I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
(
I
J
P
E
DS
)
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
,
p
p
.
40
~
50
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v8
i
1
.
p
p
4
0
-
50
40
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
JP
E
DS
A Co
m
pa
ra
tive S
tudies of
Ca
sca
d
ed Multilev
el
Inv
erte
rs
H
a
v
ing
Reduce
d
Nu
m
ber of
Sw
itches w
ith
R and R
L
-
Lo
a
d
L
ipi
k
a
Na
n
da
1
,
A.
Da
s
g
up
t
a
2
,
U.
K.
Ro
ut
3
1
-
3
De
p
a
rt
m
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
KIIT
Un
iv
e
rsit
y
,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Sep
21
,
2
0
1
6
R
ev
i
s
ed
No
v
2
6
,
2
0
1
6
A
cc
ep
ted
Dec
07
,
2
0
1
6
M
u
lt
il
e
v
e
l
in
v
e
rter
o
ff
e
rs
m
a
n
y
b
e
n
e
f
it
s
f
o
r
h
ig
h
p
o
w
e
r
a
p
p
li
c
a
ti
o
n
c
o
m
p
a
v
e
re
d
to
c
o
n
v
e
n
ti
o
n
a
l
c
a
sc
a
d
e
d
M
u
lt
i
lev
e
l
In
v
e
rter
to
p
o
lo
g
y
.
T
h
is
p
a
p
e
r
p
re
se
n
ts
S
y
m
m
e
tri
c
CM
L
I
u
sin
g
v
a
riab
le
f
re
q
u
e
n
c
y
c
a
rrier b
a
se
d
p
u
lse
w
id
th
m
o
d
u
latio
n
tec
h
n
i
q
u
e
s.
T
h
e
p
ro
p
o
se
d
to
p
o
lo
g
y
re
d
u
c
e
s
to
tal
h
a
rm
o
n
ic
d
isto
rti
o
n
a
n
d
re
d
u
c
e
d
sw
it
c
h
in
g
l
o
ss
e
s
f
o
r
se
v
e
n
lev
e
l
in
v
e
rter.
T
h
e
si
m
u
latio
n
st
u
d
y
o
f
th
e
p
r
o
p
o
se
d
t
o
p
o
lo
g
y
h
a
s
b
e
e
n
c
a
rried
o
u
t
i
n
M
AT
LAB/S
IM
UL
INK
.
T
h
e
m
a
in
o
b
jec
ti
v
e
o
f
th
is
p
a
p
e
r
is
t
o
a
c
h
iev
e
n
u
m
b
e
r
o
f
lev
e
ls
o
f
M
L
I
w
it
h
re
d
u
c
e
d
n
u
m
b
e
r
o
f
s
w
it
c
h
e
s
a
n
d
DC
p
o
w
e
r
so
u
rc
e
s co
m
p
a
re
d
to
c
o
n
v
e
n
ti
o
n
a
l
t
o
p
o
l
o
g
y
.
K
ey
w
o
r
d
:
B
id
ir
ec
tio
n
al
s
w
itc
h
S
w
itc
h
in
g
l
o
s
s
S
y
m
m
etr
ic
m
u
lt
ilev
el
i
n
v
er
ter
T
o
tal
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
Vo
ltag
e
s
tr
es
s
Co
p
y
rig
h
t
©
201
7
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
L
ip
i
k
a
Nan
d
a
,
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
KI
I
T
Un
iv
er
s
i
t
y
,
B
h
u
b
an
e
s
w
a
r
,
Od
is
h
a,
I
n
d
ia,
p
in
-
751024
.
E
m
ail: l
n
a
n
d
af
el
@
k
iit.ac
.
in
1.
I
NT
RO
D
UCT
I
O
N
I
n
a
m
u
ltil
e
v
el
i
n
v
er
ter
a
d
esire
d
o
u
tp
u
t
v
o
lta
g
e
h
as
b
ee
n
s
y
n
t
h
esized
to
s
e
v
er
al
le
v
e
ls
f
r
o
m
a
n
u
m
b
er
o
f
D
C
s
o
u
r
ce
s
as
i
n
p
u
ts
.
T
h
e
m
o
s
t
attr
ac
ti
v
e
ap
p
lica
tio
n
s
o
f
m
u
lt
ile
v
el
p
o
w
er
co
n
v
er
s
io
n
tech
n
o
lo
g
y
ar
e
in
t
h
e
m
ed
i
u
m
to
h
i
g
h
v
o
l
tag
e
r
a
n
g
e
s
[
1
]
.
A
m
u
ltil
e
v
el
i
n
v
er
ter
n
o
t
o
n
l
y
ac
h
ie
v
e
s
h
ig
h
p
o
w
er
r
ati
n
g
s
b
u
t
also
en
ab
les
th
e
u
s
e
o
f
r
en
e
w
a
b
le
en
er
g
y
s
o
u
r
ce
s
.
R
en
e
w
ab
l
e
e
n
er
g
y
s
o
u
r
es
i.e
s
o
lar
p
h
o
t
o
v
o
ltaic,
w
i
n
d
,
f
u
el
ce
lls
etc.
ca
n
b
e
ea
s
il
y
in
ter
f
ac
ed
to
m
u
ltil
e
v
el
co
n
v
er
ter
f
o
r
h
ig
h
p
o
w
er
ap
p
licatio
n
s
[
2
]
.
T
h
r
ee
d
if
f
er
en
t
to
p
o
lo
g
ies
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
m
u
l
tile
v
el
in
v
er
ter
s
i.e
ca
s
ca
d
ed
M
L
I
,
Dio
d
e
-
cla
m
p
ed
M
L
I
an
d
ca
p
a
cito
r
cla
m
p
ed
.
E
ac
h
o
f
t
h
e
to
p
o
lo
g
y
h
a
s
a
d
i
f
f
er
en
t
m
ec
h
a
n
is
m
to
p
r
o
v
id
e
v
o
ltag
e
lev
els
[
3
]
.
T
h
ese
to
p
o
lo
g
ies ar
e
w
id
el
y
r
ef
er
r
ed
to
as th
e
„
cla
s
s
ic
al
to
p
o
lo
g
ies
‟
[
4
].
On
e
m
a
j
o
r
d
is
ad
v
an
ta
g
e
o
f
m
u
ltil
e
v
el
p
o
w
er
co
n
v
er
s
io
n
is
th
at
g
r
ea
t
n
u
m
b
er
o
f
p
o
w
er
s
e
m
ico
n
d
u
cto
r
s
w
itc
h
e
s
n
ee
d
ed
.
An
o
th
er
d
is
ad
v
an
ta
g
e
o
f
m
u
ltil
e
v
el
p
o
w
er
co
n
v
er
ter
s
is
th
at
t
h
e
v
o
ltag
e
s
tep
s
ar
e
p
r
o
d
u
ce
d
b
y
i
s
o
lated
DC
v
o
ltag
e
s
o
u
r
ce
s
o
r
a
b
an
k
o
f
s
er
ie
s
ca
p
ac
ito
r
s
.
I
s
o
lated
v
o
lta
g
e
s
o
u
r
c
es
m
a
y
n
o
t
al
w
a
y
s
b
e
r
ea
d
il
y
av
ailab
le
a
n
d
s
er
ie
s
ca
p
ac
ito
r
s
r
eq
u
ir
e
v
o
ltag
e
b
alan
ce
[
5
].
T
h
er
e
ar
e
tw
o
P
W
M
m
eth
o
d
s
m
a
in
l
y
u
s
ed
in
m
u
lti
lev
el
i
n
v
er
ter
co
n
tr
o
l
s
tr
ate
g
y
.
On
e
i
s
f
u
n
d
a
m
en
ta
l
s
w
itc
h
in
g
f
r
eq
u
en
c
y
an
d
a
n
o
t
h
er
is
h
ig
h
s
witch
i
n
g
f
r
eq
u
en
c
y
.
f
o
r
h
i
g
h
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
class
i
f
ied
as
s
p
ac
e
v
ec
to
r
P
W
M,
Selectiv
e
Har
m
o
n
ic
E
le
m
i
n
atio
n
P
W
M
an
d
SP
W
M.
Am
o
n
g
t
h
ese
P
W
M
m
et
h
o
d
s
SP
W
M
is
t
h
e
m
o
s
t
p
r
ef
er
ab
le
as
it
is
s
i
m
p
le
an
d
ea
s
y
to
i
m
p
le
m
e
n
t
[
6
]
-
[
7
].
I
n
t
h
i
s
p
ap
er
SP
W
M
m
et
h
o
d
w
it
h
d
if
f
er
e
n
t c
ar
r
ier
b
ased
d
is
p
o
s
itio
n
as P
DP
W
M
an
d
A
P
ODP
W
M
h
av
e
b
ee
n
a
n
al
y
ze
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
C
o
mp
a
r
a
tive
S
tu
d
ies o
f Ca
s
ca
d
ed
Mu
ltil
ev
el
I
n
ve
r
ters
Ha
vin
g
R
ed
u
ce
d
N
u
mb
er .
.
.
.
(
Lip
ika
N
a
n
d
a
)
41
2.
E
XI
ST
I
N
G
T
O
P
O
L
O
G
I
E
S
C
o
n
v
en
t
io
n
al
ca
s
ca
d
ed
s
e
v
en
lev
el
m
u
lt
ilev
e
l
in
v
er
ter
r
eq
u
ir
e
t
w
el
v
e
s
w
itc
h
es
a
n
d
3
d
c
s
o
u
r
ce
s
s
ep
ar
atel
y
[
4
].
T
o
o
v
er
co
m
e
t
h
e
d
r
a
w
b
ac
k
s
o
f
it
n
e
x
t
to
p
o
l
o
g
ies
ar
e
m
ad
e
w
it
h
s
ev
e
n
l
ev
el
n
i
n
e
s
w
itc
h
es
3
d
c
s
o
u
r
ce
s
,
s
ev
en
le
v
el
s
ev
e
n
s
w
itc
h
es
an
d
3
d
c
s
o
u
r
ce
s
e
tc
[
7
].
T
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
i
es
ar
e
d
esig
n
ed
f
o
r
s
ev
e
n
lev
e
l
,
6
s
w
i
tch
e
s
w
it
h
4
d
c
an
d
3
d
c
s
o
u
r
ce
s
r
esp
ec
tiv
el
y
w
i
th
b
id
ir
ec
tio
n
al
s
w
itc
h
es
w
h
er
e
th
e
h
ar
m
o
n
ics ar
e
r
ed
u
ce
d
.
2
.
1
.
P
ro
po
s
ed
T
o
po
lo
g
y
-
I
T
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
i
s
d
esi
g
n
ed
w
i
th
s
i
x
s
w
itc
h
es
w
it
h
o
u
t H
-
b
r
id
g
e
a
n
d
f
o
u
r
d
c
s
o
u
r
ce
s
as s
h
o
wn
in
Fi
g
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
is
s
i
m
p
le
i
n
d
esig
n
c
o
m
p
ar
ed
to
th
e
ex
is
ti
n
g
to
p
o
lo
g
ies.
S
w
itc
h
e
s
S6
an
d
S7
ar
e
u
s
ed
f
o
r
g
en
er
ati
n
g
th
e
p
u
l
s
es
i
n
p
o
s
iti
v
e
an
d
n
eg
ativ
e
s
e
q
u
en
ce
a
n
d
s
w
i
tch
S1
is
co
n
n
ec
ted
to
th
e
lo
ad
.
I
t
is
u
s
ed
o
n
l
y
w
h
e
n
all
th
e
s
w
itc
h
es
ar
e
o
p
en
to
p
r
o
d
u
ce
ze
r
o
v
o
lta
g
e
le
v
el.
S
w
itc
h
S2
,
S3
,
an
d
S4
ar
e
u
s
ed
to
g
e
n
er
ate
th
e
le
v
els Vd
c,
2
Vd
c,
3
V
d
c
in
b
o
th
p
o
s
itiv
e
an
d
n
eg
at
iv
e
le
v
el
s
.
T
h
e
g
en
er
alize
d
ex
p
r
ess
io
n
f
o
r
th
e
n
u
m
b
er
o
f
s
w
itch
e
s
an
d
t
h
e
n
u
m
b
er
o
f
Dc
s
o
u
r
ce
s
ar
e
S=(
N+
5
)
/2
an
d
V=
(
N+
1
)
/2
W
h
er
e
N=
Nu
m
b
er
o
f
le
v
el
s
,
S
=
No
.
o
f
s
w
i
tch
e
s
an
d
V=
No
.
o
f
DC
s
o
u
r
ce
s
.
B
o
th
th
e
ca
r
r
ier
b
ased
P
W
M
t
ec
h
n
iq
u
es
i.e
I
P
D
P
W
M
an
d
A
P
OD
P
W
M
m
et
h
o
d
s
ar
e
a
n
a
l
y
ze
d
w
it
h
r
esis
ti
v
e
an
d
R
L
-
t
y
p
e
lo
ad
.
Fig
u
r
e
1
.
C
o
n
f
ig
u
r
atio
n
o
f
s
e
v
en
lev
el
s
i
x
s
w
itc
h
es
w
i
th
4
D
C
s
o
u
r
ce
s
p
r
o
p
o
s
ed
T
o
p
o
lo
g
y
T
ab
le
1
.
Sw
itch
in
g
p
atter
n
f
o
r
s
ev
e
n
lev
e
l si
x
s
w
itc
h
es 4
Dc
s
o
u
r
ce
s
S
L
.
N
o
S1
S2
S3
S4
S5
S6
D
1
D
4
D
2
D
3
D
5
D
8
D
6
D
7
D
9
D
1
2
O
u
t
p
u
t
V
o
l
t
a
g
e
1
Off
Off
Off
On
On
Off
Off
Off
Off
Off
On
V
dc
2
Off
Off
On
Off
On
Off
Off
Off
On
Off
Off
2V
dc
3
Off
On
Off
Off
On
Off
On
Off
Off
Off
Off
3V
dc
4
On
Off
Off
Off
Off
Off
Off
Off
Off
Off
Off
0
5
Off
On
Off
Off
Off
On
Off
On
Off
Off
Off
-
V
dc
6
Off
Off
On
Off
Off
On
Off
Off
Off
On
Off
-
2V
dc
7
Off
Off
Off
On
Off
On
Off
Off
Off
Off
Off
-
3V
dc
2
.
2
.
P
ro
po
s
ed
T
o
po
lo
g
y
-
I
I
I
t
is
s
i
m
p
le
i
n
d
esig
n
an
d
co
m
p
ar
ed
to
o
th
er
e
x
i
s
ti
n
g
to
p
o
lo
g
ies.
I
t
co
n
s
i
s
ts
o
f
t
h
r
ee
DC
s
o
u
r
ce
s
an
d
s
i
x
s
w
itc
h
e
s
.
th
e
g
e
n
er
ali
ze
d
ex
p
r
ess
io
n
f
o
r
th
e
n
u
m
b
er
o
f
s
w
itc
h
es
ad
n
u
m
b
er
o
f
Dc
s
o
u
r
ce
s
f
o
r
t
h
e
to
p
o
lo
g
y
i
s
g
i
v
e
n
b
y
S=(
N+
5
)
/2
an
d
V=
=(
N
-
1
)
/2
.
DC
V
DC
V
DC
V
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
40
–
50
42
B
o
th
th
e
ca
r
r
ier
b
ased
P
W
M
tech
n
iq
u
e
s
i.e
I
P
D
an
d
AP
OD
P
W
M
m
et
h
o
d
s
ar
e
an
a
l
y
ze
d
w
it
h
r
esis
ti
v
e
lo
ad
t
y
p
e.
Fig
u
r
e
2
.
C
o
n
f
ig
u
r
atio
n
o
f
s
e
v
en
lev
el
s
i
x
s
w
itc
h
es
w
i
th
3
D
C
s
o
u
r
ce
s
p
r
o
p
o
s
ed
T
o
p
o
lo
g
y
T
ab
le
2
.
C
o
n
f
ig
u
r
atio
n
o
f
7
lev
el
6
s
w
itc
h
es a
n
d
3
Dc
s
o
u
r
ce
s
S
L
.
N
o
S1
S2
S3
S4
S5
S6
D
1
D
4
D
2
D
3
D
5
D
8
D
6
D
7
O
u
t
p
u
t
V
o
l
t
a
g
e
1
Off
On
Off
O
ff
O
ff
On
Off
Off
On
Off
V
dc
2
O
n
Off
O
ff
Off
O
ff
O
n
O
n
Off
O
ff
Off
2V
dc
3
Off
O
ff
O
n
Off
O
ff
O
n
O
ff
Off
Off
Off
3V
dc
4
O
ff
Off
Off
Off
Off
Off
Off
Off
Off
Off
0
5
O
n
O
ff
Off
On
Off
O
ff
Off
On
Off
Off
-
V
dc
6
Off
O
n
O
ff
O
n
Off
O
ff
Off
Off
Off
On
-
2V
dc
7
Off
Off
Off
On
O
n
O
ff
Off
Off
Off
Off
-
3V
dc
3.
M
O
DE
S O
F
O
P
E
RAT
I
O
N
3
.
1
.
T
o
po
lo
g
y
-
1
Mo
d
e
1
Mo
d
e
2
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
DC
V
DC
V
DC
V
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
DC
V
DC
V
DC
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
C
o
mp
a
r
a
tive
S
tu
d
ies o
f Ca
s
ca
d
ed
Mu
ltil
ev
el
I
n
ve
r
ters
Ha
vin
g
R
ed
u
ce
d
N
u
mb
er .
.
.
.
(
Lip
ika
N
a
n
d
a
)
43
Mo
d
e
3
Mo
d
e
4
Mo
d
e
5
Mo
d
e
6
Mo
d
e
7
Fig
u
r
e
3
.
Dif
f
er
en
t
m
o
d
e
s
o
f
o
p
er
atio
n
o
f
7
lev
els,
6
s
w
itc
h
e
s
an
d
4
DC
s
o
u
r
ce
s
C
M
L
I
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
DC
V
DC
V
DC
V
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
DC
V
DC
V
DC
V
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
DC
V
DC
V
DC
V
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
DC
V
DC
V
DC
V
DC
V
2
S
3
S
4
S
5
S
6
S
1
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
9
D
10
D
11
D
12
D
L
O
A
D
DC
V
DC
V
DC
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
40
–
50
44
3
.
2
.
T
o
po
lo
g
y
–
II
Mo
d
e
1
Mo
d
e
2
Mo
d
e
3
Mo
d
e
4
Mo
d
e
5
Mo
d
e
6
Mo
d
e
7
Fig
u
r
e
4.
Dif
f
er
en
t
m
o
d
e
s
o
f
o
p
er
atio
n
o
f
7
lev
els,
6
s
w
itc
h
e
s
an
d
3
Dc
s
o
u
r
ce
s
C
M
L
I
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
1
S
2
S
1
D
2
D
3
D
4
D
5
D
6
D
7
D
8
D
L
O
A
D
DC
V
DC
V
DC
V
3
S
6
S
4
S
5
S
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
C
o
mp
a
r
a
tive
S
tu
d
ies o
f Ca
s
ca
d
ed
Mu
ltil
ev
el
I
n
ve
r
ters
Ha
vin
g
R
ed
u
ce
d
N
u
mb
er .
.
.
.
(
Lip
ika
N
a
n
d
a
)
45
4.
P
WM
T
E
CH
NIQU
E
S
T
h
e
ca
r
r
ier
b
ased
m
o
d
u
lat
io
n
tech
n
iq
u
es
f
o
r
m
u
ltil
e
v
el
i
n
v
e
r
ter
s
ca
n
b
e
g
en
er
all
y
cla
s
s
i
f
ie
d
in
to
t
w
o
ca
teg
o
r
ies:
p
h
ase
s
h
i
f
ted
an
d
lev
el
s
h
i
f
ted
m
o
d
u
latio
n
s
.
B
o
th
m
o
d
u
latio
n
s
c
h
e
m
es
ca
n
b
e
ap
p
lied
to
th
e
ca
s
ca
d
ed
m
u
ltil
e
v
el
i
n
v
er
ter
[
8
]
-
[
9
].
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
f
p
h
ase
s
h
i
f
ted
m
o
d
u
lati
o
n
is
m
u
ch
h
i
g
h
e
r
th
an
le
v
el
s
h
i
f
ted
m
o
d
u
la
tio
n
.
Hen
ce
le
v
el
s
h
if
ted
m
o
d
u
latio
n
tech
n
iq
u
e
i
s
b
ein
g
ch
o
s
en
.
I
n
th
i
s
p
ap
er
SP
W
M
m
et
h
o
d
w
i
th
d
i
f
f
er
e
n
t
ca
r
r
ier
b
ased
d
is
p
o
s
itio
n
as P
DP
W
M
an
d
A
P
ODP
W
M
h
av
e
b
ee
n
an
al
y
ze
d
.
Fig
u
r
e
5
.
A
P
OD
an
d
I
P
D
P
W
M
S
w
itch
in
g
Sc
h
e
m
es
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
5
.
1
.
T
o
po
lo
g
y
-
I
A
ll
th
e
s
w
itc
h
es
u
s
ed
i
n
t
h
is
cir
cu
it
ar
e
MO
S
FET
S.
T
h
e
s
w
itc
h
e
s
S
2
,
S
3
,
S
4
ar
e
b
id
ir
ec
tio
n
al
an
d
r
e
m
ain
in
g
s
w
i
tch
e
s
ar
e
u
n
id
ir
ec
tio
n
al.
th
e
lo
ad
s
ar
e
r
esis
t
iv
e
an
d
R
L
-
lo
ad
. T
h
e
DC
s
o
u
r
ce
s
ar
e
1
0
V.
Fig
u
r
e
6
.
Si
m
u
latio
n
Diag
r
a
m
o
f
P
r
o
p
o
s
ed
T
o
p
o
lo
g
y
1
Sin
e
an
d
tr
ian
g
u
lar
ca
r
r
ier
s
a
r
e
co
m
p
ar
ed
an
d
7
lev
els
ar
e
g
en
er
ated
.
B
o
th
th
e
Dc
an
d
d
if
f
er
en
t
lev
els
g
en
er
ated
ar
e
f
ed
to
lo
g
ic
g
ates
to
p
r
o
d
u
ce
g
ate
s
ig
n
al
s
.
T
h
ese
g
ate
s
i
g
n
al
s
ar
e
f
ed
to
s
w
itc
h
es
S
1
to
S
7
r
esp
ec
tiv
el
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
40
–
50
46
Fig
u
r
e
7
.
Dif
f
er
en
t le
v
els
g
e
n
e
r
atio
n
Fig
u
r
e
8
.
Gate
P
u
ls
e
Gen
er
ati
o
n
Fig
u
r
e
9
(
a)
.
Ou
tp
u
t v
o
lta
g
e
an
d
cu
r
r
en
t
w
ith
R
esi
s
ti
v
e
lo
ad
(
b
)
w
ith
R
L
-
L
o
ad
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
C
o
mp
a
r
a
tive
S
tu
d
ies o
f Ca
s
ca
d
ed
Mu
ltil
ev
el
I
n
ve
r
ters
Ha
vin
g
R
ed
u
ce
d
N
u
mb
er .
.
.
.
(
Lip
ika
N
a
n
d
a
)
47
(
a)
(
b
)
Fig
u
r
e
1
0
(
a)
.
A
P
OD
s
w
i
tch
i
n
g
s
c
h
e
m
e
(
b
)
I
P
D
s
w
itc
h
i
n
g
s
c
h
e
m
e
5
.
2
.
T
o
po
lo
g
y
II
A
ll
t
h
e
s
w
itc
h
es
u
s
ed
in
th
is
cir
cu
it
ar
e
u
n
id
ir
ec
tio
n
a
l
ex
ce
p
t
s
w
itc
h
es
S1
an
d
S2
o
f
cir
cu
it
d
iag
r
a
m
.
A
ll t
h
e
Dc
s
o
u
r
ce
s
ar
e
tak
en
a
s
1
0
Vd
c
an
d
R
esis
ta
n
ce
as 8
0
o
h
m
s
.
Fig
u
r
e
1
1
.
Si
m
u
latio
n
o
f
7
le
v
els s
i
x
s
w
i
tc
h
e
s
an
d
3
Dc
s
o
u
r
ce
s
to
p
o
lo
g
y
Fig
u
r
e
12.
I
P
D
P
W
M
s
w
itc
h
i
n
g
s
c
h
e
m
e,
7
lev
e
ls
,
6
s
w
itc
h
es,
3
DC
s
o
u
r
ce
s
C
o
m
m
e
n
ts
:
Vo
u
t=3
0
V
at
R
=8
0
o
h
m
s
a
n
d
ca
r
r
ier
f
r
eq
u
en
c
y
=
5
KHz
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
40
–
50
48
Fig
u
r
e
1
3
.
T
HD
A
n
a
l
y
s
is
A
t
R
=8
0
o
h
m
s
,
T
HD=
2
0
%,
F
u
n
d
a
m
en
tal
o
u
tp
u
t v
o
lta
g
e=
2
8
.
9
V
6.
CO
M
P
ARIS
O
N
O
F
T
WO
T
O
P
O
L
O
G
I
E
S
6
.
1
.
T
H
D
Ana
ly
s
is
T
ab
le
3.
C
o
m
p
ar
i
s
o
n
o
f
t
w
o
to
p
o
lo
g
ies
w
ith
A
P
OD
a
n
d
I
P
D
s
w
itc
h
in
g
s
c
h
e
m
es
7
l
e
v
e
l
s,
6
sw
i
t
c
h
e
s,
4
D
C
so
u
r
c
e
s T
o
p
o
l
o
g
y
P
W
M
MI
T
H
D
F
u
n
d
a
me
n
t
a
l
(
S
i
mu
l
a
t
e
d
)
F
u
n
d
a
me
n
t
a
l
(
C
a
l
c
u
l
a
t
e
d
)
A
P
O
D
0
.
8
2
3
.
7
3
2
2
.
4
6
2
3
.
7
0
.
9
2
3
.
1
5
2
4
.
9
8
2
5
.
6
1
19
2
7
.
8
2
8
.
3
I
P
D
0
.
8
2
3
.
4
8
2
2
.
5
3
2
3
.
4
0
.
9
2
3
.
1
1
2
5
.
0
9
2
5
.
9
1
1
9
.
0
8
2
7
.
9
4
2
9
.
3
7
l
e
v
e
l
s,
6
sw
i
t
c
h
e
s,
3
D
C
so
u
r
c
e
s T
o
p
o
l
o
g
y
P
W
M
MI
T
H
D
F
u
n
d
a
me
n
t
a
l
(
S
i
mu
l
a
t
e
d
)
F
u
n
d
a
me
n
t
a
l
(
C
a
l
c
u
l
a
t
e
d
)
A
P
O
D
0
.
8
2
4
.
8
7
2
2
.
6
9
2
4
.
2
0
.
9
2
4
.
7
2
2
5
.
6
6
2
6
.
3
1
2
0
.
2
9
2
8
.
9
30
I
P
D
0
.
8
2
4
.
8
2
2
2
.
8
2
2
4
.
2
0
.
9
2
4
.
6
2
5
.
7
3
2
6
.
4
1
1
9
.
8
2
9
.
0
1
2
9
.
9
Fig
u
r
e
1
4
.
T
HD
Vs M
o
d
u
latio
n
I
n
d
ex
o
f
7
lev
el
6
s
w
itc
h
es a
n
d
4
Dc
s
o
u
r
ce
s
,
C
o
m
m
e
n
t:
W
ith
in
cr
ea
s
e
o
f
Mo
d
u
latio
n
i
n
d
ex
T
HD
r
ed
u
ce
d
Mo
d
u
latio
n
i
n
d
ex
T
HD
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
C
o
mp
a
r
a
tive
S
tu
d
ies o
f Ca
s
ca
d
ed
Mu
ltil
ev
el
I
n
ve
r
ters
Ha
vin
g
R
ed
u
ce
d
N
u
mb
er .
.
.
.
(
Lip
ika
N
a
n
d
a
)
49
6
.
2
.
Vo
lt
a
g
e
Str
ess
Acr
o
s
s
Sw
it
ches
I
t
h
as
b
ee
n
o
b
s
er
v
ed
th
a
t
r
ed
u
ce
d
n
u
m
b
er
o
f
s
w
itc
h
es
g
iv
e
m
o
r
e
v
o
ltag
e
s
tr
es
s
co
m
p
ar
ed
t
o
co
n
v
e
n
tio
n
al
C
M
L
I
.
T
ab
le
4
.
Vo
ltag
e
s
tr
ess
es a
cr
o
s
s
t
h
e
s
w
itc
h
es
C
o
n
v
e
n
t
i
o
n
a
l
7
l
e
v
e
l
s 4
D
C
so
u
r
c
e
s i
n
V
7
l
e
v
e
l
s 3
D
C
so
u
r
c
e
s i
n
V
1
0
V
(
A
c
r
o
ss a
l
l
s
w
i
t
c
h
e
s)
S
1
S
2
S
3
S
4
S
5
S
6
S
1
S
2
S
3
S
4
S
5
S
6
2
8
.
4
20
10
20
40
40
1
8
.
2
1
8
.
2
30
30
30
30
Fig
u
r
e
1
5
.
C
ar
r
ier
f
r
eq
u
en
c
y
Vs S
w
itc
h
i
n
g
lo
s
s
o
f
7
lev
e
l 6
s
w
itc
h
es 4
Dc
s
o
u
r
ce
s
7.
L
O
SS
CA
L
CU
L
A
T
I
O
N
E
ac
h
Mo
s
f
et
lo
s
s
h
a
s
b
ee
n
ca
lcu
lated
f
r
o
m
s
i
m
u
la
tio
n
r
es
u
lt.
T
h
e
v
o
ltag
e
an
d
cu
r
r
en
t
wav
e
f
o
r
m
s
ar
e
o
b
s
er
v
ed
f
r
o
m
s
i
m
u
latio
n
d
iag
r
a
m
o
f
ea
ch
s
w
itc
h
a
n
d
th
u
s
p
o
w
er
is
b
ei
n
g
ca
lcu
lated
.
Fro
m
p
o
w
er
p
u
ls
e
o
f
ea
c
h
s
w
itc
h
at
d
if
f
er
en
t
ca
r
r
ier
f
r
eq
u
e
n
cies
th
e
s
w
itc
h
in
g
an
d
co
n
d
u
ctio
n
lo
s
s
es
ar
e
ca
l
cu
lated
.
A
t
ca
r
r
ier
f
r
eq
u
en
c
y
1
KHz,
d
if
f
er
en
t lo
s
s
es a
r
e
ca
lcu
lated
as
s
h
o
w
n
b
elo
w
.
T
ab
le
5
.
C
alcu
latio
n
o
f
S
w
itc
h
in
g
,
C
o
n
d
u
c
tio
n
a
n
d
T
o
tal
C
ir
cu
it lo
s
s
at
d
i
f
f
er
en
t
C
ar
r
ier
Fre
q
u
en
cie
s
S1
S2
S3
S4
S5
S6
T
o
t
a
l
S
w
t
c
h
i
n
g
l
o
ss
(
i
n
W
)
0
.
0
3
5
0
.
0
0
1
6
0
.
0
0
1
2
0
.
0
0
2
3
0
.
0
5
0
.
0
4
8
9
0
.
0
4
8
9
C
o
n
d
u
c
t
i
o
n
L
o
ss
(
i
n
W
)
0
.
0
0
4
5
0
.
0
0
4
2
0
.
0
0
4
0
.
0
0
4
2
0
.
0
0
4
5
0
.
0
0
4
1
0
.
0
0
5
T
o
t
a
l
L
o
ss
(
i
n
W
)
0
.
0
3
9
5
0
.
0
0
5
8
0
.
0
0
5
2
0
.
0
0
6
5
0
.
0
5
4
5
0
.
0
5
3
0
.
0
5
3
9
T
ab
le
6
.
L
o
s
s
at
d
if
f
er
e
n
t c
ar
r
i
er
f
r
eq
u
en
cie
s
C
a
r
r
i
e
r
F
r
e
q
u
e
n
c
i
e
s
(
i
n
K
H
z
)
I
n
p
u
t
V
o
l
t
a
g
e
(
i
n
V
o
l
t
)
I
n
p
u
t
C
u
r
r
e
n
t
(
i
n
A
mp
)
I
n
p
u
t
P
o
w
e
r
(
i
n
W
a
t
t
)
O
u
t
p
u
t
V
o
l
t
a
g
e
(
i
n
V
o
l
t
)
O
u
t
p
u
t
C
u
r
r
e
n
t
(
i
n
A
mp
)
O
u
t
p
u
t
P
o
w
e
r
(
i
n
W
a
t
t
)
C
i
r
c
u
i
t
T
o
t
a
l
L
o
ss
(
i
n
W
a
t
t
)
1
40
0
.
3
5
4
1
4
.
1
6
2
8
.
3
5
0
.
3
5
1
9
.
9
5
4
.
0
5
2
40
0
.
3
5
14
2
8
.
3
5
0
.
3
5
9
.
9
2
4
.
0
8
5
40
0
.
3
5
1
1
4
.
0
4
2
8
.
3
5
0
.
3
4
8
2
9
.
8
7
4
.
1
3
10
40
0
.
3
4
5
8
1
3
.
8
3
2
8
.
3
5
0
.
3
5
4
1
0
.
0
3
3
.
9
7
20
40
0
.
3
5
14
2
8
.
3
5
0
.
3
4
7
5
9
.
8
5
4
.
1
5
I
t sh
o
w
s
w
it
h
i
n
cr
ea
s
e
o
f
ca
r
r
i
er
f
r
eq
u
en
cie
s
s
w
itc
h
i
n
g
lo
s
s
es in
cr
ea
s
e
s
.
8.
CO
NCLU
SI
O
N
I
n
v
er
ter
o
p
er
atio
n
o
f
6
s
w
i
tch
es
an
d
4
D
C
s
o
u
r
ce
s
b
ased
to
p
o
lo
g
y
w
as
ca
r
r
ied
o
u
t
a
n
d
th
e
r
eq
u
ir
ed
o
b
j
ec
tiv
e
o
f
lo
w
h
ar
m
o
n
ics
a
n
d
7
le
v
el
o
u
tp
u
t
at
T
HD
i
s
1
9
.
0
8
%
&
F
u
n
d
a
m
e
n
tal
o
u
tp
u
t
at
2
7
.
9
V
at
MI
=1
.
I
n
v
er
ter
o
p
er
atio
n
o
f
6
s
w
itc
h
es
a
n
d
3
D
C
s
o
u
r
ce
s
b
a
s
ed
to
p
o
lo
g
y
w
a
s
ca
r
r
ied
o
u
t
an
d
th
e
r
eq
u
ir
ed
o
b
j
ec
tiv
e
o
f
lo
w
h
ar
m
o
n
ics
an
d
7
lev
el
o
u
tp
u
t
at
T
HD
is
1
9
.
8
%
&
F
u
n
d
a
m
en
tal
o
u
tp
u
t
at
2
9
.
0
1
V
at
MI
=1
.
Sw
itch
in
g
L
o
s
s
,
C
o
n
d
u
ctio
n
L
o
s
s
a
n
d
t
o
tal
cir
cu
it
lo
s
s
at
d
i
f
f
er
en
t
ca
r
r
ier
f
r
eq
u
en
cie
s
ar
e
ca
r
r
ie
d
o
u
t
s
u
cc
e
s
s
f
u
ll
y
.
Vo
ltag
e
s
tr
es
s
o
f
co
n
v
e
n
tio
n
al
an
d
m
o
d
if
ied
to
p
o
lo
g
ies ar
e
co
m
p
ar
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.