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I
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69
4
I
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Po
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Vo
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12
,
No
.
4
,
Dec
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b
er
2
0
2
1
:
23
05
–
23
13
2306
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r
th
e
o
p
er
atio
n
o
f
s
witch
in
g
s
e
q
u
en
ce
.
B
ased
o
n
t
h
e
co
m
p
ar
ativ
e
s
u
r
v
ey
,
p
r
o
p
o
s
ed
R
SML
I
is
th
e
to
tal
least
co
u
n
t o
f
elem
en
ts
with
s
y
m
m
e
tr
ical
o
p
er
atio
n
o
f
ML
I
.
T
ab
le
1
.
R
SML
I
co
m
p
a
r
is
o
n
s
tu
d
y
with
p
r
o
p
o
s
ed
Hex
a
ML
I
R
e
f
e
r
e
n
c
e
s
D
C
V
o
l
t
a
g
e
s
M
O
S
F
ET
/
I
G
B
T
D
i
o
d
e
s
C
a
p
a
c
i
t
o
r
s
To
t
a
l
e
l
e
m
e
n
t
s
O
u
t
p
u
t
v
o
l
t
a
g
e
l
e
v
e
l
P
W
M
T
e
c
h
n
i
q
u
e
M
e
t
h
o
d
o
l
o
g
y
[
2
]
,
[
1
2
]
4
5
0
0
9
7
B
i
p
o
l
a
r
(
A
P
O
D
,
P
O
D
,
P
D
)
Lo
g
i
c
g
a
t
e
s
[
1
3
]
4
11
0
0
15
9
U
n
i
p
o
l
a
r
(
A
P
O
D
,
P
O
D
,
P
D
)
-
[
1
4
]
2
7
4
2
15
9
B
i
p
o
l
a
r
(
P
O
D
)
Lo
g
i
c
g
a
t
e
s
[
1]
2
8
0
0
10
7
B
i
p
o
l
a
r
(
A
P
O
D
)
Lo
g
i
c
g
a
t
e
s
[
1
5
]
4
12
0
0
16
9
U
n
i
p
o
l
a
r
(
A
P
O
D
,
P
O
D
,
P
D
)
Lo
g
i
c
g
a
t
e
s
[
1
6
]
3
7
3
0
13
7
-
F
u
z
z
y
l
o
g
i
c
[1
7]
1
6
2
2
11
5
U
n
i
p
o
l
a
r
(
P
D
)
K
M
a
p
H
e
x
a
M
LI
2
6
0
0
8
7
B
i
p
o
l
a
r
(
A
P
O
D
,
P
O
D
,
P
D
)
Lo
g
i
c
g
a
t
e
s
I
n
d
esig
n
an
d
o
p
er
atio
n
o
f
r
e
d
u
ce
d
s
witch
m
u
ltil
ev
el
in
v
er
ter
,
co
n
tr
o
l
o
f
ea
ch
s
witch
wi
th
r
eq
u
ir
e
d
p
u
ls
e
s
eq
u
en
ce
is
d
if
f
icu
lt.
C
o
m
p
ar
in
g
th
e
n
u
m
b
er
o
f
p
u
ls
e
s
eq
u
en
ce
s
p
r
o
d
u
ce
d
f
r
o
m
PW
M
m
eth
o
d
an
d
th
e
n
u
m
b
er
o
f
s
witch
es
in
R
SM
L
I
ar
e
n
o
t
eq
u
al.
Dep
en
d
s
o
n
th
e
co
n
tr
o
l
s
tr
ateg
y
o
f
ea
c
h
s
witch
in
R
SML
I
,
p
r
o
b
lem
s
tatem
en
t
o
f
th
e
p
r
o
p
o
s
ed
r
esear
ch
wo
r
k
is
o
n
th
e
g
en
er
atio
n
o
f
p
u
ls
e
s
eq
u
en
ce
s
to
th
e
n
o
v
al
Hex
a
M
L
I
.
Or
g
an
izatio
n
o
f
t
h
is
ar
ticle
is
p
r
esen
ted
in
f
iv
e
s
ec
ti
o
n
s
.
Sectio
n
o
n
e
p
r
esen
ts
th
e
n
ee
d
an
d
s
tu
d
y
o
f
v
ar
io
u
s
r
e
d
u
ce
d
s
witch
ML
I
.
PW
M
s
tr
ateg
y
o
f
p
r
o
p
o
s
ed
H
ex
a
ML
I
f
o
r
s
witch
in
g
o
p
er
ati
o
n
s
is
ex
p
lain
e
d
in
s
ec
tio
n
two
.
Op
e
r
atio
n
o
f
p
r
o
p
o
s
ed
He
x
a
ML
I
an
d
its
v
a
r
io
u
s
m
o
d
es
f
o
r
th
e
o
u
tp
u
t
l
ev
el
g
en
e
r
atio
n
s
is
p
r
o
v
id
e
d
in
s
ec
tio
n
th
r
ee
.
Ob
t
ain
ed
r
esu
lts
an
d
d
is
cu
s
s
io
n
with
R
T
-
lab
is
g
iv
en
in
s
ec
tio
n
f
o
u
r
.
Pro
p
o
s
ed
ML
I
with
co
n
tr
o
l te
ch
n
iq
u
e
a
n
d
its
co
m
p
ar
is
o
n
o
f
T
HD
is
co
n
clu
d
ed
in
f
i
n
al
s
ec
tio
n
.
2.
P
WM
S
T
RA
T
E
G
Y
F
O
R
H
E
XA
M
L
I
Dif
f
er
en
t
m
o
d
u
latio
n
s
tr
ateg
ies
ar
e
an
aly
ze
d
an
d
u
tili
zin
g
f
o
r
th
e
o
p
e
r
atio
n
o
f
c
o
n
v
en
tio
n
al
m
u
ltil
ev
el
in
v
er
ter
s
an
d
R
SML
I
.
C
o
n
s
id
er
in
g
f
o
r
R
SML
I
,
ca
r
r
ier
b
ased
p
u
ls
e
wid
th
m
o
d
u
latio
n
tech
n
i
q
u
es
ar
e
p
r
e
f
er
ab
le
with
“
p
er
ca
r
r
ier
cy
cle”
o
f
m
u
ltil
ev
el
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
[
1
8
]
,
[
1
9
]
.
Sp
ac
e
v
ec
to
r
m
o
d
u
latio
n
tech
n
iq
u
e
is
d
ir
e
ct
m
eth
o
d
o
f
ca
r
r
ier
b
as
ed
PW
M
tech
n
iq
u
e
with
p
r
e
-
d
e
f
in
ed
i
n
v
er
ter
s
tate,
ca
r
r
ier
s
ig
n
al
tim
e
len
g
th
an
d
m
o
d
u
latio
n
cy
cle
[
2
0
]
–
[
2
2
]
.
I
n
in
d
i
r
ec
t
m
eth
o
d
,
lo
w
f
r
e
q
u
en
cy
m
o
d
u
latio
n
s
ig
n
al
is
in
ter
s
ec
tio
n
with
h
ig
h
f
r
e
q
u
en
c
y
ca
r
r
ie
r
wav
es
a
n
d
r
esu
lts
in
p
u
ls
e
g
en
er
ati
o
n
r
eq
u
ir
ed
f
o
r
th
e
o
p
er
atio
n
o
f
s
witch
in
g
s
eq
u
e
n
ce
[
1
]
,
[
2
3
]
,
[
2
4
]
.
I
n
d
ir
ec
t
m
eth
o
d
is
ea
s
y
to
im
p
lem
en
t
with
in
ter
s
ec
tio
n
tech
n
iq
u
e
o
f
ca
r
r
ier
an
d
m
o
d
u
latio
n
s
ig
n
al
f
o
r
th
e
o
p
er
a
tio
n
o
f
r
ed
u
ce
d
s
witch
ML
I
.
Saw
to
o
th
wav
e,
tr
ap
ez
o
id
al
wav
e,
u
n
ip
o
lar
an
d
b
ip
o
lar
s
in
u
s
o
id
al
wav
es
ar
e
p
r
ef
er
a
b
le
f
o
r
th
e
m
o
d
u
latio
n
wav
e.
T
r
ia
n
g
u
lar
wav
es
ar
e
u
s
ed
as
ca
r
r
ier
wa
v
es
b
ased
o
n
th
e
o
u
tp
u
t
v
o
lta
g
e
lev
el
o
f
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
[
1
5
]
,
[
2
5
]
.
Mu
lti
ca
r
r
ier
tr
ian
g
u
la
r
wav
es
ar
e
u
s
ed
f
o
r
th
e
g
e
n
er
atio
n
o
f
f
iv
e
l
ev
el
an
d
m
o
r
e
lev
el
o
u
tp
u
t.
P
h
ase
s
h
if
t
an
d
lev
el
s
h
if
t
ar
e
th
e
two
m
eth
o
d
s
o
f
m
u
lti
ca
r
r
ier
PW
M
tech
n
iq
u
e
with
th
e
ar
r
an
g
em
en
t
o
f
ca
r
r
ier
s
ig
n
als
[
1
7
]
,
[
2
6
]
.
I
n
p
r
o
p
o
s
ed
m
o
d
el,
lev
el
s
h
if
t
PW
M
with
alter
n
ativ
e
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
(
APOD)
,
p
h
ase
o
p
p
o
s
iti
o
n
d
is
p
o
s
itio
n
(
POD)
,
an
d
p
h
ase
d
is
p
o
s
itio
n
(
PD)
ar
e
u
s
ed
.
I
n
A
P
O
D
,
e
a
c
h
c
a
r
r
ie
r
t
r
i
a
n
g
u
l
a
r
w
a
v
e
is
i
n
o
p
p
o
s
i
t
i
o
n
wit
h
d
i
s
p
l
a
ce
m
e
n
t
o
f
1
8
0
0
t
o
p
h
a
s
e
o
f
i
ts
a
l
t
e
r
n
a
ti
v
e
c
a
r
r
i
e
r
w
a
v
e
.
I
n
P
OD
,
c
a
r
r
i
e
r
w
a
v
es
o
n
p
o
s
i
ti
v
e
h
a
l
f
s
i
d
e
a
r
e
i
n
p
h
a
s
e
a
n
d
c
a
r
r
i
er
w
a
v
e
s
o
n
n
e
g
a
t
i
v
e
h
a
l
f
a
r
e
i
n
o
p
p
o
s
it
i
o
n
d
is
p
l
a
c
em
e
n
t
o
f
1
8
0
0
w
i
t
h
p
o
s
i
t
i
v
e
h
a
l
f
c
a
r
r
i
e
r
w
a
v
es
.
I
n
PD
,
a
ll
c
a
r
r
ier
w
a
v
e
s
a
r
e
i
n
p
h
a
s
e
w
i
t
h
o
u
t
a
n
y
p
h
as
e
o
p
p
o
s
i
t
i
o
n
[
2
7
]
.
V
a
r
i
a
t
i
o
n
s
o
f
ca
r
r
i
e
r
a
r
r
a
n
g
e
m
e
n
t
i
n
A
P
OD
,
P
O
D
a
n
d
P
D
a
r
e
s
h
o
w
n
i
n
F
i
g
u
r
e
1
.
P
r
o
p
o
s
e
d
H
e
x
a
M
L
I
i
s
o
p
e
r
a
t
e
d
f
o
r
s
e
v
e
n
l
e
v
e
l
o
u
t
p
u
t
v
o
l
t
a
g
e
.
B
a
s
e
d
o
n
t
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
,
c
o
u
n
t
o
f
c
a
r
r
i
e
r
s
i
g
n
a
ls
(
C
)
,
a
m
p
l
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t
u
d
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f
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a
c
h
c
a
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A
m
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s
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d
f
o
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t
h
e
m
u
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t
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c
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P
W
M
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p
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r
a
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p
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(
1
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a
n
d
(
2
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.
C
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p
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t
i
v
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i
n
t
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r
s
e
c
t
i
o
n
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c
h
n
i
q
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f
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r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2088
-
8
694
R
ea
l time
s
imu
la
tio
n
o
f red
u
ce
d
s
w
itch
mu
ltil
ev
el
in
ve
r
te
r
w
i
t
h
P
WM
s
w
i
tch
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g
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K
a
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V
in
o
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K
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2307
t
h
e
g
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o
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i
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F
i
g
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r
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2
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G
e
n
e
r
at
e
d
p
u
l
s
e
s
P
1
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P
2
,
P
3
,
N
1
,
N
2
a
n
d
N
3
a
r
e
r
e
p
r
e
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n
t
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i
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i
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r
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it
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f
M
L
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.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
.
Mu
lti ca
r
r
ier
Pu
ls
e
wid
th
m
o
d
u
latio
n
tech
n
i
q
u
e
o
f
;
(
a)
alter
n
ate
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
(
APOD)
,
(
b
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p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
(
POD)
,
(
c)
p
h
ase
d
is
p
o
s
itio
n
(
PD)
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
m
u
lti ca
r
r
ier
PW
M
tech
n
iq
u
e
f
o
r
r
e
d
u
ce
d
s
witch
ML
I
Am
p
litu
d
e
o
f
m
o
d
u
latio
n
wav
e,
|
A
m
|
=
∑
|
C
i
|
n
−
1
i
=
1
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
69
4
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
23
05
–
23
13
2308
P
1
to
P
(
n
−
1
)
2
,
I
f
i=
1
to
(
n
−
1
)
2
|
A
m
|
≥
|
C
i
|
⇒
N
1
to
N
(
n
−
1
)
2
,
I
f
i=
(
n
−
1
)
2
+
1
to
(
n
-
1)
(
2
)
B
y
u
s
in
g
b
ip
o
lar
m
o
d
u
latio
n
wav
e,
n
-
1
ca
r
r
ier
s
ig
n
als
ar
e
u
s
ed
f
o
r
‘
n
’
lev
el
o
u
tp
u
t
v
o
ltag
e
[
2
8
]
.
T
h
e
s
witch
in
g
s
eq
u
en
ce
o
r
d
er
o
f
Hex
a
ML
I
is
g
iv
en
in
T
ab
le
2
.
Mo
d
u
latin
g
f
r
eq
u
e
n
cy
o
f
5
0
Hz
an
d
s
witch
in
g
f
r
eq
u
e
n
cy
o
f
5
KHz
is
u
s
ed
f
o
r
th
e
en
tire
o
p
e
r
atio
n
o
f
p
r
o
p
o
s
ed
m
o
d
el
o
f
PW
M
an
d
in
v
er
ter
.
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n
o
v
al
s
witch
in
g
s
eq
u
en
ce
c
o
m
p
a
r
ativ
e
alg
o
r
ith
m
is
p
e
r
f
o
r
m
ed
f
o
r
th
e
g
en
e
r
atio
n
o
f
g
atin
g
s
ig
n
a
l
wh
ich
is
r
e
q
u
ir
ed
f
o
r
th
e
o
p
er
atio
n
o
f
ea
c
h
s
witch
an
d
is
p
r
esen
ted
i
n
Fig
u
r
e
3
.
Var
iab
le
‘
K’
r
e
p
r
esen
ts
th
e
s
witch
n
u
m
b
er
o
f
Hex
a
ML
I
an
d
‘
J
’
is
th
e
to
tal
n
u
m
b
er
o
f
s
witch
es in
R
SML
I
.
Fig
u
r
e
3
.
Flo
w
ch
a
r
t o
f
s
witch
in
g
s
ch
em
e
f
o
r
s
ev
en
l
e
v
el
Hex
a
ML
I
T
ab
le
2
.
Switch
in
g
s
eq
u
en
ce
t
o
co
n
tr
o
l sev
en
lev
el
H
ex
a
MLI
M
o
d
e
o
f
o
p
e
r
a
t
i
o
n
V
o
l
t
a
g
e
l
e
v
e
l
S
1
S
2
S
3
S
4
S
5
S
6
1
2V
1
0
0
1
1
0
2
+
1
.
5
V
1
0
0
1
1
1
3
+
1
V
1
1
0
1
1
1
4
-
1V
1
1
1
0
1
1
5
-
1
.
5
V
1
1
1
0
0
1
6
-
2V
0
1
1
0
0
1
3.
H
E
XA
M
U
L
T
I
L
E
V
E
L
I
NV
E
RT
E
R
Hex
a
ML
I
is
th
e
co
m
p
ac
t
d
es
ig
n
o
f
r
ed
u
ce
d
s
witch
m
u
ltil
ev
el
in
v
er
ter
.
I
t
is
o
p
er
ated
with
6
p
o
wer
s
witch
es
with
an
ti
-
p
ar
allel
p
o
wer
d
io
d
es
to
g
en
er
ate
s
ev
en
l
ev
el
o
u
tp
u
t
v
o
ltag
e
.
Au
x
iliar
y
p
o
wer
s
witch
es
ar
e
n
o
t
u
s
ed
f
o
r
th
e
o
p
er
atio
n
o
f
lev
el
g
en
e
r
atio
n
.
T
wo
s
y
m
m
e
tr
ical
DC
v
o
ltag
e
s
o
u
r
ce
s
(
V
DC
)
ar
e
u
s
ed
f
o
r
th
e
u
n
eq
u
al
DC
lev
el
o
u
tp
u
t
v
o
l
tag
e
o
f
th
e
Hex
a
ML
I
.
Pro
p
o
s
ed
Hex
a
ML
I
d
esig
n
is
s
h
o
wn
in
F
ig
u
r
e
4.
Switch
es
S
1
,
S
2
,
S
5
,
S
6
ar
e
u
s
ed
f
o
r
th
e
lev
el
g
e
n
er
atio
n
a
n
d
s
witch
es
S
3
,
S
4
ar
e
f
o
r
th
e
p
o
l
ar
ity
g
en
er
atio
n
o
f
o
u
tp
u
t
lev
els.
Op
er
atio
n
o
f
e
ac
h
s
witch
is
ex
p
lain
ed
in
th
e
v
ar
io
u
s
m
o
d
e
o
f
o
p
er
atio
n
s
.
Un
eq
u
al
DC
lev
e
l
o
u
tp
u
ts
ar
e
2
V
DC
,
1
.
5
V
DC
,
V
DC
,
0
V
DC
,
-
V
DC
,
-
1
.
5
V
DC
,
-
2V
DC
.
B
y
ex
clu
d
in
g
0
V
DC
,
r
em
ain
in
g
o
u
tp
u
t
v
o
ltag
e
lev
els ar
e
p
r
esen
ted
in
s
ix
d
if
f
er
en
t m
o
d
es
o
f
o
p
er
atio
n
s
with
r
esis
tiv
e
lo
ad
.
-
Mo
d
e
1
:
T
h
r
ee
p
o
wer
s
witch
e
s
ar
e
tr
ig
g
er
ed
with
th
e
s
u
p
p
o
r
t
o
f
PW
M
m
eth
o
d
.
S
1
an
d
S
5
ar
e
co
n
d
u
cted
f
o
r
th
e
lev
el
g
en
er
atio
n
o
f
2
V
DC
an
d
s
witch
S
4
is
o
p
e
r
ate
d
f
o
r
p
o
s
itiv
e
p
o
lar
ity
.
W
ith
th
e
o
p
e
r
atio
n
o
f
s
in
g
le
lo
o
p
with
two
DC
v
o
lt
ag
e
s
o
u
r
ce
s
,
r
esu
ltan
t
v
o
ltag
e
is
th
e
s
u
m
m
atio
n
o
f
v
o
ltag
es
ac
r
o
s
s
th
e
lo
ad
.
Flo
w
o
f
cu
r
r
e
n
t th
r
o
u
g
h
lo
ad
a
n
d
s
witch
es c
o
n
d
u
cte
d
in
m
o
d
e
1
is
s
h
o
wn
in
Fig
u
r
e
5
(
a
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
R
ea
l time
s
imu
la
tio
n
o
f red
u
ce
d
s
w
itch
mu
ltil
ev
el
in
ve
r
te
r
w
i
t
h
P
WM
s
w
i
tch
in
g
…
(
K
a
n
ike
V
in
o
d
K
u
ma
r
)
2309
-
Mo
d
e
2
:
Switch
es
S
1
,
S
5
,
S
6
ar
e
co
n
d
u
cted
f
o
r
t
h
e
lev
el
g
e
n
e
r
atio
n
o
f
1
.
5
V
DC
an
d
s
witch
S
4
is
f
o
r
p
o
s
itiv
e
p
o
lar
ity
g
en
er
atio
n
.
T
h
is
m
o
d
e
is
o
f
two
lo
o
p
s
an
d
a
n
o
u
tp
u
t
v
o
ltag
e
o
f
o
n
e
an
d
h
alf
tim
es
o
f
to
tal
v
o
ltag
e
is
o
b
tain
ed
at
lo
ad
.
Fo
u
r
c
o
n
d
u
cted
s
witch
es a
n
d
cu
r
r
en
t f
lo
w
is
s
h
o
wn
in
Fig
u
r
e
5
(
b
)
.
-
Mo
d
e
3
:
V
DC
o
u
t
p
u
t
v
o
ltag
e
l
ev
el
is
g
en
er
ated
with
th
e
c
o
n
d
u
ctio
n
o
f
f
i
v
e
s
witch
es
an
d
th
r
ee
lo
o
p
s
ar
e
f
o
r
m
ed
in
Hex
a
ML
I
as
s
h
o
wn
in
Fig
u
r
e
5
(
c)
.
Switch
es
S
1
,
S
5
,
S
6
an
d
S
2
ar
e
co
n
d
u
c
ted
f
o
r
th
e
lev
el
g
en
er
atio
n
a
n
d
S
4
is
f
o
r
p
o
lar
it
y
g
en
er
atio
n
.
-
Mo
d
e
4
:
Switch
es
S
6
,
S
2
,
S
1
an
d
S
5
ar
e
co
n
d
u
cte
d
f
o
r
th
e
o
u
tp
u
t
lev
el
g
en
er
atio
n
o
f
-
V
DC
.
S
3
is
co
n
d
u
cted
f
o
r
th
e
n
e
g
ativ
e
p
o
lar
ity
g
en
e
r
atio
n
.
C
u
r
r
en
t
f
lo
w
t
h
r
o
u
g
h
th
e
r
esis
tiv
e
lo
ad
is
r
ev
er
s
ed
wh
en
co
m
p
ar
ed
to
ab
o
v
e
th
r
ee
m
o
d
es.
C
o
n
d
u
cte
d
s
witch
es a
n
d
f
lo
w
o
f
cu
r
r
e
n
t
is
s
h
o
wn
in
Fig
u
r
e
5
(
d
)
.
-
Mo
d
e
5
:
-
1
.
5
V
DC
o
u
tp
u
t
v
o
lta
g
e
is
g
en
er
ated
b
y
s
witch
in
g
ON,
S
6
,
S
2
,
S
1
with
p
u
ls
e
s
eq
u
en
ce
g
en
e
r
ated
b
y
PW
M
m
eth
o
d
.
S
3
is
co
n
d
u
cted
f
o
r
n
eg
ativ
e
p
o
la
r
ity
g
e
n
er
atio
n
.
On
e
an
d
h
alf
tim
es
o
f
o
u
tp
u
t
v
o
ltag
e
lev
el
with
tw
o
lo
o
p
s
f
o
r
m
ed
b
y
co
n
d
u
cted
s
witch
es in
p
r
o
p
o
s
ed
Hex
a
ML
I
is
s
h
o
wn
in
Fig
u
r
e
5
(
e)
.
-
Mo
d
e
6
:
Fig
u
r
e
5
(
f
)
s
h
o
ws
th
e
o
p
er
atio
n
al
m
o
d
e
o
f
-
2V
DC
with
co
n
d
u
cted
s
witch
es
an
d
cu
r
r
en
t
f
lo
w
d
ir
ec
tio
n
t
h
r
o
u
g
h
lo
ad
.
Switch
es
S
6
,
S
2
an
d
S
3
ar
e
co
n
d
u
c
ted
with
s
in
g
le
lo
o
p
o
p
er
atio
n
f
o
r
m
a
x
im
u
m
lev
el
o
f
n
e
g
ativ
e
p
o
la
r
ity
g
en
e
r
atio
n
.
Fig
u
r
e
4
.
Pr
o
p
o
s
ed
Hex
a
m
u
lt
ilev
el
in
v
er
ter
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
5
.
Var
io
u
s
o
p
er
atio
n
al
m
o
d
es o
f
Hex
a
ML
I
;
(
a)
o
u
tp
u
t v
o
ltag
e
lev
el
o
f
2
V
DC
,
(
b
)
o
u
tp
u
t
v
o
ltag
e
lev
el
o
f
1
.
5
V
DC
,
(
c)
o
u
tp
u
t
v
o
ltag
e
l
ev
el
o
f
V
DC
,
(
d
)
o
u
tp
u
t v
o
ltag
e
lev
el
o
f
-
V
DC
,
(
e)
o
u
tp
u
t v
o
ltag
e
lev
el
o
f
-
1
.
5
V
DC
,
(
f
)
o
u
tp
u
t v
o
ltag
e
lev
el
o
f
-
2V
DC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
69
4
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
23
05
–
23
13
2310
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Pro
p
o
s
ed
Hex
a
ML
I
is
d
esig
n
ed
a
n
d
s
im
u
lated
with
MA
T
L
AB
/Si
m
u
lin
k
.
T
wo
s
y
m
m
etr
ical
DC
v
o
ltag
e
s
o
u
r
ce
s
o
f
2
4
V
a
r
e
c
o
n
n
ec
ted
i
n
th
e
d
esig
n
o
f
Hex
a
ML
I
to
g
en
er
ate
s
ev
e
n
lev
el
4
8
V
o
u
tp
u
t
v
o
ltag
e
ac
r
o
s
s
r
esis
tiv
e
lo
ad
o
f
5
0
Ω
.
Prim
ar
y
cr
iter
ia
o
f
th
e
p
r
o
p
o
s
ed
wo
r
k
is
to
im
p
lem
en
t
th
e
o
p
er
atio
n
o
f
Hex
a
ML
I
with
v
ar
io
u
s
PW
M
tech
n
iq
u
es.
APOD,
POD,
PD
ar
e
t
h
e
p
r
ef
e
r
r
ed
PW
M
tech
n
iq
u
es
in
th
e
o
p
e
r
atio
n
o
f
Hex
a
ML
I
an
d
th
e
g
en
er
ated
o
u
tp
u
t
v
o
ltag
e
an
d
c
u
r
r
e
n
t
ar
e
o
b
s
er
v
ed
with
th
e
v
ar
io
u
s
m
o
d
u
latio
n
i
n
d
e
x
v
alu
es.
As
a
r
esu
ltan
t
to
f
in
d
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
o
u
tp
u
t
p
a
r
am
eter
s
,
T
HD
o
b
s
er
v
ati
o
n
o
f
th
e
p
r
o
p
o
s
ed
ML
I
is
an
aly
ze
d
u
n
d
er
v
ar
io
u
s
PW
M
tech
n
iq
u
es in
s
im
u
latio
n
as sh
o
wn
in
Fig
u
r
e
6
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(f)
(
g
)
(
h
)
Fig
u
r
e
6
.
Sev
e
n
lev
el
o
u
tp
u
t v
o
ltag
e,
cu
r
r
en
t a
n
d
th
eir
c
o
r
r
es
p
o
n
d
in
g
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
with
,
(
a)
APOD,
Mo
d
u
latio
n
I
n
d
ex
1
,
(
b
)
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Mo
d
u
latio
n
I
n
d
e
x
0
.
9
,
(
c)
APOD,
Mo
d
u
latio
n
I
n
d
ex
0
.
8
,
(
d
)
POD,
Mo
d
u
latio
n
I
n
d
e
x
1
,
(
e)
POD,
Mo
d
u
latio
n
I
n
d
e
x
0
.
9
,
(
f
)
POD,
Mo
d
u
latio
n
I
n
d
e
x
0
.
8
,
(
g
)
PD,
Mo
d
u
latio
n
I
n
d
ex
1
,
(
h
)
PD,
Mo
d
u
latio
n
i
n
d
ex
0
.
9
,
(
i)
PD,
Mo
d
u
latio
n
I
n
d
ex
0
.
8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
R
ea
l time
s
imu
la
tio
n
o
f red
u
ce
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w
itch
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ltil
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el
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ve
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r
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i
tch
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K
a
n
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V
in
o
d
K
u
ma
r
)
2311
T
o
v
er
i
f
y
t
h
e
o
b
tain
ed
o
u
tp
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t
p
ar
am
eter
s
o
f
th
e
Hex
a
ML
I
i
n
r
ea
l
tim
e,
p
r
o
p
o
s
ed
m
o
d
el
i
s
o
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ated
b
y
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R
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lin
k
m
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l
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ilt
o
n
th
e
R
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L
AB
an
d
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ed
t
o
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e
r
ea
l
tim
e
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te
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f
ac
e
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T
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7
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alo
g
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u
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ts
o
f
v
o
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e
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d
cu
r
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en
t
o
f
ML
I
in
r
e
al
tim
e
ar
e
r
ec
o
r
d
e
d
with
d
i
g
ital
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ig
n
al
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s
cillo
s
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p
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Ma
x
im
u
m
o
u
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t
r
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g
e
o
f
OP
AL
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7
0
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is
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r
o
m
1
6
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to
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o
u
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t
v
o
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f
4
8
V
is
s
ca
led
to
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it
o
f
1
6
V
an
d
s
h
o
wn
in
Fig
u
r
e
6
.
R
ea
l
tim
e
T
HD
o
b
s
er
v
a
tio
n
is
r
ec
o
r
d
ed
f
o
r
th
e
v
ar
io
u
s
ca
r
r
ier
f
r
eq
u
e
n
cy
PW
M
tech
n
iq
u
es
at
d
if
f
er
en
t
v
alu
e
o
f
m
o
d
u
latio
n
in
d
e
x
es
f
r
o
m
1
.
1
to
0
.
7
.
Ob
tain
ed
o
u
tp
u
t
v
o
ltag
es,
cu
r
r
en
ts
an
d
th
eir
c
o
r
r
esp
o
n
d
in
g
h
ar
m
o
n
ic
an
aly
s
is
ar
e
s
h
o
wn
in
Fi
g
u
r
e
6
w
ith
m
o
d
u
latio
n
in
d
e
x
o
f
1
,
0
.
9
a
n
d
0
.
8
.
Fig
u
r
e
s
6
(a
)
-
(
c)
s
h
o
ws
th
e
p
er
f
o
r
m
an
ce
p
ar
am
eter
s
an
d
T
HD
an
aly
s
is
o
f
Hex
a
ML
I
with
APOD
P
W
M
tech
n
iq
u
e.
Fig
u
r
e
s
6
(d
)
-
(
f
)
s
h
o
ws
th
e
v
o
ltag
e,
cu
r
r
en
t
an
d
T
HD
v
alu
es
o
f
p
r
o
p
o
s
e
d
ML
I
with
POD
tech
n
iq
u
e.
Fig
u
r
e
s
6
(g
)
-
(
i)
s
h
o
ws
o
u
tp
u
t
p
ar
am
eter
s
o
f
Hex
a
ML
I
with
P
D
tech
n
i
q
u
e.
T
h
e
r
ea
l
tim
e
s
im
u
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n
ex
p
er
im
e
n
tal
ar
r
an
g
em
en
t is sh
o
wn
in
Fig
u
r
e
7
.
Fig
u
r
e
7
.
R
ea
l tim
e
s
im
u
latio
n
ex
p
er
im
en
tal
s
etu
p
with
OPAL
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R
T
5
7
0
0
Simu
latio
n
an
d
r
ea
l
tim
e
co
m
p
ar
ativ
e
p
r
esen
tatio
n
o
f
r
esu
ltan
t
%THD
o
f
He
x
a
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u
n
d
er
v
ar
io
u
s
ca
r
r
ier
f
r
e
q
u
en
c
y
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tech
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iq
u
es
at
d
if
f
e
r
en
t
m
o
d
u
latio
n
in
d
ex
v
alu
es
ar
e
g
i
v
en
in
T
ab
l
e
3
.
Simu
latio
n
a
n
d
r
ea
l
tim
e
T
HD
v
alu
es
ar
e
m
ee
t
th
e
lim
its
.
PD
PW
M
tech
n
iq
u
e
g
iv
es
th
e
b
etter
p
er
f
o
r
m
an
ce
am
o
n
g
th
r
ee
tech
n
iq
u
es.
An
o
p
tim
al
v
alu
e
o
f
m
o
d
u
latio
n
in
d
e
x
v
alu
e
is
s
u
itab
le
f
o
r
0
.
9
b
ased
o
n
th
e
T
HD
r
esu
lt
an
aly
s
is
in
th
r
ee
PW
M
tech
n
iq
u
es.
C
o
m
p
ar
ativ
e
o
b
s
er
v
atio
n
b
etwe
en
s
i
m
u
lated
T
HD
an
d
r
ea
l tim
e
T
HD
ar
e
s
h
o
wn
in
Fig
u
r
e
s
8
an
d
9
to
f
in
d
th
e
b
et
ter
PW
M
tech
n
iq
u
e
an
d
m
o
d
u
latio
n
in
d
ex
.
T
ab
le
3
.
Simu
latio
n
a
n
d
R
ea
l
T
im
e
T
HD
C
o
m
p
ar
is
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HE
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ML
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7
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3
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5
9
(
a)
(
b
)
Fig
u
r
e
8
.
%THD
co
m
p
ar
is
o
n
b
etwe
en
s
im
u
latio
n
an
d
OPAL
-
R
T
,
(
a)
s
im
u
latio
n
co
m
p
ar
at
iv
e
T
HD
pe
r
f
o
r
m
an
ce
with
APOD,
POD
an
d
PD,
(
b
)
OPAL
-
R
T
co
m
p
ar
ativ
e
T
HD
p
e
r
f
o
r
m
a
n
ce
with
APOD,
POD
an
d
PD
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
69
4
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
23
05
–
23
13
2312
(
a)
(
b
)
(
c)
Fig
u
r
e
9
.
%THD
co
m
p
ar
is
o
n
b
etwe
en
APOD,
POD
an
d
PD,
(
a)
T
HD
co
m
p
ar
is
io
n
o
f
s
im
u
latio
n
an
d
OPAL
-
R
T
with
APOD
P
W
M
tech
n
iq
u
e,
(
b
)
T
HD
co
m
p
a
r
is
io
n
o
f
s
i
m
u
latio
n
an
d
OPAL
-
R
T
with
POD
P
W
M
tech
n
iq
u
e,
(
c
)
T
HD
co
m
p
ar
is
io
n
o
f
s
im
u
latio
n
an
d
OPAL
-
R
T
with
PD
PW
M
tech
n
iq
u
e
5.
CO
NCLU
SI
O
N
Hex
a
m
u
ltil
ev
el
i
n
v
er
ter
with
r
ed
u
ce
d
s
witch
co
u
n
t
is
m
o
d
eled
with
s
im
u
latio
n
an
d
r
ea
l
tim
e
p
latf
o
r
m
s
.
Sev
e
n
lev
el
o
u
tp
u
t
v
o
ltag
e
is
o
b
tain
e
d
ac
r
o
s
s
r
e
s
is
tiv
e
lo
ad
with
o
n
ly
two
DC
v
o
ltag
e
s
o
u
r
ce
s
.
Pro
p
o
s
ed
ML
I
is
v
alid
ated
with
th
e
v
a
r
io
u
s
PW
M
m
eth
o
d
s
an
d
to
f
in
d
th
e
b
est
p
er
f
o
r
m
an
ce
at
d
if
f
er
en
t
v
alu
es
o
f
m
o
d
u
latio
n
in
d
ex
.
Mu
lti
ca
r
r
ier
PW
M
tech
n
iq
u
e
s
with
p
r
o
p
e
r
lo
g
ical
e
x
p
r
ess
io
n
f
o
r
th
e
o
p
e
r
atio
n
o
f
Hex
a
ML
I
s
witch
in
g
s
eq
u
e
n
ce
is
p
e
r
f
o
r
m
ed
.
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tp
u
t
v
o
ltag
e
an
d
o
u
tp
u
t
cu
r
r
en
t
ar
e
o
b
s
er
v
ed
an
d
r
ec
o
r
d
ed
at
d
if
f
er
en
t PW
M
tech
n
iq
u
es
with
th
eir
co
r
r
esp
o
n
d
in
g
T
HD
v
alu
es with
th
e
u
s
e
o
f
OPAL
-
R
T
5
7
0
0
s
im
u
lato
r
.
C
o
m
p
ar
ativ
e
s
tu
d
y
o
f
T
HD
b
etwe
en
s
im
u
latio
n
an
d
r
ea
l
ti
m
e
o
f
p
r
o
p
o
s
ed
Hex
a
ML
I
is
p
er
f
o
r
m
ed
an
d
th
e
p
er
ce
n
tag
e
T
HD
o
f
b
o
th
co
n
d
i
tio
n
s
ar
e
with
in
ac
ce
p
tab
le
s
ta
n
d
ar
d
s
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
a
u
t
h
o
r
s
a
c
k
n
o
w
l
e
d
g
e
t
h
e
s
u
p
p
o
r
t
o
f
D
S
T
-
F
I
S
T
s
p
o
n
s
o
r
e
d
l
a
b
(
P
H
I
L
s
et
u
p
)
a
n
d
V
I
T
m
a
n
a
g
e
m
e
n
t
.
T
h
i
s
w
o
r
k
h
a
s
b
e
e
n
c
a
r
r
i
e
d
o
u
t
i
n
S
m
a
r
t
G
r
id
L
a
b
,
S
c
h
o
o
l
o
f
E
l
ec
t
r
i
c
al
E
n
g
i
n
e
e
r
i
n
g
,
V
e
l
l
o
r
e
I
n
s
t
i
t
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te
o
f
T
e
c
h
n
o
l
o
g
y
,
V
e
l
l
o
r
e
,
I
n
d
i
a
.
RE
F
E
R
E
N
C
E
S
[1
]
R.
Uth
iras
a
m
y
,
U.
S
.
Ra
g
u
p
a
t
h
y
,
a
n
d
V.
Ku
m
a
r,
“
S
tru
c
t
u
re
o
f
b
o
o
st
DC
-
li
n
k
c
a
sc
a
d
e
d
m
u
l
ti
le
v
e
l
i
n
v
e
rter
f
o
r
u
n
i
n
terru
p
ted
p
o
we
r
su
p
p
l
y
a
p
p
li
c
a
ti
o
n
s,”
IET
P
o
we
r
El
e
c
tro
n
.
,
v
o
l.
8
,
n
o
.
1
1
,
p
p
.
2
0
8
5
–
2
0
9
6
,
2
0
1
5
,
d
o
i:
1
0
.
1
0
4
9
/
iet
-
p
e
l.
2
0
1
4
.
0
7
4
6
.
[2
]
A.
Ch
it
ra
,
a
n
d
S
.
Him
a
v
a
th
i,
“
Re
d
u
c
e
d
sw
it
c
h
m
u
lt
il
e
v
e
l
in
v
e
rter
f
o
r
p
e
rfo
rm
a
n
c
e
e
n
h
a
n
c
e
m
e
n
t
o
f
i
n
d
u
c
t
io
n
m
o
t
o
r
d
riv
e
wit
h
in
telli
g
e
n
t
ro
t
o
r
re
si
sta
n
c
e
e
stim
a
to
r,
”
IET
P
o
we
r
El
e
c
tro
n
.
,
v
o
l.
8
,
p
p
.
2
4
4
4
–
2
4
5
3
,
2
0
1
5
,
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o
i:
1
0
.
1
0
4
9
/
iet
-
p
e
l.
2
0
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4
.
0
6
4
8
.
[3
]
G
.
P
.
M
,
M
.
Ba
lam
u
ru
g
a
n
,
a
n
d
S
.
Um
a
sh
a
n
k
a
r,
“
A
n
e
w
m
u
lt
i
lev
e
l
in
v
e
rter
with
re
d
u
c
e
d
n
u
m
b
e
r
o
f
sw
it
c
h
e
s,”
In
t.
J
.
Po
we
r E
lec
tro
n
.
Dr
ive
S
y
st.
,
v
o
l.
5
,
n
o
.
1
,
2
0
1
4
.
[4
]
X.
Do
n
g
,
X.
Yu
,
Z.
Yu
a
n
,
Y.
Xia
,
a
n
d
Y.
Li
,
“
An
imp
ro
v
e
d
S
P
WM
stra
teg
y
to
re
d
u
c
e
sw
it
c
h
in
g
i
n
c
a
sc
a
d
e
d
m
u
lt
il
e
v
e
l
i
n
v
e
rters
,
”
J
.
P
o
we
r E
l
e
c
tro
n
.
,
v
o
l
.
1
6
,
n
o
.
2
,
p
p
.
4
9
0
–
4
9
7
,
2
0
1
6
,
d
o
i:
1
0
.
6
1
1
3
/J
P
E.
2
0
1
6
.
1
6
.
2
.
4
9
0
.
[5
]
A.
Ba
li
k
c
i
a
n
d
E.
A
k
p
i
n
a
r,
“
A
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
with
re
d
u
c
e
d
n
u
m
b
e
r
o
f
sw
it
c
h
e
s
in
S
TAT
COM
fo
r
lo
a
d
b
a
lan
c
in
g
,
”
El
e
c
tr.
P
o
we
r S
y
st.
R
e
s.
,
v
o
l
.
1
2
3
,
p
p
.
1
6
4
–
1
7
3
,
2
0
1
5
,
d
o
i:
1
0
.
1
0
1
6
/j
.
e
p
sr.2
0
1
5
.
0
2
.
0
0
5
.
[6
]
A.
Ch
laih
a
wi,
A.
S
a
b
b
a
r,
a
n
d
H
.
Je
d
i,
“
A
h
ig
h
-
p
e
rf
o
rm
a
n
c
e
m
u
lt
il
e
v
e
l
in
v
e
rter
with
re
d
u
c
e
d
p
o
we
r
e
lec
tro
n
ic
d
e
v
ice
s,”
In
t.
J
.
P
o
we
r
E
lec
tro
n
.
D
riv
e
S
y
st.
,
v
o
l.
1
1
,
n
o
.
4
,
p
p
.
1
8
8
3
–
1
8
8
9
,
2
0
2
0
,
d
o
i:
1
0
.
1
1
5
9
1
/i
j
p
e
d
s.v
1
1
.
i4
.
p
p
1
8
8
3
-
1
8
8
9
.
[7
]
N.
G
h
a
se
m
i,
F
.
Zare
,
C.
Lan
g
t
o
n
,
a
n
d
A.
G
h
o
sh
,
“
A
n
e
w
u
n
e
q
u
a
l
DC
li
n
k
v
o
lt
a
g
e
c
o
n
f
ig
u
ra
ti
o
n
fo
r
a
sin
g
le
p
h
a
se
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
to
re
d
u
c
e
lo
w
o
rd
e
r
h
a
rm
o
n
ics
,
”
in
Pro
c
e
e
d
i
n
g
s
o
f
th
e
2
0
1
1
1
4
th
E
u
ro
p
e
a
n
Co
n
fer
e
n
c
e
o
n
Po
we
r E
lec
tro
n
ics
a
n
d
Ap
p
li
c
a
ti
o
n
s
, 2
0
1
1
,
p
p
.
1
–
9.
[8
]
M
.
S
.
Orfi
Ye
g
a
n
e
,
a
n
d
M
.
S
a
rv
i
,
“
An
im
p
ro
v
e
d
h
a
rm
o
n
ic
in
jec
ti
o
n
P
WM
-
fre
q
u
e
n
c
y
m
o
d
u
late
d
tr
ian
g
u
lar
c
a
rrier
m
e
th
o
d
wi
th
m
u
lt
i
o
b
jec
ti
v
e
o
p
ti
m
iza
ti
o
n
s
fo
r
in
v
e
rters
,
”
El
e
c
tr.
P
o
we
r
S
y
st.
Res
.
,
v
o
l.
1
6
0
,
p
p
.
3
7
2
–
3
8
0
,
2
0
1
8
,
d
o
i
:
1
0
.
1
0
1
6
/
j.
e
p
s
r.
2
0
1
8
.
0
3
.
0
1
1
.
[9
]
W.
Ch
e
n
,
a
n
d
A.
M
.
Ba
z
z
i,
“
Lo
g
ic
-
b
a
se
d
m
e
th
o
d
s
fo
r
in
tel
li
g
e
n
t
fa
u
lt
d
ia
g
n
o
sis
a
n
d
re
c
o
v
e
ry
in
p
o
we
r
e
lec
tro
n
ics
,
”
IEE
E
T
r
a
n
s.
Po
we
r
El
e
c
tro
n
.
,
v
o
l.
3
2
,
n
o
.
7
,
p
p
.
5
5
7
3
–
5
5
8
9
,
2
0
1
7
,
d
o
i:
1
0
.
1
1
0
9
/
TP
EL
.
2
0
1
6
.
2
6
0
6
4
3
5
.
[1
0
]
N.
P
ra
b
a
h
a
ra
n
,
a
n
d
K.
P
a
lan
isa
m
y
,
“
A
c
o
m
p
re
h
e
n
si
v
e
re
v
iew
o
n
re
d
u
c
e
d
sw
it
c
h
m
u
lt
il
e
v
e
l
in
v
e
rter
to
p
o
l
o
g
ies
,
m
o
d
u
lati
o
n
tec
h
n
iq
u
e
s
a
n
d
a
p
p
l
i
c
a
ti
o
n
s,”
Ren
e
w.
S
u
st
a
i
n
.
En
e
rg
y
Rev
.
,
v
o
l.
7
6
,
n
o
.
M
a
rc
h
,
p
p
.
1
2
4
8
–
1
2
8
2
,
2
0
1
7
,
d
o
i:
1
0
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1
0
1
6
/j
.
rse
r.
2
0
1
7
.
0
3
.
1
2
1
.
[1
1
]
S
.
R.
P
o
n
n
u
sa
m
y
,
M
.
S
u
b
ra
m
a
n
iam
,
G
.
Ch
risto
p
h
e
r,
a
n
d
R.
I
ru
d
a
y
a
ra
j,
“
An
im
p
ro
v
e
d
sw
it
c
h
i
n
g
to
p
o
lo
g
y
f
o
r
sin
g
le
p
h
a
se
m
u
lt
il
e
v
e
l
in
v
e
rter
with
c
a
p
a
c
it
o
r
v
o
lt
a
g
e
b
a
lan
c
i
n
g
tec
h
n
iq
u
e
,
”
J
.
Po
we
r
El
e
c
tro
n
.
,
v
o
l.
1
7
,
n
o
.
1
,
p
p
.
115
–
1
2
6
,
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0
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7
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d
o
i:
1
0
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6
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1
3
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P
E.
2
0
1
7
.
1
7
.
1
.
1
1
5
.
[1
2
]
S
.
Um
a
sh
a
n
k
a
r,
T.
S
.
S
re
e
d
e
v
i,
V.
G
.
Nith
y
a
,
a
n
d
D.
Vijay
a
k
u
m
a
r,
“
A
n
e
w
7
-
lev
e
l
sy
m
m
e
tri
c
m
u
lt
il
e
v
e
l
i
n
v
e
rte
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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R
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2313
with
m
in
im
u
m
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s,”
IS
RN
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e
c
tro
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.
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v
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[1
3
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R.
Na
g
a
ra
jan
a
n
d
M
.
S
a
ra
v
a
n
a
n
,
“
P
e
rfo
rm
a
n
c
e
An
a
ly
sis o
f
a
No
v
e
l
Re
d
u
c
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d
S
witc
h
Ca
sc
a
d
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d
M
u
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l
In
v
e
rter,”
J
.
Po
we
r E
lec
tro
n
.
,
v
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l
.
1
4
,
n
o
.
1
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p
p
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2
0
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o
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:
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6
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1
3
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P
E.
2
0
1
4
.
1
4
.
1
.
4
8
.
[1
4
]
S
.
P
.
G
a
u
tam
,
L.
Ku
m
a
r,
a
n
d
S
.
G
u
p
ta,
“
Hy
b
rid
to
p
o
l
o
g
y
o
f
sy
m
m
e
tri
c
a
l
m
u
lt
il
e
v
e
l
in
v
e
rter
u
sin
g
l
e
ss
n
u
m
b
e
r
o
f
d
e
v
ice
s,”
IET
P
o
we
r E
lec
tro
n
.
,
v
o
l.
8
,
n
o
.
1
1
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p
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t
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5
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7
.
[1
5
]
N.
P
ra
b
a
h
a
ra
n
a
n
d
K.
P
a
lan
isa
m
y
,
“
Co
m
p
a
ra
ti
v
e
a
n
a
ly
sis
o
f
sy
m
m
e
tri
c
a
n
d
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sy
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m
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tri
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r
e
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u
c
e
d
sw
it
c
h
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LI
to
p
o
lo
g
ies
u
si
n
g
u
n
ip
o
lar
p
u
lse
wid
th
m
o
d
u
latio
n
stra
teg
ies
,
”
IE
T
Po
we
r
El
e
c
tro
n
.
,
v
o
l.
9
,
p
p
.
2
8
0
8
–
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2
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e
t
-
p
e
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2
0
1
6
.
0
2
8
3
.
[1
6
]
Y.
Visw
a
n
a
th
,
K.
M
u
ra
li
k
u
m
a
r,
P
.
P
o
n
n
a
m
b
a
lam
,
a
n
d
M
.
P
.
Ku
m
a
r,
“
S
y
m
m
e
tri
c
a
l
c
a
sc
a
d
e
d
sw
it
c
h
e
d
-
d
io
d
e
m
u
lt
il
e
v
e
l
i
n
v
e
rter wit
h
f
u
z
z
y
c
o
n
tro
ll
e
r,
”
i
n
S
p
rin
g
e
r
,
2
0
1
9
,
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o
.
S
c
sd
M
li
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1
0
0
7
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7
8
-
9
8
1
-
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1
5
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5
-
4.
[1
7
]
J.
Ch
e
n
,
C.
Wan
g
,
a
n
d
J.
Li
,
“
S
in
g
le
-
p
h
a
se
ste
p
-
u
p
fiv
e
-
lev
e
l
i
n
v
e
r
ter
with
p
h
a
se
-
sh
ift
e
d
p
u
lse
wid
t
h
m
o
d
u
latio
n
,
”
J
.
Po
we
r E
lec
tro
n
.
,
v
o
l
.
1
9
,
n
o
.
1
,
p
p
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1
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4
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4
5
,
2
0
1
9
,
d
o
i
:
1
0
.
6
1
1
3
/
J
P
E.
2
0
1
9
.
1
9
.
1
.
1
3
4
.
[1
8
]
J.
Ha
m
m
a
n
,
a
n
d
F
.
S
.
v
a
n
d
e
r
M
e
rwe
,
“
Vo
lt
a
g
e
h
a
rm
o
n
ics
g
e
n
e
ra
ted
b
y
v
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lt
a
g
e
-
fe
d
in
v
e
rters
u
si
n
g
P
WM
n
a
tu
ra
l
sa
m
p
l
in
g
,
”
IE
EE
T
r
a
n
s.
Po
we
r E
l
e
c
tro
n
.
,
v
o
l
.
3
,
n
o
.
1
,
p
p
.
1
–
6
,
1
9
8
8
.
[1
9
]
G
.
Ca
rra
ra
,
S
.
G
a
rd
e
ll
a
,
M
.
M
a
rc
h
e
so
n
i,
R.
S
a
lu
tari,
a
n
d
G
.
S
c
iu
tt
o
,
“
A
n
e
w
m
u
lt
il
e
v
e
l
P
WM
m
e
th
o
d
:
a
t
h
e
o
re
ti
c
a
l
an
a
ly
sis,”
IEE
E
T
ra
n
s
.
Po
we
r E
lec
tro
n
.
,
v
o
l.
7
,
n
o
.
3
,
p
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9
9
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9
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6
3
.
1
4
5
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.
[2
0
]
A.
M
.
Ha
v
a
,
a
n
d
E
.
Ün
,
“
P
e
rfo
r
m
a
n
c
e
a
n
a
ly
sis
o
f
re
d
u
c
e
d
c
o
m
m
o
n
-
m
o
d
e
v
o
lt
a
g
e
P
WM
m
e
th
o
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s
a
n
d
c
o
m
p
a
ris
o
n
with
sta
n
d
a
rd
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WM
m
e
th
o
d
s
fo
r
th
re
e
-
p
h
a
se
v
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lt
a
g
e
-
s
o
u
rc
e
in
v
e
r
ters
,
”
IEE
E
T
ra
n
s.
P
o
we
r
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e
c
tro
n
.
,
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o
l
.
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.
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0
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7
1
9
.
[2
1
]
K.
G
o
p
a
lak
rish
n
a
n
,
M
.
S
.
Ra
j,
a
n
d
T.
S
a
ra
v
a
n
a
n
,
“
Ha
rm
o
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ic
e
v
a
lu
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ti
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f
m
u
l
ti
c
a
rrier
P
wm
tec
h
n
iq
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e
s
fo
r
c
a
sc
a
d
e
d
m
u
lt
il
e
v
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l
in
v
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M
id
d
le
-
Ea
st
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.
S
c
i.
Res
.
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l.
2
0
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n
o
.
7
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p
.
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5
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/
id
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si.me
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2
0
1
4
.
2
0
.
0
7
.
2
1
4
.
[2
2
]
K.
S
.
G
o
p
a
lak
rish
n
a
n
a
n
d
G
.
Na
ra
y
a
n
a
n
,
“
S
p
a
c
e
v
e
c
to
r
b
a
se
d
m
o
d
u
lati
o
n
sc
h
e
m
e
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r
re
d
u
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g
c
a
p
a
c
it
o
r
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S
c
u
rre
n
t
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th
re
e
-
lev
e
l
d
i
o
d
e
-
c
la
m
p
e
d
in
v
e
rter,”
El
e
c
tr.
Po
we
r
S
y
st.
Res
.
,
v
o
l.
1
1
7
,
p
p
.
1
–
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3
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0
1
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:
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6
/
j.
e
p
sr.
2
0
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4
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0
6
.
0
2
5
.
[2
3
]
H.
P
.
Ve
m
u
g
a
n
ti
,
D.
S
r
e
e
n
i
v
a
sa
ra
o
,
a
n
d
G
.
S
.
K
u
m
a
r,
“
Im
p
ro
v
e
d
p
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lse
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wid
th
m
o
d
u
lati
o
n
sc
h
e
m
e
fo
r
T
-
ty
p
e
m
u
lt
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e
v
e
l
i
n
v
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rter,”
IE
T
P
o
we
r E
lec
tro
n
.
,
v
o
l
.
1
0
,
n
o
.
8
,
p
p
.
9
6
8
–
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7
6
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0
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7
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o
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4
9
/i
e
t
-
p
e
l
.
2
0
1
6
.
0
7
2
9
.
[2
4
]
K.
V.
Ku
m
a
r
,
a
n
d
R.
S
.
K
u
m
a
r,
“
An
a
ly
sis
o
f
lo
g
ic
g
a
tes
fo
r
g
e
n
e
ra
ti
o
n
o
f
sw
it
c
h
in
g
se
q
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e
n
c
e
in
sy
m
m
e
tri
c
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n
d
a
sy
m
m
e
tri
c
re
d
u
c
e
d
sw
it
c
h
m
u
lt
il
e
v
e
l
in
v
e
rter,”
IEE
E
Ac
c
e
ss
,
v
o
l.
7
,
p
p
.
9
7
7
1
9
–
9
7
7
3
1
,
2
0
1
9
,
d
o
i
:
1
0
.
1
1
0
9
/ac
c
e
ss
.
2
0
1
9
.
2
9
2
9
8
3
6
.
[2
5
]
H.
P
.
Ve
m
u
g
a
n
ti
,
D.
S
re
e
n
iv
a
sa
r
a
o
,
G
.
S
i
v
a
K
u
m
a
r,
a
n
d
A.
S
a
i
S
p
a
n
d
a
n
a
,
“
Re
d
u
c
e
d
c
a
rrier
P
W
M
sc
h
e
m
e
with
u
n
ifi
e
d
lo
g
ica
l
e
x
p
re
ss
io
n
s
fo
r
re
d
u
c
e
d
sw
it
c
h
c
o
u
n
t
m
u
lt
i
lev
e
l
in
v
e
rters
,
”
IET
Po
we
r
El
e
c
tro
n
.
,
v
o
l.
1
1
,
n
o
.
5
,
p
p
.
912
–
9
2
1
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
4
9
/
iet
-
p
e
l.
2
0
1
7
.
0
5
8
6
.
[2
6
]
K.
V.
Ku
m
a
r
a
n
d
R.
S
.
K
u
m
a
r,
“
S
tru
c
tu
re
o
f
bo
o
st
DC
a
n
d
m
u
l
ti
l
e
v
e
l
in
v
e
rter
with
re
d
u
c
e
d
sw
it
c
h
e
s
fo
r
7
lev
e
l,
”
in
2
0
1
9
I
n
n
o
v
a
ti
o
n
s i
n
P
o
we
r a
n
d
Ad
v
a
n
c
e
d
Co
m
p
u
ti
n
g
T
e
c
h
n
o
l
o
g
y
(i
-
PA
CT
)
,
2
0
1
9
,
p
p
.
1
–
6.
[2
7
]
K.
Vin
o
d
Ku
m
a
r
,
a
n
d
R.
S
a
ra
v
a
n
a
Ku
m
a
r,
“
An
a
ly
sis o
f
sw
it
c
h
in
g
se
q
u
e
n
c
e
o
p
e
ra
ti
o
n
fo
r
re
d
u
c
e
d
s
witch
m
u
lt
il
e
v
e
l
in
v
e
rter
wi
th
v
a
ri
o
u
s
p
u
lse
wi
d
th
m
o
d
u
lati
o
n
m
e
t
h
o
d
s,”
Fro
n
t.
En
e
rg
y
Res
.
,
v
o
l.
7
,
p
p
.
1
–
1
2
,
2
0
2
0
,
d
o
i:
1
0
.
3
3
8
9
/fe
n
rg
.
2
0
1
9
.
0
0
1
6
4
.
[2
8
]
K.
Vin
o
d
K
u
m
a
r
,
a
n
d
R.
S
a
ra
v
a
n
a
Ku
m
a
r,
“
S
witch
i
n
g
se
q
u
e
n
c
e
c
o
n
tro
l
o
f
re
d
u
c
e
d
sw
it
c
h
c
o
u
n
t
m
u
l
ti
lev
e
l
i
n
v
e
rter
with
m
u
lt
i
c
a
rrier p
u
lse
wid
th
m
o
d
u
lati
o
n
,
”
I
n
t.
J
.
S
c
i.
T
e
c
h
n
o
l.
Res
.
,
v
o
l.
8
,
n
o
.
1
2
,
p
p
.
3
7
9
0
–
3
7
9
8
,
2
0
1
9
.
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