4 /()(*e +pe) l++p 89-.a() (s *3e las* *e4m

! ;3e) 1=!0 ? "##$$#1@ (* app4+A(ma*el7 3+l"s

'

! 235s@ *3e ampl(/(e4 /()(*e 89-.a() "e04eases *3e .a() a)" s*eps a* *3e 0+mpa4a*+4 *34es3+l"s () *3e *4a)s/e4 /5)0*(+) 67 a) e44+4 *e4m e!0 +/

'

!" $%&'()*+,,+ – !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <=> +? 9;8

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! "#$ $%%$&' (% '#$ )$*+,'-./ *-/.0,-

-.2$3$.2$.' /0-. $))() -.')(2+&$2 '( '#$ ')0.*%$) %+.&'-(. (% 0 156-7-' *'0/$

! "#$ $%%$&' (% '#-* /0-. $))() *#(+,2 7$

2$&)$0*$2 7$,(8 '#$ 9+0.'-z0'-(. .(-*$ ,$;$,

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!"#$%"&$ ()* +,&-".$/%"0"$12 3#/4# 5%$6 7/0$ /&. 8/"& 9/&.6".0:

! !"#$%&'()(*$&+%&*,())'-".*!*/*,(0(1(*23"+%-#*(11$1**

o 45(*)$*)6(*7-"-)(*,'(8*1+)(*9:;<*+"2*.+-"*=+"28-2)6**9>?@<*

Slew-rate

Capacitivepartition

Linear settling

Time

Out

put v

olta

ge

! 1

Transient due to charge injection

Error dueto charge injection

! 2

*

! /)*)6(*=(.-""-".*$7*)6(*6$'2*%$2(A*)6(*$&(1+)-$"+'*+%&'-7-(1*(")(1,*,'(8-".A*&1$0-2-".*-),*%+B-%+'*$5)&5)*#511(")*!"#$A**

! C+)(1*$"A*-)*,())'(,*(B&$"(")-+''3*)$8+12,*)6(*-2(+'*,)+.(*$5)&5)*0$')+.(A*)6(*,())'-".*"$8*

=(-".*'-%-)(2*=3*D>?*9)6(*+%&'-7-(1*)1+",#$"25#)+"#(*%" +"2*)6(*(77(#)-0(*'$+2*#+&+#-)+"#(*-"*)6-,*%$2(*'(EHF<*

!. $aschirotto - !nalo01to12i0ital 2ata 3on4erters 67897:; <=; o> 9;8

!ipeline A)C +on-idealities2 Opamp 5le6 7ate and 8ain Band6idth

! !le$ &ate limite+ pa&t

o -o &ese&0e 1234523 o6 the total a0aila8le settlin: time ;!<=>

! -he loa+ capacitance@ $hich has to 8e cha&:e+ o& +ischa&:e+ +u&in: the settlin:@ +epen+s on the capacito& cha&:in: in the p&e0ious sample phaseB

o In the $o&st case@ the total loa+ capacitance +u&in: the sle$in: is "#D$%$&E"'&@ &esultin:

! $he&e "#D$%$&F"#E"%($&is the total loa+ capacitance inclu+in: the pa&asitic capacitance at the ampli6ie& output "%($&B

! -he sta:e output 0olta:e +epen+s linea&lG on the sle$ &ate an+ at the en+ o6 this phase is

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <=> o? 9;8

!i#eline A)* +on-idealities2 3#am# Sle6 7ate and 8ain 9and6idt:

! !"#$%&'()*'*+,-%*%($./'0*((/$%&1'()*'0(.&*'-"(,"('.,,#-.2)*0'()*'$3*./'-"(,"('!4'"#$5% .22-#3$%&'(-'()*'*6".($-%'

o ()*'7839'2-#%*#':#*6"*%2;'$0'

! <)*'*::*2($=*')-/3'>-3*'/-.3'2.,.2$(.%2*''(5) -:'()*'?!@A'B$()'.'/-.3'2.,.2$(.%2*''( $0'

o ()*'7839'2-#%*#':#*6"*%2;'$0'

A.#$%&'(i*+tt+#-#A.%l+0-t+-2i0it%l#2%t%#3+.4e*te*&# 671470;# 2==#+>#4;1#

!ipeli&e A)* +,&-ide/litie12 3p/mp 5/i& 6/&d7idt8

! !s the 1()-+() sle-in0 1art

! the ma5imum time is 7or the e51onential settlin0 is !"9 #:+ 9 1:;+<$%=

! ! the settlin0 error o7 the sta0e out1ut volta0e at the end o7 the hold 1hase is

! The settlin0 error is time de1endent

! At Breates si0nal-de1endent errors ! it leads to harmoniB distortion

! !ssumin0 the 0ain !!oC settlin0 !t errors and the o1am1 o77set volta0e &'(C) unBorrelated

! their su1erim1osed e77eBt on the sta0e trans7er 7unBtion Ban be -ritten as

! -here &'*!+)"is the sta0e out1ut e5Bludin0 the errors Baused bE the limited o1am1 1er7ormanBe

!.#$%&'(i*+,,+#-#!.%/+0-,+-2i0i,%/#2%,%#3+.4e*,e*&# 671470;# 300#+=#4;1#

!ipeline A)C +on-idealities2 Opamp 5ain Band7idth

! !pamp &inite +,- e&&e.t on the trans&er &un.tion o& a 456-bit stage

! :he error is proportional to the output

<oltage being larger &or stage outputs .lose to the &ull s.ale

! :his is di&&erent &rom the .ase in

the error due to the ampli&ier &inite gain5

!" $%&'()*+,,+ - !.%/+01,+12)0),%/ 2%,% 3+.45*,5*& 67897:; <:8 += 9;8

!ipeline ()* +on-idealities2 *apacitor 5ismatc7

! !ac$ of t$e capacitors can /e modeled to consist

of an ideal part !0s#$ and !& plus a mismatc$ !!s#$

and !!&5 respecti6ely

! 8ncludin9 t$e capacitor mismatc$ in t$e transfer function of a s:itc$ed capacitor ;<A> is

! ?$e multiplier of t$e input 'in5i ! a 9ain error

! ?$e multiplier in t$e second term ! an error in t$e $ei9$t of t$e 6olta9e steps at t$e comparator t$res$old le6els

!" $asc(irotto - !nalo0-to-2i0ital 2ata Con4erters 67197:; <:= o> 9;1

!ipeline ADC +on-idealities2 Capacitor 5ismatch

! "#$ % &'() *%+%*()#$ ,-./0 12 34+5#()('6 )73 +$#+3$)2 !8s 9 $ =!8% =!0 !

)73 &'() *%+%*()#$ ;(<;%)*73< != 7#5> !

)73 )#)%5 ;(<;%)*7 ! (< !

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <:< o= 9;8

!"#$l"&$ ()* +o&-".$/l"0"$12 */#/3"0o4 5"16/037

! !"#$%$&'()*+,$-,%./$,0/$/11/2,$"1$,0/$2%3%2+,"#$4+-4%,20$"5$,0/$-,%./$,#%5-1/#$1652,+"5$+-$$

$

! !"#$!"#$" 7!&'(8$5"$/##"#$#/-69,-$

! :0/$.%+5$/##"#$%5;$;/<+%,+"5$"1$,0/$<"9,%./$-,/3-$%,$,0/$2"43%#%,"#$,0#/-0"9;$9/</9-$%#/$29/%#9=$<+-+*9/$

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <:9 o= 9;8

!"#el"&e A)* +o&-"deal"t"e12 34ermal +o"1e

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o!?1',( &1@(5

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A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <:= o> 9;8

!"#$%"&$'()*'+,&-".$/%"0"$12'3/4#%"&5'*%,67'8"00$9'

! !"e most c*itical cloc.ing signal in t"e 1DAC is t"e sampling cloc.

! !"e 6alling edge dete*mines t"e sampling moment8

! 9andom va*iations o6 t"e 6alling edge; *e6e**ed as cloc. <itte* o* ape*tu*e unce*tainty s!; a*e unavoida?le8

! Due to its *andom natu*e; t"e sampling cloc. <itte* does not int*oduce any 6i@ed

patte*n tones in t"e output spect*um ?ut deg*ades t"e signal-to-noise *atio8

! Bo* an input sinusoid Cit" amplitude "#$DE and 6*eFuency %&'; a sampling <itte* Cit" a standa*d deviation !! *esults in an *ms voltage e**o* o6

! C"ic" co**esponds to an output noise poCe* o6

! to ?e added to t"e FuantiGation noise and deg*ades t"e SI98

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!ipeline A)C )esi,n considerations3 Capacitor 4i5in, and 4calin,

! !"# %o'()*)+ )o(,# ,o-./# o0 * ,1(+/"#% /*2*/(+o. 3*,#% 4567 (, +"# +"#.'*l )o(,# ()"#.(+#% 0.o' +"# ,*'2l()g o2#.*+(o)

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!ipeline A)* )esign considerations: *apacitor 4i5ing and 4caling

! !he total noise po-er o/ a pipeline A12 converter -ith ! sta5es, red8ced to its inp8t, is9

o #:$ is the noise po-er at the sta5e inp8t,

o %$ the intersta5e 5ain o/ the $&' sta5e.

! !he noise contri<8tion o/ the s8<se=8ent sta5es is atten8ated <> the intersta5e 5ains

o <ac?@end sta5es can <e scaled do-n to attain po-er savin5s thro85h relaAed opamp speci/ications.

o Cn medi8m@resol8tion pipeline A2Cs, a minimal sta5e resol8tion com<ined -ith

capacitor scalin5 -ith a /actor o/ one hal/ 8ntil the matchin5 limit leads to a po-er dissipation minim8m.

o Cn hi5h@resol8tion A2Cs, on the contrar>, it is /avora<le to place a hi5h@resol8tion sta5e

8tiliEin5 a lar5e intersta5e 5ain in the /ront to atten8ate the noise contri<8tion o/ the <ac?@end sta5es.

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!ipeline A)* +onverter 0witche45capacitor implementation

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A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <8: o= 9;8

!ipeline A)* Converter Opamp 3or 4)5 and 7*AC

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!ipeline ()* +on-erter Opamp 3ain an4 5onlinearit6

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! 7o ma:e 1;# A=C

!" $aschirotto - !nalog-to-Digital Data 3onverters 67197:; <19 of 9;1

Pipeline A/D Converter Larger Capacitor for Matching

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A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <8= o> 9;8

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! 6esid.e o77set is not a pro+lem as lon: as it sta4s constant, +.t resid.e :ain linearit4 directl4 a77ects "<= and ><=.

! O77set di77erence +et1een A"C and resid.e amp is critical .nless corrected 1ith red.ndanc4.

! =oo@Aahead decision is possi+le 7or hi:hAspeed conversion, +.t needs 7inerAresol.tion comparator.

A. Baschirotto - Analo01to12i0ital 2ata Converters 67897:; <8= o> 9;8

!i#eline ()* +on-erter 0(12(3 4imulation +ode

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