ANALYSIS
AND
EXPERIMENTAL
CHARACTERIZATION
OF
IDLE
TONES
IN
2nd-ORDER
BANDPASS
ZA
MODULATORS
-
A
0.8Fm
CMOS
SWITCHED-CURRENT
CASE
STUDY
Jose'
M.
de la
Rosa,
Bel&
Pe' ez- Ve du, Fe nando Medei o, Rocio del Rio and
Angel
Rod iguez- Vazquez
Ins i u o
de
Mic oelec hica
de
Se illa,
IMSE
(CNM-CSIC)
Edi .
CNM-CICA,
A da.
Reina
Me cedes
s/n,
41012
Se illa,
SPAIN
Phone:
+34
95056666,
FAX:
+34
95056686,
E-mail: [email p o ec ed]
ABSTRACT
Ths pape analyses he onal beha iou o he quan iza ion
noise in 2nd-o de bandpass
.U
modula o s. The analysis p e i-
ously pe o med o lowpass modula o s is ex ended o he band-
pass case.
As
a
esul . closed- o m exp essions o he equency
o he idle ones a e de i ed o di e en loca ions o he signal
cen e equency. The analy ical esul s a e alida ed h ough
measu emen s om
a
silicon p o o ype ealized using ully di e -
en ial swi ched-cu en ci cui s in a s anda d 0.8pm CMOS ech-
nology'
*'.
1.
INTRODUCTION
Among o he easons,
&z zdpnss
ZA
Modula o s (BP-ZAMs)
[l] a e o in e es due o hei sui abili y
o
ealize he Ana-
log- o-Digi al
(AD)
con e sion o ei he In e media e F equency
(IF)
o Radio F equency
(RF)
signals in modem digi al adio e-
cei e s. Such
A/D
con e sion pe mi s he implemen a ion o he
IF
s age in he digi al domain, hus allowing digi al con ol o he
gain and he coe icien s o he
IF
il e .
This
has nume ous ad an-
ages as compa ed o he adi ional (analog) adio ecei e s: e-
duc ion o in e e ences, p og ammabili y, e c
...
Mos epo ed
BP-ZAMs
ob ain hei a chi ec u e by applying
a
(LP-ZAM)[2][3]. Because o his ans o ma ion, a L h-o de
LP-ZAM becomes
a
2L h-o de BP-ZAM, keeping mos o he
p ope ies o he o me . One o hese p ope ies is he p esence o
idle
ones in he ou pu spec um
o
he
modula o .
This
phenome-
non is caused by he co ela ion be ween he inpu signal and he
quan iza ion e o
[4].
The non-linea beha iou o he quan iza-
ion e o is mo e signi ican
as
he numbe o in e nal le els o
he quan ize and/o he o de o he modula o dec ease, he wo s
case co esponding o
a
1s -o de LP-ZAM wi h
a
I
-bi quan ize .
The onal beha iou
o
he quan iza ion e o in LPSAMs has
been analysed elsewhe e [5][6][7]. Howe e , e y li le has been
done cu en ly o BP-ZAMs. In
[8]
a
non-linea analysis
o
a
2nd-o de BP-LAM is epo ed assuming ha he inpu is
a
sinus-
oidal signal wi h equency equal o
a
qua e
o
he sampling e-
quency
-
he ideal signal-band cen e equency. Howe e , as we
demons a ed in
[9],
in
p ac ical ci cui s his cen e equency be-
comes shi ed due o he in luence o ci cui e o s, and such shi -
ing needs
o
be conside ed o ealis ic onal beha io analysis.
Asides wi h he analy ical conside a ions, his pape shows ex-
pe imen al e idence o he onal beha io o
a
2nd-o de BP-LAM
silicon p o o ype. The demons a ion ehicle is
a
ully di e en ial
swi ched-cu en
(SI)
ci cui , ealized in
a
0.8pm, s anda d CMOS
echnology. Measu emen s show ha he esul s ob ained o
LP-ZaMs
[5] can be ex ended o he bandpass case in o de o ex-
plain he onal beha iou o he quan iza ion e o
in BP-ZAMs.
'"ais wo k
has
been suppo ed by he Spanish CICYT P ojec
--I
+
---1
~
ans o ma ion o a
Loowpnss
EA
Modula o
TIC
97-0580
2.
IDEAL ANALYSIS
OF
2nd-ORDER
BP-XAMs
Fig.l(a) shows he block diag am
o
a
2nd-o de BP-UM. I
has been ob ained by applying
a
:-I
--
-:-?
ans o ma ion
o
a
1s -o de LP-XAM.
As
a
consequence o his ans o ma ion, he
o iginal in eg a o becomes
a
esona o . Thus, he i s s ep o-
wa ds he design
o
a
BP-ZAM is choosing
a
sui able a chi ec u e
o ealize he esona o ans e unc ion.
This
can be ealized U:;-
ing di e en opologies [2]. In his pape we will adop
a
s uc u e
consis ing o
a
eedback cascade o
wo Lossless
Disc e e ln eg c -
o s
(LDI),
shown in Fig.l(b), whe e
AF
=
1
and
AFB
=
2.
This s uc u e has been chosen because i keeps he poles inside
he uni ci cle upon changes due o e o s
o
he eedback
loop
gain. Howe e , he use o
his
esona o equi es an addi ional de-
lay block o be included in he digi al loop. see Fig.l(a),
in
o de
o achie e he equi ed delay
in
he modula o eedback loop.
2.1
Linea analysis
Assuming ha he quan iza ion e o is modelled as an addi i e
whi e
noise sou ce, he quan ize can be eplaced
by
he linea
model shown in Fig.l(c)
[6][7].
In such
;I
case, he modula o in
Fig.
1
(a)
can be iewed
as
a
wo-inpu ,
s
and
e
,
one ou pu ,
y
.
sys em. which in he 2-domain can be ep esen ed by:
(11)
whe e
STF(:)
and
NTF(:)
a e he signal ans e unc ion and he:
noise ans e unc ion, espec i ely,
Y(z)
=
STF(Z)X(Z)
+
NTF(~)E(C)
-1
-7
STF(L)
=
:
NTF(;)
=
I
+c
-
(9)
By making
z
=
exp(j2n / S). whe e
,
is he sampling e-
quency. i can be shown ha
N,( )
has one ansmission ze o a
J4,
and ha he il e ing a ound his equency is ac ually o he
band-s op ype. The inpu signal
is
allowed o pass while, a he
same ime. mos
o
he quan iza ion noise powe
is
"shaped"
so
ha
is pushed ou o he signal band. The
in-band
quan iza ion noise
powe can be calcula ed by in eg a ing he ou pu powe Spec al
.----_-.
._-_-_.
(a)
.----------~-------.-.
I'
.____.
ll
@
(C)
._-___-_-____ _-_____.
Figu e
1.
(a)
Block diag am o he modula o in his pape .
(b) LDI-loop esona o . (c) Linea model o he quan ize .
0-7803-6685-9/01/$10.0002001
IEEE
IV-774
Densi y
(PSD)
wi hin he signal bandwid h,
whe e
Sp
=
A’/(
12 ,)
is he
PSD
o he quan iza ion noise,
A
is he quan iza ion s ep,
B,!,
is he signal bandwid h and
M
=
/(2B,,,)
is he
o e sampling
a io.
F om
(3),
and assuming
ha he modula o inpu is
a
sinewa e o ampli ude A,
5
A/2
,
he
Signal- o-Noise
& i0
(
SNR
)
and he mnamic Range
(DR
)
a e
gi en by:
This ideal analysis shows ha he modula o esolu ion inc eases
wi h
M
a
a
a e o abou l.S-bi /oc a e
.
This
ideal ea u e is
achie ed only i he esona o in Fig.l(b) is ealized wi hou e o s
and he quan iza ion e o is modeled by
a
whi e noise sou ce.
2.2
Non-linea
analysis
In he linea model shown in Fig.l(c), he quan iza ion e o ,
e
=
y
-
. ,
,
is
assumed o be no co ela ed wi h he quan ize in-
pu .
.xl
.
Ac ually, his e o is
a
non-linea unc ion o
sI
,
as
il-
lus a ed in Fig.2 o an N-bi quan ize i1.
I
x,
a ies andomly
om
sample o sample in he in e al
[.Y~,~~~~,
. mas]
(see Fig.2).
e
is la gely unco ela ed wi h
sI
[4]
and he linea model p o ides good esul s. This is achie ed in
LP-ZAMs
o la ge modula o o de s and
N
>
1
[7].
The e o e,
he wo s case o applying he linea model co esponds o a
1s -o de modula o wi h
a
1-bi quan ize . Candy
[6]
demon-
s a ed ha , o
a
dc inpu signal, he in-band quan iza ion e o
powe a he modula o ou pu sha ply changes wi h
he
inpu
am-
pli ude.
This
is
illus a ed in
Fig.3(a)
o
M
=
64
and
A
=
2.
This
p ope y o he quan iza ion e o , o en known
as
noise
pa -
em,
is ansla ed o
a
2nd-o de
BP-XAM
when he inpu signal is
a single one placed a
,/4.
This is illus a ed in Fig.3(b) by
showing he simula ed in-band quan iza ion e o powe a he
ou pu
o
Fig.l(a) as a unc ion o he inpu ampli ude. This be-
ha iou can no be explained by he linea model (dashed line in
Fig.3(b)) and hence,
a
non-linea analysis is equi ed.
G ay
[5]
sol ed he non-linea di e ence equa ions o a
1 s -o de
LP-ZAM,
showing ha o dc inpu s, he quan iza ion
e o spec um is disc e e, wi h ones (o en named
idle
ones) a
---
(a)
Figu e
2.
Ideal quan ize . (a) Inpu -ou pu cha ac e is ics.
(b) Quan iza ion e o .
I.
In he igu e,
X,,
s ands o he ull-scale ange o he
quan ize . No e ha o N
=
1
,
X,,
=
A.
Inpu
le el e e ed
o
32
Figu e
3.
Noise pa e n o a
(a)
1s -o de
LP-EAM
and
(b) 2nd-o de
BP-U.
whe e
A.,
is he ampli ude o
.
and
(a)
ep esen s he ac ional
pa
o
a.
The ampli ude o hese ones is
1
A lp,,
=
-
(?XI?)-
The abo e esul s can be ex ended o he bandpass case by ap-
plying he equency ansla ion dc
--
,/4
o
(5).
This implies
ha he quan iza ion e o spec um o a 2nd-o de
BP-ZAM
wi h
a
sinusoidal signal placed a
,/4
will ha e pai s o idle ones a
No e ha he e a e ones placed a ound dc and
,/2
-
simila o
he case o 1s -o de
LP-ZAMs.
Howe e . in 2nd-o de
BP-UMs
he e a e also pai s o ones a bo h sides o
,/4
,
he mos signi -
ican being loca ed a
,/4
k
A
,/(24)
as will be demons a ed
expe imen ally in Sec ion
4.
3.
NON-IDEAL ANALYSIS
-
EFFECT OF SI
ERRORS
ON
THE SIGNAL-BAND LOCATION
In he p e ious sec ion he modula o was assumed o be ideal
excep o he inhe en quan iza ion e o . In p ac ice, ci cui pa a-
si ics modi y he ze oes o
NT,(:),
deg ading he noise-shaping
and making he in-band quan iza ion noise o inc ease.
As we demons a ed in
[9],
e o s in
SI
ci cui s cause he sig-
nal-band cen e equency (o en named
no ch
equency,
J1o
)
o
shi om i s nominal posi ion a
,/4
,
causing an e o deno ed
as
8 Io
.
which is app oxima ely gi en by:
IV-775
whe e
E,
s ands o he se ling e o [lo],
i l
is he inpu esis -
ance o he memo y cell,
O 7
is he s ee ing swi ch-on esis ance,
and
goF,
FB
a e he ou pu conduc ances o he cu en mi o s
used o ealize he
gains,
AF,
FB
,
o
he esona o
in
Fig.l(b).
Conside ing ha he quan iza ion noise powe is minimum a
,,,
,
he signal should be cen e ed a
,,,
in o de o ob ain
a
maximum
DR.
On he o he hand, placing
a
single one a a e-
quency di e en om
,/4
in
a
BP-ZAM is equi alen o apply-
ing
a
sinusoidal signal o low equency in a LP-CaM. As demon-
s a ed in
[5],
he ou pu spec um o
a
1s -o de LP-ZAM wi h
a
sinusoidal inpu signal o equency,
i
,
is disc e e, wi h ones a :
lp,,
=
s
ii'
o
17
=
1,
2,
3,
...
(9)
(14
-
?)
,
-
This esul can be ex ended o he bandpass case by applying
he equency ansla ion dc
+
,/4
o
(9).
This implies ha he
ou pu spec um o
a
2nd-o de BP-EAM will ha e idle ones a :
No e ha wo amilies o ones appea a bo h sides
o
J4,
which can co up he signal in o ma ion
as
will be demons a ed
by expe imen al measu emen s in he nex sec ion.
4.
EXPERIMENTAL RESULTS
The 2nd-o de
BP-EAM
o Fig.l(a) was ealized using ully
di e en ial egula ed- olded cascode memo y cells. The
I
-bi
quan ize was made up
o
a egene a i e la ch and an
RS
lip- lop
and he
I
-bi DAC consis ed o
a
cu en sou ce con olled by he
compa a o ou pu . These building blocks we e designed o a ain-
ing he equi emen s o di ec
A/D
con e sion in AM digi al adio
ecei e s, whose comme cial b oadcas band is om 5401cHz o
1.6MHz wi h s a ions occupying a
lokHz
wide band. This im-
poses ha he sampling equency mus be unable o e he ange
,
=
2MHz o
,
=
6.4MHz.
The ci cui was ab ica ed in
a
CMOS 0.8pm double-me al
single-poly echnology. Fig.
4
shows he mic opho og aph o he
chip. I also includes some isola e building blocks o es ing sepa-
a ely. The ac i e a ea o he modula o is 0.35"' and he powe
Figu e
4.
Mic opho og aph o he modula o .
consump ion is 42mW om
a
5V powe supply. To e alua e ihe
pe o mance o he modula o , i was a ached o
a
wo-laye
8:s.
boa d, designed ollowing
he
indica ions in
[
1
11 o educe he
swi ching noise. The
ou pu
bi s eams we e cap u ed wi h he
HP82000 da a acqusi ion sys em and Kaise (
p
=
20
)-windowed
32768-poin
FFTs
we e pe o med
on
each
o
hose bi s eams
using
MATLAB
[
121.
4.1
Measu emen s
o
an
inpu one a
,/4
Fig.5 shows wo modula o ou pu spec a when clocked a
,
=
2MHz. No e ha , because o
SI
e o s,
,,,
de ia es om
he ideal posi ion a ,/4
.
In
his case,
in
=
2Q,
oll
=
472!3,
acco ding o
(8),
yields
,,,
z
0.246 s. As Fig.5 illus a es, he e
a e ou g oups o idle ones whose equencies a e
a
unc ion o
he inpu signal ampli ude. No e ha ,
as
A,
app oaches o
A/2,
wo o hese g oups (labelled
as
L,
and
RI
in Fig.5) mo e away
om ,/4 while he o he wo g oups
(L2
and
R2
)
app oach o
J4.
The ones wi h he la ges ampli ude
(
E
-30dB
)
;a e
hose placed a :
=
11jLA/V,
goFB
=
21pA/V and
E,
=
250ppm. which
which ma ches wi h ha p edic ed by (7) o
11
=
I,
as
demon-
s a ed in Fig.6 by displaying
L,.
?
and
RI,
s.
A,/A
,
show-
ing
a
good ag eemen be ween heo y and measu emen s.
In
AM adio applica ions, ou -o -band idle ones a e c i ical be-
cause, in he p esence o non-linea e o s, can mix wi h he
inpu
signal and all in o he signal band. Fo he special case o
a
single
one a
s/4,
he mos signi ican in e modula ion componen s
( hose co esponding o
A ~
app oaching o
A
)
will all app oxi-
I
I.
I
0.1
0.2
0.3
0.4
OS
Rela i e equency
o
,
01
.
1
-so0
.
0:1
.
d.2
0.3
0.4
25
1.
Relai e equency
o
,
Figu e
5.
Measu ed modula o ou pu spec a when clocked a
,
=,
2MHz o an inpu one o
/4 and di e en ela i e
ampli udes:
(a)
A,/A
=
0.1
,
(b)
A, A
=
0.14.
IV-776
I
0.10
0.15
0.20
Figu e
6.
Idle- one loca ion s.A,/A o
an
inpu one a
J4
ma ely a
,/4,
hus no deg ading he linea i y o he modula o .
Howe e , in p ac ical applica ions he inpu signal will con ain
spec al componen s a di e en equencies, and acco ding o
(
IO).
mul iple ones will appea inside he signal band.
This
is e -
i ied by he ollowing measu emen s.
4.2 Measu emen s o an inpu one a
,,,
Placing he inpu signal a
,,,
o a BP-ZAM maximizes he
esolu ion o such a modula o . Howe e , o he case o
a
2nd-o -
de BP-LAM, a la ge numbe o idle ones will appea , hus de-
s oying he ope a ion o he modula o . Fig.7 illus a es
his
by
plo ing
a
measu ed modula o ou pu spec um when clocked a
,
=
2MHz
co esponding o
a
single one o -6dB inpu
le el’ and app oxima ely loca ed a he no ch equency.
Acco ding o (10). he equency o idle ones only depends on
he ela i e loca ion o he inpu equency wi h espec o
S/4.
Howe e .
as
also shown in
[5]
o LP-CaMs. he ampli ude
o
such ones is s ongly dependen on he inpu signal ampli ude.
Fig.8 illus a es his by plo ing he cen al pa
o
se e al meas-
u ed ou pu spec a co esponding o di e en inpu ampli udes.
The posi ion o he mos signi ican ones (see
(10))
a e labelled.
Obse e
ha
he ampli ude
o
said ones
is
no
a
mono onic unc-
ion o he inpu le el. simila ly
o
wha happens o LP-LAMS. in
which he ampli ude o idle ones is ela ed o he inpu le el
h ough a linea combina ion o o dina y Bessel unc ions
[5].
5.
CONCLUSIONS
This pape demons a ed expe imen ally he s ong co ela ion
be ween he quan iza ion noise and he inpu signal in 2nd-o de
-1000
L
0.1
0.2
0.3
0.4
0.5
Rela i e
equency
<o
Figu e
7.
Measu ed modula o ou pu spec um o
,
=
2MHz
and
a
-6dB inpu one a
491kHz
( ,,,
=
0.246
,
).
1’2.
Inpu le el
is
de ined
as
he inpu signal ampli ude e-
e ed o he DAC ou pu le el
(
=
OdB in he igu e).
%!;
0.33
0.15
0.28
b3
Relau e
equency
ojl
.
(a)
0
.
-10
J
-20
3
-30
2“
1-50
2
-60
-70
%3
0.33
0.25 0.28
0.3C
Rcl n c
equency
mjl
(C)
%:
0.23
0.25
0.18
0.3
Figu e
8.
Measu ed modula o ou pu spec a (cen al pa ) o
an
inpu one a
,,,
=
0.246 S
(6 ,,,
=
0.0045 ,
)
and di e en
ela i e ampli udes: (a) A,/A
=
0.03.
(b)A, /A
=
0.05.
(c)
A,/A
=
0.1, (d) A,/A
=
0.16.
bandpass
XA
modula o s. This phenomenon has been s udied con-
side ing ei he ha
he
noise shaping is ideal o i is deg aded by
ci cui pa asi ics.
As
a esul
o
his s udy, closed- o m
exp es-
sions o he equency
o
idle ones ha e been de i ed ega ding
di e en cases o he signal cen e equency. All esul s ha e
been alida ed by measu emen s om a 0.8pm CMOS.p o o ype.
REFERENCES
R.
Sch eie and M. Snelg o e. “Bandpass Sigma-Del a Modula ion”.
Elec o iics
Le e s.
pp. 1560-1561. No embe 1989.
F.W. Singo and
W.
M.
Snelg o e. “Swi ched-Capaci o Bandpass
Del a-Sigma
A/D
Modula ion
a
10.7
MW.
IEEE
J.
Solid-S o e
Ci -
A.K. Ong and B.A. Wooley.
“A
Two-Pa h Bandpass
ZA
Modula o o
Digi al
IF
Ex ac ion
a
20MHz”.
I€€€
JOUIII~~
o
Solid-S a e Ci cui s,
pp. 1920-1933, Decembe 1997.
W.
Benne . “Spec a
o
Quan ized Signals”. Bell Sys . Tech.
J..
R.M. G ay. “Quan iza ion noise spec a”.
IEEE
Tin scic ions
on bi o -
nm ioii
Theoiy,
pp. 1220- 1244. No embe 1990.
J.C. Candy and G.C. Temes:
“O e sanipling
Del a-Sigma
Da a
Con-
e e s
,
EEE
P ess, 1992.
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