senso s
A icle
CMOS Cu en Feedback Ope a ional Ampli ie -Based
Relaxa ion Gene a o o Capaci y o Vol age
Senso In e ace
Ladisla Polak 1, Roman So ne 1,* , Ji i Pe zela 1and Jan Je abek 2
1Depa men o Radio Elec onics, SIX Resea ch Cen e , B no Uni e si y o Technology (BUT),
Technicka 3082/12, 616 00 B no, Czech Republic; [email p o ec ed].cz (L.P.); [email p o ec ed].cz (J.P.)
2Depa men o Telecommunica ions, SIX Resea ch Cen e , B no Uni e si y o Technology (BUT),
Technicka 3082/12, 616 00 B no, Czech Republic; [email p o ec ed].cz
*Co espondence: [email p o ec ed].cz; Tel.: +420-541-146-560
Recei ed: 2 No embe 2018; Accep ed: 16 Decembe 2018; Published: 18 Decembe 2018


Abs ac :
This pape p esen s a simple elaxa ion gene a o , sui able o a senso in e ace, ope a ing
as a ansduce o capaci ance o equency/pe iod. The p oposed ci cui employs a cu en eedback
ope a ional ampli ie , ab ica ed in I3T25 0.35
µ
m ON Semiconduc o CMOS p ocess, and ou passi e
elemen s including a g ounded capaci o ( he sensed pa ame e ). I o e s a low-impedance ol age
ou pu o he gene a ed squa e wa e. Addi ional equency o DC ol age con e e o e s ou pu
in o ma ion in he o m o ol age. The expe imen al capaci ance a ia ion om 6.8 nF o 100 nF yields
ol age change in he ange om 21 mV o 106 mV wi h e o below 5% and sensi i i y 0.912 mV/nF
e alua ed o e he ull ange o change. These alues a e in good ag eemen wi h simula ion esul s
ob ained om he Ma hcad model o equency o DC ol age ansduce passi e ci cui .
Keywo ds:
capaci y senso in e ace; capaci y measu emen ; cu en eedback ope a ional ampli ie ;
elaxa ion gene a o ; squa e wa e gene a o
1. In oduc ion
Elec ical senso s o m an impo an pa o complex elec onic sys ems, which a e used in many
ields (e.g., indus y, heal hca e, consume elec onics and wi eless communica ions) [
1
]. They a e
equi ed o ans o ma ion o a ious physical quan i ies o measu able in o ma ion in he o m o
an elec ical signal ( ol age, cu en ). Such physical quan i ies, o ins ance, can be empe a u e [
2
],
mechanical p essu e [
3
], acous ic p essu e [
4
,
5
], elec omagne ic ield [
6
,
7
], humidi y [
8
],
gas [9,10]
and
biosignals [
11
,
12
]. Due o di e en ope a ing condi ions in he low- ol age (LV) design (e.g., supply
ol age and equi emen o he powe consump ion), speci ic me hods and p inciples o he eadou
sys ems mus be used. Especially, equi emen s ega ding he LV supply cause es ic ions o
he implemen a ion o s anda d me hods ha a e ocused on a di ec applica ion o qui e high
ol age le els.
Capaci ance senso s enable con e sion o a ious physical changes, o ins ance, small dis ance
and displacemen a ia ion [
13
–
16
] and wa e le el de ec ion [
17
], o measu able signals. Con inuously
ope a ing analog in e aces o capaci ance senso s use he ollowing me hods: (a) AC sou ce-based
measu emen s o sensing o ol age ac oss unknown capaci ance and cu en h ough unknown
capaci ance; (b) capaci ance di ide [
18
]; (c) esonance [
18
,
19
] and b idge ci cui s con aining he
measu ed capaci ance [
1
,
18
,
19
]; (d) me hods based on he ans e o cha ge (con aining swi ches
and hei d i ing) [
19
]; (e) di e en ial me hods [
13
–
16
] ensu ing high accu acy and linea i y;
and ( ) me hods based on he sensed capaci y as a key pa o signal gene a o [
18
,
19
] (sine wa e
oscilla o s and gene a o s o o he wa e o ms).
Senso s 2018,18, 4488; doi:10.3390/s18124488 www.mdpi.com/jou nal/senso s
Senso s 2018,18, 4488 2 o 15
The las me hod in he p e ious lis can be sui able o LV supply cases, because he signal
p ocessing, in compa ison wi h di ec measu emen o he capaci y by applied DC/AC ol age
o indi ec measu emen s expec ing high ol age le els [
15
,
16
], does no depend on he ol age
space ( ol age le els). Compa ed o Re s. [
15
,
16
], he concep p oposed in his pape is simple .
Nume ous wo ks deal wi h elaxa ion gene a o s due o hei ad an ages (e.g., low complexi y,
numbe o componen s and cos ). Di e en ial me hods, in compa ison wi h elaxa ion gene a o -based
app oaches, o e highe accu acy and low measu emen e o (uni s o pe cen ). Howe e , hese
solu ions [
15
,
16
] a e complex. In many cases, hese me hods e alua e he di e ence o capaci ies bu
no he absolu e alue o capaci ance. Fu he mo e, a ious auxilia y componen s (e.g., con ol o
swi ching, addi ional ol age o cu en sou ces) a e necessa y. The expec ed high ou pu ol age
le els [
15
,
16
] a e no a ailable in LV in eg a ed solu ions. Gene a o -based solu ions o ansduce a e
simple because enable di ec ans o ma ion o capaci y o equency (C
→
0
). Howe e , hei e o is
highe (up o 10%).
Table 1gi es an o e iew o ecen wo ks in he ield o capaci ance in e aces and ansduce s.
P e iously p oposed concep s a e e alua ed based on hei main ea u es and pa ame e s. Fea u es and
ad an ages o ou p oposed concep a e highligh ed in bold. As indica ed in Table 1, a dominan pa o
he p oposed solu ions uses gene a o -based me hods. In his wo k, we compa ed hese solu ions om
he iewpoin o he di ec ela ion o capaci ance sensing and ansduc ion. The analysis (see Table 1)
led o he ollowing conclusions: (a) he numbe o he used ac i e elemen s in many p oposed ci cui s
is high [
20
–
23
]; (b) he ac i e de ice concep employs many sub-pa s (3 o 5 cu en con eyo s) [
20
];
(c) lossless in eg a o inc eases he complexi y o he p oposed concep [
20
–
22
]; (d) decla ed measu ed
anges o “ equency s. capaci ance” dependence a e no decisi e o he quali y e alua ion— hey
always depend on he es ed capaci ance ange (no iden ical); (e) he ou pu in o ma ion in he o m
o DC ol age is una ailable; and ( ) he designs ha e simila inaccu acies (e.g., pe cen age e o ,
whe e indica ed) in simila anges [23,24].
I is impo an o men ion he me hods ha combine analog and digi al ways o signal p ocessing
o capaci ance senso in e aces [
25
–
29
]. The me hod p oposed in Re . [
25
] employs con olled
cha ging and discha ging o he sensed capaci ance and e e ence capaci ance esul ing in pulse
gene a ion wi h a a iable wid h in acco dance o he sensed capaci y alue. The me hodology in
Re . [
26
] uses simila app oach as Re . [
25
], bu he e e ence capaci o is no used he e and he ou pu
in o ma ion ( he o m o a digi al wo d) abou he capaci y is co e ed by he changes in he pe iod
measu ed by a coun e and p ocessed by a mic ocon olle . The concep in Re . [
27
] implemen s a
phase locked loop e alua ing in e ac ion o wo ing gene a o s, based on a chain o digi al in e e s.
The i s one is con olled by he sensed capaci y while he second one is d i en digi ally. P inciple
o he capaci ance measu emen , based on a p essu e senso , is desc ibed in Re . [
28
]. This me hod
modi ies he p inciple ha was p e iously p esen ed in Re . [
25
], bu i s o e all complexi y is simple ,
because only cu en sou ce, in e e and sub ac o a e used. Au ho s o he wo k [
29
] ex ended
and imp o ed a well-known p inciple ha employs wo cu en sou ces (cha ging and discha ging),
and wo compa a o s con olling RS lip- lop. Thei imp o emen consis s in he implemen a ion
o “ amp and hold” ci cui using cu en lowing h ough esis o in o de o cha ge he measu ed
capaci o and compa e ol ages a bo h elemen s. F om he e iew o hese wo ks, i is e iden ha all
he p esen ed ex emely low-powe (LP) solu ions [
25
,
27
,
28
] a ge qui e a na ow ange o he capaci y
measu emen . Un o una ely, in many cases, hese de ices equi e an ex e nal sou ce o clock o signal
o hei ull ope a ion ha signi ican ly inc eases he powe consump ion. In summa y, p inciples in
he abo e-discussed pape s a e o ally di e en om ou simple analog p oposal (a ci cui gene a es an
au onomous wa e o m) and all he desc ibed me hods equi e addi ional con ol logic, ex e nal clock
signal, synch onism and swi ching accesso y. Nex , hei o e all complexi y (mixed analog-digi al
design) and powe consump ion a e signi ican ly highe han ou simple analog p oposal.
Senso s 2018,18, 4488 3 o 15
Table 1. Compa ison o analog con inuous- ime ope a ing capaci i e senso in e aces om ecen li e a u e (ou wo k is indica ed wi h bold on s).
Re e ences
Numbe o Type o P inciple o Numbe o Type o Wa e o m Range o Numbe o Range o Ve i ica ion (Real In eg a ed Supply E o Sensi i i y = ∆ 0/∆capaci y
Ac i e Ac i e Ope a ion Elemen s Pa ame e a CSensed Decades Read Pa ame e Implemen a ion o Solu ion o he Vol age Sensi i i y = ∆V/∆C
Elemen s Elemen s (G ounded/Floa ing) Elemen s Pa ame e Ac i e De ice) Whole Sys em
Di e en ial me hods
[14] (b) (b) (b) 6 (4/2) Absolu e
di e ence o Cap -−0.9 pF→+0.9 pF - −0.12 V→+0.12 V M (CMOS) Yes 2.5 V ±1.5% 1.33 ×1011 V/F
[15] 4 CCII I (a) 5 (2/3) Rela i e
di e ence o Cap -−30%→+30% - 2 V→11 V M (4×AD844) No ±10 V <3% 7.54 ×10−6V/m
[15] 4 CCII I (a) 5 (2/3) Rela i e
di e ence o Cap -−30%→+30% - 0.4 V→2 V S (CMOS) pa ially ( ) ±1.65 V <0.23% 1.44 ×10−6V/m
[16] 4 MLT, OA II (a) 8 (3/5) Rela i e
di e ence o Cap -−100%→+100% - −10 V→+10 V M (AD844, AD633,
INA128, LF411) No N/A ±0.8% N/A
Squa e wa e o m gene a ing ci cui -based me hods
[30] 1 CCII III 3 (2/1) Cap E 100 pF→700 pF <1 441 kHz→346 kHz M (AD844) No ±10 V N/A 1.6 ×1014 Hz/F
[20] 3 CCII III 6 (5/1) Cap T 500 pF→5µF 4 150 kHz→15 Hz B (CMOS, 3×AD844) No ±6 V N/A 3 ×1010 Hz/F
[31] 1 DO-DVCC III 3 (3/0) Cap T 125 pF→10 nF <2 800 kHz→10 kHz M (5×AD844) No ±10 V N/A 8 ×1013 Hz/F
[32] 1 DVCC III 3 (2/1) Cap E 1 nF→1µF 3 10 kHz→10 Hz M (3×AD844) No ±15 V N/A 1 ×1010 Hz/F
[21] 2 CCII III 5 (4/1) (c) Cap T 10 nF→20 µF<4 410 kHz→260 Hz M (2×AD844) No N/A (e) N/A 2.1 ×1010 Hz/F
[22] 2 CCII III 5 (1/4) Cap T 0.5 nF→10 µF<5 263 kHz→25 Hz M (2×AD844) No (±5–±15) V <5% 2.6 ×1010 Hz/F
[24] 1 CCII III 4 (1/3) Cap E 100 pF→5.5 µF<5 6.9 kHz→0.14 Hz M (AD844) No N/A (e) ≤±10% 1.3 ×109Hz/F
[24] 1 CCII III 4 (1/3) Cap E 22 pF→5.5 µF<6 232 kHz→1 Hz S (CMOS) pa ially ( ) ±1.2 V ≤±10% 4.2 ×1010 Hz/F
[23] 2 CCII III 4 (3/1) Cap T 500 pF→200 nF <3 39 kHz→98 Hz M (2×AD844) No ±9 V <7% 2 ×1011 Hz/F
P oposed (C→ 0con e sion)
This wo k 1 CFOA III 4 (2/2) Cap E 4.7 nF→470 nF
6.8 nF→100 nF
3
<2
89.3 kHz→1.1 kHz
74.8 kHz→4.8 kHz
M
(CMOS CCCII, bu e ) pa ially ( ) ±1.65 V <±11%
<±6%
1.9 ×1011 Hz/F
7.5 ×1011 Hz/F
P oposed (C→Vcon e sion)
This wo k 1 CFOA III 10 (5/5) (d) Cap E 4.7 nF→470 nF
6.8 nF→100 nF
3
<2
0.134 V→0.019 V
0.106 V→0.021 V
M (CMOS CCCII,
bu e , diodes) pa ially ( ) ±1.65 V <±12%
<±5%
247 ×103V/F
912 ×103V/F
No es: I—di e en ial measu emen (
∆
C
→
V), II—b idge balancing (di e en ial measu emen o capaci y alues;
∆
C
→
V), III—gene a o (C
→
0
), IV—cha ging and discha ging o C
and e e ence capaci y and pulse wid h e alua ion, V—pe iod-modula ed me hod, VI—compa ison o phases o digi ally con olled oscilla o and oscilla o in luenced by capaci ance,
VII—see discussion in Re . [
29
], T— iangula , E—exponen ial, M—measu ed, S—simula ed, B—bo h CCII—cu en con eyo o second gene a ion, CCCII—cu en con olled
cu en con eyo o second gene a ion, CCII—cu en con eyo o second gene a ion, CFOA—cu en eedback ope a ional ampli ie , DO-DVCC—di e en ial ou pu —DVCC,
DVCC—di e en ial ol age cu en con eyo o second gene a ion, ENOB—e ec i e numbe o bi s, MLT—mul iplie , OA—ope a ional ampli ie ;
(a)
ex e nal sine wa e sou ce
equi ed;
(b)
3 ac i e de ices ( ansconduc ance s age, di e en ial and summing cu en ampli ie , swi ches, bu e , addi ional DC cu en sou ces), sensed di e ence o swi ched DC
bias cu en s;
(c)
2 capaci o s a e equi ed;
(d)
including diodes (No e ha column “numbe o passi e elemen s” includes C
sens
);
(e)
supply ol age is no men ioned in he ex ,
bu esul s indica es ±(10–15 V); ( ) simula ed/measu ed only a cell le el (layou p epa ed o ac i e de ice bu no shown o ully in eg a ed sys em).
Senso s 2018,18, 4488 4 o 15
In his pape , a no el concep o capaci ance senso in e ace is p esen ed, which is based
on he well known squa e wa e gene a o p inciple. Compa ed o Re . [
18
], whe e a me hod
employing capaci ance di ide and calcula ion om known supplying ol age is used, we p opose
a solu ion o implemen ing wo con e sions: C
sens→
0→
V
sens
. Topology o he whole ci cui y
is simple han p e iously p oposed concep s; see Re s. [
18
,
20
–
23
,
31
,
32
]. No e ha all concep s
p esen ed in
Re s. [20–24,30–32]
need an addi ional
0→
V
sens
con e e . The eby, solu ions p esen ed
in Re s. [
20
–
23
,
31
,
32
] become mo e complex han concep s p esen ed in Re s. [
24
,
30
]. The concep
o a wo-con e sions-based ansduce has no been s udied and e alua ed in hese ypes o
gene a o -based capaci ance senso in e aces.
Compa ed o s a e-o - he-a and p e iously p esen ed solu ions (see Table 1), he o iginali y and
main con ibu ions o his wo k a e as ollows: (a) a new simpli ied CMOS opology o he ac i e
elemen is p oposed and u ilized o c ea e a squa e wa e gene a o wi h a low impedance ol age
mode ou pu ; (b) a new simple capaci y o ol age sensing in e ace wi h low numbe o passi e
elemen s is ealized; and (c) an app op ia e me hod o combine o squa e-wa e gene a o (a C
sens→
0
con e e ) and equency o DC ol age ( 0→Vsens) con e e is p esen ed.
Remaining pa s o he pape a e o ganized as ollows. A new concep o he ansduce /in e ace
o he capaci ance measu emen , i s coun e pa s and hei heo e ical analysis a e desc ibed in
Sec ion 2. Expe imen al e i ica ion o he es ablished Ma hcad model o
0→
V
sens
con e sion
and esul s om measu emen s o he p oposed de ice a e p esen ed and compa ed wi h heo y
assump ion in Sec ion 3. This sec ion also con ains he e alua ion o he ob ained esul s. Finally,
Sec ion 4concludes his pape .
2. Readou Ci cui o Capaci y Measu emen
A block diag am o he capaci y measu emen , used in he p oposed solu ion, is shown in Figu e 1.
The sensed capaci o di ec ly de e mines he oscilla ion ( epea ing) equency, ma ked as
0
, o he
squa e wa e gene a o . A e ha , he equency is ans o med o he DC ol age (V
sens
). Such a
o m o he ou pu in o ma ion is e y use ul because he capaci ance can be measu ed by a low-cos
magne o-elec ic analog ol me e . The ol me e has a scale calib a ed as capaci ance o he DC
ol age can be easily p ocessed by any analog- o-digi al con e e (ADC).
Figu e 1. P inciple o he capaci y measu emen .
The in eg a ed squa e wa e gene a o o ms he co e o he abo e b ie ly desc ibed capaci y
measu emen . I s p inciple is as ollows. The gene a o consis s o a special ype o Schmi compa a o
wi h hys e esis and an RC ne wo k se ing as a lossy in eg a o [
1
,
33
]. The RC sec ion is supplied om
he ou pu o he compa a o (see Figu e 2) a e impedance sepa a ion by a simple ol age ollowe
(bu e ). Thanks o his concep (a eedback including bu e ), he p oposed opology is di e en om
he solu ion p esen ed in Re . [23]. Mo eo e , in Re . [23], complex ac i e de ices a e used.
The compa a o uses a single cu en con olled cu en con eyo o second gene a ion
(CCCII)
[34,35]
, a ol age bu e and wo esis o s. Such an a angemen o ac i e de ices is called
a cu en eedback ope a ional ampli ie (CFOA) [
33
]. The p inciple o CCCII is desc ibed by he
ollowing in e - e minal ela ions: V
Y
= 0, V
X
=V
Y
(open X), V
X
=V
Y
+R
X
I
X
and I
Z
=I
X
. The V
o
=V
z
ela ion is added by he ol age bu e .
Senso s 2018,18, 4488 5 o 15
Figu e 2. P inciple o he p oposed compa a o .
The ope a ion o he compa a o especially employs he I
Z
=I
X
ela ion. The cu en , lowing
o he X e minal, is di ec ly copied o he Z e minal. I is alid ha I
R2
=V
ou
/R
2
=
±
V
Zmax(sa )
/R
2
.
The sa u a ion ol age o he ou pu Z almos eaches he supply ol age, equals o
±
1.65 V. When
we conside a pos i e eedback o he Y e minal and ela ion be ween Y and X e minals, whe e X
e minal is e mina ed by he esis o R
1
=R
Xex
+R
Xin
and he ol age V
inp
is p esen a his node,
hen ela ion IZ=IXleads o he ollowing exp ession:
VZmax(sa ) −Vinp( e )
R1
=VZmax(sa )
R2
. (1)
Rea angemen o (1) gi es a di ec ela ion o he inpu h eshold symme ical ol ages:
±Vinp( e ) =∓VZmax(sa ) ×1−R1
R2. (2)
The comple e ci cui y o he capaci y o ol age sensing eadou is cap u ed in Figu e 3.
This ci cui y consis s o wo main blocks, namely Csens→ 0and 0→Vsens con e e s.
Figu e 3. The comple e ci cui y o he p oposed capaci y o ol age sensing in e ace ( eadou ).
2.1. The Csens→ 0Con e e
The C
sens→
0
con e e (a squa e wa e gene a o ) is ob ained, when he ol age bu e sepa a es
he high impedance ou pu node o he compa a o (see Figu e 2) and an RC ne wo k (R
3
,C
sens
) is

Senso s 2018,18, 4488 6 o 15
connec ed be ween he ou pu node and V
inp
( o R
Xex
) o he compa a o . The squa e wa e signal
a he ou pu o he bu e , ma ked as V
SQ
( ), and he signal in he node o C
sens
, ma ked as V
EXP
( ),
a e impo an o u he explana ion (see ime diag am in Figu e 4).
Figu e 4. Time diag am o ansien esponses o analysis o he gene a o ope a ion.
The ime-cons an o he C
sens
cha ging can be exp essed as a pa allel combina ion o esis o s R
1
and R3:τ=[(R1R3)/(R1+R3)]×Csens. The hal pe iod o he cha ging in e al is de ined as:
VEXP(0≤ ≤T/2) = (VEXPmax +VSQmax)h1−e−
τi, (3)
whe e V
EXPmax
=V
inp( e )
( h eshold ol age o he compa a o ) and V
SQmax
=V
Zmax(sa )
(sa u a ion
ol age o he compa a o ). Acco ding o V
EXP
( =T/2) = 2V
inp( e )
, whe e capaci o cha ges om
−Vinp( e ) o +Vinp( e ), he ollowing o mula can be w i e o =T/2:
2Vinp( e ) = (Vinp( e ) +VZmax(sa ))h1−e−T
2τi. (4)
A e ea angemen o (4), he pe iod can be exp essed as:
T=2τln VZmax(sa ) +Vinp( e )
VZmax(sa ) −Vinp( e ) !, (5)
whe e ol ages and he ime-cons an can be subs i u ed by (2) and by he abo e in oduced exp essions,
espec i ely. A e ha , he pe iod and epea ing equency 0can be calcula ed as:
T=1
0
=2Csens R1R3
R1+R3ln 2R2−R1
R1. (6)
The maximum cu en le els (magni udes do no conside ing he cu en pola i y), passing
h ough he passi e elemen s o he opology, a e de e mined as ollows:
IR2max =VZmax(sa )
R2
, (7)
IR1,3max =VZmax(sa )+Vinp( e )
R1,3
, (8)
|ICmax |=IR1,3max +IR2max . (9)
Senso s 2018,18, 4488 7 o 15
2.2. The 0→Vsens Con e e
The
0→
V
sens
con e e (see Figu e 3) consis s o a diode double including wo diodes,
wo capaci o s and wo esis o s. In many s anda d applica ions [
36
], such a concep ope a es as
a peak de ec o . Howe e , om he iewpoin o ime-cons an alues o he loa ing (
τA
=R
A
C
A
) and
g ounded (
τB
=R
B
C
B
) segmen s, ou case is di e en . Desc ip ion o he simpli ied ope a ion o his
block is p esen ed in he ollowing pa ag aph.
The V
SQ
( ) ol age changes immedia ely be ween +V
Zmax(sa )
and
−
V
Zmax(sa )
. The nega i e
pola i y o V
SQ
( ) subsequen ly cha ges C
A
o
−
V
Zmax(sa )
. When he V
SQ
( ) u ns o +V
Zmax(sa )
,
hen he maximal cu en h ough C
A
o T/2 can be ob ained as I
CAmax
= (2V
Zmax(sa ) −
V
D
)/R
A
.
He e, V
D
ma ks he ol age d op ac oss he diode (
≈
0.7 V) and R
A
is a esis o used o limi he
cha ging cu en . The maximal ol age (a change ac oss C
A
) de e mines he o e all cha ge h ough one
pe iod as ollows: Q
A
= 2(V
Zmax(sa ) −
V
D
)
×
C
A
. Due o he change o he pola i y o V
Zmax(sa )
, he
cha ge is mo ed and accumula ed by he g ounded segmen C
B
. The ime-cons an o he g ounded
segmen is e y high. In his case, i is supposed ha
τA<< τB
. Consequen ly, sligh discha ging
o C
B
in one pe iod is in luenced only by he esis o R
B
. I can be exp essed as i
RB
( ) =
dQB
( )/d
∼
=
Q
B
/T. In ac , i
RB
( ) is almos cons an due o high
τB
, he eby, I
RB
=V
sens
/R
B
. In he case o Q
A
=Q
B
(cha ge conse a ion), he ideal ela ion be ween he equency 0and ol age Vsens will be:
Vsens ∼
=2VZmax(sa ) −VDRBCA
T∼
=2VZmax(sa ) −VDRBCA 0. (10)
Using (10) and (6), i is possible o ob ain he ela ion be ween Vsens and Csens:
Vsens =VZmax(sa ) −VDRBCA
Csens R1R3
R1+R3ln 2R2−R1
R1. (11)
The limi a ion o alidi y o (11) conce ns pe iods sho e han ime equi ed o accumula e
a cha ge in he loa ing segmen . The eby, he ou pu V
sens
ol age goes o ze o. Res ic ion o he
con e e o e y la ge pe iods, whe e he loa ing segmen has as e esponse (sho ime-cons an )
han he p ocessed signal, mus be aken in o accoun . In his case, he cha ge in he ci cui o
0→
V
sens
con e sion is no subsequen ly accumula ed (mo ed om C
A
o C
B
) in each pe iod o he
inpu signal. The capaci o C
B
is cha ged di ec ly by he inpu signal whe eas, he discha ge (
τB
) is no
as enough. The eby, his app oach canno be used in he ull equency ange o he signal gene a ed
by he elaxa ion gene a o ci cui . This ange o ope a ion depends on he p ocessed equency and
ime-cons an s (τA,τB).
3. Expe imen al Ve i ica ion
The comple e CMOS opology o he CFOA is shown in Figu e 5a. Fab ica ed cells in ON
Semiconduc o C035 0.35
µ
m I3T25 CMOS [
37
] we e used o expe imen al e i ica ion o he p oposed
concep (see Figu e 5b,c). The implemen a ion o CCCII and BUFFER in o CFOA elemen is depic ed in
Figu e 2. The powe supply is
±
1.65 V and I
SETRXin
= 100
µ
A (R
Xin ∼
=
440
Ω
). The es o he ex e nal
passi e elemen s ha e he ollowing alues: R
Xex
= 560
Ω
(R
1
=R
Xex
+R
Xin
= 1 k
Ω
), R
2
= 4.7 k
Ω
and
R3= 1 kΩ. Figu e 5d depic s he ealized and measu ed p o o ype.
The p oposed CFOA de ice has he ollowing ea u es: (a)
−
3 dB bandwid s
>
49 MHz (Y
→
X),
−
3 dB bandwid h > 37 MHz (X
→
z) and
−
3 dB bandwid h > 45 MHz (z
→
o); (b) ans e s (DC analysis)
o e linea p ocessing be ween
±
1 V ( o Y
→
X),
±
1.7 mA ( o X
→
z) and
±
0.8 V ( o z
→
o); (c) e minal
esis ances eaches 100 M
Ω
(Y e minal), >66 k
Ω
(z e minal), and 280
→
3400
Ω
(X e minal) when
in e nal R
X
is adjus ed by DC bias cu en om 10 up o 350
µ
A. Te minal esis ance o he o e minal is
0.54
Ω
. Pa asi ic e minal capaci ies each alues app oxima ely om 2 pF up o 20 pF (i is depending
on he design o PCB). The DC inpu o se s a e below 2.5 mV o Y→X ans e , below 6 µA o X→z
Senso s 2018,18, 4488 8 o 15
ans e and below 10 mV o z
→
o ans e . Fo he inindica ed DC inpu ange, he maximal THD is
1.5% o X→z ans e , 0.6% o Y→X ans e , and 0.5% o z→o ans e .
(a)
(b)
(c)
(d)
Figu e 5.
(
a
) The comple e CMOS opology o CFOA; layou s o CFOA cells (on a single IC package)
ab ica ed in I3T25 p ocess: (
b
) cu en con olled cu en con eyo o second gene a ion (CCCII)
and (
c
) ol age bu e ; and (
d
) he ealized and measu ed p o o ype o eadou (CFOA and
0→
V
sens
con e e ).
The alues o he passi e elemen s in he
0→
V
sens
con e e a e as ollows: R
A
= 100
Ω
,
C
A
= 1 nF, R
B
= 1 k
Ω
and C
B
= 100 nF. Nex , 1N4148 diodes we e used. Such alues o he passi e
Senso s 2018,18, 4488 9 o 15
elemen s, ime-cons an s as well as pa ame e s in he gene a o pa o he C
sens→
0
con e e a e
in ended o expec capaci ance alues om uni s o ens o nF. The alue o V
Zmax(sa )
, equals o
±
1.5 V,
was ob ained om he expe imen s. We also suppose V
D
= 0.7 V (s anda d h eshold alue o he
1N4148 diode). Acco ding o he abo e conside ed alues, he e is p edic ed a nume ical cons an
om (11) ha allows ideal es ima ion o he ela ion be ween he p oduced DC ol age and he sensed
capaci y. I can be exp essed as Vsens ∼
=8×10−10/Csens.
The C
sens
was es ed in he ange om 100 pF o 470 nF. Dependencies o
0
on C
sens
and ou pu
ol age le els (V
SQ
and V
EXP
) on
0
a e shown in Figu e 6a,b, espec i ely. A signi ican in luence
on he accu acy o he gene a ed
0
s a s om C
sens <
1 nF. S abili y o he squa e wa e ou pu le el
is also an impo an ea u e o he co ec ope a ion o he
0→
V
sens
con e e . This esponse is
almos cons an in he whole ope a ional ange o he
0
(see Figu e 6b). Figu e 7shows he o e all
sys em pe o mance, namely V
sens
e sus C
sens
. I con ains cu es ob ained om heo y, Ma hcad
calcula ions and expe imen al measu emen s. The comple e model o he
0→
V
sens
con e e has
been implemen ed in Ma hcad in o de o e i y he co ec ness o he p oposed design. A qui e
subs an ial di e ence is isible be ween he heo y and expe imen al da a. Ne e heless, simula ion
and measu emen esul s well co ela e because he e o in he ope a ional ange om 6.8nF o
100 nF is only 5% (see Figu e 8). Fo he case C
sens <
6.8 nF, he di e ence be ween hem is caused
by he inaccu acy o
0
(no conside ed in he Ma hcad model). The eby, heo e ical alue V
sens ∼
=
8×10−10/Csens se es only o o ien a ion pu poses.
0.1
1.0
10.0
100.0
1000.0
1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06
0
[kHz]
Csens [F]
measu ed
ideal heo y
(a)
1.0
1.5
2.0
2.5
3.0
3.5
1.0E+03 1.0E+04 1.0E+05 1.0E+06
VEXP, SQ
[Vp-p]
0 [Hz]
VEXP
VSQ
(b)
Figu e 6. Fea u es o he p oposed gene a o : (a) 0 e sus Csens; (b) ou pu le els e sus 0.
0.00
0.05
0.10
0.15
0.20
0.25
110 100
Vsens
[V]
Csens [nF]
measu ed
Ma hcad analysis
ideal heo y
Vsens  0.8/(Csens [nF])
Vsens  0.34∙(Csens [nF])-0.64
Vsens  0.42∙(Csens [nF])-0.7
Figu e 7. Compa ison o he Vsens e sus Csens cu es ( heo y, Ma hcad simula ions, measu emen s).