I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
8
,
No
.
5
,
Octo
b
e
r
2
0
1
8
,
p
p
.
3
4
1
7
~
3
4
2
6
I
SS
N:
208
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
8
i
5
.
pp
3
4
1
7
-
3426
3417
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
JE
C
E
Si
m
pl
ified
Space
Vect
o
r
Pulse
Wid
th
M
o
dula
tion ba
sed o
n
S
w
itching Sche
mes
w
ith
Reduced
S
w
itching Freq
ue
ncy
and
H
a
r
m
o
n
ics for
F
i
v
e Lev
el Cas
ca
de
d H
-
bridg
e Inv
er
t
er
B
.
Siris
ha
,
P
.
Sa
t
is
h
k
u
m
a
r
De
p
a
rtme
n
t
o
f
EE
E,
Un
iv
e
rsit
y
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Os
m
a
n
ia
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
Dec
2
3
,
2
0
1
7
R
ev
i
s
ed
Mar
2
0
,
2
0
1
8
A
cc
ep
ted
Ma
r
2
8
,
2
0
1
8
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
si
m
p
li
f
ied
c
o
n
tro
l
stra
teg
y
o
f
sp
a
c
e
v
e
c
to
r
p
u
lse
w
id
th
m
o
d
u
latio
n
tec
h
n
i
q
u
e
w
it
h
a
th
r
e
e
se
g
m
e
n
t
s
w
it
c
h
in
g
s
e
q
u
e
n
c
e
a
n
d
se
v
e
n
se
g
m
e
n
t
s
w
it
c
h
in
g
se
q
u
e
n
c
e
f
o
r
h
ig
h
p
o
w
e
r
a
p
p
li
c
a
ti
o
n
s
o
f
m
u
lt
il
e
v
e
l
in
v
e
rters
.
In
t
h
e
p
r
o
p
o
se
d
m
e
th
o
d
,
th
e
i
n
v
e
rter
sw
it
c
h
in
g
se
q
u
e
n
c
e
s
a
re
o
p
ti
m
ize
d
f
o
r
m
in
i
m
iza
ti
o
n
o
f
d
e
v
ice
s
w
it
c
h
in
g
f
re
q
u
e
n
c
y
a
n
d
imp
ro
v
e
m
e
n
t
o
f
h
a
rm
o
n
ic
sp
e
c
tru
m
b
y
u
sin
g
th
e
th
re
e
m
o
st
d
e
sire
d
sw
it
c
h
in
g
sta
tes
a
n
d
o
n
e
su
it
a
b
le
re
d
u
n
d
a
n
t
sta
te
f
o
r
e
a
c
h
sp
a
c
e
v
e
c
to
r.
T
h
e
p
ro
p
o
se
d
th
re
e
-
se
g
m
e
n
t
se
q
u
e
n
c
e
is
c
o
m
p
a
re
d
w
it
h
c
o
n
v
e
n
ti
o
n
a
l
se
v
e
n
-
se
g
m
e
n
t
se
q
u
e
n
c
e
f
o
r
f
i
v
e
lev
e
l
Ca
sc
a
d
e
d
H
-
Brid
g
e
in
v
e
rter
w
it
h
v
a
rio
u
s
v
a
lu
e
s
o
f
sw
it
c
h
in
g
f
re
q
u
e
n
c
ies
in
c
lu
d
i
n
g
v
e
ry
lo
w
f
re
q
u
e
n
c
y
.
T
h
e
o
u
t
p
u
t
sp
e
c
tru
m
o
f
th
e
p
ro
p
o
se
d
se
q
u
e
n
c
e
d
e
sig
n
sh
o
w
s
th
e
re
d
u
c
ti
o
n
o
f
d
e
v
ice
s
w
it
c
h
in
g
f
re
q
u
e
n
c
y
,
c
u
rre
n
t
a
n
d
li
n
e
v
o
lt
a
g
e
T
HD
,
th
e
re
b
y
m
in
i
m
izin
g
th
e
f
il
ter
siz
e
re
q
u
irem
e
n
t
o
f
th
e
in
v
e
rter,
e
m
p
lo
y
e
d
in
in
d
u
str
ial
a
p
p
li
c
a
ti
o
n
s,
w
h
e
re
sin
u
so
i
d
a
l
o
u
t
p
u
t
v
o
lt
a
g
e
is
re
q
u
ir
e
d
.
K
ey
w
o
r
d
:
C
ascad
ed
H
-
b
r
id
g
ei
n
v
er
ter
Mu
ltil
e
v
el
i
n
v
er
ter
SVP
W
M
S
w
itc
h
in
g
s
eq
u
en
ce
T
HD
Co
p
y
rig
h
t
©
2
0
1
8
In
stit
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
.
Co
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
B
.
Sirish
a
,
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Os
m
a
n
ia
U
n
i
v
er
s
it
y
,
H
y
d
er
ab
ad
,
I
n
d
ia
.
E
m
ail:
s
ir
is
h
ab
2
0
0
7
@
y
a
h
o
o
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
W
ith
e
v
er
in
cr
ea
s
in
g
d
e
m
an
d
,
o
f
elec
tr
ical
e
n
er
g
y
a
n
d
d
ep
letin
g
f
o
s
s
il
f
u
el
r
e
s
er
v
es,
th
e
ef
f
icien
c
y
u
tili
za
t
io
n
o
f
ex
i
s
ti
n
g
r
eso
u
r
ce
s
h
av
e
b
ec
o
m
e
co
m
p
elli
n
g
r
eq
u
ir
em
e
n
t.
Hi
g
h
e
f
f
icien
c
y
p
o
w
er
elec
tr
o
n
ic
co
n
v
er
ter
to
p
o
lo
g
ies
w
it
h
o
p
tim
ized
co
n
tr
o
l stra
te
g
ies ar
e
r
eq
u
ir
ed
to
m
i
n
i
m
ize
t
h
e
e
n
er
g
y
w
a
s
te
an
d
i
m
p
r
o
v
e
th
e
p
o
w
er
q
u
alit
y
.
T
h
e
d
esig
n
o
f
co
n
tr
o
lle
d
m
ed
iu
m
v
o
ltag
e
d
r
iv
es
i
s
f
ac
ed
w
i
th
ch
al
len
g
es
th
a
t
r
elate
to
t
h
e
to
p
o
lo
g
ies
an
d
co
n
tr
o
l
o
f
t
h
e
a
n
d
m
o
to
r
s
id
e
co
n
v
er
ter
s
.
T
h
e
v
o
lta
g
e
an
d
c
u
r
r
en
t
s
w
a
v
e
f
o
r
m
s
ar
e
ef
f
ec
ted
b
y
f
ac
to
r
s
li
k
e
to
p
o
lo
g
y
u
s
ed
t
h
e
co
n
tr
o
l
al
g
o
r
ith
m
th
e
f
i
lt
er
s
ize,
ch
o
ice
o
f
s
w
i
tc
h
in
g
f
r
eq
u
e
n
c
y
an
d
t
h
e
ap
p
licatio
n
.
T
h
e
s
w
i
tch
i
n
g
o
n
o
f
m
ed
iu
m
v
o
lta
g
e
s
e
m
i
c
o
n
d
u
cto
r
d
ev
ices
al
s
o
m
a
k
e
u
p
th
e
m
aj
o
r
p
ar
t
o
f
d
ev
ice
lo
s
s
e
s
,
th
eir
r
ed
u
ct
io
n
allo
w
s
t
h
e
m
a
x
i
m
u
m
o
u
tp
u
t
p
o
w
er
w
h
ile
t
h
e
o
t
h
er
s
i
d
e
th
e
r
ed
u
ctio
n
o
f
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
ca
u
s
e
s
t
h
e
i
n
cr
ea
s
ed
h
ar
m
o
n
ic
d
i
s
to
r
ti
o
n
o
f
m
o
to
r
s
id
e
w
a
v
e
f
o
r
m
s
.
T
h
u
s
t
h
e
ar
ea
n
ee
d
ca
r
ef
u
l
co
n
s
id
er
atio
n
f
o
r
ef
f
i
cien
t
d
r
iv
e
s
y
s
te
m
[
1
]
.
Mu
lti
l
ev
el
co
n
v
er
ter
a
f
ter
m
a
n
y
ad
v
an
ta
g
e
s
lik
e
g
o
o
d
p
o
w
er
q
u
alit
y
,
lo
w
s
w
itc
h
in
g
l
o
s
s
es,
h
i
g
h
v
o
lta
g
e
ca
p
ab
ilit
y
,
lo
w
d
v
/d
t
s
tr
ess
[
2
]
.
T
h
e
th
r
ee
b
en
ch
m
ar
k
to
p
o
lo
g
ies
f
o
r
h
i
g
h
p
o
w
er
m
ed
iu
m
v
o
ltag
e
ap
p
licatio
n
s
ar
e
n
eu
tr
al
p
o
in
t
cla
m
p
ed
,
s
er
ies
ca
s
ca
d
ed
H
-
b
r
id
g
e,
f
l
y
i
n
g
ca
p
ac
ito
r
co
n
v
er
ter
ca
s
ca
d
ed
H
b
r
id
g
e
VS
C
h
as
b
ee
n
ap
p
lied
f
o
r
h
ig
h
p
o
w
er
an
d
p
o
w
er
q
u
alit
y
in
d
u
s
tr
ial
r
eq
u
i
r
e
m
e
n
t
d
u
e
to
it
s
er
ies
ex
p
a
n
s
io
n
ca
p
ab
ilit
ies
in
in
d
u
s
tr
ial
m
ai
n
ap
p
licatio
n
s
in
cl
u
d
e,
ac
tiv
e
f
ilter
,
r
ea
ctiv
e
p
o
w
er
co
m
p
e
n
s
atio
n
,
elec
tr
ic
v
eh
ic
les
p
h
o
to
v
o
ltaic
p
o
w
er
co
n
v
er
s
io
n
,
u
p
s
etc.
t
h
is
to
p
o
lo
g
y
ca
n
b
e
o
p
er
ated
at
d
if
f
er
e
n
t
s
w
i
tch
i
n
g
f
r
eq
u
e
n
cie
s
f
o
r
d
if
f
er
en
t
ap
p
licatio
n
[
3
]
.
T
h
e
H
-
b
r
id
g
e
is
s
u
p
p
lied
b
y
is
o
lated
d
.
c.
s
o
u
r
ce
s
,
co
m
p
o
s
ed
o
f
m
u
ltip
h
a
s
e
d
io
d
e
r
e
ctif
ier
s
.
Am
o
n
g
th
e
v
ar
io
u
s
s
w
i
tch
i
n
g
al
g
o
r
ith
m
s
.
P
r
o
p
o
s
ed
in
t
h
e
liter
at
u
r
e
f
o
r
m
u
l
ti
le
v
el
co
n
v
er
ter
s
,
SVM
i
s
t
h
e
m
o
s
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
1
7
–
3
4
2
6
3418
p
r
o
m
i
s
in
g
o
n
e,
w
h
ic
h
o
f
f
er
s
g
r
ea
test
f
lex
ib
il
it
y
i
n
o
p
ti
m
iz
in
g
t
h
e
s
w
itc
h
i
n
g
p
atter
n
d
esig
n
a
n
d
also
w
el
l
s
u
ited
f
o
r
d
ig
ital
i
m
p
le
m
e
n
tati
o
n
[
4
]
.
SVM
w
ith
7
-
s
e
g
m
e
n
t
s
eq
u
en
ce
i
s
g
e
n
er
all
y
u
s
ed
f
o
r
2
-
lev
el
a
n
d
3
-
lev
e
l
in
v
er
ter
to
p
o
lo
g
ies.
Fo
r
h
i
g
h
er
lev
el
in
v
er
ter
b
ec
au
s
e
o
f
d
if
f
i
c
u
lt
y
d
u
e
to
o
v
er
w
h
el
m
i
n
g
co
m
p
le
x
it
y
o
f
s
w
itc
h
in
g
s
eq
u
e
n
ce
d
esi
g
n
a
n
d
h
ea
v
y
r
elati
v
e
co
m
p
ilatio
n
l
o
ad
.
T
h
e
co
m
p
ilatio
n
lo
ad
h
a
v
e
b
ee
n
s
u
cc
es
s
f
u
l
l
y
r
ed
u
ce
d
b
y
s
i
m
p
li
f
y
i
n
g
t
h
e
r
e
q
u
ir
ed
ca
lcu
lat
io
n
o
f
r
e
f
er
en
c
e
v
ec
to
r
lo
ca
tio
n
d
u
t
y
c
y
c
le
c
alcu
latio
n
.
T
h
ese
ar
e
n
u
m
b
er
o
f
p
u
b
licatio
n
s
in
th
e
liter
atu
r
e
co
v
er
i
n
g
v
ar
io
u
s
asp
ec
ts
s
u
c
h
as
n
eu
tr
al
p
o
in
t
s
tab
ilizatio
n
o
v
er
m
o
d
u
latio
n
co
m
m
o
n
m
o
d
e
v
o
ltag
e
r
ed
u
ct
io
n
SVM
[
5
]
-
[
1
3
]
.
T
h
e
m
ai
n
f
o
c
u
s
o
f
t
h
i
s
p
ap
er
is
o
n
th
e
i
m
p
le
m
en
ta
tio
n
o
f
s
w
itc
h
i
n
g
s
eq
u
en
ce
d
e
s
ig
n
.
T
h
is
p
ap
er
p
r
esen
ts
s
i
m
p
li
f
ied
a
n
d
g
en
er
alize
d
S
VM
alg
o
r
ith
m
w
it
h
3
-
s
e
g
m
e
n
t
an
d
7
-
s
e
g
m
en
t
s
w
itc
h
in
g
s
eq
u
e
n
c
e
in
d
u
cin
g
o
v
er
m
o
d
u
latio
n
o
p
er
atio
n
to
i
m
p
r
o
v
e
th
e
o
u
tp
u
t
v
o
lta
g
e
s
p
ec
tr
u
m
b
y
m
i
n
i
m
izi
n
g
th
e
d
ev
ice
s
w
itc
h
in
g
f
r
eq
u
en
c
y
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
s
eq
u
e
n
ce
d
esi
g
n
is
a
n
al
y
ze
d
th
r
o
u
g
h
e
x
te
n
s
i
v
e
s
i
m
u
latio
n
s
f
o
r
f
iv
e
lev
e
l Cas
ca
d
ed
H
-
b
r
id
g
e
in
v
er
ter
.
2.
SPAC
E
V
E
C
T
O
R
M
O
DULAT
I
O
N
M
E
T
H
O
D
Fo
r
a
t
y
p
ical
th
r
ee
,
f
i
v
e,
an
d
s
ev
e
n
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
ter
,
w
it
h
a
s
ep
ar
ate
d
c
p
o
w
er
s
u
p
p
l
y
i
s
u
s
ed
f
o
r
ea
ch
H
-
B
r
id
g
e.
I
ts
co
r
r
esp
o
n
d
in
g
s
p
ac
e
v
o
ltag
e
v
ec
to
r
d
iag
r
a
m
i
s
ill
u
s
tr
ated
in
Fi
g
u
r
e
1
.
Fo
r
th
e
5
-
lev
el
in
v
er
ter
,
t
h
er
e
ar
e
9
6
s
m
all
tr
ia
n
g
les
a
n
d
t
h
e
v
er
tex
o
f
ea
c
h
tr
ia
n
g
le
r
ep
r
esen
ts
a
s
p
ac
e
v
ec
to
r
.
T
h
e
h
ex
a
g
o
n
al
v
ec
to
r
s
ca
n
b
e
d
iv
id
ed
in
to
s
i
x
m
aj
o
r
tr
ian
g
u
lar
s
ec
to
r
s
(
I
to
VI
)
.
O
n
l
y
t
h
e
f
ir
s
t
s
ec
to
r
o
f
th
e
co
o
r
d
in
ate
is
u
s
ed
b
ec
au
s
e
t
h
e
v
ec
to
r
s
lo
ca
ted
in
t
h
e
o
th
er
s
ec
to
r
s
ca
n
b
e
tr
an
s
f
o
r
m
e
d
to
f
ir
s
t
s
ec
to
r
b
y
clo
ck
w
is
e
r
o
tati
n
g
b
y
a
n
a
n
g
l
e
o
f
⁄
,
k
=(
1
,
2
,
3
,
4
,
5
f
o
r
s
ec
to
r
2
to
6
)
.
A
s
all
th
e
s
ec
to
r
s
ar
e
i
d
en
tical,
o
n
l
y
d
etail
s
o
f
s
ec
to
r
is
g
i
v
en
i
n
Fi
g
u
r
e
2
.
Fo
r
N
-
le
v
el
i
n
v
er
ter
th
er
e
ar
e
N3
s
w
itc
h
in
g
s
tates
th
a
t
lie
o
v
er
6
(
N
-
1)
2
tr
ian
g
le
s
.
Fi
g
u
r
e
2
g
iv
e
s
t
h
e
r
ep
r
esen
tatio
n
o
f
al
l
th
e
s
p
ac
e
v
ec
to
r
s
o
f
t
h
e
in
v
er
ter
i
n
6
0
ᵒ
co
-
o
r
d
in
ate
s
y
s
te
m
,
th
e
lo
ca
ti
o
n
o
f
th
e
r
e
f
er
en
ce
v
ec
to
r
is
id
en
ti
f
ied
ac
co
r
d
in
g
to
th
e
co
n
d
itio
n
g
iv
e
n
in
T
ab
le1
an
d
all
th
e
co
o
r
d
in
ates
ar
e
o
b
tain
ed
an
d
d
w
ell
ti
m
e
s
ar
e
ca
lcu
lated
b
ased
o
n
v
o
lt
-
s
ec
o
n
d
b
alan
ce
p
r
i
n
cip
le.
Af
ter
id
en
t
if
y
i
n
g
all
t
h
e
s
w
it
ch
in
g
s
tates,
o
u
t
o
f
m
an
y
r
ed
u
n
d
a
n
t
s
tates
d
esi
r
ed
an
d
s
u
itab
le
r
ed
u
n
d
an
t
s
tate
s
ar
e
u
til
iz
ed
f
o
r
t
h
e
s
eq
u
e
n
ce
,
i
n
th
e
i
m
p
le
m
en
ta
tio
n
o
f
t
h
e
p
r
o
p
o
s
ed
s
w
itc
h
i
n
g
s
eq
u
en
ce
th
e
m
o
s
t
d
es
ir
ed
s
w
itc
h
i
n
g
s
tate
alo
n
g
w
it
h
s
u
itab
le
r
ed
u
n
d
an
t
s
tate
ar
e
u
tili
ze
d
b
ased
o
n
th
e
n
at
u
r
e
o
f
th
e
co
-
o
r
d
in
ates
(
g
,
h
)
o
f
th
e
r
ef
er
e
n
ce
v
ec
to
r
th
e
tr
ian
g
le
s
ar
e
class
if
ied
as
T
y
p
e
-
I,
T
y
p
e
-
I
I
an
d
T
y
p
e
-
III.
Fig
u
r
e
1
.
Vo
ltag
e
v
ec
to
r
s
o
f
3
,
5
an
d
7
-
lev
el
v
o
lta
g
e
s
o
u
r
ce
in
v
er
ter
s
Fig
u
r
e
2
.
Vo
ltag
e
v
ec
to
r
s
i
n
6
0
ᵒ
c
o
-
o
r
d
in
ate
s
y
s
te
m
o
f
f
i
v
e
lev
e
l
in
v
er
ter
T
ab
le
1
.
Dete
r
m
i
n
atio
n
o
f
tr
ian
g
le
o
f
R
e
f
er
en
c
e
V
ec
to
r
1
h
g
V
V
h
g
1
h
g
V
V
h
g
R
e
f
e
r
e
n
c
e
V
e
c
t
o
r
l
i
e
s i
n
t
r
i
a
n
g
l
e
B
D
A
R
e
f
e
r
e
n
c
e
V
e
c
t
o
r
l
i
e
s i
n
t
r
i
a
n
g
l
e
C
B
D
1
;
1
1
1
h
h
g
g
h
h
g
g
1
1
;
h
h
g
g
2
2
;
1
h
h
g
g
2
2
;
1
1
;
3
3
h
h
g
g
1
;
3
3
h
h
g
g
g
r
e
f
V
T
T
g
T
g
T
g
3
3
2
2
1
1
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
S
imp
lifi
ed
S
p
a
ce
V
ec
t
o
r
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
b
a
s
ed
o
n
S
w
itch
in
g
…
(
B
.
S
ir
is
h
a
)
3419
h
r
e
f
V
T
T
h
T
h
T
h
3
3
2
2
1
1
(
2
)
r
e
f
T
T
T
T
3
2
1
(
3
)
A
ll
t
h
e
tr
ia
n
g
les
o
f
th
e
s
p
ac
e
v
ec
to
r
d
ia
g
r
a
m
ar
e
clas
s
i
f
i
ed
as
T
y
p
e
-
I,
II,
an
d
I
I
I
b
as
ed
o
n
t
h
e
i
n
te
g
er
co
o
r
d
in
ates o
f
th
e
r
ef
er
e
n
ce
v
ec
to
r
in
6
0
ᵒ
ax
is
an
d
ar
e
g
i
v
en
as:
T
y
p
e
-
I
:
w
h
er
e
b
o
th
(
g
,
h
)
ar
e
o
d
d
o
r
ev
en
th
e
th
r
ee
m
o
s
t
d
esire
d
s
tate
s
f
o
r
t
h
e
t
h
r
ee
v
er
tices
o
f
(
g
1
,
h
1
)
(
g
2
,
h
2
)
(
g
3
,
h
3
)
ar
e
1
,
2
,
3
=
i
S
B
i
S
Y
i
,
S
R
i
,
an
d
o
n
e
r
ed
u
n
d
an
t
s
tate
2
r
'
Br
'
Yr
'
Rr
'
S
,
S
,
S
jr
S
th
at
e
x
is
t
s
f
o
r
s
p
ac
e
v
ec
to
r
(
g
2
,
h
2
)
.
T
y
p
e
-
I
I
:
f
o
r
t
h
e
lo
ca
tio
n
o
f
r
e
f
er
en
ce
v
ec
to
r
Vr
is
g
1
is
e
v
e
n
an
d
h
1
is
o
d
d
,
th
e
t
h
r
ee
m
o
s
t
d
esire
d
s
tate
s
ar
e
1
,
2
,
3
=
i
S
B
i
S
Y
i
,
S
R
i
,
an
d
th
e
r
ed
u
n
d
an
t sta
te
1
r
'
Br
'
Yr
'
Rr
'
S
,
S
,
S
jr
S
f
o
r
th
e
s
p
ac
e
v
ec
to
r
(
g
1
,
h
1
)
.
T
y
p
e
-
III:
if
g
1
is
o
d
d
an
d
h
1
i
s
ev
e
n
t
h
e
m
o
s
t
d
esire
d
s
tate
1
,
2
,
3
=
i
S
B
i
S
Y
i
,
S
R
i
,
an
d
th
e
r
ed
u
n
d
an
t
s
tate
1
r
'
Br
'
Yr
'
Rr
'
S
,
S
,
S
jr
S
f
o
r
th
e
s
p
ac
e
v
ec
to
r
(
g
1
,
h
1
)
.
3.
SWI
T
CH
I
N
G
S
E
Q
U
E
NCE
DE
S
I
G
N
T
h
e
u
n
iq
u
e
s
w
itc
h
i
n
g
s
ta
to
r
in
ea
c
h
tr
ian
g
le
ar
e
d
eter
m
i
n
ed
u
s
i
n
g
t
h
r
ee
m
o
s
t
d
esire
d
s
w
itc
h
in
g
s
tates
3
,
2
,
1
ji
S
i
an
d
o
n
e
s
w
i
tch
i
n
g
r
ed
u
n
d
an
t
s
tate
3
,
2
,
1
r
'
Br
'
Yr
'
Rr
'
S
,
S
,
S
jr
S
ar
e
u
tili
ze
d
f
o
r
i
m
p
le
m
en
t 7
s
e
g
m
en
t a
n
d
3
-
s
e
g
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
.
I
n
co
n
v
e
n
tio
n
al
S
VM
Sev
e
n
-
s
eg
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
i
s
i
m
p
le
m
en
ted
f
o
r
t
w
o
le
v
el
o
r
3
-
lev
el
SVM
b
u
t
f
o
r
r
ea
l
ti
m
e
b
ec
a
u
s
e
o
f
i
n
cr
ea
s
ed
co
m
p
u
tatio
n
al
b
u
r
d
en
b
ec
au
s
e
o
f
lar
g
e
n
u
m
b
er
o
f
s
w
itc
h
in
g
s
tates
o
f
m
u
ltil
e
v
el
in
v
er
ter
i
m
p
le
m
e
n
tatio
n
f
o
r
h
i
g
h
er
lev
el
b
ec
o
m
e
s
o
v
er
w
h
el
m
i
n
g
.
I
n
t
h
e
p
r
o
p
o
s
ed
SV
P
W
M
m
e
th
o
d
th
e
o
p
ti
m
u
m
s
w
i
tch
in
g
s
ta
tes
ar
e
s
elec
te
d
f
o
r
th
e
s
eq
u
e
n
ce
s
u
c
h
t
h
at
t
h
er
e
w
ill b
e
o
n
l
y
o
n
e
v
o
ltag
e
lev
e
l
c
h
ar
g
e
s
p
er
co
m
m
u
ta
tio
n
.
T
h
e
Ge
n
er
ali
s
ed
s
ev
e
n
s
eg
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
f
o
r
d
i
f
f
er
en
t
t
y
p
es o
f
tr
ia
n
g
les is
:
T
y
p
e
-
I
: T
h
e
s
eq
u
e
n
ce
f
o
r
T
y
p
e
-
I
tr
ian
g
les
ar
e
4
2
2
2
2
2
4
2
2
1
1
3
3
2
'
2
3
3
1
1
2
2
T
S
T
S
T
S
T
S
T
S
T
S
T
S
j
j
j
j
j
j
j
(
4
)
T
y
p
e
-
I
I
: T
h
e
s
eq
u
en
ce
f
o
r
T
y
p
e
-
I
I
tr
ian
g
le
s
ar
e
4
2
2
2
2
2
4
1
1
2
2
3
3
1
'
1
3
3
2
2
1
1
T
S
T
S
T
S
T
S
T
S
T
S
T
S
j
j
j
j
j
j
j
(
5
)
T
y
p
e
-
I
I
I
: T
h
e
s
eq
u
en
ce
f
o
r
T
y
p
e
-
I
I
I
tr
ian
g
les
ar
e
4
2
2
2
2
2
4
1
1
3
3
2
2
1
'
1
2
2
3
3
1
1
T
S
T
S
T
S
T
S
T
S
T
S
T
S
j
j
j
j
j
j
j
(
6
)
Gen
er
alize
d
t
h
r
ee
o
r
f
iv
e
s
e
g
m
en
t
s
w
itc
h
i
n
g
s
eq
u
e
n
ce
co
n
s
is
ti
n
g
o
f
t
h
r
ee
m
o
s
t
d
esire
d
s
tates
[
Sj
i]
i=1
,
2
,
3
o
f
th
r
ee
t
y
p
es o
f
tr
ian
g
le
is
e
x
p
r
ess
ed
as
T
y
p
e
-
1
: T
h
e
s
eq
u
en
ce
f
o
r
T
y
p
e
-
I
tr
ian
g
les
ar
e
2
2
2
2
2
2
1
1
3
3
1
1
2
2
T
S
T
S
T
S
T
S
T
S
j
j
j
j
j
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
1
7
–
3
4
2
6
3420
T
y
p
e
-
I
I
: T
h
e
s
eq
u
en
ce
f
o
r
T
y
p
e
-
I
I
tr
ian
g
le
s
ar
e
2
2
2
2
1
1
2
2
3
3
2
2
1
1
T
S
T
S
T
S
T
S
T
S
j
j
j
j
j
(
8
)
T
y
p
e
-
I
I
I
: T
h
e
s
eq
u
en
ce
f
o
r
T
y
p
e
-
I
I
I
tr
ian
g
les
ar
e
2
2
2
2
1
1
3
3
3
2
3
3
1
1
T
S
T
S
T
S
T
S
T
S
j
j
j
j
j
(
9
)
I
n
th
r
ee
-
s
e
g
m
en
t
s
w
itc
h
i
n
g
s
e
q
u
en
ce
t
h
e
lead
in
g
a
n
d
tr
ailin
g
s
tate
o
v
er
a
s
w
itc
h
es
p
er
io
d
is
s
a
m
e
as
s
ev
e
n
-
s
eg
m
e
n
t s
w
itc
h
i
n
g
s
eq
u
e
n
ce
.
4.
CALCU
L
A
T
I
O
N
O
F
SW
I
T
CH
I
NG
F
R
E
Q
U
E
NCY
Fo
r
an
y
m
u
ltil
e
v
el
in
v
er
ter
th
e
s
w
itch
in
g
d
ev
ices
m
a
y
n
o
t
h
av
e
th
e
s
a
m
e
d
ev
ice
s
w
itc
h
i
n
g
f
r
eq
u
en
c
ies.
T
h
e
av
er
ag
e
s
w
it
ch
in
g
f
r
eq
u
e
n
c
y
i
s
d
ef
i
n
ed
as
to
tal
n
u
m
b
er
o
f
s
w
i
tch
i
n
g
o
f
all
th
e
s
w
itc
h
es
p
er
s
ec
o
n
d
to
th
e
n
u
m
b
er
o
f
ac
t
iv
e
d
ev
ices o
f
t
h
e
in
v
er
ter
(
F a
v
g
_
s
w
)
f
(
a
vg
_
sw
)
=
F
(ideal
–
Avg
_sw
)
,
I
f
lead
in
g
s
tate
o
f
th
e
n
ex
t
s
eq
u
en
ce
is
eq
u
al
to
tr
ailin
g
s
tat
e
o
f
th
e
p
r
o
ce
ed
in
g
s
eq
u
en
ce
.
N
fs
N
N
F
s
ph
Sw
A
v
g
id
e
a
l
)
)(
(
(
1
0
)
Np
h
–
Nu
m
b
er
o
f
co
m
m
u
tati
n
g
p
h
ase
s
Ns
–
Nu
m
b
er
o
f
co
m
p
le
te
s
w
i
tch
i
n
g
ac
t
io
n
s
(
„
o
n
‟
an
d
„
o
f
f
‟
t
r
an
s
itio
n
)
p
er
p
h
ase
N
–
Nu
m
b
er
o
f
d
ev
ice
s
p
er
co
m
m
u
ta
tio
n
f
s
=
s
w
i
tch
in
g
f
r
eq
u
en
c
y
T
ab
le
2
.
Fre
q
u
en
c
y
Co
m
p
o
n
e
n
ts
f
o
r
S
ev
e
n
-
s
e
g
m
e
n
t a
n
d
T
h
r
ee
-
s
e
g
m
e
n
t
S
w
itc
h
in
g
P
atter
s
f
o
r
Fiv
e
L
ev
e
l
C
ascad
ed
I
n
v
er
ter
F
r
e
q
u
e
n
c
y
c
o
mp
o
n
e
n
t
s o
f
d
i
f
f
e
r
e
n
t
s
w
i
t
c
h
i
n
g
p
a
t
t
e
r
n
s
F
r
e
q
u
e
n
c
y
7
-
se
g
me
n
t
-
sw
i
t
c
i
n
g
se
q
u
e
n
c
e
3
-
se
g
me
n
t
-
sw
i
t
c
h
i
n
g
se
q
u
e
n
c
e
F
(ideal
-
a
vg
-
sw)
4
24
2
1
3
fs
fs
12
24
2
2
1
2
fs
fs
Eq
u
i
v
a
l
e
n
t
i
n
v
e
r
t
e
r
f
r
e
q
u
e
n
c
y
f
s
=
4
F
(ideal
-
Avg
-
sw)
f
s
/2
=
6
F
(ideal
-
Avg
-
s
w)
Fo
r
th
e
s
a
m
e
id
ea
l
a
v
e
r
ag
e
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
,
th
e
in
v
er
t
er
eq
u
iv
ale
n
t
f
r
eq
u
e
n
c
y
f
o
r
t
h
r
ee
-
s
e
g
m
e
n
t
w
ill
b
e
d
o
u
b
le
th
at
o
f
s
e
v
en
-
s
eg
m
e
n
t
s
eq
u
en
ce
(
5
0
%
m
o
r
e)
.
Fo
r
th
e
s
a
m
e
in
v
er
ter
eq
u
iv
a
len
t
f
r
eq
u
e
n
c
y
,
th
e
id
ea
l
av
er
ag
e
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
f
o
r
th
r
ee
s
e
g
m
e
n
t
is
eq
u
al
to
t
w
o
t
h
i
r
d
o
f
t
h
e
co
r
r
esp
o
n
d
i
n
g
s
e
v
en
-
s
e
g
m
e
n
t
s
eq
u
en
ce
n
u
m
b
er
o
f
e
x
tr
a
co
m
m
u
tatio
n
s
al
s
o
in
cr
ea
s
e
s
th
e
d
ev
ice
f
r
eq
u
en
c
y
a
n
d
av
er
ag
e
s
w
itch
in
g
f
r
eq
u
en
c
y
.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
ab
o
v
e
s
w
itch
in
g
s
eq
u
en
ce
s
f
o
r
S
VP
W
M
tech
n
iq
u
e
i
s
ev
al
u
ate
d
f
o
r
Fiv
e
lev
el
ca
s
ca
d
ed
H
-
B
r
id
g
e
I
n
v
e
r
ter
w
it
h
D
C
i
n
p
u
t
v
o
ltag
e
o
f
1
0
0
V.
C
o
r
r
esp
o
n
d
in
g
to
th
e
m
o
d
u
latio
n
in
d
e
x
o
f
0
.
8
7
.
T
h
e
p
ar
am
e
ter
s
o
f
I
n
d
u
c
tio
n
m
o
to
r
f
o
r
s
i
m
u
latio
n
ar
e,
s
tato
r
r
esis
tan
ce
(
R
s
)
=2
.
3
Ω
,
r
o
to
r
r
esis
tan
ce
(
R
r
)
=2
.
5
Ω
,
s
tato
r
leak
ag
ein
d
u
ctan
c
e
=0
.
2
8
H,
m
u
t
u
ali
n
d
u
cta
n
ce
=0
.
2
4
H,
Nu
m
b
er
o
f
p
o
les=4
,
r
ated
f
r
eq
u
en
c
y
=5
0
Hz,
Mo
m
en
t
o
f
in
er
tia=0
.
0
0
2
5
J
,
Da
m
p
in
g
co
ef
f
icie
n
t(
B
)
=0
.
0
0
0
1
2
4
.
Fro
m
T
ab
le
3
it
is
s
h
o
w
n
t
h
at
f
o
r
t
h
e
s
a
m
e
in
v
er
ter
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
t
h
e
id
ea
l
av
er
a
g
e
s
w
itch
in
g
f
r
e
q
u
en
c
y
f
o
r
t
h
r
ee
s
e
g
m
e
n
t
s
w
i
tch
i
n
g
s
eq
u
e
n
ce
is
2
/3
o
f
th
e
id
ea
l a
v
er
ag
e
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
f
o
r
s
ev
e
n
s
eg
m
en
t s
w
itc
h
in
g
s
eq
u
e
n
ce
.
Fro
m
T
ab
le
4
it is
s
h
o
wn
th
at
f
o
r
t
h
e
s
a
m
e
id
ea
l
av
er
a
g
e
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
,
th
e
in
v
er
ter
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
f
o
r
t
h
r
ee
s
e
g
m
e
n
t
s
w
itc
h
in
g
s
eq
u
en
ce
i
s
5
0
% h
i
g
h
er
t
h
an
t
h
at
o
f
s
e
v
e
n
s
e
g
m
en
t s
w
i
tch
i
n
g
s
eq
u
e
n
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
S
imp
lifi
ed
S
p
a
ce
V
ec
t
o
r
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
b
a
s
ed
o
n
S
w
itch
in
g
…
(
B
.
S
ir
is
h
a
)
3421
T
ab
le
3
.
I
d
ea
l A
v
er
a
g
e
Dev
ice
Fre
q
u
en
c
y
o
f
Se
v
en
-
s
eg
m
e
n
t
an
d
T
h
r
ee
-
s
eg
m
e
n
t
S
w
i
tch
i
n
g
Seq
u
en
ce
s
f
o
r
d
if
f
er
e
n
t
S
w
i
tch
i
n
g
Fre
q
u
e
n
ci
es
I
n
v
e
r
t
e
r
Eq
u
i
v
a
l
e
n
t
F
r
e
q
u
e
n
c
y
i
n
H
z
I
d
e
a
l
A
v
e
r
a
g
e
d
e
v
i
c
e
f
r
e
q
u
e
n
c
y
o
f
se
v
e
n
-
s
e
g
me
n
t
sw
i
t
c
h
i
n
g
se
q
u
e
n
c
e
F
(
ideal
-
avg
-
sw)
i
n
H
z
I
d
e
a
l
A
v
e
r
a
g
e
d
e
v
i
c
e
f
r
e
q
u
e
n
c
y
o
f
t
h
r
e
e
-
se
g
me
n
t
sw
i
t
c
h
i
n
g
se
q
u
e
n
c
e
F
(ideal
-
a
vg
-
sw)
i
n
H
z
6
0
0
1
5
0
1
0
0
9
0
0
2
2
5
1
5
0
1
0
5
0
2
6
2
1
7
5
2
1
0
0
5
2
5
3
5
0
3
0
0
0
7
5
0
5
0
0
T
ab
le
4
.
I
n
v
er
ter
E
q
u
iv
ale
n
t
F
r
eq
u
en
c
y
o
f
S
e
v
en
-
s
e
g
m
en
t a
n
d
T
h
r
ee
-
s
eg
m
e
n
t
S
w
i
tch
i
n
g
Seq
u
en
ce
s
f
o
r
d
if
f
er
e
n
t I
d
ea
l
Av
er
ag
e
De
v
ic
e
S
w
itch
i
n
g
Fre
q
u
e
n
cies
I
d
e
a
l
A
v
e
r
a
g
e
d
e
v
i
c
e
f
r
e
q
u
e
n
c
y
o
f
se
v
e
n
-
s
e
g
me
n
t
sw
i
t
c
h
i
n
g
se
q
u
e
n
c
e
F
(ideal
-
a
vg
-
sw)
i
n
H
z
I
n
v
e
r
t
e
r
Eq
u
i
v
a
l
e
n
t
F
r
e
q
u
e
n
c
y
o
f
se
v
e
n
-
s
e
g
me
n
t
sw
i
t
c
h
i
n
g
se
q
u
e
n
c
e
F
(ideal
-
a
vg
-
sw)
i
n
Hz
I
n
v
e
r
t
e
r
Eq
u
i
v
a
l
e
n
t
F
r
e
q
u
e
n
c
y
o
f
t
h
r
e
e
-
se
g
me
n
t
sw
i
t
c
h
i
n
g
se
q
u
e
n
c
e
F
(ideal
-
a
vg
-
sw)
i
n
H
z
1
5
0
6
0
0
9
0
0
2
2
5
9
0
0
1
3
5
0
2
6
2
1
0
5
0
1
5
7
2
5
2
5
2
1
0
0
3
1
5
0
7
5
0
3
0
0
0
4
5
0
0
Fig
u
r
e
3
g
i
v
es
t
h
e
li
n
e
v
o
lta
g
e
s
p
ec
tr
u
m
o
v
er
b
r
o
d
er
r
an
g
e
(
1
2
5
0
0
Hz)
w
it
h
in
v
er
ter
s
w
itc
h
in
g
f
r
eq
u
en
c
y
o
f
2
1
0
0
Hz.
T
h
e
h
ar
m
o
n
ics
ap
p
ea
r
as
s
id
e
b
an
d
ar
o
u
n
d
in
v
er
ter
eq
u
i
v
ale
n
t
f
r
eq
u
en
c
y
.
T
h
e
id
ea
l
av
er
ag
e
d
ev
ice
s
w
i
tch
i
n
g
f
r
eq
u
en
c
y
b
ein
g
5
2
5
Hz.
T
h
e
T
HD
o
b
tain
ed
f
o
r
s
ev
en
-
s
e
g
m
en
t
s
e
q
u
en
ce
is
1
9
.
4
1
%.
Fig
u
r
e
4
g
i
v
es
t
h
e
li
n
e
v
o
lta
g
e
s
p
ec
tr
u
m
o
v
er
b
r
o
d
er
r
an
g
e
(
1
2
5
0
0
Hz)
w
it
h
i
n
v
er
ter
s
w
it
ch
in
g
f
r
eq
u
e
n
c
y
o
f
3
1
5
0
Hz.
Fo
r
th
e
s
a
m
e
id
ea
l
a
v
er
ag
e
d
ev
ice
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
(
5
2
5
)
,
th
e
in
v
er
ter
is
s
i
m
u
lated
f
o
r
th
r
ee
-
s
eg
m
e
n
t
s
w
i
tch
i
n
g
s
eq
u
en
ce
.
T
h
e
h
ar
m
o
n
ic
s
a
p
p
ea
r
as
s
i
d
e
b
an
d
ar
o
u
n
d
in
v
er
ter
eq
u
i
v
alen
t
f
r
eq
u
e
n
c
y
o
f
3
1
5
0
Hz.
T
h
e
m
a
g
n
i
tu
d
e
o
f
h
ar
m
o
n
ics
i
s
r
ed
u
ce
d
to
lar
g
e
r
am
o
u
n
t
g
i
v
i
n
g
le
s
s
er
v
alu
e
o
f
T
HD
w
h
ic
h
is
1
6
.
3
2
%.
Fig
u
r
e
5
s
h
o
w
s
th
e
l
in
e
v
o
lta
g
e
s
p
ec
tr
u
m
o
f
f
i
v
e
lev
el
ca
s
ca
d
ed
in
v
er
ter
o
v
er
1
2
.
5
KHz
w
i
th
t
h
r
ee
-
s
eg
m
e
n
t s
w
itc
h
i
n
g
s
eq
u
e
n
ce
w
it
h
s
w
itc
h
in
g
f
r
eq
u
en
c
y
o
f
4
7
4
5
Hz
.
Fig
u
r
e
3
.
L
in
e
Vo
ltag
e
s
p
ec
tr
u
m
o
f
f
iv
e
le
v
el
ca
s
ca
d
ed
in
v
er
ter
o
v
er
1
2
.
5
K
Hz
w
it
h
s
e
v
en
-
s
eg
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
-
2
0
0
-
1
0
0
0
100
200
S
e
l
e
c
t
e
d
s
i
g
n
a
l
:
2
5
c
y
c
l
e
s
.
F
F
T
w
i
n
d
o
w
(
i
n
r
e
d
)
:
3
c
y
c
l
e
s
T
i
m
e
(
s
)
0
2000
4000
6000
8000
10000
12000
0
1
2
3
4
5
6
7
8
F
r
e
q
u
e
n
c
y
(
H
z
)
F
u
n
d
a
m
e
n
t
a
l
(
5
0
H
z
)
=
2
2
8
.
6
,
T
H
D
=
1
9
.
4
1
%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l
)
f
s
w
=
2
1
0
0
H
z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
1
7
–
3
4
2
6
3422
Fig
u
r
e
4
.
L
in
e
Vo
ltag
e
s
p
ec
tr
u
m
o
f
f
iv
e
le
v
el
ca
s
ca
d
ed
in
v
er
ter
o
v
er
1
2
.
5
KHz
w
it
h
t
h
r
ee
-
s
eg
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
f
o
r
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
o
f
3
1
5
0
Hz
Fig
u
r
e
5
.
L
in
e
Vo
ltag
e
s
p
ec
tr
u
m
o
f
f
iv
e
le
v
el
ca
s
ca
d
ed
in
v
er
ter
o
v
er
1
2
.
5
KHz
w
it
h
t
h
r
ee
-
s
eg
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
w
i
th
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
o
f
4
7
4
5
Hz
Fig
u
r
e
6
g
i
v
es
t
h
e
li
n
e
v
o
lta
g
e
s
p
ec
tr
u
m
o
v
er
b
r
o
d
er
r
an
g
e
(
1
2
5
0
0
Hz)
w
it
h
in
v
er
ter
s
w
itc
h
in
g
f
r
eq
u
en
c
y
o
f
1
1
2
5
Hz.
T
h
e
h
ar
m
o
n
ics
ap
p
ea
r
as
s
id
e
b
an
d
ar
o
u
n
d
in
v
er
ter
eq
u
iv
ale
n
t
f
r
e
q
u
en
c
y
(
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
)
.
T
h
e
T
HD
o
b
tain
ed
is
1
6
.
9
2
%.
Fig
u
r
e
7
g
i
v
es
t
h
e
li
n
e
v
o
lta
g
e
s
p
ec
tr
u
m
o
v
er
b
r
o
d
er
r
an
g
e
(
1
2
5
0
0
Hz)
w
it
h
in
v
er
ter
s
w
itc
h
in
g
f
r
eq
u
en
c
y
o
f
7
5
0
Hz.
Fo
r
th
e
s
a
m
e
id
ea
l
a
v
er
ag
e
d
e
v
ice
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
(
1
8
7
Hz)
,
th
e
in
v
er
ter
i
s
s
i
m
u
lated
f
o
r
s
ev
e
n
-
s
e
g
m
en
t
s
w
itc
h
in
g
s
eq
u
e
n
ce
.
T
h
e
h
ar
m
o
n
ics
ap
p
ea
r
as
s
id
e
b
an
d
ar
o
u
n
d
i
n
v
er
ter
eq
u
iv
ale
n
t
f
r
eq
u
e
n
c
y
o
f
7
5
0
Hz.
Fro
m
F
ig
u
r
e
8
it
is
s
h
o
w
n
th
at
t
h
e
p
h
ase
v
o
lta
g
e
T
HD
i
n
cr
ea
s
es
at
h
i
g
h
er
in
v
er
ter
f
r
eq
u
en
c
ies
i
n
ca
s
e
o
f
th
r
ee
-
s
eg
m
e
n
t
s
w
i
tch
in
g
p
atter
n
co
m
p
ar
ed
to
s
ev
en
–
s
eg
m
en
t
s
w
itc
h
i
n
g
p
atter
n
.
T
ab
le
5
s
h
o
w
s
t
h
e
T
HD
o
f
li
n
e
p
h
a
s
e
an
d
c
u
r
r
en
t
o
f
f
i
v
e
le
v
el
ca
s
ca
d
ed
in
v
er
te
r
f
o
r
s
ev
e
n
-
s
e
g
m
e
n
t
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
-
2
0
0
0
200
S
e
l
e
c
t
e
d
s
i
g
n
a
l
:
2
5
c
y
c
l
e
s
.
F
F
T
w
i
n
d
o
w
(
i
n
r
e
d
)
:
3
c
y
c
l
e
s
T
i
m
e
(
s
)
0
2000
4000
6000
8000
10000
12000
0
1
2
3
4
5
6
X
=
3
.
1
5
e
+
0
3
Y
=
0
.
0
2
5
5
F
r
e
q
u
e
n
c
y
(
H
z
)
F
u
n
d
a
m
e
n
t
a
l
(
5
0
H
z
)
=
2
1
2
,
T
H
D
=
1
6
.
3
2
%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l
)
0
.
5
f
s
w
=
3
1
5
0
H
z
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
-
2
0
0
0
200
S
e
l
e
c
t
e
d
s
i
g
n
a
l
:
2
5
c
y
c
l
e
s
.
F
F
T
w
i
n
d
o
w
(
i
n
r
e
d
)
:
3
c
y
c
l
e
s
T
i
m
e
(
s
)
0
2000
4000
6000
8000
10000
12000
0
1
2
3
4
5
6
X
=
4
.
7
2
e
+
0
3
Y
=
0
.
3
9
3
F
r
e
q
u
e
n
c
y
(
H
z
)
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l
)
F
u
n
d
a
m
e
n
t
a
l
(
5
0
H
z
)
=
2
1
2
,
T
H
D
=
1
5
.
8
2
%
0
.
5
f
s
w
=
4
7
2
5
H
z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
S
imp
lifi
ed
S
p
a
ce
V
ec
t
o
r
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
b
a
s
ed
o
n
S
w
itch
in
g
…
(
B
.
S
ir
is
h
a
)
3423
s
w
itc
h
in
g
s
eq
u
en
ce
.
T
ab
le
6
s
h
o
w
s
t
h
e
T
HD
o
f
lin
e
p
h
a
s
e
an
d
cu
r
r
en
t
o
f
f
iv
e
le
v
el
ca
s
ca
d
ed
in
v
er
ter
f
o
r
th
r
ee
-
s
eg
m
e
n
t s
w
i
tch
in
g
s
eq
u
en
ce
.
Fig
u
r
e
6
.
L
in
e
Vo
ltag
e
s
p
ec
tr
u
m
of
f
iv
e
le
v
el
ca
s
ca
d
ed
in
v
er
ter
o
v
er
1
2
.
5
KHz
w
it
h
t
h
r
ee
-
s
eg
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
w
i
t
h
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
o
f
1
1
2
5
Hz
Fig
u
r
e
7
.
L
in
e
Vo
ltag
e
s
p
ec
tr
u
m
o
f
f
iv
e
le
v
el
ca
s
ca
d
ed
in
v
er
ter
o
v
er
1
2
.
5
KHz
w
it
h
s
e
v
en
-
s
eg
m
e
n
t
s
w
itc
h
i
n
g
s
eq
u
en
ce
w
i
th
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
o
f
7
5
0
Hz
T
ab
le
5
.
T
HD
o
f
L
in
e
P
h
ase
a
n
d
cu
r
r
en
t o
f
f
i
v
e
lev
e
l Cas
ca
d
ed
I
n
v
er
ter
f
o
r
Sev
en
-
s
eg
m
e
n
t S
w
i
tc
h
i
n
g
S
eq
u
en
ce
I
n
v
e
r
t
e
r
s
w
i
t
c
h
i
n
g
F
r
e
q
u
e
n
c
y
V
L
L
i
n
e
v
o
l
t
a
g
e
TH
D
A
s a
%
o
f
f
u
n
d
a
me
n
t
a
l
V
P
h
L
i
n
e
v
o
l
t
a
g
e
T
H
D
A
s a
%
o
f
f
u
n
d
a
me
n
t
a
l
I
(
c
u
r
r
e
n
t
)
T
H
D
A
s a
%
o
f
f
u
n
d
a
me
n
t
a
l
6
0
0
1
2
.
0
4
2
3
.
5
1
5
.
3
9
9
0
0
1
2
.
6
2
3
3
.
4
1
5
.
0
7
1
0
5
0
1
1
.
2
9
2
7
.
0
8
5
.
6
6
2
1
0
0
1
1
.
3
9
2
9
.
0
3
5
.
0
4
3
0
0
0
1
0
.
3
4
2
6
.
6
4
5
.
3
5
4
2
0
0
1
0
.
2
4
2
6
.
7
3
5
.
4
6
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
-
2
0
0
0
200
S
e
l
e
c
t
e
d
s
i
g
n
a
l
:
2
5
c
y
c
l
e
s
.
F
F
T
w
i
n
d
o
w
(
i
n
r
e
d
)
:
3
c
y
c
l
e
s
T
i
m
e
(
s
)
0
2000
4000
6000
8000
10000
12000
0
1
2
3
4
5
6
X
=
1
.
1
2
e
+
0
3
Y
=
0
.
3
4
7
F
r
e
q
u
e
n
c
y
(
H
z
)
F
u
n
d
a
m
e
n
t
a
l
(
5
0
H
z
)
=
2
1
1
.
9
,
T
H
D
=
1
6
.
9
2
%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l
)
0
.
5
f
s
w
=
1
1
2
5
H
z
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
-
2
0
0
0
200
S
e
l
e
c
t
e
d
s
i
g
n
a
l
:
2
5
c
y
c
l
e
s
.
F
F
T
w
i
n
d
o
w
(
i
n
r
e
d
)
:
3
c
y
c
l
e
s
T
i
m
e
(
s
)
0
2000
4000
6000
8000
10000
12000
0
1
2
3
4
5
6
7
8
X
=
7
5
0
Y
=
0
.
0
6
7
5
F
r
e
q
u
e
n
c
y
(
H
z
)
F
u
n
d
a
m
e
n
t
a
l
(
5
0
H
z
)
=
2
2
7
.
7
,
T
H
D
=
1
8
.
9
9
%
M
a
g
(
%
o
f
F
u
n
d
a
m
e
n
t
a
l
)
f
s
w
=
7
5
0
H
z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
1
7
–
3
4
2
6
3424
T
ab
le
6
.
T
HD
o
f
L
in
e
P
h
ase
a
n
d
C
u
r
r
e
n
t o
f
Fi
v
e
L
ev
e
l
C
asc
ad
ed
I
n
v
er
ter
f
o
r
T
h
r
ee
-
s
eg
m
e
n
t
S
w
i
tc
h
i
n
g
S
eq
u
en
ce
I
n
v
e
r
t
e
r
s
w
i
t
c
h
i
n
g
F
r
e
q
u
e
n
c
y
V
L
L
i
n
e
v
o
l
t
a
g
e
TH
D
A
s a
%
o
f
f
u
n
d
a
me
n
t
a
l
V
P
h
L
i
n
e
v
o
l
t
a
g
e
T
H
D
A
s a
%
o
f
f
u
n
d
a
me
n
t
a
l
I
(
c
u
r
r
e
n
t
)
T
H
D
A
s a
%
o
f
f
u
n
d
a
me
n
t
a
l
6
0
0
1
0
.
5
1
3
0
.
2
1
4
.
2
2
9
0
0
9
.
5
0
2
9
.
3
3
4
.
3
2
1
0
5
0
9
.
6
6
2
8
.
9
3
4
.
4
2
2
1
0
0
8
.
3
7
2
8
.
0
5
4
.
4
7
3
0
0
0
7
.
8
4
2
7
.
8
5
4
.
4
3
4
2
0
0
7
.
9
5
2
7
.
3
5
4
.
4
5
Fig
u
r
e
8
.
P
h
ase
V
o
ltag
e
T
HD
at
v
ar
io
u
s
i
n
v
er
ter
f
r
eq
u
e
n
cies
f
o
r
7
-
se
g
m
e
n
t a
n
d
3
-
s
eg
m
e
n
t s
w
itc
h
in
g
P
atter
n
s
Fro
m
Fi
g
u
r
e
9
it
is
s
h
o
w
n
th
at
t
h
e
L
i
n
e
v
o
ltag
e
T
HD
an
d
cu
r
r
en
t
T
HD
d
ec
r
ea
s
es
at
h
ig
h
er
in
v
er
ter
f
r
eq
u
en
c
ies i
n
ca
s
e
o
f
t
h
r
ee
-
s
eg
m
e
n
t
s
w
itc
h
in
g
p
atter
n
co
m
p
ar
ed
to
s
ev
e
n
–
s
e
g
m
e
n
t s
witch
i
n
g
p
atter
n
.
Fig
u
r
e
9
.
L
in
e
V
o
ltag
e
a
n
d
cu
r
r
en
t T
HDs a
t v
ar
io
u
s
i
n
v
er
ter
f
r
eq
u
en
cie
s
f
o
r
7
-
s
e
g
m
e
n
t a
n
d
3
-
s
eg
m
en
t
s
w
itc
h
in
g
p
atter
n
s
500
1000
1500
2000
2500
3000
3500
4000
4500
4
5
6
7
8
9
10
11
12
13
s
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
V
l
i
n
e
a
n
d
c
u
r
r
e
n
t
T
H
D
f
o
r
7
a
n
d
3
s
e
g
m
e
n
t
p
a
t
t
e
r
n
s
I
(
T
H
D
)
-
7
s
e
g
p
a
t
t
e
r
n
I
(
T
H
D
)
-
3
s
e
g
p
a
t
t
e
r
n
V
l
i
n
e
(
T
H
D
)
-
3
s
e
g
p
a
t
t
e
r
n
V
l
i
n
e
(
T
H
D
)
-
7
s
e
g
p
a
t
t
e
r
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
S
imp
lifi
ed
S
p
a
ce
V
ec
t
o
r
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
b
a
s
ed
o
n
S
w
itch
in
g
…
(
B
.
S
ir
is
h
a
)
3425
6.
CO
NCLU
SI
O
N
T
h
is
p
a
p
er
p
r
esen
ts
g
e
n
er
al
S
VP
W
M
tech
n
iq
u
e
b
a
s
ed
o
n
s
ev
en
–
s
e
g
m
e
n
t
an
d
t
h
r
ee
-
s
e
g
m
en
t
o
n
l
in
e
s
w
itc
h
in
g
p
atter
n
s
f
o
r
N
-
le
v
e
l
in
v
er
ter
.
T
h
e
t
w
o
s
w
itc
h
i
n
g
p
atter
n
s
ar
e
s
i
m
u
lated
f
o
r
f
i
v
e
lev
e
l
ca
s
ca
d
ed
in
v
er
ter
.
O
n
e
o
f
t
h
e
i
m
p
o
r
tan
t
f
ea
t
u
r
e
o
f
th
i
s
tec
h
n
iq
u
e
i
s
t
h
a
t,o
u
t
o
f
lar
g
e
n
u
m
b
er
o
f
s
w
i
t
ch
in
g
s
tate
s
o
f
th
e
f
i
v
e
le
v
el
i
n
v
er
ter
,
t
h
e
d
esire
d
s
w
itch
in
g
s
tates
a
n
d
m
o
s
t
s
u
itab
le
r
ed
u
n
d
an
t
s
tates
ar
e
s
elec
ted
f
o
r
th
e
b
o
t
h
s
eq
u
en
ce
p
atter
n
s
s
u
c
h
t
h
at
,
th
e
tech
n
iq
u
e
i
s
i
m
p
le
m
e
n
ted
o
n
lin
e
w
i
th
n
o
n
ee
d
o
f
lo
o
k
u
p
tab
le
.
I
n
th
e
th
r
ee
-
s
eg
m
e
n
t
s
w
i
tch
in
g
s
eq
u
en
ce
,
th
e
i
n
v
er
ter
eq
u
iv
a
len
t
f
r
eq
u
en
c
y
is
5
0
%
h
i
g
h
er
t
h
a
n
th
a
t
o
f
s
e
v
en
-
s
eg
m
e
n
t
,
h
ar
m
o
n
ics
ap
p
ea
r
as
s
id
eb
an
d
ar
o
u
n
d
h
i
g
h
i
n
v
er
ter
f
r
eq
u
e
n
c
y
,
a
n
d
t
h
e
m
ag
n
it
u
d
e
o
f
lo
w
er
o
r
d
er
h
ar
m
o
n
ic
s
is
r
ed
u
ce
d
f
o
r
t
h
r
ee
s
e
g
m
en
t
g
iv
i
n
g
les
s
er
v
a
lu
e
o
f
L
i
n
e
v
o
lt
ag
e
a
n
d
c
u
r
r
en
t
T
HDs
w
h
e
n
c
o
m
p
ar
ed
to
t
h
at
o
f
s
ev
e
n
-
s
e
g
m
e
n
t
s
w
itc
h
i
n
g
p
atte
r
n
.
RE
F
E
R
E
NC
E
S
[1
]
J.
Ro
d
ríg
u
e
z
,
J.
L
a
i,
a
n
d
F
.
P
e
n
g
,
“
M
u
lt
i
L
e
v
e
l
Co
n
v
e
rters
:
A
S
u
rv
e
y
o
f
T
o
p
o
lo
g
ies
,
C
o
n
tr
o
ls
a
n
d
A
p
p
li
c
a
ti
o
n
s
”
,
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l
.
4
9
,
n
o
.
4
,
p
p
.
7
2
4
-
7
3
8
,
A
u
g
.
2
0
0
2
.
[2
]
P.
S
a
ti
sh
Ku
m
a
r,
J.
A
m
a
rn
a
th
,
S
.
V
.
L
.
Na
ra
sim
h
a
m
,
“
A
F
a
st
S
p
a
c
e
-
v
e
c
to
r
P
u
lse
w
it
h
M
o
d
u
latio
n
M
e
th
o
d
f
o
r
D
io
d
e
-
c
la
m
p
e
d
M
u
lt
i
-
lev
e
l
I
n
v
e
rter
F
e
d
In
d
u
c
ti
o
n
M
o
to
r”
,
Asia
n
P
o
we
r E
lec
tro
n
ics
J
o
u
rn
a
l
,
v
o
l.
4
,
n
o.
1
,
A
p
ril
2
0
1
0
.
[3
]
P.
S
a
ti
sh
Ku
m
a
r
,
“
A
Ne
w
G
e
n
e
ra
l
T
o
p
o
lo
g
y
f
o
r
C
a
sc
a
d
e
d
M
u
lt
il
e
v
e
l
In
v
e
rters
w
it
h
In
c
re
a
se
d
N
u
m
b
e
r
o
f
lev
e
ls
Ba
se
d
o
n
Dia
g
o
n
a
l
DC
S
o
u
rc
e
H
-
Brid
g
e
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Ad
v
a
n
c
e
s
in
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ics
En
g
o
n
e
e
rin
g
,
v
o
l.
3,
n
o.
3,
pp.
175
-
1
8
4
,
2
0
1
4
.
[4
]
S
a
n
m
in
W
e
i
a
n
d
Bin
W
u
,
“
A
G
e
n
e
ra
l
S
p
a
c
e
V
e
c
to
r
P
W
M
c
o
n
tro
l
A
lg
o
r
it
h
m
f
o
r
M
u
lt
i
-
lev
e
l
in
v
e
rt
e
rs”
,
IEE
E
2
0
0
3
,
pp
.
5
6
2
-
568
.
[5
]
Am
it
Ku
m
a
r
G
u
p
ta
a
n
d
As
h
w
in
M
.
K
h
a
m
b
a
d
k
o
n
e
,
“
A
Ge
n
e
ra
l
S
p
a
c
e
V
e
c
to
r
P
W
M
A
lg
o
rit
h
m
fo
r
M
u
lt
i
L
e
v
e
l
In
v
e
rters
,
I
n
c
lu
d
in
g
O
p
e
ra
ti
o
n
in
O
v
e
r
m
o
d
u
l
a
ti
o
n
R
a
n
g
e
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ic
s
,
v
o
l
.
2
2
,
n
o.
2
,
M
a
rc
h
2
0
0
7
.
[6
]
A
n
sh
u
m
a
n
T
rip
a
ti
,
Kh
a
m
b
a
d
k
o
n
e
a
n
d
S
.
K
.
P
a
n
d
a
,
“
Dire
c
t
M
e
th
o
d
o
f
o
v
e
r
M
o
d
u
latio
n
w
it
h
I
n
teg
r
a
ted
C
lo
se
d
L
o
o
p
S
tato
r
F
lu
x
V
e
c
to
r
C
o
n
tr
o
l
”
,
IEE
E
T
ra
n
s.
o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
2
0
,
n
o
.
5
,
p
p
.
1
1
6
1
-
1
1
6
8
,
S
ep
.
2
0
0
5
.
[7
]
B.
S
iri
sh
a
,
P.
S
a
ti
sh
K
u
m
a
r,
N.S
u
sh
e
e
la
,
“
T
h
re
e
P
h
a
se
T
w
o
L
e
g
Ne
u
tral
P
o
i
n
t
Clam
p
e
d
Co
n
v
e
rter
w
it
h
o
u
t
p
u
t
DC
V
o
l
tag
e
Re
g
u
latio
n
a
n
d
In
p
u
t
P
o
w
e
r
F
a
c
to
r
Co
rre
c
ti
o
n
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m (
IJ
PE
DS
)
,
v
ol
.
2
,
n
o
.
2
,
Ju
n
e
2
0
1
2
.
[8
]
A.
Na
b
a
e
,
I.
T
a
k
a
h
a
sh
i,
c
d
H.
A
k
a
g
i,
“
A
Ne
w
Ne
u
tral
-
p
o
in
t
C
lam
p
e
d
p
wm
In
v
e
rter
”
,
IEE
E
T
ra
n
s.
In
d
.
A
p
p
l.
,
v
o
l.
1A
-
1
7
,
n
o
.
5
,
p
p
.
5
18
-
5
2
3
,
S
e
p
t/
O
c
t
1
9
8
2
.
[9
]
B.
S
ir
ish
a
,
P.
S
a
ti
s
h
K
u
m
a
r
,
“
A
S
p
a
c
e
V
e
c
to
r
P
u
lse
W
id
th
M
o
d
u
lati
o
n
T
e
c
h
n
iq
u
e
f
o
r
F
iv
e
L
e
v
e
l
Ca
s
c
a
d
e
d
H
-
Brid
g
e
In
v
e
rter
In
c
lu
d
in
g
Ov
e
r
M
o
d
u
latio
n
Re
g
io
n
w
it
h
F
P
GA
Im
p
le
m
e
n
tatio
n
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
p
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
s (
IJ
PE
DS
)
,
v
o
l
.
8
,
n
o
.
3,
S
e
p
tem
b
e
r
2
0
1
7
.
[1
0
]
B.
S
iri
sh
a
,
P.
S
a
ti
sh
K
u
m
a
r
,
“I
m
p
lem
e
n
tatio
n
o
f
F
P
GA
b
a
s
e
d
S
p
a
c
e
V
e
c
to
r
P
W
M
M
e
th
o
d
f
o
r
F
iv
e
L
e
v
e
l
C
a
sc
a
d
e
d
In
v
e
rter”
,
IEE
E
7
th
Po
we
r
In
d
i
a
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
(
PI
ICON
2
0
1
6
)
a
t
Bi
k
a
n
e
r
Ra
j
a
sth
a
n
,
No
v
e
mb
e
r
2
5
-
2
7
2
0
1
6
.
[1
1
]
B.
S
iri
sh
a
,
P.
S
a
ti
sh
K
u
m
a
r
,
“
A
S
im
p
li
f
ied
S
p
a
c
e
V
e
c
to
r
P
W
M
fo
r
Ca
sc
a
d
e
d
H
-
Brid
g
e
In
v
e
rter
in
c
lu
d
in
g
Ov
e
r
M
o
d
u
latio
n
Op
e
ra
ti
o
n
”
,
13
th
I
n
t
e
rn
a
ti
o
n
a
l
IE
EE
In
d
ia
Co
n
f
e
re
n
c
e
INDICO
N
2
0
1
6
a
t
IIS
C
,
Ben
g
a
l
u
ru
,
I
n
d
i
a
.
De
c
e
mb
e
r 1
6
-
1
8
,
2
0
1
6
.
[1
2
]
D.W
.
K
a
n
g
,
Y
.
H
.
L
e
e
,
B.
S
.
S
u
h
,
C.
H
.
C
h
o
i,
a
n
d
D.S
.
Hy
u
n
,
“
A
Ca
rrier
w
a
v
e
-
b
a
se
d
s
v
p
wm
u
sin
g
P
h
a
se
-
v
o
lt
a
g
e
R
e
d
u
n
d
a
n
c
ies
f
o
r
M
u
l
ti
lev
e
l
H
-
b
rid
g
e
I
n
v
e
rter
”
,
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
I
n
d
u
stria
l
E
lec
tro
n
ics
,
C
o
n
tr
o
l,
a
n
d
I
n
stru
me
n
ta
ti
o
n
(
IECON
)
,
v
o
l.
1
,
p
p
.
3
2
4
-
3
2
9
,
1
9
9
9
.
[1
3
]
N.
Ce
lan
o
v
ic
a
n
d
D.
Bo
ro
y
e
v
i
c
h
,
“
A
F
a
st
S
p
a
c
e
V
e
c
to
r
M
o
d
u
l
a
ti
o
n
A
lg
o
rit
h
m
f
o
r
M
u
lt
il
e
v
e
l
T
h
re
e
P
h
a
se
Co
n
v
e
rters
”
,
IEE
E
T
r
a
n
s
o
n
I
n
d
u
stry
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
3
7
,
n
o
.
2
,
p
p
.
6
3
7
-
6
4
1
,
2
0
0
1
.
[1
4
]
“
V
o
lt
a
g
e
S
o
u
rc
e
I
n
v
e
rters
w
it
h
P
h
a
se
-
sh
if
ted
U
n
ip
o
lar
s
p
wm
”
,
IEE
E
T
tra
n
s.
o
n
I
n
d
u
stry
A
p
p
li
c
a
ti
o
n
s
,
v
o
l.
3
5
,
no.
5
,
p
p
.
1
1
1
8
-
1
1
2
3
,
1
9
9
9
.
[1
5
]
D.W
.
Ka
n
g
,
Y.H.
L
e
e
,
B.
S
.
S
u
h
,
C.
H.
Ch
o
i
,
a
n
d
D.S
.
Hy
u
n
,
“
A
Ca
rrier
w
a
v
e
-
b
a
se
d
s
v
p
wm
u
sin
g
P
h
a
se
-
v
o
lt
a
g
e
R
e
d
u
n
d
a
n
c
ies
f
o
r
M
u
lt
il
e
v
e
l
H
-
b
rid
g
e
I
n
v
e
rter
”
,
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
I
n
d
u
str
ial
El
e
c
tro
n
i
c
s,
C
o
n
tr
o
l,
a
n
d
I
n
stru
m
e
n
tatio
n
(
I
ECON
),
v
o
l.
1
,
p
p
.
3
2
4
-
3
29
,
1
9
9
9
.
[1
6
]
N.
Ce
lan
o
v
ic
a
n
d
D.
Bo
ro
y
e
v
i
c
h
,
“
A
F
a
st
S
p
a
c
e
V
e
c
to
r
M
o
d
u
lati
o
n
A
lg
o
rit
h
m
f
o
r
M
u
lt
il
e
v
e
l
T
h
re
e
P
h
a
se
C
o
n
v
e
rters
”
,
IEE
E
T
r
a
n
s
o
n
I
n
d
u
stry
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
3
7
,
n
o
.
2
,
p
p
.
6
3
7
-
6
4
1
,
2
0
0
1
.
[1
7
]
B
.S.
S
u
h
,
G.
S
i
n
h
a
,
M
.
D.
M
a
n
jrek
a
r
,
a
n
d
T
.
A
.
L
ip
o
,
“
M
u
lt
il
e
v
e
l
P
o
w
e
r
Co
n
v
e
rsio
n
-
a
n
o
v
e
rv
ie
w
o
f
T
o
p
o
lo
g
ies
a
n
d
M
o
d
u
latio
n
S
trate
g
ies
”
,
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
on
O
p
ti
m
iza
ti
o
n
o
f
E
lec
tri
c
a
l
a
n
d
E
lec
tro
n
ic
E
q
u
ip
m
e
n
t
(o
p
ti
m
),
v
o
l.
2
,
p
p
.
1
0
1
-
1
0
5
,
1
9
9
8
.
[1
8
]
Hu
,
Ho
n
g
y
a
n
Wan
g
,
Y
a
n
De
n
g
a
n
d
X
iag
n
i
n
g
,
“
A
S
i
m
p
le
S
VPW
M
A
lg
o
rit
h
m
o
f
M
u
lt
il
e
v
e
l
in
v
e
rter
”
,
Po
we
r
El
e
c
tro
n
ics
S
p
e
c
ia
li
stic
C
o
n
fer
e
n
c
e
,
Ach
e
n
,
2
0
0
4
.
[1
9
]
M
.
L
.
T
o
lb
e
rt
a
n
d
F
.
Z.
P
e
n
g
,
“
M
u
lt
i
-
L
e
v
e
l
c
o
n
v
e
rter
f
o
r
Larg
e
El
e
c
tri
c
Dri
v
e
s
”
,
IEE
E
T
ra
n
s.
In
d
u
s.
A
p
p
li
c
a
.
,
v
o
l
.
35
,
no.
1
,
p
p
3
6
-
44
,
1
9
9
9
.
[2
0
]
B.
S
.
S
u
h
a
n
d
D.S
.
Hv
u
n
,
“
A
Ne
w
N
-
L
e
v
e
l
Hig
h
Vo
lt
a
g
e
In
v
e
rsio
n
S
y
ste
m
”
,
IEE
E
T
ra
n
s.
o
n
In
d
u
s
tria
l
E
lec
tro
n
ics
,
v
o
l.
4
4
,
n
o
.
14
,
p
p
.
1
0
7
-
I
1
5
,
1
9
9
7
.
[2
1
]
L
.
Yiq
iao
a
n
d
C.
O.
Nw
a
n
k
p
a
,
“
A
N
e
w
Ty
p
e
o
f
S
TAT
COM
b
a
s
e
d
o
n
Ca
sc
a
d
in
g
V
o
l
tag
e
S
o
u
rc
e
In
v
e
rters
w
i
th
P
h
a
s
e
-
sh
if
ted
U
n
ip
o
lar S
P
W
M
”
,
IEE
E
T
ra
n
s.
o
n
I
n
d
u
stry
Ap
p
li
c
a
t
io
n
s
,
v
o
l.
3
5
,
n
o
.
5
,
p
p
.
1
1
1
8
-
1
1
2
3
,
1
9
9
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
1
7
–
3
4
2
6
3426
[2
2
]
D.W
.
Ka
n
g
,
Y.H.
L
e
e
,
B.
S
.
S
u
h
,
C.
H.
Ch
o
i,
a
n
d
D.S
.
H
y
u
n
,
“
A
C
a
rrier
w
a
v
e
-
b
a
se
d
S
V
P
W
M
u
sin
g
P
h
a
se
-
Vo
lt
a
g
e
R
e
d
u
n
d
a
n
c
ies
f
o
r
M
u
l
ti
lev
e
l
H
-
b
rid
g
e
I
n
v
e
rter
”
,
In
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
Co
n
tr
o
l
,
a
n
d
In
stru
me
n
ta
ti
o
n
(
IECON)
,
v
o
l.
1
,
p
p
3
2
4
-
3
2
9
,
1
9
9
9
.
[2
3
]
Kra
u
se
,
P
.
C.
,
„S
im
u
latio
n
o
f
S
y
m
m
e
tri
c
a
l
In
d
u
c
ti
o
n
M
a
c
h
i
n
e
ry
”
,
IEE
E
T
r
a
n
s.
Po
we
r
A
p
p
a
ra
t
u
s
S
y
ste
ms
,
v
ol
.
P
A
S
-
8
4
,
n
o
.
1
1
,
p
p
.
1
0
3
8
-
1
0
5
3
,
1
9
6
5
.
[
2
4
]
G
h
a
n
i,
S
.
N.,
“
Dig
it
a
l
Co
m
p
u
t
e
r
S
im
u
latio
n
o
f
T
h
re
e
-
p
h
a
se
In
d
u
c
t
io
n
M
a
c
h
in
e
Dy
n
a
m
ics
-
A
G
e
n
e
ra
li
z
e
d
A
p
p
ro
a
c
h
”
,
IEE
E
T
ra
n
s I
n
d
u
st
ry
Ap
p
l
.,
v
o
l.
2
4
,
n
o
.
1
,
p
p
.
1
0
6
-
1
1
4
,
1
9
8
8
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
B
.
S
irish
a
o
b
tain
e
d
h
e
r
B.
E
d
e
g
re
e
in
El
e
c
tri
c
a
l
&
El
e
c
tro
n
i
c
s
En
g
in
e
e
rin
g
f
ro
m
Os
m
a
n
ia
Un
iv
e
rsit
y
a
n
d
M
.
E
d
e
g
re
e
f
r
o
m
JN
T
U,
H
y
d
e
r
a
b
a
d
a
n
d
p
e
rsu
in
g
P
h
.
D.
in
th
e
a
re
a
o
f
m
u
lt
il
e
v
e
li
n
v
e
rter
s
.
S
h
e
is
c
u
rre
n
tl
y
w
o
r
k
in
g
a
s
As
sista
n
t
P
ro
f
e
ss
o
r
in
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Un
iv
e
rsit
y
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
(A
u
to
n
o
m
o
u
s),
O
s
m
a
n
ia
Un
iv
e
rsit
y
,
H
y
d
e
ra
b
a
d
,
T
e
lan
g
a
n
a
,
In
d
ia.
He
r
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
P
o
w
e
r
El
e
c
tro
n
ics
,
m
u
lt
il
e
v
e
l
in
v
e
rters
a
n
d
d
riv
e
s
.
Dr
.
P.
S
a
tish
K
u
m
a
r
wa
s
b
o
rn
in
Ka
rim
n
a
g
a
r,
A
n
d
h
ra
P
ra
d
e
sh
,
IND
IA
in
1
9
7
4
.
He
o
b
tain
e
d
th
e
B.
T
e
c
h
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
i
n
e
e
rin
g
f
ro
m
J
NTU
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Ka
k
in
a
d
a
in
1
9
9
6
.
He
o
b
tain
e
d
M
.
T
e
c
h
d
e
g
re
e
in
p
o
w
e
r
e
lec
tro
n
ics
in
2
0
0
3
a
n
d
P
h
.
D.
i
n
2
0
1
1
f
ro
m
JN
T
UH
,
H
y
d
e
ra
b
a
d
.
He
h
a
s
m
o
re
th
a
n
1
6
y
e
a
rs o
f
tea
c
h
in
g
a
n
d
re
se
a
rc
h
e
x
p
e
rien
c
e
a
n
d
p
re
se
n
tl
y
w
o
rk
in
g
a
s
S
e
n
io
r
A
ss
ist
a
n
t
P
ro
f
e
ss
o
r
in
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Un
iv
e
rsit
y
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Os
m
a
n
ia
Un
iv
e
rsit
y
,
Hy
d
e
ra
b
a
d
,
IND
I
A
.
He
p
re
se
n
ted
m
a
n
y
re
se
a
r
c
h
p
a
p
e
rs
in
v
a
rio
u
s
n
a
ti
o
n
a
l
a
n
d
in
tern
a
ti
o
n
a
l
jo
u
rn
a
ls
a
n
d
c
o
n
f
e
re
n
c
e
s.
Ac
h
iev
e
d
Aw
a
rd
f
o
r
Re
se
a
r
c
h
Ex
c
e
ll
e
n
c
e
a
n
d
Be
st
y
o
u
n
g
tea
c
h
e
r
Aw
a
rd
-
2
0
1
4
.
Ho
ld
s
UG
C
-
M
a
jo
r
Re
se
a
rc
h
P
ro
jec
t
a
n
d
S
ERB(DS
T
)
-
Re
se
a
r
c
h
P
ro
jec
ts
o
n
m
u
lt
il
e
v
e
l
in
v
e
rters
.
His
re
s
e
a
rc
h
in
tere
sts
in
c
lu
d
e
P
o
w
e
r
El
e
c
tro
n
ics
Driv
e
s,
M
u
l
ti
lev
e
l
in
v
e
rters
,
M
a
tri
x
Co
n
v
e
rters
a
n
d
sp
e
c
ial
m
a
c
h
in
e
s.
Evaluation Warning : The document was created with Spire.PDF for Python.