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ap
er
a
n
e
w
t
y
p
e
o
f
s
y
m
m
etr
ical
m
u
ltil
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el
i
n
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ter
h
as
b
ee
n
a
n
al
y
ze
d
b
ased
o
n
p
er
f
o
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m
an
c
e
p
ar
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eter
s
th
r
o
u
g
h
v
ar
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s
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tech
n
iq
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es
a
n
d
th
e
s
i
m
u
latio
n
r
es
u
lt
s
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er
e
v
alid
at
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w
it
h
th
e
h
elp
o
f
p
r
o
to
ty
p
e
m
o
d
el.
2.
NE
W
SYM
M
E
T
RICA
L
M
U
L
T
I
L
E
V
E
L
I
NVE
RT
E
R
Mo
r
e
n
u
m
b
er
o
f
s
w
i
tch
e
s
r
eq
u
ir
ed
f
o
r
tr
ad
itio
n
al
m
u
l
tile
v
el
in
v
er
ter
s
,
d
u
e
to
th
i
s
cir
cu
it
co
s
t,
in
s
ta
llatio
n
ar
ea
an
d
s
w
itc
h
i
n
g
lo
s
s
es
b
ec
o
m
es
h
i
g
h
an
d
co
n
tr
o
l
cir
cu
i
t
also
co
m
p
licated
.
T
o
o
v
er
co
m
e
t
h
i
s
p
r
o
b
lem
a
n
e
w
to
p
o
lo
g
y
i
n
tr
o
d
u
ce
d
in
Fig
u
r
e
1
.
T
h
is
to
p
o
lo
g
y
co
n
s
i
s
ts
o
f
3
au
x
iliar
y
s
w
i
tch
e
s
,
4
m
ai
n
s
w
itc
h
es,
3
d
io
d
es
an
d
th
r
ee
DC
s
o
u
r
ce
s
to
f
o
r
m
s
ev
e
n
le
v
el.
T
h
is
n
e
w
to
p
o
lo
g
y
ac
h
ie
v
es
r
ed
u
ctio
n
in
t
h
e
n
u
m
b
er
o
f
m
ai
n
p
o
w
er
s
w
itc
h
es
b
y
4
2
%
.
T
h
e
n
ex
t
h
i
g
h
er
lev
el
ca
n
b
e
o
b
tain
ed
b
y
ad
d
in
g
a
s
in
g
le
s
w
itc
h
,
a
d
io
d
e
an
d
a
DC
s
o
u
r
ce
.
V
DC
V
DC
V
DC
S1
S2
S3
D2
S4
S5
S6
S7
L
O
A
D
Fig
u
r
e
1
.
S
y
m
m
e
tr
ical
m
u
lti
le
v
el
in
v
er
ter
I
n
o
r
d
er
to
o
b
tain
3
V
DC
at
t
h
e
o
u
tp
u
t,
th
e
s
w
i
tch
e
s
S1
,
S2
,
S3
,
S4
an
d
S5
w
er
e
ON.
T
h
e
lo
ad
is
co
n
n
ec
ted
b
et
w
ee
n
S4
a
n
d
S5
.
I
n
th
is
m
o
d
e,
all
th
e
t
h
r
ee
s
o
u
r
ce
s
w
er
e
co
n
n
ec
ted
i
n
s
er
i
es
w
h
ic
h
p
r
o
d
u
ce
s
3V
DC
at
th
e
o
u
tp
u
t.
W
h
e
n
S2
,
S3
,
S4
an
d
S5
w
er
e
ON
a
n
d
d
io
d
e
D1
c
o
n
d
u
cts,
o
n
l
y
t
w
o
s
o
u
r
ce
s
w
er
e
in
s
er
ies
an
d
g
en
er
ate
2
V
DC
.
T
o
g
et
V
DC
at
th
e
o
u
tp
u
t,
s
w
itc
h
S3
,
S4
an
d
S5
is
ON
a
n
d
d
io
d
e
D2
an
d
D1
co
n
d
u
cts.
T
h
e
o
u
tp
u
t
v
o
lta
g
e
le
v
el
s
at
th
e
n
e
g
ati
v
e
h
al
f
c
y
cle
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er
e
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h
iev
ed
b
y
co
n
n
ec
ti
n
g
t
h
e
lo
ad
b
et
w
ee
n
S6
an
d
S7
in
s
tead
o
f
S4
an
d
S
5.
3.
M
O
DULAT
I
O
N
S
T
RA
T
E
G
Y
B
ip
o
lar
m
u
lticar
r
ier
b
ased
P
W
M
s
tr
ateg
ie
s
w
er
e
u
s
ed
to
s
w
itc
h
t
h
e
p
o
w
er
d
ev
ices
t
o
p
r
o
d
u
ce
s
ev
er
al
le
v
els
a
t
th
e
o
u
tp
u
t
v
o
ltag
e.
T
h
e
P
W
M
b
ased
s
tr
at
eg
ies
ar
e
m
o
s
t
p
o
p
u
lar
b
ec
au
s
e
o
f
ca
r
r
ier
,
w
h
ic
h
co
n
tr
o
ls
in
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ter
o
u
tp
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t
v
o
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g
e
th
u
s
o
b
tai
n
ed
b
y
ad
j
u
s
tin
g
th
e
co
n
d
u
ct
in
g
p
er
io
d
s
o
f
p
o
w
er
s
e
m
ico
n
d
u
cto
r
s
w
itc
h
es.
C
ar
r
ier
b
ased
s
tr
ate
g
ies
c
lass
if
ied
a
s
s
in
g
le
ca
r
r
i
er
an
d
m
u
lticar
r
ier
s
tr
ateg
ie
s
.
Mu
lticar
r
ier
P
W
M
s
tr
ateg
ie
s
s
u
ch
a
s
,
P
h
ase
d
i
s
p
o
s
itio
n
P
W
M,
A
lter
n
ate
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
P
W
M
an
d
C
ar
r
ier
o
v
er
lap
p
in
g
P
W
M
w
er
e
i
m
p
l
e
m
en
t
in
t
h
is
p
ap
er
.
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ar
r
ier
b
ased
m
eth
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d
o
p
er
ate
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ased
o
n
th
e
co
m
p
ar
is
o
n
o
f
m
o
d
u
lati
n
g
s
ig
n
al
w
i
th
ca
r
r
ier
s
ig
n
al
s
w
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er
e
ca
r
r
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s
i
g
n
al
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n
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e
tr
ia
n
g
u
lar
,
s
a
w
to
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th
a
n
d
an
y
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t
h
er
s
h
ap
e
b
ased
o
n
co
n
tr
o
l f
r
ee
d
o
m
d
eg
r
ee
in
cl
u
d
in
g
a
m
p
li
tu
d
e,
f
r
eq
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e
n
c
y
a
n
d
o
f
f
s
et
s
b
et
w
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n
ca
r
r
ie
r
s
.
Fo
r
g
ettin
g
‘
m
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1
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r
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d
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ip
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Stra
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T
h
e
ca
r
r
ier
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co
n
s
is
t
o
f
s
a
m
e
f
r
eq
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e
n
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y
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a
n
d
s
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to
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d
e
A
c
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h
e
m
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la
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g
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a
s
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m
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e
A
m
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d
f
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en
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d
is
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lace
d
at
th
e
m
id
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le
o
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t
h
e
ca
r
r
ier
s
et.
T
h
e
f
r
eq
u
en
c
y
r
atio
m
f
is
d
ef
i
n
ed
.
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n
t
h
i
s
p
ap
e
r
,
th
e
m
o
d
u
la
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g
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r
eq
u
en
c
y
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f
i
s
tak
en
a
s
2
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o
d
u
lati
n
g
i
n
d
ex
m
a
v
ar
ied
f
r
o
m
0
.
7
to
1
.
0
.
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Ma
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1
7
:
28
–
35
30
m
f
=
f
c
/ f
m
T
h
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am
p
lit
u
d
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m
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d
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3
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1
.
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Dis
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Str
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s
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ith
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lace
d
ab
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e
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d
b
el
o
w
th
e
ze
r
o
r
ef
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e
n
ce
.
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h
e
ca
r
r
ier
ar
r
an
g
e
m
e
n
t
f
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r
s
e
v
en
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l
i
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ter
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s
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g
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M
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s
h
o
w
n
i
n
Fig
u
r
e
2
.
f
o
r
m
a
=
0
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8
an
d
m
f
=
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Fig
u
r
e
2
.
Mu
lticar
r
ier
A
r
r
a
n
g
e
m
en
t f
o
r
P
DP
W
M
Stra
teg
y
3
.
2
.
Alt
er
na
t
e
P
ha
s
e
O
pp
o
s
it
io
n
Dis
po
s
it
io
n St
ra
t
eg
y
T
h
e
s
ix
ca
r
r
ier
s
ar
e
p
h
ase
d
is
p
lace
d
f
r
o
m
ea
ch
o
t
h
er
b
y
1
8
0
d
eg
r
ee
s
alter
n
atel
y
w
it
h
id
en
tical
f
r
eq
u
en
c
y
an
d
p
ea
k
to
p
ea
k
a
m
p
lit
u
d
e.
Fig
u
r
e
3
Sh
o
w
s
m
u
lticar
r
ier
a
r
r
an
g
e
m
en
t
f
o
r
A
P
OD
m
et
h
o
d
f
o
r
m
a
=
0
.
8
an
d
m
f
=
20.
Fig
u
r
e
3
.
Mu
lticar
r
ier
A
r
r
a
n
g
e
m
en
t f
o
r
A
P
ODP
W
M
Stra
teg
y
3
.
1
Ca
rr
ier
O
v
er
la
pp
ing
Str
a
t
eg
y
T
h
e
C
OP
W
M
s
tr
ateg
y
u
ti
liz
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th
e
co
n
tr
o
l
f
r
ee
d
o
m
d
e
g
r
ee
o
f
er
ec
t
o
f
f
s
et
s
a
m
o
n
g
ca
r
r
ier
s
.
T
h
e
p
r
in
cip
le
o
f
C
OP
W
M
is
to
u
s
e
a
n
u
m
b
er
o
f
o
v
er
lap
p
in
g
ca
r
r
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s
w
i
th
m
o
d
u
lati
n
g
s
i
g
n
al.
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h
e
s
ix
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r
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d
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ch
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h
at
t
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b
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.
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h
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ag
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is
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g
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4
s
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r
m
a
=
0
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8
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d
m
f
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31
Fig
u
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4
.
Mu
lticar
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an
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o
r
C
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s
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4.
SI
M
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8
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1
.
6
4
1
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6
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.
4
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0
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7
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6
5
Fig
u
r
e
2
1
.
%T
HD
co
m
p
ar
is
o
n
o
f
v
ar
io
u
s
m
o
d
u
lat
io
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in
d
ices
Fig
u
r
e
2
2
.
V
RMS
co
m
p
ar
is
o
n
o
f
v
ar
io
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s
m
o
d
u
latio
n
in
d
ices
6.
CO
NCLU
SI
O
N
I
n
t
h
is
p
ap
er
,
th
e
v
ar
io
u
s
m
o
d
u
latio
n
s
tr
ateg
ie
s
f
o
r
r
ed
u
ce
d
s
w
itc
h
s
e
v
e
n
le
v
el
S
y
m
m
etr
ic
al
I
n
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er
ter
h
av
e
b
ee
n
d
is
c
u
s
s
ed
.
T
h
e
v
ar
io
u
s
p
er
f
o
r
m
a
n
ce
p
ar
a
m
eter
s
lik
e
%T
HD
,
V
RM
S
,
Di
s
to
r
tio
n
Facto
r
an
d
C
r
est
Facto
r
h
a
v
e
b
ee
n
a
n
al
y
s
ed
a
n
d
ev
al
u
ated
.
I
t
i
s
o
b
s
er
v
e
d
th
at
th
e
C
ar
r
ier
O
v
er
lap
p
in
g
P
W
M
p
r
o
v
id
es
least
%T
HD
an
d
Dis
to
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tio
n
f
ac
to
r
f
o
r
all
m
a
a
n
d
p
r
o
v
id
es
m
a
x
i
m
u
m
R
MS
v
o
ltag
e
s
w
h
en
co
m
p
ar
ed
to
o
th
er
t
w
o
s
tr
ateg
ie
s
.
A
t
t
h
e
s
a
m
e
ti
m
e
A
P
OD
s
tr
ate
g
y
p
r
o
v
id
es
n
o
m
i
n
al
cr
es
t
f
ac
to
r
.
T
h
e
s
i
m
u
latio
n
r
es
u
lt
s
w
er
e
clo
s
e
l
y
m
atc
h
ed
w
i
th
e
x
p
er
i
m
en
tal
r
es
u
lts
.
RE
F
E
R
E
NC
E
S
[1
]
Ag
e
li
d
is
V
.
G
,
Ca
lais,
M
,
“
A
p
p
li
c
a
ti
o
n
S
p
e
c
if
ic
Ha
r
m
o
n
ic
P
e
rf
o
r
m
a
n
c
e
E
v
a
lu
a
ti
o
n
o
f
M
u
l
ti
c
a
rrier
P
W
M
T
e
c
h
n
iq
u
e
s”
,
IEE
E
P
ES
C
,
p
p
.
1
7
2
-
1
7
8
,
1
9
9
8
.
[2
]
A
z
i
z
J.
A
,
S
a
la
m
Z,
“
A
n
e
w
p
u
lse
w
id
th
m
o
d
u
latio
n
(
P
W
M
)
sc
h
e
m
e
f
o
r
m
o
d
u
lar
stru
c
tu
re
d
m
u
lt
il
e
v
e
l
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter”
,
In
t.
J
o
u
rn
a
l
o
f
E
l
e
c
tro
n
ics
,
v
o
l.
9
1
,
N
o
.
4
,
p
p
2
1
1
-
2
2
6
,
2
0
0
4
.
[3
]
Ba
b
a
e
i
E,
“
A
c
a
sc
a
d
e
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
to
p
o
lo
g
y
w
it
h
re
d
u
c
e
d
n
u
m
b
e
r
o
f
s
w
it
c
h
e
s”
,
IEE
E
T
ra
n
s.
Po
w
e
r
El
e
c
tro
n
.
,
v
o
l
.
2
3
,
n
o
.
6
,
p
p
.
2
6
5
7
–
2
6
6
4
,
2
0
0
8
.
[4
]
Ca
rra
ra
.
G
,
G
a
rd
e
ll
a
.
S
,
M
a
rc
h
e
s
o
n
i.
M
,
S
a
lu
tari.
R
,
S
c
iu
tt
o
.
G
,
“
A
n
e
w
m
u
lt
il
e
v
e
l
P
W
M
m
e
th
o
d
:
a
th
e
o
re
ti
c
a
l
a
n
a
ly
sis”
,
IEE
E
T
ra
n
s
.
Po
we
r E
le
c
tro
n
ics
,
v
o
l.
7
,
p
p
.
4
9
7
–
5
0
5
,
1
9
9
2
.
[5
]
Da
h
id
a
h
M
.
S
.
A
,
A
g
e
li
d
is
V
.
G
,
“
S
e
lec
ti
v
e
h
a
r
m
o
n
ic
e
li
m
in
a
ti
o
n
P
W
M
c
o
n
tr
o
l
f
o
r
c
a
sc
a
d
e
d
m
u
lt
il
e
v
e
l
v
o
lt
a
g
e
so
u
rc
e
c
o
n
v
e
rters
:
A
g
e
n
e
ra
li
z
e
d
f
o
r
m
u
la”
,
IEE
E
T
ra
n
s.
P
o
we
r E
lec
tro
n
,
v
o
l.
2
3
,
n
o
.
4
,
p
p
.
1
6
2
0
–
1
6
3
0
,
2
0
0
8
.
[6
]
Erso
y
Be
s
e
r
y
,
Biro
l
A
ri
f
o
g
lu
,
S
a
b
ri
Ca
m
u
r,
Esra
Ka
n
d
e
m
ir
Be
se
r,
”
De
sig
n
a
n
d
A
p
p
li
c
a
ti
o
n
o
f
a
S
in
g
le
P
h
a
se
M
u
lt
il
e
v
e
l
In
v
e
rter
S
u
i
tab
le
f
o
r
u
sin
g
a
s
a
V
o
lt
a
g
e
Ha
r
m
o
n
ic
S
o
u
rc
e
”
,
J
o
u
r
n
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l
1
0
,
No
.
2
,
p
p
1
3
8
-
1
4
5
,
2
0
1
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
R
E
S
I
SS
N:
2089
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4864
F
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a
s
ed
I
mp
leme
n
ta
tio
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o
f S
ymm
etri
ca
l R
ed
u
ce
d
S
w
itch
Mu
ltil
ev
el
I
n
ve
r
ter (
K
.
V
en
ka
ta
r
a
ma
n
a
n
)
35
[7
]
Ha
iwe
n
,
L
,
T
o
lb
e
rt,
L
.
M
,
Oz
p
in
e
c
i,
B,
Zh
o
n
g
,
D,
“
Co
m
p
a
riso
n
o
f
f
u
n
d
a
m
e
n
tal
f
re
q
u
e
n
c
y
a
n
d
P
W
M
m
e
th
o
d
s
a
p
p
li
e
d
o
n
a
h
y
b
rid
c
a
sc
a
d
e
d
M
u
lt
il
e
v
e
l
in
v
e
rter”
,
3
4
th
IEE
E
Co
n
f
e
re
n
c
e
o
n
In
d
u
stri
a
l
e
lec
tro
n
ics
.
Pro
c
.
p
p
.
3
2
3
3
-
3
2
3
7
,
2
0
0
8
.
[8
]
Ja
n
a
K.C,
Biswa
s
S
.
K,
T
h
a
k
u
ra
P
,
“
A
S
i
m
p
le
a
n
d
Ge
n
e
ra
li
z
e
d
S
p
a
c
e
V
e
c
to
r
P
W
M
Co
n
tro
l
o
f
Ca
s
c
a
d
e
d
H
-
Brid
g
e
M
u
lt
il
e
v
e
l
In
v
e
rters
”
,
IEE
E
I
n
ter
n
a
t
i
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
In
d
u
stri
a
l
T
e
c
h
n
o
lo
g
y
.
Pro
c
,
.
p
p
1
2
8
1
-
1
2
8
6
,
2
0
0
6
.
[9
]
Kre
in
P
.
T
,
Ne
e
B.
M
,
W
e
ll
s
R,
“
Ha
r
m
o
n
ic
e
li
m
in
a
ti
o
n
sw
it
c
h
in
g
th
ro
u
g
h
m
o
d
u
latio
n
”
,
IEE
E
W
o
rk
sh
o
p
o
n
Co
mp
u
ter
s i
n
P
o
we
r E
lec
tro
n
ics
.
Pro
c
.
p
p
.
1
2
3
–
1
2
6
,
2
0
0
4
.
[1
0
]
Krish
n
a
S
,
“
Ha
rm
o
n
ic
El
im
in
a
ti
o
n
b
y
S
e
lec
ti
o
n
o
f
S
w
it
c
h
in
g
A
n
g
le
a
n
d
DC
Vo
lt
a
g
e
s
in
Ca
sc
a
d
e
d
M
u
lt
il
e
v
e
l
In
v
e
rters
”
,
1
5
th
N
a
ti
o
n
a
l
p
o
we
r sy
ste
m co
n
fer
e
n
c
e
(
NPS
C)
.
P
r
o
c
.
p
p
.
1
1
9
-
1
2
4
,
2
0
0
8
.
[1
1
]
M
a
rti
n
a
Ca
lais,
La
w
re
n
c
e
J.Bo
rle,
V
a
ss
il
io
s
G
.
Ag
e
li
d
is.
,
“
A
n
a
l
y
sis
o
f
m
u
lt
ic
a
rrier
P
W
M
m
e
th
o
d
s
f
o
r
a
sin
g
le
p
h
a
se
f
iv
e
le
v
e
l
in
v
e
rter”
,
IEE
E
Co
n
f.
Rec
.
:
0
-
7
8
0
3
-
7
0
6
7
-
8
/
0
1
,
p
p
.
1
3
5
1
-
1
3
5
6
,
2
0
0
1
.
[1
2
]
M
e
k
h
il
e
f
S
,
Om
a
r
A
.
M
,
Ra
h
im
N.A
,
“
M
o
d
e
ll
in
g
o
f
th
re
e
-
p
h
a
se
u
n
if
o
rm
s
y
m
m
e
tri
c
a
l
sa
m
p
li
n
g
d
ig
it
a
l
P
W
M
f
o
r
p
o
w
e
r
c
o
n
v
e
rter”
,
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l
.
5
4
,
n
o
.
1
,
p
p
.
4
2
7
-
4
3
2
,
2
0
0
7
.
[1
3
]
M
o
h
a
n
.
N,
Un
d
e
lan
d
T
.
M
a
n
d
Ro
b
b
i
n
s
W
.
P
,
P
o
w
e
r
El
e
c
tro
n
ics
:
Co
n
v
e
rters
,
A
p
p
li
c
a
ti
o
n
s,
a
n
d
De
sig
n
,
2
n
d
e
d
.
Ne
w
Yo
rk
:
Jo
h
n
W
il
e
y
&
S
o
n
s,
1
9
9
5
.
[1
4
]
Na
ja
f
i,
E.
;Ya
ti
m
,
A
.
;S
a
m
o
sir,
A
.
S
,
“
A
n
e
w
to
p
o
l
o
g
y
–
Re
v
e
rsin
g
V
o
lt
a
g
e
(RV
)
-
f
o
r
m
u
lt
i
lev
e
l
in
v
e
rt
e
rs”
,
IEE
E
2
n
d
In
ter
n
a
t
io
n
a
l
Po
we
r a
n
d
En
e
rg
y
Co
n
fer
e
n
c
e
.
Pro
c
.
p
p
.
6
0
4
–
6
0
8
,
2
0
0
8
.
[1
5
]
Ro
o
z
b
e
h
Na
d
e
ri.
,
A
b
d
o
lrez
a
Ra
h
m
a
ti
,
“
P
h
a
se
–
sh
if
ted
c
a
rrier
P
W
M
tec
h
n
iq
u
e
f
o
r
g
e
n
e
ra
l
c
a
sc
a
d
e
d
in
v
e
rters
”
,
IEE
E
T
ra
n
s.o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l
.
,
No
.
1
3
,
p
p
1
9
-
1
4
,
2
0
0
8
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
K.V
e
n
k
a
tara
m
a
n
a
n
w
a
s
b
o
rn
in
1
9
7
5
in
P
a
n
r
u
ti
.
He
h
a
s
o
b
tain
e
d
B.
E
(El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
)
a
n
d
M
.
E
(
P
o
w
e
r
El
e
c
rto
n
ics
a
n
d
Driv
e
s)
d
e
g
r
e
e
s
in
2
0
0
2
a
n
d
2
0
0
9
re
sp
e
c
ti
v
e
l
y
f
ro
m
A
n
n
a
m
lai
Un
iv
e
rsit
y
,
Ch
id
a
m
b
a
ra
m
,
In
d
ia
a
n
d
A
n
n
a
Un
iv
e
rsity
,
Ch
e
n
n
a
i,
In
d
ia.
He
h
a
s
b
e
e
n
w
o
rk
in
g
in
th
e
tea
c
h
in
g
f
i
e
ld
f
o
r
a
b
o
u
t
1
1
y
e
a
rs.
Hi
s
a
re
a
s
o
f
in
tere
st
in
c
lu
d
e
in
v
e
rter,
c
o
n
v
e
rter
a
n
d
d
riv
e
s.
He
h
a
s
8
p
u
b
li
c
a
ti
o
n
s
i
n
i
n
tern
a
ti
o
n
a
l
j
o
u
rn
a
ls.
He
h
a
s
p
re
se
n
t
e
d
1
0
tec
h
n
ica
l
p
a
p
e
rs
in
v
a
rio
u
s
n
a
ti
o
n
a
l
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si
m
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in
telli
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re
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re
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f
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g
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d
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m
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tac
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m
b
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-
+
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1
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4
3
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8
9
9
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7
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k
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m
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r
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n
1
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9
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m
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.
c
o
m
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