Op imiza ion o Con inuous-Time Pipeline
ADC A chi ec u es o Wideband
Medium-Resolu ion Applica ions
I án Ramí ez Lechuga
A Mas e ’s Thesis Submi ed o he Facul y o he
Escola Tècnica d’Enginye ia de Telecomunicació de Ba celona
Uni e si a Poli ècnica de Ca alunya
In pa ial ul ilmen o he equi emen s o he deg ee o
MASTER IN ELECTRONIC ENGINEERING
Supe iso s:
P o . Geo ges Gielen
P o . Xa ie A agonès Ce e a
Assis an -supe iso :
Xin a Zheng
Academic yea 2024 – 2025
©Copy igh KU Leu en
Wi hou w i en pe mission o he supe iso s and he au ho i is o bidden o
ep oduce o adap in any o m o by any means any pa o his publica ion. Reques s
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add essed o Depa emen Elek o echniek, Kas eelpa k A enbe g 10 pos bus 2440,
B-3001 Leu en, +32-16-321130 o by email [email p o ec ed].
A w i en pe mission o he supe iso s is also equi ed o use he me hods, p oduc s,
schema ics and p og ammes desc ibed in his wo k o indus ial o comme cial use,
and o submi ing his publica ion in scien i ic con es s.
P e ace
I would like o s a by hanking e e yone in he E asmus p og am who has made
my s ay in Leu en possible. I would also like o hank my p omo o , P o esso
Geo ges Gielen, o sugges ing such an in e es ing opic o my hesis. And o show
my deepes app ecia ion o my assis an supe iso , Xin a Zheng, o leading me
h ough e e y s ep o his p ojec . I also hank he ju y o eading and e alua ing
his ex . My since e g a i ude also goes o my amily and iends, especially hose
who kep me company on long wo king nigh s a he lib a y.
I án Ramí ez Lechuga
i
Con en s
P e ace i
Abs ac i
Lis o Figu es and Tables
Lis o Abb e ia ions and Symbols ii
1 In oduc ion 1
1.1 Mo i a ion ................................ 1
1.2 S a emen o pu pose ........................... 3
1.3 Me hodology and p ocedu e ....................... 3
1.4 Thesis ou line ............................... 3
2 Wideband Medium-Resolu ion ADCs 5
2.1 Gain-Cen ic ADC Model ........................ 5
2.2 Disc e e- ime Nyquis ADCs ...................... 6
2.3 Con inuous- ime Σ∆ ADCs ....................... 7
2.4 Con inuous- ime Pipeline ADCs ..................... 8
2.5 Conclusion ................................ 9
3 Con inuous-Time Pipeline ADC: A chi ec u e De ini ion 11
3.1 F om DT o CT Pipeline ........................ 11
3.2 Design Challenges ............................ 19
3.3 Conclusion ................................ 22
4 Con inuous-Time Pipeline ADC: A chi ec u e Design Explo a ion 23
4.1 MATLAB Model O e iew ....................... 23
4.2 Model o non-ideali ies .......................... 33
4.3 Conclusion ................................ 37
5 Con inuous-Time Pipeline ADC: A chi ec u e Op imiza ion
Resul s 39
5.1 Pa ame e op imiza ion ......................... 39
5.2 Digi al signal econs uc ion il e .................... 40
5.3 Signal T ans e Func ion ......................... 43
5.4 Non-ideali ies ............................... 45
5.5 Conclusion ................................ 48
6 Conclusion 49
ii
Con en s
A Sus ainabili y Analysis and E hical Implica ions 51
A.1 Sus ainabili y Analysis .......................... 51
A.2 E hical implica ions ........................... 53
Bibliog aphy 55
iii
Abs ac
Con inuous- ime pipeline (CT-Pipeline) ADCs a e an eme ging analog- o-digi al
medium- esolu ion con e e a chi ec u e. Recen ly demons a ed examples p o e
ha hey a e capable o achie ing la ge bandwid hs han hose o s a e-o - he-a
con inuous- ime Σ∆ ADCs, which un il now we e he p e e ed wideband medium-
esolu ion ADC choice.
In his wo k, his ype o con e e is demons a ed h ough a MATLAB Simulink
model. Th oughou hese pages, a de ailed analysis and explana ion o his opology
is p o ided, while p oposing solu ions o some o he ecu ing design challenges.
Wi h ega d o he implemen a ion, he use o powe -e icien VCO quan ize s has
been e alua ed. A compa ison is also conduc ed be ween wo al e na i es o he
digi al econs uc ion il e . In addi ion, he mos common non-ideali ies and hei
e ec s a e also in oduced and alida ed by simula ion.
The de eloped model o a 4-s age con inuous- ime pipeline ADC achie es a SNDR
o 80 dB o e a 400-MHz bandwid h. I is in ended o se e as an ini ial s ep owa ds
he implemen a ion o a CT-Pipeline ha achie es an SNDR o 70 dB.
i
Lis o Figu es and Tables
Lis o Figu es
1.1 Pe o mance o ele an ecen ly demons a ed ADCs, p esen ed in
ISSCC and VLSI [16]. The plo highligh s DT-Pipeline, CT-Σ∆ and
CT-Pipeline a chi ec u es. The pe o mance objec i e o his p ojec is
also ma ked .................................. 2
2.1 Gain Cen ic ADC Model [25]........................ 6
2.2 DT Nyquis ADCl [22]............................ 7
3.1 1-s age DT pipeline wi h back-end ADC wi h i s an i-aliasing il e and
bu e ..................................... 12
3.2
Resul o emo ing he sample and hold and bu e and pushing he il e
in o he ADC ................................. 13
3.3 Cu en signals examples om a esidue gene a o . IV I ep esen s he
signal om he analog pa h, IDAC he one om he DAC and IRES he
ou pu esidue. The di e ence be ween signals wi h and wi hou delay
alignmen is showcased [25]......................... 14
3.4 E ec o adding a hal clock cycle compensa ion delay o he DAC
ou pu . Signals in g ey ha e no compensa ion, in black a e adding a
hal cycle delay. Residue signal ( ) is conside ably minimized [22]. . . 14
3.5 N-s age pipeline ADC [26].......................... 17
3.6 1-s age CT pipeline ollowed by a back-end ADC ............. 18
3.7 D i ing cu en wa e o m o a DT and a CT pipeline ADC o he same
SNR [26]................................... 19
3.8 Double sampling quan ize and i s e ec on an inpu a sampling
equency [19]................................. 21
4.1 MATLAB Simulink CT Pipeline ADC model ............... 24
4.2
F equency- ype VCO quan ize ci cui , model and equency spec um in
a ious nodes [28]............................... 26
4.3 Digi al econs uc ion il e ......................... 28
4.4 Noise minimiza ion algo i hm block diag am ............... 29
4.5
F equency spec um be o e ( ed) and a e (blue) applying he equency
mask ope a ion ................................ 30
Lis o Figu es and Tables
4.6 S a ic and delay e o s caused by misma ch in DAC [18]......... 34
4.7 Maximum SNR o he CT Pipeline ADC due o he NRZ DAC ji e
limi a ion. OSR = 4 and in =BW = 400MHz ............. 36
5.1 Ou pu equency spec um o lash quan ize e sion, impulse
calib a ion (le ) s noise cancella ion ( igh ) econs uc ion echniques . 41
5.2 Ou pu equency spec um o VCO quan ize e sion, impulse
calib a ion (le ) s noise cancella ion ( igh ) econs uc ion echniques . 41
5.3
SNDR s numbe o aps o lash quan ize e sion, impulse calib a ion
s noise cancella ion econs uc ion echniques .............. 42
5.4
SNDR s numbe o aps o VCO quan ize e sion, impulse calib a ion
s noise cancella ion econs uc ion echniques .............. 42
5.5 Compa ison o STF: ideal, same il e pe s age design, di e en il e
wi h speci ic Q design ............................ 44
5.6 Compa ison o STF: Flash s VCO quan ize s ............... 44
5.7 STF wi h di e en econs uc ion il e implemen a ions ......... 45
5.8 DAC Misma ch s a ic, delay, ise and all ime e o s ........... 46
5.9 Maximum SNR due o di e en ji e le els o h ee sepa a e inpu
equencies .................................. 47
5.10 Fi s s age hi d-o de nonlinea i y e ec on SNDR ............ 47
Lis o Tables
5.1
Pa ame e op imiza ion o he lash sub-ADC e sion o he CT Pipeline.
40
i
Lis o Abb e ia ions and
Symbols
Abb e ia ions
ADC Analog- o-Digi al Con e e
BW Bandwid h
CT Con inuous-Time
DAC Digi al- o-Analog Con e e
DEM Dynamic Elemen Ma ching
DR Dynamic Range
DT Disc e e-Time
FF Flip-Flop
FFT Fas Fou ie T ans o m
FIR Fini e Impulse Response
IIR In ini e Impulse Response
ISG In e -S age Gain
ISI In e -Symbol In e e ence
LS Leas Squa es
LSB Leas Signi ican Bi
LTI Linea Time In a ian
MSB Mos Signi ican Bi
NRZ Non-Re u n- o-Ze o
NSD Noise Spec al Densi y
NTF Noise T ans e Func ion
OSR O e Sampling Ra io
PRBS Pseudo-Random Bi Sou ce
QTZ Quan ize
S&H Sample & Hold
SNR Signal- o-Noise Ra io
SNDR Signal- o-Noise-and-Dis o ion Ra io
STF Signal T ans e Func ion
VCO Vol age Con olled Oscilla o
ii
2. Wideband Medium-Resolu ion ADCs
Figu e 2.1: Gain Cen ic ADC Model [25]
he case, he digi al block would no be able o p ope ly econs uc he signal, and
he ou pu noise would be much g ea e han he quan iza ion one.
2.2 Disc e e- ime Nyquis ADCs
Acco ding o he model p esen ed in he p e ious sec ion, di e en ypes o ADC
could be dis inguished. Fo example, by o e seeing he quan iza ion noise dis ibu ion
o e he equency spec um, a dis inc ion can be made be ween Nyquis ADCs,
in which he noise is uni o mly dis ibu ed o e he Nyquis bandwid h, and noise-
shaping ADCs, wi h shaped quan iza ion noise. I we we e o look a he a chi ec u e
o he analog gain block, we could sepa a e disc e e- ime ADCs, hose ha use
swi ched capaci o il e s, om con inuous- ime ADCs, which employ ac i e-RC o
gm-C il e s.
Disc e e- ime (DT) Nyquis con e e s ha e been he de aul choice o mos ADC
applica ions. The wideband medium- esolu ion case is no di e en . Disc e e- ime
pipeline ADCs ha e his o ically been used o achie e he desi ed bandwid h [
21
] [
11
]
[1].
The i s elemen p esen in a disc e e- ime pipeline ADC chain is a sample and
hold (S&H) ci cui . Because o his, an an i-aliasing il e is needed up on . I s
pu pose is o a enua e all ou -o -band componen s, so ha when sampling occu s,
no images appea in-band ha migh in e e e wi h he signal bins. The design o
his il e is no easy since he bandwid h will be close o he Nyquis equency.
Ideally, a s eep oll-o ou o he signal bandwid h would be desi ed, o ensu e a
be e supp ession o ou -o -band componen s. To achie e his, a high-o de il e
would be needed, which would come a he cos o high a ea occupancy and high
powe consump ion. An al e na i e app oach which has been commonly used is o
inc ease he o e sampling a io (OSR), de ined as he quo ien be ween he Nyquis
equency and he signal bandwid h. I he Nyquis equency is pushed away om
he il e cu o , hen s eep a enua ion is no as impo an . Bu his echnique
6
2.3. Con inuous- ime Σ∆ ADCs
Figu e 2.2: DT Nyquis ADCl [22]
also has some penal ies. The possibili y o inc easing he sampling equency is
echnology limi ed and employing ime-in e lea ing s a egies migh be equi ed. A
highe sampling equency will also inc emen he powe consump ion o he digi al
s age and he decima ion il e .
Ano he issue wi h disc e e- ime con e e s in gene al is ela ed o he d i ing
capabili ies o hese ci cui s. Since he inpu is a swi ched capaci ance, i will equi e
a speci ic bu e on-chip o eed a high peak cu en . Designing such bu e is complex
and is ca ied ou wi h class-A o class-AB ampli ie a chi ec u es [
26
]. I is usually
a ele an sou ce o noise and dis o ion, wi h an impo an powe consump ion, and
i may equi e a highe supply ol age han he ADC [22].
Acco ding o he gi en desc ip ion, a ypical disc e e- ime Nyquis ADC signal
chain is p esen ed in Figu e 2.2. I s a s wi h an an i-aliasing il e . As was p e iously
discussed, his block is powe -hung y and complex o design, which jus i ies why i is
o en implemen ed o -chip. Then, a d i ing bu e is needed, which adds conside ably
o he powe demand. I d i es a sample and hold ci cui , ha equi es a decen ly
sized capaci o o sa is y he noise pe o mance o he gi en applica ion. The ADC
hen pe o ms he con e sion and ans o ms he signal in o he digi al domain.
Las ly, a decima ion il e is employed, o emo e he e ec s o aliasing du ing he
downsampling ope a ion.
2.3 Con inuous- ime Σ∆ ADCs
As he limi a ions o he disc e e- ime con e e s became appa en , new con inuous-
ime a chi ec u es appea ed as candida es. The mos success ul was he con inuous-
ime Σ∆ ADC. I sol ed mos o he p oblems he disc e e- ime pipeline a ia ion
had by mo ing he sampling quan ize o he end o he analog chain.
In his ype o con e e , he analog gain block consis s o a cascade o in eg a o s.
Wi h his s uc u e, an a enua ion o he signal bins mul iples o he sampling
equency is achie ed be o e he las sampling quan ize . Tha means ha he
an i-aliasing il e ha p e iously p eceded he ADC can be elaxed o e en emo ed,
as i s unc ion is inhe i ed in he con e e ’s a chi ec u e.
7
2. Wideband Medium-Resolu ion ADCs
Ano he block whose equi emen s a e eased is he inpu bu e , as he inpu is no
longe capaci i e bu ins ead esis i e. In o de o ob ain he same kT/C noise in a
disc e e- ime a chi ec u e as he mal noise in a con inuous- ime one, he peak d i ing
cu en should be much highe [
25
][
26
]. Consequen ly, powe and a ea consump ion
a e g ea ly educed.
Relaxing bo h he an i-aliasing il e and he d i ing bu e equi emen s means
ha con inuous- ime Σ∆ ADCs a e much easie o in eg a e han disc e e- ime ones.
No only do less ci cui blocks need o be designed, bu i is much easie o achie e
ce ain speci ica ions (such as signal dis o ion) wi h a single ADC block han wi h
a whole signal chain.
The main limi a ion o his ype o con e e is e ealed as highe bandwid hs
a e needed. To achie e a high SNDR, Σ∆ ADCs employ noise-shaping, a echnique
which consis s in mo ing he quan iza ion noise in he signal band o highe ou -o -
band equencies. I s e ec i eness depends on he o de o he modula o . Fo ha
modula ion o be possible and o achie e be e noise shaping, i is necessa y o
he sampling equency o be much g ea e han he bandwid h. Fo hese easons,
a high OSR > 20 [
25
] is o en used. As bandwid h equi emen s become mo e
demanding, he sampling a e needed is excessi ely high. Closing he eedback loop
wi h such equencies is bo h powe -hung y and complex, ende ing his a chi ec u e
no easible o ce ain applica ions.
Ano he less impo an p oblem ound in hese ypes o con e e s is ela ed o
hei signal ans e unc ion (STF). Due o he na u e o he modula ion applied o
achie e noise shaping, some powe e icien s uc u es p esen a peak ou side o he
signal bandwid h. I high-ampli ude ou -o -band signals we e p esen a he inpu ,
sa u a ion could occu , e ec i ely limi ing he dynamic ange (DR) o he ADC. [
19
]
Rega ding he powe consump ion, he con inuous- ime Σ∆ achie es no able
sa ings wi h espec o Nyquis ADC a chi ec u es, because o he emo al o
elaxa ion o he il e , bu e and sample and hold blocks. Howe e , o wideband
con e e s, he clock dis ibu ion and he decima ion il e o he Σ∆ will consume
mo e due o he highe equency. [23]
2.4 Con inuous- ime Pipeline ADCs
A no el a chi ec u e has been ecen ly demons a ed ha add esses mos o he
conce ns discussed in his chap e : he con inuous- ime pipelined ADC. In b ie , i s
design mimics a disc e e- ime pipeline while emo ing he sample and hold ci cui y
and combining he il e and ADC in he same block. Re u ning o he gain-cen ic
ADC model p esen ed in Sec ion 2.1, i is as i he analog gain block o he pipeline
was eplaced by a con inuous- ime one (some addi ional a chi ec u e modi ica ions
a e equi ed). I p omises o b idge he gap be ween he wo p e ious ypes o
con e e s by combining i s indi idual ad an ages wi hou many o he d awbacks.
Fi s , since i is a con inuous- ime ADC, i does no employ a S&H a he inpu .
The esis i e beha io makes i easily d i en wi hou he need o a speci ic bu e . Also,
in eg a ing he il e inside he ADC means ha inhe en an i-aliasing is p esen while
8
2.5. Conclusion
allowing a much simple il e design han in i s disc e e- ime coun e pa . The e o e,
he con inuous- ime pipeline e ains he main ad an ages ha he con inuous- ime
Σ∆ had o e disc e e- ime Nyquis ADCs.
The CT pipeline ADC is simila o he disc e e- ime one in he sense ha i can
achie e a wide bandwid h wi hou ha ing o adop ex eme o e sampling ( ypically,
OSR = 4). I could e en achie e highe sampling equencies han disc e e- ime
pipelines [
26
] (i ime-in e lea ing echniques a e no conside ed) because se ling
ime equi emen s o ampli ie s a e no longe a necessi y. Tha makes i easie o
design, less powe -demanding and mo e obus o clock ji e han con inuous- ime
Σ∆ con e e s o wideband applica ions, al hough Σ∆s a e mo e powe e icien
a lowe bandwid hs. Fu he mo e, i s signal ans e unc ion p esen s a s eepe
oll-o .
As will be u he de eloped in he nex chap e , his a chi ec u e can achie e
an imp o emen in powe and a ea, o he same le els o noise and dis o ion,
when compa ed o disc e e- ime Nyquis ADCs, while also p o iding he bene i o
con inuous- ime a chi ec u es. I can each g ea e bandwid hs han con inuous- ime
Σ∆ con e e s wi h a lowe o e sampling a io. Hence, he con inuous- ime pipeline
ADC p esen s i sel as he mos p omising op ion o wideband medium- esolu ion
analog- o-digi al con e e applica ions.
2.5 Conclusion
In his chap e , he main ypes o ADC his o ically used in wideband medium-
esolu ion applica ions ha e been p esen ed. I has been explained how he disc e e-
ime Nyquis ADCs, al hough sui able, show some design complica ions due o hei
inpu d i eabili y and an i-aliasing il e equi emen s. La e , i has been shown
ha con inuous- ime Σ∆ con e e s ha e been employed o o e come hese issues.
Howe e , i has been s a ed ha hei o e sampling demands p e en hem om
being used in wideband scena ios. Finally, he con inuous- ime pipeline ADC has
been in oduced, which a oids he disad an ages o disc e e- ime con e e s while
being able o achie e wide bandwid hs, essen ially u ning hem in o he heo e ically
p e e ed a chi ec u e.
9
Chap e 3
Con inuous-Time Pipeline ADC:
A chi ec u e De ini ion
In his chap e , he a chi ec u e o he con inuous- ime pipeline ADC is in oduced.
Fi s , an in-dep h explana ion will be gi en, so ha he eade can unde s and
he unc ion o each subblock and i s impo ance o he o e all sys em. Then, an
analysis will be p o ided o di e en pe o mance pa ame e s, such as noise, linea i y
and powe . Finally, he main design di icul ies o he con inuous- ime pipeline a e
p esen ed, as well as he mos ele an s a e-o - he-a solu ions.
3.1 F om DT o CT Pipeline
3.1.1 The DT Pipeline ADC
The con inuous- ime pipeline ADC is a no el a chi ec u e ha has i s o igins in
se e al modi ica ions applied o a disc e e- ime pipeline con e e o bene i om he
ad an ages o con inuous- ime ope a ion. Because o ha , he ollowing explana ion
will s a om he disc e e- ime a chi ec u e.
Conside he disc e e- ime pipeline ADC shown in Figu e 3.1. I consis s o one
s age o pipelining ollowed by a back-end ADC. In his example, bo h he quan ize s
and DACs a e mul i-bi . The block diag am also displays bo h he an i-aliasing il e
and he bu e used o d i e he sample and hold ci cui .
The ope a ing p inciple o a disc e e- ime pipeline ADC is he ollowing. In
he i s subs age, he mos signi ican bi s
N1
(MSBs) a e con e ed o he digi al
domain by he quan ize QTZ1. Since his in o ma ion has al eady been acqui ed,
he nex pipeline s ages only need o ob ain he emaining
N−N1
bi s,
N
being he
o al bi esolu ion o he ADC. This means ha he componen associa ed wi h he
i s digi al alue can be simply emo ed om he signal.
To achie e his, DAC1 is used. This block con e s he ou pu o he quan ize
back in o he analog domain. The di e ence be ween his signal and he s age inpu
is hen calcula ed. The esul is a esidue con aining he in o ma ion o he
N−N1
leas signi ican bi s. As he ob ained signal has a peak alue ha co esponds o he
11
3. Con inuous-Time Pipeline ADC: A chi ec u e De ini ion
Figu e 3.1: 1-s age DT pipeline wi h back-end ADC wi h i s an i-aliasing il e
and bu e
weigh o he
N−N1
bi , i can be ampli ied o ake ull ad an age o he dynamic
ange o he quan ize in he nex s age. I bo h QTZ1 and QTZ2 use he same
e e ence ol age, his gain G1 can be 2
N1
, al hough a ac ion o i is usually selec ed
o accoun o po en ial con e sion e o s.
This ope a ion o ampli ying a esidue signal is he co e mechanism o pipelining
con e e s. As he signal is mul iplied by a gain
Gi>
1, so is he s ep size o he nex
quan ize . This ansla es in o a elaxa ion o he inpu and esolu ion equi emen s
o each o he sub-ADCs.
The con e ed alues o all s ages add up o he ADC ou pu . I is also necessa y
o compensa e o he di e en gains be ween s ages. In his example, i means
di iding he ou pu o QTZ2 by G1. Bo h o hese ope a ions a e pe o med in he
digi al domain.
In he p e ious chap e , he undamen al changes needed o ansi ion om a
disc e e- ime o a con inuous- ime pipeline ADC we e b ie ly in oduced. These
consis o emo ing he sample and hold ci cui , also elimina ing he d i ing bu e
as a consequence, and pushing he an i-aliasing il e inside he ADC. The esul s o
hese modi ica ions a e displayed in Figu e 3.2.
I a con e e wi h he a chi ec u e p esen ed in Figu e 3.2 was designed, i would
no wo k p ope ly. Due o a ious e ec s ela ed o he con inuous- ime ope a ion,
some signals would cause sa u a ion. The e o e, se e al co ec ions mus be made.
The di e en causes and hei espec i e solu ions will be p esen ed in he nex
subsec ions.
3.1.2 Delay alignmen
Since he sample and hold ci cui a he ADC inpu has been elimina ed, he signal
om he analog pa h ha p oduces he esidue is now iden ical o he inpu . The
emo al o he disc e iza ion a i ac implies ha i will be con inuous ins ead o
holding he alue o he du a ion o a clock pe iod. Howe e , he sub-ADC-DAC
12
3.1. F om DT o CT Pipeline
Figu e 3.2: Resul o emo ing he sample and hold and bu e and pushing he
il e in o he ADC
pa h s ill ope a es o e ime s eps. This di e ence will become e iden once he
esidue be ween he wo signals is calcula ed.
An example o he signals om he inpu and ou pu nodes o a esidue gene a ing
block is shown in Figu e 3.3. The wa e o ms speci ied as w/o delay a e he ones
co esponding o he a chi ec u e p esen ed in Figu e 3.2. As can be seen, he e is a
delay be ween he a i al o he signal om he analog pa h and he DAC, causing a
g ea e peak- o-peak swing in he esidue han expec ed. The goal o he ADC-DAC
coa se app oxima ion is o minimize he di e ence signal as much as possible, so
ha he in e s age gain can be inc eased and he o e all con e sion can bene i om
i . Hence, his misalignmen mus be co ec ed.
The appa en delay has wo componen s:
•
One clock pe iod, accoun ing o he ADC con e sion, da a p opaga ion and
se ling ime.
•
An addi ional hal -clock pe iod o e ec i e delay o he DAC, which is he one
ha causes he bes possible esidue minimiza ion, as can be seen in Figu e 3.4.
Pionee con inuous- ime pipeline wo k [
8
] p oposed o implemen hese one-
and a hal -cycle delay co ec ions using a p edic i e il e on he sub-ADC-DAC
pa h. Func ionally, i is as i a nega i e delay had been in oduced. Howe e , his
app oach is no e y p ac ical. To make alue p edic ions, his il e would equi e a
posi i e phase. Howe e , o high equencies, he esponse mus u n in o a nega i e
phase. O he wise, he il e would no espec causali y, meaning ha he ou pu
would no only depend on pas and p esen inpu s. Fo his o be accomplished, a
wide-bandwid h ope a ional ampli ie would be needed, which is e y complex o
implemen a high equencies.
13
3. Con inuous-Time Pipeline ADC: A chi ec u e De ini ion
Figu e 3.3: Cu en signals examples om a esidue gene a o .
IV I
ep esen s he
signal om he analog pa h,
IDAC
he one om he DAC and
IRES
he ou pu esidue.
The di e ence be ween signals wi h and wi hou delay alignmen is showcased [25]
Figu e 3.4: E ec o adding a hal clock cycle compensa ion delay o he DAC
ou pu . Signals in g ey ha e no compensa ion, in black a e adding a hal cycle
delay. Residue signal ( ) is conside ably minimized [22]
14
3.1. F om DT o CT Pipeline
The adop ed solu ion has been o ins ead in oduce a posi i e delay in he analog
signal pa h. I can be ealized by using passi e delay elemen s, which ha e a simple
implemen a ion. LC- o RC-la ice delay lines a e employed [
26
] [
19
] [
15
]. Al hough
he i s can achie e be e esidue cancella ion o e a wide bandwid h, he la e
occupies less silicon a ea. Ano he disad an age o he RC-la ice a ian is ha i s
inpu impedance dec eases a highe equencies, demanding a highe d i ing cu en .
A mo e in-dep h compa ison can be ound in [25] and [26].
3.1.3 Residue ampli ying il e s
The nex ele an aspec o discuss is ela ed o he in e s age block a chi ec u e. As
was an icipa ed be o e, in Figu e 3.2, when he an i-aliasing il e is pushed inside
he ADC i is placed nex o he di e en gain blocks. Implemen a ion-wise, he wo
unc ionali ies a e combined in he same ci cui block: he esidue-ampli ying il e .
In p e ious disc e e- ime a chi ec u es, he magni ude o he esidue signal had
a con ined alue. In pa icula , i s ange was
±VF S/M
, whe e
VF S
e e s o he
ull-scale ol age o he M-le el ADC and DAC pai . Howe e , in p ac ice, la ge
alues can appea due o ce ain implemen a ion e o s, such as compa a o o se s.
As he inpu is now con inuous, i s alue is no longe bounded. I s ill depends
on he sub-ADC and DAC esolu ion, bu also on he sampling a e. I he signal
p esen s e y as changes, he e will be no ad an age in u ilizing a la ge numbe o
quan ize le els. Some ypical es ablished alues o hese ci cui s a e a i s -s age
esolu ion be ween 3 and 5 bi s and an o e sampling a io OSR = 4. [15]
As he esidue p esen s highe peaks, he in e s age gain mus be educed acco d-
ingly. A p ede e mined alue, as was he numbe o quan ize le els in disc e e ime,
no longe exis s. Ins ead, a smalle gain should be selec ed so ha he peak- o-peak
o he esidue signal does no sa u a e he nex s age. The ou pu o he esidue-
ampli ying il e should be a ac ion o he nex quan ize dynamic ange (a swing
o hal he dynamic ange is ecommended in [21]).
Wi h espec o he il e ing sec ion, inhe i an i-aliasing is now pa o he
a chi ec u e. As he il e ha p e iously p eceded he con e e is b oken down and
dis ibu ed o e he a ious pipeline s ages, and he signal is es o ed wi h a digi al
econs uc ion il e , an equi alen unc ionali y is achie ed o ha o an an i-aliasing
il e ollowed by a Nyquis ADC (de ailed in Sec ion 3.2.3). Fo example, six h-o de
il e ing could be achie ed wi h h ee second-o de s ages. This implemen a ion
choice o e s se e al ad an ages ha will be discussed la e in his chap e .
The il e can also be used o p o ide some a enua ion o he leakage signal.
Achie ing a pe ec cancela ion is e y complex, since misma ches will exis be ween
he sub-ADC-DAC and he delay pa hs. Fo ins ance, he empe a u e e ec can
a ec he ol age e e ence o he ADC and DAC o he alue o he esis ances
and capaci ances esponsible o he delay. In e s age il e ing also has he du y o
educing he alue o hese leakage componen s.
Since he inpu o he i s quan ize has no ecei ed a p ope an i-aliasing
ea men , image signals will appea a he ou pu o he sub-DAC. These componen s
will inc ease he magni ude o he esidue signal, limi ing he maximum selec able
15
3. Con inuous-Time Pipeline ADC: A chi ec u e De ini ion
As was al eady discussed in Sec ion 3.1.3, a easonable ag eed-upon c i e ion
is o use second-o de il e s ages, as hey p o ide a good ade-o be ween he
ele an pa ame e s. The gene al ans e unc ion o a second-o de il e is ecalled
in he ollowing equa ion:
G(s) = ω2
0
s2+ω0
Qs+ω2
0
(3.3)
I he il e s we e designed wi hou gi ing majo impo ance o hei pa ame e s
and
0
was selec ed as he desi ed ADC bandwid h, he pe o mance will no be as
expec ed. A signi ican dB d oop will be obse ed in he STF a he edge o he
band ( 0), esul ing om he p oduc o many s ages.
Some ecommenda ions o a oid encoun e ing his p oblem a e sugges ed in
[
19
]. Fo example, he a icle p oposes a
0
ha is 10% highe han he equi ed
bandwid h.
Ano he pa ame e o conside is he quali y ac o Q. A g ea e Qp o ides a
na owe esonance and less d oop a
0
. Howe e , a highe noise loo will also be
ob ained. A good s a egy consis s o selec ing s ages wi h di e en quali y ac o s
[
19
]. The las s age can use he g ea e Q, as a ha poin he noise is al eady
signi ican ly a enua ed when e e ing o he inpu .
3.3 Conclusion
In his hi d chap e , an in-dep h e iew o he con inuous- ime pipeline ADC
a chi ec u e was pe o med. The mos ele an building blocks, as well as he main
design challenges o his ype o con e e , ha e been discussed.
A e his chap e , he eade should ha e a be e unde s anding o he co e
ad an ages o his a chi ec u e and he jus i ica ions behind hem.
Howe e , h oughou hese pages, i has also been e idenced ha he imple-
men a ion o his no el ADC p esen s a ious complexi ies ha a e cu en ly being
add essed a he o e on o esea ch cen e s.
22
Chap e 4
Con inuous-Time Pipeline ADC:
A chi ec u e Design Explo a ion
In he p e ious chap e , he eade was able o lea n no only abou he con inuous-
ime pipeline ADC a chi ec u e, bu also abou he discussion opics a ound i in
cu en s a e-o - he-a esea ch. In he ollowing sec ions, he main wo k ha
encompasses his p ojec is p esen ed. An explo a ion o he a chi ec u al design
op ions o he con e e is pe o med. This ask has been ca ied ou employing
ci cui modeling echniques and simula ion so wa e. This chap e is going o ocus
on he demons a ion o he de eloped models.
4.1 MATLAB Model O e iew
To explo e and op imize di e en design choices, a MATLAB Simulink model o
a con inuous- ime pipeline ADC has been de eloped. I s base o m is shown in
Figu e 4.1. I consis s o a 3-s age CT pipeline ollowed by a back-end ADC.
In his i s sec ion, he main blocks ha make up his model a e p esen ed. They
a e designed and op imized wi h he goal o ob aining 80 dB SNDR o e a 400 MHz
bandwid h wi h an OSR = 4 and an inpu dynamic ange o
±
1
V
. Di e en op ions
and a chi ec u e conside a ions complemen each o he explana ions.
4.1.1 Subs age ADCs and DACs
The i s elemen ha will be discussed a e he subs age ADCs and DACs. As could
be expec ed, hei ele ance is c ucial o he pipeline pe o mance.
Quan ize
Quan ize s play an impo an ole in he con e e , since hey a e he ones ha
ans o m he analog inpu in o he digi al domain, which is he sole pu pose o
he ADC. When i comes o quan ize a chi ec u es, wo o hem we e modeled
and es ed in his wo k: lash ADCs and VCO(Vol age Con olled Oscilla o )-based
ADCs.
23
4. Con inuous-Time Pipeline ADC: A chi ec u e Design Explo a ion
Figu e 4.1: MATLAB Simulink CT Pipeline ADC model
24
4.1. MATLAB Model O e iew
The ope a ion o a lash ADC is ela i ely s aigh o wa d: a esis i e ladde
is used o gene a e N ol age e e ences, he di e ence o which wi h he inpu
is ampli ied and ed in o Ncompa a o s. The esul ing Nsignals cons i u e he
con e ed digi al alue [12].
Due o i s design simplici y, his ADC opology is he one ha can achie e he
highes bandwid h. The maximum sampling a e is only limi ed by he p eampli ie
la ency and he se ling ime o he compa a o s [28].
I s main d awback is i s limi ed scalabili y. As he numbe o quan iza ion
le els Ninc eases, so does p opo ionally he numbe o compa a o s, ampli ie s
and esis o s ha mus be in eg a ed. This implies a subs an ial inc emen in a ea,
powe and inpu capaci ance. The e o e, lash ADC esolu ion is ypically limi ed o
a ound 6 o 7 bi s [
23
] [
28
]. Howe e , his is no an issue when ying o selec a
quan ize o he pipeline subs ages, as he maximum esolu ion is al eady limi ed o
a ound 4 o 5 bi s [21].
Ano he conce n wi h lash quan ize s is hei po en ial inaccu acies caused by
misma ches be ween he di e en elemen s. This issue is echnology-dependen and
i s e ec could only be educed by inc easing he a ea o he con e e elemen s.
A model o a lash ADC was added o Simulink, o be simula ed in di e en
con igu a ions. I consis s o a sample and hold ollowed by a block ha implemen s
he compa ison wi h he a ay o e e ence ol ages. The model has wo ou pu s: an
in ege alue in he ange [0
, N −
1], whe e Nis he numbe o quan ize le els, and
a no malized ol age in he ange [−V e , V e ].
The o he ype o sub-ADC p oposed o his wo k is he VCO-based quan ize .
These con e e s ha e been g owing in popula i y in ecen yea s, as hey a e
compa ible wi h digi al implemen a ion echniques and a e he e o e easily scalable
wi h echnology.
VCO quan ize s usually employ a ing oscilla o whose inpu ol age is he one
ha needs o be con e ed and ha con ols he oscilla ion equency. The di e en
phases o he ing a e ed in o a block ha coun s he o al numbe o ansi ions
pe clock pe iod. This quan i y ends up being he con e ed digi al alue.
The pa icula quan ize modeled in his wo k is a equency- ype VCO quan ize
[
28
]. In his case, a single lip- lop (FF) coun s he ansi ions o each phase. This
implies ha he maximum numbe o ansi ions pe clock pe iod is one o , in o he
wo ds, ha he VCO equency is limi ed o hal o he sampling a e. The ou pu
o his FF goes h ough a i s -o de di e ence block. I is implemen ed wi h an
addi ional FF and an XOR ga e and i s ou pu is a logical 1each ime a ansi ion
has been de ec ed (see Figu e 4.2) [28].
A VCO-based quan ize p esen s se e al ad an ages o e a lash ADC. I has
imp o ed noise pe o mance because i con ains an in eg a ing unc ion in he chain.
Al hough he STF has a gain o uni y, he noise ans e unc ion is
NTF
= 1
−z−1
[24], which means ha noise is i s -o de shaped.
VCO quan ize s a e also mo e obus o misma ch-based e o s. The eason is
ha he ou pu changes by sequen ial ansi ions ins ead o equi ing p ecise ol age
compa isons. The e o s o igina ing om misma ch a e, he e o e, sp ead o e ime,
which educes hei e ec s.
25
4. Con inuous-Time Pipeline ADC: A chi ec u e Design Explo a ion
Figu e 4.2: F equency- ype VCO quan ize ci cui , model and equency spec um
in a ious nodes [28]
The VCO quan ize model in Simulink was based on he one shown in Figu e 4.2.
I consis s o an in eg a o , a sample-and-hold block and a di e en ia o . The
in eg a o models he unc ion o ol age- o-phase con e sion, while he sampling
and di e en ia o a e equi alen o he digi al ans o ma ion blocks [28].
Al hough VCO-based ADCs o e se e al ad an ages, hey a e s ill in e io o
lash when i comes o p o iding an accu a e low-la ency quan iza ion. They a e also
mo e p one o in oduce signal dis o ion. Since in he i s pipeline s age con e sion
speed and linea i y a e c i ical, a hyb id a chi ec u e was adop ed: using a lash
ADC in he i s s age and a VCO-based quan ize in he es [
27
]. Th oughou his
documen , each ins ance ha e e s o he VCO quan ize implemen a ion will imply
ha his mixed app oach is being applied.
NRZ DAC
The design o he sub-DAC, pa icula ly he i s s age one, is c i ical because i
in oduces mos o he non-ideali ies ha deg ade he pe o mance o he con e e , as
will be discussed in he second sec ion o his chap e . The e o e, p ope a chi ec u e
selec ion mus be a p io i y.
A c i e ion o dis inguishing di e en ypes o DAC is he shape o he ou pu
signal. Fo his applica ion, a Non-Re u n- o-Ze o (NRZ) pulse, in which he ou pu
is main ained a he same le el h oughou he du a ion o he whole clock pe iod, is
desi ed. Al e na i e op ions ha swi ch be ween ze o and non-ze o alues du ing a
pe iod cause la ge cu en s a he inpu o he esidue ampli ie and comp omise i s
nonlinea i y [20].
26
4.1. MATLAB Model O e iew
Rega ding i s implemen a ion, examples o esis i e [
19
] [
15
] and cu en s ee ing
DACs [
26
] [
27
] a e ound in he li e a u e. On he one hand, esis i e DACs add he
leas amoun o he mal noise possible [
20
] and a e mo e powe e icien . They can
also bene i om an easie implemen a ion, as hey a e simple ci cui s and can ake
ad an age o he i ual g ound p o ided by he inpu o he nex -s age ampli ie [
19
].
In con as , he cu en -s ee ing DAC has a as e esponse and be e p ecision.
The model o he NRZ DAC is qui e simple. I is based on a unc ion ha
con ains a ec o wi h he alues o each DAC le el and ou pu s he co ec ol age
o he gi en digi al inpu . A e his unc ion, a sample-and-hold ope a ion akes
place. An ex a e m can also be added o he ou pu ha models he ji e e o o
he DAC, which will be u he explained in sec ion 4.2.2.
4.1.2 Recons uc ion il e
Some econs uc ion il e echniques we e al eady explo ed in sec ion 3.2.1. The key
akeaway om hose explana ions is ha he implemen a ion o his block is complex
(some imes being o -chip), equi es o eg ound calib a ion and is o en suscep ible
o a ia ions s emming om sou ces such as empe a u e.
Fo his wo k, wo al e na i es we e es ed: a noise cancella ion il e and a
o eg ound impulse esponse calib a ion.
Digi al Noise Cancella ion Fil e
The i s echnique consis s o applying a Leas Squa es (LS) algo i hm o he
equency spec um o he signal a he inpu s o he econs uc ion il e . The
pu pose o his algo i hm is o achie e in-band noise minimiza ion. While in e es ing
because i allows con ol o he ull in-band esponse, i s compu a ion-hea y na u e
demands o be implemen ed ou side o he chip, and p io calib a ion will be needed.
This me hod is based on he noise cancela ion p esen ed in [
4
]. The analysis
shown in he a icle demons a es ha he LS algo i hm can es o e he inpu signal
while emo ing almos all noise con ibu ions.
The blocks ha compose he il e a e shown in Figu e 4.3. I consis s o h ee
FIR s ages, each om one o he ou pu s o he sub-ADCs. The back-end ADC
ou pu is ea ed as a e e ence o he algo i hm. As can be obse ed om Figu e 4.3,
he signals ge compensa ed o bo h in e s age gain and delay in ad ance o achie e
a p ope cancella ion.
In o de o es ima e he FIR coe icien s, he LS algo i hm o noise minimiza ion
is applied o e he nodes equi ing cancela ion. Howe e , some signal p ocessing
is equi ed be o ehand, as he ope a ions need o be pe o med in he equency
domain. Each o he s eps o his p ocessing chain is de ailed in he nex lis and
can be app ecia ed in Figu e 4.4:
1.
FIR inpu cons uc ion. Fo each o he p ocessed nodes, an a ay o signals is
cons uc ed such ha each one is delayed by one sample om he nex one, as
in he inpu o a FIR il e . The wid h o his a ay equals he numbe o FIR
coe icien s o each s age (Nin Figu e 4.4).
27
4. Con inuous-Time Pipeline ADC: A chi ec u e Design Explo a ion
Figu e 4.3: Digi al econs uc ion il e
2.
Signal windowing. To p e en image componen s om appea ing in-band, he
signal is mul iplied by a window. The selec ed one was he Hanning ype.
3.
FFT calcula ion, o mo e in o he equency domain p io o he LS algo i hm.
4.
F equency masking. The pu pose o his ope a ion is o elimina e all equency
componen s whose noise minimiza ion is no equi ed. This includes he dc,
inpu signal
1
, and ou -o -band bins (see Figu e 4.5). O iginally, i was in ended
o keep only he componen s inside he con e e bandwid h. Howe e , wi h
his es ic ion, a sha p noise loo ise ou o he cu o equency o 400
MHz was obse ed, and he ou pu signal was isibly con amina ed. Full-band
noise cancella ion was also conside ed, bu achie ing good pe o mance o e
such a wide bandwid h p o ed di icul o he algo i hm and he esul s we e
no as desi ed. A comp omise was eached be ween bo h op ions, since he
inal spec um selec ed a e masking occupied hal o he ull ange, up o
s/2=1.6GHz.
All signals esul ing om hese p ocessing ope a ions will be e e ed o as
Fs,i
(Figu e 4.4), whe e sis he s age numbe wi hin he pipeline and iindica es a speci ic
ec o .
The da a coming om he back-end quan ize ,
b
[
n
]in Figu e 4.4, does no
unde go he same p ocess, since i does no equi e any il e coe icien s. I is used
ins ead as a e e ence alue o he LS algo i hm. The e o e, i s ill needs o be
con e ed o he same FFT domain. Ope a ions 2 o 4 o he p e ious i em lis a e
applied o b[n] o gene a e he ec o F e .
1
Since a Hanning window is used, he signal is composed by a o al o h ee bins; i e we e
emo ed o sa e y
28
4.1. MATLAB Model O e iew
Figu e 4.4: Noise minimiza ion algo i hm block diag am
29
4. Con inuous-Time Pipeline ADC: A chi ec u e Design Explo a ion
Figu e 4.5: F equency spec um be o e ( ed) and a e (blue) applying he equency
mask ope a ion
The LS algo i hm o noise minimiza ion can now be applied o he ob ained
da a. Conside ing he no a ion gi en abo e, i could be exp essed as:
N1
X
i=1
F1i·b1i+
N2
X
i=1
F2i·b2i+
N3
X
i=1
F3i·b3i+F e = 0 (4.1)
The di e en summa ions can be compac ed in o ma ix o m o simplici y. By
de ining F
i
=
[Fi1Fi2...FiN ]
and b
i
=
[bi1bi2...biN ]T
he equa ion can be ew i en as
F1·b1+F2·b2+F3·b3+F e = 0 (4.2)
The e ms o each s age a e conca ena ed oge he , as in F
b
=
[F1F2F3]
and
b= [b1b2b3]T, p oducing:
Fb·b=−F e (4.3)
The exp ession abo e is he same as he one p esen ed in [
4
]. Applying some
algeb a, he op imal alue o he coe icien s bis eached:
b=−hRe(FH
bFb)i−1
Re(FH
bF e )(4.4)
Whe e
b
is a ec o con aining he conca ena ion o he coe icien s o s ages 1 o
3, Fband F e a e as de ined p e iously and FH
bis he He mi ian anspose o Fb.
30
4.1. MATLAB Model O e iew
A e his ini ial calcula ion s ep, he coe icien s ba e in oduced in he digi al
noise cancella ion il e and he econs uc ion du ing no mal pipeline ope a ion can
p oceed.
Fo eg ound impulse esponse calib a ion
The o he me hod es ed o digi al econs uc ion consis s o a o eg ound calib a ion
o ind he coe icien s o each o he s ages based on hei espec i e impulse esponses.
I is based on he s a egy used in [
19
]. The main ad an age i in oduces when
compa ed o he p e ious one is ha i is possible o implemen i on-chip. Howe e ,
calib a ion is s ill equi ed. A de ailed explana ion o i s wo king p inciple is p o ided
below.
Recall he esul s o equa ion 3.1. The inpu can be econs uc ed by a il e ha
p ocesses each o he ADC ou pu s wi h he a ious esidue-ampli ying il e ans e
unc ions. In his case, a simila bu di e en app oach is used o es o e he signal.
Conside he ol ages
Vi
o be he ou pu o he di e en quan ize s and
Vb
he ou pu o he back-end ADC. T ans e unc ions can be de ined ha ela e he
ol age o each node wi h he back-end as:
Vb(s)
Vi(s)=Hi(s)(4.5)
Wi h his exp ession, he ou pu ol age o he back-end s age could be exp essed
as:
Vb=
N
Y
i=1
Gi(s)·X0−
N
X
i=1
Hi(s)·Vi(4.6)
Whe e
X0
is he inpu o he pipeline,
Gi
(
s
)is he ans e unc ion o he esidue-
ampli ying il e in s age iand
Vi
,
Vb
and
Hi
(
s
)a e as de ined o equa ion 4.5. I is,
hen, possible o de elop a econs uc ion mechanism i he ans e unc ions
Hi
(
s
)
a e known:
Vb+
N
X
i=1
Hi(s)·Vi=
N
Y
i=1
Gi(s)·X0(4.7)
The esul o his ope a ion is he inpu signal
X0
il e ed by he o ali y o
he s ages. The econs uc ion would be comple ed by di iding by he cumula i e
in e s age dc gain.
1
QN
i=1 Gi(0) · Vb+
N
X
i=1
Hi(s)·Vi!=1
QN
i=1 Gi(0) · N
Y
i=1
Gi(s)·X0!(4.8)
The implemen ed echnique is based on ob aining a digi al app oxima ion o he
ans e unc ions
Hi
(
s
)[
19
]. Conside now he 3-s age + back-end CT pipeline om
he model being discussed. I he inpu was le as an open ci cui and an impulse
was applied o he node V3, he ou pu o he back-end would be:
31
Chap e 5
Con inuous-Time Pipeline ADC:
A chi ec u e Op imiza ion
Resul s
In he las chap e , he main wo k o his p ojec was p esen ed, consis ing in
he explo a ion, analysis and modeling o a ious blocks and e ec s ha appea in
con inuous- ime pipeline ADCs. The ask will end wi h se e al simula ions pe o med
wi h he de eloped models. The esul s and conclusions eached om hese es s
make up he con en o his chap e .
5.1 Pa ame e op imiza ion
Once he model was cons uc ed, he nex s ep was o selec he op imal combina ion
o pa ame e s ha de ine he a chi ec u e. O e se e al simula ions, di e en alues
we e es ed, and a inal decision was made based on he pe o mance esul s. Fo a
gi en sub-ADC-DAC a chi ec u e, he wo main pa ame e s ha mus be op imized
a e he sub-s age quan ize esolu ion and in e s age gain.
As was i s men ioned in Chap e s 2and 3, i should be he goal o he designe
o maximize he gain be ween s ages, since he inpu - e e ed noise le el depends on
his a iable. Howe e , his gain canno be a bi a ily la ge, as ha will p o oke
sa u a ion a he inpu o he quan ize s.
Acco ding o hese guidelines, he pa ame e op imiza ion p ocess unde aken
goes h ough he ollowing s eps. Fi s , a esolu ion combina ion o each subs age is
selec ed om he ange o sui able ealis ic alues. The a chi ec u e is hen simula ed.
By obse ing he in e media e wa e o ms, a gain o each pipeline s age is chosen. A
ule o humb was gi en in p e ious chap e s, which consis s in choosing a alue ha
gua an ees ha he ou pu swing o each il e is wi hin hal o he nex quan ize
dynamic ange.
To e alua e he pe o mance o ADC sys ems, se e al igu es o me i (FoM),
such as he Sch eie FoM [
23
], can be employed. Howe e , hese igu es equi e he
knowledge o he con e e powe consump ion o hei calcula ion. This in o ma ion
39
5. Con inuous-Time Pipeline ADC: A chi ec u e Op imiza ion Resul s
N◦o le els S age gain
S age 1 S age 2 S age 3 S age 4 G1 G2 G3 SNDR
7 7 7 63 3 6 2 71.6
7 7 7 127 3 6 2 74.1
7 15 15 63 3 8 5 74.3
7 15 15 127 3 8 5 74.6
15 15 15 31 5 8 5 77.4
15 15 15 63 5 8 5 79.9
15 15 15 127 5 8 5 80.6
15 31 31 31 6 11 8 80.7
15 31 31 63 6 11 8 80.9
15 31 31 127 6 11 8 81.0
Table 5.1: Pa ame e op imiza ion o he lash sub-ADC e sion o he CT Pipeline.
is simply no a ailable due o he limi ed model being used. The e o e, he signal-
o-noise and dis o ion a io (SNDR) will ins ead be assessed o a chi ec u al
compa ison.
This p ocedu e was i s applied o he e sion o he model ha uses lash ADCs
in all subs ages. The esul s a e shown in Table 5.1. The maximum numbe o bi s o
a lash quan ize was chosen o be 7 [
23
]. As can be seen om he esul s, inc easing
he sub-quan ize s esolu ion pas 4 bi s does p o ide diminishing e u ns. The e o e,
he a chi ec u e using 4-bi subs age lash ADCs, a 7-bi back-end quan ize , and
in e s age gains o 5, 8 and 5, espec i ely, was deemed as he op imal solu ion.
An equi alen me hod was used o he a chi ec u e using a lash ADC on he
i s s age and a VCO quan ize on he es o hem. The same solu ion (4-bi
subs ages and 7-bi back-end) appea ed as he p e e ed candida e. These pa ame e
combina ions a e he ones selec ed o he es o simula ion esul s in his chap e .
5.2 Digi al signal econs uc ion il e
The wo implemen ed digi al signal econs uc ion al e na i es will be compa ed
in his sec ion. To b ie ly summa ize each o he ad an ages al eady discussed
(Sec ion 4.1.2), ecall ha he impulse calib a ion me hod can be suppo ed on-chip,
whe eas he LS noise cancela ion echnique is mo e compu a ionally demanding and
necessi a es o -chip implemen a ion. Howe e , he la e can o e be e con ol
o e he equency spec um since i ope a es di ec ly o e i . Bo h al e na i es
equi e o eg ound calib a ion.
The ou pu equency spec um, as well as he noise pe o mance pa ame e s, o
bo h echniques and bo h lash and VCO quan ize e sions a e shown in Figu e 5.1
and Figu e 5.2, o an inpu equency o in =BW/5 = 80MHz.
The esul s we e as expec ed. The noise cancela ion il e can o e a lowe noise
loo o e he equency spec um. This cha ac e is ic also ansla es o a conside able
40
5.2. Digi al signal econs uc ion il e
Figu e 5.1: Ou pu equency spec um o lash quan ize e sion, impulse cali-
b a ion (le ) s noise cancella ion ( igh ) econs uc ion echniques
Figu e 5.2: Ou pu equency spec um o VCO quan ize e sion, impulse
calib a ion (le ) s noise cancella ion ( igh ) econs uc ion echniques
imp o emen o e he SNR, SNDR and ENOB igu es. The VCO quan ize s a e also
able o ou pe o m he lash ADCs.
Ano he majo di e ence is he numbe o aps needed o he il e s. Recall ha
he impulse calib a ion echnique aims o ob ain an FIR app oxima ion o an IIR
esponse. As such, he selec ed numbe o aps di ec ly a ec s he quali y o his
es ima ion. Fo he p e ious simula ion esul s, 32, 28 and 26 aps we e used o
s ages 1 o 3, espec i ely. The noise cancela ion il e can ob ain a simila o be e
esponse wi h a much mo e compac FIR s age.
Figu e 5.3 and Figu e 5.4 show he pe o mance achie able wi h bo h il e
e sions gi en a o al numbe o aps o he econs uc ion il e s ages. I is e iden
ha he noise cancela ion echnique can achie e simila pe o mance wi h 20 o 30
less aps. The il e choice will hen conside ably impac he powe consump ion o
41
5. Con inuous-Time Pipeline ADC: A chi ec u e Op imiza ion Resul s
Figu e 5.3: SNDR s numbe o aps o lash quan ize e sion, impulse calib a ion
s noise cancella ion econs uc ion echniques
Figu e 5.4: SNDR s numbe o aps o VCO quan ize e sion, impulse calib a ion
s noise cancella ion econs uc ion echniques
42
5.3. Signal T ans e Func ion
he pipeline a chi ec u e.
By he conside a ions abo e, i migh seem as i he noise cancela ion il e
p o ides an o e all pe o mance imp o emen o e he impulse-calib a ion me hod.
Howe e , a compa ison o he STFs o bo h il e s in he nex sec ion migh sugges
he opposi e.
5.3 Signal T ans e Func ion
The simula ion esul s p e iously shown display he ou pu pe o mance o a speci ic
equency inpu (in pa icula ,
in
= 80
MHz
). Howe e , i is necessa y o e alua e
he beha io o e he ull equency band. The signal ans e unc ion (STF) is he
p e e ed me hod o assess his.
As explained in Sec ion 3.1.4, he ideal STF o a con inuous- ime pipeline ADC
is he p oduc o he ans e unc ion o all esidue-ampli ying il e s ages. In his
case, a uni y gain up o 400 MHz and a six h-o de oll-o a e wa ds would be
expec ed. In o de o achie e his, using a s anda d second-o de il e wi h he
desi ed cu o equency pe s age is no enough, and ca e ul conside a ion has o be
gi en o he selec ion o he quali y ac o o he ans e unc ion.
The plo in Figu e 5.5 shows he STF o di e en il e design app oaches.
Fi s , an ideal six h-o de Bu e wo h is shown, o ha e a e e ence o compa e o.
Nex , each o he il e s ages has been buil using he same s anda d second-o de
Bu e wo h esponse (
bu e ()
unc ion in Ma lab) wi h a cu o equency o 400
MHz. Las ly, an al e na i e is displayed ha implemen s di e en il e ans e
unc ions wi h speci ically selec ed quali y ac o s ( alues in Sec ion 4.1.3) and a
il e cu o equency o 440 MHz. As can be obse ed, signal ones a 400 MHz will
su e a se e e dB a enua ion wi hou he p ope il e design.
The nex compa ison shows he di e ence be ween he STF when using lash-
and VCO-based quan ize s. As has been s a ed, VCO-based quan ize s ha e a uni y
gain STF bu a i s -o de NTF o quan iza ion noise, which is shaped a he ou pu .
These dynamics can be app ecia ed a highe equencies and a e shown in Figu e 5.6.
The las commen is de o ed o he digi al signal econs uc ion il e . All o
he abo e STF plo s ha e been ob ained by using he impulse calib a ion me hod.
When swi ching o he noise cancella ion coe icien s, he esponse is as in Figu e 5.7
As can be obse ed, i is a om ideal and he il e will no achie e uni y
gain o e he desi ed applica ion bandwid h no six h-o de a enua ion o ou -o -
band componen s. The eason behind his is ha he LS algo i hm does no ha e
in o ma ion abou he BW, only on he equency mask. As e ealed in Sec ion 4.1.2,
in-band o ull-band masking did no p o ide he equi ed noise pe o mance. The
hyb id app oach o masking un il
= 1
.
6
GHz
ob ains a ema kable SNDR, bu
canno achie e a uni y gain ac oss he en i e band.
43
5. Con inuous-Time Pipeline ADC: A chi ec u e Op imiza ion Resul s
Figu e 5.5: Compa ison o STF: ideal, same il e pe s age design, di e en il e
wi h speci ic Q design
Figu e 5.6: Compa ison o STF: Flash s VCO quan ize s
44
5.4. Non-ideali ies
Figu e 5.7: STF wi h di e en econs uc ion il e implemen a ions
5.4 Non-ideali ies
The e ec s o he non-ideali ies desc ibed in Sec ion 4.2 on he pe o mance o he
ADC ha e been checked by se e al simula ions. The esul s aim o se limi s o he
maximum ole able e o s ha he con e e can wi hs and.
5.4.1 DAC misma ch
The modeling echniques o he di e en e o s induced by he i s DAC misma ch
we e elabo a ed in Sec ion 4.2.1. In summa y, s a ic, delay, ise and all imes a e
added as a pe cen age o andom a ia ion ollowing Equa ion 4.12. A Mon e Ca lo
simula ion in Cadence Vi uoso is pe o med whe e, o a speci ied s anda d de ia ion
o he e o , a ious andomized i e a ions e alua e he pe o mance o he con e e .
The g aphs in Figu e 5.8 demons a e he CT-pipeline SNDR o a ious le els o
s anda d de ia ion o he s a ic, delay, and ise and all ime a iables. The Mon e
Ca lo simula ion was pe o med on 200 andom i e a ions. In he plo , he mean
SNDR alue ob ained o each de ia ion is ma ked wi h a do symbol. The
±
3
σ
a ia ions a e also displayed.
I is no s aigh o wa d o de ine a ole ance bounda y o each o hese e o s.
In he physical implemen a ion o he con e e , hese a e mainly subjec o p ocess
a ia ions ha a e echnology dependen . I is clea , o example, ha a misma ch
45
5. Con inuous-Time Pipeline ADC: A chi ec u e Op imiza ion Resul s
Figu e 5.8: DAC Misma ch s a ic, delay, ise and all ime e o s
be ween uni elemen s causing s a ic di e ences in he ol age le el can ha e a
de imen al e ec on he con e e pe o mance. In hese cases, he design o
calib a ion and e o compensa ion echniques [
18
][
27
] appea s o be manda o y o
achie e he SNDR equi ed by he applica ion.
5.4.2 Clock ji e
The e ec o clock ji e on he i s DAC has also been es ed. The de ails o how i
has been in oduced in o he Simulink model we e discussed in Sec ion 4.2.2.
The simula ion ca ied ou e alua es he SNR o di e en le els o clock ji e
o e h ee sepa a e inpu equencies. I used he lash quan ize s and he impulse
calib a ion econs uc ion e sion o he model.
In Figu e 5.9, he ji e is speci ied wi h i s oo mean squa e (RMS) alue in
picoseconds. No e om he g aph ha , o he desi ed bandwid h o 400 MHz, a
ji e ms
= 0
.
1
ps
would al eady se a limi
SNRMAX
= 75
dB
. E en a low ji e
le el could hampe he pe o mance igu es o he con e e . I is e iden ha
high-speed ADCs mus add ess his di icul y. Some discussion in his ega d can be
ound in [3].
5.4.3 Fil e Nonlinea i y
Wi h espec o he hi d-o de nonlinea i y expec ed om he esidue-ampli ying
il e , i has been modeled ollowing Equa ion 4.15. The simula ion esul s a e shown
in Figu e 5.10.
The esul s do no seem as es ic i e as o he o he s udied non-ideali ies. Pe -
o mance deg ada ion migh be obse ed o ampli ie s wi h a hi d-o de nonlinea i y
coe icien a ound 10−2, which is a qui e elaxed equi emen .
46
5.4. Non-ideali ies
Figu e 5.9: Maximum SNR due o di e en ji e le els o h ee sepa a e inpu
equencies
Figu e 5.10: Fi s s age hi d-o de nonlinea i y e ec on SNDR
47
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