ISCAS
2000
-
IEEE
In e na ional Symposium on Ci cui s and Sys ems, May
28-31,
2000,
Gene a, Swi ze land
HIGH-ORDER CASCADE MULTIBIT
CA
MODULATORS
FOR
xDSL APPLICATIONS
R.
del
Rio, E Medei o,
B.
Pe' ez-Ve dLi,
and
A.
Rod iguez-V izquez
Ins i u o
de
Mic oelec dnica
de
Se illa
-
CNM-CSIC
Edi icio
CICA-CNM, C/Ta ia
s/n,
41012-
Se illa, SPAIN
Phone:
+34
95
5056666.
Fax:
+34
95
5056686,
E-mail:
[email p o ec ed]
ABSTRACT
This pape explo es he use o CA modula o s o AD con e -
sion in xDSL applica ions. Two high-o de mul ibi a chi ec u es,
he 2-I-lm0 modula o [7] and ano el2-1-1-lmb cascade (MASH),
a e p oposed o achie e 14bi dynamic ange
@
4.4MSls using low
o e sampling a io. They show e y low sensi i i y o he in emal
DAC linea i y e o , wi h no calib a ion equi ed. Simula ions show
his pe o mance can be achie ed in p esence o ci cui impe ec-
ions, using submic on digi al CMOS p ocesses.
1.
INTRODUCTION
CAModula o s (CAMs) ha e been success ully employed in he
pas o IOW-, medium- equency AD con e sion
[l].
The use o
o e sampling and noise-shaping echniques in hese con e e s
a oids he need
o
ex emely accu a e analog building blocks, wha
makes hem e y sui able in he con ex o poo -analog-pe o mance
submic on CMOS p ocesses. Such ad an ages ha e encou aged
designe s o widen he bandwid h
o
EA
con e e s
up
o he da a
acquisi ion and communica ion anges [2]-[SI, demanding high- es-
olu ion and high-speed ope a ion.
Conside ing only quan iza ion noise, he dynamic ange
DR
o
a
CAM can be oughly es ima ed
as
ollows:
L
IC
J
whe e
L
s ands o he modula o o de ,
M
o i s o e sampling
a io, and
B
o he in e nal quan ize esolu ion in bi s.
In high-speed applica ions, inc easing he signal bandwid h
,
while main aining an achie able sampling equency
,
implies he
use
o
a
mode a e
M,
since
M
=
s/(2 x). In his scena io, he
na u al way o inc ease DR in o de
o
cope wi h high- esolu ion
speci ica ions
is
o eso o high-o de (inc easing
L),
mul ibi
(inc easing
B)
CAMs.
Howe e , wo impo an d awbacks a ise:
On he one hand, unlike 1s - and 2nd-o de loops, high-o de
loops a e no uncondi ionally s able.
On he o he , he linea i y o he mul ibi CAM is ul ima ely lim-
i ed by ha o he mul ibi DAC in he eedback pa h.
Bo h p oblems ha e been pa ially o e come; ac ually,
high-o de ZAMs ha e been s abilized h ough se e al echniques
[I]:
i.e., p ope choice o he scaling ac o s, use
o
mul ipa h eed-
o wa d s uc u es, o ese ing o he in e nal a iables i uns able
ope a ion
is
de ec ed. On he o he hand,
a
common s a egy o pal-
lia e he s ong dependence on he in e nal DAC linea i y is using
calib a ion ei he in he analog
o
in he digi al domain
[I].
Ne e heless, cascade mul ibi a chi ec u es o e come hese
pe o ming he high-o de il e ing by cascading low-o de
(1
s -
and 2nd-) CAMs o gua an ee uncondi ional s abili y, and
using mul ibi quan iza ion only a he las s age
o
he cascade
o a enua e he in luence o he DAC non-linea i y [2].
This pape explo es he use o such a chi ec u es o ob ain
[email p o ec ed]/s
-
speci ica ions in he ange o xDSL equi emen s.
In Sec ion
2,
wo cascade mul ibi a chi ec u es a e conside ed:
a
4 h-o de 3-s age cascade (wi h he s uc u e 2-1-1) and
a
5 h-o de
4-s age cascade (2-1
-1
-l),
bo h including mul ibi quan iza ion. Sec-
ion
3
is dedica ed o analyze he impac
o
ci cui impe ec ions
deg ading he modula o s pe o mance.
p oblems wi h nei he calib a ion no ese ing equi ed by:
2.
CASCADE MULTIBIT
XAMs
Fig.1 shows
a
gene ic L h-o de N-s age cascade mul ibi CAM.
I includes single-bi quan ize s in
all
s ages excep he
las
one
which
has
a
mul ibi quan ize . In cascade CAMs, he quan iza ion
e o induced in each s age
is
emodula ed by he ollowing one in
he cascade. Once in he digi al domain, by p ope ly combining he
ou pu s o he s ages, i is possible o cancel ou he quan iza ion
e o in
all
s ages excep ha in he las one, which appea s a he
modula o ou pu a enua ed by
a
shaping unc ion o o de equal o
he summa ion o he o de o
all
s ages. Thus, ideally, he ollowing
is ob ained
o
he Z-domain ou pu :
IL
-1
W-L,)
Y(z)=z-LX(z)+d(l
-z-
)
EN(Z)--d(l
--z
)
E,(z)
(2)
whe e
X(z)
is
he Z- ans o m o he modula o inpu ,
d
is an scala
la ge han uni y esul ing om p ope scaling
o
he ans e ed sig-
nal
o
p e en o e loading o he s ages,
E$z)
is he las -s age
quan iza ion e o ,
E,(z)
is he e o induced in he las -s age DAC,
Fig.
1:
Gene ic L h-o de N-s age cascade mul ibi CAM.
(*)
This wo k has been pa ially suppo ed by he ESPRIT P ojec 29261 MIXMODEST, and he CICYT P ojec TIC 97-0580
0-7803-5482-6/99/$10.00 02000
IEEE
11-37
and
L
=
L,
+
.
.
.
+
L,.
No e ha
ED(z)
is
(L
-
L,) h -o de
shaped, wha signi ican ly elaxes he DAC linea i y speci ica ions,
wi h nei he co ec ion no calib a ion equi ed.
Se e al cascade mul ibi CAMS ha e been epo ed:
a
3 d-o de
2-1 cascade (2-lmb) [2],
a
4 h-o de 2-2 cascade (2-2mb)
[3],
and a
4 h-o de 2-1-1 cascade (2-12mb)
[7].
Acco ding o eq.(2),
DAC-induced e o is 2nd-o de shaped in he i s wo modula o s
and 3 d-o de shaped in he las one. Thus, while in he 2-lmb and
2-2mb a chi ec u es he in-band powe o such e o is a enua ed by
M5,
i is a enua ed by
M7
in he 2-12mb. This conside ably
educes he sensi i i y o he la e o he DAC
ZNL,
simpli ying
he e o e i s design. Fig.2 illus a es he 2-12mb cascade CAM.
A 5 h-o de 4-s age 2-1-1-1 cascade using mul ibi quan iza ion
in he las s age (2-13mb), Fig.3, has been de eloped as an ex ension
o he o me o one mo e o de , while p ese ing i s p ope ies. Ide-
ally, he ollowing Z-domain ou pu is ob ained o bo h modula o s:
Digi al
HI(?)
=
z-'
whe e i has been assumed ha he ela ionships among digi al and
analog coe icien s and he alues o he digi al il e s
H&z),
k
=
1,
,..,
6
a e hose in Table 1 and 2, espec i ely.
The e o e, he in-band e o powe a bo h modula o ou pu s is
Digi al/Analog Analog
_I
d
-
1
--
&?I'
=
g,
831
O-
s,g,g,
(4)
whe e
c i
=
[A/(28- 1)12/12
is
he powe o he las -s age
quan iza ion e o
(A
s ands o he las -s age quan ize ull+ale)
and
c i
ep esen s he DAC-induced e o powe . No e ha his
e o is a enua ed by
M9
in he 2-13mb.
2.1
In eg a o weigh op imiza ion
Wha e e se o coe icien s (in eg a o weigh s in Fig.2 and
3)
ul illing he ela ionships in Table
1
and 2 leads o he exp essions
in eq.(3). Ne e heless, he ollowing conside a ions mus be aken
in o accoun in ac ual implemen a ions:
The le el o he signal ans e ed om one s age o he nex in
he cascade mus be low enough o a oid o e loading he la e .
I
*
Cancella ion
Logic
Fig.
2:
4 h-o de 2-1-1 cascade mul ibi CAM (2-12mb).
'
Cancella ion
Logic
Fig.
3:
5 h-o de 2-1-1-1 cascade mul ibi ZAM (2-13mb).
TABLE
1:
Digi al ans e unc ions and ela ionships o he
2-1'
ZAM.
I
Digi al
I
Digi al/Analog
I
Analog
I
H2(z)
=(1
-z-1)2
d,
=
-
g,'
=2g,'g2
s,gzg3
U
d2
= 0
g,'
=
s3"g4
H3(Z)
=
2-1
TABLE
2:
Digi al ans e unc ions and ela ionships
o
he
2-1''
CAM.
.
I~_
,
I
82'
=
2g,'g,
H,(z)
=
z-1
d,
=
0
I
The ou pu swing equi ed o he in eg a o s, which depends on
hei weigh s
as
well as on he inpu le el, mus be physically
achie able. In SC implemen a ions his limi is de e mined by
he supply ol ages.
Digi al coe icien s
d,
and
d,
,
which ampli y he las -s age
quan iza ion e o in eq.(3), should be
as
small
as
possible.
Addi ional conside a ions in o de o simpli y he design a e:
Digi al coe icien s should be
0,
1 o mul iple o 2.
Mul ibi quan ize gain mus be such ha he loop gain
o
he las
s age equals uni y. Mo eo e , i should no be oo la ge in o de
11-38
o simpli y he design o he mul ibi quan ize .
Table
3
p esen s good selec ions o he in eg a o weigh s o he
2-I2mb and 2-13mb, o which he ou pu swing equi emen is
educed o only he e e ence ol ages.
In
addi ion, in bo h cases he
las -s age quan iza ion e o is ampli ied only by 2,
d,
=
d,
=
2
in eq.(3). This means a sys ema ic
loss
o esolu ion o 6dB (Ibi )
espec o he ideal case gi en in eq.(l). Howe e , his loss is small
when compa ed o ha caused by s abiliza ion and non-linea i y co -
ec ion mechanisms used in o he app oaches
[
13.
Ano he 5 h-o de
mul ibi cascade we ini ially conside ed, a 2-2-lmb CAM, was dis-
ca ded a his poin because he se o coe icien s equi ed o a oid
o e loading lead o
d,
=
8
(3bi sys ema ic
loss).
TABLE
3:
Analog and digi al coe icien s in Fig.2 and
3.
Shaded
cells
co espond o
he
2-13,nb modula o
These coe icien s p esen wo addi ional ad an ages:
Because he la ges weigh in all h ee-weigh in eg a o s can be
easily ob ained as a combina ion o he o he s, an
SC
implemen-
a ion will only equi e wo-b anch in eg a o s. No e ha only
one b anch is needed o he i s in eg a o .
The o al numbe o uni a y capaci o s is only 16 o he 2-12mb
and
19
o he 2-13mb modula o , smalle han in o he cascade
ZAMs
-
29 uni a ies in
[5]
and
[8],
and
44
in
[6].
3.
CIRCUIT NON-IDEALITIES
Excep o he DAC-induced e o s, he a chi ec u al s udy in
Sec ion 2 assumes ideal condi ions. Ne e heless, ci cui impe ec-
ions deg ading he CAM pe o mance mus be aken in o accoun in
p ac ice. These non-ideali ies can be g ouped in wo ca ego ies:
hose a ec ing he quan iza ion noise ans e unc ion, whose
e ec s ongly depends on he a chi ec u e conside ed, o
ins ance in eg a o leakage and weigh misma ching, and
hose ha can be modeled as an e o sou ce a he i s in eg a-
o ; such app oxima ion is jus i ied by he ac ha he con ibu-
ion
o
emaining in eg a o s is a enua ed
by
inc easing powe s
o he o e sampling a io. This is he case o he mal noise,
de ec i e se ling in in eg a o s, e c.
3.1
In eg a o leakage and weigh misma ching
The ideal s udy de eloped in Sec ion 2 assumes ha he ela ion-
ships o Table
1
and 2 a e ul illed and ha he ans e unc ion
o
he in eg a o s is exac ly
z-'/(
1
-
-l)
.
Howe e , hese assump-
ions a e no alid in p ac ice:
On he one hand, ac ual alues o in eg a o weigh s di e om
nominal ones due o misma ch in capaci o s a ios.
On he o he , he in eg a o ans e unc ion abo e is modi ied
by he ini e DC-gain o he ampli ie s.
0
1
2
3
4
5
81
s
(a)
B
(bi )
2
3
4
5
B
(bi )
Fig.
4:
Modula o esolu ion
s.
las -quan ize esolu ion o :
(a)
2-1
,mb
CAM and (b) 2-
1
3mb
CAM.
(A,
=
2500,
weigh
misma ch
(
=
0.1
%,
and
DAC
INL
=
0.4% FS)
Bo h non-ideali ies esul in an incomple e cancella ion o he
quan iza ion e o o he o me s ages and deg ade he modula o
DR
[9]. Analysis shows ha he ex a in-band e o powe due o
hese non-ideali ies is:
whe e
A,
s ands o he opamp DC-gain, e e s o misma ching
in weigh s g,,
g,,
g3and
g,",
and
c :
=
A2/12 is he quan iza ion
e o powe
o
a single-bi quan ize .
No e ha hese ex a e o con ibu ions can in p ac ice mask
hose in eq.(4), since hey a e only a enua ed by M3 and M5
.
Fig.4
shows simula ion esul s o he e ec i e esolu ion
o
he 2-12mb
and 2-1
3mb
modula o s when a ying he las -s age quan ize eso-
lu ion
B,
wi h
M
ac ing as a pa ame e (depic ed o e each cu e).
No e ha cu es sa u a e in he p esence o hese non-ideali ies,
leading o a p ac ical limi o he use
o
mul ibi quan iza ion
-
g ossly es ima ed by he hick solid line. Inc easing
B
o e his limi
would no u he imp o e he modula o
DR.
Ne e heless, esolu-
ions below his limi a c enough o signi ican ly elax he ci cui
equi emen s wi h espec o single-bi app oaches.
3.2
O he ci cui s impe ec ions
Di e en
[M,
B]
pai s can be a p io i selec ed om Fig.4 o he
2-I2mb and he 2-13mb modula o s, in o de o ul il speci ica ions
o [email p o ec ed]/s. Ne e heless, as ope a ion equencies inc ease
11-39
in
ZAMs,
he de ec i e se ling o SC in eg a o s becomes one o he
dominan e o s limi ing he modula o s pe o mance. Thus, he
inal choice among possible
[M,
B] pai s mus be done in p ac ice
conside ing he opamp dynamic equi emen s in ol ed. Table 4
shows an es ima ion
o
he equi ed opamp bandwid h
(GBW)
o
he di e en
[M,
B] pai s ob aining >13bi o bo h modula o s.
M
=
16, B
=
4
o he 2-I2m6 modula o and
M
=
14,
B
=
3
o he 2-13mb a e he less demanding pai s o 14bi esolu ion.
No e ha mul ibi quan iza ion signi ican ly elaxes he dynamic
equi emen s wi h espec o
a
single-bi app oach. Fo ins ance,
a
2-12 modula o wi h single-bi quan iza ion would equi e
M
=
22
o ob ain 14bi esolu ion. This highe
M
would lead o an inc ease
o -35% on he powe consump ion pe opamp.
TABLE
4:
Es ima ed opamp
GBW o
ope a ion a 4.4MS/s.
2-1~~0
14
61.6
+I
0.5
0.5
0.1
25
20
0.2
68
20%
2.25
0.9
+1/%2’
20
3
0.4%FS
86.4dB
(14.1
bi )
-91.5dB
-95.5dB
102.4dB
.IOl.ldB
/
The o e all in luence o ci cui impe ec ions on he modula o
pe o mance has been e alua ed using SDOF’T [9],
a
sizing ool o
SC CAMS. This ool combines accu a e analy ical exp essions o
each e o con ibu ion and s a is ical op imiza ion, wha allows
us
o ind op imized, non-o e sized speci ica ions o he building
blocks. Table 5 summa izes he ci cui equi emen s p o iding
[email p o ec ed]/s o bo h a chi ec u es, aking in o accoun he di -
e en e o con ibu ions (e.g., quan iza ion and he mal noise, se -
ling e o , capaci o misma ching, ini e opamp DC-gain).
Fig.5
shows beha io al simula ion esul s using ASIDES [9] o
he
signal- o-(noise+dis o ion)
a io
SNDR
o
bo h modula o s in
he p esence o he ci cui s impe ec ions in Table
5.
The maximum
SNDR, ob ained o
a
-5dB inpu le el,
is
80.5dB o he 2-I2m6 and
79dB o he 2-13mb. The DR
is
86dB and 84.5dB, espec i ely.
These esul s p esen bo h a chi ec u es
as
good candida es o
ob ain high- esolu ion, high-speed ope a ion in xDSL applica ions,
wi h
a
mode a e powe consump ion. In ac , wi h he explo ed mod-
ula o s, DAC non-linea i ies up
o
0.4%FS
can be ole a ed wi h
mode a e equi emen s o he building blocks.
-
Uni
-
Mllz
‘
pF
pF
9’0
pp n/L
46
kQ
dB
-2
mA/
nL4
niV
bi
-
-
-
-
-
80
70
-
60
s
50
M
e
9
40
‘
30
20
10
CONVERTER
(Non-linea i y
(INL)
5
Iynamic ange
Inpu le el (dB)
Fig.
5:
SNDR as
a
unc ion o he inpu le el.
0.4%FS
87.7dB
TABLE
5:
Modula o sizing esul s
Uni a y capaci o
0.5
Capaci o non-linea i y
_i
Sigma
[NTEGRATORS
DC-gain
2
DC-gain non-linea i y
5
Maximum ou pu cu en
Di e en ial ou pu swing
:OMPARATORslHys e esiS
5
I
20
A/D/A ]Resolu ion I4
’henna1 noise -95.9dB
ncomple e se ling noise -102.3dB
*.
Only hi d in eg a o needs +2V ou pu swing
4.
REFERENCES
[I]
S.
R.
No swo hy,
R.
Sche eie and
G.
C. Temes (Edi o s)::
“Del a-Sigma Da a Con e e s: Theo y, Design and Simula-
ion”, IEEE P ess, 1996.
[2] B. B and and B. A. Wooley: “A 50-MHz Mul ibi CA Modula-
o o 12-b 2-MHz AD Con e sion”,
IEEE
J.
o Soli -S a e,
Ci cui s, ol. 26, pp. 1746-1756, Dec. 1991.
[3] N. Tan and
S.
E iksson: “Fou h-O de Two-S age Del a-Sigma
Modula o Using Bo h
1
Bi and Mul ibi Quan ize s”, Eleci
onics Le e s, ol. 29, pp. 937-938, May 1993.
[4]
G.
M. Yin and
W.
Sansen: “A High-F equency and High-Reso-
lu ion Fou h-O de
CA
A/D
Con e e in BICMOS Technol-
ogy”, in P oc.
o
Eu opean Solid-S a e Ci cui Con , pp.
1-4,
Sep . 1993.
[5] A. Ma ques, e al.: “A 15-b Resolu ion 2-MHz Nyquis Ra e
AZ
ADC in
a
1 -pm CMOS Technology”. IEEE
J.
o
Soli&S a e
Ci cui s, ol. 33, n.
7,
pp. 1065-1075, July 1998.
[6] A. Feldman, e
al.:
“A 13-Bi , 1.4-MSIs Sigma-Del a Modula o
o
RF
Baseband Channel Applica ions”.
IEEE
J.
o
Solid-S a e
Ci cui s, ol. 33, n.
10,
pp. 1462-1469, Oc . 1998.
[7]
E
Medei o, e
al.:
“A
13-bi , 2.2-MS/s, 55-mW Mul ibi Cas:
cade
CA
Modula o in CMOS 0.7-pm Single-Poly Techno$-
ogy”.
IEEE
J.
o
Solid-S a e Ci cui s, ol. 34, n.
6,
pp. 748-760,
June 1999.
[8]
Y.
Gee s, e al.:
“A
3.3-V, 15-bi , Del a-Sigma ADC wi h aSig-
nal Bandwid h o 1.1 MHz o ADSL Applica ions”. IEEE
J.
$
Solid-S a e Ci cui s, ol. 34, n. 7, pp. 927-936, July 1999.
[9] .F. Medei o, B. PC ez-Ve dli and A. Rod iguez-Vizquez:
“Top-Down
Design
o
High-Pe o mance Sigma-Del a
Modu-
la o s”, Kluwe Academic Publishe s, Bos on, 1998.
11-40