Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 32
0
~
32
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.8
700
3
20
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Modelling and Design of Inve
rter Threshold Quantization
Bas
e
d Current Comparat
or using Artifi
ci
al Neu
r
al
Net
w
ork
s
V
eepsa
Bha
t
i
a
*
,
N
e
et
a Pandey
**
, A
s
o
k
Bha
t
t
a
cha
r
yy
a**
*Indira
Gandh
i Delhi Techn
i
cal Univ
ersity
for
Women, Delhi, I
ndia
**Delhi
Tech
nological University
, Delh
i, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 1, 2015
R
e
vi
sed Oct
4,
2
0
1
5
Accepted Oct 21, 2015
P
e
rform
ance of
a M
O
S
bas
e
d ci
rcuit
is
highly
influenced b
y
th
e transisto
r
dimensions chosen for that circui
t. Thus, pr
oper dimension
i
ng of th
e
tra
n
sistors play
s
a
key
role
in de
te
rm
ining its overall performance. While
choosing the dimension is critical, it
is
equally
d
i
fficult, prim
arily
du
e
to
com
p
lex m
a
the
m
atica
l
form
ulat
ions that com
e
i
n
to pla
y
when
m
oving into
the subm
icron le
vel.
The dr
ain c
u
rrent is th
e m
o
st affec
t
ed p
a
ra
m
e
ter whic
h
in turn
aff
ects
al
l oth
e
r par
a
m
e
te
rs. Thus
,
ther
e
is
a
cons
tant
ques
t
to
com
e
u
p
with techniques
and procedure
to si
mplif
y
the dimensioning
pr
ocess
while
still keeping th
e param
e
ters under check
.
This stu
d
y
presen
ts one
such novel
techn
i
que
to es
t
i
m
a
te
the
trans
i
s
t
or dim
e
ns
ions
for a
curr
ent
com
p
arato
r
structure, using
the artificial neural
networks approach.
The ap
proach
us
es
Multila
ye
r perc
eptrons as the artif
ici
a
l neur
al
network archit
ectur
es. Th
e
techn
i
que
involv
e
s a two step pr
ocess. In
the f
i
rst step
, tr
aining
and test d
a
ta
are obtained b
y
doing SPICE simulations
of modelled cir
c
uit us
ing 0.18
μ
m
TSMC CMOS t
echnolog
y
par
a
meters. In
the second step, th
is training and
test da
ta
is ap
plied
to th
e de
velope
d n
e
ural
network ar
chitecture using
MATLAB R2007b.
Keyword:
Artificial n
e
u
r
al n
e
two
r
k
s
Aspe
ct ratio el
e
m
ents
CMOS inv
e
rter
Current c
o
m
p
arator
Mu
ltilayer p
e
rcep
tro
n
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Veepsa Bhatia,
Depa
rt
m
e
nt
of
El
ect
roni
cs
an
d C
o
m
m
uni
cati
on
En
gi
nee
r
i
n
g,
In
di
ra
Ga
nd
hi
Del
h
t
i
Tec
hni
c
a
l
Uni
v
ersi
t
y
f
o
r
Wom
e
n,
Kashm
e
re Gat
e
, Del
h
i,
In
dia.
Em
a
il: v
eep
sa@g
m
a
il.co
m
1.
INTRODUCTION
Th
e last few y
ears hav
e
witnessed
a trem
end
o
u
s
g
r
owth
i
n
th
e
field
o
f
i
n
tellig
en
t system
s su
ch
as
fuzzy
l
o
gi
c an
d ex
pert
sy
st
em
s. Inspi
r
ed
b
y
bi
ol
ogi
cal
ne
ural
net
w
o
r
k
s
,
one s
u
c
h
succe
ss has bee
n
ac
hi
eve
d
in
evo
l
u
tion
of artificial n
e
u
r
al n
e
tworks (ANNs) [1
].
ANNs are ch
aract
erized
b
y
th
eir
d
i
stin
ctiv
e capab
ilities
o
f
ex
h
i
b
itin
g
massiv
e
p
a
rall
elis
m
,
g
e
n
e
rali
zatio
n
ab
ility an
d
b
e
ing
g
ood
fun
c
tion
app
r
ox
im
a
t
o
r
s. Th
is
rend
ers
th
em u
s
efu
l
for so
lv
i
n
g
a v
a
riety o
f
p
r
ob
lem
s
in
p
a
ttern
reco
gn
itio
n, pred
ictio
n
,
o
p
tim
i
zatio
n
and
asso
ciativ
e
me
m
o
ry [2
]-[4]. Add
ition
a
lly, th
ey are also
bein
g
em
p
l
o
y
ed in
circu
it m
o
d
e
llin
g
[5
].
Trad
ition
a
l app
r
o
a
ch
fo
r determin
atio
n
o
f
t
h
e
d
e
sign
param
e
ters o
f
an
y circu
it em
p
l
o
y
s
math
e
m
atica
l
m
o
d
e
llin
g
an
d an
alysis o
f
variou
s equ
a
tion
s
. Th
is pro
c
ed
ure is
qu
iet co
m
p
lex
an
d
ar
duo
us
especi
al
l
y
whe
n
w
o
r
k
i
n
g i
n
subm
i
c
ron t
e
c
h
n
o
l
o
gy
w
h
er
e
t
h
e de
pen
d
e
n
ce of
vari
ous
ci
rcui
t
param
e
t
e
rs i
s
go
ve
rne
d
by
com
p
l
e
x and
no
n
-
l
i
n
ear eq
u
a
t
i
ons. A
n
al
t
e
rn
ativ
e ap
proach
to
redu
ce th
is co
m
p
lex
ity
is
p
r
ov
id
ed
b
y
artificial n
e
u
r
al n
e
two
r
k
(ANN) wh
ere th
e
n
e
two
r
k
is train
e
d
to
im
ita
te
th
e b
e
h
a
v
i
ou
r o
f
the
ci
rcui
t
bei
n
g
d
e
si
gne
d.
Recently, ANNs ha
ve bee
n
used to m
o
del analog
a
n
d digital circuits, specifically foc
u
ssi
ng
on
det
e
rm
i
n
at
i
on of t
r
a
n
si
st
o
r
di
m
e
nsi
ons
, as i
n
[
6
]
-
[
9
]
.
F
u
rt
her
,
i
n
[
1
0]
, t
h
e swi
t
c
hi
n
g
c
h
aract
eri
s
t
i
c
s of
C
M
OS
i
nve
rt
er ha
ve a
l
so bee
n
m
ode
l
l
e
d whi
l
e
M
i
cro
w
a
v
e t
r
an
si
st
ors a
n
d ci
rcui
t
m
odel
l
i
ng hav
e
been el
uci
d
at
ed i
n
[1
1]
-[
1
2
]
.
I
n
[
1
3]
t
h
e s
p
ee
d c
o
nt
r
o
l
t
h
e s
p
ee
d
o
f
a
D
o
u
b
l
e
S
t
ar I
n
d
u
ct
i
o
n
M
o
t
o
r
ha
s
bee
n
m
odel
l
e
d
In
d
u
ct
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
32
0 – 32
9
32
1
Mo
to
r. Furth
e
r, in
[14
]
a so
lu
tion
for OTA circu
its mo
d
e
lling
h
a
s
b
een
p
r
o
p
o
s
ed. An
illu
stratio
n
o
f
t
echn
o
l
o
gy
i
n
d
e
pen
d
e
n
t
ci
rc
ui
t
s
si
zi
ng
f
o
r
ba
si
c anal
o
g
ci
rc
ui
t
s
has
bee
n
d
e
scri
be
d i
n
[
1
5
]
.
In
t
h
i
s
pa
per,
a
s
a fi
rst
,
a
cu
rr
ent
c
o
m
p
arat
or
st
ruct
ure
ha
s
been
m
odel
l
e
d
an
d t
r
a
n
si
st
o
r
di
m
e
nsi
ons
o
f
th
e co
n
s
titu
en
t tr
an
sisto
r
s ar
e d
e
ter
m
i
n
ed
u
s
ing
ANN
. Two
ANN ar
ch
itectu
r
es h
a
v
e
b
e
en
used
t
o
separat
e
l
y
m
odel
t
h
e di
f
f
ere
n
t
st
ages
of t
h
e c
u
r
r
ent
c
o
m
p
ara
t
or.
The t
r
ai
ni
n
g
a
nd t
e
st
dat
a
have
bee
n
obt
a
i
ned
fr
om
t
h
e SPIC
E
sim
u
l
a
t
i
ons of t
h
e ci
rc
ui
t
u
s
i
ng
0.
18
μ
m
TSM
C
param
e
t
e
rs. The
neu
r
a
l
net
w
o
r
k t
o
ol
bo
x o
f
M
A
TLAB
R
2
00
7
b
has
bee
n
use
d
t
o
t
r
ai
n
AN
N
arc
h
i
t
ect
ures.
T
h
e t
r
ai
ne
d
net
s
ha
ve
bee
n
si
m
u
l
a
t
e
d i
n
M
A
TLAB
t
o
obt
ai
n t
h
e t
r
a
n
si
st
o
r
di
m
e
nsi
ons
whi
c
h ar
e sub
s
eq
ue
nt
l
y
used
fo
r ve
ri
fy
i
ng t
h
e cu
rre
nt
co
m
p
arato
r
fu
nctio
n
a
lity
an
d d
e
term
in
in
g
v
a
riou
s p
e
rform
a
n
ce p
a
ram
e
ters.
2.
C
URR
EN
T COM
P
AR
A
T
OR
A curre
nt comparat
or is a ve
ry popular current m
ode
circuit that com
p
ares
an
inpu
t curren
t
with
a
refe
rence c
u
r
r
e
n
t
and
pr
o
v
i
d
e
s
out
p
u
t
as v
o
l
t
a
ge [1
6]
–[
24
]. It essen
tially
calcu
lates th
e d
i
fferen
ce
b
e
tween
th
e inp
u
t
and
t
h
e referen
ce cu
rren
t and
d
e
picts th
e resu
lts as a
v
o
ltag
e
lev
e
l at th
e
ou
tp
u
t
. Howev
e
r, th
ese
circuits [16]-[24] are not com
p
lete
curre
nt c
o
m
p
arators as
they lack th
e di
ffe
re
nci
n
g st
ruct
ure an
d di
r
ect
ly
pr
ocess t
h
e
pr
e-cal
cul
a
t
e
d
di
ffe
rence
bet
w
e
e
n t
h
e
i
n
put
a
n
d referen
ce cu
rren
ts to
ob
tain
th
e
ou
tpu
t
vo
ltage
l
e
vel
.
Th
us, f
o
r t
h
e st
r
u
ct
u
r
es of [
1
6]
–[
2
4
]
t
o
be
co
n
s
i
d
ered
fu
lly functio
n
a
l cu
rren
t co
m
p
arato
r
s, it is
necessa
ry
to i
n
clu
d
e a
cu
rre
nt di
ffe
renci
n
g
struct
ure
at t
h
e input. T
h
e
current
com
p
arator em
ployed a
nd
m
o
d
e
lled
in
this p
a
p
e
r elimi
n
ates th
is drawb
a
ck
an
d
u
s
es an
in
tern
ally g
e
n
e
rated
referen
ce
for com
p
ariso
n
with
th
e inp
u
t
cu
rren
t, th
ereby eli
m
in
atin
g
t
h
e
n
eed
of an
ad
d
ition
a
l cu
rren
t d
i
fferen
c
i
n
g stru
ct
u
r
e.
2.1. Modeled Current Com
p
ar
ator
Thi
s
m
odel
l
e
d
cu
rre
nt
c
o
m
p
arat
or
i
s
s
h
ow
n i
n
Fi
gu
re
1.
It
c
o
m
p
ri
ses
of
t
h
r
ee st
a
g
e
s
nam
e
l
y
a
cu
rren
t to
vo
lt
ag
e con
v
e
rter (Stag
e
1); a symme
tric in
v
e
rt
er (Stag
e
2
)
and
an
add
ition
a
l in
v
e
rter
(Stage 3
)
.
A
bri
e
f
de
scri
pt
i
o
n
of eac
h
st
age
i
s
as f
o
l
l
o
ws:
St
age
1 c
o
m
p
rising
a
diode c
o
nnected NM
OS
(Mn1) is designe
d
t
o
p
r
o
v
i
d
e
a
n
out
put
v
o
l
t
a
ge (
V
GS,ref
) eq
ual
t
o
hal
f
o
f
vol
t
a
ge s
w
i
n
g o
f
the fo
llowing
sy
mmetric in
v
e
rter for
gi
ve
n
refe
renc
e cu
rre
nt
(
I
ref
).
The i
n
p
u
t c
u
r
r
e
nt w
h
e
n
e
v
er
d
i
ffers
f
r
om
I
ref
, a
d
e
v
i
ation
in
th
e valu
e
fro
m
V
GS,ref
i
s
obse
r
ved at
t
h
e gat
e
of M
n
1
.
T
h
e St
age
2 c
o
m
p
ri
si
ng
M
p
2
-
M
n
2 i
s
a
sym
m
et
ri
cal
C
M
OS i
n
vert
e
r
wi
t
h
switch
i
ng
vo
ltag
e
equ
a
l to
V
GS,ref
.
It
pr
o
v
i
d
e
s
an out
put
eq
ual
t
o
V
GS,ref
for an in
p
u
t of
V
GS,ref
.
Any
de
vi
at
i
o
n
fr
om
V
GS,ref
at
input of Sta
g
e
2 ca
uses a
larger v
a
riatio
n at
its o
u
t
pu
t.
Thus when input c
u
rrent
(
I
in
) <
I
re
f
th
e
out
put
o
f
St
ag
e 1
bec
o
m
e
s l
e
ss t
h
a
n
V
GS,ref
whi
c
h
i
n
t
u
r
n
m
a
kes
o
u
t
p
ut
of St
age 2 hi
g
h
. Si
m
i
l
a
rl
y
when
I
in
>
I
ref
t
h
e
o
u
t
p
ut
of St
age 2 bec
o
m
e
s
l
o
w.
Stag
e 3 co
m
p
risin
g
M
p
3
-
M
n
3
i
s
an
ad
d
ition
a
l
CMOS inv
e
rt
er th
at
pr
o
v
i
d
es
rai
l
t
o
rai
l
swi
n
g
at
t
h
e
out
put
n
ode
.
Fi
gu
re
1.
M
o
d
e
l
l
e
d C
u
r
r
e
n
t
C
o
m
p
arat
or
Fo
r m
o
d
e
lling th
e circu
it, asp
ect ratio
o
f
t
h
e tran
si
st
or
s
use
d
i
n
St
a
g
es
1 an
d
2 can
be cal
cul
a
t
e
d
usi
n
g t
h
e f
o
l
l
o
wi
n
g
m
e
t
hod:
The t
r
an
si
st
or
M
n1,
bei
n
g di
ode c
o
n
n
ect
e
d
,
ope
rat
e
s i
n
sat
u
rat
i
o
n regi
o
n
.
The re
fere
nc
e curre
nt
I
ref
is related
t
o
th
e g
a
te to so
urce
v
o
ltag
e
V
GS,ref
by
,
,
(
1
)
whe
r
e t
h
e sy
m
bol
s
ha
ve t
h
ei
r
usu
a
l
m
eani
n
g
s
. He
nce
aspec
t
rat
i
o
f
o
r M
n
1
i
s
gi
ven
by
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
l
i
ng a
n
d
Desi
g
n
of
I
n
ve
rt
er
Thre
sh
ol
d
Qu
a
n
t
i
z
at
i
o
n
B
a
se
d
C
u
r
r
ent
C
o
m
p
a
r
at
or
…
(Veep
sa Bha
t
ia
)
32
2
,
,
(
2
)
Th
e inv
e
rter i
n
Stag
e 2
is sy
mmetric so
tran
sistors Mp
2 an
d
Mn2
also o
p
e
rate in
satu
ration
reg
i
on at i
t
s
swi
t
c
hi
n
g
t
h
res
hol
d
(
V
GS,ref
). E
quat
i
n
g
d
r
ai
n c
u
r
r
ent
s
o
f
M
p
2
an
d M
n
2
gi
ve
s
,
,
,
,
(3
)
Usin
g
,
,
a
n
d
,
,
fo
r stage
2
,
(3
) m
odi
fies to
2
2
,0
,
,
,
22
22
no
x
p
o
x
GS
r
e
f
T
n
G
S
r
e
f
D
D
T
o
p
Mn
Mp
CW
CW
XV
V
V
V
V
LL
(4
)
or
22
,0
,
,
,
22
n
G
Sr
e
f
T
n
p
G
Sr
e
f
D
D
T
o
p
Mn
Mp
WW
VV
VV
V
LL
(5
)
or
,
1
,
,
(
6
)
The
val
u
e
o
f
s
w
i
t
c
hi
n
g
t
h
res
hol
d
vol
t
a
g
e
of
t
h
e st
a
g
e
2 C
M
OS
In
vert
e
r
i
s
gi
ven
by
,
,
,
(
7
)
The
as
pect ratio for
Mn2 and Mp2 are related
as:
,
,
,
,
(
8
)
Th
e asp
ect rati
o
of CMOS inv
e
rter in
Stag
e 3
is k
e
p
t
id
entical to
th
e one u
s
ed
in
Stage 2
for th
e sak
e
of
regu
larity.
2.
2. R
o
l
e
o
f
N
e
ural
Netw
or
ks
The m
e
thod
outlined in
section
2.1 for as
pect ratio
s cal
culation is effective for ha
nd calculation.
Wh
en
wo
rk
ing with
sm
all g
e
o
m
etry d
e
v
i
ces, th
is m
e
th
o
d
does
not
provide correct
estimatio
n
for asp
e
ct ratio
due
t
o
c
o
m
p
l
e
x
no
nl
i
n
ea
r de
pen
d
e
n
ce
of
d
r
ai
n cu
rre
nt
(
I
D
) o
n
gate-s
o
u
rc
e(
V
GS
), drain-s
o
urce(
V
DS
)
an
d bu
lk
-
source (
V
BS
)
v
o
l
t
a
ges. T
h
e
ge
n
e
ral
ex
pre
ssi
o
n
f
o
r
d
r
ai
n c
u
r
r
e
n
t
i
n
l
e
vel
3 [
2
5]
m
odel
i
s
gi
v
e
n
by
2
|
Φ
|
2
|
Φ
|
2
|
Φ
|
(9
)
w
h
er
e
,
∆
a
n
d
t
h
e
sy
m
bol
s
h
a
ve t
h
ei
r
u
s
ual
m
eani
ng.
T
h
e
drai
n c
u
r
r
e
n
t
o
f
(9) is sim
p
lified
for lin
ear an
d satu
ration
reg
i
o
n
s
resp
ectiv
el
y as
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
32
0 – 32
9
32
3
2
|
Φ
|
2
|
Φ
|
2
|
Φ
|
(1
1)
whe
r
e
F
re
p
r
ese
n
t
s
depe
n
d
en
c
e
o
f
t
h
e
b
u
l
k
depl
et
i
o
n c
h
a
r
ge
o
n
t
h
e t
h
re
e di
m
e
nsi
onal
ge
om
et
ry
of t
h
e
M
O
SFET
a
n
d
i
s
gi
ve
n
by
∙
|
|
(
1
2
)
Here
, pa
ram
e
ters F
s
a
nd F
n
are
em
pi
ri
cal
para
m
e
t
e
rs and are
i
n
fl
ue
nce
d
by
sho
r
t
cha
n
nel
and
nar
r
o
w
channel effects
res
p
ectively.
It is clear from (9)
–
(12) t
h
at the nonlinear
and
com
p
l
e
x d
e
pen
d
e
n
ce of drai
n
cur
r
ent
on
va
ri
o
u
s pa
ram
e
ters m
a
kes exact
aspect
rat
i
o
s det
e
rm
i
n
at
i
on t
o
o l
a
b
o
r
i
ous t
h
r
o
u
g
h
ha
n
d
cal
cul
a
t
i
ons. T
h
e ne
ural
net
w
or
ks,
wi
t
h
(
9
)
– (
1
2
)
as f
unct
i
on a
p
p
r
o
x
i
m
at
ors, ca
n h
o
w
e
v
er
be em
pl
oy
ed t
o
provide suffici
ently reliable
and acc
urate results. The cu
rrent piece of work illustrate
s the use of ANNs i
n
determ
ining the cha
nnel le
ngth a
n
d wi
dth
of
each
of the t
r
a
n
sistors in Figure
1.
3.
CO
NST
R
U
C
T
ION OF A
N
N
MO
DELS
A ne
u
r
o
n
i
s
o
n
e o
f
t
h
e
basi
c el
em
ent
s
i
n
AN
N m
odel
whi
c
h com
p
ri
s
e
s of
set
o
f
i
n
put
s
,
wei
ght
coef
fi
ci
ent
s
, al
so
kn
o
w
n
as s
y
napt
i
c
wei
ght
s, an
d a
n
act
i
v
at
i
on
fu
nct
i
o
n
[1
5]
.
Neu
r
o
n
s
fo
rm
t
h
e basi
s
of
a
n
in
pu
t
layer
t
h
at h
a
s sen
s
ory u
n
its to
co
llect th
e in
fo
rm
ati
o
n
fro
m its
en
v
i
ro
n
m
en
t, an
o
u
t
p
u
t
layer an
d
a
num
ber o
f
opt
i
onal
i
n
t
e
rm
edi
a
t
e
l
a
y
e
r(s) c
a
l
l
e
d hi
dde
n l
a
y
e
rs. These
hi
d
d
en l
a
y
e
rs per
f
o
r
m
t
h
e t
a
sk o
f
trans
f
orm
i
ng input space t
o
ou
tput space.
T
h
e net
w
ork is t
r
aine
d usi
ng
se
ts of inputs
with
their c
o
rresponding
o
u
t
p
u
t
s t
h
rou
g
h
a trai
n
i
ng
alg
o
rith
m
.
Here Mu
ltilaye
r Percep
tron
(MLP) algorith
m
i
s
u
s
ed
for
find
ing
opt
i
m
i
zed aspe
ct
rat
i
o
s
of
t
h
e
devi
ces
use
d
i
n
Fi
g
u
re
1.
The MLP is t
h
e m
o
st common arc
h
itecture
em
ploy
ed f
o
r
A
NN
[
26]
a
n
d ca
n i
m
pl
em
ent
ar
bi
t
r
ary
m
a
ppi
n
g
s bet
w
een i
n
p
u
t
an
d o
u
t
p
ut
[2
7]
-
[
3
0
]
.
It
uses
b
ack p
r
o
p
a
g
at
i
o
n as l
earni
ng
al
go
ri
t
h
m
wherei
n t
h
e
sy
napt
i
c
st
re
n
g
t
h
s
are
sy
st
em
at
i
call
y
m
odi
fi
ed s
o
t
h
at
net
w
or
k a
p
pr
o
x
i
m
at
es t
h
e
d
e
si
red
res
p
ons
e m
o
re
closely. The
MLP arc
h
itecture is s
h
own i
n
Figure 2
where
Li, Lj(j =
1,
2,.
.
k)
,
Lo
re
present
respecti
v
ely the
in
pu
t layer,
k
h
i
dd
en layers
an
d
t
h
e
o
u
t
p
u
t layer. Th
e i
n
pu
t layer receiv
es th
e i
n
put v
a
riab
les
u
s
ed
for
cl
assi
fi
cat
i
on.
The
net
w
or
k
p
r
oces
ses t
h
e i
n
put
dat
a
p
r
ese
n
t
at
i
n
p
u
t
l
a
y
e
r an
d cal
c
u
l
a
t
i
ons a
r
e
per
f
o
r
m
e
d i
n
subseque
nt layers until an output is
reached at every output node. Thi
s
out
put is subse
que
ntly com
p
ared
agai
nst
desi
re
d
o
u
t
p
ut
an
d e
r
r
o
r i
s
com
puted. The error is t
h
en propa
g
ate
d
backwa
rds
through the ANN a
nd
is u
s
ed
to adjust th
e syn
a
p
tic
weigh
t
s th
at co
n
t
ro
l t
h
e
net
w
o
r
k
.
The
t
r
ai
ni
n
g
pr
oce
d
u
r
e
i
s
desc
ri
be
d
w
i
t
h
t
h
e
hel
p
o
f
Fi
gu
re 3.
Fi
gu
re
2.
M
L
P
St
r
u
ct
ure
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
l
i
ng a
n
d
Desi
g
n
of
I
n
ve
rt
er
Thre
sh
ol
d
Qu
a
n
t
i
z
at
i
o
n
B
a
se
d
C
u
r
r
ent
C
o
m
p
a
r
at
or
…
(Veep
sa Bha
t
ia
)
32
4
3.
1. Desi
gn of
AN
N M
o
del
f
o
r
ST
AGE
1
The
AN
N st
r
u
ct
ure
of Fi
gu
re
2 i
s
use
d
t
o
m
odel
Stage 1. The inputs to
the network a
r
e current
I
ref
an
d th
e
g
a
te to sou
r
ce vo
ltag
e
V
GS,ref
(=
V
DS,re
f
) wh
ile th
e chan
n
e
l len
g
t
h
(
L
Mn1
) an
d wi
dt
h
(
W
Mn1
) are
re
g
a
rd
e
d
as the network out
puts.
He
nc
e, two
ne
urons
each in i
nput and
output layer we
re em
ployed and the M
L
P of
Fi
gu
re
2 i
s
t
r
ai
ned
.
T
h
e ch
an
nel
wi
dt
h a
nd
l
e
ngt
h
o
f
t
h
e t
r
ansi
st
or
were
vari
e
d
ra
n
dom
l
y
bet
w
een
0.
2
8
μ
m
and 6.
0
μ
m
.
For eac
h com
b
ination
of as
pec
t
ratios ele
m
ents,
current from the curre
nt
source was als
o
va
ried
fr
om
100
nA t
o
2.
5m
A and t
h
e cor
r
es
po
n
d
i
n
g gat
e
t
o
so
u
r
c
e
vol
t
a
g
e
s (
V
GS
,ref
) were
ob
tain
ed. Th
is set of d
a
ta
co
m
p
risin
g
o
f
1
477
sam
p
les was th
en
u
tilized
to
t
r
ain
t
h
e
ANN stru
ct
u
r
e in
Figure
2
em
p
l
o
y
in
g
Lev
e
n
b
e
rg
–
Marquardt (L
M) bac
k
propagation m
e
thod a
s
the tr
a
i
ning algorithm
.
In
accordance with
the
above
con
s
i
d
erat
i
o
ns
,
t
h
e si
m
u
l
a
t
i
ons
we
re
per
f
o
r
m
e
d on
M
A
TL
AB
R
2
0
0
7
b
Ne
ural
Net
w
or
k t
o
ol
bo
x
by
con
s
i
d
eri
n
g
3
0
0
0
ep
oc
hs a
n
d
a l
ear
ni
n
g
rat
e
o
f
1.
2. T
h
e
a
c
t
i
v
at
i
on
fu
nct
i
on
f
o
r
hi
d
d
e
n
l
a
y
e
rs’
ne
ur
o
n
s
was
t
a
ken t
o
be t
a
nge
nt
-si
g
m
o
i
d
fu
nct
i
o
n
whi
l
e p
u
re l
i
n
ear
f
unct
i
o
n
was c
hos
en
f
o
r
o
u
t
p
ut
l
a
y
e
r. T
h
e t
r
ai
ni
n
g
error
was aimed at 1x10
-6
and t
h
e t
r
ai
ni
n
g
was st
op
pe
d
whe
n
val
i
d
at
i
on c
h
ec
ks rea
c
hed t
h
ei
r m
a
xi
m
u
m
val
u
e.
T
h
e c
o
rres
p
on
di
n
g
di
m
e
nsi
ons
o
f
t
r
ansi
st
or M
n
1
(c
han
n
el
l
e
ng
t
h
(
L
Mn1
)
an
d
w
i
d
t
h (
W
Mn1
)) w
e
r
e
obt
ai
ne
d aft
e
r t
r
ai
ni
n
g
an
d t
h
e val
u
e o
f
V
GS,ref
was estim
ated
t
h
r
o
ug
h SP
IC
E si
m
u
l
a
ti
on by
ap
pl
y
i
ng
I
ref
=5
μ
A.
Tw
o hi
d
d
e
n
l
a
y
e
rs havi
ng
5 neu
r
ons
, an
d 4
neu
r
o
n
s res
p
e
c
t
i
v
el
y
were sel
ect
ed aft
e
r car
ry
i
ng
out
t
h
e
AN
N i
m
pl
em
ent
a
t
i
on
of ci
rc
ui
t
t
h
ro
u
gh a
num
ber o
f
i
t
e
r
a
t
i
ons i
n
whi
c
h t
h
e n
u
m
b
er
of
hi
d
d
en l
a
y
e
rs an
d
num
ber
of
neu
r
o
n
s i
n
eac
h l
a
y
e
r we
re
vari
e
d
.
I
n
t
h
e
fi
rst iteratio
n
,
a si
n
g
le layer with a sing
le n
e
uron was
em
pl
oy
ed.
H
o
weve
r,
a si
n
g
l
e
hi
d
d
e
n
l
a
y
e
r
i
n
t
h
e
A
N
N
m
odel
l
i
ng o
f
s
t
age1
p
r
o
d
u
ce
d a l
a
rge
m
e
an s
qua
re
error as
well as large % e
r
ror betw
ee
n desi
red and estim
ated val
u
e of
V
GS
r
e
f
, as depi
ct
e
d
i
n
Fi
gu
re 4
.
Hence
t
h
e m
odel
l
i
ng
of t
h
e ci
rc
ui
t
was car
ri
ed
us
i
ng
2 hi
dde
n l
a
y
e
rs. N
u
m
e
ro
us i
t
e
rat
i
o
ns
were ca
rri
e
d
o
u
t
by
varying the
num
ber of
neurons in each
hidden layer
begi
nning
with one i
n
eac
h layer a
n
d fi
nally an
opt
im
u
m
sol
u
t
i
o
n was re
ached
wi
t
h
kee
p
i
n
g ne
ur
on
s as 5 and
4 i
n
t
h
e l
a
y
e
r 1 and 2
respect
i
v
el
y
for w
h
i
c
h t
h
e t
r
ai
ni
n
g
er
ro
r
w
a
s f
ound
to
b
e
1
.
6
3x10
-5
. Th
e resu
lts o
f
iteration
s
of stag
e1
h
a
v
e
b
een con
s
o
lid
ated
and
illu
strated
in
Figure 5, whe
r
ein % error be
tween
desi
re
d and
est
i
m
at
ed
val
u
e V
GSref
h
a
s b
een
p
l
o
tted
with
resp
ect to th
e
num
ber o
f
ne
u
r
o
n
s i
n
hi
d
d
en
l
a
y
e
r 2 fo
r
di
ff
erent
fi
xed
val
u
es o
f
n
u
m
b
er of
neu
r
ons i
n
h
i
dde
n l
a
y
e
r 1 (
NL1
)
.
Sol
i
d
l
i
n
e
f
o
r
NL
1=5
i
s
t
h
e desi
re
d c
h
ar
act
eri
s
t
i
c
whi
c
h y
i
el
ds m
i
nim
u
m
% error
bet
w
ee
n
desi
red
a
n
d
esti
m
a
ted
v
a
lu
e o
f
V
GSref
.
Fi
g
u
re
6 de
pi
ct
s t
h
e fi
nal
M
L
P
devel
ope
d f
o
r
St
age 1
wi
t
h
o
n
e i
n
put
l
a
y
e
r,
on
e
out
put
l
a
y
e
r
an
d t
w
o
hi
d
d
e
n
l
a
y
e
rs com
p
ri
si
ng
2
,
2,
5 a
n
d
4
neu
r
ons
res
p
ect
i
v
el
y
.
Fi
gu
re
3.
A
N
N
Trai
ni
ng
P
r
oc
edu
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
32
0 – 32
9
32
5
Fi
gu
re
4.
St
age
1
-
% E
r
r
o
r
bet
w
een
d
e
sir
e
d an
d estim
a
t
ed
valu
e of
V
GSref
. Vs Num
b
er o
f
Neu
r
ons
in Hi
dde
n
Layer
1
Fi
gu
re
5.
St
age
1
-
% E
r
r
o
r
bet
w
een
d
e
sir
e
d an
d estim
a
t
ed
valu
e of
V
GSref
. Vs Num
b
er o
f
Neu
r
ons
in Hi
dde
n
Layer
2 fo
r d
i
ff
er
en
t f
i
x
e
d v
a
l
u
es
o
f
Nu
m
b
er of
Neur
on
s in
H
i
dd
en Layer
1
Fi
gu
re
6.
M
L
P
use
d
fo
r i
m
pl
em
ent
i
ng st
a
g
e
1
3.
2. Desi
gn of
AN
N M
o
del
f
o
r
S
t
age
2
Sim
ilar to Stage 1, the
ANN
structure of Fi
gure 2
i
s
use
d
t
o
m
odel
St
age 2. T
h
e t
r
ai
ni
n
g
ap
pr
oac
h
use
d
he
re i
s
s
a
m
e
as t
h
at
de
scri
be
d i
n
su
b
s
ect
i
on
3.
1.
T
h
e c
h
an
nel
l
e
n
g
t
h
s a
n
d c
h
an
nel
wi
dt
hs a
r
e
vari
e
d
bet
w
ee
n 0
.
1
8
μ
m
and 6.
0
μ
m wh
ile th
e in
pu
t vo
ltag
e
(
V
in
) i
s
chan
ge
d fr
om
0 V t
o
1.8
V d
u
r
i
n
g
SPIC
E
si
m
u
latio
n
s
. A to
tal o
f
1
365
sa
m
p
les were co
llected
in
th
is case. Th
e i
n
pu
ts to
th
e
n
e
two
r
k
are i
n
pu
t vo
ltage
(
V
in
), t
h
e
out
pu
t
vol
t
a
ge
(
V
out
)
,
and
cha
n
nel
l
e
ngt
hs (
L
Mp2
and
L
Mn2
)
of t
r
an
si
st
ors M
p2 a
n
d M
n
2.
The
o
u
t
p
ut
s
are the c
h
annel
widths
(
W
Mp2
and
W
Mn2
)
of
tr
an
sistor
s Mp2
an
d
M
n
2. H
e
n
c
e an
inp
u
t
layer
w
ith
4
n
e
ur
on
s and
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Mo
del
l
i
ng a
n
d
Desi
g
n
of
I
n
ve
rt
er
Thre
sh
ol
d
Qu
a
n
t
i
z
at
i
o
n
B
a
se
d
C
u
r
r
ent
C
o
m
p
a
r
at
or
…
(Veepsa Bhati
a
)
32
6
out
put
l
a
y
e
r
w
i
t
h
2
ne
ur
o
n
s
were
sel
ect
ed.
The
n
u
m
b
er
of
hi
dde
n l
a
y
e
rs
was t
h
en
i
n
creased
t
o
t
w
o
an
d
sim
i
l
a
r proces
s was carri
e
d
out
.
It
was o
b
s
erve
d t
h
at
by
keepi
n
g ne
u
r
ons as
6 an
d 7 i
n
t
h
e l
a
y
e
r 1 an
d 2
respectively
a
m
i
nim
u
m
% erro
r
of
0
.
1
1
%
between
desire
d and estim
ated value
of
V
out
was
achie
ved.
In
an
attem
p
t
to
ex
p
l
o
r
e th
e p
o
ssi
b
ility
o
f
o
b
t
ain
i
ng
sm
aller tran
sisto
r
sizes as co
mp
ared
to
th
o
s
e o
f
two
h
i
dd
en layers,
an
o
t
h
e
r
h
i
dd
en layer was added
.
Th
e
nu
m
b
er of
n
e
uro
n
s
were in
itially fix
e
d
as
on
e p
e
r
hid
d
e
n
l
a
y
e
r and t
h
e
n
pr
o
g
ressi
vel
y
i
n
crease
d
.
It
wa
s obs
er
ved t
h
at
t
h
e % err
o
r
be
t
w
een
desi
re
d
and est
i
m
at
ed
val
u
e
of
V
out
i
s
m
i
nim
u
m
(0.1
6% )
whe
n
num
ber
of ne
ur
on
s ar
e 6, 4 an
d 5 re
spect
i
v
el
y
i
n
hi
dde
n l
a
y
e
r 1, 2 an
d
3
wi
t
h
cha
n
nel
wi
dt
h
of t
r
ans
i
st
or M
P
2 a
n
d
M
N
2
(
W
Mp2
and
W
Mn2
)
equal to
1
6
.854
4
µ
m
an
d
5.1729
µm
r
e
sp
ectiv
ely.
Fu
r
t
h
e
r
,
wh
en nu
m
b
er
s of
n
e
ur
on
s ar
e 8,
1
0
and
7 i
n
hi
dde
n l
a
y
e
r 1
,
2 an
d 3
res
p
ect
i
v
el
y
,
t
h
e
val
u
e
of % e
r
r
o
r
bet
w
ee
n d
e
s
i
red a
nd est
i
m
at
ed val
u
e
o
f
V
out
equal
t
o
2
.
43
% an
d ch
an
nel
wi
dt
h o
f
t
r
ansi
st
o
r
MP2
an
d MN2 (
W
Mp2
and
W
Mn
2
)
equ
a
l to 6.23
µm
an
d
1
.
797
2 µm
r
e
sp
ectiv
ely.
Hence t
h
e
r
e i
s
a t
r
ade off bet
w
een t
h
e
num
ber o
f
ne
ur
o
n
s
and t
r
ansi
st
or
si
zi
ng. H
o
wev
e
r, we ha
ve
cho
s
en t
h
ree h
i
dde
n l
a
y
e
rs h
a
vi
n
g
8
neu
r
o
n
s,
10
neu
r
ons
and
7 ne
ur
o
n
s
respect
i
v
el
y
,
gi
vi
n
g
p
r
efe
r
e
n
ce t
o
sm
al
l
t
r
ansi
st
or si
zes o
v
er
n
u
m
ber of ne
u
r
o
n
s. Fi
gu
re
7 de
pi
ct
s t
h
e fi
nal
M
L
P de
vel
o
pe
d f
o
r
St
age
2
wi
t
h
o
n
e
i
n
p
u
t
l
a
y
e
r,
on
e o
u
t
p
ut
l
a
y
e
r
and
t
h
re
e hi
dd
en l
a
y
e
rs c
o
m
p
ri
si
n
g
4,
2
,
8
,
1
0
a
nd
7
ne
ur
ons
res
p
ect
i
v
el
y
.
Th
e
tr
ain
i
ng
erro
r
fo
r Stag
e 2 im
p
l
e
m
en
tatio
n
achiev
ed
a v
a
l
u
e
of
9
.
9
751
8 x10
-7
.
Fi
gu
re
7.
M
L
P
St
r
u
ct
ure
de
ve
l
ope
d
fo
r st
a
g
e
2
4.
R
E
SU
LTS AN
D ANA
LY
SIS
The curre
nt com
p
arator of Fi
gure
1 is
desig
n
ed
fo
r a refe
r
e
nce cu
rre
nt o
f
5
μ
A. Th
e
p
o
w
e
r
su
pp
ly
(
V
DD
)
of
1.
8
V
i
s
use
d
.
The
t
r
ai
ni
n
g
a
n
d t
e
s
t
dat
a
i
s
gat
h
e
r
ed t
h
r
o
ug
h
S
P
IC
E si
m
u
l
a
t
i
ons
ba
sed
o
n
TSM
C
0.
18
μ
m
C
M
OS t
ech
nol
ogy
param
e
t
e
rs. As
di
scu
ssed
i
n
s
ect
i
on
2.
1, t
h
e
val
u
e
o
f
V
GS,r
ef
for
gi
ven
re
f
e
rence
cu
rren
t is tak
e
n
as
V
DD
/2
(0
.
9
V
)
fo
r St
a
g
e
1. T
h
e
di
m
e
nsi
ons
f
o
r t
r
a
n
s
i
st
or M
n
1 a
r
e
com
put
ed
usi
n
g t
h
e
m
e
t
hod de
scri
bed i
n
sect
i
o
n
3.
1. As St
a
g
e
2 uses a sy
m
m
et
ri
cal
i
nvert
er
, t
h
e out
put
v
o
l
t
a
ge i
s
V
DD
/2
for
an
in
pu
t
V
GS,ref
of
V
DD
/2
.
Fo
r
st
age
2,
t
h
e
i
n
put
s are
t
a
ke
n as
V
in
=
V
out
=
0.
9
V,
an
d t
h
e c
h
a
nnel
l
e
n
g
t
h
s
ar
e t
a
ke
n
as
L
p
=
L
n
= 0.18
μ
m
.
The res
u
l
t
s
obt
ai
ne
d
fr
o
m
M
A
TLAB
f
o
r
St
ag
es
1 and
2 are
s
u
mma
rized
res
p
ectively in
Tabl
e
1 a
n
d
Ta
bl
e 2
.
The c
u
r
r
ent
c
o
m
p
arat
or can a
l
so be
desi
gne
d f
o
r
any
r
e
fe
r
e
nce
val
u
e
ot
h
e
r t
h
a
n
5µ
A
by
t
r
ai
ni
n
g
t
h
e
M
L
P net
w
or
k
fo
r st
age
1 (
F
i
g
u
r
e
4)
whi
l
e
keepi
ng t
h
e de
si
gns
of
st
ages
2 an
d
3 u
n
al
t
e
red
.
Al
t
e
r
n
at
i
v
el
y
,
i
t
can be em
phas
i
zed t
h
at
St
age
s
2 an
d 3 o
n
ce
desi
g
n
ed
fo
r bot
h i
n
p
u
t
an
d
out
p
u
t
o
f
V
DD
/
2
can be
uni
v
e
rsal
l
y
e
m
ployed for a
n
y curre
nt com
p
arat
or
with a
ny refere
nce
va
lu
e,
j
u
st b
y
altering
th
e
design aspects of sta
g
e 1.
This
renders the struct
ure
hi
ghly
flexi
b
le and m
o
re a
d
apta
ble.
Tabl
e
1. R
e
s
u
l
t
o
f
si
m
u
l
a
t
i
on
of
A
N
N
o
f
st
a
g
e
1 i
n
M
A
T
L
A
B
Para
m
e
ters
Values
I
nputs
to NN
I
re
f
V
GS
,re
f
5µA
0.
9V
Outputs
of
NN
W
Mn
1
L
M
n1
0.
2811
µ
m
1.
6020
µ
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
32
0 – 32
9
32
7
Tabl
e
2. R
e
s
u
l
t
o
f
si
m
u
l
a
t
i
on
of
A
N
N
o
f
st
a
g
e
2 a
n
d
3
i
n
M
A
TLAB
Para
m
e
ters
Values
I
nputs
to NN
V
in
V
out
L
M
p2
L
M
n2
0.
9V
0.
9V
0.
18µ
m
0.
18µ
m
Outputs
of
NN
W
Mp
2
W
M
n2
6.
2335
µ
m
1.
7972
µ
m
Fo
r t
h
e pu
rpo
s
e o
f
v
e
rification
and
testin
g, th
e m
o
d
e
lled
cu
rren
t co
m
p
arato
r
is sim
u
lat
e
d
in
SPIC
E
by
co
nsi
d
eri
n
g
t
h
e est
i
m
at
ed aspect
rat
i
os
o
f
t
r
a
n
si
st
o
r
s M
n
1
,
M
n
2 a
n
d
M
p2
(Ta
b
l
e
2
and
3
)
usi
n
g
0
.
1
8
μ
m
TSM
C
t
ech
nol
ogy
a
n
d a
s
u
p
p
l
y
Vol
t
a
ge
o
f
1
.
8
V.
T
h
e
val
u
e o
f
V
GS,ref
(sta
ge
1)
f
o
r
a
n
in
put
re
fere
nce c
u
r
r
en
t
(
I
ref
) of
5
μ
A
an
d th
e
V
out
(stag
e
2
)
fo
r an
i
n
pu
t
vo
ltag
e
(
V
in
)
of
0
.
9
V
a
r
e det
e
rm
i
n
ed.
The
sam
e
hav
e
bee
n
rep
o
rt
e
d
i
n
t
h
e
Tabl
e 4 al
on
g wi
t
h
t
h
ei
r
d
e
si
red val
u
es
and
perce
n
t
a
g
e
erro
r. T
h
e l
a
y
out
o
f
t
h
e m
odel
l
e
d
cu
rren
t co
m
p
arato
r
was d
e
velo
p
e
d
u
s
i
n
g
Micro
w
i
n
d
Software as illustrated
in
Figu
re
8
.
Po
st-layo
u
t
si
m
u
latio
n
s
were carried
ou
t an
d
th
e
resu
lts are sh
own
in
Table 4. It is found that there is close agre
e
m
ent
bet
w
ee
n
desi
re
d a
n
d
est
i
m
at
ed
val
u
es
f
o
r
b
o
t
h p
r
e a
n
d
post
l
a
y
out
resul
t
s
.
Fi
gu
re
8.
Lay
o
u
t
o
f
t
h
e M
o
de
l
l
e
d C
u
r
r
e
n
t
C
o
m
p
arat
or
Tabl
e
4.C
o
m
p
ari
s
o
n
bet
w
ee
n
desi
re
d a
n
d es
t
i
m
a
t
e
d val
u
es
Para
m
e
ter Desired
value
E
s
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ou
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Mo
del
l
i
ng a
n
d
Desi
g
n
of
I
n
ve
rt
er
Thre
sh
ol
d
Qu
a
n
t
i
z
at
i
o
n
B
a
se
d
C
u
r
r
ent
C
o
m
p
a
r
at
or
…
(Veep
sa Bha
t
ia
)
32
8
5.
CO
NCL
USI
O
N
This
work int
r
oduces
a
pioneer
desi
g
n
of
an
i
m
pl
em
ent
e
d
c
u
r
r
en
t
com
p
arat
or
with the
help of
ANNs. Th
e
ANN im
p
l
e
m
en
tatio
n
is si
m
p
le an
d
cu
rtails th
e m
a
n
u
a
l la
b
our n
e
ed
ed
t
o
so
l
v
e th
e com
p
lex
math
e
m
atica
l
eq
u
a
tion
s
g
overn
i
n
g
th
e functio
n
i
ng
of
th
e tran
sisto
r
s at th
e su
b
m
icr
o
n
lev
e
l wh
ere sh
ort
channel effects
play vital roles. Sa
tisf
actor
y p
e
rf
or
m
a
n
ce f
o
r
the circ
uit has been
reco
rded
fo
r th
e
p
r
edicted
aspect
rat
i
os
p
a
ram
e
t
e
rs usi
n
g
AN
N.
F
u
rt
h
e
r t
h
e
l
a
y
out
h
a
s al
so
bee
n
d
e
vel
o
ped
f
o
r
t
h
i
s
c
u
r
r
ent
c
o
m
p
arat
or
and
t
h
e
Pre
-
l
a
y
out
a
n
d P
o
st
-l
a
y
out
resul
t
s
a
r
e
found to be
in
close a
g
reem
ent.
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I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
32
0 – 32
9
32
9
BIOGRAP
HI
ES OF
AUTH
ORS
Veeps
a
Bha
tia
was born in 197
7. She r
eceived
B.E.
degr
ee in Electronics
and Communication
Engineering for Amravati University
, India in 19
99. She completed her Masters in Engineer
ing
from Delhi College of
Engin
eer
ing, Delhi Ind
i
a in 2005
and is
currently
pursuing Ph.D. from
Delhi T
echno
log
i
ca
l Universit
y
,
Delhi,
India
.
Sh
e
is
curr
entl
y wo
rking as
an As
s
i
s
t
ant P
r
ofes
s
o
r
in Depar
t
ment o
f
Electron
i
cs
an
d Communicatio
n
Engin
eering
at Indira Gandhi
Delhi
Techn
i
cal
Univers
i
t
y
for
W
o
m
e
n, Delhi,
I
ndia.
S
h
e has
a
t
each
ing and
ind
u
s
t
r
y
exper
i
enc
e
of 15
ye
ars
and
her areas of interest are curr
ent
mode circuits
, Analog to digital converters and
digital s
y
stem
design.
Neeta Pandey
w
a
s born in 1966. She did her M.
E.
in Microel
e
ctronics from
Birla Institut
e
of
Techno
log
y
and
Scien
ces, Pilan
i
and Ph. D.
fro
m Guru Gobind Singh Indrapr
a
stha University
Delhi. She has
served in Cent
ral El
ectron
i
cs
Engine
ering Re
search Institu
te
,
Pilani, Indi
an
Institute
of T
ech
nolog
y, De
lhi,
Pri
y
adarshin
i Col
l
ege of
Com
puter Scien
c
e
,
Noi
d
a and Bh
ara
t
i
Vid
y
ap
ee
th’s
C
o
lleg
e
of
Engin
eering
,
De
lhi
in
Various
c
a
pa
cit
i
es
. At
pres
en
t,
s
h
e is
As
s
i
s
t
ant
Professor in ECE departmen
t
,
Delhi Technolo
g
ic
al University. A life member of ISTE, and
member of IEEE, USA, she has published pap
e
rs
in Intern
at
io
nal, Na
tion
a
l Jo
urnals of reput
e
and conf
eren
ces
.
Her r
e
s
ear
ch in
t
e
res
t
s
ar
e
in Ana
l
og and
Digit
a
l
VLS
I
Des
i
gn.
Asok Bhattacha
r
yya ob
tain
ed
M. Tech
. and
Ph.D. degree fr
om
Institute of
Radio Ph
y
s
ics
,
Calcutta Univ
er
sity
, India in th
e
y
e
ar 1970 and
1981, respectiv
ely
.
He jo
ined D
e
lhi Colleg
e of
Engineering in
May
1974 and since th
en he
is with the same college and has worked in differ
e
nt
c
a
p
ac
itie
s of
Le
cture
r
, Assista
n
t
Profe
ssor,
Profe
ssor, Professor and Head of
the
Department
and
as Offici
ating
D
i
rec
t
or of
the
In
stitute
. Prof
. A.
Bhatta
char
yya
h
a
s worked
in di
fferent
fi
elds-
Digital S
y
s
t
em Design, Analog Sy
stem Design,
Easi
l
y
test
able a
nd diagn
o
sable Digital
s
y
stems/Fault to
leran
t
Computing and Medica
l Im
age P
r
oces
s
i
ng area
. Bes
i
de
s
his
reputed
research publ
ic
a
tions, he has aut
hored two rese
a
r
ch m
onographs. He is a fellow of IETE, lif
e
member of ISTE and sen
i
or member of
IEEE
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