Design
o
a band-pass sigma-del a modula o
wi h educed
numbe
o
opamps
A.
P.
VegaLea~
F.
Munoz,
R.
G.
Ca ajal, A. To alba,
J.
Tombs and L.G. F anquelo
Dp o.
de
lng. Elee/ oniea, Escuela Supe io de Ingenie os, Uni e sidad
de
Se illa, Se illa, Spain
Abs ac
This pape
is
in ended o compa e he pe o mance
o
a Band-Pass con e e s uc u e and i s Low-Pass
p o o ype 2nd o de Sigma-Del a Analog
o
Digi al
con e e . Fo his pu pose Ma lab simula ions o
he
4 h o de Band-Pass con e e ha e been
pe o med and i s powe consump ion
calc~la ed
when using he equi alen Op-Amp used m he
Low-Pass modula o . Fi s
o
all will be desc ihed
he me hod used o calcula e he ans e unc ion
and, hus he s uc u e
o he
Band-Pass s uc u e o
be es ed. A e a band-pass ans e unc ion has
been ob ained i is implemen ed using educed
numbe
o
opamps. This opology is compa ed o
he exis ing ones and a sys em le el simula ion and
cha ac e isa ion is pe o med. Finally, ji e
limi a ions a e s udied. T ansis o le el simula ions
using Spec e ha e been done in o de o alida e
MA TLAB simula ions p io o layou design.
1. In oduc ion
In applica ions whe e an IF signal bas
o,
be
demodula ed and con e ed o digi al, wo solu IOns
may be used. The i s one consis s in do,:",-
con e ing he signal
o
base-band and con e mg
o. Two con e e s would
be
needed. This solu ion
is
sensible
o
he misma ch be ween he eal and
imagina y b anches
o
he demodula o . O he
p oblems as o se and
II
noise sensi i i ies a ec
he pe o mance
o he
low-pass con e sion,
An
al e na i e solu ion is o pe o m a band-pass
AID con e sion
o
he
IF
signal and demodula e in
he digi al domain. This can be accomplished using
a band-pass sigma-del a modula o .
ThIS
me hod
IS
ee om he wo-pa h misma ch
beCliuse
i uses
only one con e e . The low equency disables he
e ec s
o
he
II
noise.
The
main disad an age
o
hese s uc u es is he e ec
o
ji e on he SNDR.
This makes necessa y o build a low ji e y clock
ha ensu es ha he inpu sampled signal SNR is
euough no o deg ade hc modula o 's
pe o mance. ,
Two me hods a e a ailable o ind an app opna e
ans e unc ion o he band-pass modula o ,
'The
simples way is o s a wi h
an
exis ing low-pass
s uc u e and pe o m a low-pass- o-band-pass
ans o ma ion [I]. The second mc hod
is
o design
he ans e unc ion ia a Gene alised Fil e
App oxima o [2]. These a e ou ines ha adjus he
poles and ze os
o H(z)
o accomplish wi h he
ampli ude speci ica ions demanded by he designe .
A e ha design, a s abili y s udy mus
be
pe o med o gua an ee he co ec beha iou .
T ans o ming an exis ing low-pass in o a band-pass
s uc u e
is
mo e used because low-pass s uc u es
a e be e known and widely used. The p esen
design will be buil om an exis ing 2
nd
o de Low-
Pass con e e and a Low-pass- o-band-pass
ans o ma ion will be applied.
2.
Ioow-Pass p o o ype
A good app oach in designing band-pass
modula o s is s a ing wi h a sui able low-pass
s uc u e. The s a egy
o
building a low-pass
p o o ype enables us o ake ad an age .
o
he
s abili y pe o mance and he
nOIse
p ope ies ha
a e well s udied o low-pass sys ems. Once a e
ensu ed hese p ope ies
in
he low-pass modula o ,
we can a on he ask
o
uns o ming o a band-
pass modula o p ese ing bo h s abili y and noise
pe o mance. The inal band-pass s uc u e mus i
he needed equi emen s o signal band and o e -
sampling a io. Once he low pass s uc u. e
~s
designed, a low-pass- o-band-pass ans o ma IOn IS
applied, This ans o ma ion mus map he poles
and ze os a ound he
wo=O
equency o hei inal
wo=w, equency. The e a e
wo
app oaches o go
ahead wi h his ans o ma ion. Each
o
hem has
ad an ages ha mus be s udied in o de
o
choose
he
one ha i s ou needs,
a) Gene alised
N-pa h
ans o ma ion
is
achie ed doing z,,"
+1-
ZN.
This
ans o ma ion p ese es modula o dynamics
bu inc ease he modula o o de unnecessa ily
(N)2)
o esul in a band-pass cen ed a ,/2
o
z+
(aliasing p oblems).
b) Seeond
o de
Low-Pass-To-Band-Pass
ans o ma ions gi e ull con ul o e he
pass-band loca ion bu do no p ese e
modula o dynamics. Fo his s a egy, he
l ans onna ion:
z,,"-z'(z+aY(a'z+I),
whe e-I<a<l
(I)
.<0 gi es sys ems close o DC.
0>0
gi es sys ems close
o
,/2.
When
a=O
(I)
Z7-Z'
and he esul is a
Band-Pass s uc u e wi h ,l4 cen al
equency.
This way. s abili y is gua an eed as well as he
modula o dynamics. This will hen be he
app oach
o
be ollowed in o de o build he
p oposed s uc u e.
In igu e I is ep esen ed he
2""
o de Low-Pass
p o o ype.
I
has been widely s udicd and,
hUB.
is a
good s a ing poin o build ha band pass
modula o . Once SUbs i u ing Z by
-- .
he s uc u e
is he one depic ed in igu e
2.
I is clea ly seen ha
in eg a o s ( igu e
I)
a e ans o med in o
esona o s, bu he o e all s uc u e is unchanged.
In igu e 2 is ep esen ed he esul
o
his
ans o ma ion.
3. Cha ac e isa ion
o
a low-pass
p o o ype
The i s s ep in he desigu
o
a band-pass
modula o using
he
low-pass o band-pass
ans o ma ion me hod is o desigu i s low-pass
p o o ype. This low-pass p o o ype is he one
depic ed in igu e I. Mul iple simula ions ha e been
pe o med o ully eha ac e ise i s dynamic
beha iou . The esul s
o
hese simula ions, using
bo h MIDAS [12] and MATLAB
[II],
a e shown
in igu es
3,
4.
To accomplish an op imum beha iou
we
look in o
he esul s o build ou sys em using he bes
coe icien s o imp o e SNDR and i s sensi i i y o
a ia ions
o
hese eoe icien s, as well as he
pe o mance ha will be needed in he desigu
o
he
ci cui 's building blocks
[I,
10].
AI his poin ( unc ional sys em simula ion) alues
o bandwid h, maximum inpu ampli ude, op-amp
dynamic speci ica ions a e all ela ed o a
no malised equency ,. Once a alue o , is
de ined, all he o he pa ame e s can be known as
absolu e alues.
Once is de ined ou low-pass p o o ype, he
<:
by
_Z·2
ans o ma ion is pe o med.
In igu e 4 a e ep esen ed he alues ha can be
aken
o
design he opamp. On he x axis is
ep esen ed he a io; Tsl(2·TAU). E e y cu e has
been calcula ed o a SRn, being
SR=SRn·2· ,V_
4.
Band-Pass s uc u e
Se e al op ions a e a ailable o implemen he
ans o med pass-band modula o . The di ec
ans onna ion consis s in eplacing in he low-pass
s uc u e he in eg a ocs by esona o s ( igu e 2)
modi ying he second adde o main ain he desi ed
ans e unc ion. Resona o s a e usually buil
using wo opamps. This is a d awback in he design
o
low-powe ci cui s. A i s al e na i e is
o
design a single opamp esona o . This s uc u e,
157
depic ed in ib'll e 5,
is
desc ibed in
[2).
The use
o
his s uc u e complica es he clocking scheme,
adding 6 ex a clocks
a
hal he sampling
equency. In his kind
o
s uc u es i is ex emely
impo an
o
kccp a s ic con ol on clock phases o
a oid sigual dependen clock eedlh ough ha will
appea inband as an image
o
he inpu equency
a ound
/4.
Ano he solu ion
o
ob ain a band-pass modula o is
eplacing he esona o s by Two-Delay In eg a o s
as d awn
in
igu e 6.
In
his s uc u e in eg a o s
only use addi ion, he is why bo h inpu and ou pu
pola i ies need
o
be in e ed e e y wo delays.
This e ec is modelled mUl iplying hose siguals by
he sequence: {I, I,
-I,
-I,
I, I,
-I,
-I,
...
}. As
in
he
case
o
esona o s. wo in eg a o s a e needed o
pe o m be wo-delay in eg a ion.
In
[3]
a di e en
solu ion
is
ob ained
o
build an equi alen band-
pass sys em as be one
in
igu e 6. The in e es ing
poin
o
his is he possibili y
o
implemen ing an
N'"
o de s uc u e using N opamps. In igu e 6 is
d awn be block diag am o a one bi modula o
(p oposed in [3]) ha sol es he p oblem using a
minimum numbe
o
opamps. This consis s
in
down-con e ing he inpu sigual
o
i s base-band I
and Q componen s. Once he signal
is
down-
con e ed, i is p ocessed in he base-band egion
and inally up-con e ed o i s o iginal IF. Looking
close we scc ba while one b anch is in eg a ing a
a iable inpu , he olbe one is in eg a ing a "0",
ha is, Iba b anch emains wi h a ixed ou pu
du ing Iba cycle. We can ob ain he wo-delay
in eg a o wi h only one opamp ha has wo
in eg a ing capaci o s connec ed. Du ing odd
cycles, he i s capaci o is in eg a ing while he
o he is idling (disconnec ed). Do ing e en cycles,
he second capaci o
is
in eg a ing while he i s
one is idle. This solu ion has he disad an age
o
Ibe
deg ada ion
o
he signal because
o
pa h
misma ch be ween he I and Q b anches. A solu ion
o ob ain a good ma ching is also p oposed in [3].
The solu ion p esen ed he e depa s om igu e 6
and implemen s he wo-delay in eg a o blocks
using a single opamp, leading o he s uc u e
p oposed in igu e 7. This s uc u e does no down-
con e
o
p ocess I and Q b anehes ( liS p oposed
in [3]) a oiding he p oblems ha a e de i ed om
I and Q b anches misma ch. This opology is
implemen ed wi h he single opsmp SC ei eui!
d awn in igu e
8.
To accomplish he wo-<lelay
in eg a ion, he opamp is p o ided wi h 2 capaci o s
ha hold bo h, I and Q. b anches. A e e y cycle
one
o
he b anches is in eg a ing while he o he is
idle. The p oblem
o
gain sensi i i y can be
neglec ed due o he low SNDR sensi i i y o
in eg a ion gain
o
his s uc u e ( ig. 9,10).
Powe consump ion will be iden ical han o he
Band-Wid h equi alen Base-Band Sigma-Del a
Modula o and opamp pe o mance emains simila
o hose needed o Base-Band modula o (Fig. 10).
The e only emains he disad an age
o
he
eme
o
ji e
in
band-pass s uc u es ha equi es a e y
good clock.
5. Band-Pass simula ion
The
band-pass s uc u e based upon he ci eui
o
igu e 7 bas been simula ed using
MA
TLAB,
aod
i s
SC
e sion using CADENCE (Fig.
8).
In igu es
9,10
is
shown he pe onnance expec ed h ough
simula ion.
In
igu e 10 is depic ed he SNDR loss o di e en
alues
o
he Slew-Ra e and he BandWid h
o
he
ope a ional ampli ie s used o implemen he wo-
delay in eg a o s.
The
x -axis is no malised o
Ts
and he SR is no malised o Del a/Ts. These esul s
a e simila o hose ob ained o
he
opamps used
wi h a low-pass sigma-del a modula o , hus ha ing
simila powe consump ion. Because
o
his and
ha
we
use same
numbe
o
opamps o band-
equi alen low-pass
and
band-pass modula o s,
band-pass modula o s can accomplish he same
powe consump ion
as
he la e .
6. Simula ions using CADENCE and
MATLAB
Once
is he band-pass modula o cha ac e ised, he
s uc u e
o
igu e 7 has been implemen ed in a SC
ci cui ( igu e 8) and simula ed wi h CADENCE
(Spec e).
In
igu e
II
is ep esen ed he equency
esponse o bo h (MA TLAB and Spec e)
simula ions. Di e en ial Opamps ha e been
emula ed wi h an Analog
HDL
as
well
as
he
compa a o and ol age double s.
In
he
mal
e sion
o
his pape ully ansis o -le el esul s
using Spec e will
be
included.
Simila pa ame e s we e used in bo h cases:
GI=O.25
G2=0.5
Inpu sigual ampli ude=o 0.35·Del a
Inpu sigual
equency:
0.6·Sigual-Band/2
OSR=256
Ideal condi ions we e supposed o ji e ,
compa a o and opamp pe o mance.
7. Ji e in iuence in Band-Pass
modula o s
In
band-pass modula o s, whe e siguals a e no
hea ily o e -sampled, ji e is a majo p oblem o
he equency esponse
o
ou sys em. Clock ji e
esul s in non-uni o m sampling
and
inc eases he
o al
eno
powe
in he quan ize ou pu .
An
es ima ion
o his
e o is calcula ed in [8]. Once he
inpu analog sigual is sampled, he ji e has no
in luencc on he sys em
as
i beha es as an analog
sampled-da a compu e [IJ.
I
he inpu da a
is
sampled wi hou ji e , he sys em will ha e a
158
co ec beha iou e en
i
i s in e nal clocking is
a ec ed
by
ji e . Then, ji e - ela ed p oblems will
appea a he inpu sample
and
hold s age.
I
is
p o en ha unde
an
unco ela ed gaussian andom
ji e
wi h s anda d de ia ion dT, he
powe
o
he
e o signal is:
Sj'."= A2·(2·pi-
xdT)'/2
Whe e A is he signal ampli ude and ,
is
i s
equency.
This e o will be
o
in e es inside he signal hand.
Since he
ji e
is conside ed whi e, he
powe
e o
is educed
by
he o e sampling a io (M), which
is
4 in he p oposed
band-~ass
s uc u e.
Sin.""",<Del a'·(2·pi·dT) /(8
'M)
To e alua e he ole a ed ji e , one mus calcula ed
he maximum
SNR
desi ed
a
he
sys em's
ou pu
and limi he
SNR
o
a sampled inpu sigual (wi h
ji e )
o
ha alue.
I
we
expec
o
ha e a
maximum ou pu SNDR
o
100dB, he jille mus
be
limi ed
as
o ob ain a sampled inpu sigual
SNR
o
mo e han
dB's
when ji e is p esen .
In
o de o compa e he e ec s
o
clock
ji e
in
ou sys em some
MA
TLAB simula ions ha e heen
pe o med.
The
ji e ha a ec s he clock has
di e en simula ed magui udes:
a)
NULL
ji e .
b)
100 ppm.
An inpu sinusoid signal is sampled using
an
OSR
(O e -sampling Ra io)
o
256 o a low-pass
modula o
and
OSR~
o a
/4
cen al pass
equency modula o . F equency esponses a e
sampling
o
each case a e shown in igu es
12, 13.
F equency is ela ed o
FI,
whe e , is he
sampling equency.
I
is clea ly seen ha he e ec
o
ji e
on
he
spec a is wo sened when dee easing he OSR. This
makes band-pass modula o s much mo e sensi i e
o clock ji e han low-pass modula o s. This is he
majo d awback ha p esen band-pass modula o s.
The
nex se
o
simula ions shows he dependency
o
OSR
in he e ec
o
ji e . A ji e
o
50ppm has
heen applied o di e en equency
pu e
sinusoidal
signals.
The
e ec
o
ji e makes he spec a o
loose a ound 30dB in
SNR
when mo ing he
wo king equency om base-hand o
/4.
These simula ions a e summa ised in igu e 16.
They show he e ec
o
ji e
in bo h low-pass and
band-pass modula o s. As expec ed, he e ec on
he band-pass modula o is much highe .
8. Conclusions
A wo-delay in eg a o using a single opamp is used
o build a band-pass sigma-del a modula o . Only
wo
opamps whe e needed o implemen a
4'"
o de
s uc u e wi h a simila powe consump ion as
equi alen low-pass modula o s.
[I)
[2)
[3)
[4]
[5J
[6]
Re e ences
"DELTA-SIGMA DATA CONVERTERS,
heo y, design and simula ion". S e en
R.
No swo hy, Richa d Sch eie and Gabo
C.
Te nes.
IEEE
P ess.
"ANALOG CIRCUIT DESIGN ... " Willy
Sansen, Rudy
J.
Van
de
Plasshe and Johan
H.
Huijsing.
Kluwe
Academic
Publishe s.
"A FOURTH-ORDER BANDPASS DELTA-
SIGMA MODULATOR WITH REDUCED
NUMBER OF OP-AMPS". Bang·Sup Song.
IEEE Jou nal
o
solid-s a e ci cui s. Vol 30,
No.
12,
Decembe 1995.
"DESIGN OF LOW·VOLTAGE LOW.
POWER CMOS DELTA-SIGMA
AID
CONVERTERS". Vicenzo Peluso, Michiel
S eyae .
Winy
Sansen. Kluwe Academic
Publishe s.
"THE DESIGN OF LOW-VOLTAGE, LOW-
POWER SIGMA-DELTA MODULATORS".
Shah ia Robii, B uce
A.
Wooley Kluwe
Academic PublisheIll.
"TOP-DOWN DESIGN OF HIGH·
PERFORMANCE SIGMA·DELTA
MODULATORS". Fe nando Medei o, Angel
Pe ez-Ve du, Angel Rod iguez-Vazquez.
KJuwe Academic Publishe s.
[7]
[8]
[9]
[IOJ
[Ill
[12]
Figu es
''MODELING AND HIGH-RESOWTION
SIGMA·DELTA MODULATORS". Louis
Albe Williams Ill, Augus 1993, S an o d
Uni e si y. ICL93-022
"THE DESIGN OF SIGMA-DELTA
MODULATION ANALOG-TO·DIGITAL
CONVERTERS". Be nha d E.
Bose ,
B uce
A.
Wooley. IEEE Jou nal
o
solid-s a e ci cui s.
Vol
SC·23, pp.l298-1308. Decembe 1995.
"SWITCHE!)'cAPACITOR BANDPASS
DELTA-SIGMA
AID
MODULATION AT
10.7
MHz". F ank
W.
Singo ,
W.
Ma in
Snelg o e. IEEE Jou nal
o
solid-s a e ci cui s.
Vol
30,
No.3,
Ma ch
1995.
"A
9()O..mV
LOW-POWER
DS
AID
CONVERTER WITH
77-dB
DYNAMIC
RANGE".
Vicenzo
Peluso,
Pe e
Vanco enland
Augus o
M.
Ma ques, Miehiel Sley.e , Will;
Sansen. IDEE Jou nal
o
solid-s ale ci cui s.
Vol 33,
No.
12, Decembe 1998.
"SIGNAL PROCESSING ALGORITHMS
IN
MATLAB". Samuel D. S eams, Ru h A. Da id
"MIDAS USER MANUAL". Shah ia Rabii,
Louis A. Williams Ill, Be nha d E. Bose ,
B uce
A.
Wooley
S an o d Uni e si y, Oc . 1997
Figu e 1.
2"
o de
Low-pass p o o ype.
Figu e
2.
4 h
o de
Band-Pass modula o using esona o s.
}o~jgu e
3.
SNDR
oc
a 2
nd
o de
LP
S uc u e
Figu e
4.
Opamp
Spui icaiions
o
a
lnd
o de
LP
s uc u e
159
FIgu e 5. Swi ched Capaci o implemen a ion
o
a esona o
Figu e
6.
4'" o de Band-Pass modula o
0:
.
,.
INP
.,.
INN
••
:.-y'
0>
.
,.
'0
C.,
C,
V
eul
~OUT
0
C,
Figu e 7. Swi ched capaci o implemen a ion o a Band-Pass Sigman-Del a modula o using a educed
numbe
o
opamps
LP s uc u e
160

Figu e 10, 11. Band-pass F equeucy esponse
a) NULL b) 100
ppm
Figu e 12. Ji e y signals o OSR=256
Figu e 14. E ec
o
ji e when
Sampling~a~p~u~ ~e~!!~
,
..
lM)sl.HIhlW
a) Low-po.s modula o
a) NULL ji e
b)
100 ppm
Figu e 13. Ji e y signals o
OSR=4
Figu e 15 E ec
o
ji e
on a) low-pass modula o and b) band-pass modula o .
161