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I
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8
6
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4
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i
m
p
u
l
s
e
p
o
w
e
r
m
a
k
e
u
s
e
o
f
t
h
e
c
a
p
a
c
i
t
o
r
c
h
a
r
g
i
n
g
p
o
w
e
r
s
u
p
p
l
y
(
C
C
P
S
)
s
u
c
h
f
l
a
s
h
l
a
m
p
s
,
m
e
d
i
c
a
l
s
te
r
i
l
i
z
at
i
o
n
,
r
o
c
k
c
r
u
s
h
i
n
g
,
a
n
d
e
l
e
c
t
r
o
m
a
g
n
e
t
i
c
r
a
il
g
u
n
s
,
a
m
o
n
g
m
a
n
y
o
t
h
e
r
a
p
p
l
i
c
a
t
i
o
n
a
r
e
as
.
A
f
u
ll
b
r
i
d
g
e
c
o
n
v
e
r
t
e
r
a
l
o
n
g
w
i
t
h
s
e
r
i
es
p
h
a
s
e
-
s
h
i
f
t
w
it
h
p
a
r
a
l
l
el
i
n
p
u
t
an
d
o
u
t
p
u
t
f
o
r
C
C
PS
i
s
d
e
s
i
g
n
e
d
a
n
d
e
x
a
m
i
n
e
d
i
n
t
h
i
s
w
o
r
k
[
6
]
.
A
d
d
i
ti
o
n
a
l
l
y
,
a
t
h
o
r
o
u
g
h
a
n
a
l
y
s
i
s
o
f
t
h
e
i
n
d
u
s
t
r
i
a
l
u
s
es
o
f
L
L
C
r
e
s
o
n
a
n
t
c
o
n
v
e
r
t
e
r
s
i
s
l
e
d
,
w
it
h
a
f
o
c
u
s
o
n
s
o
l
a
r
s
y
s
t
e
m
s
,
el
e
c
tr
i
c
v
e
h
i
cl
e
(
E
V
)
c
h
a
r
g
i
n
g
,
p
o
we
r
s
u
p
p
l
y
f
o
r
L
E
D
l
i
g
h
t
i
n
g
d
r
i
v
e
r
s
,
a
n
d
l
i
q
u
i
d
c
r
y
s
t
a
l
d
i
s
p
l
a
y
(
L
C
D
)
t
e
l
e
v
is
i
o
n
s
[
1
]
.
F
o
r
h
y
b
r
i
d
DC
s
y
s
te
m
s
,
t
h
r
e
e
-
p
o
r
t
r
es
o
n
a
n
t
t
o
p
o
l
o
g
i
e
s
s
u
c
h
as
L
C
C
,
L
L
C
,
a
n
d
L
C
L
a
r
e
c
r
u
ci
a
l
b
ec
a
u
s
e
t
h
e
y
o
f
f
e
r
s
o
f
t sw
i
t
c
h
i
n
g
o
p
e
r
a
t
io
n
w
i
t
h
z
e
r
o
(
Z
VS
)
f
o
r
a
c
t
i
v
e
s
wi
t
c
h
es
a
n
d
z
e
r
o
c
u
r
r
e
n
t
s
w
it
c
h
i
n
g
(
Z
C
S
)
f
o
r
d
i
o
d
e
r
e
c
t
i
f
i
e
r
s
,
w
h
i
c
h
i
n
c
r
ea
s
es
s
y
s
t
e
m
d
e
p
e
n
d
a
b
i
li
t
y
a
n
d
e
f
f
i
c
i
e
n
c
y
.
C
C
a
n
d
C
V
m
o
d
e
s
a
r
e
a
ls
o
u
s
e
d
f
o
r
b
a
t
ter
y
c
h
a
r
g
i
n
g
.
B
y
r
e
d
u
c
i
n
g
r
e
a
ct
i
v
e
l
o
s
s
es
,
r
e
s
o
n
a
n
t
c
a
p
a
c
i
t
o
r
s
f
u
r
t
h
e
r
i
m
p
r
o
v
e
p
e
r
f
o
r
m
a
n
c
e
b
y
r
e
m
o
v
i
n
g
D
C
b
i
a
s
[
7
]
,
[
8
]
.
T
h
is
ar
ticle
s
u
g
g
ests
a
n
ew
AOC
ap
p
r
o
ac
h
th
at
o
v
er
co
m
es
th
e
d
is
ad
v
an
ta
g
es
o
f
th
e
tr
a
d
i
tio
n
al
C
C
ch
ar
g
in
g
s
tr
ateg
y
o
f
len
g
th
y
c
h
ar
g
in
g
tim
es
a
n
d
t
h
e
C
P
ch
a
r
g
in
g
ap
p
r
o
ac
h
o
f
h
ig
h
r
eso
n
a
n
t
cu
r
r
en
t
s
tr
ess
b
y
u
tili
zin
g
an
L
C
C
r
eso
n
an
t
co
n
v
er
ter
'
s
ca
p
ac
ity
to
ac
h
iev
e
a
h
ig
h
er
a
v
er
ag
e
o
u
tp
u
t
c
u
r
r
e
n
t.
T
h
ese
s
p
ee
d
s
u
p
th
e
ch
ar
g
in
g
p
r
o
ce
s
s
all
th
e
way
th
r
o
u
g
h
[
9
]
.
B
ased
o
n
s
tate
p
lan
e
an
aly
s
is
,
th
i
s
s
t
u
d
y
ex
am
i
n
es
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
witch
in
g
f
r
eq
u
e
n
cy
an
d
o
u
tp
u
t
v
o
ltag
e
wh
en
m
ain
tain
in
g
a
f
ix
ed
li
m
itin
g
v
alu
e
f
o
r
th
e
r
eso
n
an
t
cu
r
r
e
n
t
[
1
0
]
.
T
h
is
s
t
u
d
y
p
r
esen
ts
a
d
esig
n
m
eth
o
d
o
lo
g
y
a
n
d
an
aly
tical
f
o
r
m
u
l
atio
n
f
o
r
a
p
ar
allel
-
r
eso
n
an
t
in
v
er
ter
with
lo
a
d
-
in
d
ep
en
d
e
n
t
Z
C
S
.
Desp
ite
ch
a
n
g
es
in
lo
ad
,
th
e
s
u
g
g
ested
i
n
v
er
ter
m
ain
tain
s
a
co
n
s
is
ten
t
o
u
tp
u
t
v
o
ltag
e
am
p
litu
d
e
an
d
Z
C
S
[
1
1
]
.
Po
wer
f
a
cto
r
p
r
e
-
r
eg
u
latio
n
is
an
o
t
h
er
cr
u
cial
elem
en
t
f
o
r
en
h
an
cin
g
p
o
wer
q
u
ality
an
d
r
ed
u
cin
g
lo
s
s
es,
p
ar
ticu
lar
ly
in
E
V
ch
ar
g
er
s
an
d
C
C
PS
.
B
y
u
tili
zin
g
f
ewe
r
co
m
p
o
n
en
ts
an
d
o
f
f
er
i
n
g
m
o
r
e
ef
f
ec
tiv
e
en
e
r
g
y
co
n
v
er
s
io
n
,
th
e
b
r
id
g
eless
is
o
lated
h
alf
-
b
r
id
g
e
c
o
n
v
e
r
ter
ar
ch
itectu
r
e
p
er
m
its
in
h
er
en
t
p
o
wer
f
ac
to
r
c
o
r
r
ec
tio
n
[
1
2
]
.
T
h
is
s
tu
d
y
s
u
g
g
ests
a
th
r
ee
-
p
h
ase
wy
e
-
wy
e
c
o
u
p
le
d
C
L
L
L
C
r
eso
n
an
t
co
n
v
er
ter
as
th
e
b
asis
f
o
r
a
b
id
ir
ec
tio
n
al
o
n
b
o
ar
d
ch
ar
g
in
g
s
y
s
tem
.
A
th
r
ee
-
p
h
ase
wy
e
-
wy
e
lin
k
ed
C
L
L
L
C
r
eso
n
an
t
c
o
n
v
er
ter
at
th
e
b
ac
k
an
d
a
b
id
ir
ec
tio
n
al
to
tem
p
o
le
co
n
v
er
ter
at
th
e
f
r
o
n
t
m
ak
e
u
p
its
two
-
s
tag
e
d
esi
g
n
.
Pu
ls
e
f
r
eq
u
en
c
y
m
o
d
u
latio
n
is
u
s
ed
b
y
th
is
th
r
ee
-
s
tag
e,
r
ea
r
-
s
tag
e,
wy
e
-
wy
e
co
n
n
ec
ted
C
L
L
L
C
r
eso
n
an
t
co
n
v
er
ter
to
co
n
f
ir
m
a
co
n
s
tan
t
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t
f
o
r
th
e
ch
ar
g
in
g
s
y
s
tem
[
1
3
]
.
T
h
is
an
aly
s
es
th
e
d
esi
g
n
an
d
o
p
e
r
atio
n
o
f
a
s
er
ies
r
e
s
o
n
an
t
co
n
v
er
ter
,
wh
ich
is
em
p
lo
y
ed
as
a
co
n
s
ta
n
t
cu
r
r
en
t
p
o
wer
s
o
u
r
ce
with
co
n
tr
o
llab
le
o
u
t
p
u
t
cu
r
r
en
t
[
1
4
]
.
T
o
p
r
ev
en
t
h
i
g
h
-
v
o
ltag
e
s
tr
ik
in
g
ar
cs,
a
h
ig
h
-
v
o
ltag
e
DC
p
o
wer
s
u
p
p
ly
th
at
u
s
es
s
er
ies
r
eso
n
an
t
co
n
s
tan
t
cu
r
r
e
n
t
ch
ar
g
in
g
is
d
esig
n
ed
[
1
5
]
.
a
r
ec
o
n
f
ig
u
r
ab
le
r
eso
n
an
t
c
o
n
v
e
r
ter
with
a
l
o
w
co
m
p
o
n
en
t
co
u
n
t
is
r
ec
o
m
m
en
d
ed
in
[
1
6
]
f
o
r
C
V
an
d
C
C
b
atter
y
ch
ar
g
in
g
f
o
r
elec
tr
ic
v
eh
icles,
Z
VS
-
ca
p
ab
le
s
in
g
le
-
s
tag
e
f
u
ll
-
b
r
id
g
e
co
n
v
er
ter
s
ca
n
h
an
d
le
l
ar
g
e
v
o
ltag
e
r
an
g
es
an
d
h
ig
h
-
p
o
wer
le
v
els,
wh
ich
m
ak
es
t
h
em
ap
p
r
o
p
r
iate
f
o
r
in
tr
icate
AC
-
DC
o
r
DC
-
AC
tr
an
s
itio
n
s
u
n
d
er
ch
an
g
ea
b
l
e
lo
ad
cir
cu
m
s
tan
ce
s
[
1
7
]
.
B
y
u
s
in
g
r
eso
n
an
t
f
r
eq
u
e
n
cy
in
s
tead
o
f
s
witch
in
g
f
r
eq
u
en
cy
,
in
ter
leav
ed
to
p
o
lo
g
ies
in
p
u
ls
e
f
r
eq
u
en
cy
m
o
d
u
latio
n
(
PF
M)
co
n
v
er
ter
s
d
ec
r
ea
s
e
cu
r
r
e
n
t r
i
p
p
le
an
d
d
is
p
er
s
e
lo
ad
c
u
r
r
en
t
ac
r
o
s
s
m
an
y
p
h
ases
[
1
8
]
.
Asy
m
m
etr
ic
C
L
L
C
r
eso
n
an
t
co
n
v
er
ter
s
,
o
n
th
e
o
th
e
r
h
an
d
,
p
r
o
v
id
e
b
i
d
ir
ec
tio
n
al
p
o
wer
tr
a
n
s
m
is
s
io
n
with
ad
ap
tiv
e
s
o
f
t
s
tar
t
tech
n
iq
u
es
th
at
p
r
io
r
itize
cu
r
r
e
n
t
lim
itatio
n
s
an
d
p
er
m
it
s
ea
m
less
o
p
er
atio
n
u
n
d
er
a
r
an
g
e
o
f
lo
ad
cir
cu
m
s
tan
ce
s
[
1
9
]
.
Du
e
t
o
its
b
e
n
ef
its
,
wh
ic
h
in
clu
d
e
c
o
n
tin
u
o
u
s
lin
ea
r
ity
,
lo
w
c
h
ar
g
in
g
tim
e,
h
ig
h
ef
f
icien
cy
,
lo
w
h
ea
t
m
a
n
ag
em
en
t
s
y
s
tem
,
a
n
d
less
lo
s
s
es,
th
e
co
n
s
tan
t
cu
r
r
e
n
t
(
C
C
)
ch
ar
g
in
g
s
tr
ateg
y
h
as
o
u
tp
er
f
o
r
m
ed
t
h
e
co
n
s
ta
n
t
v
o
ltag
e
(
C
V)
ch
ar
g
in
g
tec
h
n
iq
u
e
[
2
0
]
.
T
h
e
d
is
ad
v
a
n
tag
es
o
f
s
im
u
ltan
eo
u
s
ch
ar
g
in
g
u
s
in
g
s
ep
a
r
ate
v
o
lta
g
e
-
f
ed
L
L
C
r
eso
n
an
t
c
o
n
v
e
r
ter
s
in
clu
d
e
two
-
s
tag
e
c
o
n
v
e
r
s
io
n
lo
s
s
es
as
well
as
h
ig
h
er
ex
p
e
n
s
es,
v
o
lu
m
e,
a
n
d
co
n
tr
o
l
co
m
p
lex
ity
.
T
h
is
wo
r
k
a
d
d
r
ess
es
th
ese
p
r
o
b
lem
s
b
y
in
te
g
r
atin
g
L
L
C
r
eso
n
an
t
co
n
v
er
ter
with
an
is
o
lated
q
u
asi
-
Z
s
o
u
r
ce
in
v
er
ter
f
o
r
a
s
in
g
le
-
s
tag
e
co
n
v
er
s
io
n
at
a
v
ar
ia
b
le
v
o
lta
g
e
lev
el
f
o
r
a
s
im
u
ltan
eo
u
s
ch
ar
g
in
g
s
y
s
tem
[
2
1
]
.
T
h
e
C
2
L
3
r
e
s
o
n
an
t
to
p
o
lo
g
y
is
u
s
ed
to
ac
h
iev
e
a
f
air
b
alan
ce
b
etwe
en
th
o
s
e
m
ea
s
u
r
es.
Hig
h
ac
cu
r
ac
y
an
d
q
u
ick
s
p
ee
d
a
r
e
g
u
ar
an
tee
d
b
y
th
e
s
u
g
g
este
d
eq
u
alize
r
,
wh
ich
h
y
b
r
id
izes c
o
n
s
tan
t c
u
r
r
e
n
t (
C
C
)
an
d
co
n
s
tan
t v
o
ltag
e
(
C
V)
b
alan
ce
in
n
u
m
er
o
u
s
eq
u
aliza
t
io
n
s
tag
es [
2
2
]
.
T
h
i
s
p
a
p
e
r
s
u
g
g
e
s
t
s
a
b
i
d
i
r
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c
t
i
o
n
a
l
w
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l
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s
p
o
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t
r
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n
s
m
i
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i
o
n
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y
s
t
e
m
d
e
s
i
g
n
f
o
r
a
p
o
w
e
r
b
a
n
k
.
T
h
e
p
r
o
p
o
s
e
d
d
e
s
i
g
n
i
s
b
a
s
e
d
o
n
c
i
r
c
u
i
t
s
f
o
r
d
e
t
e
c
t
i
n
g
A
C
c
u
r
r
e
n
t
,
v
o
l
t
a
g
e
,
a
n
d
p
h
a
s
e
,
b
i
d
i
r
e
c
t
i
o
n
a
l
A
C
–
D
C
a
n
d
b
i
d
i
r
e
c
t
i
o
n
a
l
D
C
–
D
C
c
i
r
c
u
i
t
s
,
a
n
d
a
n
M
S
P
4
3
0
L
M
C
U
f
u
n
c
t
i
o
n
i
n
g
a
s
a
c
o
n
t
r
o
l
l
e
r
.
D
e
s
i
g
n
g
i
v
e
n
i
n
[
2
3
]
m
i
g
h
t
i
m
p
r
o
v
e
p
o
w
e
r
b
a
n
k
s
'
m
o
b
i
l
i
t
y
w
h
i
l
e
a
c
h
i
e
v
i
n
g
B
W
P
T
b
a
s
e
d
o
n
t
h
e
s
i
m
u
l
a
t
i
o
n
f
i
n
d
i
n
g
s
.
I
n
t
h
i
s
w
o
r
k
,
P
2
r
e
s
o
n
a
n
t
c
o
n
f
i
g
u
r
a
t
i
o
n
i
s
c
o
n
s
i
d
e
r
e
d
f
o
r
f
a
s
t
-
c
h
a
r
g
i
n
g
a
p
p
l
i
c
a
t
i
o
n
s
w
i
t
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c
o
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t
a
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r
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t
o
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t
p
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f
o
r
d
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f
f
e
r
e
n
t
l
o
a
d
c
o
n
d
i
t
i
o
n
s
.
2.
O
B
J
E
CT
I
V
E
S O
F
T
H
E
W
O
RK
ARE AS F
O
L
L
O
WS
P
o
w
e
r
c
o
n
v
e
r
t
e
r
s
w
o
r
k
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n
t
h
e
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d
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a
o
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r
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n
a
n
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n
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c
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a
p
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n
d
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d
u
c
t
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v
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a
c
t
a
n
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e
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s
c
a
n
c
e
l
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a
c
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t
w
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t
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m
m
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t
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n
c
e
c
o
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v
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t
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s
,
o
r
r
e
s
o
n
a
n
t
c
o
n
v
e
r
t
e
r
s
(
R
C
)
.
T
h
i
s
r
e
s
u
l
t
s
i
n
d
e
c
r
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a
s
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d
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o
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c
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V
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a
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p
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o
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a
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E
M
I
.
R
e
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a
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d
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q
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
183
2
-
18
39
1834
o
v
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r
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d
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b
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p
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a
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l
c
o
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b
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a
t
i
o
n
s
)
.
T
h
e
P
2
-
RC
,
w
h
i
c
h
i
s
a
h
y
b
r
i
d
c
o
n
f
i
g
u
r
a
t
i
o
n
,
o
f
f
e
r
s
g
r
e
a
t
f
l
e
x
i
b
i
l
i
t
y
,
h
e
a
l
t
h
i
e
r
l
o
a
d
r
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g
u
l
a
t
i
o
n
,
a
n
d
i
m
p
r
o
v
e
d
e
f
f
i
c
i
e
n
c
y
u
n
d
e
r
v
a
r
i
o
u
s
o
p
e
r
a
t
i
n
g
c
i
r
c
u
m
s
t
a
n
c
e
s
:
i
)
T
o
d
e
r
i
v
e
m
a
t
h
e
m
a
t
i
c
a
l
m
o
d
e
l
i
n
g
o
f
t
h
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P
2
r
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s
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a
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t
c
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v
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r
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r
;
ii
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D
e
s
i
g
n
P
2
r
e
s
o
n
a
n
t
c
o
n
v
e
r
t
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r
p
a
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a
m
e
t
e
r
s
;
a
n
d
i
i
i
)
T
o
a
n
a
l
y
z
e
a
n
d
e
v
a
l
u
a
t
e
P
2
r
e
s
o
n
a
n
t
c
o
n
v
e
r
t
e
r
f
o
r
c
o
n
s
t
a
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t
c
u
r
r
e
n
t
a
p
p
l
i
c
a
t
i
o
n
s
.
3.
P
2
RE
SO
NAN
T
CO
NVER
T
E
R
Fig
u
r
e
1
s
h
o
ws
th
e
b
lo
ck
d
ia
g
r
am
f
o
r
th
is
p
r
o
p
o
s
ed
wo
r
k
.
An
in
v
er
ter
r
u
n
n
in
g
at
th
e
P
2
r
eso
n
an
t
co
n
v
er
ter
s
at
r
eso
n
an
ce
f
r
eq
u
en
cy
(
P2
-
R
C
)
tr
an
s
f
o
r
m
s
th
e
s
y
s
tem
'
s
in
p
u
t
d
ir
ec
t
cu
r
r
en
t
(
DC
)
in
to
alter
n
atin
g
cu
r
r
en
t
(
AC
)
.
T
wo
in
d
u
cto
r
s
(
L
1
,
L
2
)
,
a
n
d
two
ca
p
ac
ito
r
s
(
C
1
,
C
2
)
in
th
is
co
n
v
er
ter
f
u
n
c
tio
n
u
n
d
e
r
r
eso
n
an
t
cir
cu
m
s
tan
ce
s
to
tr
an
s
m
it
p
o
wer
ef
f
ec
tiv
ely
an
d
with
th
e
f
ewe
s
t
p
o
s
s
ib
le
lo
s
s
es.
So
f
t
s
witch
in
g
is
f
ea
s
ib
le
d
u
r
in
g
r
eso
n
an
t
f
r
eq
u
en
cy
o
p
e
r
atio
n
,
wh
ich
l
o
wer
s
s
witch
in
g
lo
s
s
es a
n
d
b
o
o
s
ts
s
y
s
tem
ef
f
ec
tiv
en
ess
.
B
esid
es,
th
e
P2
R
C
wo
r
k
s
as
an
ac
tiv
e
im
p
ed
an
ce
-
m
atch
i
n
g
n
etwo
r
k
b
etwe
en
th
e
s
o
u
r
ce
an
d
th
e
lo
ad
,
d
estab
ilizin
g
th
e
s
y
s
tem
at
d
y
n
am
ic
lo
ad
s
a
n
d
p
r
o
v
id
i
n
g
s
tab
ilit
y
u
n
d
er
s
tatic
lo
ad
s
.
T
h
e
o
u
tp
u
t
o
f
t
h
e
P2
R
C
is
an
A
C
v
o
ltag
e
th
at
g
ets
tr
an
s
f
o
r
m
ed
to
a
DC
v
o
ltag
e
u
s
in
g
a
d
io
d
e
b
r
id
g
e
r
ec
ti
f
ier
.
I
n
ad
d
itio
n
,
a
co
n
tr
o
ller
r
ec
o
n
f
ig
u
r
es
t
h
e
s
w
itch
in
g
f
r
eq
u
e
n
cy
o
f
t
h
e
in
v
er
ter
’
s
o
u
tp
u
t
to
k
ee
p
it
at
th
e
r
eso
n
an
t
f
r
e
q
u
en
c
y
an
d
ac
h
iev
e
a
co
n
s
tan
t
cu
r
r
en
t
o
u
tp
u
t
w.
r
.
t
to
lo
ad
c
h
an
g
es.
Fro
m
d
esig
n
co
n
s
id
er
atio
n
,
t
h
e
P2
R
C
p
r
o
v
id
es
g
o
o
d
a
n
d
e
f
f
icien
t w
o
r
k
in
g
a
b
ilit
y
f
o
r
C
C
ap
p
licatio
n
s
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
P
2
r
eso
n
an
t c
o
n
v
er
ter
3
.
1
.
M
a
t
hema
t
ica
l
m
o
dellin
g
o
f
pro
po
s
ed
co
nv
er
t
er
T
o
co
m
p
r
e
h
en
d
th
e
p
r
o
p
er
ties
o
f
an
y
R
C
to
p
o
lo
g
y
,
m
at
h
em
atica
l m
o
d
elin
g
is
n
ec
ess
ar
y
.
T
h
is
en
tails
d
eter
m
in
in
g
th
e
e
x
p
r
ess
io
n
s
f
o
r
f
u
n
d
am
e
n
tal
p
ar
a
m
eter
s
s
u
ch
as
ch
ar
ac
ter
is
tic
im
p
e
d
an
c
e
(
Z
C
)
,
l
o
ad
c
u
r
r
e
n
t
(I
2
)
,
s
o
u
r
ce
c
u
r
r
en
t
(I
1
)
,
v
o
ltag
e
g
ain
(
M)
,
an
d
cu
r
r
en
t
g
ai
n
(
H)
,
am
o
n
g
o
th
er
s
,
a
n
d
m
o
n
ito
r
in
g
th
e
L
I
C
C
co
n
d
itio
n
[
2
4
]
,
[
2
5
]
.
First,
a
Π
-
s
tr
u
ctu
r
ed
P2
R
C
o
p
er
ated
with
R
esis
tiv
e
o
r
C
ap
ac
iti
v
e
lo
ad
ed
with
a
n
im
p
ed
an
ce
o
f
Z
2
is
s
elec
ted
.
T
h
e
s
tr
u
ctu
r
e'
s
b
r
an
ch
r
ea
ctan
ce
’
s
ar
e
X
1
,
X
2
,
an
d
X
3
,
r
e
p
r
esen
ted
in
T
ab
le
1
.
Fro
m
th
e
L
I
C
C
co
n
d
itio
n
,
if
it
is
r
ea
r
r
an
g
ed
th
en
th
e
d
esig
n
co
n
s
tr
ain
ts
ar
e
L
1
=
L
2
,
C
1
=
2
C
.
T
h
er
ef
o
r
e
,
it
b
ec
o
m
es a
s
R
eso
n
an
t f
r
eq
u
en
cy
=
ω=
1
√
l
1
c
1
=
1
√
c
2
(
l
1
+l
)
=
√
c
1
-
c
2
l
2
c
1
c
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2
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ly
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T
a
b
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(
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a
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ig
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o
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1
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n
(
M)
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n
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cu
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c
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ti
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i
n
T
a
b
l
e
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
R
eso
n
a
n
t c
o
n
ve
r
ter fo
r
fa
s
t
-
ch
a
r
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in
g
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p
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n
s
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R
ema
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a
Gesh
ma
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u
ma
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1835
T
ab
le
1
.
Ma
th
em
atica
l m
o
d
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g
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l
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∏
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L
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l
t
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n
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3
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L
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T
ab
le
2
.
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ec
if
icatio
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d
d
e
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ig
n
o
f
P2
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an
t c
o
n
v
er
ter
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p
e
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i
f
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c
a
t
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g
n
I
o
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g
l
o
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d
c
u
r
r
e
n
t
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5
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I
2
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R
M
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o
f
l
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d
c
u
r
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e
n
t
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o
r
m
f
a
c
t
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r
*
I
o
=
5
.
55
A
V
D
C
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D
C
i
n
p
u
t
v
o
l
t
a
g
e
t
o
i
n
v
e
r
t
e
r
=
2
0
0
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V
1
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u
n
d
a
me
n
t
a
l
A
C
v
o
l
t
a
g
e
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2
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2
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1
8
0
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F
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w
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t
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h
i
n
g
f
r
e
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e
n
c
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z
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2
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n
a
n
t
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n
d
u
c
t
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r
s
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2
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.
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6
e
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4
H
R
o
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a
d
r
e
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s
t
a
n
c
e
=
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C
1
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e
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n
a
n
t
c
a
p
a
c
i
t
o
r
s
=
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2
L
1
=
1
.
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e
−
7
F
t
c
=
C
h
a
r
g
i
n
g
t
i
m
e
=
50
msec
C
2
=
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e
so
n
a
n
t
c
a
p
a
c
i
t
o
r
s=
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1
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=
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.
81
5
e
−
8
F
T
ab
le
3
.
T
h
eo
r
etica
l
ca
lcu
latio
n
s
o
f
P2
r
eso
n
a
n
t c
o
n
v
er
ter
Th
e
o
r
e
t
i
c
a
l
c
a
l
c
u
l
a
t
i
o
n
s
X
1
=
X
2
=
X
3
=
Br
a
n
c
h
i
m
p
e
da
n
c
e
s
=
32
.
42
Ω
Z
=
A
C
l
o
a
d
i
m
p
e
d
a
n
c
e
s
=
8
R
o
π
2
=
8
1
.
0
5
Ω
V
O
=
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a
d
v
o
l
t
a
g
e
s
= I
o
Z
=
405
.
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a
n
d
I
2
=
AC
lo
a
d
c
ur
r
e
n
t
=
V
1
X
3
=
5
.
5
5
A
M
=
V
o
l
t
a
g
e
g
a
i
n
=
Z
X
3
=
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.
5
,
a
n
d
H
=
C
u
r
r
e
n
t
g
a
i
n
=
X
3
Z
=
0
.
4
I
1
=
AC
so
ur
c
e
c
ur
r
e
n
t
=
I
2
H
=
13
.
875
A
a
n
d
I
1
pe
a
k
=
Pe
a
k
s
o
ur
c
e
c
ur
r
e
n
t
=
I
1
∗
√
2
=
19
.
6
2
2
2
A
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
P2
R
C
is
o
p
er
ated
with
r
esis
tiv
e
an
d
ca
p
ac
itiv
e
lo
ad
in
t
h
e
MA
T
L
AB
en
v
ir
o
n
m
e
n
t.
A
s
P2
R
C
i
s
u
s
ed
to
claim
a
lo
ad
-
in
d
ep
en
d
en
t c
o
n
s
tan
t c
u
r
r
en
t,
th
e
d
if
f
er
en
t lo
ad
s
ar
e
ap
p
lied
an
d
v
er
i
f
ied
with
th
eo
r
etica
l
an
d
s
im
u
latio
n
r
esu
lts
.
T
h
e
g
a
te
s
ig
n
als o
f
S1
,
S2
,
S3
,
an
d
S
4
o
f
th
e
in
v
er
ter
with
2
5
k
Hz
o
p
er
atin
g
f
r
eq
u
e
n
cy
ar
e
s
h
o
wn
in
Fig
u
r
e
2
.
Fig
u
r
e
3
d
is
p
lay
s
th
e
MO
SF
E
T
v
o
ltag
e
an
d
cu
r
r
en
t
wav
ef
o
r
m
s
o
f
th
e
s
witch
'
s
(
S1
)
in
v
er
ter
'
s
s
witch
in
g
ch
ar
ac
ter
is
tics
.
4
.
1
.
Ana
ly
s
is
o
f
P
2
RC
wit
h
re
s
is
t
iv
e
lo
a
d
Af
ter
ap
p
ly
in
g
th
e
ab
o
v
e
g
ate
p
u
ls
es
to
th
e
in
v
er
ter
,
with
2
0
0
V
o
f
DC
in
p
u
t
v
o
ltag
e
with
a
r
esis
tiv
e
lo
ad
o
f
1
0
0
Ω
ap
p
lied
,
th
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
e
n
t
wav
ef
o
r
m
ar
e
s
h
o
wn
in
Fig
u
r
e
4
.
T
h
e
in
v
er
ter
o
u
tp
u
t is ap
p
lied
as in
p
u
t to
R
C
,
its
o
u
tp
u
t w
av
ef
o
r
m
s
ar
e
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
e
o
u
t
p
u
t o
f
P2
R
C
i
s
g
iv
en
as
in
p
u
t
to
th
e
DB
R
,
it
s
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
e
n
t
wav
ef
o
r
m
s
o
f
th
e
DB
R
with
1
0
0
Ω
ar
e
s
h
o
wn
in
Fig
u
r
e
6
.
All
th
e
r
esu
lts
s
h
o
wn
ab
o
v
e
f
o
r
a
s
in
g
le
r
esis
tiv
e
lo
ad
o
f
1
0
0
Ω
,
f
o
r
o
th
er
v
alu
es
o
f
r
esis
tiv
e
lo
ad
r
esu
lts
ar
e
tab
u
lated
in
T
ab
le
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
183
2
-
18
39
1836
Fig
u
r
e
2
.
Gate
s
ig
n
als f
o
r
in
v
e
r
ter
s
witch
es
Fig
u
r
e
3
.
MO
SF
E
T
s
witch
in
g
ch
ar
ac
ter
is
tics
o
f
cu
r
r
en
t a
n
d
v
o
ltag
e
Fig
u
r
e
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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&
Dr
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s
t
I
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2088
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o
d
eled
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esig
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d
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im
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lated
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o
r
v
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r
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s
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o
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m
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r
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t
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o
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g
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th
eo
r
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an
d
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im
u
latio
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r
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lts
tab
u
lated
in
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ab
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4
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laim
s
o
f
th
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wo
r
k
:
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h
e
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tp
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t v
o
ltag
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im
p
r
o
v
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d
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y
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tab
u
lated
in
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b
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h
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m
p
ar
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in
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t
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k
s
o
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r
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cu
r
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en
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as
s
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u
r
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h
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as
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1
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k
s
o
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r
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r
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en
t.
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h
e
claim
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at
th
e
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r
o
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aws
le
s
s
p
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k
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en
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r
o
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n
T
a
b
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5
.
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ltag
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ain
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u
r
r
en
t
g
ai
n
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o
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r
ce
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u
r
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n
t
,
a
n
d
lo
ad
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r
r
en
ts
ar
e
v
alid
ated
with
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ath
em
atica
l
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aly
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is
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d
s
im
u
latio
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r
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h
m
s
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3
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im
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le
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e
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ted
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d
if
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p
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ag
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r
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(
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O
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ad
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t
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Fig
u
r
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.
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h
e
d
if
f
er
en
t c
a
p
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itiv
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ad
r
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l
ts
ar
e
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u
lated
in
T
a
b
le
6
.
F
i
g
u
r
e
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n
d
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L
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r
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.
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o
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tp
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t a
t lo
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d
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F
T
ab
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.
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itio
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ter
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ab
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5
.
C
o
m
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r
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aly
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t
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r
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s
t
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v
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o
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d
o
f
1
0
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h
ms
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r
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me
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e
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e
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a
i
n
0
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4
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4
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1
(
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u
r
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r
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t
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8
7
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2
(
l
o
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d
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r
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5
5
5
.
5
4
5.
CO
NCLU
SI
O
N
T
h
e
P2
R
C
is
a
m
ath
em
atica
l
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
ch
ar
g
er
o
f
5
A,
wh
ich
was
v
alid
ated
with
th
eo
r
etica
l
an
d
s
im
u
latio
n
r
es
u
lts
b
y
ap
p
ly
in
g
2
0
0
V
DC
at
a
f
r
eq
u
en
cy
o
f
2
5
k
Hz.
I
t
is
ea
s
y
to
s
ee
th
e
ch
ar
g
er
'
s
u
n
iq
u
e
f
ea
tu
r
es,
s
u
c
h
as its
h
ig
h
g
ain
o
f
2
.
5
,
lin
ea
r
ity
in
lo
ad
v
o
ltag
e,
a
n
d
co
n
s
tan
t c
u
r
r
en
t f
ea
tu
r
e
as
p
er
d
esig
n
e
d
.
Sin
ce
P2
R
C
h
as
b
ee
n
s
h
o
wn
to
lo
wer
p
e
ak
s
o
u
r
ce
c
u
r
r
e
n
t
b
y
2
0
%
wh
en
co
m
p
ar
ed
t
o
tr
ad
itio
n
al
L
C
L
,
th
is
to
p
o
lo
g
y
h
as
b
ee
n
u
s
ed
f
o
r
C
C
ch
ar
g
i
n
g
.
T
h
e
p
r
o
p
o
s
ed
wo
r
k
is
v
alid
ated
with
r
esis
tiv
e
an
d
ca
p
ac
itiv
e
lo
a
d
s
;
n
ee
d
to
v
alid
ate
with
a
b
atter
y
t
o
claim
as
a
5
A
C
C
ch
ar
g
er
.
ACK
NO
WL
E
G
M
E
N
T
T
h
e
au
th
o
r
s
d
ee
m
it
a
p
leasu
r
e
to
en
th
u
s
iast
ically
th
an
k
Dr
.
V.
R
am
esh
B
ab
u
,
Hea
d
o
f
th
e
Dep
ar
tm
en
t
o
f
E
lectr
ical
an
d
E
lectr
o
n
ic
E
n
g
i
n
ee
r
in
g
is
a
s
o
u
r
ce
o
f
e
n
co
u
r
ag
em
en
t.
W
e
ar
e
g
r
atef
u
l
to
p
r
in
cip
al
Dr
.
C
.
D.
Naid
u
f
o
r
all
th
e
f
ac
ilit
ies
p
r
o
v
id
ed
f
o
r
th
e
s
m
o
o
th
p
r
o
g
r
ess
o
f
th
e
p
r
o
ject
wo
r
k
an
d
p
r
ep
ar
atio
n
o
f
t
h
e
p
ap
e
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
183
2
-
18
39
1838
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.
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