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.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
,
p
p
.
220
~
230
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v
9
.
i1
.
pp
2
2
0
-
230
220
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e.
co
m/jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JP
E
DS
I
m
ple
m
e
ntatio
n o
f
Ca
sca
ded bas
ed
Rev
ersing
Volta
g
e
M
ultilevel Inv
ert
er using
Multi
Ca
rrier
M
o
dula
tion
Strategies
S.
Na
g
a
ra
j
a
Ra
o
1
,
D.
V.
Ash
o
k
K
u
m
a
r
2
,
Ch.
Sa
i B
a
bu
3
1
,3
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
,
JN
T
Un
iv
e
rsit
y
,
Ka
k
in
a
d
a
,
A
P
,
In
d
ia
2
P
r
o
f
e
ss
o
r,
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
ri
n
g
,
RG
M
CE
T
,
Na
n
d
y
a
l,
A
P
,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
5
,
2
0
1
7
R
ev
i
s
ed
Dec
9
,
2
0
1
7
A
cc
ep
ted
J
an
3
,
2
0
1
8
In
th
is
p
a
p
e
r,
a
c
a
sc
a
d
e
d
b
a
se
d
re
v
e
rsin
g
v
o
lt
a
g
e
(CBRV
)
m
u
lt
il
e
v
e
l
in
v
e
rter
stru
c
tu
re
is
p
r
o
p
o
se
d
i
n
o
r
d
e
r
to
c
o
m
p
e
n
sa
te
th
e
m
a
jo
r
d
ra
w
b
a
c
k
s
in
th
e
c
o
n
v
e
n
ti
o
n
a
l
m
u
lt
il
e
v
e
l
in
v
e
rters
.
T
h
e
p
ro
p
o
se
d
t
o
p
o
lo
g
y
re
q
u
ires
les
s
n
u
m
b
e
r
o
f
c
o
m
p
o
n
e
n
ts,
les
s c
a
rrier sig
n
a
ls an
d
g
a
te d
riv
e
s
w
h
e
n
c
o
m
p
a
re
d
to
e
x
isti
n
g
m
u
lt
il
e
v
e
l
in
v
e
rters
p
a
rti
c
u
larly
a
t
h
ig
h
e
r
le
v
e
ls.
T
h
e
re
f
o
re
,
th
e
c
o
m
p
lex
it
y
a
n
d
o
v
e
ra
ll
c
o
st
a
r
e
g
re
a
tl
y
re
d
u
c
e
d
p
a
rti
c
u
larly
f
o
r
h
ig
h
e
r
o
u
t
p
u
t
v
o
lt
a
g
e
le
v
e
ls.
T
h
is
p
a
p
e
r
a
lso
p
re
se
n
t
s
th
e
m
o
st
re
le
v
a
n
t
c
o
n
tro
l
a
n
d
m
o
d
u
latio
n
m
e
th
o
d
s
b
y
a
tri
a
n
g
u
lar
b
a
se
d
m
u
lt
i
c
a
rrier
p
u
lse
w
id
th
m
o
d
u
latio
n
(
P
W
M
)
sc
h
e
m
e
f
o
r
th
e
p
ro
p
o
se
d
CBR
V
in
v
e
rter
to
p
o
lo
g
y
.
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
c
o
m
p
a
riso
n
b
e
twe
e
n
d
iff
e
r
e
n
t
m
o
d
u
latio
n
stra
teg
ies
f
o
r
CBRV
in
v
e
rter
t
o
p
o
l
o
g
y
b
a
se
d
o
n
sin
u
so
i
d
a
l
a
n
d
sp
a
c
e
v
e
c
to
r
re
fe
re
n
c
e
s
w
it
h
m
u
lt
i
tri
a
n
g
u
lar
c
a
rrier
w
a
v
e
s.
T
h
e
w
o
rk
stri
v
e
h
a
rd
to
p
re
se
n
t
th
e
sc
ru
ti
n
y
th
a
t
h
a
s
b
e
e
n
m
a
d
e
b
e
twe
e
n
v
a
rio
u
s
P
W
M
c
o
n
tro
l
tec
h
n
i
q
u
e
s
f
o
r
1
–
Ф
se
v
e
n
lev
e
l
CBRV
in
v
e
rter
str
u
c
tu
re
.
T
h
e
c
o
m
p
a
riso
n
is
m
a
d
e
in
term
s
o
f
T
o
tal
Ha
r
m
o
n
ic
Disto
rti
o
n
(T
HD
)
a
n
d
f
u
n
d
a
m
e
n
tal
RM
S
v
o
lt
a
g
e
.
F
in
a
ll
y
,
th
e
sim
u
latio
n
re
su
l
ts
a
re
in
c
lu
d
e
d
to
v
e
rify
th
e
e
ff
e
c
ti
v
e
n
e
ss
o
f
th
e
p
ro
p
o
se
d
CBRV
in
v
e
rter t
o
p
o
lo
g
y
a
n
d
v
a
li
d
a
te t
h
e
p
ro
p
o
se
d
th
e
o
ry
.
A
h
a
rd
w
a
r
e
s
e
t
u
p
w
a
s
d
e
v
e
lo
p
e
d
f
o
r
a
1
–
Ф
se
v
e
n
l
e
v
e
l
CBRV
in
v
e
rter
to
p
o
lo
g
y
u
sin
g
F
P
G
A
b
a
se
d
p
u
lse
g
e
n
e
ra
ti
o
n
.
K
ey
w
o
r
d
:
DC
-
DC co
n
v
e
rter
M
u
lt
il
e
v
e
l
in
v
e
rter (M
L
I)
Re
n
e
wa
b
le en
e
rg
y
so
u
rc
e
(RES
)
S
IM
O
Co
p
y
rig
h
t
©
201
8
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
:
S.Na
g
ar
aj
a
R
ao
,
R
esear
ch
Sch
o
lar
Dep
ar
te
m
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
i
n
ee
r
in
g
,
J
a
w
ah
ar
lal
Ne
h
r
u
T
ec
h
n
o
lo
g
ic
al
Un
i
v
er
s
it
y
,
Kak
i
n
ad
a,
A
n
d
h
r
a
P
r
a
d
esh
,
5
3
3
0
0
3
,
I
n
d
ia.
E
m
ail:
n
ag
ar
aj
r
ao
m
tech
@
g
m
a
il.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Mu
lti
-
le
v
el
in
v
er
ter
s
(
ML
I
s
)
w
it
h
v
ar
io
u
s
s
tr
u
ct
u
r
es
h
a
v
e
m
o
r
e
co
n
s
id
er
atio
n
in
t
h
e
r
ec
en
t
i
m
p
le
m
en
ta
tio
n
s
.
T
h
ese
i
n
v
er
ter
s
ar
e
u
s
ed
i
n
v
ar
io
u
s
ap
p
li
ca
tio
n
s
s
u
ch
as
elec
tr
ic
v
e
h
ic
les,
elec
tr
ic
m
o
to
r
d
r
iv
es,
ac
ti
v
e
p
o
w
er
f
ilter
s
,
s
tatic
co
m
p
e
n
s
ato
r
s
an
d
r
e
n
e
wab
le
en
er
g
y
s
o
u
r
ce
s
[
1
,
2
]
.
Mu
ltil
e
v
el
in
v
er
ter
s
h
av
e
b
ee
n
co
n
s
id
er
ed
f
o
r
m
a
n
y
ad
v
an
ta
g
e
s
s
u
ch
a
s
lo
w
er
h
ar
m
o
n
ic
s
,
h
i
g
h
p
o
w
er
q
u
alit
y
,
lo
w
elec
tr
o
m
ag
n
etic
in
ter
f
er
en
ce
a
n
d
lo
w
er
s
w
i
tch
i
n
g
lo
s
s
es.
T
h
e
q
u
alit
y
o
f
a
m
u
lti
-
le
v
el
i
n
v
e
r
ter
is
d
eter
m
i
n
ed
b
y
t
h
e
n
u
m
b
er
o
f
le
v
els.
B
u
t
in
cr
ea
s
i
n
g
t
h
e
n
u
m
b
er
o
f
o
u
t
p
u
t
lev
el
s
lead
s
to
an
in
cr
ea
s
e
in
th
e
n
u
m
b
er
o
f
co
m
p
o
n
e
n
t
s
an
d
t
h
er
eb
y
in
cr
ea
s
es
th
e
co
m
p
lex
i
t
y
o
f
co
n
tr
o
l
an
d
also
in
v
er
ter
o
p
er
atio
n
.
So
,
th
e
n
u
m
b
er
o
f
s
e
m
ico
n
d
u
cto
r
d
ev
ice
s
m
u
s
t
b
e
r
ed
u
ce
d
.
C
o
n
v
e
n
tio
n
a
l
M
L
I
s
ar
e
class
i
f
ied
as
n
e
u
tr
al
p
o
i
n
t
cla
m
p
ed
(
NP
C
)
,
ca
s
ca
d
ed
H
-
b
r
id
g
e
(
C
HB
)
co
n
v
er
ter
s
an
d
f
l
y
i
n
g
ca
p
ac
ito
r
(
FC
)
.
T
h
ese
t
h
r
ee
t
y
p
e
s
o
f
ML
I
s
r
eq
u
ir
e
m
o
r
e
n
u
m
b
er
o
f
co
m
p
o
n
e
n
ts
s
u
c
h
as
s
w
i
tch
e
s
,
cla
m
p
in
g
d
io
d
es
an
d
ca
p
ac
ito
r
s
.
A
s
th
e
n
u
m
b
e
r
o
f
v
o
ltag
e
lev
e
ls
‘
m
’
r
ai
s
es,
t
h
e
n
u
m
b
er
o
f
s
w
i
tch
es
i
n
cr
ea
s
e
s
ac
co
r
d
in
g
to
‘
2
×(
m
-
1
)
’
f
o
r
th
e
co
n
v
e
n
tio
n
al
ML
I
s
b
u
t
f
o
r
th
e
p
r
o
p
o
s
ed
ca
s
ca
d
e
b
ased
r
ev
er
s
in
g
v
o
lta
g
e
ML
I
(
C
B
R
V
M
L
I
)
s
tr
u
ct
u
r
e
[
1
0
.
1
1
]
it is
o
n
l
y
‘
m
+3
’
.
T
h
is
p
ap
er
p
r
esen
ts
a
1
–
Ф
s
e
v
en
lev
e
l
C
B
R
V
M
L
I
s
tr
u
ct
u
r
e
b
ased
o
n
m
u
ltil
e
v
el
d
c
l
in
k
(
ML
D
C
L
)
an
d
a
f
u
ll
b
r
id
g
e
in
v
er
ter
.
W
h
en
co
m
p
ar
ed
to
th
e
co
n
v
e
n
tio
n
al
M
L
I
s
,
th
e
p
r
o
p
o
s
ed
C
B
R
V
in
v
er
ter
s
tr
u
c
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
leme
n
ta
tio
n
o
f Ca
s
ca
d
e
d
b
a
s
ed
R
ev
ers
in
g
V
o
lta
g
e
Mu
ltil
ev
el
I
n
ve
r
ter u
s
in
g
…
(
S
.
N
a
g
a
r
a
ja
R
a
o
)
221
ca
n
h
a
v
e
s
u
p
er
io
r
p
er
f
o
r
m
a
n
c
e
b
y
i
m
p
le
m
en
t
in
g
t
h
e
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
P
W
M)
tech
n
iq
u
es.
T
h
is
p
ap
er
also
p
r
esen
t
s
t
h
e
m
o
s
t
r
ele
v
a
n
t
co
n
tr
o
l
an
d
m
o
d
u
latio
n
m
eth
o
d
s
b
y
a
p
h
ase
d
i
s
p
o
s
itio
n
m
u
lti
ca
r
r
ier
w
it
h
m
o
d
i
f
ied
s
p
ac
ev
ec
to
r
P
W
M
tech
n
iq
u
e
[
8
]
f
o
r
ML
DC
L
i
n
v
er
ter
an
d
co
m
p
ar
in
g
t
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
C
B
R
V
i
n
v
er
ter
s
w
i
th
p
h
a
s
e
d
is
p
o
s
itio
n
m
u
l
ti
ca
r
r
ier
s
in
e
P
W
M
tech
n
iq
u
e
a
n
d
p
r
o
p
o
s
ed
C
B
R
V
s
tr
u
ct
u
r
e
v
alid
ated
ex
p
er
i
m
en
t
all
y
t
h
r
o
u
g
h
FP
G
A
b
ased
p
u
ls
e
g
en
er
atio
n
.
T
h
e
b
lo
ck
d
iag
r
am
o
f
C
B
R
V
ML
I
is
d
ep
icted
in
Fig
u
r
e
1
[
3
]
.
I
t
co
n
s
is
ts
o
f
m
ai
n
l
y
le
v
el
g
en
er
ato
r
(
L
G)
an
d
p
o
lar
it
y
g
e
n
er
ato
r
(
PG)
u
n
i
ts
to
g
en
er
ate
r
eq
u
ir
e
d
n
u
m
b
er
o
f
lev
el
s
[
4
]
.
T
h
e
b
asic id
ea
o
f
th
e
C
B
R
V
s
tr
u
ct
u
r
e
as
a
M
L
I
is
th
at
t
h
e
L
G
g
en
er
ate
s
t
h
e
r
eq
u
ir
ed
p
o
s
itiv
e
lev
e
ls
a
n
d
t
h
e
P
G
r
e
v
er
s
es
t
h
e
d
ir
ec
tio
n
w
h
e
n
th
e
v
o
lta
g
e
p
o
lar
it
y
r
eq
u
ir
es
to
b
e
ch
an
g
ed
f
o
r
n
e
g
ati
v
e
p
o
lar
it
y
.
I
n
th
e
p
r
o
p
o
s
ed
C
B
R
V
ML
I
s
tr
u
c
tu
r
e
th
er
e
is
n
o
n
ee
d
to
o
p
e
r
ate
all
th
e
s
w
itc
h
es
at
h
i
g
h
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
,
th
e
L
G
u
n
it
s
w
itc
h
es
o
p
er
ate
at
h
ig
h
f
r
eq
u
en
c
y
a
n
d
P
G
u
n
it
s
w
itc
h
es
o
p
er
ate
at
f
u
n
d
a
m
en
tal
f
r
eq
u
en
c
y
.
P
G
u
n
i
t
s
w
itc
h
es
ar
e
u
s
ed
f
o
r
r
ev
er
s
e
v
o
ltag
e
ap
p
ea
r
an
ce
ac
r
o
s
s
t
h
e
lo
a
d
an
d
ar
e
tr
ig
g
er
ed
b
y
s
i
m
p
le
p
u
ls
e
g
e
n
er
ato
r
.
Fig
u
r
e1
.
B
lo
ck
Diag
r
a
m
o
f
P
r
o
p
o
s
ed
C
B
R
V
ML
I
2.
P
RO
P
O
SE
D
CB
RV
I
NV
E
R
T
E
R
ST
R
UCTU
RE
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
p
r
o
p
o
s
ed
1
–
Ф
CB
R
V
ML
I
is
s
h
o
w
n
i
n
Fig
u
r
e
4
.
It
co
n
s
is
ts
o
f
a
m
u
ltil
e
v
el
d
c
s
o
u
r
ce
,
L
G
u
n
it,
P
G
u
n
it
(
s
in
g
le
-
p
h
a
s
e
f
u
ll
-
b
r
id
g
e
i
n
v
er
ter
)
an
d
a
lo
ad
[
5
,
6
]
.
Fig
u
r
e
2
.
1
–
Ф
Sev
en
L
e
v
el
C
B
R
V
I
n
v
er
ter
T
h
e
co
m
p
o
n
e
n
ts
co
m
p
ar
i
s
o
n
f
o
r
p
r
o
d
u
cin
g
1
–
Ф
s
ev
e
n
-
le
v
el
o
u
tp
u
t
v
o
ltag
e
f
o
r
th
e
p
r
o
p
o
s
ed
C
B
R
V
an
d
co
n
v
e
n
tio
n
al
ca
s
ca
d
ed
b
ased
in
v
er
ter
s
ar
e
g
i
v
en
i
n
T
ab
le
1
.
I
t
clea
r
ly
s
h
o
w
s
s
u
b
s
tan
tial
co
m
p
o
n
e
n
t
r
ed
u
ctio
n
w
it
h
t
h
e
p
r
o
p
o
s
ed
C
B
R
V
ML
I
s
tr
u
ct
u
r
e
[
8
]
.
T
h
is
s
av
i
n
g
in
co
m
p
o
n
e
n
ts
i
n
cr
ea
s
es
as
t
h
e
n
u
m
b
er
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
220
–
2
3
0
222
v
o
ltag
e
le
v
el
i
n
cr
ea
s
es
as
m
e
n
tio
n
ed
b
ef
o
r
e.
Fo
r
a
1
–
Ф
s
ev
en
-
le
v
el
CB
R
V
in
v
er
ter
,
th
e
s
w
itch
in
g
s
eq
u
e
n
ce
to
g
en
er
ate
t
h
e
r
eq
u
ir
ed
lev
els
ar
e
g
iv
e
n
in
T
ab
le
2
.
T
ab
le
1
: Co
m
p
o
n
e
n
t
s
C
o
m
p
ar
is
o
n
to
Gen
er
ate
1
–
Ф
Sev
e
n
-
L
ev
el
Ou
tp
u
t
C
o
mp
o
n
e
n
t
s
P
r
o
p
o
se
d
Ex
i
st
i
n
g
S
w
i
t
c
h
e
s
10
12
C
l
a
mp
i
n
g
d
i
o
d
e
s
0
0
C
a
p
a
c
i
t
o
r
s
0
0
D
C
so
u
r
c
e
s
3
3
T
ab
le
2
:
S
w
itc
h
i
n
g
Seq
u
en
ce
t
o
Gen
er
ate
th
e
1
–
Ф
Sev
en
L
e
v
el
O
u
tp
u
t
f
o
r
C
B
R
V
I
n
v
er
ter
S
.
N
o
L
G
U
n
i
t
P
G
U
n
i
t
V
o
l
t
a
g
e
L
e
v
e
l
s
O
n
S
w
i
t
c
h
e
s
O
f
f
S
w
i
t
c
h
e
s
O
n
S
w
i
t
c
h
e
s
O
f
f
S
w
i
t
c
h
e
s
1
S
a1
, S
a3
,
S
a6
S
a2
, S
a4
,
S
a5
S
a7
, S
a8
S
a9
, S
a
10
+ V
dc
2
S
a1
, S
a4
,
S
a6
S
a2
, S
a3
,
S
a5
S
a7
, S
a8
S
a9
, S
a
10
+
2
V
dc
3
S
a2
, S
a4
,
S
a6
S
a1
, S
a3
,
S
a5
S
a7
, S
a8
S
a9
, S
a
10
+
3
V
dc
4
S
a1
, S
a3
,
S
a5
S
a2
, S
a4
,
S
a6
S
a7
, S
a8
S
a9
, S
a
10
0
5
S
a2
, S
a4
,
S
a6
S
a1
, S
a3
,
S
a5
S
a9
, S
a
10
S
a7
, S
a8
-
3
V
dc
6
S
a1
, S
a4
,
S
a6
S
a2
, S
a3
,
S
a5
S
a9
, S
a
10
S
a7
, S
a8
-
2
V
dc
7
S
a1
, S
a3
,
S
a6
S
a2
, S
a4
,
S
a5
S
a9
, S
a
10
S
a7
, S
a8
-
V
dc
T
h
e
m
a
x
i
m
u
m
o
u
tp
u
t
v
o
ltag
e
o
f
L
G
u
n
it f
o
r
t
h
e
p
r
o
p
o
s
ed
C
B
R
V
is
o
b
tain
ed
b
y
u
s
i
n
g
eq
u
atio
n
(
1
)
V
0
,
ma
x
=
∑
=
1
-
-
-
-
-
-
-
-
-
-
-
-
(
1
)
T
h
e
eq
u
atio
n
(
1
)
illu
s
tr
ates
th
e
o
u
tp
u
t
le
v
el
o
f
t
h
e
L
G
u
n
it
a
n
d
th
e
p
o
s
it
iv
e
a
n
d
n
eg
at
iv
e
lev
el
s
ar
e
s
y
n
t
h
esized
b
y
u
s
i
n
g
t
h
e
PG
u
n
it.
A
t lo
ad
(
V
o
)
,
th
e
s
y
n
th
e
s
ized
s
tep
p
ed
o
u
tp
u
t v
o
ltag
e
le
v
el
w
i
ll b
e
o
b
tain
ed
b
y
u
s
i
n
g
t
h
e
E
q
u
atio
n
(
2
)
an
d
(
3
)
.
V
0
,
ma
x
=
∑
+
V
o
n
i
=
1
,
If
S
a7
,
S
a8
=
1
-
-
-
-
-
-
-
-
-
-
-
-
(
2
)
V
0
,
ma
x
=
∑
−
V
0
n
i
=
1
,
I
f
S
a9
,
S
a1
0
=
1
-
-
-
-
-
-
-
-
-
-
-
-
(
3
)
3.
P
RO
P
O
SE
D
M
O
DULAT
I
O
N
ST
RA
T
E
G
I
E
S
T
h
e
p
u
ls
e
g
en
er
atio
n
ap
p
r
o
ac
h
f
o
r
th
e
s
w
itc
h
es
o
f
L
G
u
n
it
an
d
P
G
u
n
it
f
o
r
th
e
s
ev
e
n
-
le
v
el
C
B
R
V
in
v
er
ter
ar
e
d
ep
icted
in
Fig
u
r
e
3
.
3
.
1
.
G
ener
a
t
io
n o
f
P
uls
es
f
o
r
L
G
Unit
I
n
th
is
ap
p
r
o
ac
h
,
m
u
ltip
le
ca
r
r
ier
m
o
d
u
latio
n
tec
h
n
iq
u
e
is
i
n
co
r
p
o
r
ated
in
to
th
e
s
in
u
s
o
id
al
P
W
M
an
d
m
o
d
i
f
ied
s
p
ac
e
v
ec
to
r
P
W
M
tech
n
iq
u
es
to
p
r
o
d
u
ce
P
W
M
s
w
itc
h
in
g
s
i
g
n
als
f
o
r
th
e
L
G
u
n
i
t
in
t
h
e
C
B
R
V
in
v
er
ter
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
u
l
atio
n
s
c
h
e
m
e
i
s
b
ased
o
n
t
h
e
u
n
ip
o
lar
,
s
y
m
m
etr
ic
P
W
M
s
w
it
ch
in
g
tech
n
iq
u
e
[
7
,
8]
.
I
t
co
m
p
ar
es
s
i
n
u
s
o
id
al
o
r
s
p
ac
e
v
ec
to
r
m
o
d
u
lat
io
n
s
i
g
n
als
alo
n
g
w
i
th
in
-
p
h
ase
le
v
e
l
-
s
h
i
f
ted
tr
ia
n
g
u
lar
ca
r
r
ier
s
ig
n
al
s
.
T
h
ese
m
o
d
if
ie
d
m
o
d
u
latio
n
s
ig
n
al
s
h
a
v
e
th
e
s
a
m
e
f
r
eq
u
en
c
y
‘
f
0
’
a
n
d
a
m
p
litu
d
e
‘A
r
’
.
Si
n
ce
th
e
m
o
d
u
la
tio
n
is
s
y
m
m
etr
ic,
th
e
p
r
o
p
o
s
ed
m
o
d
u
lat
io
n
s
i
g
n
als
ar
e
s
a
m
p
led
b
y
th
e
tr
ia
n
g
u
lar
ca
r
r
ier
s
ig
n
al
o
n
ce
in
ev
er
y
ca
r
r
ier
c
y
cle.
T
h
e
ca
r
r
ier
s
ig
n
al
is
a
tr
ain
o
f
tr
ian
g
u
lar
w
av
e
f
o
r
m
w
i
th
f
r
eq
u
en
c
y
‘
f
c
’
,
an
d
a
m
p
lit
u
d
e
‘
A
c
’
.
T
h
e
p
u
ls
e
g
e
n
er
atio
n
m
et
h
o
d
o
lo
g
y
i
s
d
ep
icted
in
Fi
g
u
r
e
4
an
d
5
f
o
r
t
h
e
p
r
o
p
o
s
ed
s
ev
en
le
v
el
C
B
R
V
i
n
v
er
ter
u
s
i
n
g
s
in
u
s
o
id
al
an
d
s
p
ac
e
v
ec
to
r
P
W
M
s
t
r
ateg
ies
.
Fo
r
an
m
-
lev
el
i
n
v
er
ter
,
(m
-
1
/2
)
ca
r
r
ier
s
ar
e
n
ee
d
ed
to
g
en
er
ate
p
u
ls
e
s
f
o
r
th
e
p
r
o
p
o
s
ed
CB
R
V
in
v
er
ter
i.e
,
f
o
r
a
s
e
v
en
lev
el
in
v
er
ter
th
r
ee
ca
r
r
ier
s
ig
n
al
s
(
V
tri1
, V
tri2
an
d
V
tri3
)
ar
e
u
s
ed
an
d
th
e
s
e
s
i
g
n
als
w
er
e
co
m
p
ar
ed
w
it
h
a
r
ef
er
en
ce
s
ig
n
al
(
V
ref
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
leme
n
ta
tio
n
o
f Ca
s
ca
d
e
d
b
a
s
ed
R
ev
ers
in
g
V
o
lta
g
e
Mu
ltil
ev
el
I
n
ve
r
ter u
s
in
g
…
(
S
.
N
a
g
a
r
a
ja
R
a
o
)
223
Fig
u
r
e
3
.
Gen
er
atio
n
o
f
p
u
ls
es
f
o
r
th
e
p
r
o
p
o
s
ed
s
ev
en
-
lev
el
CB
R
V
i
n
v
er
ter
T
h
eo
r
etica
lly
,
f
o
r
a
m
u
ltip
le
ca
r
r
ier
an
d
a
s
in
g
le
r
ef
er
e
n
ce
s
ig
n
al,
t
h
e
m
o
d
u
l
atio
n
in
d
e
x
(
M)
is
d
ef
in
ed
b
y
eq
u
atio
n
(
4
)
.
=
(
−
1
)
2
∗
-
-
-
-
-
-
-
-
-
-
-
-
(4
)
w
h
er
e
‘
m
’
r
ep
r
esen
ts
t
h
e
n
u
m
b
er
o
f
lev
els.H
e
n
ce
,
f
o
r
th
e
p
r
o
p
o
s
ed
R
V
s
ev
en
le
v
el
i
n
v
er
te
r
s
,
th
e
m
o
d
u
la
tio
n
in
d
ex
(
M)
is
d
ef
i
n
ed
b
y
eq
u
ati
o
n
(
5
)
.
=
3
∗
-
-
-
-
-
-
-
-
-
-
-
-
(
5
)
T
h
e
p
r
in
cip
le
o
f
t
h
e
p
r
o
p
o
s
ed
P
W
M
tech
n
iq
u
es
u
s
i
n
g
i
n
-
p
h
ase
tr
ian
g
u
lar
ca
r
r
ier
f
o
r
a
s
e
v
en
-
lev
el
C
B
R
V
in
v
er
ter
a
t
M=
1
a
n
d
m
f
=
4
0
is
s
h
o
w
n
i
n
Fig
u
r
e
4
a
n
d
5
r
esp
ec
tiv
el
y
.
I
n
s
t
e
a
d
o
f
m
a
i
n
t
ai
n
i
n
g
t
h
e
s
a
m
e
w
i
d
t
h
o
f
al
l
p
u
l
s
e
s
a
s
i
n
t
h
e
c
a
s
e
o
f
m
u
l
t
i
-
p
u
l
s
e
m
o
d
u
l
a
ti
o
n
,
t
h
e
w
i
d
t
h
o
f
e
a
c
h
p
u
l
s
e
i
s
v
a
r
i
e
d
i
n
p
r
o
p
o
r
t
i
o
n
t
o
t
h
e
a
m
p
l
i
t
u
d
e
o
f
a
si
n
e
w
a
v
e
e
v
a
l
u
a
t
e
d
a
t
t
h
e
c
e
n
tr
e
o
f
t
h
e
s
a
m
e
p
u
l
s
e
[
1
]
,
a
n
d
t
h
e
r
e
f
o
r
e
T
H
D
i
s
r
e
d
u
c
e
d
si
g
n
i
f
i
c
a
n
t
l
y
.
T
h
e
g
a
t
i
n
g
s
i
g
n
a
l
s
a
r
e
g
e
n
e
r
a
t
e
d
b
y
c
o
m
p
a
r
i
n
g
a
sinusoidal
o
r
s
p
a
c
e
v
e
c
t
o
r
r
e
f
e
r
e
n
c
e
s
i
g
n
a
l
w
i
t
h
a
t
ri
a
n
g
u
l
a
r
c
a
r
r
i
e
r
w
a
v
e
o
f
f
r
e
q
u
e
n
c
y
f
c
.
Fi
g
u
r
e
4
an
d
5
d
e
m
o
n
s
tr
ate
t
h
e
s
i
n
e
o
r
s
p
ac
e
v
ec
to
r
b
ased
in
-
p
h
a
s
e
tr
ian
g
le
m
et
h
o
d
f
o
r
a
s
i
n
g
le
p
h
ase
s
ev
e
n
-
lev
e
l
in
v
er
ter
.
T
h
er
ein
,
t
h
e
p
h
ase
m
o
d
u
latio
n
s
ig
n
al
is
co
m
p
ar
e
d
w
ith
t
h
r
ee
(
(
n
-
1
/2
)
in
g
en
er
al)
in
-
p
h
a
s
e
tr
ian
g
le
w
a
v
e
f
o
r
m
s
to
p
r
o
d
u
ce
+
3
V
dc
, + 2
V
dc
, +
V
dc
an
d
0
u
s
in
g
L
G
u
n
i
t
s
w
itc
h
es
.
Fig
u
r
e
4
.
Mu
lti
C
ar
r
ier
Sin
u
s
o
i
d
al
P
W
M
w
it
h
In
-
P
h
ase
T
r
ian
g
u
lar
C
ar
r
ier
(
MCS
P
W
M)
0
0
.
0
0
2
0
.
0
0
4
0
.
0
0
6
0
.
0
0
8
0
.
0
1
0
.
0
1
2
0
.
0
1
4
0
.
0
1
6
0
.
0
1
8
0
.
0
2
0
.
5
1
1
.
5
2
2
.
5
3
T
i
m
e
(
S
e
co
n
d
s)
V
o
l
t
a
g
e
(
V
o
l
t
s)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
220
–
2
3
0
224
T
o
ac
h
iev
e
th
e
m
ax
i
m
u
m
a
m
p
litu
d
e
o
f
t
h
e
f
u
n
d
a
m
e
n
tal
p
h
ase
v
o
lta
g
e,
th
e
o
f
f
s
et
v
o
lta
g
e
,
V
offset
,
is
ad
d
ed
to
th
e
s
i
n
u
s
o
id
al
s
i
g
n
al
[
9
,
1
0
]
,
w
h
er
e
th
e
m
a
g
n
itu
d
e
o
f
V
off
set
is
g
i
v
e
n
b
y
eq
u
at
io
n
(
6
)
.
T
h
e
ad
d
itio
n
o
f
th
e
V
offset
to
th
e
s
i
n
u
s
o
id
al
m
o
d
u
la
tio
n
s
i
g
n
a
l r
esu
l
ts
i
n
s
p
ac
e
v
ec
to
r
PW
M
tech
n
iq
u
e
[
9
]
.
2
)
(
m
i
n
m
a
x
V
V
V
o
f
f
s
e
t
-
-
-
-
-
-
-
-
-
-
-
-
(
6
)
I
n
eq
u
atio
n
(
6
)
,
V
m
ax
is
th
e
m
ax
i
m
u
m
m
a
g
n
it
u
d
e
o
f
th
e
s
a
m
p
led
r
ef
er
en
ce
p
h
ase
v
o
lta
g
e,
w
h
i
le
V
m
i
n
is
th
e
m
i
n
i
m
u
m
m
ag
n
it
u
d
e
o
f
t
h
e
th
r
ee
s
a
m
p
led
r
ef
er
en
ce
p
h
a
s
e
v
o
ltag
e,
in
a
s
a
m
p
li
n
g
in
ter
v
al.
Fig
u
r
e
5
.
Mu
lti
C
ar
r
ier
Sp
ac
e
Vec
to
r
P
W
M
w
it
h
In
-
P
h
ase
T
r
ian
g
u
lar
C
ar
r
ier
(
MCS
VP
W
M)
3
.
2
G
ener
a
t
io
n o
f
pu
ls
es f
o
r
P
G
un
it
:
S
w
itc
h
es
o
f
P
G
u
n
it
ar
e
u
s
ed
to
g
en
er
ate
p
o
s
itiv
e
an
d
n
e
g
at
iv
e
lev
el
s
o
f
s
e
v
en
-
le
v
el
o
u
tp
u
t
v
o
lta
g
e,
w
h
ic
h
is
tr
ig
g
er
ed
b
y
u
s
in
g
ti
m
e
b
ased
p
u
ls
e
g
e
n
er
ato
r
w
i
th
a
f
u
n
d
a
m
e
n
tal
f
r
eq
u
en
c
y
.
T
h
e
s
w
itch
e
s
‘
S
a7
’
a
n
d
‘S
a8
’
ar
e
ac
ti
v
ated
at
th
e
s
a
m
e
in
s
ta
n
t
i
n
itia
l
l
y
w
it
h
0
º
d
el
a
y
u
s
i
n
g
p
u
ls
e
g
en
er
ato
r
an
d
s
w
itc
h
es
‘
S
a9
’
a
n
d
‘S
a10
’
ar
e
ac
ti
v
ated
w
it
h
d
elay
o
f
1
8
0
º
.
T
h
e
s
w
itc
h
es
‘
S
a7
’
an
d
‘
S
a8
’
ar
e
ac
ti
v
ated
to
g
e
n
er
ate
t
h
e
p
o
s
iti
v
e
lev
els o
f
s
e
v
e
n
-
lev
el
o
u
tp
u
t a
c
r
o
s
s
th
e
lo
ad
an
d
t
h
e
s
w
itc
h
es
‘
S
a9
’
a
n
d
‘
S
a10
’
ar
e
ac
tiv
ated
t
o
g
en
er
ate
n
eg
at
iv
e
lev
els
o
f
s
ev
e
n
-
le
v
el
o
u
tp
u
t
t
o
p
r
esen
t
ac
r
o
s
s
lo
ad
.
W
h
en
th
e
s
w
itc
h
e
s
‘
S
a7
’
a
n
d
‘
S
a8
’
a
r
e
tu
r
n
ed
ON,
th
e
s
w
itc
h
es
‘
S
a9
’
an
d
‘
S
a10
’
ar
e
tu
r
n
ed
OFF an
d
v
ice
-
v
er
s
a.
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
T
h
e
p
r
o
p
o
s
ed
1
–
ф
s
ev
en
-
le
v
el
C
B
R
V
i
n
v
er
ter
h
as
b
ee
n
s
i
m
u
lated
a
n
d
an
al
y
ze
d
f
o
r
v
ar
io
u
s
m
o
d
u
latio
n
i
n
d
ices
u
s
in
g
M
C
SP
W
M
an
d
MC
SVP
W
M
s
tr
a
teg
ies
an
d
th
e
co
r
r
esp
o
n
d
in
g
h
ar
m
o
n
ic
s
p
ec
tr
u
m
ar
e
p
r
esen
ted
.
T
h
e
s
i
m
u
lati
o
n
r
esu
lt
s
o
f
th
e
1
–
Ф
s
ev
e
n
-
lev
el
C
B
R
V
i
n
v
er
ter
u
s
in
g
MCS
P
W
M
an
d
MCS
VP
W
M
w
it
h
i
n
-
p
h
ase
tr
i
an
g
u
lar
ca
r
r
ier
s
a
n
d
it
s
co
r
r
es
p
o
n
d
in
g
h
ar
m
o
n
ic
s
p
ec
tr
u
m
f
o
r
M
=
0
.
8
5
an
d
m
f
=
1
0
0
a
r
e
s
h
o
w
n
i
n
th
e
f
i
g
u
r
es
6
to
9
.
Si
m
ula
t
io
n P
a
ra
m
et
er
s
:
I
n
p
u
t V
o
lta
g
e
=
3
0
0
Vo
lts
S
w
itc
h
in
g
Fre
q
u
e
n
c
y
=
5
KHz
L
o
ad
R
esi
s
tan
ce
=
1
0
Ω
0
0
.
0
0
2
0
.
0
0
4
0
.
0
0
6
0
.
0
0
8
0
.
0
1
0
.
0
1
2
0
.
0
1
4
0
.
0
1
6
0
.
0
1
8
0
.
0
2
0
0
.
5
1
1
.
5
2
2
.
5
3
T
i
m
e
(
S
e
co
n
d
s)
V
o
l
t
a
g
e
(
V
o
l
t
s)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
leme
n
ta
tio
n
o
f Ca
s
ca
d
e
d
b
a
s
ed
R
ev
ers
in
g
V
o
lta
g
e
Mu
ltil
ev
el
I
n
ve
r
ter u
s
in
g
…
(
S
.
N
a
g
a
r
a
ja
R
a
o
)
225
Fig
u
r
e
6.
P
h
ase
v
o
ltag
e
o
f
1
–
Ф
s
ev
en
-
le
v
el
C
B
R
V
i
n
v
er
ter
u
s
i
n
g
MC
SP
W
M
(
M=
0
.
8
an
d
m
f
=
1
0
0
)
Fig
u
r
e
7
.
Har
m
o
n
ic
s
p
ec
tr
u
m
o
f
1
–
Ф
s
ev
en
-
le
v
el
C
B
R
V
in
v
er
ter
u
s
in
g
M
C
SP
W
M
(
M=
0
.
8
an
d
m
f
=
1
0
0
)
Fig
u
r
e
6
s
h
o
w
s
th
e
s
i
m
u
la
tio
n
w
av
e
f
o
r
m
o
f
t
h
e
s
e
v
en
-
le
v
el
C
B
R
V
i
n
v
er
ter
o
u
tp
u
t
u
s
i
n
g
M
C
SP
W
M.
T
h
e
v
alu
e
o
f
f
u
n
d
a
m
e
n
tal
v
o
lta
g
e
o
f
t
h
e
i
n
v
er
ter
is
2
3
9
.
8
V
(
its
R
MS
v
al
u
e
i
s
1
6
9
.
6
V)
.
Fig
u
r
e
7
s
h
o
w
s
t
h
e
co
r
r
esp
o
n
d
in
g
T
HD
p
lo
t o
f
th
e
s
ev
e
n
-
le
v
el
i
n
v
er
ter
.
T
h
e
%T
HD
v
alu
e
o
f
7
-
le
v
el
C
B
R
V
i
n
v
er
ter
is
2
4
.
3
3
%.
Fig
u
r
e
8
.
P
h
ase
v
o
ltag
e
o
f
1
–
Ф
s
ev
en
-
le
v
el
C
B
R
V
i
n
v
er
ter
u
s
i
n
g
MC
S
V
P
W
M
(
M=
0
.
8
an
d
m
f
=
1
0
0
)
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
0
.
0
8
0
.
0
9
0
.
1
-
3
0
0
-
2
0
0
-
1
0
0
0
100
200
300
T
i
m
e
(
S
e
co
n
d
s)
V
o
l
t
a
g
e
(
V
o
l
t
s)
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
0
.
0
8
0
.
0
9
0
.
1
-
3
0
0
-
2
0
0
-
1
0
0
0
100
200
300
T
i
m
e
(
S
e
co
n
d
s)
V
o
l
t
a
g
e
(
V
o
l
t
s)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
220
–
2
3
0
226
Fig
u
r
e
9
.
Har
m
o
n
ic
Sp
ec
tr
u
m
o
f
1
–
Ф
Sev
en
-
L
ev
el
C
B
R
V
I
n
v
er
ter
Usi
n
g
MC
S
V
P
W
M
(
M=
0
.
8
an
d
m
f
=
100)
Fig
u
r
e
8
s
h
o
w
s
th
e
s
i
m
u
la
tio
n
w
av
e
f
o
r
m
o
f
t
h
e
s
e
v
en
-
le
v
el
C
B
R
V
i
n
v
er
ter
o
u
tp
u
t
u
s
i
n
g
M
C
SP
W
M.
T
h
e
v
alu
e
o
f
f
u
n
d
a
m
e
n
tal
v
o
lta
g
e
o
f
th
e
i
n
v
er
ter
is
2
7
5
.
7
(
i
ts
R
M
S
v
al
u
e
i
s
1
9
5
V)
.
Fig
u
r
e
9
s
h
o
w
s
t
h
e
co
r
r
esp
o
n
d
in
g
T
HD
p
lo
t o
f
th
e
s
ev
e
n
-
le
v
el
i
n
v
er
ter
.
T
h
e
%T
HD
v
alu
e
o
f
7
-
le
v
el
C
B
R
V
i
n
v
er
ter
is
2
1
.
8
4
%.
E
f
f
ec
t
o
f
M
o
du
la
t
io
n ind
ex
(
M
)
:
I
f
M
is
i
n
b
et
w
ee
n
0
≤
M
≤
0
.
3
3
,
o
n
ly
t
h
e
f
ir
s
t
tr
ia
n
g
u
lar
wav
e
(
V
tr
i1
)
is
co
m
p
ar
ed
w
it
h
t
h
e
r
ef
er
en
ce
s
i
g
n
al,
th
en
th
e
i
n
v
er
ter
b
eh
av
io
r
is
s
i
m
ilar
to
th
at
o
f
a
co
n
v
en
t
io
n
al
t
h
r
ee
-
le
v
el
P
W
M
in
v
er
ter
.
Ho
w
e
v
er
,
if
M
i
s
m
o
r
e
th
a
n
0
.
3
3
an
d
les
s
t
h
a
n
0
.
6
6
,
o
n
ly
V
tr
i1
an
d
V
tr
i2
tr
i
an
g
u
lar
s
ig
n
al
s
ar
e
co
m
p
ar
ed
w
ith
th
e
r
ef
er
e
n
ce
s
ig
n
al,
th
e
n
th
e
ou
tp
u
t
v
o
lta
g
e
co
n
s
is
ts
o
f
f
i
v
e
v
o
lta
g
e
lev
els.
T
h
e
m
o
d
u
latio
n
in
d
ex
i
s
s
et
to
b
e
m
o
r
e
th
an
0
.
6
6
to
p
r
o
d
u
ce
s
ev
e
n
lev
el
o
u
tp
u
t
v
o
lta
g
e.
T
h
e
e
f
f
ec
t
o
f
‘
M’
f
o
r
t
h
e
s
tep
ch
a
n
g
es
in
m
o
d
u
latio
n
in
d
ice
s
w
i
th
th
e
co
r
r
esp
o
n
d
in
g
lo
ad
v
o
ltag
e
is
s
h
o
w
n
i
n
Fig
u
r
e
1
0
to
g
en
er
ate
t
h
r
ee
,
f
i
v
e
a
n
d
s
e
v
e
n
lev
els
r
esp
ec
tiv
e
l
y
[
1
2
]
.
(
a)
(
b
)
Fig
u
r
e
1
0
.
Dy
n
a
m
ic
r
esp
o
n
s
e
(
a)
s
tep
ch
an
g
e
s
in
m
o
d
u
lat
io
n
in
d
ex
(
b
)
P
h
ase
v
o
ltag
e
w
a
v
e
f
o
r
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
leme
n
ta
tio
n
o
f Ca
s
ca
d
e
d
b
a
s
ed
R
ev
ers
in
g
V
o
lta
g
e
Mu
ltil
ev
el
I
n
ve
r
ter u
s
in
g
…
(
S
.
N
a
g
a
r
a
ja
R
a
o
)
227
5.
I
M
P
L
E
M
E
NT
AT
I
O
N
O
F
C
B
RV
I
NVER
T
E
R
US
I
N
G
F
P
G
A
B
ASE
D
P
UL
SE
G
E
NE
RATI
O
N
T
h
e
p
r
o
t
o
ty
p
e
m
o
d
e
l
o
f
p
r
o
p
o
s
e
d
c
a
s
c
a
d
e
d
b
a
s
e
d
R
V
ML
I
is
im
p
l
em
en
te
d
u
s
in
g
X
il
in
x
Sp
a
r
t
a
n
F
PGA
[
1
3
,
1
4
]
t
o
v
a
l
i
d
a
t
e
t
h
e
s
im
u
l
at
io
n
r
e
s
u
l
ts
.
T
h
e
h
a
r
d
w
ar
e
r
e
a
l
i
za
t
i
o
n
ci
r
c
u
i
t
o
f
th
e
p
r
o
p
o
s
e
d
s
y
s
t
em
f
e
d
R
-
l
o
a
d
is
d
e
p
i
c
t
e
d
in
Fi
g
u
r
e
11
an
d
1
2
.
T
h
e
p
r
o
t
o
ty
p
e
m
o
d
e
l
c
o
n
s
is
ts
o
f
c
a
s
ca
d
e
b
as
e
d
R
V
in
v
e
r
t
e
r
,
R
e
s
is
t
iv
e
l
o
a
d
,
F
PG
A
c
o
n
t
r
o
ll
e
r
,
PC
,
B
u
f
f
e
r
c
i
r
cu
i
t
,
O
p
t
o
i
s
o
la
t
o
r
an
d
D
r
iv
e
r
c
i
r
c
u
it
.
Fig
u
r
e
1
1
.
I
m
p
le
m
en
ta
tio
n
o
f
1
-
ϕ
s
e
v
e
n
-
le
v
el
C
B
R
V
I
n
v
er
te
r
Usi
n
g
FP
G
A
P
r
o
ce
s
s
o
r
Fig
u
r
e
1
2
.
VHDL
C
o
d
e
S
u
cc
ess
f
u
l
l
y
E
m
b
ed
d
ed
in
FP
GA
f
o
r
1
-
ϕ
Sev
en
-
L
e
v
el
C
B
R
V
I
n
v
e
r
ter
Gen
er
atio
n
o
f
p
u
l
s
es
u
s
i
n
g
M
C
SP
W
M
an
d
MC
SVP
W
M
tech
n
iq
u
es
t
h
r
o
u
g
h
Xili
n
x
I
SE
ar
e
d
ep
icted
in
Fi
g
u
r
e
1
3
an
d
1
4
r
esp
ec
tiv
el
y
.
F
ig
u
r
e
1
3
.
G
en
e
r
a
t
i
o
n
o
f
Pu
l
s
es
Us
in
g
MC
S
PW
M
M
e
th
o
d
T
h
r
o
u
g
h
X
i
li
n
x
I
S
E
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
220
–
2
3
0
228
F
ig
u
r
e
1
4
.
G
en
e
r
a
t
i
o
n
o
f
Pu
l
s
es
Us
in
g
MC
S
V
PW
M
M
eth
o
d
th
r
o
u
g
h
Xi
l
in
x
I
S
E
Fig
u
r
e
1
5
.
E
x
p
er
im
e
n
tal
O
u
tp
u
t P
h
ase
Vo
lta
g
e
o
f
1
–
Ф
Sev
e
n
-
L
e
v
el
C
B
R
V
I
n
v
er
ter
Usi
n
g
MC
S
P
W
M
Fig
u
r
e
1
5
s
h
o
w
s
t
h
e
ex
p
er
i
m
en
tal
o
u
tp
u
t
p
h
a
s
e
v
o
lta
g
e
wav
ef
o
r
m
o
f
s
e
v
e
n
-
lev
el
C
B
R
V
in
v
er
ter
u
s
i
n
g
MCS
P
W
M.
T
h
e
R
MS
v
alu
e
o
f
f
u
n
d
a
m
en
ta
l
v
o
ltag
e
o
f
th
e
in
v
er
ter
is
1
6
8
.
1
V.
Fig
u
r
e
1
5
s
h
o
w
s
th
e
co
r
r
esp
o
n
d
in
g
T
HD
p
lo
t
o
f
t
h
e
s
e
v
e
n
-
le
v
el
in
v
er
ter
.
T
h
e
%
T
HD
v
alu
e
o
f
s
ev
e
n
-
le
v
el
C
B
R
V
i
n
v
er
ter
is
2
5
.
1
7
%.
Fig
u
r
e
1
6
.
E
x
p
er
im
e
n
tal
O
u
tp
u
t P
h
ase
Vo
lta
g
e
o
f
1
–
ф
Sev
e
n
-
L
e
v
el
C
B
R
V
I
n
v
er
ter
Usi
n
g
MCS
VP
W
M
Fig
u
r
e
1
6
s
h
o
w
s
t
h
e
ex
p
er
i
m
en
tal
o
u
tp
u
t
p
h
a
s
e
v
o
lta
g
e
wav
ef
o
r
m
o
f
s
e
v
e
n
-
lev
el
C
B
R
V
in
v
er
ter
u
s
i
n
g
MC
SVP
W
M.
T
h
e
R
MS
v
alu
e
o
f
f
u
n
d
a
m
en
tal
v
o
lta
g
e
o
f
th
e
i
n
v
er
ter
is
1
9
3
.
2
V.
Fig
u
r
e
1
5
s
h
o
w
s
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
leme
n
ta
tio
n
o
f Ca
s
ca
d
e
d
b
a
s
ed
R
ev
ers
in
g
V
o
lta
g
e
Mu
ltil
ev
el
I
n
ve
r
ter u
s
in
g
…
(
S
.
N
a
g
a
r
a
ja
R
a
o
)
229
co
r
r
esp
o
n
d
in
g
T
HD
p
lo
t
o
f
t
h
e
s
e
v
e
n
-
le
v
el
in
v
er
ter
.
T
h
e
%
T
HD
v
a
lu
e
o
f
s
ev
e
n
-
le
v
el
C
B
R
V
i
n
v
er
ter
is
2
3
.
8
8
%.
6.
CO
M
P
ARIS
O
N
O
F
SI
M
UL
AT
I
O
N
AN
D
E
XP
E
RIM
E
N
T
AL
R
E
S
UL
T
S
I
n
th
i
s
s
ec
tio
n
,
s
i
m
u
latio
n
an
d
ex
p
er
im
e
n
tal
o
u
tp
u
t
p
h
a
s
e
v
o
ltag
e
w
a
v
e
f
o
r
m
s
a
n
d
co
r
r
e
s
p
o
n
d
in
g
T
HD
s
p
ec
tr
u
m
o
f
p
r
o
p
o
s
ed
1
-
ϕ
s
e
v
en
-
le
v
el
C
B
R
V
i
n
v
er
te
r
s
y
s
te
m
ar
e
d
ep
icted
in
F
ig
u
r
e
6
to
1
6
f
o
r
th
e
MCS
P
W
M
an
d
MCS
VP
W
M
m
o
d
u
latio
n
tec
h
n
iq
u
e
s
r
esp
ec
tiv
el
y
.
T
ab
le
3
s
h
o
w
s
th
e
s
i
m
u
la
tio
n
an
d
ex
p
er
i
m
e
n
tal
r
es
u
lts
o
f
o
u
tp
u
t
p
h
ase
v
o
lta
g
e
(
Vr
m
s
)
an
d
h
ar
m
o
n
ic
co
n
te
n
t
o
f
C
B
R
V
i
n
v
er
ter
f
o
r
d
if
f
er
e
n
t
m
o
d
u
latio
n
i
n
d
ices.
Fro
m
th
e
s
i
m
u
la
tio
n
a
n
d
ex
p
er
i
m
en
tal
an
al
y
s
is
,
it
i
s
o
b
s
er
v
ed
th
a
t
t
h
e
m
a
x
i
m
u
m
o
u
tp
u
t
p
h
ase
v
o
lta
g
e
a
n
d
l
o
w
er
T
HD
is
ac
h
ie
v
ed
b
y
u
s
i
n
g
MC
SVP
W
M
m
o
d
u
latio
n
tech
n
iq
u
e.
Fro
m
th
e
s
i
m
u
latio
n
h
ar
m
o
n
ic
s
p
ec
tr
al
a
n
al
y
s
is
,
i
t
is
o
b
s
er
v
ed
th
a
t
th
e
o
u
tp
u
t
v
o
ltag
e
T
HD
o
f
t
h
e
p
r
o
p
o
s
ed
1
-
ϕ
s
ev
e
n
-
lev
e
l
ca
s
ca
d
e
b
ased
R
V
in
v
er
ter
s
y
s
te
m
u
s
i
n
g
MC
SP
W
M
an
d
MCS
VP
W
M
m
o
d
u
latio
n
tech
n
iq
u
e
s
ar
e
2
4
.
3
3
%
an
d
2
1
.
8
4
% r
esp
ec
tiv
el
y
f
o
r
t
h
e
m
o
d
u
latio
n
i
n
d
ex
o
f
0
.
8
.
Har
m
o
n
ic
s
p
ec
tr
u
m
o
f
t
h
e
p
r
o
to
t
y
p
e
s
y
s
te
m
f
o
r
th
e
p
r
o
p
o
s
ed
m
o
d
u
latio
n
tech
n
iq
u
es
ar
e
ca
r
r
ied
u
s
in
g
d
ig
ital
s
to
r
ag
e
o
s
cillo
s
co
p
e
an
d
th
e
r
esu
lts
ar
e
p
r
esen
ted
in
f
i
g
u
r
es
1
1
to
1
6
f
o
r
MCS
P
W
M
an
d
MC
SVP
W
M
m
o
d
u
lat
i
o
n
tech
n
iq
u
e
s
r
esp
ec
ti
v
el
y
.
I
t
is
o
b
s
er
v
ed
t
h
at
t
h
e
T
HD
o
f
o
u
tp
u
t v
o
lta
g
es a
r
e
2
5
.
1
7
% a
n
d
2
2
.
4
6
% r
esp
ec
tiv
ely
f
o
r
th
e
m
o
d
u
latio
n
in
d
e
x
o
f
0
.
8
5
.
T
ab
le
3
: Fu
n
d
a
m
e
n
tal
O
u
tp
u
t
Vo
ltag
e
(
V
r
m
s
)
an
d
% T
HD
of
1
–
Ф
Sev
en
-
L
e
v
el
C
B
R
V
I
n
v
e
r
ter
Usi
n
g
MCS
P
W
M
an
d
MCS
VP
W
M
M
o
d
u
l
a
t
i
o
n
In
d
e
x
(M)
N
u
m
b
e
r
o
f
L
e
v
e
l
s
PW
M
T
e
c
h
n
i
q
u
e
M
C
S
PW
M
M
C
S
V
PW
M
S
i
m
u
l
a
t
i
o
n
E
x
p
e
r
i
m
e
n
t
a
l
S
i
m
u
l
a
t
i
o
n
E
x
p
e
r
i
m
e
n
t
a
l
V
r
m
s
(V)
T
HD
(
%
)
V
r
m
s
(V)
T
HD
(
%
)
V
r
m
s
(V)
T
HD
(
%
)
V
r
m
s
(V)
T
HD
(
%
)
0
.
8
7
-
L
e
v
e
l
1
6
9
.
6
2
4
.
3
3
1
6
8
.
1
2
5
.
1
7
1
9
5
2
1
.
8
4
1
9
3
.
2
2
2
.
4
6
0
.
7
7
-
L
e
v
e
l
1
4
8
.
4
2
5
.
3
1
1
4
5
.
8
2
6
.
7
1
7
0
.
8
2
4
.
2
7
1
6
8
.
6
2
5
.
6
0
.
6
5
-
L
e
v
e
l
1
2
7
.
3
3
3
.
4
6
1
2
5
.
9
3
5
.
1
1
4
6
.
3
2
5
.
5
8
1
4
4
.
5
2
7
.
1
0
.
5
5
-
L
e
v
e
l
1
0
6
4
0
.
2
3
1
0
4
.
7
4
2
.
3
1
2
1
.
9
3
5
.
4
7
1
1
9
.
7
3
6
.
3
0
.
4
5
-
L
e
v
e
l
8
4
.
7
9
4
4
.
5
2
8
3
.
1
4
6
.
2
9
7
.
5
2
4
2
.
1
3
9
5
.
8
4
4
.
3
0
.
3
3
-
L
e
v
e
l
6
3
.
5
7
6
4
.
5
4
6
1
.
4
6
5
.
8
7
3
.
2
3
4
9
.
3
6
7
5
.
4
5
1
.
2
T
h
er
ef
o
r
e
f
r
o
m
tab
le
3
,
it
is
o
b
s
er
v
ed
th
at
th
e
s
i
m
u
la
tio
n
r
esu
lt
s
ar
e
v
alid
ated
w
ith
t
h
e
ex
p
er
im
e
n
ta
l
r
esu
lt
s
w
ith
a
n
ac
ce
p
tab
le
er
r
o
r
o
f
±
2
%.
Fro
m
th
e
an
al
y
s
is
,
it
is
n
o
ticed
th
at
t
h
e
m
a
g
n
it
u
d
e
o
f
o
u
tp
u
t
v
o
lta
g
e
an
d
n
u
m
b
er
o
f
le
v
els
v
ar
y
f
o
r
d
if
f
er
e
n
t
m
o
d
u
latio
n
i
n
d
ices.
7.
CO
NCLU
SI
O
N
C
o
m
p
ar
in
g
w
it
h
co
u
n
ter
p
ar
t
w
ell
-
k
n
o
w
n
an
d
r
ec
en
t
M
L
I
s
tr
u
ct
u
r
es,
th
e
p
r
o
p
o
s
ed
C
B
R
Vin
v
er
ter
s
tr
u
ct
u
r
e
ca
m
e
w
it
h
r
ed
u
ce
d
n
u
m
b
er
o
f
s
w
itc
h
i
n
g
d
ev
ices,
g
ate
d
r
iv
er
cir
cu
its
,
DC
v
o
lt
ag
e
s
u
p
p
lie
s
,
ca
r
r
ier
s
ig
n
al
s
an
d
le
s
s
in
s
tallatio
n
ar
ea
.
T
h
e
p
r
o
p
o
s
ed
R
V
in
v
er
ter
s
ar
e
u
s
ed
in
p
o
w
er
ap
p
licatio
n
s
s
u
c
h
a
s
HVD
C
,
P
V
s
y
s
te
m
s
,
B
ac
k
to
B
ac
k
c
o
n
v
er
ter
s
,
R
ea
cti
v
e
p
o
w
er
co
m
p
e
n
s
atio
n
,
UP
S,
FAC
T
S
etc.
I
n
th
e
p
r
o
p
o
s
ed
s
tr
u
ct
u
r
e,
th
e
s
w
itc
h
i
n
g
o
p
er
atio
n
is
s
ep
ar
ated
in
to
h
i
g
h
-
a
n
d
lo
w
-
f
r
eq
u
e
n
c
y
p
ar
ts
.
T
h
is
w
ill
ad
d
u
p
to
t
h
e
ef
f
icien
c
y
o
f
th
e
co
n
v
er
ter
as
w
ell
as
r
ed
u
cin
g
t
h
e
s
ize
an
d
co
s
t
o
f
t
h
e
f
i
n
al
p
r
o
to
t
y
p
e.
T
h
e
m
o
d
if
ied
m
o
d
u
latio
n
tec
h
n
iq
u
es
d
ep
en
d
s
o
n
th
e
s
w
i
tch
i
n
g
s
tates
o
f
in
v
er
ter
an
d
w
as
s
u
cc
ess
f
u
ll
y
i
m
p
le
m
e
n
ted
u
s
i
n
g
FP
GA
b
as
ed
p
u
ls
e
g
e
n
er
atio
n
.
RE
F
E
R
E
NC
E
S
[1
]
J.Ro
d
ríg
u
e
z
,
J.S
.
L
a
i,
a
n
d
F
.
Z.
P
e
n
g
,
”
M
u
lt
il
e
v
e
l
In
v
e
rters
:
A
S
u
r
v
e
y
o
f
T
o
p
o
lo
g
ies
,
Co
n
tr
o
ls,
a
n
d
A
p
p
li
c
a
ti
o
n
s”
,
IEE
ET
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
V
o
l
.
4
9
,
N
o
.
4
,
A
u
g
u
st 2
0
0
2
,
p
p
.
7
2
4
-
7
3
9
.
[2
]
Y.
Ch
e
n
g
,
C.
Qia
n
,
M
.
L
.
Cro
w
,
S
.
P
e
k
a
re
k
,
a
n
d
S
.
A
tcitt
y
,
“
A
Co
m
p
a
riso
n
o
f
Dio
d
e
-
Cla
m
p
e
d
a
n
d
Ca
sc
a
d
e
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
f
o
r
a
S
TAT
COM
w
it
h
En
e
rg
y
S
to
ra
g
e
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
I
n
d
u
stria
l
E
lec
tro
n
ics
,
V
o
l.
5
3
,
No
.
5
,
2
0
0
6
,
p
p
.
1
5
1
2
-
1
5
2
1
.
d
o
i
:1
0
.
1
1
0
9
/T
IE.
2
0
0
6
.
8
8
2
0
2
2
.
[3
]
M
.
M
a
li
n
o
w
s
k
i,
K.
G
o
p
a
k
u
m
a
r,
J.
Ro
d
rig
u
e
z
a
n
d
M
.
P
e
re
z
,
“
A
S
u
rv
e
y
o
n
Ca
sc
a
d
e
M
u
lt
il
e
v
e
l
I
n
v
e
rters
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
In
d
u
stri
a
l
E
lec
tro
n
ics
,
V
o
l.
5
7
,
No
.
7
,
2
0
0
9
,
p
p
.
2
1
9
7
-
2
2
0
6
.
d
o
i:
1
0
.
1
1
0
9
/T
IE.
2
0
0
9
.
2
0
3
0
7
6
7
.
[4
]
S
u
G
.
J
a
n
d
A
d
a
m
s
D.
J.,
'
M
u
lt
il
e
v
e
l
DC
li
n
k
in
v
e
rte
r
fo
r
b
ru
s
h
les
s
p
e
rm
a
n
e
n
t
ma
g
n
e
t
mo
to
rs
wit
h
v
e
ry
lo
w
in
d
u
c
ta
n
c
e
,
”
in
Co
n
f
.
Re
c
.
2
0
0
1
I
EE
E
-
IA
S
A
n
n
u
.
M
e
e
ti
n
g
,
v
o
l
.
2
,
p
p
.
8
2
9
-
8
3
4
.
[5
]
G
u
i
-
Jia
S
u
'
M
u
lt
il
e
v
e
l
DC
li
n
k
in
v
e
rter'
In
d
u
stry
a
p
p
li
c
a
ti
o
n
s
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
V
o
l
u
m
e
:
4
1
,
Iss
u
e
:
3
Dig
it
a
l
Ob
jec
t
Id
e
n
ti
f
ier:
1
0
.
1
1
0
9
/T
IA
.
2
0
0
5
.
8
4
7
3
0
6
.
P
u
b
li
c
a
ti
o
n
Ye
a
r:
2
0
0
5
,
p
p
.
8
4
8
-
8
5
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.