26 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 1, FEBRUARY 1998
The Floa ing Capaci o as a
Di e en ial Building Block
Manel Gasulla-Fo ne , S uden Membe , IEEE, Josep Jo dana-Ba nils, S uden Membe , IEEE,
Ram´on Pall´as-A eny, Fellow, IEEE, and Josep Ma ia To en s, Membe , IEEE
Abs ac — This pape analyzes he ad an ages and limi a-
ions o using he loa ing- (o lying-) capaci o echnique as a
building block wi h di e en ial inpu and ei he di e en ial o
single-ended ou pu o implemen ol age ampli ie s, mul iplex-
e s, and cohe en ampli ude demodula o s. Theo e ical analysis,
suppo ed by expe imen al esul s, shows ha he ully di e -
en ial con igu a ion has a be e common-mode ejec ion a io
(CMRR). Howe e , i he ou pu signal, once ampli ied, mus be
single ended, hen i may be be e o ha e a loa ing capaci o
wi h single-ended ou pu in ampli ie s and some mul iplexe s
whe eas in demodula o s a loa ing capaci o wi h di e en ial
ou pu yields a be e CMRR.
Index Te ms—Capaci o swi ching, CMRR, da a acquisi ion,
di e en ial ampli ie s, mul iplexing, sampling me hods, syn-
ch onous de ec ion.
I. INTRODUCTION
THE loa ing- (o lying-) capaci o echnique is a com-
mon me hod o low-le el signal ampli ica ion [1] and
mul iplexing [2]–[4]. Fig. 1 shows he basic loa ing-capaci o
ci cui . Fi s , swi ches and close and cha ges o
he di e en ial inpu ol age (assumed cons an ). Nex ,
and open and and close, so ha , excep o
s ay capaci ances o , he cha ge s o ed by is
sha ed by , assuming i was p e iously ully discha ged,
in acco dance wi h
(1)
And he e o e
(2)
This means ha he di e en ial ou pu ol age ideally
depends only on he di e en ial inpu ol age , hus yielding
a e y high common mode- ejec ion a io (CMRR) wi hou he
necessi y o any componen ma ching.
When he loa ing-capaci o echnique is used o ampli i-
ca ion [1] o demodula ion [5] o mul iplexing [2], he ci cui
ou pu in Fig. 1 is usually g ounded and connec ed o he inpu
o a single-ended ampli ie ha p o ides gain and low ou pu
impedance [1], [5]. This is a conside able ad an age because
i allows us o use an op-amp-based ampli ie , which is less
Manusc ip ecei ed June 1, 1997; e ised Ma ch 27, 1998. This wo k was
suppo ed by he Spanish DGICYT, P ojec PB93-0961.
The au ho s a e wi h he Di isi´
o d’Ins umen aci´
o i Bioenginye ia, Depa -
amen d’Enginye ia Elec `
onica, Uni e si a Poli `
ecnica de Ca alunya, 08034
Ba celona, Spain.
Publishe I em Iden i ie S 0018-9456(98)05492-8.
Fig. 1. Floa ing capaci o ci cui .
C
s
1
o
C
s
4
a e s ay capaci ances.
expensi e han an ins umen a ion ampli ie . Fu he mo e, by
using swi ches able o wi hs and high ol ages i is possible o
pick ou small di e en ial ol ages supe imposed on e y high
common-mode ol ages. In mul iplexe s, howe e , some imes
none o hei ou pu e minals a e g ounded [3], [4] bu a e
connec ed o an ins umen a ion ampli ie .
The e o e, he ques ion a ises as o whe he i is be e o
use he loa ing capaci o as a building block wi h di e en ial
inpu bu single-ended ou pu , o as a ully di e en ial ci cui .
A sa is ac o y answe can only be gi en by conside ing he
ac ha an ampli ie mus ollow he loa ing capaci o .
II. THEORETICAL ANALYSIS
A. Fully Di e en ial Floa ing Capaci o
Analog swi ches ha e s ay capaci ances o g ound, which
acco ding o swi ch echnology can change om he ON o
he OFF s a e. These changes a e dis ega ded he e. In Fig. 1,
pa allel capaci ances a e g ouped oge he . Le he swi ches
ha e ze o ON esis ance.
is de ined as he cha ge on he op pla es o , ,
, ; and as he cha ge on he op pla es o ,
, plus he cha ge on he bo om pla es o , . A any
andom ime pe iod , i s , a e closed and ,
a e opened. The cha ge will esul om he ac ual inpu
ol ages on he op pla es o , plus he cha ge s o ed
on he op pla es o , , a he p e ious ime pe iod
(assuming ha has no been ese be ween samples). The
same will apply o , gi ing
(3)
0018–9456/98$10.00 1998 IEEE
GASULLA-FORNER e al.: FLOATING CAPACITOR AS A DIFFERENTIAL BUILDING BLOCK 27
When and close, he elec ic cha ge will quickly
edis ibu e among capaci ances. As he o al cha ge a each
side, and , canno change, we ha e
(4)
Equa ing exp essions (3) and (4) in he ans o m domain [6]
shows ha a e many clock cycles he ol age a each ou pu
e minal equals ha a he espec i e inpu e minal, which a e
assumed o be cons an . Tha is , .
Inpu and ou pu signals can be desc ibed in e ms o
di e en ial and common-mode ol ages, ,
, , .
Fully di e en ial ci cui s can be desc ibed by ou ans e
unc ions as ollows [7]:
(5)
He e, , , , and .
The CMRR (CMRR ) is he e o e in ini e
because he inpu common mode ol age canno p oduce any
di e en ial ou pu ol age.
In p ac ice, he inpu ol age will no be uly cons an
and when closing and he e will be some cha ge
edis ibu ion o “upda e” he ol age ac oss . Bu i he
swi ching a e is as enough as compa ed wi h he a e o
change o he inpu signal, a s eady s a e will be eached
a he quickly.
B. Floa ing Capaci o wi h Single-Ended Ou pu
In Fig. 1, i he bo om side o he ou pu ci cui is g ounded,
hen when and a e closed, (3) is s ill alid (wi h
). Howe e , when and close, he cha ge
will emain cons an , bu pa o will un o he g ound.
The ou pu ol age will hen ul ill he condi ion
(6)
As be o e, he ou pu ol age a e many clock cycles can
be calcula ed by assuming he inpu ol ages o be cons an ,
(7)
I he inpu signals a e again desc ibed by di e en ial and
common mode ol ages, can be w i en as
(8)
F om (7),
(9)
The e o e, he CMRR is now,
CMRR (10)
which is smalle han ha o a ully di e en ial loa ing
capaci o ci cui .
C. E ec o Ou pu Ampli ie on he CMRR
Bo h he ully di e en ial and he single-ended ci cui s need
an ou pu ampli ie o p o ide gain and low ou pu impedance.
I his ampli ie has a di e en ial inpu , he o e all CMRR
will be [7],
CMRR CMRR CMRR (11)
whe e CMRR and CMRR a e he espec i e CMRR’s o
he loa ing capaci o ci cui and he ampli ie . This means ha
CMRR will be smalle han ha o each s age, i hey ha e
he same sign, and will be he la ges o hem all, i hey ha e
opposi e signs. Hence, i he ully di e en ial loa ing capaci o
is used because o i s high CMRR, hen CMRR mus be e y
high oo, o he wise i could yield a low CMRR .
Fo low- equency signal ampli ica ion, ampli ie s p o ide
a high CMRR wi h di e en ial inpu and di e en ial ou pu
buil om ma ched op amps, wi hou equi ing any ma ched
esis o [8]. The e o e, i a ully di e en ial ampli ie wi h
high CMRR is al eady a ailable, he e is no need o an
inpu ampli ie s age based on he loa ing capaci o . Howe e ,
di e en ial ampli ie s wi h single-ended ou pu ha e a much
smalle CMRR han ha o ully di e en ial ampli ie s. In
addi ion, CMRR dec eases o low gain. The e o e, o low-
gain applica ions, a loa ing capaci o ci cui wi h single-ended
ou pu may ha e a la ge CMRR han a common di e en ial
ampli ie .
I he loa ing capaci o ci cui is used as a cohe en am-
pli ude demodula o [5], i s swi ches ypically ope a e a he
ca ie equency. Fo equencies abou 1 kHz o highe , an-
sien s, ON esis ance, and limi ed OFF isola ion in swi ches
can yield a CMRR ha is lowe han CMRR o a di -
e en ial ampli ie wo king a low- equency (demodula ed
signal). Consequen ly, in his case i should be ad an ageous o
place a ully di e en ial loa ing capaci o demodula o ahead
o a di e en ial ampli ie , a he han using a single-ended
demodula o ollowing a di e en ial ampli ie wo king a he
ca ie equency [5].
The loa ing capaci o is also used in ully di e en ial mul-
iplexe s [3], [4]. In Fig. 2, using a loa ing capaci o makes
i possible o simul aneously sample all inpu signals and hen
sequen ially ampli y each sampled signal by using a common
di e en ial (o ully di e en ial) ampli ie . Jus as in low-
equency ampli ica ion, a loa ing capaci o wi h single-ended
ou pu may ha e a la ge CMRR han a common di e en ial
ampli ie bu only o low-gain applica ions equi ing a single-
ou pu .
On he o he hand, i o he ully di e en ial ci cui
and , hen acco ding o (5), . The e o e,
he ampli ie (and inpu swi ches) mus wi hs and he inpu
common mode ol age p esen a any inpu channel. In case
28 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 1, FEBRUARY 1998
Fig. 2. Fully di e en ial mul iplexe .
o la ge common-mode ol ages, i may be be e o use an
ampli ie wi h single-ended inpu a e he loa ing capaci o
ci cui because his only applies he di e en ial inpu ol age
o he ampli ie . Al e na i ely, i he e is gal anic isola ion
be ween signal g ound and ampli ie g ound, i is easible
o use s anda d swi ches and a di e en ial ampli ie a e he
loa ing capaci o ci cui because mos o he signal common
mode ol age will be applied ac oss he insula ion ba ie .
In summa y, i is be e o use a ully di e en ial loa ing
capaci o ci cui a he han a loa ing capaci o wi h a single-
ended ou pu o cohe en ampli ude demodula o s, and i
may be e en be e o simul aneous mul iplexing. Fo la ge
common mode ol ages, ei he in mul iplexe s, ampli ie s o
demodula o s, i is be e o use a loa ing capaci o wi h
single-ended ou pu .
III. EXPERIMENTAL RESULTS AND DISCUSSION
The ci cui shown in Fig. 1 was buil using CMOS swi ches
(CD4053B and MAX303). As he esul s we e simila o bo h
models, only hose o he CD4053B a e p esen ed. The ci cui
ou pu was connec ed o an ins umen a ion ampli ie . The
same ci cui was used ei he as an ampli ie o as a cohe en
demodula o . When wo king as an ampli ie , he swi ching
equency mus be much highe han he equency o he
(di e en ial) inpu signal. When wo king as a cohe en de-
modula o , he swi ching equency was he ca ie equency.
The e e ence ci cui had F, du y cycle
10% o he clock signal (10% sample, 90% hold) and he
unknown pa asi ic capaci ances inhe en o componen s and
ci cui layou . Bo h ou pu con igu a ions, ully di e en ial and
single ended, we e es ed o each ci cui .
Table I shows he CMRR o he demodula o when he
ollowing ampli ie was he INA 110 wi h a gain o 500 ( o
he ully di e en ial demodula o ) o 100 ( o he demodula o
wi h single-ended ou pu ). He e he ampli ie wo ks a DC and,
om he da a shee , i s ypical CMRR a dc is 110 dB o gains
o 100 and highe . We i s measu ed he e e ence ci cui . The
i s ow in Table I shows ha i he ca ie equency is low,
he ampli ie acco ding o (11) limi s he CMRR o he ully
di e en ial ci cui . Bu om 10 kHz up, he e is a educ ion
TABLE I
FREQUENCY DEPENDENCE OF THE CMRR (dB) OF A COHERENT DEMODULATOR
BASED ON A FLOATING CAPACITOR CIRCUIT. FD: FULLY DIFFERENTIAL
FLOATING CAPACITOR; SE: FLOATING CAPACITOR WITH SINGLE-ENDED OUTPUT
in CMRR a ibu able o he demodula o . Ne e heless, he
CMRR is e y high. When he ou pu o he loa ing capaci o
ci cui is g ounded he demodula o de e mines he o e all
CMRR. I dec eases by 8 dB a 10 Hz, as p edic ed by (10),
and 30 dB a 100 kHz.
Nex , i was e i ied ha , as p edic ed by he heo e ical
models, had no in luence on he CMRR. A educed
du y cycle , howe e , esul ed in a educed CMRR a high
equencies. Table I shows he esul s o %. An analysis
was hen made o he in luence o . When was educed
om 1 F o 100 nF, he low- equency CMRR o he ully
di e en ial demodula o i s inc eased by abou 20 dB, om
107 o 126 dB. This can be explained by (11) i each s age has
a CMRR wi h opposi e sign. By he same oken, i he inpu
e minals o he ampli ie a e in e ed, he CMRR should
dec ease. E ec i ely, i educed o 107 dB, he same as o
he e e ence ci cui . Fo he single-ended demodula o , when
nF he CMRR educed by abou 20 dB, as p edic ed
by (10).
The pa asi ic impedance was hen inc eased by connec ing a
100 pF capaci o , i s om he op side o g ound, in pa allel
wi h , and nex om he bo om side o g ound, in pa allel
wi h . Again, he CMRR inc eased (o dec eased) o he
ully di e en ial demodula o and was smalle o he single-
ended demodula o , as p edic ed by (10). No e ha in e ing
inpu connec ions o he ins umen a ion ampli ie wo ks in
opposi e ways o and . In addi ion, should no
a ec he esul s o he single-ended ci cui , bu om 1 kHz
up, a la ge educes he CMRR.
When he loa ing capaci o was used o ampli y low e-
quency signals (0.1 Hz), he esul s o he equency depen-
dence o he CMRR (Table II) we e simila o hose o he
demodula o , as expec ed. Fo 1 Hz and 10 Hz inpu signals i
is necessa y o inc ease he minimal sampling equency, bu
o he wise he esul s a e he same.
The INA114 was also used as a di e en ial ampli ie . Fo
he ully di e en ial ci cui he CMRR inc eased o abou 120
dB a low equencies because he INA114 has a be e CMRR
a dc han he INA110. The CMRR o he ully di e en ial
ci cui a highe equencies and o he single-ended ci cui
was simila .
GASULLA-FORNER e al.: FLOATING CAPACITOR AS A DIFFERENTIAL BUILDING BLOCK 29
TABLE II
FREQUENCY DEPENDENCE OF THE CMRR (dB) OF AN AMPLIFIER BASED
ON A FLOATING CAPACITOR CIRCUIT WHEN THE INPUT SIGNAL
IS 0.1 HZ. FD: FULLY DIFFERENTIAL FLOATING CAPACITOR;
SE: FLOATING CAPACITOR WITH SINGLE-ENDED OUTPUT
IV. CONCLUSIONS
The loa ing-capaci o ci cui p o ides an excellen CMRR
when used as ully di e en ial ampli ie o demodula o . The
CMRR o he loa ing-capaci o ci cui wi h single-ended
ou pu , depends on he a io be ween he capaci ance o he
sampling capaci o and s ay capaci ance om he ci cui
high side o g ound (10). Second-o de e ec s educe he
CMRR a equencies abo e 1 kHz. This educ ion is g ea e
o he single-ended ci cui .
Wha e e he applica ion, he loa ing-capaci o ci cui e-
qui es a ollowing ampli ie p o iding ol age gain and low
ou pu impedance. I he signal, once ampli ied, mus be single
ended, hen i may be be e o ha e a loa ing capaci o wi h
single-ended ou pu in ampli ie s and some mul iplexe s while
in demodula o s a loa ing capaci o wi h di e en ial ou pu
yields a be e CMRR. Fo la ge common mode inpu ol ages,
i is also be e o use a loa ing capaci o wi h single-ended
ou pu .
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[1] J. Williams, “Applica ions o a swi ched-capaci o building block,”
Applica ion No e 3, Linea Technology Inc., Milpi as, CA, July 1985.
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III—Sample-and-holds, ins umen a ion ampli ie s, and analog mul-
iplexe s,” IEEE Mic o, ol. 2, pp. 20–35, No . 1982.
[3] D. H. Sheingold, Ed., Analog-Digi al Con e sion Handbook, 3 d ed.
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[4] P. H. Ga e , Ad anced Ins umen a ion and Compu e I/O Design.
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[5] R. Pall´as-A eny and O. Casas, “A no el di e en ial synch onous de-
modula o o ac signals,” IEEE T ans. Ins um. Meas., ol. 45, pp.
413–416, Ap . 1996.
[6] K. R. Lake and W. M. C. Sansen, Design o Analog In eg a ed Ci cui s
and Sys ems. New Yo k: McG aw-Hill, 1994.
[7] R. Pall´
as-A eny and J. G. Webs e , “Common mode ejec ion a io o
cascaded di e en ial ampli ie s ages,” IEEE T ans. Ins um. Meas., ol.
40, pp. 677–681, Aug. 1991.
[8] , “Common mode ejec ion a io in di e en ial ampli ie s,” IEEE
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Manel Gasulla-Fo ne (S’97) ecei ed he En-
ginye de Telecomunicaci´o deg ee in 1992 om
he Uni e si a Poli `
ecnica de Ca alunya, Ba celona,
Spain, whe e he is cu en ly pu suing he Ph.D.
deg ee in elec onics.
In 1993, he joined he Depa men o Elec onic
Enginee ing, Uni e si a Poli `
ecnica de Ca alunya,
as a Lec u e . His cu en esea ch in e es is in
he ield o elec ical impedance measu emen and
subsu ace imaging.
Josep Jo dana-Ba nils (S’93) ecei ed he En-
ginye de Telecomunicaci´
o deg ee in 1990 om
he Uni e si a Poli `
ecnica de Ca alunya, Ba celona,
Spain, whe e he is cu en ly pu suing he Ph.D.
deg ee in elec onics.
In 1993, he joined he Depa men o Elec onic
Enginee ing, Uni e si a Poli `ecnica de Ca alunya,
as a Lec u e . His cu en esea ch in e es is in
he ield o elec ical impedance measu emen and
subsu ace imaging.
Ram´
on Pall´
as-A eny (F’98) ecei ed he Inge-
nie o Indus ial and Doc o Ingenie o Indus ial de-
g ees om he Uni e si a Poli ´
ecnica de Ca alunya,
Ba celona, Spain, in 1975 and 1982, espec i ely.
He is a P o esso o Elec onic Enginee ing a he
Uni e si a Poli ´
ecnica de Ca alunya, and eaches
cou ses in se e al a eas o medical and elec onic
ins umen a ion. In 1989–1990, he was a Visi -
ing Fulb igh Schola a he Uni e si y o Wiscon-
sin, Madison. He does esea ch on ins umen a ion
me hods based on elec ical impedance measu e-
men s, high esolu ion ECG and elec omagne ic compa ibili y in elec onic
sys ems. He is he au ho o Basic Elec onic Ins umen s (1987), Senso s and
Signal Condi ioning, 2nd ed. (1994), and Signal Acquisi ion and Dis ibu ion
(1993), coau ho o An In oduc ion o Bioenginee ing (1988) and o Elec o-
magne ic In e e ence in Elec onic Sys ems (1991), all published in Spanish
by Ma combo, Ba celona, Spain. He is also coau ho (wi h John G. Webs e )
o Senso s and Signal Condi ioning (New Yo k: Wiley, 1991).
D . Pall´
as-A eny was a ecipien , wi h John G. Webs e , o he 1991 And ew
R. Chi P ize Pape Awa d om he IEEE Ins umen a ion and Measu emen
Socie y. He is a membe o he Biomedical Enginee ing Socie y, and he
In e na ional Socie y o Measu emen and Con ol.
Josep Ma ia To en s (M’90) ecei ed he
Enginye de Telecomunicaci´
o and Doc o Enginye
de Telecomunicaci´o deg ees in 1989 and 1996
espec i ely, om he Uni e si a Poli `
ecnica de
Ca alunya, Ba celona, Spain.
In 1989, he joined he Depa men o Elec onic
Enginee ing as a Lec u e , and cu en ly he
is an Associa e P o esso a he Uni e si a
Poli `
ecnica de Ca alunya. His esea ch in e es s
a e in elec onic ins umen a ion, nondes uc i e
es ing, and elec ical impedance spec oscopy,
mainly applied in soil and ce amic s uc u es.