Ex emely low- ol age low-powe di e en ial
di e ence cu en con eyo using
mul iple-inpu bulk-d i en echnique
KUMNGERN, M.; KHATEB, F.; KULEJ, T.
AEU - In e na ional Jou nal o Elec onics and Communica ions
2020, ol. 123, Augus 2020, pp. 1−11
ISSN: 1434-8411
DOI: h ps://doi.o g/10.1016/j.aeue.2020.153310
Accep ed manusc ip
© 2020. This manusc ip e sion is made a ailable unde he CC-BY-NC-ND 4.0 license
h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/
dspace. u b .cz
Ex emely low- ol age low-powe di e en ial di e ence
cu en con eyo using mul iple-inpu bulk-d i en echnique
Mon ee Kumnge n1, Fabian Kha eb2,3, Tomasz Kulej4
1 Depa men o Telecommunica ions Enginee ing, Facul y o Enginee ing, King
Mongku ’s Ins i u e o Technology Ladk abang, Bangkok 10520, Thailand
2 Depa men o Mic oelec onics, B no Uni e si y o Technology, Technická 10, B no,
Czech Republic
3 Facul y o Biomedical Enginee ing, Czech Technical Uni e si y in P ague, nám. Sí ná 3105,
Kladno, Czech Republic
4 Depa men o Elec ical Enginee ing, Czes ochowa Uni e si y o Technology, 42-201
Czes ochowa, Poland
[email p o ec ed], kha eb@ eec. u b .cz, [email p o ec ed]
Abs ac
In his pape , a new di e en ial di e ence cu en con eyo (DDCC) wi h ul a-low ol age
and low-powe capabili y is p esen ed. The DDCC is designed by using a non- ailed
di e en ial pai wi h mul iple-inpu bulk-d i en MOS ansis o echnique o ob ain a ail- o-
ail inpu common-mode swing and ex emely low supply ol age. The MOS ansis o s
biased in he sub- h eshold egion ha e been used o achie e ex emely low powe
consump ion. The pe o mance o he p oposed DDCC is e alua ed by simula ion esul s
using SPICE p og am and MOS ansis o s pa ame e s p o ided by a s anda d n-well 0.18 µm
CMOS p ocess om TSMC. A ail- o- ail inpu common-mode ange was shown and a high
accu acy was exp essed. The bandwid h was 2.2 kHz and he o al ha monic dis o ion was 1
% o an inpu signal wi h ampli ude o 240 mVp-p, ob ained a supply ol age o 0.3 V and
powe dissipa ion o 28.6 nW. The p oposed DDCC has been used o ealize a six h-o de
low-pass il e o applica ion o elec oca diog am (ECG) applica ions.
Keywo ds:
Di e en ial di e ence cu en con eyo ; sub h eshold echnique; bulk-d i en echnique;
mul iple-inpu bulk-d i en echnique; low ol age and low powe ; high-o de il e ; analog
ci cui
1. In oduc ion
The second gene a ion cu en con eyo (CCII) is a basic building block which can ind many
applica ions in analog signal p ocessing applica ions such as con inuous- ime il e s, signal
gene a o s, nonlinea ci cui s, elec ical elemen s ( esis ance, induc ance, mem is ance)
simula o s/emula o s ci cui s and da a con e e s [1]-[7]. In compa ison o ope a ional
ampli ie (op-amp)-based ci cui s, CCII-based ci cui s o e se e al ad an ages: simple ci cui
s uc u e, alle ia ing he need o bo h loa ing passi e componen s and ma ched esis o s,
wide equency bandwid h, e sa ile and high accu acy in ealizing he in ended
cha ac e is ics, la ge dynamic ange and low supply ol age equi emen [8]. A numbe o
CCIIs is a ailable in open li e a u e [9]-[19]. The ea ly s uc u e o CCII is a con en ional
CCII which o e s h ee e minals, namely y-, x- and z- e minals [9]. The uni y ol age gain
can be ob ained be ween y- and x- e minals while he uni y cu en gain can be ob ained
be ween x- and z- e minals. Howe e , a single CCII may be limi ed o some applica ions:
ob aining di e en ial ol age o cu en inpu signals equi emen s, posi i e and nega i e o
eedback connec ions and alle ia ing he need o loa ing esis o s, e c. The e o e, he e a e
se e al s uc u es o CCIIs which ha e been de eloped o inc ease he pe o mance o
con en ional CCII: di e en ial di e ence cu en con eyo (DDCC) [10], di e en ial ol age
cu en con eyo (DVCC) [11], dual X second gene a ion cu en con eyo (DX-CCII) [12],
ex a X second gene a ion cu en con eyo (EX-CCII) [13], di e en ial second gene a ion
cu en con eyo (DCCII) [14], ully di e en ial second-gene a ion cu en con eyo
(FDCCII) [15]. These s uc u es imp o ed he pe o mance o con en ional CCII, which has
one y- e minal, one x- e minal and one z- e minal, by adding y- e minal and/o x- e minal o
ob ain adding/sub ac ing ol age and cu en di e encing capabili y. This wo k ocuses on
he DDCC which p o ides he ad an ages o con en ional CCII and a i hme ic ope a ion
capabili y o di e en ial di e ence ampli ie (DDA) [16] in o single de ice. Thus, he
con en ional DDCC has h ee y- e minals, one x- e minal and one z- e minal, whe e adding
and sub ac ing ol age can be ob ained h ough wo plus- ype y- e minals and one minus-
ype y- e minal. The DDCC wi h bo h plus- ype and minus- ype y- e minals is con enien o
ealizing posi i e and nega i e eedback applica ions such as nega i e eedback o il e s and
posi i e eedback o oscilla o s. The e a e DDCC based analogue ci cui s ha ha e been
epo ed in li e a u e in ecen yea s, o example, see [17]–[21]. Un o una ely, hese ci cui s
do no p o ide ul a-low ol age and ul a-low powe ope a ion.
A p esen , he analogue ci cui s ope a ing wi h ul a-low supply ol age and ul a-low
powe consump ion a e o g own in e es , due o he ac ha hese ci cui s can be applied in
po able elec onics and biomedical de ices [22]. The analogue signal p ocessing ci cui s such
as con inuous- ime il e s [23]–[25], ampli ie s [26]-[27], p ecision ec i ie s [28]–[29], a e
usually equi ed o applica ions. The e a e many ac i e de ices ope a ing wi h ul a-low
supply ol age and ul a-low powe consump ion a ailable in open li e a u e such as
ope a ional ansconduc ance ampli ie s (OTAs) [30]–[32], cu en con eyo s [33]–[34],
DDA [35] e c.
Focusing on DDCC ope a ed wi h ul a-low supply ol age and ul a-low powe
consump ion, his de ice has been al eady in oduced using di e en MOS echniques [36]–
[41]. Se e al DDCCs based on bulk-d i en (BD) MOS echnique [36], [37], quasi- loa ing
ga e (QFG) [36], BD QFG MOS echnique [36], [38], mul iple-inpu bulk-d i en (MIBD)
QFG MOS echnique [39], [40], mul iple-inpu bulk-d i en (MIBD) [40], ha e been
p oposed. I conside he supply ol age and powe consump ion, he ci cui s in [36], [37] use
0.6 V (±0.3) o supply ol age and consume abou 18.5 µW o powe , he ci cui in [38] uses
a 1 V o supply ol age and consumes 37 µW o powe , he ci cui in [39] uses a 0.5 V o
supply ol age and consumes 1.7 µW and he ci cui s in [40] uses a 0.4 V o supply ol age
and consumes 0.14 µW o powe . I should be no ed in [36]–[40] ha he supply ol age and
powe consump ion, espec i ely, o DDCCs a e scaled down om 1 V o 0.4 V and 37 µW
o 0.14 µW. Un il now, DDCC ope a ing wi h 0.3 V supply ol age and consuming 38 nW o
powe is in oduced [41]. The inpu s age o DDCCs in [36]–[40] is ealized based on
di e en ial s uc u e which needs a ail cu en . A ail cu en is usually implemen ed by a
MOS ansis o , which inc eases he minimum supply ol age by a leas 𝑉𝐷𝑆(𝑠𝑎𝑡). Thus, he
lowes supply ol age o hese DDCCs [36]–[40] is a ound 0.4 V [40]. Unlike he DDCCs in
[36]–[40], he DDCC in [41] is based on a non- ailed di e en ial ampli ie , and is able o
ope a e om supply ol age as low as 0.3 V, which canno be achie ed o a DDCC wi h a
ail cu en di e en ial ampli ie . The ci cui in [41] can ope a e wi h ex emely low supply
ol age, bu shows ela i ely poo accu acy o he ol age/cu en gains, which is he esul o
i s simple s uc u e and low open-loop ol age gain o he y-x ampli ie . This also esul s in
ela i ely low alue o he esis ance Rx, seen om i s x e minal.
In o de o o e come he abo e issues, a high pe o mance DDCC which can ope a e
wi h ul a-low supply ol age and ul a-low powe consump ion has been p oposed in his
pape . The p oposed DDCC can ope a e om supply ol age as low as 0.3-V, which is
possible hanks o he use o non- ailed di e en ial pai in i s inpu s age. The mul iple-inpu
bulk-d i en echnique is also used o educe a numbe o MOS di e en ial pai s. The DDCC
shows ul a-low supply ol age and ul a-low powe consump ion using h ee echniques,
namely, sub h eshold biasing, dynamic h eshold MOS and bulk-d i en MOS echniques. The
bulk-d i en echnique is used in he inpu s age and hanks o his a ail- o- ail inpu common-
mode ange can be ob ained. The pe o mance o he p oposed DDCC was e alua ed by
simula ion, using SPICE and ansis o s pa ame e s o a s anda d n-well 0.18 µm CMOS
p ocess om TSMC. Simula ions showed he bandwid h o 2.2 kHz and he o al ha monic
dis o ion o 1 % o an inpu signal wi h ampli ude o 240 mVp-p, ob ained a supply ol age
o 0.3 V and powe dissipa ion o 28.6 nW. The p oposed DDCC has been used o ealize a
six h-o de low-pass il e o elec oca diog am (ECG) applica ions.
2. P oposed ul a-low ol age MIBD DDCC
In his wo k he mul iple-inpu bulk-d i en (MIBD) MOS ansis o (MOST) echnique, [40]
was applied. The symbol and implemen a ion o he MIBD MOS a e shown in Figs. 1(a) and
Fig. 1(b) espec i ely. The MIBD MOST is a mul iple-inpu de ice which is ealized using
pa allel connec ions o capaci o s CBi and esis o s RLi, whe e i = 1, 2, …, N, while i s ga e
e minal is p ope ly biased wi h DC ol age Vb. Assuming ha an n-well CMOS p ocess was
applied in he design , only he p-channel MOS ansis o s can be con olled in such a way. The
esis o RL should possess high esis ance alue which can be implemen ed using wo
ansis o s ML ope a ing in cu -o egion as shown in Fig. 1(b). The small-signal model o he
MIBD MOST ha has been used o AC small-signal analysis is shown in Fig. 1(c). The gmb is
he bulk ansconduc ance, o is he ou pu esis ance, he capaci ances CBS, CBD, CBSUB a e
espec i ely he pa asi ic capaci ances bulk-sou ce, bulk-d ain and bulk-subs a e. The
capaci ance CMi is he pa asi ic capaci ance be ween ga e and d ain o he ansis o MLi, he
esis ance RMi is he ou pu esis ance o he ansis o MLi while he capaci ance CBi is he
inpu capaci ance.
GVin1
S
D
VinN
BVb
(a)
CB1
S
D
B
Vin1
VinN
CBN
GVb
RL1
RLN
ML
ML

(b)
CBS
VinN CBD
RMN
CMN
CBN
Vin1
CM1
CB1
RM1 B
CBSUB
Sub
D
o
gmbVBS
S
(c)
Fig. 1. MIBD PMOST [40]: (a) symbol o MIBD, (b) MIBD implemen a ion, (c) small-signal
model.
F om Fig. 1(c), assuming 1/CBi << RLi, CMi << CBi he inpu ansconduc ances (𝑔𝑚𝑖) o
MIBD MOST can be gi en [40] by 𝒈𝒎𝒊=𝑪𝑩𝒊
𝑪𝑻𝑶𝑻𝒈𝒎𝒃 (1)
whe e 𝑪𝑻𝑶𝑻 is he o al capaci ance looking in o inpu po which can be gi en by
𝑪𝑻𝑶𝑻=𝑪𝑩𝑺+𝑪𝑩𝑫+𝑪𝑩𝑺𝑼𝑩+∑𝑪𝑴𝒊+
𝑵
𝒊=𝟏 ∑𝑪𝑩𝒊
𝑵
𝒊=𝟏 (2)
The ol age a bulk e minal 𝑽𝑩 can be gi en by
𝑽𝑩≈∑𝑪𝑩𝒊
𝑪𝑻𝑶𝑻𝑽𝒊𝒏,𝒊
𝑵
𝒊=𝟏 (3)
The ela ion be ween he inpu s- e e ed noise powe s o he MIBD MOST 𝒗𝒏,𝒊
𝟐





compa ed o he BD MOST 𝒗𝒏,𝑩
𝟐





can be exp essed by
𝒗𝒏,𝒊
𝟐





=(𝑪𝑻𝑶𝑻
𝑪𝑩,𝒊)𝟐𝒗𝒏,𝑩
𝟐





(4)
whe e 𝑪𝑻𝑶𝑻 is he o al capaci ance looking in o he inpu po . I can be concluded om (4)
ha he inpu - e e ed noise o he MIBD MOST is inc eased by 𝑪𝑻𝑶𝑻 𝑪𝑩,𝒊
⁄, bu he maximum
inpu signal ange is also inc eased wi h he same a io, hence he dynamic ange (DR) is no
a ec ed by his a io.
Fig. 2 shows he ci cui symbol o DDCC and i s po ela ions can be exp essed by
(
𝑰𝒚𝟏
𝑰𝒚𝟐
𝑰𝒚𝟑
𝑽𝒙
𝑰𝒛
)
=
(
𝟎
𝟎
𝟎
𝜷𝟏
𝟎 𝟎
𝟎
𝟎
−𝜷𝟐
𝟎 𝟎
𝟎
𝟎
𝜷𝟑
𝟎 𝟎
𝟎
𝟎
𝟎
𝜶 𝟎
𝟎
𝟎
𝟎
𝟎
)
(
𝑽𝒚𝟏
𝑽𝒚𝟐
𝑽𝒚𝟑
𝑰𝒙
𝑽𝒛
)
(5)
whe e 𝛽1=1−𝜀1𝑣, 𝛽2=1−𝜀2𝑣, 𝛽3=1−𝜀3𝑣 ep esen he ol age gain be ween x-
e minal and y1-, y2-, y3- e minals, espec i ely, 𝛼=1−𝜀𝑖 ep esen s he cu en gain
be ween z- e minal and x- e minal, whe eas 𝜀1𝑣, 𝜀2𝑣, 𝜀3𝑣 (|𝜀1𝑣|, |𝜀2𝑣|, |𝜀3𝑣|≪1 and |𝜀𝑖|≪1)
ep esen espec i ely ol age and cu en acking e o s. Fo ideal case, 𝛽1= 𝛽2= 𝛽3= 𝛼 =1.
DDCC
y1
z
Vy1
Vz
Iz
x
Vx
Ix
y3
Vy3
y2
Vy2
Iy2
Iy3
Iy1
Fig. 2. Elec ical symbol o DDCC.
VSS
VDD
M1y2y3
y3
M5M6
VB
M9M10
M13
M11 M16
VB
IB
MB
VB
VSS
zx
y2
M2M4M3
M7
M12 M8
M14 M17 M18
y1
M15
Fig. 3. P oposed 0.3 V MIBD DDCC.
The p oposed in e nal s uc u e o he DDCC is shown in Fig. 3. The ansis o s, M1-
M6, o he ci cui o m a non- ailed bulk-d i en di e en ial ampli ie [42] which is ealized
using he MIBD MOST echnique o ob ain mul iple-inpu di e en ial ampli ie and o educe
a numbe o MOS ansis o pai s. This non- ailed a chi ec u e p o ides a good CMRR [32],
[35], [42], which can imp o e he accu acy o DDCC when i is connec ed in a nega i e
eedback uni y-gain con igu a ion. The non- ailed di e en ial ampli ie p o ides an ul a-low
supply ol age o he ci cui because he ol age ac oss ail cu en sou ce is absen [35]. The
c oss-coupled ansis o s M7 and M8 a e added o o m a posi i e eedback and p o ide some
inc emen o he DC gain and gain bandwid h p oduc (GBW) pe o mance o di e en ial
ampli ie . These ansis o s will gene a e nega i e conduc ance, i.e. -gm7 and -gm8, o
dec easing he o al conduc ance a he d ain e minals o M9 and M10. The diode-connec ed
ansis o s M9 and M10 a e used o he load o di e en ial ampli ie which dec easing he
o al conduc ance by -gm7 and -gm8 and consequen ly o imp o ing he DC gain and GBW o
di e en ial ampli ie [35].
The ansis o s M11-M14 a e used o mi o he ou pu cu en s o di e en ial ampli ie
and con e ed cu en signals in o a single ol age a he d ain e minals o M13 and M14. The
ou pu s age consis s o ansis o s M15-M18 when ansis o s M15 and M16 wo k as ou pu
ampli ie ope a ing in class-AB, loaded wi h he cu en sou ce using ansis o s M17 and M18.
The high cu en d i ing capabili y can be ob ained by inc easing he quiescen d ain cu en s
o M17 and M18. To ob ain a uni y-gain ol age ollowe , he ou pu e minal (d ain o
ansis o M15) is connec ed o he inpu bulk e minals o ansis o s M2 and M3 hus o ming
a nega i e eedback loop. The uni y-gain cu en ollowe can be ob ained using
complemen a y ansis o s M16 and M18 o mi o he cu en om x- e minal o z- e minal.
The minimum supply ol age 𝑽𝑫𝑫min(𝐢𝐧) o he inpu s age is gi en by
𝑽𝑫𝑫𝐦𝐢𝐧(𝐢𝐧)=𝐦𝐚𝐱(𝑽𝑮𝑺,𝑴𝒊+𝑽𝑫𝑺(𝒔𝒂𝒕),𝑴𝒋) (6)
whe e 𝑖 = 2, 4, 9, 10 and 𝑗 = 1, 3, 5, 6. Le ing 𝑉𝐷𝑆(sa ) = 𝑉𝐷𝑆(𝑠𝑎𝑡),𝑀15−𝑀18, he minimum
supply ol age 𝑉𝐷𝐷min(ou ) o he ou pu s age is app oxima ely 𝑉𝐷𝐷min(ou ) = 2𝑉𝐷𝑆(sa ).
Assume ha ci cui is biased in sub- h eshold egion and le ing |𝑉𝐺𝑆|,𝑀2−𝑀4 = 𝑉𝐺𝑆,𝑀9−𝑀10 =
𝑉𝐷𝑆(sa ), he 𝑽𝑫𝑫min o bo h inpu and ou pu s ages is 2𝑉𝐷𝑆(sa ) which is app oxima ely equal
o 6 o 8 𝑈𝑇 [35], whe e 𝑈𝑇 is abou 26 mV a oom empe a u e.
Assuming pe ec symme y o he i s s age (M1 – M14), he ol age ans e a ios 𝛽1, 𝛽2,
𝛽3, can be exp essed by: 𝜷𝒊=𝑽𝒙
𝑽𝒚𝒊 =𝑨𝒐𝒊
𝟏+𝑨𝒐𝒊 (7)
whe e 𝐴𝑜𝑖 (𝑖 = 1…3) is he open-loop ol age gain o he in e nal di e en ial di e ence
ampli ie (M1-M15 and M17) om 𝑖 - h inpu , ha is gi en by:
𝑨𝒐𝒊=𝒈𝒎𝒊
𝒈𝒅𝒔𝟏𝟑+𝒈𝒅𝒔𝟏𝟒∙𝒈𝒎𝟏𝟓
𝒈𝒅𝒔𝟏𝟒+𝒈𝒅𝒔𝟏𝟓 (8)
whe e, 𝑔𝑑𝑠𝑖 and 𝑔𝑚𝑖 a e espec i ely he ou pu conduc ance and he ga e ansconduc ance
o Mi espec i ely (𝑖 = 1…N). The ansconduc ance gmi ep esen s he ansconduc ance o
he i s s age om i- h inpu , which can be app oxima ed as:
𝒈𝒎𝒊≅𝟐𝒈𝒎𝒃𝟏,𝟑 𝒈𝒎𝟏𝟐,𝟏𝟒/𝒈𝒎𝟗,𝟏𝟎
(𝟏−𝒎)+𝒈∑/𝒈𝒎𝟗,𝟏𝟎∙(𝑪𝑩𝒊
𝑪𝑻𝑶𝑻) (9)
whe e gmbi deno es he bulk ansconduc ance o Mi, m=gm7,8/gm9,10, g= gds1,3 +gds7,8 +gds9,10.
The cu en ans e a io α o he o e all DDCC can be exp essed as:
𝜶=𝒈𝒎𝟏𝟔
𝒈𝒎𝟏𝟓 (10)
The open-loop bandwid h o he in e nal di e en ial-di e ence ampli ie men ioned abo e is
limi ed mainly by he h ee pa asi ic poles associa ed wi h in e nal nodes o his ci cui . The
i s pole is associa ed wi h he d ain node o M9 (M10):
𝒑𝟏=−𝒈𝒎𝟗,𝟏𝟎[(𝟏−𝒎)+𝒈∑/𝒈𝒎𝟗,𝟏𝟎]
𝑪∑𝟏 ∙(𝑪𝑩𝒊
𝑪𝑻𝑶𝑻) (11)
whe e C1 is he o al capaci ance associa ed wi h his node. The second pole is associa ed
wi h he ou pu o he i s gain s age (d ain e minal o M13):
𝒑𝟐=−(𝟏+ 𝒈𝒎𝟏𝟓
𝒈𝒅𝒔𝟏𝟓+𝒈𝒅𝒔𝟏𝟕)𝑪𝒈𝒅𝟏𝟓+𝑪∑𝟐 (12)
whe e C2 is he o al capaci ance associa ed wi h his node, excep Cgd15. The hi d pole is
associa ed wi h he x e minal o he DDCC:
𝒑𝟑=−𝒈𝒎𝟏𝟓
𝑪𝒙 (13)
whe e Cx is he o al capaci ance associa ed wi h he x e minal.
Assuming ha he DDCC is p ope ly equency compensa ed, he poles p1 and p3 should be
loca ed well abo e he 3-dB equency o he y-x ollowe . In such a case, he 3-dB equency
o he ol age gain o his ollowe is app oxima ely equal o he GBW p oduc o he in e nal
di e en ial-di e ence ampli ie men ioned ea lie and can be app oxima ed as:
𝒇𝟑𝒅𝑩=𝒈𝒎𝒊
𝑪𝒈𝒅𝟏𝟓 (14)
The 3-dB equency o he x-z cu en ollowe is also limi ed by he abo e men ioned e ec s,
and o y and z e minals sho ed o g ound o AC signals can be app oxima ed by (14) as
well.
The i- h inpu e e ed he mal noise o he p oposed DDCC can be app oxima ed by:
𝑣𝑛2



=1
2∙8𝑘𝑇
3(𝑔𝑚𝑏1,3
2)[𝑔𝑚1,3+(𝑔𝑚2,4+𝑔𝑚5,6)(𝑔𝑚1,3
𝑔𝑚2,4)2+𝑔𝑚7,8+𝑔𝑚9,10+(1−
𝑚)2(𝑔𝑚9,10
𝑔𝑚12,14)2(𝑔𝑚12,14+𝑔𝑚11,13)](𝐶𝑇𝑂𝑇
𝐶𝐵,𝑖)2 (15)
I is wo h no ing, ha he op imum noise pe o mance is ob ained when all ansis o s M1-M4
a e iden ical [42].
The inpu esis ance seen om he x- e minal can be app oxima ed as:
𝑹𝒙≈𝒓𝒅𝒔𝟏𝟒‖𝒓𝒅𝒔𝟏𝟓
𝑨𝒐𝒊 (16)
whe e i is assumed ha Aoi is iden ical o e e y i=1..3.
Finally, he ou pu esis ance o he DDCC seen om he z- e minal is gi en by:
DDCC
y1z
x
y3
y2
R1
R2
DDCC
y1z
x
y3
y2
C1
R2
C2
DDCC
y1z
x
y3
y2
R3
R4
DDCC
y1z
x
y3
y2
C3
R4
C4
DDCC
y1z
x
y3
y2
R5
R6
DDCC
y1z
x
y3
y2
C5
R6
C6
Vou -
Vou +
Vin+
Vin-
Fig. 9. Six h-o de Bu e wo h low-pass il e .
The six h-o de maximally la low-pass il e was designed by cascading h ee
second-o de low-pass il e s, which a e a anged as ollows: s age 1, equency scaling ac o
(FSF) = 1, Q = 0.518: s age 2, FSD = 1, Q = 0.707: s age 3, FSF = 1, Q = 1.932. The e o e,
he no malized ans e unc ion o six h-o de Bu e wo h low-pass il e is:
𝑉𝑜𝑢𝑡(𝑠)
𝑉𝑖𝑛(𝑠) =( 1
𝑠2+1.93𝑠+1)( 1
𝑠2+1.414𝑠+1)( 1
𝑠2+0.518𝑠+1) (19)
The p oposed six h-o de Bu e wo h low-pass il e was designed wi h he cu -o
equency 𝑓𝑜 o 100 Hz. The i s s age, second s age and he hi d s age we e designed wi h
he cu -o equencies o 70 Hz, 100 Hz and 148 Hz, espec i ely. The alue o capaci ances
C1 and C2 o each s age will be equalled and he alue o esis ances R1 and R2 o each s age
will be used o adjus he alue o quali y ac o . Thus he il e in Fig. 9 was designed as
ollows: 𝐶1 = 𝐶2 = 300 pF, 𝑅1 = 5.8 M, 𝑅2 = 3 M, 𝐶3 = 𝐶4 = 220 pF, 𝑅3 = 5.8 M, 𝑅4 =
2.5 M, 𝐶5 = 𝐶6 = 220 pF, 𝑅5 = 1.8 M, 𝑅6 = 14 M. In p ac ice, hese high alues o
esis ances and la ge alues o capaci ance can be implemen ed o -chip. The high alues o
esis ances we e used because he high linea i y and wide inpu ange o il e can be
ob ained.

1.0 10 100 1.0k 10k
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
20
F equency, Hz
Gain, dB
P oposed
Theo e ical
Fig. 10. Simula ed equency esponse o he six h-o de Bu e wo h low-pass il e .
1.0 10 100 1.0k 10k
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
20
F equency, Hz
Gain, dB
Theo e ical
Temp.=0-75°C
10 100 300
-10.0
-7.5
-5.0
-2.5
0
F equency, Hz
Gain, dB
Zooming
Fig. 11. Simula ed equency esponse o he six h-o de Bu e wo h low-pass il e o
di e en empe a u e.
Fig. 10 shows he simula ed equency esponses o he p oposed six h-o de
Bu e wo h low-pass il e . The cu -o equency o he il e was 99 Hz and he DC ol age
gain was -2.4 dB while he il e consumed 172 nW o powe . The simula ed equency
esponse was also compa ed wi h heo e ical cu e. Fig. 11 shows he a ia ions o he
equency esponse o empe a u e a ied om 0 o 75 °C. The simula ion esul shows ha
he DC ol age gain a ied be ween -2.12 dB and -4.34 dB, whe eas he a ia ions o he cu -
o equency o he il e we e negligible.
Fig. 12 shows he simula ed ansien esponse o he il e when he 10 Hz sinusoidal
inpu ol age signal wi h he ampli ude o 240 mV (peak- o-peak) was applied. This esul can
be shown he ope a ion o inpu ol age swing o 240 mV (peak- o-peak) wi h he o al
ha monic dis o ion (THD) o 1.09 %.
To es he linea i y o he p oposed il e , a single one es and wo- one es ha e been
in es iga ed. Fig. 13 shows he esul s o he single one es o he p oposed il e when he
inpu equency o 10 Hz was supplied whe eas ampli ude o inpu sinusoidal ol age was
a ied. The THD was 1.09 % when he ampli ude o inpu ol age was inc eased o 240 mV
(peak- o-peak). The wo- one es has been in es iga ed by applying wo inpu equencies o
50 Hz and 60 Hz in o he ci cui and he ampli ude o inpu sinusoidal ol ages was a ied.
The simula ed 3 d in e -modula ion dis o ion (IMD) was shown in Fig. 14. I can be ound
ha ampli ude o he ou pu signal o a 2% 3 d IMD was 50 mV while he ampli ude o he
inpu signal was 140 mV (peak- o-peak).
050 100 150 200 250 300 350 400 450 500
-160
-120
-80
-40
0
40
80
120
160
Time, ms
Vol age, mV
Vin
Vou
Fig. 12. Simula ed
ansien esponse wi h inpu ol age swing.
Fig. 13. THD a ia ion e sus ampli ude o he inpu sinusoidal ol age a 10 Hz
.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
050 100 150 200 250 300
THD, %
Vin (peak- o-peak), mV
Fig. 14
. The hi d-o de IMD e sus he inpu ol age.
In case o noise es ing, he p oposed
six h-o de Bu e wo h low-pass il e was
simula ed o e alua e he in eg a ed inpu e e ence noise o he bandwid h o 100 Hz. F om
ou simula ion, i can be ound ha an inpu - e e ed noise ol age was 338 µV ms
whe eas an
ou pu -
e e ed noise ol age was 238 µV ms. I a single- one es has been used o de ine he
dynamic ange (DR), a THD o 1.09 % (Vin = 84.8 mV ms), he DR was 48 dB.
The p oposed
six h-o de low-pass il e has been compa ed wi h p e ious wo ks [23],
[24], [43]-[45] as shown in Table II. I can be shown ha he p oposed DDCC can be applied
o biomedical sys ems because he ci cui can ope a e wi h ul a-low supply ol age and ul a-
low powe consump ion. In o de o e alua e and compa e he pe o mance o he il e s in
Table II, he ollowing s anda d Figu e o Me i (FoM) [46] was used
𝐹𝑜𝑀= 𝑃×𝑉𝐷𝐷
𝑁×𝑓𝑐×𝐷𝑅 (20)
0.0
0.5
1.0
1.5
2.0
2.5
25 50 75 100 125 150
3 d IMD, %
Vin (peak- o-peak), mV
Table II. Compa ison o he p oposed il e o some p e ious six h-o de low-pass il e s.
This wo k
2000 [43]
2014 [44]
2019 [23]
2019 [24]
2019 [45]
Technology [m]
0.18
0.8
0.35
0.13
0.18
20
Supply ol age [V]
0.3
±1.5
0.5
0.25
1
10
Topology
CMOS
CMOS
CMOS
CMOS
CMOS
a-IGZO TFT
Numbe o ac i e
6-DDCC
8-OTA
50-MOS
5-FDDTA, 1-
OTA
6-OTA
3-DDA
Numbe o passi e
9-R & 6-C
6-C
6-C
5-C
5-C
15-C, 24-MSW†
Fil e o de
6 h LP
(Bu e wo h)
6 h LP
(Bu e wo h)
6 h LP
(Bessel)
5 h LP
(Bu e wo h)
5 h LP
(Bu e wo h)
6 h LP
(Bu e wo h)
A chi ec u e
Fully di .
Single-ended
Single-ended
Fully di .
Fully di .
Fully di .
Bandwid h [Hz]
99
2.4
2.4
100
250
272
Noise [V ms]
339
<50
0.43E-12 A*
4.7
134
-
DC gain [dB]
-2.5
-10
0
~ -6
-7
-0.65
Powe consump ion [W]
172E-9
10E-6
7.21E-9
603E-9
41E-9
0.537E-3
Dynamic ange [dB]
48@1%THD
[email p o ec ed]%THD
51.1@4%THD
57
61.2
-
FOM
1.76E-12
3.47E-8
4.9E-12
5.29E-12
5.47E-13
-
No e: * cu en -mode il e , †
MSW = MOS swi ch,
a-IGZO TFT = amo phous indium-gallium-zinc oxide (a-IGZO) hin- ilm ansis o (TFT)
DDA = di e en ial di e ence ampli ie , R = esis o , C = capaci o
FDDTA = ully di e en ial di e ence ansconduc ance ampli ie ,
OTA = ope a ional ansconduc ance ampli ie
5. Conclusion
This pape p esen s a new di e en ial di e ence cu en con eyo (DDCC) wi h ul a-low
ol age and low-powe capabili y o applica ion o biomedical sys ems. The DDCC is
designed by using a non- ailed di e en ial pai wi h mul iple-inpu bulk-d i en MOS
ansis o echnique o ob ain a ail- o- ail inpu common-mode ange and ex emely low
supply ol age. The MOS ansis o s biased in he sub- h eshold egion ha e been used o
achie e ul a-low powe consump ion. The p oposed DDCC is capable o ope a ing wi h a
supply ol age as low as 0.3 V and consumes abou 28.6 nW o s a ic powe . The p oposed
DDCC has been used o ealize a six h-o de Bu e wo h low-pass il e o applica ion o
elec oca diog am sys ems as applica ion example. The pe o mance o he p oposed DDCC
is e alua ed by simula ion esul s using SPICE p og am and MOS ansis o s pa ame e s
p o ided by a s anda d n-well 0.18 µm CMOS p ocess om TSMC.

Acknowledgmen
This wo k was suppo ed by Facul y o Enginee ing, King Mongku ’s Ins i u e o Technology
Ladk abang unde g an 2563-02-01-012. Resea ch desc ibed in his pape was inanced by
he Na ional Sus ainabili y P og am unde g an LO1401. Fo he esea ch, in as uc u e o
he SIX Cen e was used.
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