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es
a
n
aly
tica
l
m
o
d
elin
g
o
f
th
e
r
eso
n
an
t
tan
k
u
s
in
g
th
e
f
ir
s
t
h
ar
m
o
n
ic
ap
p
r
o
x
im
atio
n
(
FHA
)
an
d
a
d
etailed
co
m
p
o
n
e
n
t
s
izin
g
s
tr
ateg
y
[
1
9
]
-
[
2
5
]
.
E
x
p
e
r
im
en
tal
ev
al
u
atio
n
o
f
th
e
d
e
v
elo
p
ed
p
r
o
to
ty
p
e
d
em
o
n
s
tr
ates
s
tab
le
L
E
D
cu
r
r
en
t
r
eg
u
latio
n
,
a
n
ef
f
icien
cy
ex
ce
e
d
in
g
9
5
%,
an
d
a
r
ed
u
ctio
n
o
f
in
p
u
t
cu
r
r
e
n
t
T
HD
f
r
o
m
1
3
4
%
to
1
7
%.
T
h
e
s
e
r
esu
lts
h
ig
h
lig
h
t
th
e
p
o
te
n
tial
o
f
th
e
p
r
o
p
o
s
ed
ar
ch
itectu
r
e
t
o
m
ee
t
in
ter
n
ati
o
n
al
s
tan
d
ar
d
s
wh
ile
s
u
p
p
o
r
tin
g
r
eliab
le,
e
n
er
g
y
-
ef
f
icien
t,
an
d
s
u
s
tain
ab
le
p
u
b
li
c
lig
h
tin
g
in
f
r
astru
ctu
r
es [
2
6
]
.
2.
M
E
T
H
O
D
2
.
1
.
P
r
o
j
ec
t
s
pecif
ica
t
io
ns
Fo
r
th
is
ap
p
licatio
n
,
th
e
m
ain
d
esig
n
o
b
jectiv
es
f
o
r
th
e
p
o
wer
co
n
v
er
te
r
ar
e
lo
w
c
o
s
t
,
h
ig
h
-
en
er
g
y
ef
f
icien
cy
,
a
n
d
a
wid
e
o
p
e
r
atin
g
r
an
g
e.
T
h
e
p
r
o
p
o
s
ed
1
5
0
W
L
E
D
d
r
iv
er
ad
o
p
ts
a
two
-
s
t
ag
e
ar
ch
itectu
r
e
with
f
iv
e
lev
els
o
f
p
o
wer
c
o
n
v
e
r
s
io
n
,
en
a
b
lin
g
an
ef
f
icien
t
d
is
tr
ib
u
tio
n
o
f
f
u
n
ctio
n
al
b
lo
c
k
s
.
T
h
e
f
ir
s
t
s
tag
e
is
r
esp
o
n
s
ib
le
f
o
r
g
en
e
r
atin
g
a
r
eg
u
lated
DC
v
o
ltag
e
w
h
ile
p
r
o
v
id
in
g
PF
C
.
T
h
e
s
ec
o
n
d
s
tag
e
is
b
ased
o
n
an
L
L
C
r
eso
n
an
t c
o
n
v
er
ter
,
p
o
we
r
ed
b
y
a
h
alf
-
b
r
id
g
e
in
v
er
te
r
,
wh
ich
ef
f
icien
tly
d
r
iv
es th
e
L
E
D
lo
ad
.
Un
lik
e
co
n
v
e
n
tio
n
al
PW
M
DC
-
DC
co
n
v
er
ter
s
,
wh
ich
ar
e
g
en
er
ally
c
h
ar
ac
ter
ized
b
y
lim
ited
ef
f
icien
cy
d
u
e
to
th
e
lac
k
o
f
g
alv
an
ic
is
o
latio
n
an
d
p
r
ec
is
e
cu
r
r
e
n
t
co
n
t
r
o
l,
th
e
h
alf
-
b
r
i
d
g
e
L
L
C
to
p
o
lo
g
y
o
f
f
er
s
s
u
p
er
i
o
r
L
E
D
cu
r
r
e
n
t
r
eg
u
latio
n
a
n
d
s
ig
n
if
ican
tly
h
ig
h
er
ef
f
icien
cy
.
Mo
r
eo
v
er
,
t
h
is
ap
p
r
o
ac
h
h
el
p
s
r
ed
u
ce
t
h
e
co
s
t
a
n
d
s
ize
o
f
t
h
e
L
E
D
d
r
iv
er
s
y
s
tem
.
C
o
m
p
ar
ed
t
o
th
e
L
C
C
to
p
o
lo
g
y
,
th
e
L
L
C
to
p
o
lo
g
y
p
r
o
v
id
es
b
etter
en
e
r
g
y
ef
f
icien
cy
th
an
k
s
to
its
lo
wer
s
witc
h
in
g
lo
s
s
es
an
d
its
ab
ilit
y
to
o
p
er
ate
in
r
eso
n
a
n
t
m
o
d
e
o
v
er
a
wid
er
lo
ad
r
an
g
e.
W
h
ile
th
e
L
C
C
to
p
o
l
o
g
y
ca
n
ac
h
iev
e
s
tr
icter
v
o
ltag
e
r
eg
u
latio
n
,
it
o
f
te
n
r
esu
lts
in
h
ig
h
er
co
n
tr
o
l
co
m
p
lex
ity
an
d
g
r
ea
ter
lo
s
s
es
at
lig
h
t
lo
ad
.
T
h
er
ef
o
r
e,
th
e
L
L
C
t
o
p
o
lo
g
y
r
e
p
r
esen
ts
an
o
p
tim
al
co
m
p
r
o
m
is
e
b
et
wee
n
p
er
f
o
r
m
an
ce
,
e
f
f
icien
c
y
,
an
d
im
p
lem
en
tatio
n
s
im
p
licity
,
m
ak
in
g
it
p
ar
ticu
lar
ly
well
-
s
u
ited
f
o
r
h
ig
h
-
ef
f
icien
c
y
L
E
D
d
r
iv
e
r
ap
p
l
icatio
n
s
.
T
h
e
L
E
D
d
r
iv
er
we
p
r
o
p
o
s
e
is
b
ased
o
n
a
two
-
s
tag
e
ar
ch
itectu
r
e,
c
o
m
p
r
is
in
g
a
r
eso
n
an
t L
L
C
co
n
v
er
t
er
an
d
a
PF
C
s
tag
e,
as illu
s
tr
ated
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
L
E
D
d
r
iv
er
is
b
ased
o
n
an
L
L
C
r
eso
n
an
t c
o
n
v
er
ter
2
.2
.
J
us
t
if
ica
t
io
n f
o
r
s
elec
t
in
g
t
he
ha
lf
-
bridg
e
L
L
C
t
o
po
lo
g
y
T
h
e
co
n
v
er
ter
s
elec
ted
f
o
r
o
u
tp
u
t
cu
r
r
e
n
t
r
eg
u
latio
n
is
b
ased
o
n
th
e
L
L
C
r
eso
n
an
t
to
p
o
lo
g
y
,
as
illu
s
tr
ated
in
Fig
u
r
e
2
.
I
t
co
n
s
is
ts
o
f
two
p
o
wer
s
witch
es
(
M1
an
d
M2
)
,
a
s
er
ies
ca
p
a
cito
r
(
C
r
)
,
a
s
er
ies
in
d
u
cto
r
(
L
r
)
,
a
p
ar
allel
in
d
u
ct
o
r
(
L
m
)
,
a
n
o
p
tio
n
al
tr
an
s
f
o
r
m
er
,
a
f
u
ll
-
b
r
id
g
e
r
ec
tific
atio
n
s
tag
e
(
D1
,
D2
,
D3
,
D4
)
,
an
d
an
o
u
tp
u
t f
ilter
ca
p
ac
ito
r
(
C
0
).
T
h
e
m
ain
a
d
v
an
tag
e
o
f
th
e
L
L
C
r
eso
n
an
t
to
p
o
lo
g
y
lie
s
in
its
ab
ilit
y
to
ac
h
iev
e
z
er
o
-
v
o
lta
g
e
s
witch
in
g
(
Z
VS)
f
o
r
th
e
s
witch
in
g
d
ev
ices
M1
a
n
d
M
2
o
v
er
th
e
en
tire
o
p
er
atin
g
r
a
n
g
e.
Un
lik
e
th
e
s
er
ies
r
eso
n
an
t
co
n
v
er
ter
,
th
e
L
L
C
co
n
v
er
ter
ca
n
o
p
er
ate
ef
f
icien
tly
u
n
d
er
lig
h
t
-
lo
ad
co
n
d
itio
n
s
b
y
in
cr
ea
s
in
g
th
e
s
witch
in
g
f
r
eq
u
e
n
cy
.
I
n
th
is
ca
s
e,
th
e
im
p
ed
an
ce
o
f
t
h
e
p
ar
allel
in
d
u
cto
r
L
m
in
cr
ea
s
es
p
r
o
p
o
r
tio
n
ally
with
f
r
eq
u
e
n
cy
,
wh
ich
p
r
e
v
en
ts
an
in
cr
ea
s
e
in
cir
cu
latin
g
cu
r
r
en
t
u
n
d
er
lig
h
t
lo
ad
s
a
co
m
m
o
n
d
r
aw
b
ac
k
in
co
n
v
en
tio
n
al
p
ar
allel
r
eso
n
an
t
to
p
o
lo
g
ies.
As
p
r
ev
io
u
s
ly
m
en
tio
n
e
d
,
th
e
L
L
C
r
eso
n
an
t
to
p
o
lo
g
y
co
m
b
in
es
th
e
b
en
ef
its
o
f
b
o
th
s
er
ies
an
d
p
ar
allel
r
eso
n
an
t
cir
cu
its
wh
il
e
elim
in
atin
g
t
h
eir
r
esp
ec
tiv
e
lim
itatio
n
s
.
I
t
s
u
p
p
o
r
ts
a
wid
e
lo
ad
r
an
g
e
,
wh
ile
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
0
8
8
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8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
0
8
4
-
1095
1086
m
ain
tain
in
g
a
lim
ited
s
witch
in
g
f
r
eq
u
e
n
cy
v
ar
iatio
n
a
n
d
m
in
im
izin
g
cir
cu
latin
g
cu
r
r
en
t
with
in
th
e
r
eso
n
a
n
t
tan
k
.
Mo
r
e
o
v
er
,
th
e
L
L
C
c
o
n
v
er
ter
p
r
o
v
id
es
m
u
ltip
le
d
eg
r
ee
s
o
f
d
esig
n
f
lex
i
b
ilit
y
,
m
ak
in
g
it
h
ig
h
ly
ad
ap
tab
le
to
s
p
ec
if
ic
ap
p
licatio
n
r
eq
u
ir
em
en
ts
.
I
ts
d
esig
n
is
f
u
r
th
er
s
im
p
lifie
d
b
y
th
e
u
s
e
o
f
th
e
FHA
m
eth
o
d
,
wh
ich
f
ac
ilit
ates a
cc
u
r
ate
m
o
d
elin
g
an
d
o
p
tim
izatio
n
.
Fig
u
r
e
2
.
S
ec
o
n
d
s
tag
e
o
f
th
e
p
r
o
p
o
s
ed
LLC
-
T
y
p
e
L
E
D
d
r
iv
er
2
.
3
.
O
pera
t
ing
p
rinciple o
f
t
he
L
L
C
re
s
o
na
nt
t
o
po
lo
g
y
T
h
e
an
aly
s
is
o
f
th
e
L
L
C
r
eso
n
an
t
co
n
v
er
ter
is
s
ig
n
if
ican
tly
s
im
p
lifie
d
b
y
ap
p
ly
in
g
th
e
F
HA
o
f
th
e
s
q
u
ar
e
wav
ef
o
r
m
s
.
T
h
e
L
L
C
r
eso
n
an
t
tan
k
ac
ts
as
a
f
ilte
r
,
atten
u
atin
g
th
e
h
ig
h
er
-
o
r
d
e
r
h
ar
m
o
n
ics
o
f
th
e
s
q
u
ar
e
-
wav
e
v
o
ltag
e
s
u
p
p
lied
b
y
th
e
in
v
er
ter
.
As
a
r
esu
lt,
t
h
e
o
u
tp
u
t
p
o
wer
is
p
r
i
m
ar
ily
t
r
an
s
f
er
r
ed
t
h
r
o
u
g
h
th
e
f
u
n
d
am
e
n
tal
f
r
eq
u
en
c
y
co
m
p
o
n
e
n
t
o
f
th
e
wav
ef
o
r
m
.
T
h
is
ap
p
r
o
x
im
atio
n
is
ap
p
lied
d
ir
ec
tly
to
th
e
in
p
u
t
v
o
ltag
e,
w
h
ich
is
a
s
q
u
ar
e
wa
v
e
g
e
n
er
ated
b
y
s
witch
es
M1
an
d
M2
f
r
o
m
a
DC
s
o
u
r
ce
.
T
h
e
s
q
u
ar
e
wav
ef
o
r
m
is
th
en
ap
p
r
o
x
im
ated
as a
s
in
u
s
o
id
al
wav
ef
o
r
m
at
th
e
s
am
e
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
f
o
r
th
e
p
u
r
p
o
s
e
o
f
an
aly
s
is
an
d
d
esig
n
.
2
.
4
.
I
np
ut
v
o
lt
a
g
e
cha
ra
ct
er
is
t
ics
T
h
e
in
p
u
t
v
o
ltag
e
to
th
e
L
L
C
co
n
v
er
ter
,
d
en
o
ted
as
V
B
u
s
,
i
s
th
e
r
eg
u
lated
DC
v
o
ltag
e
p
r
o
v
id
ed
b
y
th
e
f
ir
s
t
s
tag
e.
T
h
e
s
witch
es
M1
an
d
M2
o
p
er
ate
at
a
5
0
%
d
u
ty
cy
cle,
with
a
1
8
0
°
p
h
ase
s
h
if
t
b
etwe
en
th
em
,
p
r
o
d
u
cin
g
a
s
q
u
ar
e
-
wa
v
e
v
o
lt
ag
e
o
s
cillatin
g
b
etwe
en
0
V
an
d
V
B
u
s
.
T
h
e
DC
co
m
p
o
n
en
t
,
eq
u
al
to
V
B
u
s
/2
,
i
s
b
lo
ck
ed
b
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ito
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ce
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s
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ated
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Fig
u
r
e
3
.
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h
e
co
r
r
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g
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in
u
s
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o
ltag
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t
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t
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t
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n
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er
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First Ha
r
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o
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ic
Ap
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Fig
u
r
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3
.
(
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Fig
u
r
e
3
.
Simu
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o
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tem
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t v
o
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ate
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o
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t
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r
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u
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t
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ain
ly
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er
iv
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f
r
o
m
th
e
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u
n
d
am
e
n
tal
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r
eq
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en
c
y
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m
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o
n
e
n
t.
T
h
e
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p
u
t
v
o
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e
is
th
er
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o
r
e
e
x
p
r
ess
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u
s
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g
th
e
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ir
s
t h
ar
m
o
n
ic
ap
p
r
o
x
im
atio
n
,
as sh
o
wn
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(
1
)
.
Vd
FHA
= (
4
.
V
Bus
/
2
.
)
s
in
(
w
t)
(
1
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2
.
5
.
E
qu
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is
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a
nce
F
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
Hig
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r
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4
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ates
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ter
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t f
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n
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e
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u
n
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o
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ter
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r
o
x
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m
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at
o
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ly
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u
n
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o
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t
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im
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e
d
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ce
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n
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e
r
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e
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iv
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e
r
s
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r
o
m
th
e
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Fig
u
r
e
5
illu
s
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ates
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e
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o
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el
o
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th
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iv
ale
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t
lo
ad
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esis
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ce
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e
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r
im
ar
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it
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ep
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s
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u
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o
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al
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r
r
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t
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o
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r
ce
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a
s
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ar
e
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e
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o
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e
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r
s
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e
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r
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p
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t.
T
h
e
o
u
tp
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t
cu
r
r
en
t i
sFHA
is
th
en
d
eter
m
in
e
d
as
(
2
)
:
Is
FHA
= (
I
LED*
/2
)
s
in
(
w
t
)
(
2
)
Vs
FHA
is
g
iv
en
as
(
3
)
an
d
(
4
)
:
Vs
FHA
= +V
LED
if s
in
(
w
t)
> 0
(
3
)
Vs
FHA
=
-
V
LED
if si
n
(
w
t)
< 0
(
4
)
T
h
e
f
u
n
d
am
en
tal
h
ar
m
o
n
ic
eq
u
atio
n
o
f
Vs
FHA
is
g
iv
en
as
(
5
)
:
Vs
FHA
= (
4
.
V
LED
/
)
s
in
(
w
t)
(
5
)
Fig
u
r
e
4
.
Simp
lifie
d
AC
eq
u
iv
alen
t c
ir
cu
it o
f
th
e
L
L
C
c
o
n
v
e
r
ter
Fig
u
r
e
5
.
Der
iv
ati
o
n
o
f
th
e
eq
u
iv
alen
t
lo
ad
r
esis
tan
ce
R
ac
Af
ter
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r
o
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s
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e
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o
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e
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r
r
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t
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s
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o
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m
er
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im
ar
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o
m
e
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u
s
o
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ase
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ch
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er
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e
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r
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s
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o
r
m
er
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u
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t
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ilter
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d
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e
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ef
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r
e
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e
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b
y
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n
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iv
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esis
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ce
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n
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ted
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r
allel
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e
m
a
g
n
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L
m
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n
ce
th
e
h
ar
m
o
n
ic
co
m
p
o
n
en
t
o
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o
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o
t
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n
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i
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te
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wer
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er
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e
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v
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n
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e
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o
n
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e
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n
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e
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ted
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y
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i
n
g
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y
b
y
I
s
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s
h
o
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th
e
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iv
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t
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it
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o
d
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is
illu
s
tr
ated
in
Fig
u
r
e
6
.
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ac
s
=
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FHA
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s
FHA
= 8
.
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LED
/
²
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LED
,
R
ac
s
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8
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6
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u
r
n
s
r
a
t
i
o
(
n
=
Ns
),
t
h
e
e
q
u
i
v
a
l
e
n
t
l
o
a
d
r
e
s
i
s
t
a
n
c
e
R
acs
r
e
f
e
r
r
e
d
t
o
t
h
e
p
r
i
m
a
r
y
s
i
d
e
i
s
o
b
t
a
i
n
e
d
a
s
(
7
)
.
R
a
c
p
=
8
.
²
²
*R
LED
(
7
)
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.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
0
8
4
-
1095
1088
Af
ter
ap
p
ly
in
g
th
e
n
ec
ess
ar
y
s
tep
s
f
o
r
th
e
f
ir
s
t
h
ar
m
o
n
ic
a
p
p
r
o
x
im
atio
n
,
t
h
e
cir
cu
it
i
n
t
h
e
r
ef
er
e
n
ce
d
f
ig
u
r
e
ca
n
b
e
an
al
y
ze
d
in
its
s
im
p
lifi
ed
f
o
r
m
,
as illu
s
tr
ated
in
Fig
u
r
e
7
.
Fig
u
r
e
6
.
R
acs
Ap
p
r
o
x
im
atio
n
o
f
th
e
o
u
tp
u
t c
ir
c
u
it
Fig
u
r
e
7
.
Simp
lifie
d
o
u
tp
u
t c
ir
cu
it o
f
th
e
c
o
n
v
e
r
ter
2
.
6
.
T
ra
ns
f
er
f
un
ct
io
n o
f
t
he
LLC
-
led
driv
er
T
h
e
L
L
C
r
eso
n
an
t
cir
cu
it,
s
i
m
p
lifie
d
u
s
in
g
th
e
f
ir
s
t
h
ar
m
o
n
ic
ap
p
r
o
x
im
atio
n
o
f
th
e
s
q
u
ar
e
-
wav
e
s
ig
n
als,
is
illu
s
tr
ated
in
Fig
u
r
e
8
.
T
h
is
ap
p
r
o
x
im
atio
n
a
llo
ws
th
e
co
m
p
lex
s
witch
in
g
wav
ef
o
r
m
s
t
o
b
e
r
ep
r
esen
ted
b
y
th
eir
f
u
n
d
am
en
tal
s
in
u
s
o
id
al
co
m
p
o
n
en
t,
wh
ich
s
im
p
lifie
s
th
e
an
aly
s
is
o
f
th
e
r
eso
n
an
t
b
eh
av
io
r
.
T
h
e
m
o
d
el
p
r
o
v
id
es
an
ef
f
ec
tiv
e
way
to
s
tu
d
y
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
c
h
ar
ac
ter
is
tics
o
f
th
e
co
n
v
er
ter
u
n
d
er
s
tead
y
-
s
tate
o
p
er
atio
n
.
T
h
e
r
ef
o
r
e,
it
is
wi
d
ely
u
s
ed
in
th
e
d
esig
n
a
n
d
o
p
tim
izatio
n
o
f
h
i
g
h
-
ef
f
icien
cy
L
L
C
r
eso
n
a
n
t c
o
n
v
er
ter
s
.
Fig
u
r
e
8
.
AC
eq
u
iv
ale
n
t c
ir
cu
i
t o
f
th
e
p
r
o
p
o
s
ed
L
E
D
d
r
i
v
er
T
h
e
eq
u
iv
ale
n
t
elec
tr
ical
cir
cu
it
is
a
v
o
ltag
e
d
iv
id
er
:
th
e
v
o
ltag
e
r
atio
is
eq
u
al
to
th
e
r
a
tio
o
f
th
e
im
p
ed
an
ce
s
.
(
)
=
(
)
(
)
=
+
(
8
)
{
(
)
=
∗
+
1
∗
1
=
1
+
1
∗
→
{
(
)
=
∗
+
1
∗
,
=
(
)
=
∗
1
+
(
)
∗
(
9
)
(
)
=
=
(
m
−
1
)
(
0
)
²
(
²
²
−
1
)
+
(
Q
(
m
−
1
)
ω
0
)
(
2
0
2
−
1
)
∗
(
1
0
)
M
v
=
=
∗
=
4
.
s
i
n
(
)
4
2
s
i
n
(
)
=
2
.
(
1
1
)
Or
:
=
1
√
,
p
=
1
√
.
, ω
0
=
1
√
.
,
R
a
c
p
=
8
.
²
²
*R
LED
(
1
2
)
L
p
= L
r
+L
m
,
m
=
,
=
√
−
1
a
ω
0
=
ω
(
1
3
)
As
s
h
o
wn
in
(
1
0
)
,
th
er
e
ar
e
two
r
eso
n
an
ce
f
r
eq
u
en
cies:
o
n
e
d
eter
m
i
n
ed
b
y
L
r
an
d
C
r
,
an
d
th
e
o
th
e
r
d
eter
m
in
ed
b
y
L
p
an
d
C
r
.
In
(
1
4
)
in
d
icate
s
th
at
th
e
v
o
ltag
e
g
ain
is
eq
u
al
to
u
n
ity
at
th
e
r
eso
n
an
ce
f
r
eq
u
e
n
cy
(
ω
₀)
,
r
e
g
ar
d
less
o
f
lo
a
d
v
ar
iati
o
n
s
,
an
d
is
g
iv
e
n
b
y
(
1
4
)
.
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
Hig
h
-
efficien
cy
tw
o
-
s
ta
g
e
LED
d
r
iver wi
th
in
teg
r
a
ted
P
F
C
a
n
d
LL
C
…
(
Ma
r
r
ef
Mo
h
a
mme
d
A
min
e
)
1089
M
v
=
(
−
1
)
.
ω
²
ω
0
2
−
ω
²
=
2
.
= 1
a
= ω
0
(
14
)
2
.
7
.
L
E
D
s
elec
t
io
n
Fo
r
th
is
wo
r
k
,
5
7
3
0
-
ty
p
e
L
E
Ds
wer
e
s
elec
ted
,
ea
ch
r
ated
at
0
.
5
W
,
o
p
er
atin
g
at
a
f
o
r
w
ar
d
v
o
ltag
e
b
etwe
en
3
V
an
d
3
.
4
V
with
a
n
o
m
in
al
cu
r
r
en
t
o
f
1
5
0
m
A.
T
o
f
o
r
m
a
5
0
W
m
o
d
u
le,
two
s
tr
in
g
s
o
f
ten
L
E
Ds
co
n
n
ec
ted
in
s
er
ies
wer
e
ass
e
m
b
led
in
p
ar
allel.
T
h
r
ee
o
f
th
e
s
e
5
0
W
m
o
d
u
les
wer
e
t
h
en
c
o
n
n
ec
ted
in
p
ar
allel,
ac
h
iev
in
g
a
t
o
tal
p
o
wer
o
f
1
5
0
W
.
T
h
e
s
u
p
p
ly
v
o
ltag
e
o
f
th
e
s
y
s
tem
is
b
etwe
en
3
0
V
an
d
3
4
V
(
V
LED
).
2
.
8
.
Ca
lcula
t
i
o
n o
f
re
s
o
na
nt
circ
uit
pa
ra
m
et
er
s
Acc
o
r
d
in
g
t
o
th
e
r
elatio
n
:
P
Led
=
V
Led
*
I
Led
:
I
Led
= 4
.
6
9
A
(
1
5
)
W
e
also
h
av
e:
P
Led
=
R
Led
*
i
Led
²
.
T
h
u
s
,
th
e
L
E
D
r
esis
tan
ce
is
ca
lcu
lated
as
(
1
6
)
.
R
led
= 6
.
8
2
Ω
(
1
6
)
Fo
r
th
e
in
p
u
t v
o
ltag
e
a
m
p
litu
d
e
V
dFHA
,
we
tak
e
th
e
v
alu
e
o
f
t
h
e
f
u
n
d
am
en
tal
h
a
r
m
o
n
ic:
V
dFHA
=
∗
(
/
2
)
=
254
.
6
w
ith
V
Bus
=4
0
0
V
(
1
7
)
Fo
r
th
e
L
E
D
v
o
ltag
e
am
p
litu
d
e
V
LEDFHA
,
we
also
tak
e
th
e
v
al
u
e
o
f
th
e
f
u
n
d
am
en
tal
h
ar
m
o
n
ic:
V
LEDFHA
=
∗
=
41
(
1
8
)
T
h
e
f
ilter
g
ain
is
ca
lcu
lated
b
y
(
1
9
)
.
=
√
−
1
= 1
.
1
2
,
m
= 5
(
1
9
)
T
r
an
s
f
o
r
m
e
r
tu
r
n
s
r
atio
s
elec
tio
n
:
n
=
=
2
∗
*
M
v
(
2
0
)
n
= 7
T
h
e
eq
u
iv
ale
n
t L
E
D
r
esis
tan
ce
in
th
e
s
im
p
lifie
d
m
o
d
el
R
acp
is
d
eter
m
in
ed
b
y
(
2
1
)
.
R
acp
=
8
.
²
²
*
R
LED
= 2
7
0
,
8
8
Ω
(
2
1
)
T
h
e
q
u
ality
f
ac
to
r
is
s
et
to
:
Q
=
0
.
4
<
1
.
T
h
er
ef
o
r
e,
f
o
r
th
e
s
er
ies
r
eso
n
an
t
cir
cu
it
p
ar
am
eter
s
,
i
m
p
o
s
in
g
Q
an
d
0
= 2
π
*
f
0
,
we
h
av
e:
Z
r
= L
∗
0
=
∗
0
Z
r
= R
acp
*
Q,
Zr
=
√
(
2
2
)
L
r
=
∗
0
and
C
r
=
1
∗
0
∗
(
2
3
)
Fin
ally
,
th
e
m
ag
n
etizin
g
in
d
u
ctan
ce
L
p
is
d
ef
in
ed
b
y
th
e
in
d
u
ctan
ce
r
atio
:
m
=
L
P
/L
r
=
5
.
(
L
P
=L
m
+
L
r
)
A
s
u
f
f
icien
t v
alu
e
o
f
m
e
n
s
u
r
es c
u
r
r
en
t stab
ilit
y
th
r
o
u
g
h
th
e
L
E
Ds.
T
h
e
p
ar
allel
r
eso
n
an
t
f
r
eq
u
en
cy
is
g
iv
e
n
b
y
:
p
=
1
√
(
+
)
.
(
2
4
)
2
.
9
.
Ca
lcula
t
ed
p
a
r
a
m
et
er
s
Fin
ally
,
b
ased
o
n
t
h
e
d
esig
n
o
f
th
e
r
eso
n
a
n
t
cir
cu
it,
th
e
c
alcu
lated
p
ass
iv
e
co
m
p
o
n
e
n
t
v
alu
es
ar
e
s
u
m
m
ar
ized
in
T
ab
le
1
.
T
h
ese
p
ar
am
eter
s
ar
e
d
er
i
v
ed
f
r
o
m
th
e
p
r
o
p
o
s
ed
d
esig
n
m
eth
o
d
o
lo
g
y
,
co
n
s
id
er
in
g
th
e
r
eq
u
ir
ed
o
p
e
r
atin
g
co
n
d
itio
n
s
o
f
th
e
L
L
C
r
eso
n
an
t
c
o
n
v
er
ter
.
T
h
e
s
elec
tio
n
o
f
th
ese
c
o
m
p
o
n
en
ts
en
s
u
r
e
s
o
p
tim
al
r
eso
n
an
t
b
eh
av
i
o
r
,
im
p
r
o
v
e
d
ef
f
icien
c
y
,
an
d
s
tab
le
o
p
er
atio
n
u
n
d
e
r
v
ar
y
in
g
l
o
ad
c
o
n
d
itio
n
s
.
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.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
0
8
4
-
1095
1090
T
ab
le
1
.
C
alcu
lated
p
a
r
am
eter
s
o
f
th
e
p
r
o
p
o
s
ed
L
E
D
d
r
iv
e
r
P
a
r
a
me
t
e
r
s
D
e
si
n
g
P
a
r
a
me
t
e
r
s
D
e
si
n
g
L
m
6
8
8
µ
H
m
5
L
r
1
7
2
µ
H
Q
0
.
4
C
r
1
4
.
6
8
n
F
M
v
1
.
1
2
f
0
1
0
0
K
H
Z
n
7
2
.
1
0
.
B
o
de
d
ia
g
ra
m
T
h
e
B
o
d
e
d
iag
r
am
o
f
th
e
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
9
.
I
t
h
ig
h
lig
h
ts
th
e
f
r
eq
u
en
c
y
r
esp
o
n
s
e
o
f
th
e
p
r
o
p
o
s
ed
f
ilter
,
clea
r
ly
illu
s
tr
atin
g
th
e
lo
wer
a
n
d
u
p
p
e
r
cu
to
f
f
f
r
eq
u
en
cies
as
well
as
th
e
co
r
r
esp
o
n
d
in
g
b
an
d
wid
th
.
T
h
is
an
aly
s
is
m
ak
es
it
p
o
s
s
ib
le
to
ass
es
s
th
e
s
y
s
tem
’
s
s
tab
ilit
y
an
d
d
y
n
a
m
ic
b
eh
av
io
r
,
c
o
n
f
ir
m
in
g
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
f
ilter
with
in
th
e
in
ten
d
e
d
o
p
e
r
atin
g
r
an
g
e.
Fig
u
r
e
9
.
B
o
d
e
d
iag
r
am
o
f
t
h
e
s
y
s
tem
2
.
1
1
.
Det
er
m
ina
t
i
o
n o
f
m
a
x
i
m
um
a
nd
m
ini
m
um
v
o
lt
a
g
e
g
a
ins
T
h
e
m
ax
im
u
m
an
d
m
in
im
u
m
v
o
ltag
e
g
ain
s
ar
e
ca
lcu
lated
as
(
2
5
)
a
n
d
(
26
)
:
M
min
=
2
.
*
n
=
2
.
32
410
*
7
= 1
.
0
9
(
2
5
)
M
max
=
2
.
*
n
=
2
.
32
3
90
*
7
=1
.
1
4
(
2
6
)
T
o
p
r
ev
e
n
t
th
e
o
p
er
atin
g
p
o
in
t
f
r
o
m
e
n
ter
in
g
th
e
ca
p
ac
itiv
e
r
eg
io
n
,
th
e
m
ax
im
u
m
v
o
ltag
e
g
ain
m
u
s
t
in
clu
d
e
a
d
esig
n
m
ar
g
i
n
.
T
h
is
m
ar
g
in
is
s
et
to
0
.
1
5
×
M
max
.
T
h
er
ef
o
r
e,
th
e
v
alu
e
o
f
M
max
is
ad
ju
s
ted
a
s
(
2
7
)
:
M
max
= 1
.
14
*
1
.
1
5
=
1
.
31
(
2
7
)
2
.
1
2
.
Det
er
m
ina
t
i
o
n o
f
t
he
s
wit
ching
f
re
qu
ency
ra
ng
e
T
h
e
m
in
im
u
m
s
witch
in
g
f
r
e
q
u
en
cy
f
min
an
d
t
h
e
m
ax
im
u
m
s
witch
in
g
f
r
eq
u
en
c
y
f
max
ar
e
ca
lcu
lated
an
d
p
r
esen
te
d
:
f
max
=
1
2
.
√
.
= 9
9
K
Hz
(
2
8
)
f
min
=
√
1
+
(
1
−
1
2
)
= 6
1
.
7
K
Hz,
k
=
(
2
9
)
3.
I
M
P
L
E
M
E
NT
A
T
I
O
N
Fig
u
r
e
1
0
p
r
esen
ts
th
e
o
v
e
r
a
ll
f
u
n
ctio
n
al
b
lo
ck
d
iag
r
am
o
f
th
e
d
ev
elo
p
ed
s
y
s
tem
.
I
t
in
clu
d
es
a
co
n
tr
o
l
b
o
ar
d
d
esig
n
ed
to
d
r
iv
e
th
e
h
alf
-
b
r
id
g
e
in
v
er
ter
as
w
ell
as
th
e
m
ea
s
u
r
em
en
t
d
ev
ice
s
.
T
h
e
L
E
D
d
r
iv
er
in
teg
r
ates
b
o
th
th
e
h
alf
-
b
r
id
g
e
in
v
er
ter
an
d
th
e
L
L
C
r
eso
n
an
t
cir
cu
it,
s
u
p
p
lied
b
y
a
DC
b
u
s
v
o
ltag
e
(
V
BUS
)
g
en
er
ated
f
r
o
m
a
PF
C
s
tag
e.
T
h
e
co
m
p
lete
s
y
s
tem
d
r
i
v
es a
1
5
0
W
5
7
3
0
-
ty
p
e
L
E
D
lam
p
.
Alth
o
u
g
h
th
e
in
teg
r
ated
tr
a
n
s
f
o
r
m
er
ap
p
r
o
ac
h
in
L
L
C
r
eso
n
an
t
co
n
v
e
r
ter
d
esig
n
allo
ws
c
o
m
b
in
in
g
th
e
m
ag
n
etic
co
m
p
o
n
en
ts
L
r
an
d
L
m
in
to
a
s
in
g
le
co
r
e
th
u
s
r
ed
u
cin
g
th
e
m
ag
n
etic
co
m
p
o
n
en
t
co
u
n
t
—
th
e
v
alu
e
o
f
L
r
is
d
if
f
icu
lt
to
co
n
tr
o
l
in
th
e
p
r
ac
tical
d
esig
n
o
f
a
tr
an
s
f
o
r
m
er
.
Desig
n
in
g
t
h
e
r
eso
n
an
t
ci
r
cu
it
s
o
m
etim
es
r
eq
u
ir
es
iter
ativ
e
ad
ju
s
tm
en
ts
to
ac
co
u
n
t
f
o
r
th
e
f
in
al
L
r
v
alu
e
o
b
tain
e
d
af
ter
tr
an
s
f
o
r
m
e
r
co
n
s
tr
u
ctio
n
.
T
h
e
f
in
al
d
esig
n
o
f
th
e
r
eso
n
an
t n
etwo
r
k
is
s
u
m
m
ar
ized
in
T
a
b
le
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
Hig
h
-
efficien
cy
tw
o
-
s
ta
g
e
LED
d
r
iver wi
th
in
teg
r
a
ted
P
F
C
a
n
d
LL
C
…
(
Ma
r
r
ef
Mo
h
a
mme
d
A
min
e
)
1091
3
.
1
.
F
ina
l
r
eso
na
nt
net
wo
r
k
des
ig
n
T
o
ev
alu
ate
th
e
ef
f
icien
c
y
o
f
th
e
p
r
o
p
o
s
ed
L
E
D
d
r
iv
e
r
,
a
p
r
o
to
ty
p
e
was
b
u
ilt
an
d
test
ed
.
T
ab
le
2
s
u
m
m
ar
izes
th
e
s
y
s
tem
s
p
ec
if
icatio
n
s
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
v
er
ter
al
o
n
g
with
th
e
c
h
a
r
ac
ter
is
tics
o
f
th
e
co
m
p
o
n
en
ts
em
p
lo
y
ed
.
T
h
e
d
esig
n
p
r
o
ce
s
s
co
n
s
id
er
ed
s
e
v
er
al
k
ey
p
ar
am
ete
r
s
,
in
clu
d
i
n
g
L
E
D
s
elec
tio
n
,
tr
an
s
f
o
r
m
er
tu
r
n
s
r
atio
(
n
)
,
m
ax
im
u
m
(
M
max
)
an
d
m
in
im
u
m
(
M
min
)
v
o
ltag
e
g
ain
,
ef
f
e
ctiv
e
r
esis
tiv
e
lo
ad
r
ef
lecte
d
to
th
e
t
r
an
s
f
o
r
m
e
r
p
r
im
ar
y
(
R
acp
)
,
in
d
u
cta
n
ce
r
atio
(
m
)
b
etwe
en
m
a
g
n
et
izin
g
an
d
r
eso
n
an
t
in
d
u
ctan
ce
s
,
q
u
ality
f
ac
t
o
r
(
Q
)
,
r
eso
n
a
n
t
f
r
e
q
u
en
c
y
(
f
r
)
,
a
n
d
th
e
v
alu
es
o
f
t
h
e
s
er
ies
r
eso
n
an
t
ca
p
ac
ito
r
(
C
r
)
,
r
eso
n
an
t in
d
u
ctan
ce
(
L
r
)
,
an
d
m
ag
n
etizin
g
in
d
u
ctan
ce
(
L
m
).
Fig
u
r
e
10
.
Ph
o
to
o
f
th
e
p
r
o
p
o
s
ed
p
r
o
t
o
ty
p
e
T
ab
le
2
.
Pra
ctica
l sp
ec
if
icatio
n
s
o
f
th
e
p
r
o
p
o
s
ed
L
E
D
d
r
iv
er
P
a
r
a
me
t
e
r
s
F
i
n
a
l
d
e
s
i
g
n
P
a
r
a
me
t
e
r
s
F
i
n
a
l
d
e
s
i
g
n
L
p
5
8
0
µ
H
m
4
.
9
L
r
1
1
8
µ
H
Q
0
.
4
C
r
15
n
F
/
1
0
0
0
V
M
v
1
.
1
2
f
0
9
8
K
H
Z
n
7
3
.
2
.
E
x
perim
ent
a
l
re
s
ult
E
x
p
er
im
en
tal
test
s
wer
e
p
er
f
o
r
m
ed
o
n
t
h
e
d
ev
el
o
p
ed
L
L
C
-
b
ased
L
E
D
d
r
iv
er
to
v
a
lid
ate
th
e
th
eo
r
etica
l
ca
lcu
latio
n
s
an
d
s
im
u
latio
n
r
esu
lts
.
T
h
e
p
r
o
to
t
y
p
e
in
teg
r
ates
a
h
alf
-
b
r
i
d
g
e
i
n
v
er
ter
s
tag
e
alo
n
g
with
a
PF
C
f
r
o
n
t
-
en
d
.
As
an
i
n
itial
s
tep
,
g
ate
d
r
iv
e
s
ig
n
als
wer
e
test
ed
to
en
s
u
r
e
p
r
o
p
er
o
p
er
atio
n
.
Fig
u
r
e
1
1
s
h
o
ws
th
e
m
ea
s
u
r
e
d
g
ate
v
o
lt
ag
es
ap
p
lied
to
th
e
MO
SF
E
T
s
at
a
s
witch
in
g
f
r
eq
u
en
cy
o
f
9
8
k
Hz,
co
n
f
ir
m
in
g
co
m
p
lian
ce
with
th
e
d
esig
n
s
p
ec
if
icatio
n
s
.
Fig
u
r
e
1
2
d
e
p
icts
th
e
m
ea
s
u
r
ed
wav
ef
o
r
m
s
o
f
V
d
a
n
d
V
dFHA
,
wh
er
ea
s
Fig
u
r
e
1
3
s
h
o
ws
V
s
an
d
I
s
.
Un
d
er
n
o
m
in
al
l
o
a
d
co
n
d
itio
n
s
,
Fig
u
r
e
1
4
illu
s
tr
ates
th
e
r
eso
n
a
n
t
ca
p
ac
ito
r
v
o
ltag
e
(
V
cr
)
,
th
e
r
e
s
o
n
an
t
in
d
u
cto
r
c
u
r
r
e
n
t
(
i
Lr
)
,
a
n
d
th
e
v
o
ltag
e
V
d
with
in
th
e
L
L
C
r
eso
n
an
t
tan
k
.
Fin
ally
,
Fig
u
r
e
1
5
p
r
esen
ts
t
h
e
m
ea
s
u
r
ed
v
o
ltag
e
a
n
d
c
u
r
r
en
t
ac
r
o
s
s
a
1
5
0
W
L
E
D
la
m
p
in
s
tead
y
-
s
tate
o
p
er
atio
n
,
d
em
o
n
s
tr
atin
g
s
tab
l
e
p
er
f
o
r
m
an
ce
a
n
d
h
i
g
h
-
q
u
ality
p
o
wer
d
eliv
er
y
f
r
o
m
th
e
d
r
iv
er
.
Fig
u
r
e
1
1
.
W
av
ef
o
r
m
s
at
r
ated
lo
ad
V
g1
;V
g2
Fig
u
r
e
1
2
.
W
av
ef
o
r
m
s
at
r
ated
lo
ad
V
d
;V
dFHA
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.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
0
8
4
-
1095
1092
3
.
3
.
Study
o
f
t
o
t
a
l
ha
rmo
nic
dis
t
o
rt
io
n
a
nd
po
wer
f
a
ct
o
r
co
rr
ec
t
io
n
o
f
t
he
inp
ut
c
urr
ent
a
nd
im
pro
v
ed
re
s
ults di
s
cu
s
s
io
n
T
h
e
an
al
y
s
is
s
h
o
ws
th
at
th
e
p
r
o
p
o
s
ed
s
y
s
tem
with
a
PF
C
s
ta
g
e
r
e
d
u
ce
s
th
e
T
HD
o
f
th
e
in
p
u
t
cu
r
r
en
t
f
r
o
m
o
v
er
1
3
4
%
(
Fig
u
r
e
1
6
)
to
ar
o
u
n
d
1
7
%
(
Fig
u
r
e
1
7
)
.
T
h
is
s
ig
n
if
ican
t
r
ed
u
ctio
n
d
em
o
n
s
tr
ates
im
p
r
o
v
e
d
p
o
wer
q
u
ality
a
n
d
c
o
m
p
lian
ce
with
elec
tr
ical
g
r
i
d
h
a
r
m
o
n
ic
s
tan
d
ar
d
s
.
I
n
ter
m
s
o
f
ef
f
icie
n
cy
,
th
e
d
e
v
elo
p
ed
p
r
o
to
ty
p
e
ac
h
iev
es
a
m
ea
s
u
r
ed
co
n
v
er
s
io
n
ef
f
icien
cy
ex
ce
e
d
in
g
9
5
%.
T
h
is
p
er
f
o
r
m
an
ce
i
s
co
m
p
ar
ab
le
to
o
r
s
u
p
er
io
r
to
s
ev
er
al
r
e
p
o
r
ted
L
E
D
d
r
iv
er
ar
ch
itectu
r
es.
Fo
r
e
x
am
p
le,
th
e
C
r
C
M
b
o
o
s
t
PF
C
co
m
b
in
e
d
with
a
n
L
L
C
r
eso
n
an
t
co
n
v
e
r
ter
in
[
6
]
r
ea
ch
es
ef
f
icien
cies
ar
o
u
n
d
9
2
–
9
4
%,
wh
ile
th
e
s
in
g
le
-
s
tag
e
s
o
f
t
-
s
witch
in
g
d
r
iv
er
in
[
7
]
ac
h
iev
es a
p
p
r
o
x
i
m
ately
9
0
%.
Similar
ly
,
th
e
h
ig
h
-
b
r
ig
h
tn
ess
L
E
D
d
r
iv
er
p
r
ese
n
ted
in
[
1
2
]
r
e
p
o
r
ts
ef
f
icien
cies
n
ea
r
9
4
%.
T
h
e
p
r
o
p
o
s
ed
d
esig
n
,
th
er
e
f
o
r
e
,
o
f
f
er
s
im
p
r
o
v
ed
ef
f
icien
cy
wh
ile
s
im
u
ltan
eo
u
s
ly
r
ed
u
cin
g
T
HD
m
o
r
e
e
f
f
ec
tiv
el
y
th
an
m
a
n
y
e
x
is
tin
g
s
o
lu
tio
n
s
.
Fig
u
r
e
1
3
.
W
av
ef
o
r
m
s
at
r
ated
lo
ad
V
s
; I
s
Fig
u
r
e
1
4
.
W
av
ef
o
r
m
s
at
r
ated
lo
ad
V
cr
; i
Lr
; V
d
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