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
.
24
0
~
25
1
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.i
1
.
p
p
24
0
-
25
1
240
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
J
P
E
DS
S
m
a
ll
-
Sig
na
l AC
M
o
del and Clo
se
d Lo
o
p Contro
l o
f
Inte
rlea
v
ed
Three
-
Phas
e Bo
o
st Conv
erte
r
H
.
V.
G
urura
j
a
Ra
o
1
,
K
a
runa
M
ud
liy
a
r
2
,
R.
C.
M
a
la
3
1,
3
E&E
De
p
a
rtm
e
n
t,
M
a
n
ip
a
l
In
st
it
u
te o
f
T
e
c
h
n
o
lo
g
y
,
M
A
HE,
Ka
r
n
a
tak
a
,
In
d
ia
2
M
o
d
e
ll
i
n
g
En
g
i
n
e
e
r,
Kn
o
rr
-Bre
m
se
Tec
h
n
o
lo
gy
Ce
n
tre In
d
ia,
P
u
n
e
,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
4
,
2
0
1
7
R
ev
i
s
ed
Dec
31
,
2
0
1
7
A
cc
ep
ted
Feb
11
,
2
0
1
8
Re
n
e
wa
b
le
e
n
e
rg
y
so
u
rc
e
s
a
r
e
in
c
re
a
sin
g
l
y
b
e
in
g
u
se
d
to
d
a
y
a
n
d
so
lar
e
n
e
rg
y
is
th
e
m
o
st
re
a
d
il
y
a
n
d
a
b
u
n
d
a
n
tl
y
a
v
a
il
a
b
le
e
n
e
rg
y
so
u
rc
e
.
Bo
o
st
c
o
n
v
e
rters
a
re
a
n
in
teg
ra
l
p
a
rt
o
f
a
n
y
so
lar
e
n
e
rg
y
s
y
ste
m
.
In
o
rd
e
r
to
o
b
tain
m
a
x
i
m
u
m
p
o
ss
ib
le
e
n
e
rg
y
f
ro
m
th
e
so
lar
s
y
st
e
m
m
u
lt
i
-
p
h
a
se
i
n
terle
a
v
e
d
b
o
o
st
c
o
n
v
e
rters
a
re
u
se
d
.
T
h
is
p
a
p
e
r
p
re
se
n
ts
th
e
s
m
a
ll
-
sig
n
a
l
a
c
m
o
d
e
ll
in
g
a
n
d
c
l
o
se
d
l
o
o
p
c
o
n
tro
l
o
f
th
re
e
-
p
h
a
se
in
terle
a
v
e
d
b
o
o
st
c
o
n
v
e
rter.
S
tate
–
sp
a
c
e
m
o
d
e
ll
in
g
m
e
th
o
d
o
l
o
g
y
h
a
s
b
e
e
n
a
d
o
p
ted
to
h
a
v
e
li
n
e
a
rize
d
e
q
u
iv
a
len
t
m
o
d
e
l
o
f
th
e
b
o
o
st
c
o
n
v
e
rter.
T
h
e
in
terle
a
v
e
d
th
re
e
-
p
h
a
se
b
o
o
st
c
o
n
v
e
rter
is
a
v
e
ra
g
e
d
o
v
e
r
it
s
o
n
e
sw
it
c
h
in
g
p
e
ri
o
d
a
n
d
p
e
rtu
r
b
e
d
w
it
h
s
m
a
ll
a
c
v
a
riatio
n
s
a
n
d
f
in
a
ll
y
li
n
e
a
riz
e
d
a
ro
u
n
d
i
ts
q
u
ies
c
e
n
t
p
o
in
t
t
o
h
a
v
e
a
s
m
a
ll
sig
n
a
l
a
c
m
o
d
e
l.
Ty
p
e
III
c
o
m
p
e
n
sa
to
r
is
e
m
p
lo
y
e
d
to
im
p
ro
v
e
th
e
f
re
q
u
e
n
c
y
re
sp
o
n
se
a
n
d
c
lo
se
d
lo
o
p
c
o
n
t
ro
l
o
f
th
re
e
-
p
h
a
se
b
o
o
st
c
o
n
v
e
rter.
T
h
e
c
o
n
tro
ll
e
r
d
e
sig
n
p
r
o
c
e
d
u
re
is
d
isc
u
ss
e
d
in
d
e
tail.
T
h
e
e
ff
e
c
t
o
f
rig
h
t
-
h
a
lf
p
lan
e
z
e
ro
i
n
n
o
n
-
m
in
im
u
m
p
h
a
se
s
y
st
e
m
a
n
d
th
e
a
p
p
ro
p
riate
p
o
le
-
z
e
ro
p
lac
e
m
e
n
ts
to
o
v
e
rc
o
m
e
th
e
m
a
x
i
m
u
m
p
h
a
se
la
g
in
su
c
h
s
y
ste
m
is
d
isc
u
ss
e
d
.
T
h
e
c
o
m
p
e
n
sa
ted
c
lo
se
d
l
o
o
p
sy
ste
m
is
t
e
ste
d
f
o
r
lo
a
d
v
a
riatio
n
s
to
o
b
se
rv
e
th
e
tran
sie
n
t
re
sp
o
n
se
.
K
ey
w
o
r
d
:
T
h
r
ee
-
p
h
ase
b
o
o
s
t c
o
n
v
er
ter
State
-
s
p
ac
e
m
o
d
elli
n
g
T
y
p
e
I
I
I
co
m
p
en
s
a
to
r
Vo
ltag
e
m
o
d
e
co
n
tr
o
l
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
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
H.
V.
Gu
r
u
r
aj
a
R
ao
,
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
,
Ma
n
ip
al
I
n
s
tit
u
te
o
f
T
ec
h
n
o
lo
g
y
,
M
A
HE
,
Ma
n
ip
al
Ud
u
p
i d
is
tr
ict,
Kar
n
ata
k
a
s
tate
,
I
n
d
ia.
P
in
: 5
7
6
1
0
4
.
E
m
ail:
g
u
r
u
r
aj
.
r
ao
@
m
an
ip
al.
e
d
u
1.
I
NT
RO
D
UCT
I
O
N
DC
to
D
C
co
n
v
er
ter
s
ar
e
w
i
d
ely
u
s
ed
in
p
h
o
to
v
o
ltaic
s
y
s
te
m
s
as
a
p
o
w
er
i
n
ter
f
ac
e.
R
ath
er
t
h
a
n
co
n
v
e
n
tio
n
al
b
o
o
s
t
co
n
v
er
ter
s
,
m
u
l
tip
h
a
s
e
b
o
o
s
t
co
n
v
er
ter
s
ar
e
p
r
ef
er
r
ed
s
in
ce
th
e
y
o
f
f
er
s
ev
er
al
ad
v
a
n
ta
g
es
th
at
ar
e
v
er
y
d
es
ir
ab
le
in
lo
w
v
o
ltag
e
a
n
d
h
i
g
h
p
o
w
er
ap
p
licatio
n
s
.
Fir
s
t,
s
e
v
er
al
p
ar
allel
p
o
w
er
s
tag
e
s
ar
e
ad
d
ed
in
p
ar
allel
to
th
e
co
n
v
en
tio
n
al
d
c
-
d
c
co
n
v
er
ter
to
a
ttain
m
u
lt
i
-
p
h
ase
b
o
o
s
t
[
1
]
,
[
9
]
;
it
i
n
cr
ea
s
es
t
h
e
p
o
w
er
r
atin
g
a
n
d
cu
r
r
en
t
h
a
n
d
lin
g
ca
p
ab
ilit
y
o
f
th
e
co
n
v
er
ter
.
Seco
n
d
,
d
u
e
to
in
ter
leav
ed
s
w
itc
h
i
n
g
s
ch
e
m
e,
ef
f
ec
tiv
e
p
u
ls
e
f
r
eq
u
e
n
c
y
is
i
n
cr
ea
s
ed
b
y
n
u
m
b
er
o
f
p
h
ase
ti
m
es a
n
d
it a
l
s
o
r
ed
u
ce
s
t
h
e
m
a
g
n
i
tu
d
e
o
f
in
d
u
cto
r
r
ip
p
le
cu
r
r
en
t f
lo
w
i
n
g
i
n
to
th
e
f
ilter
ca
p
ac
ito
r
,
th
er
eb
y
r
ed
u
cin
g
t
h
e
s
ize
o
f
th
e
f
il
ter
[
2
]
,
[
5
].
Mo
s
t
o
f
th
e
d
c
-
d
c
co
n
v
er
ter
a
p
p
licatio
n
s
y
s
te
m
s
d
e
m
a
n
d
it
s
o
u
tp
u
t
to
b
e
h
eld
co
n
s
tan
t,
in
s
p
ite
o
f
v
ar
iatio
n
s
in
in
p
u
t
o
r
lo
ad
[
3
]
.
I
t
ca
n
b
e
ac
h
iev
ed
b
y
d
es
ig
n
in
g
a
co
n
tr
o
l
cir
cu
it
t
h
at
c
h
a
n
g
e
s
t
h
e
d
u
t
y
c
y
cle
r
atio
,
s
o
as to
m
ain
tain
t
h
e
o
u
t
p
u
t v
o
lta
g
e
co
n
s
ta
n
t a
n
d
is
eq
u
al
to
t
h
e
d
esire
d
r
e
f
er
e
n
ce
v
o
ltag
e.
I
n
ad
d
itio
n
to
r
eg
u
lat
in
g
t
h
e
o
u
tp
u
t
v
o
lta
g
e,
th
e
f
ee
d
b
ac
k
s
y
s
te
m
s
h
o
u
ld
b
e
s
tab
le,
an
d
t
h
e
tr
an
s
ie
n
t
r
e
s
p
o
n
s
e
s
h
o
u
ld
m
ee
t
th
e
d
esire
d
s
p
ec
if
icatio
n
s
.
T
h
u
s
,
th
e
f
o
r
e
m
o
s
t
o
b
j
ec
tiv
e
o
f
a
ty
p
ica
l
DC
-
DC
co
n
v
er
ter
is
to
m
ai
n
tai
n
its
o
u
tp
u
t
v
o
ltag
e
c
o
n
s
tan
t,
in
s
p
ite
o
f
d
is
tu
r
b
an
ce
in
i
n
p
u
t
v
o
lta
g
e,
lo
ad
cu
r
r
en
t
an
d
a
n
y
p
ar
asit
ic
ef
f
ec
t
o
f
cir
c
u
i
t
ele
m
e
n
ts
.
So
,
it
is
u
t
m
o
s
t
i
m
p
o
r
tan
t
to
ad
j
u
s
t
th
e
d
u
t
y
c
y
c
le
to
k
ee
p
o
u
tp
u
t
v
o
ltag
e
co
n
s
tan
t
.
T
h
e
n
eg
at
iv
e
f
ee
d
b
ac
k
co
n
tr
o
l
tec
h
n
iq
u
e
i
s
ad
o
p
ted
to
f
ee
d
th
e
s
e
n
s
ed
o
u
t
p
u
t
v
o
ltag
e
to
t
h
e
co
n
tr
o
ller
wh
ich
i
n
t
u
r
n
v
ar
ies
th
e
d
u
t
y
c
y
cle
to
r
eg
u
late
t
h
e
o
u
tp
u
t v
o
lta
g
e.
[
3
]
.
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
-
8694
S
ma
ll
S
ig
n
a
l
A
C
Mo
d
el
a
n
d
C
lo
s
ed
Lo
o
p
C
o
n
tr
o
l
o
f I
n
terl
ea
ve
d
3
P
h
a
s
e
B
o
o
s
t
…
(
H.
V
.
Gu
r
u
r
a
ja
R
a
o
)
241
Ma
n
y
d
esi
g
n
p
r
o
ce
d
u
r
es
i
n
th
e
li
ter
atu
r
e
ar
e
e
m
p
ir
ical
l
y
d
er
iv
ed
,
it
s
d
er
iv
atio
n
p
r
o
ce
s
s
an
d
d
escr
ip
tio
n
s
ar
e
n
o
t
p
r
o
v
id
ed
.
T
h
u
s
,
f
o
r
a
g
iv
e
n
s
y
s
te
m
it
is
d
if
f
ic
u
lt
to
f
o
llo
w
a
n
d
e
v
al
u
a
te
th
ese
p
r
o
ce
d
u
r
es
[
4
]
,
[
7
]
.
I
n
th
is
p
ap
er
t
y
p
e
I
I
I
co
m
p
e
n
s
ato
r
i
s
m
at
h
e
m
ati
ca
ll
y
a
n
al
y
ze
d
a
n
d
e
m
p
lo
y
ed
.
A
li
n
ea
r
co
n
tr
o
l
tech
n
iq
u
e
ca
n
b
e
ap
p
lied
to
a
lin
ea
r
s
y
s
te
m
,
b
u
t
all
t
h
e
s
w
it
ch
m
o
d
e
p
o
w
er
s
u
p
p
l
y
s
y
s
te
m
s
ar
e
n
o
n
-
li
n
ea
r
a
s
th
e
s
y
s
te
m
d
u
r
in
g
o
n
e
s
w
i
tch
i
n
g
s
u
b
-
i
n
ter
v
al
is
n
o
t
t
h
e
s
a
m
e
as
in
o
t
h
er
s
u
b
-
i
n
ter
v
al.
So
,
th
e
p
o
w
er
co
n
v
er
ter
s
y
s
te
m
n
ee
d
s
to
b
e
m
o
d
eled
t
o
a
lin
ea
r
s
y
s
te
m
i
n
o
r
d
er
t
o
a
p
p
ly
a
lin
ea
r
co
n
tr
o
l
tech
n
iq
u
e.
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
s
m
all
s
ig
n
al
ac
m
o
d
eli
n
g
i
s
to
p
r
ed
ict
h
o
w
s
m
all
s
i
g
n
al
lo
w
-
f
r
eq
u
en
c
y
ac
v
ar
iatio
n
s
i
n
d
u
t
y
c
y
cle
r
es
u
lt
s
in
s
m
all
s
ig
n
al
lo
w
f
r
eq
u
en
c
y
ac
v
ar
iatio
n
s
i
n
t
h
e
co
n
v
er
ter
v
o
l
tag
e
a
n
d
cu
r
r
en
t
w
a
v
e
f
o
r
m
s
.
I
n
ter
leav
ed
b
o
o
s
t
co
n
v
er
ter
s
ar
e
n
o
w
ex
te
n
s
i
v
el
y
u
s
ed
f
o
r
w
id
e
r
an
g
e
o
f
ap
p
licatio
n
s
.
B
en
ef
it
s
o
f
m
u
ltid
ev
ice
i
n
ter
leav
ed
co
n
v
e
r
ter
s
o
v
er
co
n
v
en
tio
n
al
co
n
v
er
ter
s
f
o
r
f
u
e
l c
ell
ap
p
licatio
n
s
i
s
d
is
c
u
s
s
ed
in
[
1
0
]
.
A
P
V
f
ed
in
ter
leav
ed
b
o
o
s
t
co
n
v
er
ter
i
s
p
r
o
p
o
s
ed
f
o
r
ag
r
icu
l
tu
r
al
ap
p
licatio
n
s
i
n
[
1
1
]
.
S
m
a
ll
s
i
g
n
a
l
m
o
d
el
f
o
r
n
p
h
a
s
e
i
n
ter
lea
v
ed
b
o
o
s
t
co
n
v
er
ter
is
p
r
esen
ted
in
[
1
2
]
.
On
l
y
o
p
en
lo
o
p
co
n
tr
o
l
s
tu
d
ie
s
ar
e
p
er
f
o
r
m
ed
.
T
h
e
s
m
al
l
s
i
g
n
al
ac
co
n
v
er
ter
m
o
d
el
is
o
b
tain
ed
b
y
r
e
m
o
v
i
n
g
s
witch
i
n
g
h
ar
m
o
n
ic
s
a
n
d
av
er
a
g
i
n
g
all
s
u
b
-
in
ter
v
al
w
a
v
e
f
o
r
m
s
o
v
er
o
n
e
s
w
i
tch
i
n
g
p
er
io
d
.
An
a
v
er
a
g
ed
m
o
d
el
i
m
p
lies
t
h
e
d
is
ap
p
ea
r
an
ce
o
f
a
n
y
s
w
i
tch
i
n
g
e
v
en
t
to
th
e
b
en
ef
it
o
f
a
s
m
o
o
t
h
l
y
v
ar
y
i
n
g
co
n
ti
n
u
o
u
s
s
ig
n
al.
T
h
e
av
er
ag
ed
v
o
ltag
es
a
n
d
cu
r
r
en
ts
,
i
n
g
e
n
er
al
co
m
p
r
is
e
s
n
o
n
lin
ea
r
f
u
n
ctio
n
s
o
f
th
e
co
n
v
er
ter
d
u
t
y
c
y
c
le,
v
o
ltag
e
s
,
an
d
cu
r
r
en
ts
a
n
d
r
esu
lts
i
n
a
s
y
s
te
m
o
f
n
o
n
li
n
ea
r
d
if
f
er
en
tial
eq
u
at
io
n
s
[
4
]
.
Hen
ce
,
it
m
u
s
t
b
e
lin
e
ar
ized
to
co
n
s
tr
u
ct
a
s
m
al
l
-
s
i
g
n
al
lin
ea
r
co
n
v
er
ter
m
o
d
el
a
n
d
is
d
is
c
u
s
s
ed
in
g
e
n
er
al
in
s
ec
tio
n
2
.
2.
ST
A
T
E
SP
ACE A
VE
R
AG
E
M
O
DE
L
I
t
is
a
co
m
m
o
n
p
r
ac
tice
to
s
elec
t
s
tate
v
ar
iab
les
b
a
s
ed
o
n
e
n
er
g
y
s
to
r
ag
e
ele
m
e
n
t
s
[6
].
Un
li
k
e
co
n
v
e
n
tio
n
al
d
c
-
d
c
co
n
v
er
ter
w
h
ic
h
h
as
t
w
o
s
tates d
u
r
in
g
ea
ch
s
w
itc
h
in
g
p
er
io
d
,
d
u
e
to
in
t
er
leav
ed
s
w
i
tch
i
n
g
s
eq
u
en
ce
o
f
m
u
lti
-
P
h
ased
co
n
v
er
ter
,
it
u
n
d
er
g
o
es
v
ar
io
u
s
d
i
f
f
er
en
t
s
ta
tes,
d
ep
en
d
in
g
o
n
th
e
n
u
m
b
er
o
f
p
h
ase.
T
h
e
d
u
r
atio
n
o
f
ea
ch
s
tate
is
d
er
iv
ed
w
it
h
r
elativ
e
to
its
d
u
t
y
r
atio
an
d
th
e
s
w
itc
h
i
n
g
p
er
io
d
.
I
n
th
r
ee
-
p
h
ase
dc
-
d
c
co
n
v
er
ter
,
th
e
d
if
f
er
e
n
t
p
h
ase
s
w
i
tch
e
s
ar
e
o
p
er
ated
w
ith
r
elati
v
e
p
h
ase
s
h
i
f
t
s
o
f
1
2
0
d
eg
r
ee
[
1
3
]
.
Phase I
Phase II
Phase III
Ts
(D-2/3)Ts
(1-D)Ts
I
II
III
IV
V
VI
rl
1
L
1
S
11
ron
11
C
rl
2
L
2
rl
3
L
3
ron
12
ron
13
S
12
S
13
S
21
S
22
S
23
rc
V
in
ron
21
ron
22
ron
23
R
Fig
u
r
e
1
.
T
h
r
ee
-
P
h
ase
I
n
ter
lea
v
ed
s
w
itc
h
i
n
g
p
u
ls
e
Fig
u
r
e
2
.
T
h
r
ee
-
P
h
ase
b
o
o
s
t c
o
n
v
er
ter
T
h
e
g
ate
p
u
l
s
e
f
o
r
in
ter
lea
v
e
d
th
r
ee
-
p
h
ase
d
c
-
d
c
co
n
v
er
ter
is
s
h
o
w
n
Fi
g
u
r
e.
1
.
Du
e
to
i
n
ter
leav
ed
s
w
itc
h
in
g
,
th
e
t
h
r
ee
-
p
h
ase
s
y
s
te
m
ex
h
ib
its
s
ix
s
tates
in
ea
c
h
s
w
i
tch
i
n
g
c
y
cle.
T
h
e
s
tates
I
,
I
I
I
an
d
V
last
s
f
o
r
(
D
–
2
/3
)
,
w
h
ile
s
tates I
I
,
I
V,
an
d
VI
last
s
f
o
r
(
1
-
D)
ti
m
es t
h
e
s
w
itch
in
g
p
er
io
d
T
s
[
1
3
]
.
Fo
r
a
th
r
ee
-
p
h
a
s
e
d
c
-
d
c
co
n
v
er
ter
s
h
o
w
n
i
n
Fi
g
u
r
e
2
,
o
p
e
r
atin
g
i
n
co
n
tin
u
o
u
s
co
n
d
u
c
ti
o
n
m
o
d
e
,
o
p
er
atin
g
s
tate
s
f
o
r
m
t
h
e
s
ta
te
v
ec
to
r
x
(
t)
,
an
d
th
e
in
d
ep
e
n
d
en
t
s
o
u
r
ce
s
th
a
t
d
r
iv
e
th
e
co
n
v
er
ter
f
o
r
m
t
h
e
in
p
u
t
v
ec
to
r
u
(
t)
.
Du
r
i
n
g
ea
c
h
s
u
b
in
ter
v
al
o
f
a
s
w
i
tch
in
g
p
er
io
d
,
th
e
co
n
v
er
ter
r
ed
u
ce
s
to
th
e
lin
ea
r
cir
cu
it
th
at
ca
n
b
e
r
ep
r
esen
ted
b
y
t
h
e
f
o
llo
w
in
g
s
tate
eq
u
atio
n
s
as,
dx
(
t
)
d
(
t
)
=
A
n
x
(
t
)
+
B
n
u
(
t
)
(
1
)
y
(
t
)
=
C
n
x
(
t
)
+
E
n
u
(
t
)
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8694
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
:
24
0
–
25
1
242
Du
r
in
g
ea
ch
o
f
th
e
s
u
b
in
ter
v
a
ls
,
t
h
e
cir
c
u
it
co
n
f
ig
u
r
atio
n
is
d
if
f
er
en
t
an
d
r
ep
r
esen
t
d
i
f
f
er
en
t
l
in
ea
r
cir
cu
its
;
h
e
n
ce
,
t
h
e
co
r
r
esp
o
n
d
in
g
s
tate
eq
u
atio
n
m
a
tr
ices
m
a
y
also
d
i
f
f
er
.
T
h
ese
s
tate
e
q
u
atio
n
s
ar
e
u
s
ed
to
o
b
tain
s
m
a
ll-
s
i
g
n
a
l a
c
m
o
d
el
[
2
]
,
[
6
].
Sin
ce
t
h
e
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
o
f
t
h
e
co
n
v
er
ter
is
g
e
n
er
al
l
y
v
er
y
m
u
c
h
g
r
ea
ter
th
a
n
t
h
e
co
n
v
er
ter
in
p
u
t
f
r
eq
u
en
c
y
v
a
r
iatio
n
s
,
th
e
eq
u
i
lib
r
iu
m
s
tate
eq
u
atio
n
s
o
f
t
h
e
co
n
v
er
ter
is
g
iv
e
n
as,
0 =
A
X
+
B
U
(
3)
Y
=
C
X
+
DU
(
4
)
W
h
er
e,
A
=
(
A
1
+
A
3
+
A
5
)
(
D
−
2
3
)
…
+
(
A
2
+
A
4
+
A
6
)
(
1
−
D
)
(
5
)
B
=
(
B
1
+
B
3
+
B
5
)
(
D
−
2
3
)
…
+
(
B
2
+
B
4
+
B
6
)
(
1
−
D
)
(
6
)
C
=
(
C
1
+
C
3
+
C
5
)
(
D
−
2
3
)
…
+
(
C
2
+
C
4
+
C
6
)
(
1
−
D
)
(
7
)
E
=
(
E
1
+
E
3
+
E
5
)
(
D
−
2
3
)
…
+
(
E
2
+
E
4
+
E
6
)
(
1
−
D
)
(
8
)
Her
e
X
,
U
an
d
Y
r
ep
r
esen
t
th
e
s
tate,
in
p
u
t
an
d
o
u
tp
u
t
v
ec
t
o
r
s
r
esp
ec
tiv
el
y
a
n
d
D
is
t
h
e
d
u
t
y
c
y
cle.
B
y
p
er
tu
r
b
atio
n
a
n
d
lin
ea
r
izat
io
n
o
f
th
e
co
n
v
er
ter
w
a
v
ef
o
r
m
s
ar
o
u
n
d
its
q
u
ie
s
ce
n
t
o
p
er
atin
g
p
o
in
t
[
2
]
,
[
1
4
]
,
th
e
s
tate
eq
u
atio
n
o
f
t
h
e
s
m
all
s
ig
n
al
ac
m
o
d
el
is
g
i
v
en
a
s
,
dx
(
t
)
dt
=
A
x
̂
(
t
)
+
B
u
̂
(
t
)
+
M
d
̂
(
t
)
(
9
)
y
̂
(
t
)
=
C
x
̂
(
t
)
+
N
d
̂
(
t
)
(
1
0
)
w
h
er
e
û
(
t)
an
d
d
̂
(
t
)
r
ep
r
esen
t
s
m
all
ch
a
n
g
e
s
i
n
t
h
e
i
n
p
u
t
v
ec
to
r
an
d
d
u
t
y
r
atio
.
T
h
e
v
ec
to
r
x
̂
(
t
)
an
d
ŷ
(
t)
ar
e
th
e
r
es
u
lti
n
g
s
m
all
d
e
v
iatio
n
s
i
n
t
h
e
s
tate
a
n
d
o
u
tp
u
t
v
ec
to
r
.
Her
e
i
t
is
as
s
u
m
ed
t
h
at
,
in
co
m
p
ar
is
io
n
w
it
h
t
h
e
q
u
ie
s
ce
n
t
v
al
u
es
,
t
h
es
e
d
ev
iatio
n
s
ar
e
m
u
c
h
les
s
[
2
]
.
T
h
e
m
atr
ice
s
M
an
d
N
ar
e
g
i
v
en
as
M
=
(
(
A
1
+
A
3
+
A
5
)
−
(
A
2
+
A
4
+
A
6
)
)
X
…
+
(
(
B
1
+
B
3
+
B
5
)
−
(
B
2
+
B
4
+
B
6
)
)
U
(
1
1
)
=
(
(
C
1
+
C
3
+
C
5
)
−
(
C
2
+
C
4
+
C
6
)
)
X
…
+
(
(
E
1
+
E
3
+
E
5
)
−
(
E
2
+
E
4
+
E
6
)
)
U
(
1
2
)
rl
1
L
1
ron
11
C
rl
2
L
2
rl
3
L
3
ron
12
ron
13
R
rc
V
in
rl
1
L
1
ron
11
C
rl
2
L
2
rl
3
L
3
ron
13
R
ron
22
rc
V
in
Fig
u
r
e
3
(
a)
State
I
,
I
I
I
an
d
V
Fig
u
r
e
3
(
b
)
State
II
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
-
8694
S
ma
ll
S
ig
n
a
l
A
C
Mo
d
el
a
n
d
C
lo
s
ed
Lo
o
p
C
o
n
tr
o
l
o
f I
n
terl
ea
ve
d
3
P
h
a
s
e
B
o
o
s
t
…
(
H.
V
.
Gu
r
u
r
a
ja
R
a
o
)
243
rl
1
L
1
ron
11
C
rl
2
L
2
rl
3
L
3
ron
12
R
ron
23
rc
V
in
rl
1
L
1
C
rl
2
L
2
rl
3
L
3
ron
11
R
ron
21
rc
ron
12
V
in
Fig
u
r
e
3
(
c)
State
I
V
Fig
u
r
e
3
(
d
)
State
VI
2
.
1
S
m
a
ll Sig
na
l a
c
m
o
dellin
g
o
f
T
hree
-
P
ha
s
e
B
o
o
s
t
C
o
nv
er
t
er
Fig
u
r
e.
2
s
h
o
w
s
a
T
h
r
ee
-
P
h
ase
b
o
o
s
t
co
n
v
er
ter
w
it
h
s
y
n
c
h
r
o
n
o
u
s
s
w
itc
h
i
n
g
.
Ver
y
lo
w
v
o
ltag
e
d
r
o
p
ac
r
o
s
s
th
e
MO
S
FET
s
co
m
p
ar
ed
to
d
i
o
d
es,
r
esu
ltin
g
in
h
ig
h
er
ef
f
icie
n
c
y
is
t
h
e
p
r
i
m
e
ad
v
a
n
ta
g
e
o
f
s
y
n
ch
r
o
n
o
u
s
s
w
itch
in
g
d
c
-
d
c
co
n
v
er
ter
[
1
4
]
.
T
h
e
co
n
d
u
ctio
n
lo
s
s
es
o
f
t
h
e
MO
SF
E
T
s
ar
e
m
o
d
eled
b
y
o
n
-
r
esis
ta
n
ce
r
on
,
t
h
e
d
c
r
esis
ta
n
c
e
o
f
t
h
e
i
n
d
u
cto
r
as
r
l
a
n
d
eq
u
iv
ale
n
t
s
er
ie
s
r
esi
s
ta
n
ce
o
f
th
e
ca
p
ac
ito
r
as
r
c
.
T
h
e
in
d
u
cto
r
cu
r
r
en
t a
n
d
ca
p
ac
ito
r
v
o
ltag
e
b
ei
n
g
i
n
d
ep
en
d
en
t
s
tat
es o
f
th
e
co
n
v
er
ter
co
m
p
r
is
e
t
h
e
s
tate
v
ec
to
r
.
T
h
e
in
p
u
t v
o
lta
g
e
V
in
(
t)
b
ein
g
in
d
ep
en
d
en
t
s
o
u
r
ce
co
m
p
r
is
e
t
h
e
in
p
u
t v
ec
to
r
as,
(
)
=
[
1
(
)
2
(
)
3
(
)
(
)
]
′
(
1
3
)
u
(
t
)
=
[
V
in
(
t
)
]
(
1
4
)
T
h
e
o
u
tp
u
t v
ec
to
r
is
f
o
r
m
ed
b
y
th
e
o
u
tp
u
t p
o
r
t v
o
ltag
e
v
ar
ia
b
le
V
o
(
t)
y
(
t
)
=
[
v
o
(
t
)
]
(
1
5
)
I
n
o
r
d
er
to
h
av
e
s
ta
te
eq
u
atio
n
s
f
o
r
ea
ch
s
u
b
i
n
ter
v
a
l,
th
e
ci
r
cu
it
is
an
al
y
ze
d
f
o
r
s
ix
d
i
f
f
er
en
t
s
tates
d
u
r
in
g
it
s
s
w
itc
h
in
g
p
er
io
d
.
2
.1
.
1
St
a
t
e
I
:
A
ll
th
e
t
h
r
ee
lo
w
s
id
e
s
w
itc
h
e
s
S
11
,
S
12
a
n
d
S
13
ar
e
clo
s
ed
,
w
h
ile
it
s
co
m
p
le
m
en
tar
y
s
w
i
t
ch
es
S
21
,
S
22
an
d
S
23
ar
e
let
o
p
en
.
.T
h
e
r
ed
u
ce
d
l
in
ea
r
cir
cu
it is
s
h
o
w
n
in
Fig
u
r
e
3
(
a)
T
h
e
s
tate
eq
u
atio
n
s
f
o
r
in
d
u
c
t
o
r
v
o
ltag
e,
L
1
d
i
L1
(
t
)
dt
=
V
in
(
t
)
−
i
L1
(
t
)
(
rl
1
+
r
on
11
)
(
1
6
)
L
2
d
i
L2
(
t
)
dt
=
V
in
(
t
)
−
i
L2
(
t
)
(
rl
2
+
r
on
12
)
(
1
7
)
L
3
d
i
L3
(
t
)
dt
=
V
in
(
t
)
−
i
L3
(
t
)
(
rl
3
+
r
on
13
)
(
1
8
)
C
ap
ac
ito
r
cu
r
r
en
t,
C
d
v
c
(
t
)
dt
=
−
(
v
c
(
t
)
R
+
rc
)
(
1
9
)
a
n
d
Ou
tp
u
t
v
o
ltag
e,
v
o
(
t
)
=
(
v
c
(
t
)
R
R
+
rc
)
(
20)
2
.
1
.
2
St
a
t
e
I
I
:
T
h
e
lo
w
s
id
e
s
w
itc
h
S
12
i
s
tu
r
n
ed
OFF;
w
h
i
le
it’s c
o
m
p
le
m
en
tar
y
S
22
is
t
u
r
n
ed
ON.
T
h
u
s
th
e
s
to
r
ed
en
er
g
y
i
n
in
d
u
cto
r
L
2
is
f
r
ee
w
h
ee
led
t
h
r
o
u
g
h
s
w
itc
h
S
22
.
T
h
u
s
,
th
e
r
ed
u
ce
d
lin
ea
r
cir
cu
i
t is s
h
o
w
n
i
n
Fig
u
r
e
3
(
b
)
T
h
e
p
h
ase
I
an
d
p
h
ase
I
I
I
co
n
tin
u
e
s
to
s
to
r
e
en
er
g
y
,
t
h
u
s
t
h
e
p
h
a
s
e
I
I
in
d
u
cto
r
v
o
ltag
e
i
s
g
iv
e
n
as,
d
i
L2
(
t
)
dt
=
V
in
(
t
)
−
i
L2
(
t
)
(
rl
2
+
+
R
r
c
R
+
rc
)
…
−
v
c
(
t
)
R
R
+
rc
(
2
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8694
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
:
24
0
–
25
1
244
C
ap
ac
ito
r
cu
r
r
en
t,
C
d
v
c
(
t
)
dt
=
i
L2
(
t
)
R
R
+
rc
−
v
c
(
t
)
R
+
rc
(
2
2
)
Ou
tp
u
t v
o
lta
g
e,
v
o
=
(
Rr
c
R
+
rc
)
i
L2
(
t
)
+
(
R
R
+
rc
)
v
c
(
t
)
(
2
3
)
2
.
1
.
3
St
a
t
e
I
I
I
:
State
I
I
I
is
s
i
m
ilar
to
s
tate
I
,
w
h
e
r
e
all
t
h
e
lo
w
s
id
e
s
w
itc
h
es a
r
e
clo
s
ed
an
d
th
e
in
d
u
cto
r
s
s
to
r
e
en
er
g
y
.
2
.
1
.
4
St
a
t
e
I
V
:
C
o
m
p
le
m
en
tar
y
S
23
i
s
tu
r
n
ed
ON.
T
h
u
s
th
e
s
to
r
ed
en
er
g
y
in
in
d
u
cto
r
L
3
is
f
r
ee
w
h
ee
le
d
th
r
o
u
g
h
s
w
itc
h
S
23
.
T
h
e
r
ed
u
ce
d
l
in
ea
r
cir
cu
it is
s
h
o
w
n
in
F
ig
u
r
e
3
(
c)
.
T
h
u
s
t
h
e
p
h
ase
I
I
I
in
d
u
c
to
r
v
o
ltag
e
i
s
g
i
v
e
n
as,
L
3
d
i
L3
(
t
)
dt
=
V
in
(
t
)
−
i
L3
(
t
)
(
rl
3
+
r
on
23
+
R
r
c
R
+
rc
)
…
−
v
c
(
t
)
R
R
+
rc
(
2
4
)
C
ap
ac
ito
r
cu
r
r
en
t,
C
d
v
c
(
t
)
dt
=
i
L3
(
t
)
R
R
+
rc
−
v
c
(
t
)
R
+
rc
(
2
5
)
Ou
tp
u
t v
o
lta
g
e
,
v
o
=
(
Rr
c
R
+
rc
)
i
L3
(
t
)
+
(
R
R
+
rc
)
v
c
(
t
)
(
2
6
)
2
.
1
.
5
Sta
t
e
V
:
S
tate
V
is
s
i
m
i
lar
to
s
tate
I
,
w
h
er
e
all
t
h
e
lo
w
s
id
e
s
w
i
tch
e
s
ar
e
clo
s
ed
a
n
d
th
e
i
n
d
u
cto
r
s
s
to
r
e
en
er
g
y
.
2.
1
.
6
St
a
t
e
VI
:
T
h
e
lo
w
s
id
e
s
w
i
tch
S
11
i
s
tu
r
n
ed
OFF;
w
h
i
le
it
’
s
co
m
p
le
m
e
n
tar
y
S
21
is
tu
r
n
ed
ON.
T
h
u
s
th
e
s
to
r
ed
en
er
g
y
i
n
i
n
d
u
cto
r
L
1
i
s
f
r
ee
w
h
ee
led
th
r
o
u
g
h
s
w
itc
h
S
11
.
T
h
e
r
ed
u
ce
d
lin
ea
r
cir
cu
it
is
s
h
o
w
n
Fig
u
r
e
3
(
d
)
.
T
h
u
s
th
e
p
h
ase
I
in
d
u
cto
r
v
o
lt
ag
e
is
g
iv
e
n
as,
d
i
L1
(
t
)
dt
=
V
in
(
t
)
−
i
L1
(
t
)
(
rl
1
+
r
on
21
+
R
r
c
R
+
rc
)
…
−
v
c
(
t
)
R
R
+
rc
(
2
7
)
C
ap
ac
ito
r
cu
r
r
en
t,
C
d
v
c
(
t
)
dt
=
i
L1
(
t
)
R
R
+
rc
−
v
c
(
t
)
R
+
rc
(
28)
Ou
tp
u
t v
o
lta
g
e,
v
o
=
(
Rr
c
R
+
rc
)
i
L1
(
t
)
+
(
R
R
+
rc
)
v
c
(
t
)
(
2
9
)
T
h
e
s
ix
s
tate
m
atr
ices,
in
p
u
t
v
ec
to
r
s
a
n
d
o
u
t
p
u
t
v
ec
to
r
s
ar
e
id
en
ti
f
ied
a
n
d
e
v
alu
a
ted
f
o
r
s
tate
-
s
p
ac
e
av
er
ag
ed
eq
u
atio
n
s
[
2
]
.
T
h
e
a
p
p
r
o
x
im
a
tio
n
s
co
n
s
id
er
ed
h
er
e
ar
e,
all
th
e
th
r
ee
p
h
ase
in
d
u
ctan
ce
is
s
a
m
e
an
d
its
r
ati
n
g
to
o
,
th
u
s
it
s
d
c
r
esis
t
an
ce
is
ap
p
r
o
x
i
m
atel
y
eq
u
al
t
o
ea
ch
o
th
er
,
an
d
ca
n
b
e
g
iv
e
n
as
r
l
.
S
i
m
ilar
l
y
,
al
l
th
e
s
a
m
e
r
ated
MO
SF
E
T
’
s
o
n
-
r
esis
ta
n
ce
is
ap
p
r
o
x
i
m
ated
to
r
on
an
d
l
et
rl
+
r
on
=
rl
′
.
A
l
s
o
,
R
+
r
c
=
R
as R
>>
r
c
T
h
u
s
,
u
s
in
g
(
5
)
an
d
(
1
6
)
t
o
(
2
9
)
th
e
Av
er
ag
ed
m
a
tr
ix
A
,
is
g
iv
en
b
y
[
−
(
r
l′
+
rc
D
́
L
1
)
0
0
−
D
́
L
1
0
−
(
r
l′
+
rc
D
́
L
2
)
0
−
D
́
L
2
0
0
−
(
r
l′
+
rc
D
́
L
3
)
−
D
́
L
3
D
́
C
D
́
C
D
́
C
−
1
CR
]
(
3
0
)
Si
m
i
lar
l
y
,
u
s
i
n
g
(
6
)
,
(
7
)
an
d
(
1
6
)
to
(
2
9
)
th
e
av
er
ag
ed
m
atr
ix
B
an
d
C
,
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
-
8694
S
ma
ll
S
ig
n
a
l
A
C
Mo
d
el
a
n
d
C
lo
s
ed
Lo
o
p
C
o
n
tr
o
l
o
f I
n
terl
ea
ve
d
3
P
h
a
s
e
B
o
o
s
t
…
(
H.
V
.
Gu
r
u
r
a
ja
R
a
o
)
245
B
=
[
1
L
1
⁄
1
L
2
⁄
1
L
3
⁄
0
]
(
3
1
)
C
=
[
D
́
rc
D
́
rc
D
́
rc
1
]
(
3
2
)
Usi
n
g
(
11
)
an
d
(
12
)
,
v
ec
to
r
co
ef
f
icie
n
t
o
f
d
̂
(
t
)
i
s
g
i
v
e
n
as,
=
[
1
2
3
−
2
]
′
(
3
3
)
N
=
[
−
V
in
rc
R
D
́
2
]
(
3
4
)
Fig
u
r
e
4
.
Sm
all
-
s
ig
n
al
a
c
m
o
d
el
o
f
T
h
r
ee
-
P
h
ase
b
o
o
s
t
c
o
n
v
e
r
te
r
T
h
e
s
m
a
ll
s
i
g
n
al
ac
eq
u
atio
n
s
ar
e
o
b
tain
ed
b
y
p
er
tu
r
b
atio
n
w
it
h
s
m
all
ac
v
ar
iatio
n
an
d
li
n
ea
r
izatio
n
w
it
h
r
e
m
o
v
a
l
o
f
D
C
ter
m
s
an
d
h
i
g
h
er
o
r
d
er
ter
m
s
[
2
]
,
[
1
4
]
.
T
h
u
s
,
s
m
all
-
s
i
g
n
al
m
o
d
el
is
f
o
u
n
d
b
y
ev
a
lu
at
io
n
of
(
9
)
,
(
1
0
)
.
W
h
en
w
r
itte
n
in
s
ca
lar
f
o
r
m
,
th
e
t
h
r
ee
-
p
h
ase
i
n
d
u
cto
r
v
o
ltag
e
s
a
r
e
g
i
v
en
a
s
,
L
1
d
i
̂
L1
(
t
)
dt
=
v
̂
in
(
t
)
−
i
̂
L1
(
t
)
(
rl
′
+
rc
D
́
)
−
v
̂
c
(
t
)
D
́
…
+
(
V
in
D
́
)
d
̂
(
t
)
(
3
5)
L
2
d
i
̂
L2
(
t
)
dt
=
v
̂
in
(
t
)
−
i
̂
L2
(
t
)
(
rl
′
+
rc
D
́
)
−
v
̂
c
(
t
)
D
́
…
+
(
V
in
D
́
)
d
̂
(
t
)
(
3
6
)
L
3
d
i
̂
L3
(
t
)
dt
=
v
̂
in
(
t
)
−
i
̂
L3
(
t
)
(
rl
′
+
rc
D
́
)
−
v
̂
c
(
t
)
D
́
…
+
(
V
in
D
́
)
d
̂
(
t
)
(
3
7
)
T
h
e
ca
p
ac
ito
r
cu
r
r
en
t is g
iv
e
n
as,
C
d
v
̂
c
(
t
)
dt
=
i
̂
L1
(
t
)
D
́
+
i
̂
L2
(
t
)
D
́
+
i
̂
L3
(
t
)
D
́
−
v
̂
c
(
t
)
R
…
−
(
v
̂
in
R
D
́
2
)
d
̂
(
t
)
(
3
8
)
T
h
e
o
u
tp
u
t e
q
u
atio
n
,
v
̂
o
(
t
)
=
(
i
̂
L1
(
t
)
+
i
̂
L2
(
t
)
+
i
̂
L3
(
t
)
)
D
́
rc
−
v
̂
c
(
t
)
…
−
(
v
̂
in
rc
R
D
́
2
)
d
̂
(
t
)
(
3
9
)
C
ir
cu
its
c
o
r
r
es
p
o
n
d
in
g
to
e
q
u
atio
n
s
(
3
5
)
–
(
(
3
9
)
ar
e
co
m
b
in
ed
in
to
a
c
o
m
p
lete
s
m
all
-
s
ig
n
al
ac
eq
u
iv
a
len
t
ci
r
cu
it
m
o
d
el
o
f
n
o
n
-
id
ea
l
th
r
e
e
-
p
h
as
e
b
o
o
s
t
c
o
n
v
er
te
r
as
s
h
o
w
n
in
Fig
u
r
e
4
.
T
h
is
w
ill
ai
d
in
f
r
e
q
u
en
cy
r
es
p
o
n
s
e
b
ase
d
c
o
n
t
r
o
l sy
s
tem
d
esi
gn.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8694
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
:
24
0
–
25
1
246
2
.
2
C
lo
s
ed
l
o
o
p
c
o
n
t
r
o
l
o
f
t
h
re
e
ph
a
s
e
b
o
o
s
t
c
o
n
v
er
t
e
r
Op
en
lo
o
p
ch
ar
ac
ter
is
tics
i
s
e
s
s
e
n
tial
to
an
al
y
s
e
th
e
p
er
f
o
r
m
an
ce
a
n
d
s
tab
ilit
y
o
f
th
e
co
n
tr
o
l
s
y
s
te
m
th
at
r
e
g
u
la
tes
t
h
e
co
n
v
er
ter
o
u
tp
u
t
v
o
lta
g
e.
T
h
e
n
ec
e
s
s
ar
y
tr
an
s
f
e
r
f
u
n
ctio
n
is
o
b
tai
n
ed
b
y
m
a
k
i
n
g
th
e
li
n
e
v
o
ltag
e
v
ar
iatio
n
û
(
s
)
ze
r
o
an
d
th
en
s
o
l
v
i
n
g
f
o
r
th
e
tr
an
s
f
er
f
u
n
ctio
n
f
r
o
m
d
̂
(
s
)
to
v
̂
o
(
s
)
[
2
]
,
[
1
4
]
.
T
h
u
s
,
v
̂
o
(
s
)
d
̂
(
s
)
=
C
(
SI
−
A
)
−
1
M
+
N
(
4
0
)
v
̂
o
d
̂
=
G
do
(
(
1
+
s
ω
es
r
)
(
1
−
s
ω
r
hp
)
(
1
+
s
Q
ω
o
+
s
2
ω
o
2
)
)
(
4
1
)
W
h
er
e,
DC
g
ai
n
i
s
g
i
v
e
n
b
y
,
G
do
=
V
g
(
3R
(
3R
D
′
2
−
rl′
)
(
3R
D
′
2
+
rl′
)
(
3R
D
′
+
D
′
rc
+
rl′
)
)
ω
o
=
√
(
3R
D
′
2
+
D
′
rc
+
rl′
C
L
R
)
;
Q
=
ω
o
(
1
1
CR
+
D
′
rc
+
r
l
′
L
)
;
ω
r
hp
=
1
−
s
(
3
D′
2
R
−
(
r
l
′
)
L
)
;
ω
es
r
=
1
+
(
s
1
C
r
c
⁄
)
T
h
e
th
r
ee
-
p
h
ase
b
o
o
s
t
co
n
v
er
ter
in
its
v
o
lta
g
e
m
o
d
e
co
n
tr
o
l
w
il
l
h
a
v
e
f
o
u
r
m
ain
c
h
ar
ac
t
er
is
tics
,
a
d
o
u
b
le
p
o
le
d
u
e
to
L
C
f
ilter
w
h
i
c
h
m
o
v
es
w
it
h
o
p
er
atin
g
co
n
d
itio
n
s
,
an
E
SR
ze
r
o
d
u
e
to
eq
u
iv
ale
n
t
s
er
ie
s
r
esis
ta
n
ce
o
f
o
u
tp
u
t
ca
p
ac
ito
r
,
R
i
g
h
t
h
a
lf
p
lan
e
ze
r
o
a
n
d
f
in
all
y
a
v
ar
iab
le
g
ai
n
d
ep
en
d
en
t
u
p
o
n
t
h
e
i
n
p
u
t
v
o
ltag
e
o
f
th
e
co
n
v
er
ter
[
2
]
.
C
lo
s
ed
lo
o
p
co
n
tr
o
l
s
y
s
te
m
s
ar
e
u
s
u
all
y
as
s
o
ci
ated
w
it
h
s
t
ab
ilit
y
a
n
d
r
esp
o
n
s
e
t
i
m
e
is
s
u
es
w
h
ic
h
m
a
y
co
n
d
itio
n
all
y
a
f
f
ec
t t
h
e
o
u
tp
u
t;
e
v
en
t
h
o
u
g
h
co
n
tr
o
l lo
o
p
allo
w
s
t
h
e
co
n
v
er
ter
to
ad
j
u
s
t to
lo
ad
v
ar
iatio
n
s
o
r
ch
an
g
es
in
th
e
in
p
u
t
v
o
lta
g
e
[
1
0
]
.
Fo
r
co
m
p
e
n
s
ated
s
y
s
te
m
,
h
i
g
h
DC
g
ai
n
e
n
s
u
r
es
t
h
at
t
h
e
s
tead
y
-
s
ta
te
er
r
o
r
b
etw
ee
n
t
h
e
o
u
tp
u
t
a
n
d
th
e
r
e
f
er
en
ce
s
i
g
n
al
is
s
m
all
[
4
]
,
[
5
]
.
E
n
o
u
g
h
p
h
a
s
e
m
ar
g
in
an
d
b
a
n
d
w
id
th
en
s
u
r
es sat
is
f
ac
to
r
y
s
tab
ili
t
y
m
ar
g
i
n
a
n
d
tr
an
s
ie
n
t r
esp
o
n
s
e
[
4
]
,
[
1
4
]
.
2
.
2
.
1
Rig
ht
ha
lf
pla
ne
ze
ro
A
th
r
ee
-
p
h
a
s
e
b
o
o
s
t
co
n
v
er
ter
in
v
o
lta
g
e
m
o
d
e
co
n
tr
o
l
w
ill
h
av
e
an
ad
d
itio
n
al
ze
r
o
i
n
th
e
r
ig
h
t
h
a
lf
.
W
ith
r
ig
h
t
h
al
f
ze
r
o
,
it
is
a
ch
allen
g
in
g
d
esi
g
n
tas
k
to
s
tab
ilize
co
n
v
er
ter
w
h
en
o
p
er
at
in
g
w
it
h
v
o
lta
g
e
m
o
d
e
co
n
tr
o
l
[
5
]
,
[
9
]
.
R
HP
ze
r
o
i
s
in
tr
o
d
u
ce
d
w
h
en
th
e
d
u
t
y
r
atio
is
in
cr
ea
s
ed
(
lo
w
-
s
id
e
s
w
itc
h
is
o
f
b
o
o
s
t
co
n
v
er
ter
is
s
w
i
tch
ed
o
n
f
o
r
a
lo
n
g
er
d
u
r
atio
n
)
.
T
h
e
o
u
tp
u
t
in
itial
l
y
r
ed
u
ce
s
,
i
n
s
p
ite
o
f
t
h
e
co
n
tr
o
l
co
m
m
an
d
tr
y
in
g
to
i
n
cr
ea
s
e
it.
T
h
is
i
n
f
a
ct
is
th
e
ch
ar
ac
ter
i
s
tics
o
f
a
ze
r
o
in
t
h
e
r
i
g
h
t
h
al
f
; a
r
is
e
i
n
th
e
co
n
tr
o
l c
o
m
m
a
n
d
to
th
e
s
y
s
te
m
r
es
u
lts
in
an
in
i
t
ial
r
ed
u
ctio
n
in
th
e
o
u
tp
u
t
r
es
p
o
n
s
e.
A
f
ter
ab
o
u
t
4
to
5
ti
m
e
s
th
e
ti
m
e
co
n
s
ta
n
t
ass
o
ciate
d
w
ith
t
h
e
r
ig
h
t
h
alf
ze
r
o
,
th
e
o
u
tp
u
t
f
o
llo
w
s
t
h
e
i
n
p
u
t
co
n
tr
o
l
co
m
m
a
n
d
.
Hen
c
e
in
a
s
y
s
te
m
w
i
th
a
R
HP
ze
r
o
,
th
e
co
n
tr
o
l
s
y
s
te
m
w
il
l
ta
k
e
a
ce
r
tain
ti
m
e
to
r
esp
o
n
d
to
an
y
c
h
a
n
g
e
s
i
n
t
h
e
o
u
t
p
u
t;
r
esp
o
n
s
e
i
s
n
o
t
i
m
m
ed
iate
[
5
]
.
I
n
o
r
d
er
to
o
v
er
co
m
e
th
i
s
p
r
o
b
le
m
a
n
d
to
s
tab
ilize
th
e
s
y
s
te
m
,
t
h
e
lo
o
p
b
an
d
w
id
t
h
m
u
s
t
b
e
m
u
c
h
le
s
s
t
h
an
t
h
e
f
r
eq
u
en
c
y
o
f
th
e
r
ig
h
t
h
al
f
ze
r
o
[
7
]
,
[
3
]
.
3.
RE
SU
L
T
S AN
D
D
I
S
CU
SS
I
O
N
3
.
1
T
y
pe
I
I
I
Co
m
pen
s
a
t
o
r
Desig
n P
ro
ce
du
re
T
y
p
e
I
I
I
co
m
p
en
s
ato
r
h
as
a
p
h
ase
a
n
g
le
9
0
°
at
s
o
m
e
f
r
eq
u
e
n
cies.
R
eq
u
ir
ed
p
h
ase
b
o
o
s
t
is
th
er
ef
o
r
e
av
ailab
le
to
attai
n
t
h
e
d
esire
d
p
h
ase
m
ar
g
in
.
F
ig
u
r
e
5
s
h
o
ws
a
clo
s
ed
lo
o
p
th
r
ee
-
p
h
ase
b
o
o
s
t
co
n
v
er
ter
w
it
h
t
y
p
e
I
I
I
co
m
p
en
s
a
to
r
in
its
f
ee
d
b
ac
k
p
ath
.
A
t
y
p
e
I
I
I
co
m
p
e
n
s
ato
r
w
ill
h
a
v
e
t
w
o
ze
r
o
s
an
d
th
r
ee
p
o
les,
w
i
th
a
p
o
le
at
th
e
o
r
ig
in
[
3
]
.
Her
e,
it i
s
in
ten
d
ed
to
p
lace
ze
r
o
s
co
in
c
id
en
t,
o
n
e
p
o
le
at
o
r
i
g
in
an
d
t
h
e
r
e
m
ai
n
in
g
p
o
le
s
co
in
cid
en
t to
ea
ch
o
t
h
er
.
T
h
u
s
eq
u
atio
n
(
4
2
)
g
iv
es t
h
e
d
esire
d
tr
an
s
f
er
f
u
n
ctio
n
.
C
(
s
)
=
K
(
1
+
s
ω
Z
)
2
s
(
1
+
s
ω
P
)
2
(
4
2
)
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
-
8694
S
ma
ll
S
ig
n
a
l
A
C
Mo
d
el
a
n
d
C
lo
s
ed
Lo
o
p
C
o
n
tr
o
l
o
f I
n
terl
ea
ve
d
3
P
h
a
s
e
B
o
o
s
t
…
(
H.
V
.
Gu
r
u
r
a
ja
R
a
o
)
247
Fig
u
r
e
5
.
C
lo
s
ed
l
o
o
p
v
o
lt
ag
e
m
o
d
e
co
n
t
r
o
ll
ed
th
r
e
e
-
p
h
ase
b
o
o
s
t
co
n
v
e
r
t
er
Fro
m
(
4
2
)
,
at
an
y
f
r
eq
u
e
n
c
y
ω
,
th
e
a
m
p
l
itu
d
e
a
n
d
p
h
ase
o
f
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
ar
e
g
i
v
e
n
b
y
(
4
3
)
an
d
(
4
4
)
r
esp
ec
tiv
el
y
a
n
d
(
4
4
)
is
r
e
w
r
itt
en
as (
4
5
)
.
C
(
j
ω
)
=
K
ω
|
(
1
+
j
ω
ω
z
)
2
|
|
(
1
+
j
ω
ω
P
)
2
|
=
K
ω
1
+
(
ω
ω
Z
)
2
1
+
(
ω
ω
P
)
2
(
4
3
)
φ
[
C
(
j
ω
)
]
=
φ
(
K
j
ω
)
+
φ
(
1
+
j
ω
ω
Z
)
2
−
φ
(
1
+
j
ω
ω
P
)
2
(
4
4
)
φ
[
C
(
j
ω
)
]
=
−
π
2
+
2φ
(
1
+
j
ω
ω
Z
)
−
2φ
(
1
+
j
ω
ω
P
)
(
4
5
)
Fro
m
(
4
5
)
,
th
e
p
h
as
e
o
f
C
(
jω
)
co
m
p
r
is
e
o
f
a
co
n
s
ta
n
t
v
alu
e
o
f
–
π
/2
d
u
e
to
t
h
e
p
o
le
at
t
h
e
o
r
i
g
in
,
an
d
a
v
ar
iab
le
p
o
r
tio
n
as a
f
u
n
ctio
n
o
f
f
r
eq
u
e
n
c
y
ω
,
φ
v
(
j
ω
)
=
2
ta
n
−
1
ω
(
ω
P
−
ω
Z
)
ω
2
+
ω
Z
ω
P
(
4
6
)
A
t t
h
e
g
eo
m
etr
ic
m
ea
n
o
f
th
e
ω
z
an
d
ω
p
th
e
m
a
x
i
m
u
m
v
ar
ia
b
le
p
h
ase
an
g
le
o
cc
u
r
s
a
n
d
is
g
iv
e
n
as,
ω
m
=
√
ω
P
ω
Z
(
4
7
)
Her
e,
let
ω
m
b
e
th
e
m
ax
i
m
u
m
p
h
ase
f
r
eq
u
e
n
c
y
o
f
a
t
y
p
e
I
I
I
co
m
p
e
n
s
ato
r
.
L
et
k
=
ω
P
ω
Z
(
4
8
)
T
h
en
th
e
m
ax
i
m
u
m
p
h
ase
o
f
φ
v
(
ω
)
ca
n
b
e
w
r
i
tten
a
s
,
φ
v
(
ω
m
)
=
2
ta
n
−
1
(
k
−
1
2
√
k
)
(
4
9
)
Fin
all
y
,
t
h
e
m
a
x
i
m
u
m
p
h
ase
o
f
th
e
t
y
p
e
I
I
I
co
m
p
en
s
ato
r
is
g
iv
en
a
s
,
φ
[
C
(
j
ω
m
)
]
=
−
π
2
+
2
ta
n
−
1
(
k
−
1
2
√
k
)
(
5
0
)
Vg
rl1
L1
ron
11
C
Driver
ron
21
rc
Load
Vref
+
_
S
11
S
21
Vc
d
PWM
rl2
L2
ron
12
Driver
–
120º
ron
22
S
12
S
22
rl3
L3
ron
13
Driver
–
240º
ron
23
S
13
S
23
Vi
Vo
C
2
R2
C
1
C3
R3
R1
+
_
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8694
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
:
24
0
–
25
1
248
Her
e,
‘
k
’
is
a
m
ea
s
u
r
e
o
f
t
h
e
s
ep
ar
atio
n
b
et
w
ee
n
t
h
e
ze
r
o
an
d
p
o
le
f
r
eq
u
en
c
y
.
Du
e
to
R
HP
ze
r
o
in
th
e
b
o
o
s
t c
o
n
v
er
ter
,
it is
n
o
n
-
m
i
n
i
m
u
m
p
h
a
s
e
s
y
s
te
m
,
b
ec
au
s
e
o
f
w
h
ich
e
x
tr
a
p
h
ase
la
g
is
ad
d
ed
to
th
e
s
y
s
te
m
an
d
it
m
ak
e
s
t
h
e
s
y
s
te
m
co
n
d
itio
n
all
y
s
tab
le.
D
u
e
to
R
HP
ze
r
o
,
th
e
s
y
s
te
m
’
s
p
h
a
s
e
p
lo
t
g
o
es
b
elo
w
-
1
8
0
º
,
(
m
o
r
e
n
e
g
ati
v
e)
,
b
u
t
co
m
e
s
b
a
ck
a
g
ai
n
to
-
1
8
0
º
.
T
h
u
s
,
it
is
r
eq
u
ir
ed
to
h
a
v
e
a
p
h
a
s
e
b
o
o
s
t
at
m
a
x
i
m
u
m
p
h
a
s
e
lag
f
r
eq
u
e
n
c
y
ω
mp
[
3
]
.
A
ls
o
,
t
o
attain
d
esire
d
p
h
ase
m
ar
g
i
n
an
d
f
o
r
lo
o
p
s
tab
ilit
y
,
p
h
ase
b
o
o
s
t
is
n
ec
ess
ar
y
at
th
e
cr
o
s
s
o
v
er
f
r
eq
u
en
c
y
to
o
.
T
h
u
s
th
e
m
ax
i
m
u
m
p
h
ase
b
o
o
s
t
f
r
eq
u
en
c
y
ω
m
b
y
t
y
p
e
I
I
I
c
o
m
p
e
n
s
ato
r
is
r
eq
u
ir
ed
to
b
e
p
lace
d
s
o
m
e
w
h
er
e
b
et
w
ee
n
ω
mp
a
n
d
ω
c
[
3
]
.
T
h
e
ω
m
i
s
g
iv
e
n
b
y
,
ω
m
=
α
√
ω
mp
ω
c
(
5
1
)
I
n
o
r
d
er
t
o
attain
th
e
d
esire
d
p
h
ase
m
ar
g
i
n
an
d
b
an
d
w
id
th
,
α
n
ee
d
to
b
e
a
d
j
u
s
ted
.
T
h
u
s
,
b
y
ad
j
u
s
tin
g
th
e
‘
α
’
o
n
tr
ial
a
n
d
er
r
o
r
b
asis
,
u
n
co
n
d
itio
n
al
s
tab
ili
t
y
ca
n
b
e
ac
h
iev
ed
.
On
ce
t
h
e
ω
m
is
s
el
ec
ted
f
o
r
th
e
g
i
v
e
n
s
y
s
te
m
,
a
n
d
p
r
o
v
id
ed
th
e
ω
m
,
G
p
, ω
mp
a
n
d
φ
p
ar
e
n
o
ted
.
Usi
n
g
(
5
0
)
an
d
(
4
6
)
,
it c
an
b
e
w
r
itt
en
as,
2
ta
n
−
1
(
ω
c
(
ω
p
−
ω
z
)
ω
c
2
+
ω
z
ω
p
)
=
φ
m
−
φ
p
−
π
2
(
5
2
)
ω
c
(
ω
p
−
ω
z
)
ω
c
2
+
ω
p
ω
z
=
ta
n
(
φ
m
−
φ
p
2
−
π
4
)
(
5
3
)
B
ased
o
n
(
5
2
)
an
d
(
5
3
)
,
th
e
f
o
llo
w
i
n
g
t
w
o
e
q
u
atio
n
s
ar
e
o
b
tain
ed
,
ω
p
ω
z
=
ω
m
2
(
5
4
)
ω
p
−
ω
z
=
ω
d
(
5
5
)
W
h
er
e
ω
d
is
d
ef
in
ed
as,
ω
d
=
ta
n
(
φ
m
−
φ
P
2
−
π
4
)
(
ω
d
+
ω
mp
)
(
5
6
)
Fro
m
(
5
4
)
an
d
(
5
5
)
,
th
e
co
m
p
en
s
ato
r
’
s
ze
r
o
an
d
p
o
le
f
r
eq
u
en
cies a
r
e
g
i
v
e
n
as,
ω
z
=
0
.
5
(
√
ω
d
2
+
ω
m
2
−
ω
d
)
(
6
0
)
ω
p
=
0
.
5
(
√
ω
d
2
+
ω
m
2
+
ω
d
)
(
6
1
)
T
h
e
s
ep
ar
atio
n
f
ac
to
r
is
b
e
ca
lcu
lated
as,
k
=
√
ω
d
2
+
ω
m
2
+
ω
d
√
ω
d
2
+
ω
m
2
−
ω
d
(
6
2
)
Fro
m
(
5
0
)
,
it is
k
n
o
w
n
t
h
at,
|
C
(
j
ω
c
)
|
=
K
ω
c
1
+
(
ω
c
ω
Z
)
2
1
+
(
ω
c
ω
P
)
2
A
t t
h
e
cr
o
s
s
o
v
er
f
r
eq
u
e
n
c
y
,
|
C
(
j
ω
c
)
|
G
P
=
1
T
h
u
s
,
th
e
g
ain
K
is
,
K
=
ω
c
(
1
+
(
ω
c
ω
P
)
2
)
G
P
(
1
+
(
ω
c
ω
z
)
2
)
(
6
3
)
(
6
4
)
(
6
5
)
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
-
8694
S
ma
ll
S
ig
n
a
l
A
C
Mo
d
el
a
n
d
C
lo
s
ed
Lo
o
p
C
o
n
tr
o
l
o
f I
n
terl
ea
ve
d
3
P
h
a
s
e
B
o
o
s
t
…
(
H.
V
.
Gu
r
u
r
a
ja
R
a
o
)
249
F
ig
u
re
6
.
F
re
q
u
e
n
c
y
re
sp
o
n
se
o
f
T
h
re
e
-P
h
a
se
b
o
o
st co
n
v
e
rt
er
3
.
2
Co
ntr
o
l Sy
s
t
e
m
De
s
ig
n f
o
r
T
hree
-
P
ha
s
e
B
o
o
s
t
Co
nv
e
rt
er
Desig
n
s
p
ec
i
f
icatio
n
s
o
f
t
h
r
ee
p
h
ase
b
o
o
s
t c
o
n
v
er
ter
is
g
iv
e
n
T
a
b
le.
1
.
T
ab
le.
1
.
T
h
r
ee
-
P
h
ase
B
o
o
s
t c
o
n
v
er
ter
d
esig
n
s
p
ec
i
f
icatio
n
s
S
p
e
c
i
f
i
c
a
t
i
o
n
s
V
in
1
2
V
V
o
ut
4
0
V
P
o
w
e
r
7
0
0
w
a
t
t
s
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
1
0
0
k
H
z
T
h
r
e
e
-
P
h
a
se
C
o
mp
o
n
e
n
t
d
e
t
a
i
l
s
P
h
a
se
I
n
d
u
c
t
a
n
c
e
,
D
C
R
S
w
i
t
c
h
O
N
R
e
si
st
a
n
c
e
mΩ
C
a
p
a
c
i
t
a
n
c
e
,
ESR
I
6
.
0
8
µ
H
,
5
mΩ
S
11
2
0
5
6
µ
F
,
1
0
mΩ
S
21
2
0
II
6
.
0
8
µ
H
,
5
mΩ
S
12
2
0
S
22
20
III
6
.
0
8
µ
H
,
5
mΩ
S
13
20
S
23
20
3
.
2
.
1
C
o
m
pen
s
a
t
o
r
Desig
n
Fig
u
r
e
6
s
h
o
w
s
t
h
e
o
p
en
lo
o
p
,
co
n
tr
o
l
-
to
-
o
u
tp
u
t,
u
n
co
m
p
e
n
s
ated
,
B
o
d
e
p
lo
t
f
o
r
t
h
r
ee
-
p
h
ase
b
o
o
s
t
co
n
v
er
ter
.
Fro
m
Fi
g
u
r
e
6
th
e
co
m
p
e
n
s
ato
r
ca
n
b
e
d
esig
n
e
d
b
y
f
o
llo
w
i
n
g
t
h
e
p
r
o
ce
d
u
r
e
g
iv
e
n
f
r
o
m
(
4
2
)
to
(
6
2
)
.
T
h
e
cr
o
s
s
o
v
er
f
r
eq
u
e
n
c
y
i.e
.
th
e
b
an
d
w
id
t
h
o
f
t
h
e
co
m
p
e
n
s
ated
s
y
s
te
m
is
g
en
er
all
y
ch
o
s
e
n
to
b
e
less
th
an
o
n
e
-
f
i
f
t
h
o
f
s
w
itc
h
i
n
g
f
r
e
q
u
en
c
y
[
2
]
,
[
4
]
.
I
n
th
is
ca
s
e,
t
h
e
ch
o
s
e
n
cr
o
s
s
o
v
er
f
r
eq
u
e
n
c
y
is
7
k
Hz.
T
h
e
g
ain
an
d
th
e
p
h
ase
a
n
g
le
at
7
k
Hz
ar
e
n
o
ted
to
aid
in
co
m
p
e
n
s
a
t
o
r
d
esig
n
.
F
r
o
m
Fi
g
u
r
e
6
,
th
e
g
ain
an
d
t
h
e
p
h
a
s
e
an
g
le
at
7
k
Hz
w
er
e
f
o
u
n
d
to
b
e
3
6
.
5
d
B
an
d
-
1
5
9
°
r
esp
ec
tiv
el
y
an
d
also
t
h
e
m
a
x
i
m
u
m
p
h
ase
lag
d
u
e
to
R
HP
ze
r
o
d
ip
s
at
7
0
k
Hz.
A
p
h
as
e
m
ar
g
i
n
of
70°
°
is
co
n
s
id
e
r
ed
to
en
s
u
r
e
g
o
o
d
s
tab
ilit
y
an
d
b
etter
tr
an
s
ien
t
r
esp
o
n
s
e.
-
6
0
-
4
0
-
2
0
0
20
40
60
80
M
a
g
n
i
t
u
d
e
(
d
B
)
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
90
135
180
225
270
315
360
P
h
a
s
e
(
d
e
g
)
Bode
Diagram
Gm
=
10.7 dB (at 4.39e
+
004 Hz) , Pm
=
69.3 de
g (at 6.99e
+
003 Hz)
F
r
e
q
u
e
n
c
y
(
H
z
)
U
n
co
m
p
e
n
sa
t
e
d
sy
st
e
m
C
o
m
p
e
n
sa
t
e
d
sy
st
e
m
-
6
0
-
4
0
-
2
0
0
20
40
60
80
M
a
g
n
i
t
u
d
e
(
d
B
)
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
90
135
180
225
270
315
360
P
h
a
s
e
(
d
e
g
)
H
i
g
h
D
C
G
a
i
n
Evaluation Warning : The document was created with Spire.PDF for Python.