Recei ed 5 June 2024, accep ed 16 June 2024, da e o publica ion 20 June 2024, da e o cu en e sion 12 July 2024.
Digi al Objec Iden i ie 10.1109/ACCESS.2024.3417333
Low-Vol age Low-Powe Di e en ial Di e ence
Cu en Con eyo T ansconduc ance Ampli ie
and I s Applica ion o a Ve sa ile
Analog Fil e
MONTREE KUMNGERN 1, FABIAN KHATEB 2,3,4, AND TOMASZ KULEJ 5
1Depa men o Telecommunica ions Enginee ing, School o Enginee ing, King Mongku ’s Ins i u e o Technology Ladk abang, Bangkok 10520, Thailand
2Depa men o Mic oelec onics, B no Uni e si y o Technology, 601 90 B no, Czech Republic
3Facul y o Biomedical Enginee ing, Czech Technical Uni e si y in P ague, 272 01 Kladno, Czech Republic
4Depa men o Elec ical Enginee ing, Uni e si y o De ence, 662 10 B no, Czech Republic
5Depa men o Elec ical Enginee ing, Cze¸s ochowa Uni e si y o Technology, 42-201 Cze¸s ochowa, Poland
Co esponding au ho s: Mon ee Kumnge n ([email p o ec ed]) and Fabian Kha eb (kha eb@ u b .cz)
This wo k was suppo ed by he Uni e si y o De ence, B no, wi hin he O ganiza ion De elopmen P ojec VAROPS.
ABSTRACT This pape p esen s a new low- ol age low-powe di e en ial di e ence cu en con eyo
ansconduc ance ampli ie (DDCCTA). The p oposed DDCCTA u ilizes a mul iple-inpu ga e-d i en MOS
ansis o (MIGD-MOST) ope a ing in he sub h eshold egion o achie e low supply ol age, minimum
numbe o MOS di e en ial pai s and minimum powe consump ion. To show he ad an ages o he p oposed
DDCCTA, i was used o ealize a e sa ile analog il e . The il e uses h ee DDCCTAs, wo g ounded
capaci o s, and wo g ounded esis o s o ealize 65 ans e unc ions o low-pass, high-pass, band-pass,
band-s op, and all-pass il e s by app op ia ely selec ing he inpu and ou pu e minals wi hou changing he
il e opology. The il e also has he ad an ages o high-inpu impedance, which is ideal o ol age-mode
ci cui s, independen con ol o he na u al equency and quali y ac o , and he abili y o elec onically une
he na u al equency. The p oposed DDCCTA and e sa ile analog il e we e designed and simula ed using
SPICE wi h TSMC 0.18 µm CMOS echnology o e i y he new ci cui s. The p oposed il e uses ±0.5 V
o supply ol age and 103 µW o powe .
INDEX TERMS Di e en ial di e ence cu en con eyo ansconduc ance ampli ie , analog il e , bulk-
d i en MOS ansis o , low- ol age low-powe .
I. INTRODUCTION
The second-gene a ion cu en con eyo (CCII) was in o-
duced in [1] and [2] as a e sa ile ac i e building block
o ealizing analog ci cui s. CCII based ci cui s o e be e
pe o mance in e ms o highe bandwid h, linea i y, and
dynamic ange compa ed o ope a ional ampli ie (op-amp)
based ci cui s [3],[4]. This ac i e elemen has h ee e minals
( he y-, x-, and z- e minal) and i s ideal cha ac e is ic can
be gi en by Vy=Vxand Ix=Iz[2]. The CCII can
be used in analog signal p ocessing, o example, o ealize
The associa e edi o coo dina ing he e iew o his manusc ip and
app o ing i o publica ion was Sai-Weng Sin .
analog il e s [5],[6], signal gene a o s [7],[8], and p ecision
ec i ie s [9],[10],[11]. Howe e , CCII based ci cui s lack
he capabili y o elec onic uning.
The ope a ional ansconduc ance ampli ie (OTA) is an
ac i e building block ha o e s elec onic uning capabili y.
I s ideal cha ac e is ics can be gi en by Io=gm(V+−V−)
[12], whe e Iois he ou pu cu en , gmis he ansconduc-
ance gain, V+and V−a e espec i ely he non-in e ing
and in e ing inpu ol ages. The inpu ol age o his de ice
can be con e ed o ou pu cu en using i s ansconduc ance
gain, whe e ansconduc ance gain is an in insic cha ac e -
is ic o he OTA ha can be gi en as he a io o he cu en
ou pu o he inpu ol age. Typically, he ansconduc ance
VOLUME 12, 2024
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M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
gain o an OTA can be con olled by a bias cu en / ol age.
Thus, i he inpu ol age is ixed o an app op ia e alue, he
ou pu cu en can be con olled by adjus ing he ansconduc-
ance gain. The OTA also o e s mul iple ad an ages, such
as easy implemen a ion o i s in e nal s uc u e ( he simple
OTA s uc u e can be implemen ed using a bipola junc ion
ansis o (BJT) o CMOS echnology). OTA-based ci cui s
can educe he numbe o needed passi e esis o s, o elimi-
na e hem a all, making hem sui able o implemen a ion in
in eg a ed ci cui s (ICs).
Based on he design o new ac i e elemen s o ana-
log signal p ocessing [13], he ad an ages o he CCII and
OTA can be inco po a ed in o a single ac i e building block,
he so-called ‘‘cu en con eyo ansconduc ance ampli ie
(CCTA)’’ [14]. The i s s age o he CCTA is a CCII cascaded
by an OTA. The ad an ages o he CCTA can be con i med by
applica ions in analog il e s and sinusoidal oscilla o s [15],
[16],[17],[18]. Un o una ely, CCII is a single-end ac i e
elemen - namely he e is a single e minal o he x-, y-
, and z- e minals, which limi s he applica ions o holding
he signal in di e en ial o ms and/o he addi ion and sub-
ac ion o signals. To o e come hese limi a ions, ce ain
ac i e elemen s ha e been p oposed, such as he di e en ial
di e ence cu en con eyo (DDCC) [19], he di e en ial
ol age cu en con eyo (DVCC) [20], and he ully di -
e en ial second-gene a ion cu en con eyo (FDCCII) [21].
These ac i e building blocks can be used o ealize analog
il e s [22],[23],[24], sinusoidal oscilla o s [25],[26], and
ins umen a ion ampli ie s [27],[28]. Simila ly, o he con-
en ional CCII, hese ac i e elemen s s ill lack an elec onic
uning abili y. Based on he ealiza ion concep o new ac i e
elemen s p esen ed in [13], new ac i e elemen s, such as
he di e en ial di e ence cu en con eyo ansconduc ance
ampli ie (DDCCTA) [29] and he ully di e en ial cu en
con eyo ansconduc ance ampli ie (FDCCTA) [30], ha e
been p oposed. The DDCCTA is he ocus o his wo k,
whe e i was ealized by using DDCC a i s s age and
cascaded by an OTA a he nex s age. The DDCCTA can
be used o ealize analog ci cui s wi h an elec onic uning
capabili y and o acili a e he ealiza ion o eedback addi-
ional/sub ac ion ol age signals. Many applica ions o he
DDCCTA/DVCCTA ha e been in oduced in [31],[32],[33],
[34],[35],[36],[37], and [38].
Howe e , he p e ious DDCCTA s uc u es we e no
designed o low supply ol age and low powe consump ion,
i.e., he DDCCTA s uc u e in [29] uses ±1.25 V o supply
ol age and consumes 1.8 mW o powe , he DVCCTA
s uc u e in [36] uses ±1.4 V o supply ol age and consumes
4.4 mW o powe . Se e al DDCCTA applica ions in [31],
[32],[33],[34], and [35] use CMOS implemen a ion o he
DDCCTA in [29]. These used supply ol ages o ±3 V
o [31],±2 V o [32] and [33],±1.5 V o [34] and [37],
±0.9 V o [35].
In his pape , a new low- ol age low-powe di e en-
ial di e ence cu en con eyo ansconduc ance ampli ie
(DDCCTA) is p oposed. The MOS di e en ial pai o he
DDCCTA was ealized using he mul iple-inpu ga e-d i en
MOS ansis o (MIGD-MOST) echnique; hence, a mini-
mum numbe o MOS di e en ial pai s can be ob ained.
The sou ce deg ada ion using wo MOSTs ope a ing in
he iode egion was used o inc ease he linea i y o he
ansconduc ance gain. The ci cui ope a ed wi h ±0.5 V
o supply ol age and consumed 34.3 µW o powe . The
p oposed DDCCTA was used o ealize a e sa ile analog
il e . The il e employed h ee DDCCTAs, wo g ounded
capaci o s, and wo g ounded esis o s. This il e showed
ha he mul iple-inpu mul iple-ou pu o he DDCCTA can
o e many ol age-mode ans e unc ions o low-pass il e
(LPF), high-pass il e (HPF), band-pass il e (BPF), band-
s op il e (BSF), and all-pass il e (APF) by app op ia ely
selec ing inpu and ou pu e minals wi hou changing he
il e opology. The na u al equency and quali y ac o o
all il e s was able o be con olled elec onically and inde-
penden ly. The p oposed DDCCTA and e sa ile analog il e
we e designed and simula ed in SPICE wi h TSMC 0.18 µm
CMOS echnology o alida e he new ci cui s. The e sa ile
analog il e consumed 103 µW o powe .
FIGURE 1. Con en ional DDCCTA: (a) in e nal block s uc u e,
(b) elec ical symbol.
II. CIRCUIT DESCRIPTION
A. PROPOSED 1-V DDCCTA
The con en ional DDCCTA is shown in Fig. 1- Fig. 1 (a)
shows he concep o ealiza ion o he DDCCTA which
consis s o a DDCC and a TA ( ansconduc ance ampli ie ),
and Fig. 1 (b) shows he elec ical symbol o he DDCCTA.
The po cha ac e is ics o Fig. 1 (b) can be gi en by [29]
Vx=Vy1+Vy2−Vy3
Iz=Ix
Io=gmVz


(1)
whe e gmis he ansconduc ance gain o he DDCCTA.
I should be no ed ha he DDCC and TA in Fig. 1(a)
a e a single ou pu e minal (z- and o- e minals). The in e -
ing inpu ol age e minal (–) o he TA is no used and is
connec ed o he g ound. In his wo k, he in e ing inpu
e minal o he TA was used as an addi ional inpu ol age,
and he dual-ou pu z- e minals o he DDCC and plus/minus
o- e minals o he TA we e a ailable and used as addi ional
ou pu cu en s o he DDCCTA.
Fig. 2shows he p oposed DDCCTA- Fig. 2(a) shows he
CMOS implemen a ion and Fig. 1(b) shows he elec ical
symbol. Compa ed o Fig. 1 (b), he in e ing inpu ol age
e minal o TA in Fig. 2 (b) is a ailable and is connec ed o
92524 VOLUME 12, 2024
M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
FIGURE 2. The p oposed DDCCTA, (a) CMOS implemen a ion, (b) elec ical symbol.
FIGURE 3. MIGD MOST: (a) symbol, (b) implemen a ion o he MIGD
MOST, (c) implemen a ion o RMOS.
he z- e minal o he DDCC; he nonin e ing e minal o he
TA is V1. The minus- ype ou pu e minal (o–) o he TA is
ob ained using he c oss-coupled cu en mi o s. The ou pu
cu en o he z- e minal o he DDCC is copied o he zc-
e minal using he cu en mi o s echnique.
The ideal cha ac e is ics o Fig. 2 (b) can be exp essed by
Vx=Vy1−Vy2+Vy3
Iz=Ix
Izc =Ix
Io±= ±gm(Vz−V1)







(2)
The CMOS ci cui in Fig. 2 (a) consis s o wo blocks. The
i s one, composed o he ansis o s M1-M11, is a second-
gene a ion di e en ial-di e ence cu en con eyo (DDCC)
wi h a doubled z ou pu . The second block (M1-M19) is a
linea ansconduc ance ampli ie (TA). The DDCC ci cui
is based on an unbu e ed ope a ional ampli ie (M1-M6and
M9) ope a ing in uni y-gain con igu a ion. I s inpu s age
exploi s a di e en ial pai , M1, M2, biased by a lipped
ol age ollowe consis ing o he ansis o s M1and M3.
Such a con igu a ion can ope a e o VDD as low as VGS +
VDSsa ; hus, i is especially sui able o LV designs. The
ansis o s o he inpu pai a e loaded by he cu en sinks
M4and M5, which de e mine he quiescen cu en s o M1
and M2. In o de o inc ease he numbe o inpu s (i.e.,
o ealize he di e en ial-di e ence unc ion), he ga e-d i en
inpu ansis o s M1and M2we e eplaced by mul iple-
inpu de ices, as shown in Fig. 3. The mul iple inpu s we e
c ea ed by a capaci i e summing ci cui , connec ed o he
ga e o a common MOS ansis o . In o de o p o ide
p ope biasing o he ga e e minal o DC, each capaci o
was bypassed by a la ge esis ance RMOS, ealized as an
an i-pa allel connec ion o wo MOS ansis o s ope a ing
in a cu o egion. Due o he ol age a enua ion in o-
duced by he passi e elemen s, he common-mode inpu
ange also inc eased. This achie ed an accep able ange o
inpu signals, while using ga e-d i en ansis o s wi h lowe
inpu noise and la ge ansconduc ances as hei bulk-d i en
coun e pa s.
The ou pu s age o he in e nal op-amp (M6, M9) ope a es
in he so-called supe class AB [39], which imp o es i s
powe e iciency. The ou pu signal o he i s s age con ols
he ga e o M6. A he same ime, i is p o ided a he
ga e o M9 ia he capaci o CB. The quiescen cu en o
M9is well con olled by he biasing ansis o Mband he
la ge esis ance RMOS is ealized as desc ibed p e iously.
The capaci ance CBand he la ge esis ance RMOS c ea e a
high-pass il e wi h a cu o equency o a ound 1 Hz. Fo
equencies well-abo e his alue, he AC signal a he ga e o
M9 ollows he one a he ga e o M6. In such a way, class AB
ope a ion o he ou pu s age is achie ed. The capaci ance CC
is used o a Mille equency compensa ion o he wo-s age
in e nal ope a ional ampli ie .
VOLUME 12, 2024 92525
M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
Neglec ing he impac o he limi ed common-mode ejec-
ion a io (CMRR) o he in e nal ope a ional ampli ie , he
signal a he x- e minal can be exp essed as:
Vx=KxVy1−Vy2+Vy3(3)
whe e, assuming iden ical capaci ances CB, he ol age gain
Kxcan be exp essed as:
Kx=
gm1,2
2( ds2|| ds5) (gm6+gm9) ( ds6+ ds9)
1+gm1,2
2( ds2|| ds5) (gm6+gm9) ( ds6+ ds9)(4)
whe e he symbols used ha e hei usual meaning. No e ha
he ansconduc ance o he inpu ansis o s M1and M2in
he abo e o mula is di ided by 2 due o he inpu capaci i e
di ide . Due o he wo-s age s uc u e, howe e , he alue o
Kxis close o uni y, wi h a gain e o ypically less han 1%.
The esis ance seen a he x- e minal is gi en by:
x=1
gm1,2
2( ds2|| ds5) (gm6+gm9)(5)
Since he ansis o s M7and M8(M10 and M11) a e con olled
wi h he same ol ages as M6(M9), he cu en s a he z- and
zc- e minals (neglec ing second o de e ec s) a e equal o he
cu en a he x- e minal. Thus, he cu en Ixis con eyed o
he e minals z and zc. The ou pu esis ances a he z- and
zc- e minals a e iden ical and gi en by:
z=1
( ds7|| ds10)(6)
The second block o he p oposed DDCCTA, namely he
ansconduc ance ampli ie , can be conside ed as a cu en
mi o s uc u e. I s inpu di e en ial s age exploi s he lin-
ea iza ion p inciple p oposed by K ummenache and Joehl
o ansis o s ope a ing in he s ong in e sion egion [40].
He e, he same p inciple is used o weakly in e ed de ices.
The linea iza ion ansis o s M3and M4ope a e in a deep
iode egion wi h VDS =0 a he ope a ing poin , ac ing as
sou ce degene a i e esis o s. Con olling hese esis ances
wi h he inpu di e en ial ol age o he ampli ie u he
imp o es i s linea i y. Assuming ha he used cu en mi o s
composed o o he ansis o s ha e a cu en gain equal o
uni y, he ci cui ansconduc ance can be exp essed as:
gm=4k
4k+1·Ise
npUT
(7)
whe e npis he sub h eshold slope ac o o a p-channel
ansis o , UTis he he mal po en ial, Ise is he biasing
cu en and kis he a io o he aspec a ios o M3,4 o M1,2
gi en by:
k=(W/L)3,4
(W/L)1,2
(8)
The coe icien ka ec s ci cui linea i y. The op imum lin-
ea i y is achie ed o k=0.5[41].
The cu en mi o s used in he s uc u e a e based on
he so called sel -cascode ansis o s, which p o ide a la ge
ou pu esis ance o he ci cui and consequen ly la ge DC
Vo1=(sC2gm3+gm1gm2) (V2−V1)+sC2gm3(V7−V6)
+gm1gm2V4+sC2gm1(V5−V3)
D(s)(10)
Vo2=sC1gm2(V2−V1)+gm2gm3(V6−V7)+(sC1gm2+gm2gm3)V4
+s2C1C2+sC2gm3(V5−V3)
D(s)(11)
Vo3=sC1gm2(V1−V2)+gm2gm3(V7−V6)+(sC1gm2+gm2gm3)V4
+gm2gm3(V5−V3)
D(s)(12)
Vo4=s2C1C2(V1−V2)+sC2gm3(V7−V6)+gm1gm2V4
+sC2gm1(V5−V3)
D(s)(13)
Vo5=s2C1C2(V1−V2)+s2C1C2+gm1gm2(V6−V7)
+gm1gm2V4+sC2gm1(V5−V3)
D(s)(14)
Vo6=


s2C1C2gm3R1+sC1gm1gm2R1(V2−V1)
+s2C1C2gm3R1(V7−V6)+sC1gm1gm2R1V4
+s2C1C2gm1R1(V5−V3)


D(s)(15)
Vo7=(gm3R2)s2C1C2(V1−V2)+s2C1C2+gm2gm3(V6−V7)
+gm1gm2V4+sC2gm1(V5−V3)
D(s)(16)
92526 VOLUME 12, 2024
M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
FIGURE 4. P oposed e sa ile analog il e using DDCCTAs.
ol age gain o he ansconduc ance ampli ie , which can be
app oxima ed as:
A ∼
=gm[(gm8 ds8 ds8c)|| (gm14 ds14 ds14c)](9)
In o de o ealize he unc ion o he DDCCTA desc ibed
by (2), he ansconduc ance ampli ie is con olled by he
di e ence o ol ages Vzand V1.
B. PROPOSED VERSATILE ANALOG FILTER
Fig. 4shows he p oposed e sa ile analog il e using DDCC-
TAs as ac i e elemen s. The ci cui uses h ee DDCCTAs, wo
g ounded capaci o s, and wo g ounded esis o s. I should
be no ed ha he use o g ounded passi e componen s is
p e e ed o in eg a ed ci cui s. Inpu s V1 o V7possess a
high impedance le el, which is ideal o ol age mode ci -
cui s, hence no addi ional bu e ci cui is needed. Using (2)
and nodal analysis, he ou pu ol ages Vo1 o Vo7can be
exp essed as (10)–(16), shown a he bo om o he p e ious
page, whe e D(s)=s2C1C2+sC2gm3+gm1gm2.
The ob aining a ian il e ing unc ion can be shown in
Table 1. F om Table 1, he equi ed il e ing unc ions can
be ob ained by app op ia e applying he inpu signals and
selec ion o ou pu nodes, while he inpu s ha a e no used
should be connec ed o g ound. Thanks o he DDCCTAs, he
plus/minus inpu ol age e minals a e a ailable, he in e -
ing inpu ol age is absen and many ou pu ol ages wi h
di e en ypes o il e ing unc ions can be ob ained. Thus,
om Table 1, he p oposed il e o e s 65 ans e unc ions,
as bo h in e ing and non-in e ing ans e unc ions o LPF,
HPF, BPF, BSF, and APF can be ob ained. No e ha he
ou pu s Vo1 o Vo5p o ide a uni y ol age gain.
I ol age gains o LPF, HPF, BPF, BSF, and APF a e
equi ed, hey can be ob ained om he ou pu s Vo7o Vo6
o some il e ing unc ions.
The na u al equency (ωo), bandwid h (ωoQ), and qual-
i y ac o (Q) can be gi en by:
ωo= gm1gm2
C1C2
(17)
ωo
Q=gm3
C1
(18)
Q=1
gm3sC1gm1gm2
C2
(19)
The na u al equency can be con olled elec onically by gm1
and gm2, he quali y ac o can be a ied elec onically by gm3
FIGURE 5. The DC ans e cha ac e is ics and i s e o s, (a) ol age
swings o Vy1, Vy2 and Vx, (b) e o s o ol ages Vy1, Vy2 and Vx.
when gm1=gm2and C1=C2. Thus, he na u al equency
and quali y ac o can also be independen ly con olled.
C. NON-IDEAL ANALYSIS
A non-ideal DDCCTA can be cha ac e ized by:
Vx=β1kkVy1+β2kVy2−β3kVy3
Iz=αkIx
Izc =αkIx
Io±= ±gmnk (Vz−V1)







(20)
whe e βjk (j=1,2,3) and αk ep esen espec i ely he ol -
age and cu en ans e gain o he k h DDCCTA and gmnk
is he non-ideal ansconduc ance gain o he k h DDCCTA.
Usually, he ans e gains o he DDCCTA de ia e om uni y
by he ol age and cu en acking e o s. Mo e accu a ely,
βjk =(1 −ε jk ) and αk=(1−εik ), whe e ε jk (ε jk ≪1)
and εik (|εik |≪1), ep esen espec i ely he ol age and
cu en acking e o s o he DDCCTA.
The non-ideal ansconduc ance gmn o he DDCCTA a a
equency nea he cu -o equency can be exp essed by [42]
gmn (s)∼
=gm(1−µs)(21)
whe e µ=1ωgm and ωgm deno es he i s pole equency
o he gm.
Taking in o accoun he non-ideali ies in (21) o he
DDCCTA1, he DDCCTA2, and he DDCCTA3, he
non-ideali ies can be ob ained as:
Vx=β11Vy1−β21Vy2+β31Vy3
Iz=α1Ix
Io±= ±gmn1(Vz−V1)


o DDCCTA1(22)
VOLUME 12, 2024 92527

M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
TABLE 1. Ob aining a ian il e ing unc ions o he p oposed e sa ile analog il e .
92528 VOLUME 12, 2024
M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
FIGURE 6. The ansconduc ance cha ac e is ic wi h di e en se ing
cu en s, (a) DC cha ac e is ic, (b) AC cha ac e is ic.
FIGURE 7. The pa asi ic impedances a x-, z-, o- e minals o he DDCCTA.
Vx=β12Vy1−β22Vy2+β32Vy3
Iz=α2Ix
Io±= ±gmn2(Vz−V1)


o DDCCTA2(23)
Vx=β13Vy1−β23Vy2+β33Vy3
Iz=α3Ix
Io±= ±gmn3(Vz−V1)


o DDCCTA3(24)
The denomina o o he p oposed e sa ile analog il e can
be w i en as:
D(s)
=ns2C1C2β21β13α1α3+sC2gmn3β21β12α1+gmn1gmn2o
(25)
Using (21),(25) becomes:
D(s)=ns2(C1C2β21β13α1α3+gm1gm2µ1µ3
−C2gm3β21β12α1µ2)+s(C2gm3β21β12α1
−gm1gm2µ3−gm1gm2µ1)+gm1gm2}(26)
TABLE 2. T ansis o aspec a ios o he DDCCTA.
o
D(s)=ns2C1C2β21β13α1α3
1−C2gm3β21β12α1µ2−gm1gm2µ1µ3
C1C2β21β13α1α3
+sC2gm3β21β12α11−gm1gm2µ3+gm1gm2µ1
C2gm2β21β12α1
+gm1gm2}(27)
The non-ideal e ec o he ansconduc ance o he DDCCTA
can be made negligible by sa is ying he ollowing condi ion:
C2gm3β21β12α1µ2−gm1gm2µ1µ3
C1C2β21β13α1α3≪1
gm1gm2µ3+gm1gm2µ1
C2gm3β21β12α1≪1)(28)
The na u al equency, bandwid h, and quali y ac o can be
ew i en as:
ωo= gm1gm2
C1C2β21β13α1α3
(29)
ωo
Q=gm3β12
C1β13α3
(30)
Q=1
gm3β12 sC1gm1gm2β13α3
C2β21α1
(31)
The ol age and cu en acking e o s will sligh ly de ia e
he na u al equency, bandwid h, and quali y ac o om he
heo e ical alue. Howe e , since he il e has he abili y o
elec onically une i s own equency, bandwid h and quali y
ac o , any a ia ion in hese pa ame e s caused by PVT
and MC can be co ec ed by he eadjus men o he se ing
cu en .
Conside ing he e ec o pa asi ic pa ame e s o he
capaci o s C1and C2when Vo1and Vo3a e used in
applica ions, he pa asi ic impedances o loads (o pa a-
si ic impedances/capaci ances o he nex s age) will a ec
he cha ac e is ics o he il e ing unc ions. Thus, a high
impedance load is equi ed o connec he ou pu s Vo1and
Vo3. I low impedance loads a e applied, bu e ci cui s a e
needed.
III. SIMULATION RESULTS
To alida e he heo e ical analysis o he p oposed ci cui ,
he DDCCTA and he e sa ile analog il e we e simula ed
in SPICE using 0.18 µm CMOS echnology om TSMC.
The ansis o aspec a ios and capaci o alues a e gi en in
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M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
FIGURE 8. Simula ed magni ude and phase equency esponses o (a) LPF, (b) HPF, (c) BPF, (d) BSP, (e) APF.
Table 2. These we e simila o he DDCC in [43], and he TA
in [44]. The powe supplies we e gi en as VDD = −VSS =
0.5 V and IB=2.5 µA.
Fig. 5 (a) shows he DC ans e cha ac e is ic be ween
Vy1, Vy2 and Vxwhen he inpu s Vy1 and Vy2 we e swep
om –280 mV o 280 mV, and Fig. 5 (b) shows he ol age
e o s. The ol age e o s be ween Vy1and Vxwe e –2.15 mV
a Vy1=0 mV, and -3.6 mV and 1.9 mV a Vy1=–280 mV
and 280 mV, espec i ely. The ol age e o s be ween Vy2
and Vxwe e –2.15 mV a Vy2=0 mV, and –2.22 mV and
–2.08 mV a Vy2=–280 mV and 280 mV, espec i ely.
Mon e Ca lo analysis o he o se ol age a he x- e minal
was in es iga ed. Based on he simula ion o 200 uns, he
co esponding mean alue o o se ol age was ound o be
–2.67 mV.
Fig. 6shows he ansconduc ance cha ac e is ic wi h
di e en se ing cu en s (Ise ). Fig. 6 (a) shows he anscon-
duc ance cha ac e is ic e sus he DC inpu Vin o he TA, and
Fig. 6 (b) shows he ansconduc ance cha ac e is ic e sus
he inpu equency Vin o he TA. No e ha he inpu ol age
ange shown in Fig. 6 (a) is su icien o he p oposed appli-
ca ion, bu his ange can be ex ended by using bulk-d i en
inpu ansis o s ins ead o ga e-d i en ansis o s i
necessa y.
Fig. 7shows he pa asi ic impedances a he x-, z-, o-
e minals o he DDCCTA, which we e 2.67 k, 1.59 M,
and 5.54 M, espec i ely.
Fig. 8shows simula ed magni ude and phase equency
esponses o he LPF, HPF, BPF, BSF, and APF when he
p oposed il e in Fig. 4was gi en as C1=C2=0.37 nF,
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M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e
FIGURE 9. Simula ed equency esponses o (a) LPF, (b) HPF, (c) BPF, (d) BSP, (e) APF wi h di e en biasing cu en Ise 3.
TABLE 3. Compa ison o he p oposed il e ’s p ope ies wi h hose o some p e ious il e s.
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