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:
h
ttp
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//ij
p
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s
.
ia
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co
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THD
r
educ
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a 1
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lev
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e
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using
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a
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co
ntrol tec
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Dew
a
n Ash
ik
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Aiv
e
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M
d Ash
ra
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in
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pa
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)
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th
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c
a
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ted
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rts
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q
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al
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I
n
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ter
Mu
ltil
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T
o
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ar
m
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tio
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T
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s
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c
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a
rticle
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n
d
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r th
e
CC B
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li
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se
.
C
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s
p
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A
uth
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r
:
Dew
an
Ash
ik
u
r
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ah
am
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Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
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lectr
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g
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g
,
Un
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Gr
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ak
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B
an
g
lad
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E
m
ail:
ash
ik
@
u
ap
-
b
d
.
ed
u
1.
I
NT
RO
D
UCT
I
O
N
A
m
u
ltil
ev
el
in
v
er
ter
(
ML
I
)
i
s
a
ty
p
e
o
f
p
o
wer
elec
tr
o
n
ics
s
y
s
tem
th
at
co
n
v
er
ts
m
u
ltip
le
lo
w
-
lev
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DC
in
p
u
ts
in
to
an
AC
o
u
tp
u
t
with
ad
ju
s
tab
le
f
r
eq
u
en
cy
a
n
d
v
o
ltag
e
[
1
]
.
Mu
ltil
ev
el
in
v
er
ter
s
(
ML
I
s
)
ar
e
s
o
p
h
is
ticated
iter
atio
n
s
o
f
tw
o
-
lev
el
in
v
e
r
ter
s
d
esig
n
ed
f
o
r
m
ed
iu
m
-
an
d
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
[
2
]
.
T
h
e
th
r
ee
-
lev
el
co
n
v
er
ter
[
3
]
s
er
v
e
d
as
th
e
f
o
u
n
d
atio
n
al
co
n
ce
p
t th
at
in
itiated
th
e
ev
o
lu
tio
n
o
f
ML
I
s
.
T
h
ey
co
n
s
is
t
o
f
a
n
etwo
r
k
o
f
p
o
wer
s
em
ico
n
d
u
ct
o
r
s
an
d
ca
p
ac
itiv
e
v
o
ltag
e
s
o
u
r
ce
s
th
at
ca
n
d
eliv
e
r
a
s
tep
p
ed
v
o
ltag
e
wav
ef
o
r
m
r
esem
b
lin
g
a
s
in
u
s
o
id
al
s
h
ap
e
wh
en
i
n
ter
co
n
n
ec
ted
an
d
r
eg
u
lated
[
4
]
.
T
h
e
g
r
o
win
g
u
s
e
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
in
clu
d
in
g
s
o
lar
p
h
o
to
v
o
ltaic
an
d
win
d
en
er
g
y
s
y
s
tem
s
,
n
ec
ess
itates
th
e
d
ev
elo
p
m
e
n
t
o
f
cu
ttin
g
-
ed
g
e
tech
n
o
lo
g
y
f
o
r
ef
f
icien
t
i
n
teg
r
atio
n
[
5
]
.
Mu
ltil
ev
el
in
v
e
r
ter
s
(
ML
I
s
)
o
f
f
e
r
s
u
p
er
io
r
o
u
tp
u
t
wav
ef
o
r
m
q
u
a
lity
,
r
ed
u
ce
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
im
p
r
o
v
ed
elec
tr
o
m
ag
n
etic
co
m
p
atib
ilit
y
,
an
d
a
m
o
d
u
lar
s
tr
u
ctu
r
e,
m
ak
in
g
t
h
em
s
u
itab
le
f
o
r
a
wid
e
r
an
g
e
o
f
ap
p
licatio
n
s
[
6
]
.
T
h
eir
e
f
f
ic
ien
cy
,
h
ig
h
v
o
ltag
e
ca
p
ac
ity
,
an
d
im
p
r
o
v
ed
p
er
f
o
r
m
an
ce
m
ak
e
t
h
ese
d
ev
ices h
ig
h
ly
attr
ac
tiv
e
in
p
o
wer
elec
tr
o
n
ics [
7
]
,
[
8
]
.
C
o
n
v
en
t
io
n
a
l
m
u
l
t
il
ev
e
l
in
v
e
r
ter
to
p
o
lo
g
ie
s
l
ik
e
f
ly
in
g
c
ap
ac
it
o
r
,
d
io
d
e
-
c
lam
p
ed
,
an
d
ca
s
c
ad
ed
H
-
b
r
id
g
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co
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v
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ter
s
f
a
ce
a
r
ap
id
in
cr
ea
s
e
in
p
o
we
r
d
e
v
ice
s
wi
th
h
ig
h
er
o
u
tp
u
t
v
o
lt
ag
e
l
ev
e
l
s
.
T
h
is
ex
p
o
n
en
ti
al
g
r
o
wt
h
co
m
p
lic
at
es
th
e
in
v
er
t
er
,
r
e
s
u
lt
in
g
in
in
cr
ea
s
ed
co
s
t
s
,
l
o
s
s
e
s
,
an
d
m
o
r
e
s
t
r
in
g
en
t
co
n
tr
o
l
an
d
th
er
m
al
m
an
a
g
em
en
t
n
ee
d
s
[
8
]
.
V
ar
i
o
u
s
to
p
o
lo
g
ie
s
wer
e
p
r
o
p
o
s
e
d
to
ad
d
r
e
s
s
th
e
i
s
s
u
e
s
wi
th
co
n
v
en
tio
n
al
ML
I
[
9
]
,
[
1
0
]
.
P
r
io
r
s
tu
d
ie
s
[
1
1
]
h
av
e
h
ig
h
l
ig
h
ted
t
h
e
l
im
it
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io
n
s
a
s
s
o
c
ia
te
d
w
i
th
co
n
v
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io
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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I
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N:
2088
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8
6
9
4
THD
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ed
u
ctio
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in
a
1
3
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leve
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mu
ltil
ev
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in
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ter u
s
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(
Dewa
n
A
s
h
iku
r
R
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h
a
ma
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1983
m
o
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la
r
s
tr
u
c
tu
r
es
.
A
li
s
h
a
h
e
t
a
l.
[
1
2
]
i
n
tr
o
d
u
ce
d
a
to
p
o
lo
g
y
w
i
th
tw
o
r
ev
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s
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-
co
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ec
te
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ty
p
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s
t
r
u
c
tu
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e
s
,
ac
h
i
ev
in
g
a
9
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lev
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o
u
tp
u
t
w
ith
o
u
t
an
H
-
b
r
id
g
e
.
Ho
s
s
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.
[
1
3
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p
r
o
p
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s
e
d
a
m
o
d
if
ied
H
-
b
r
id
g
e
in
v
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ter
u
s
in
g
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d
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s
,
c
ap
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ci
t
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s
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an
d
m
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tip
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C
s
o
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to
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ea
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v
ar
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u
s
v
o
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ag
e
le
v
el
s
,
wi
th
ca
p
ac
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s
ch
ar
g
ed
t
o
t
w
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th
e
in
p
u
t
v
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tag
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f
o
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en
h
an
ce
d
m
o
d
u
la
tio
n
p
er
f
o
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m
an
c
e.
Mu
l
ti
lev
el
in
v
er
t
er
s
(
ML
I
s
)
u
s
e
m
u
l
t
ip
l
e
i
n
v
er
ter
u
n
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f
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v
ar
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u
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s
[
1
4
]
-
[
1
6
]
.
W
h
il
e
th
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s
tep
p
ed
o
u
tp
u
t
ca
n
in
tr
o
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g
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o
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in
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ch
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in
ML
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s
.
ML
I
s
ex
h
ib
it
s
ev
er
a
l
l
im
it
at
io
n
s
,
m
o
s
t
n
o
t
ab
ly
t
h
e
r
eq
u
ir
em
en
t
f
o
r
n
u
m
er
o
u
s
p
o
w
er
s
wi
tch
e
s
,
wh
ich
in
cr
e
as
e
s
d
es
ig
n
co
m
p
lex
i
ty
[
1
7
]
-
[
2
0
]
.
A
l
th
o
u
g
h
lo
w
-
v
o
lt
ag
e
s
wi
tc
h
e
s
ca
n
b
e
u
s
ed
,
ea
ch
d
ev
ic
e
s
ti
ll
n
ee
d
s
d
ed
ic
at
ed
g
at
e
-
d
r
iv
i
n
g
an
d
p
r
o
tec
t
io
n
ci
r
cu
itry
,
th
e
r
eb
y
elev
at
in
g
co
s
t
an
d
s
y
s
t
em
in
tr
ica
cy
.
T
o
m
i
t
ig
a
te
th
es
e
ch
a
l
len
g
e
s
,
v
ar
io
u
s
in
n
o
v
at
iv
e
M
L
I
co
n
f
ig
u
r
a
t
io
n
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
th
a
t
r
ed
u
ce
th
e
n
u
m
b
er
o
f
D
C
s
o
u
r
ce
s
an
d
b
r
id
g
e
s
w
it
ch
e
s
r
el
at
iv
e
to
co
n
v
en
tio
n
al
ar
ch
it
ec
tu
r
e
s
[
2
1
]
,
[
2
2
]
.
Ho
w
ev
er
,
in
o
r
d
er
to
g
en
er
a
te
o
u
tp
u
t
v
o
lt
ag
e
s
w
ith
co
n
s
is
ten
t
s
tep
l
ev
e
l
s
,
m
an
y
o
f
t
h
es
e
m
o
r
e
r
ec
en
t
in
v
er
ter
s
s
t
il
l r
ely
o
n
n
u
m
er
o
u
s
b
id
i
r
ec
t
io
n
a
l
s
w
i
tch
e
s
[
2
3
]
,
[
2
4
]
.
R
e
s
ea
r
ch
o
n
ca
s
ca
d
e
d
m
u
lt
il
ev
e
l
in
v
er
t
er
s
(
ML
I
s
)
h
a
s
s
h
o
wn
th
a
t
v
ar
io
u
s
co
n
f
ig
u
r
a
ti
o
n
s
,
s
u
ch
a
s
u
n
id
i
r
ec
t
io
n
a
l
s
w
it
ch
e
s
,
en
ab
le
h
ig
h
er
o
u
tp
u
t
v
o
l
tag
e
l
ev
e
ls
wh
il
e
r
ed
u
cin
g
co
m
p
o
n
en
t
co
u
n
t
s
an
d
co
s
t
s
[
2
3
]
.
Ho
w
ev
er
,
ch
al
len
g
e
s
p
e
r
s
is
t
r
eg
ar
d
in
g
th
e
n
e
ed
f
o
r
l
ar
g
er
D
C
-
lin
k
v
o
lt
ag
e
s
an
d
e
f
f
ec
tiv
e
m
u
l
ti
lay
e
r
m
o
d
u
la
t
io
n
t
ec
h
n
iq
u
es
.
Mo
s
t
ex
i
s
t
in
g
s
tu
d
ie
s
h
av
e
f
o
cu
s
ed
o
n
eq
u
a
l
-
s
t
ep
s
wi
tch
in
g
-
a
n
g
l
e
m
eth
o
d
s
,
l
ac
k
in
g
a
s
y
s
te
m
a
ti
c
co
m
p
ar
i
s
o
n
wi
t
h
s
in
u
s
o
id
al
s
w
it
ch
in
g
-
an
g
le
tech
n
iq
u
e
s
u
n
d
e
r
id
en
ti
ca
l
o
p
er
a
tin
g
co
n
d
it
io
n
s
[
2
5
]
.
Sw
i
tch
in
g
an
g
l
es
d
e
ter
m
in
e
th
e
in
v
er
ter
s
w
it
ch
in
g
i
n
s
tan
ts
an
d
d
ir
ec
tly
co
n
tr
o
l
t
h
e
h
ar
m
o
n
i
c
co
n
t
en
t
o
f
th
e
o
u
tp
u
t
v
o
l
tag
e
[
2
6
]
.
On
e
s
wi
tch
in
g
an
g
le
i
s
u
s
ed
to
r
eg
u
la
te
th
e
f
u
n
d
a
m
en
ta
l
v
o
l
tag
e
,
wh
i
le
th
e
r
em
a
in
i
n
g
an
g
le
s
a
r
e
s
e
le
ct
e
d
to
e
lim
in
ate
s
p
ec
if
ic
l
o
w
-
o
r
d
er
h
ar
m
o
n
i
c
s
[
2
7
]
.
T
h
u
s
,
wi
th
(
m
)
s
wi
tch
in
g
an
g
l
es
,
u
p
to
(
m
-
1
)
h
a
r
m
o
n
ic
o
r
d
er
s
c
an
b
e
e
li
m
in
at
ed
b
y
s
o
lv
in
g
th
e
co
r
r
e
s
p
o
n
d
in
g
h
ar
m
o
n
ic
eq
u
a
tio
n
s
.
T
h
i
s
s
tu
d
y
ad
d
r
e
s
s
e
s
th
e
lim
i
t
at
io
n
s
o
f
p
r
ev
io
u
s
M
AT
L
A
B
-
b
as
ed
m
e
th
o
d
s
f
o
r
id
en
ti
f
y
in
g
s
w
it
ch
i
n
g
an
g
le
s
in
m
o
d
u
l
at
io
n
p
er
f
o
r
m
a
n
ce
b
y
em
p
lo
y
in
g
P
SI
M
d
u
e
to
i
t
s
u
s
e
r
-
f
r
ien
d
ly
s
im
u
la
tio
n
ca
p
a
b
il
it
ie
s
.
I
t
co
m
p
ar
e
s
eq
u
a
l
-
s
t
ep
an
d
s
in
u
s
o
id
a
l
s
w
it
ch
in
g
-
an
g
le
m
e
th
o
d
s
f
o
r
a
1
3
-
lev
el
ca
s
c
ad
ed
H
-
b
r
i
d
g
e
i
n
v
er
t
er
,
u
ti
li
zin
g
a
co
n
s
i
s
t
en
t
a
n
a
ly
t
ic
al
ap
p
r
o
ac
h
s
u
p
p
o
r
ted
b
y
b
o
th
s
i
m
u
l
a
tio
n
s
an
d
lab
o
r
ato
r
y
ex
p
er
i
m
en
t
s
.
T
h
e
r
e
s
u
lt
s
in
d
i
ca
te
th
at
b
o
th
m
e
th
o
d
s
ac
h
iev
e
v
e
r
y
lo
w
to
ta
l
h
ar
m
o
n
i
c
d
i
s
to
r
tio
n
(
T
HD
)
,
p
r
o
v
id
in
g
v
al
u
ab
le
in
s
i
g
h
t
s
f
o
r
im
p
l
em
en
ta
ti
o
n
.
2.
M
E
T
H
O
D
D
eter
m
in
in
g
c
o
n
d
u
ctio
n
(
s
witch
in
g
)
an
g
les
i
n
a
n
ML
I
is
cr
itical
f
o
r
g
en
er
atin
g
p
r
o
p
er
g
atin
g
s
ig
n
als.
T
wo
m
eth
o
d
s
ar
e
co
m
m
o
n
ly
u
s
ed
:
th
e
eq
u
al
-
an
g
l
e
tech
n
iq
u
e,
wh
ich
ap
p
lies
u
n
if
o
r
m
co
n
d
u
ctio
n
p
er
io
d
s
,
an
d
th
e
s
in
u
s
o
id
al
-
a
n
g
le
tech
n
iq
u
e,
wh
ich
v
ar
ies
th
ese
p
er
io
d
s
b
ased
o
n
a
d
e
f
in
ed
f
o
r
m
u
la.
T
h
e
f
o
r
m
u
la
is
s
h
o
wn
i
n
(
1
)
.
=
s
in
−
1
(
)
(
1
)
W
h
er
e
Vo
d
en
o
tes
th
e
o
u
tp
u
t
v
o
ltag
e
at
a
s
p
ec
if
ic
m
o
m
e
n
t,
wh
ile
Vm
d
en
o
tes
th
e
p
ea
k
v
o
ltag
e
o
f
th
at
lev
el.
Fo
r
ex
am
p
le,
t
o
d
ev
el
o
p
a
5
-
le
v
el
m
u
ltil
ev
el
in
v
er
ter
u
s
in
g
(
1
)
.
To
d
e
v
elo
p
a
5
-
lev
el
ML
I
is
r
eq
u
ir
ed
:
n
u
m
b
er
o
f
H
-
b
r
id
g
es
=
2
,
n
u
m
b
er
o
f
I
GB
T
s
=
8
,
n
u
m
b
er
o
f
D
C
s
o
u
r
ce
s
=
2
,
an
d
n
u
m
b
er
o
f
g
ate
p
u
ls
es =
8
.
W
e
k
n
o
w
th
at
f
o
r
a
co
m
p
lete
cy
cle
tim
e
p
er
io
d
,
T
=
3
6
0
°
an
d
f
o
r
a
50
Hz
s
ig
n
al,
T
=
1
=
1
50
=
0
.
0
2
s
ec
.
I
n
Fig
u
r
e
1
,
th
e
e
x
p
ec
ted
o
u
tp
u
t
o
f
5
-
lev
el
ML
I
is
s
h
o
wn
.
T
h
e
ca
lcu
latio
n
p
r
o
c
ess
f
o
r
ea
ch
a
n
g
le
is
lik
e:
-
W
h
en
th
e
s
u
p
p
ly
v
o
ltag
e
V1
=
0
v
,
=
s
in
−
1
24
=
0
°
-
W
h
en
th
e
s
u
p
p
ly
v
o
ltag
e
V2
=
1
2
v
,
=
s
in
−
1
12
24
=
3
0
°
-
W
h
en
th
e
s
u
p
p
ly
v
o
ltag
e
V3
=
2
4
v
,
=
s
in
−
1
24
24
=
9
0
°
-
W
h
en
th
e
s
u
p
p
ly
v
o
ltag
e
V1
=
-
1
2
v
,
=
s
in
−
1
−
12
24
=
-
30
°
-
W
h
en
th
e
s
u
p
p
ly
v
o
ltag
e
V1
=
-
2
4
v
,
=
s
in
−
1
−
24
24
=
-
90
°
T
h
e
wo
r
k
f
lo
w
p
r
esen
ted
in
F
ig
u
r
e
2
f
o
ll
o
ws
s
ev
er
al
ess
en
tial
s
tag
es.
I
n
itially
,
a
s
witch
i
n
g
d
ev
ice
lik
e
an
I
GB
T
o
r
MO
SF
E
T
is
ch
o
s
en
.
T
h
e
in
v
er
ter
lev
el
is
d
ef
in
ed
,
a
n
d
th
e
cir
cu
it
is
m
o
d
eled
in
PS
I
M
with
p
r
ed
eter
m
in
e
d
s
witch
in
g
an
g
l
es
f
o
r
E
q
u
al
Step
an
d
Sin
u
s
o
id
al
An
g
le
ap
p
r
o
ac
h
es.
T
h
e
s
i
m
u
latio
n
g
en
e
r
ates
o
u
tp
u
t
wav
e
f
o
r
m
s
,
wh
ic
h
ar
e
an
aly
ze
d
f
o
r
FF
T
s
p
ec
tr
u
m
an
d
T
HD
v
alu
es,
o
r
g
an
ize
d
i
n
tab
u
lar
f
o
r
m
.
T
h
e
m
eth
o
d
o
l
o
g
y
o
f
th
is
wo
r
k
is
s
h
o
wn
in
Fig
u
r
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1982
-
1
9
9
3
1984
T
h
e
p
r
o
p
o
s
ed
ML
I
cir
cu
it,
d
e
p
icted
in
Fig
u
r
e
3
,
f
ea
tu
r
es
th
r
ee
H
-
b
r
id
g
e
in
v
er
ter
m
o
d
u
les
co
n
n
ec
ted
in
s
er
ies,
with
ea
ch
m
o
d
u
le
s
u
p
p
lied
b
y
a
s
ep
ar
ate
DC
s
o
u
r
ce
(
1
2
V
,
2
4
V,
an
d
3
6
V
)
f
r
o
m
b
atter
ies
t
o
ac
h
iev
e
a
s
p
ec
if
ic
o
u
tp
u
t
v
o
lt
ag
e.
T
h
is
d
esig
n
elim
in
ates
th
e
n
ee
d
f
o
r
ca
p
ac
ito
r
s
o
r
v
o
lta
g
e
-
clam
p
in
g
d
io
d
es
d
u
e
to
th
e
s
er
ies co
n
n
ec
tio
n
o
f
AC
ter
m
in
al
v
o
ltag
es with
in
t
h
e
ca
s
ca
d
ed
in
v
er
ter
s
tr
u
ct
u
r
e.
E
ac
h
in
v
er
ter
u
n
it
u
tili
ze
s
o
n
e
o
f
f
o
u
r
I
GB
T
s
witch
es
(
I
GB
T
-
1
,
I
GB
T
-
2
,
I
G
B
T
3
,
an
d
I
GB
T
-
4
)
,
u
n
iq
u
ely
id
en
tifie
d
f
o
r
ea
ch
lev
el
in
v
er
ter
.
T
h
e
m
u
ltil
ay
er
o
u
tp
u
t
is
ac
h
iev
ed
th
r
o
u
g
h
a
d
r
iv
er
cir
cu
it
th
at
ac
tiv
ates
I
GB
T
s
in
a
p
r
im
ar
y
m
u
ltil
ev
el
in
v
er
ter
[
2
6
]
.
T
h
i
s
s
etu
p
u
s
es
f
o
u
r
I
GB
T
s
to
cr
ea
te
a
s
in
g
le
-
p
h
ase
ca
s
ca
d
ed
asy
m
m
etr
ical
s
witch
in
g
DC
v
o
ltag
e
s
o
u
r
ce
ML
I
,
r
esu
ltin
g
in
th
r
ee
lev
els
o
f
DC
v
o
ltag
e.
T
h
e
lo
ad
r
ec
ei
v
es
a
1
3
-
lev
el
AC
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
a
n
H
-
b
r
i
d
g
e
with
an
ad
d
itio
n
al
s
ix
teen
I
GB
T
s
.
Fig
u
r
e
1
.
E
x
p
ec
ted
o
u
tp
u
t w
av
ef
o
r
m
o
f
5
-
lev
el
ML
I
Fig
u
r
e
2
.
W
o
r
k
f
lo
w
d
iag
r
am
Fig
u
r
e
3
.
E
x
p
er
im
e
n
tal
wo
r
k
f
l
o
w
o
f
th
is
r
esear
ch
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
N
u
m
er
o
u
s
s
o
f
twar
e
p
latf
o
r
m
s
-
s
u
ch
as
PS
PICE,
Pro
teu
s
PS
I
M,
MA
T
L
AB
/S
im
u
lin
k
,
an
d
M
u
ltis
im
-
ar
e
av
ailab
le
f
o
r
elec
tr
o
n
ic
cir
cu
it
s
im
u
latio
n
.
Am
o
n
g
th
em
,
PS
I
M
is
wid
ely
r
eg
ar
d
ed
as
esp
ec
ially
ef
f
ec
tiv
e
f
o
r
m
o
d
elin
g
a
n
d
a
n
aly
zin
g
p
o
wer
elec
tr
o
n
ic
s
y
s
tem
s
[
3
]
:
i)
Ver
y
f
ast s
im
u
latio
n
s
p
ee
d
,
es
p
ec
ially
f
o
r
h
ig
h
-
f
r
eq
u
en
cy
s
witch
in
g
cir
cu
its
;
ii)
User
-
f
r
ien
d
ly
in
te
r
f
ac
e
with
e
asy
s
ch
em
atic
d
esig
n
an
d
m
in
i
m
al
s
etu
p
tim
e
;
iii)
Stab
le
an
d
ac
cu
r
ate
m
o
d
elin
g
o
f
s
witch
in
g
d
ev
ices (
MO
SF
E
T
s
,
I
GB
T
s
,
D
io
d
es)
;
iv
)
Su
p
p
o
r
ts
MA
T
L
AB
/Si
m
u
lin
k
co
-
s
im
u
latio
n
f
o
r
ad
v
an
ce
d
c
o
n
tr
o
l d
esig
n
s
; a
n
d
v)
Pro
v
id
es b
u
ilt
-
in
to
o
ls
f
o
r
FF
T
,
T
HD,
an
d
p
er
f
o
r
m
an
ce
a
n
aly
s
is
.
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
6
9
4
THD
r
ed
u
ctio
n
in
a
1
3
-
leve
l
mu
ltil
ev
el
in
ve
r
ter u
s
in
g
…
(
Dewa
n
A
s
h
iku
r
R
a
h
a
ma
n
)
1985
T
h
e
s
ch
em
atic
d
iag
r
am
s
o
f
th
e
1
3
-
lev
el
ML
I
a
r
e
s
h
o
wn
in
Fig
u
r
e
4
.
I
n
th
is
d
esig
n
,
1
2
I
GB
T
s
ar
e
u
s
ed
to
f
o
r
m
th
r
ee
H
-
b
r
id
g
es,
an
d
th
e
lo
a
d
ter
m
in
al
is
co
n
n
ec
ted
to
a
r
esis
tiv
e
lo
ad
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
is
m
ea
s
u
r
ed
ac
r
o
s
s
th
is
lo
ad
.
T
h
r
ee
asy
m
m
etr
ical
DC
v
o
ltag
e
s
o
u
r
ce
s
(
1
2
V,
2
4
V
,
an
d
3
6
V)
ar
e
u
s
ed
at
th
e
s
u
p
p
ly
ter
m
in
al.
Gatin
g
p
u
ls
es
ar
e
a
p
p
lied
to
th
e
I
GB
T
g
ate
t
er
m
in
als
to
c
o
n
tr
o
l
th
eir
s
witch
in
g
s
tates
an
d
th
e
o
p
er
atio
n
o
f
ea
c
h
H
-
b
r
i
d
g
e.
T
h
e
s
witch
in
g
an
g
les f
o
r
th
e
g
ate
p
u
ls
es we
r
e
ca
lcu
lated
m
an
u
ally
f
o
r
b
o
th
ca
s
es.
T
h
e
p
r
o
p
o
s
ed
an
g
le
co
n
tr
o
l
m
eth
o
d
ef
f
ec
tiv
ely
elim
in
ate
s
ce
r
tain
lo
wer
-
o
r
d
e
r
h
ar
m
o
n
ics
wh
ile
m
ain
tain
in
g
t
h
e
f
u
n
d
am
en
tal
v
o
ltag
e,
th
er
eb
y
s
ettin
g
th
e
s
witch
in
g
an
g
les.
T
h
is
a
p
p
r
o
ac
h
s
ig
n
if
ican
tly
r
ed
u
ce
s
s
witch
in
g
lo
s
s
es,
v
o
lt
ag
e
s
tr
ess
o
n
p
o
wer
d
ev
ices,
a
n
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
T
h
e
s
y
s
tem
's
h
ar
m
o
n
ic
p
er
f
o
r
m
an
ce
is
ev
alu
ated
b
y
ex
am
in
in
g
th
e
v
o
ltag
e
wav
ef
o
r
m
d
eliv
er
ed
to
a
1
k
Ω
r
esis
tiv
e
lo
ad
.
T
h
e
o
u
tp
u
t
o
f
th
i
s
wo
r
k
h
as
b
ee
n
g
en
er
a
ted
in
P
SI
M
s
o
f
tw
ar
e.
Fo
r
th
e
1
3
-
l
ev
e
l
in
v
er
t
er
,
th
e
o
u
tp
u
t
v
o
lt
ag
e
h
as
b
ee
n
m
ea
s
u
r
ed
ac
r
o
s
s
th
e
lo
ad
r
e
s
i
s
to
r
.
Fo
r
b
o
t
h
o
f
th
e
m
eth
o
d
s
,
eq
u
a
l
-
s
tep
s
wi
tch
in
g
an
g
le
an
d
s
i
n
u
s
o
id
al
s
wi
tc
h
in
g
an
g
le,
t
h
e
o
u
t
p
u
t
v
o
l
tag
e
h
a
s
b
ee
n
s
h
o
wn
in
Fig
u
r
e
5
an
d
F
ig
u
r
e
6
.
T
h
e
an
g
le
s
ar
e
d
ete
r
m
i
n
ed
th
r
o
u
g
h
m
a
n
u
a
l
ca
l
cu
l
at
io
n
f
o
r
eq
u
a
l
-
s
t
ep
s
w
it
ch
in
g
,
an
d
f
o
r
s
in
u
s
o
id
a
l
a
n
g
le
s
wi
tc
h
in
g
,
t
h
e
p
r
o
p
o
s
ed
f
o
r
m
u
l
a
h
a
s
b
e
en
u
s
ed
,
wh
ich
i
s
m
en
t
io
n
ed
in
(
1
)
.
T
h
e
v
o
l
tag
e
o
u
tp
u
t
w
av
e
f
o
r
m
s
ar
e
s
h
o
wn
i
n
Fig
u
r
e
5
,
wh
er
e
V
P1
o
n
th
e
y
-
ax
i
s
d
en
o
t
es
th
e
v
a
lu
e
o
f
t
h
e
o
u
tp
u
t
v
o
l
tag
e
an
d
th
e
x
-
a
x
i
s
d
en
o
t
e
s
t
im
e
in
m
il
l
is
ec
o
n
d
s
.
Fig
u
r
e
4
.
C
ir
cu
it
d
iag
r
am
o
f
1
3
-
lev
el
ML
I
Fig
u
r
e
5
.
Vo
ltag
e
wav
ef
o
r
m
f
o
r
1
3
-
lev
el
ML
I
in
eq
u
al
-
s
tep
-
an
g
le
s
witch
in
g
Fig
u
r
e
6
.
Vo
ltag
e
wav
ef
o
r
m
f
o
r
1
3
-
lev
el
ML
I
in
s
in
u
s
o
id
al
s
witch
in
g
an
g
le
tec
h
n
iq
u
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1982
-
1
9
9
3
1986
I
n
Fig
u
r
e
6
,
Vo
u
t
o
n
th
e
y
-
a
x
is
d
en
o
tes
th
e
o
u
tp
u
t
v
o
ltag
e
(
V)
,
wh
ile
th
e
x
-
ax
is
r
ep
r
esen
ts
tim
e
in
m
illi
s
ec
o
n
d
s
(
m
s
)
.
T
h
e
1
3
-
lev
el
m
u
ltil
ev
el
in
v
er
te
r
(
ML
I
)
u
s
in
g
th
e
Sin
u
s
o
id
al
Switch
in
g
An
g
le
T
ec
h
n
iq
u
e
p
r
o
d
u
ce
s
an
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
r
a
n
g
in
g
f
r
o
m
ap
p
r
o
x
im
ately
−7
2
V
to
+7
2
V,
co
m
p
r
is
in
g
th
ir
teen
v
o
ltag
e
lev
els
th
at
r
esem
b
le
a
s
in
u
s
o
id
al
wav
e.
T
h
e
tec
h
n
iq
u
e'
s
ef
f
ec
tiv
en
ess
is
d
em
o
n
s
tr
ated
th
r
o
u
g
h
ad
ju
s
ted
s
witch
in
g
an
g
les
th
at
y
ield
a
s
y
m
m
etr
ical
wav
e
f
o
r
m
,
r
ed
u
ce
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
lo
wer
s
witch
in
g
s
tr
ess
,
an
d
im
p
r
o
v
e
d
o
u
t
p
u
t v
o
ltag
e
q
u
ality
.
Mu
ltil
ev
el
in
v
er
ter
s
ar
e
n
o
w
wid
ely
u
s
ed
in
in
d
u
s
tr
y
f
o
r
v
a
r
io
u
s
ap
p
licatio
n
s
[
2
7
]
.
R
esear
ch
er
s
an
d
en
g
in
ee
r
s
wo
r
ld
wid
e
co
n
tin
u
e
to
d
ev
elo
p
n
ew
to
p
o
lo
g
ies,
co
n
tr
o
l
s
tr
ateg
ies,
an
d
o
p
er
a
tin
g
tech
n
iq
u
es
to
im
p
r
o
v
e
th
eir
p
er
f
o
r
m
an
ce
.
T
h
ese
d
ev
elo
p
m
e
n
ts
aim
to
en
h
an
ce
en
e
r
g
y
ef
f
icien
cy
,
r
eliab
ilit
y
,
an
d
co
s
t
-
ef
f
ec
tiv
en
ess
,
m
ak
in
g
m
u
ltil
ev
el
in
v
er
ter
s
in
cr
ea
s
in
g
ly
a
ttra
ctiv
e
co
m
p
ar
ed
with
co
n
v
en
tio
n
al
two
-
lev
el
to
p
o
lo
g
ies.
I
n
th
is
s
y
s
tem
,
th
e
in
v
er
ter
is
co
n
n
ec
ted
in
s
er
ies
with
an
L
C
f
ilter
,
wh
ich
r
ed
u
ce
s
h
ig
h
-
o
r
d
er
h
ar
m
o
n
ics
in
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
p
r
o
v
id
es
a
m
o
r
e
s
in
u
s
o
id
al
v
o
ltag
e
wav
ef
o
r
m
to
th
e
lo
ad
.
As
s
h
o
wn
in
Fig
u
r
e
7
,
th
e
in
p
u
t
v
o
ltag
e
o
f
t
h
e
L
C
f
ilter
is
d
eter
m
in
ed
b
y
t
h
e
s
witch
in
g
s
tate
S(j)
o
f
th
e
in
v
er
ter
an
d
ca
n
b
e
ex
p
r
ess
ed
as
V
in
=
S(j)
×
V
dc
,
w
h
er
e
S(j)
=
4
-
j
,
Vin
is
th
e
in
p
u
t
v
o
ltag
e
o
f
th
e
L
C
f
ilter
,
Vd
c
is
th
e
D
C
s
u
p
p
ly
v
o
ltag
e,
an
d
S(j)
is
th
e
s
witch
in
g
f
u
n
ctio
n
o
f
th
e
in
v
e
r
ter
,
r
ep
r
esen
tin
g
th
e
s
witch
in
g
s
tate
co
r
r
esp
o
n
d
in
g
to
ea
ch
o
p
er
atin
g
co
n
d
itio
n
.
Fig
u
r
e
7
.
L
C
f
ilter
cir
c
u
it
T
wo
eq
u
atio
n
s
ca
n
b
e
u
s
ed
to
d
escr
ib
e
th
e
L
C
f
ilter
,
wh
ich
is
th
e
d
ep
ictio
n
in
th
e
ab
o
v
e
Fig
u
r
e
7
.
T
h
e
cu
r
r
e
n
t
th
r
o
u
g
h
th
e
f
ilter
i
n
d
u
ctan
ce
is
r
e
p
r
esen
ted
b
y
in
(
2
)
.
=
-
Vr
–
Vc
(
2
)
T
h
e
ca
p
ac
ito
r
v
o
ltag
e
f
o
llo
ws
,
wh
ich
is
r
ep
r
esen
ted
i
n
(
3
)
.
=
–
i0
(
3
)
W
h
er
e
i
is
th
e
to
tal
cu
r
r
en
t
f
lo
win
g
th
r
o
u
g
h
th
e
cir
cu
it.
I
n
ca
s
e
o
f
th
is
r
esear
ch
,
u
s
in
g
th
is
f
o
r
m
u
la,
we
h
av
e
ca
lcu
lated
th
e
v
al
u
es
o
f
t
h
e
c
ap
ac
ito
r
an
d
in
d
u
cto
r
f
o
r
a
1
3
-
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
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6
9
4
I
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t J Po
w
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lec
&
Dr
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s
t
,
Vo
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r
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2
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ase
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g
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h
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r
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r
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e
r
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er
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ad
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13
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lev
el
ML
I
.
Fig
u
r
e
1
2
.
s
h
o
ws
th
e
r
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u
tp
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t
wav
ef
o
r
m
o
f
t
h
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3
-
lev
el
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u
s
in
g
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e
p
r
o
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s
in
u
s
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o
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la.
Af
ter
a
p
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ly
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g
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e
L
C
f
ilter
,
t
h
e
p
r
ac
tical
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u
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t
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ec
o
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es
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o
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g
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o
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ed
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o
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t
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iew
in
Fig
u
r
e
1
3
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le
s
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ik
es in
th
e
wav
ef
o
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m
.
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h
e
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r
o
p
o
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ed
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eth
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e
r
s
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E
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ar
m
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.
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lik
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al
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ir
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atio
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ly
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cle.
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h
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ates
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ith
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r
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o
l stru
ctu
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e.
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h
e
s
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u
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t
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ex
h
ib
its
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s
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k
e
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e
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n
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u
r
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en
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ticu
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en
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GB
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tu
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f
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ile
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o
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n
.
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esear
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h
h
as
in
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icate
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th
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im
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ar
is
o
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o
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k
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wn
in
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ab
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3.
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ab
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3
.
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e
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el
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k
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13
I
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r
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f
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[
1
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,
“
A
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w
mu
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1
5
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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&
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i Sy
s
t
I
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N:
2088
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8
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4
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Dewa
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iku
r
R
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h
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ma
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1989
A
13
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lev
el
in
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ter
'
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HD
p
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f
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s
in
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ested
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,
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th
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th
e
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h
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ig
n
if
ican
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u
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t
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u
ality
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y
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o
wer
in
g
th
e
T
HD
to
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%.
Fig
u
r
e
12
.
Pra
ctica
l o
u
tp
u
t w
a
v
ef
o
r
m
f
o
r
1
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le
v
el
ML
I
Fig
u
r
e
13
.
Af
ter
ap
p
ly
in
g
t
h
e
L
C
f
ilter
4.
CO
NCLU
SI
O
N
T
h
e
wo
r
k
c
o
m
p
ar
es
eq
u
al
-
s
tep
an
d
s
in
u
s
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id
al
s
witch
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g
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an
g
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co
n
tr
o
l
m
eth
o
d
s
f
o
r
a
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lev
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m
etr
ic
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ed
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r
.
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esti
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wed
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at
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s
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d
al
an
g
le
m
eth
o
d
s
ig
n
if
ican
tly
r
ed
u
ce
d
o
u
tp
u
t
v
o
ltag
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
with
T
HD
d
ec
r
ea
s
in
g
f
r
o
m
1
5
.
1
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%
to
2
.
2
4
%
af
ter
L
C
f
ilter
in
g
.
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h
is
in
d
icate
s
th
at
s
in
u
s
o
id
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s
witch
in
g
an
g
les
im
p
r
o
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e
wav
ef
o
r
m
q
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ality
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d
p
r
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id
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n
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icien
t
m
ea
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f
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h
a
r
m
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ic
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ed
u
ctio
n
wh
ile
m
ain
tain
in
g
a
lo
w
s
witch
in
g
f
r
eq
u
e
n
cy
.
Ov
er
all,
th
e
ex
p
er
im
en
tal
an
d
m
o
d
elin
g
r
esu
lts
s
h
o
wed
g
o
o
d
ag
r
ee
m
e
n
t,
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o
u
g
h
th
e
h
a
r
d
war
e
p
r
o
to
ty
p
e
d
is
p
lay
ed
s
witch
in
g
s
p
ik
es
d
u
e
to
n
o
n
-
id
ea
l
ef
f
ec
ts
,
co
n
tr
asti
n
g
th
e
s
im
u
latio
n
'
s
id
ea
l
ass
u
m
p
tio
n
s
.
E
n
h
an
ce
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1982
-
1
9
9
3
1990
tech
n
iq
u
es
lik
e
d
ea
d
-
tim
e
o
p
tim
izatio
n
o
r
s
n
u
b
b
er
cir
c
u
its
m
ay
im
p
r
o
v
e
wav
ef
o
r
m
q
u
ality
i
n
r
ea
l
ap
p
licatio
n
s
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
u
s
es
a
s
im
p
le
s
witch
in
g
-
an
g
le
ca
lcu
latio
n
,
o
f
f
er
i
n
g
a
p
r
ac
tical
alter
n
ativ
e
to
co
m
p
lex
m
o
d
u
latio
n
tech
n
i
q
u
es
wh
ile
ac
h
iev
in
g
ac
ce
p
ta
b
le
h
ar
m
o
n
ic
p
er
f
o
r
m
an
ce
.
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h
e
s
tu
d
y
f
o
cu
s
es
o
n
wav
ef
o
r
m
q
u
ality
an
d
T
HD
r
ed
u
ctio
n
,
leav
in
g
asp
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ts
lik
e
co
n
v
er
ter
ef
f
icien
cy
an
d
lo
n
g
-
ter
m
d
e
p
en
d
a
b
ilit
y
f
o
r
f
u
tu
r
e
r
esear
c
h
.
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tu
r
e
r
esear
ch
will
ex
p
a
n
d
th
e
s
u
g
g
ested
a
p
p
r
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h
to
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ig
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er
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lev
el
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u
ltil
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el
in
v
er
ter
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n
f
ig
u
r
atio
n
s
,
ex
am
i
n
e
s
witch
in
g
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lo
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s
an
d
e
f
f
icien
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a
n
aly
s
is
,
ap
p
ly
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s
ef
u
l
s
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ik
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m
i
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tech
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es,
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n
tr
ast
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g
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ested
ap
p
r
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a
ch
with
s
o
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h
is
ticated
m
o
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latio
n
s
tr
ateg
ies
lik
e
s
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tiv
e
h
ar
m
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n
ic
elim
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(
SHE
-
PW
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,
an
d
ass
ess
th
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s
tr
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s
in
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tim
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o
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in
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to
r
-
d
r
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an
d
r
en
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en
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y
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p
licatio
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s
.
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t
o
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ested
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e
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n
m
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o
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e
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ip
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s
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ee
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s
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ilit
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ef
f
icien
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,
an
d
p
o
wer
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s
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es
in
in
d
u
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o
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d
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ap
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licatio
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s
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will b
e
ex
p
er
im
en
tally
ass
ess
ed
in
f
u
t
u
r
e
wo
r
k
.
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h
is
s
tu
d
y
p
r
im
ar
ily
f
o
c
u
s
es
o
n
th
e
r
ed
u
ctio
n
o
f
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
in
a
1
3
-
lev
el
asy
m
m
etr
ic
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
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er
ter
u
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aly
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ter
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RE
F
E
R
E
NC
E
S
[
1
]
M
.
H
.
R
a
s
h
i
d
,
Po
w
e
r
El
e
c
t
ro
n
i
c
s:
D
e
v
i
c
e
s,
C
i
r
c
u
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t
s,
a
n
d
Ap
p
l
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n
s,
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t
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t
i
o
n
.
P
e
a
r
s
o
n
,
2
0
1
4
.
[
2
]
J.
R
o
d
r
i
g
u
e
z
e
t
a
l
.
,
“
M
u
l
t
i
l
e
v
e
l
C
o
n
v
e
r
t
e
r
s:
A
n
e
n
a
b
l
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n
g
t
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c
h
n
o
l
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y
f
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h
-
p
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n
s
,”
Pr
o
c
e
e
d
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n
g
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o
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e
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EEE
,
v
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l
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9
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n
o
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2
0
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2
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2
3
5
.
[
3
]
D
.
A
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d
T.
K
.
C
h
a
k
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n
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t
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a
l
J
o
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s.
v
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6
.
i
4
.
p
p
2
5
7
0
-
2
5
8
1
.
[
4
]
R
.
B
a
r
z
e
g
a
r
k
h
o
o
,
M
.
F
o
r
o
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s
h
,
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.
S
.
Le
e
,
F
.
B
l
a
a
b
j
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r
g
,
a
n
d
Y
.
P
.
S
i
w
a
k
o
t
i
,
“
S
w
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t
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h
e
d
-
c
a
p
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c
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t
o
r
m
u
l
t
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l
e
v
e
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n
v
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s
:
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c
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m
p
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h
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n
si
v
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v
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w
,
”
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EE
E
T
r
a
n
s
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c
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Po
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s
,
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l
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0
9
/
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2
0
2
2
.
3
1
6
4
5
0
8
.
[
5
]
N
.
M
u
k
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n
d
a
n
C
M
e
t
a
l
.
,
“
A
n
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w
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0
9
/
TI
A
.
2
0
2
2
.
3
2
1
8
5
2
3
.
[
6
]
A
.
R
.
L
o
p
e
z
,
C
.
J.
C
o
r
t
e
s
,
C
.
A
.
Li
mo
n
e
s
-
P
o
z
o
s
,
J.
M
.
S
o
sa,
J.
A
g
u
a
y
o
,
a
n
d
S
.
D
e
Le
o
n
A
l
d
a
c
o
,
“
O
p
t
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ma
l
sw
i
t
c
h
i
n
g
a
n
g
l
e
s
c
a
l
c
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l
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t
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f
o
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m
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m
,
a
c
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mp
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r
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s
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n
,
”
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n
2
0
2
0
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EEE
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t
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r
n
a
t
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t
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s
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C
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p
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g
(
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)
,
I
EEE,
N
o
v
.
2
0
2
0
,
p
p
.
1
–
6.
d
o
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:
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1
1
0
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.
2
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2
0
.
9
2
5
8
6
8
0
.
[
7
]
C
.
I
.
O
d
e
h
,
A
.
L
e
w
i
c
k
i
,
a
n
d
M
.
M
o
r
a
w
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,
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si
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-
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a
r
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s
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d
p
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I
EEE
Ac
c
e
ss
,
v
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l
.
9
,
p
p
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4
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2
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4
3
.
[
8
]
A
.
A
.
T
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a
,
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.
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a
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.
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,
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