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DIFI
E
D
CUK
DC
-
D
C
P
O
WE
R
CO
NV
E
R
T
E
R
T
h
e
p
r
o
p
o
s
ed
DC
-
DC
p
o
wer
c
o
n
v
er
ter
is
a
m
o
d
if
icatio
n
r
esu
lt o
f
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
[
2
1
]
.
T
h
e
b
asic
s
ch
em
e
o
f
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
is
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
o
u
g
h
th
e
a
ctiv
e
s
witch
in
g
d
ev
ice
is
s
h
o
wn
u
s
in
g
m
etal
o
x
id
e
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e
m
ico
n
d
u
ct
o
r
f
ield
ef
f
ec
t
tr
a
n
s
is
to
r
(
MO
SF
E
T
)
,
o
th
er
ty
p
e
s
witch
in
g
d
ev
ice
ca
n
also
b
e
u
s
ed
.
Un
d
e
r
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
,
it c
an
b
e
s
h
o
wn
th
at
th
e
v
o
ltag
e
r
atio
is
;
̄
=
1
−
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
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L
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o
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n
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ified
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ter fo
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n
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d
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e
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witch
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g
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er
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h
e
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n
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ter
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as
a
ca
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ab
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p
r
o
d
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ce
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t
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h
ig
h
er
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an
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in
p
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t
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h
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wer
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as c
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tin
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o
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s
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n
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t c
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ip
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o
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o
u
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t v
o
ltag
e
is
r
ev
er
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ed
.
As
it
is
s
h
o
wn
in
Fig
u
r
e
3
,
th
e
r
e
is
a
th
ir
d
ter
m
i
n
al
th
at
a
lo
a
d
ca
n
b
e
co
n
n
ec
ted
.
T
h
e
v
o
ltag
e
r
atio
o
f
th
e
th
ir
d
ter
m
i
n
al
is
;
̄
=
1
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−
(
2
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I
f
th
e
lo
ad
is
co
n
n
ec
ted
to
th
e
th
ir
d
ter
m
in
al,
th
e
lo
ad
v
o
ltag
e
is
alwa
y
s
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ig
h
er
th
an
th
e
in
p
u
t
v
o
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e.
T
h
e
v
o
ltag
e
p
o
lar
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o
f
th
is
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i
r
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ter
m
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al
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n
o
t
r
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er
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ed
.
Fo
r
th
e
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am
e
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ty
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cles,
th
e
v
o
lta
g
e
o
f
th
ir
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ter
m
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al
is
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ig
h
er
th
a
n
th
e
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ter
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Fo
r
tu
n
ately
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o
u
r
ap
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licatio
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e
d
esire
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o
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t
p
u
t
v
o
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e
is
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y
s
h
ig
h
er
th
a
n
th
e
in
p
u
t v
o
ltag
e.
If
t
h
e
l
o
a
d
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s
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o
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e
c
t
e
d
t
o
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r
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e
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m
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l
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e
r
a
s
s
h
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w
n
i
n
F
i
g
u
r
e
4
(
a
)
c
a
n
b
e
o
b
t
a
i
n
e
d
.
T
h
e
l
o
a
d
v
o
l
t
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g
e
i
s
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l
w
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y
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i
g
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h
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n
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n
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t
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n
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n
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l
b
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o
s
t
DC
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DC
p
o
w
e
r
c
o
n
v
e
r
t
e
r
.
Dif
f
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t
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e
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n
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n
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o
n
e,
h
o
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er
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e
p
o
wer
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n
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e
r
ter
in
Fig
u
r
e
4
h
as
a
co
n
tin
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o
u
s
o
u
t
p
u
t
cu
r
r
en
t
with
th
e
ass
o
ci
ated
lo
w
r
ip
p
le
c
o
n
ten
t.
I
f
a
b
id
ir
e
ctio
n
al
p
o
wer
f
lo
w
is
d
esire
d
,
th
en
b
i
d
ir
ec
tio
n
al
s
witch
es
a
s
s
h
o
wn
in
Fig
u
r
e
4
(
b
)
m
u
s
t
b
e
u
s
ed
.
Dep
en
d
i
n
g
o
n
th
e
p
o
wer
f
lo
w,
th
e
n
ew
p
o
wer
co
n
v
er
te
r
ca
n
b
e
o
p
e
r
ated
as
a
b
o
o
s
t
o
r
b
u
ck
DC
-
DC
co
n
v
er
ter
.
T
h
e
co
n
v
er
ter
to
p
o
lo
g
y
d
er
iv
a
tio
n
m
eth
o
d
th
at
is
u
s
ed
in
th
is
p
ap
er
h
as a
ls
o
b
ee
n
d
is
cu
s
s
ed
in
[
2
2
]
.
d
E
−
=
1
d
E
o
v
d
L
Q
D
C
L
o
a
d
−
=
1
d
L
E
v
o
C
o
L
Fig
u
r
e
3
.
Mo
d
if
icatio
n
o
f
C
u
k
p
o
wer
co
n
v
er
ter
(
a)
(
b
)
Fig
u
r
e
4
.
(
a
)
Step
-
u
p
an
d
(
b
)
b
id
ir
ec
tio
n
al
m
o
d
i
f
ied
C
u
k
DC
-
DC
co
n
v
er
ter
3.
O
UT
P
UT
VO
L
T
AG
E
ANA
L
YS
I
S
I
n
th
e
p
r
ev
io
u
s
s
ec
tio
n
,
th
e
o
u
tp
u
t
v
o
ltag
e
ex
p
r
ess
io
n
s
h
av
e
b
ee
n
d
er
i
v
ed
b
y
n
eg
lectin
g
th
e
v
o
ltag
e
d
r
o
p
s
ac
r
o
s
s
in
d
u
cto
r
s
an
d
s
witch
in
g
p
o
wer
d
e
v
ices.
I
n
th
is
s
ec
tio
n
,
o
u
tp
u
t
v
o
ltag
e
an
a
ly
s
is
th
at
tak
es
in
to
ac
co
u
n
t
th
e
v
o
ltag
e
d
r
o
p
s
ac
r
o
s
s
th
e
in
d
u
cto
r
s
an
d
s
witch
in
g
d
ev
ices
is
p
r
esen
ted
.
T
r
an
s
is
to
r
Q
an
d
d
io
d
e
D
i
n
Fig
u
r
e
4
(
a)
wo
r
k
c
o
m
p
lem
e
n
tar
y
.
I
f
tr
a
n
s
is
to
r
Q
r
ec
eiv
es
an
ON
(
OFF)
s
ig
n
al
th
en
d
io
d
e
D
is
tu
r
n
ed
OFF
(
ON)
.
I
n
o
r
d
er
to
m
ak
e
it
m
o
r
e
g
en
er
al,
it
is
as
s
u
m
ed
th
at
th
e
v
o
ltag
e
d
r
o
p
s
ac
r
o
s
s
th
e
tr
an
s
is
to
r
an
d
d
io
d
e
d
u
r
in
g
co
n
d
u
ctio
n
a
r
e
;
=
+
(
3
)
=
+
(
4
)
wh
er
e
V
Q
an
d
V
D
ar
e
th
e
c
o
n
s
t
an
t
co
m
p
o
n
en
ts
,
a
n
d
R
Q
ar
e
R
D
ar
e
th
e
r
esis
tiv
e
co
m
p
o
n
en
ts
o
f
v
o
ltag
e
d
r
o
p
s
an
d
i
Q
an
d
i
D
ar
e
cu
r
r
en
ts
o
f
tr
an
s
is
to
r
an
d
d
io
d
e,
r
esp
ec
tiv
ely
.
T
h
e
r
esis
tan
ce
s
o
f
th
e
in
d
u
cto
r
s
L
d
an
d
L
o
ar
e
R
d
an
d
R
o
,
r
esp
ec
tiv
ely
.
C
ap
ac
ito
r
s
C
an
d
C
o
ar
e
ass
u
m
ed
as
id
ea
l
ca
p
ac
ito
r
s
with
n
o
in
d
u
cta
n
ce
n
o
r
r
esis
tan
ce
.
T
h
e
ca
p
ac
ito
r
eq
u
i
v
alen
t
s
er
ies
r
esis
tan
ce
s
ca
n
b
e
n
eg
lecte
d
in
th
i
s
an
aly
s
is
as
th
e
av
er
ag
e
v
alu
e
o
f
ca
p
ac
ito
r
c
u
r
r
e
n
t
is
ze
r
o
d
u
r
in
g
s
tead
y
-
s
tate.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
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n
C
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n
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o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
2
4
7
-
3
2
5
7
3250
Fig
u
r
e
5
(
a)
s
h
o
ws
th
e
co
n
v
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ter
co
n
d
it
io
n
wh
en
tr
a
n
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o
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ig
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al.
Un
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itio
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ctin
g
th
e
cu
r
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en
ts
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d
d
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o
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e
D
is
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r
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ed
OFF.
B
ase
d
o
n
th
e
cir
cu
it
in
Fig
u
r
e
5
(
a
)
,
th
e
f
o
llo
win
g
s
tat
e
s
p
ac
e
eq
u
atio
n
is
o
b
tain
ed
;
[
0
0
]
=
[
−
0
(
+
)
+
−
0
+
(
0
+
)
−
(
+
)
−
−
(
0
+
)
+
−
0
−
1
0
0
0
1
0
0
0
]
[
0
0
]
+
[
0
(
−
)
+
−
(
−
)
−
0
−
0
]
(
5
)
wh
er
e
Δ
=L
d
L
o
-
M
2
an
d
M
i
s
th
e
m
u
tu
al
in
d
u
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ce
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etwe
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n
d
u
cto
r
s
L
d
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d
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o
.
F
i
g
u
r
e
5
(
b
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s
h
o
w
s
t
h
e
c
o
n
v
e
r
t
e
r
s
t
a
t
e
w
h
e
n
t
r
a
n
s
i
s
t
o
r
Q
r
e
c
e
i
v
e
s
a
n
O
F
F
s
i
g
n
a
l
.
U
n
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e
r
t
h
i
s
c
o
n
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i
t
i
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n
,
t
h
e
t
r
a
n
s
i
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o
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i
s
t
u
r
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e
d
O
F
F
a
n
d
c
u
r
r
e
n
t
s
a
r
e
f
l
o
w
i
n
g
t
h
r
o
u
g
h
t
h
e
d
i
o
d
e
D
.
B
a
s
e
d
o
n
t
h
e
c
i
r
c
u
i
t
i
n
F
i
g
u
r
e
5
(
b
)
,
t
h
e
f
o
l
l
o
w
i
n
g
i
s
o
b
t
a
i
n
e
d
;
[
0
0
]
=
[
−
0
(
+
)
+
−
0
+
(
0
+
)
−
0
−
+
(
+
)
−
(
0
+
)
+
−
1
0
0
0
0
1
0
0
0
]
[
0
0
]
+
[
0
(
−
)
+
−
(
−
)
−
0
−
0
]
(
6
)
T
r
a
n
s
i
s
t
o
r
Q
r
ec
eiv
es a
n
ON
s
ig
n
al
d
u
r
in
g
ON
p
er
io
d
an
d
r
ec
eiv
es a
n
OFF s
ig
n
al
d
u
r
i
n
g
O
FF
p
er
io
d
.
B
y
tak
in
g
th
e
av
er
ag
e
o
f
(
5
)
an
d
(
6
)
o
v
er
o
n
e
s
witch
in
g
p
er
io
d
th
e
n
th
e
s
tate
-
s
p
ac
e
av
er
ag
e
eq
u
atio
n
o
f
th
e
co
n
v
er
ter
ca
n
b
e
o
b
tain
ed
[
2
3
]
.
I
f
it
is
ass
u
m
ed
th
at
L
d
=
L
0
,
R
d
=
R
0
,
an
d
M
=
0
,
t
h
en
th
e
f
o
llo
win
g
s
tead
y
-
s
tate
eq
u
atio
n
is
o
b
tain
ed
;
(
a)
(
b
)
Fig
u
r
e
5
.
C
o
n
v
er
ter
c
o
n
d
itio
n
wh
en
tr
an
s
is
to
r
Q
r
ec
eiv
es a
n
(
a)
ON
-
s
ig
n
al
an
d
(
b
)
OFF
-
s
ig
n
al
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
mo
d
ified
C
u
k
DC
-
DC
co
n
ve
r
ter fo
r
d
c
micro
g
r
id
s
ys
tems
(
A
n
d
r
ia
z
is
Da
h
o
n
o
)
3251
0
=
[
−
[
+
+
(
1
−
)
]
−
[
+
(
1
−
)
]
−
(
1
−
)
0
−
[
+
(
1
−
)
]
−
[
+
+
(
1
−
)
]
−
1
−
−
0
0
0
1
0
0
0
]
[
̄
̄
0
̄
̄
0
]
+
[
[
−
−
(
1
−
)
]
−
[
+
(
1
−
)
]
0
−
0
]
(
7
)
Ba
se
d
o
n
(
7
)
we
ca
n
o
b
tain
th
e
f
o
llo
win
g
;
̄
=
1
−
(
8
)
̄
=
(
9
)
̄
=
1
−
−
+
(
1
−
)
1
−
−
(
1
−
2
+
2
2
)
+
+
(
1
−
)
(
1
−
)
2
(
1
0
)
Th
e
lo
ad
v
o
ltag
e
is
;
̄
=
+
̄
=
−
−
(
1
−
)
1
−
−
(
1
−
2
+
2
2
)
+
+
(
1
−
)
(
1
−
)
2
(
1
1
)
In
(
1
0
)
is
th
e
o
u
tp
u
t
v
o
ltag
e
e
x
p
r
ess
io
n
o
f
co
n
v
en
tio
n
al
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
an
d
(
1
1
)
is
th
e
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
te
r
.
Fo
r
th
e
s
am
e
o
u
tp
u
t
v
o
ltag
e,
two
tim
es
o
f
th
e
in
p
u
t
v
o
ltag
e
f
o
r
e
x
am
p
le
,
th
e
co
n
v
e
n
tio
n
al
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
n
ee
d
s
d
u
t
y
cy
cle
o
f
2
/3
a
n
d
th
e
m
o
d
if
ie
d
C
u
k
p
o
wer
c
o
n
v
e
r
ter
n
ee
d
s
d
u
ty
c
y
cle
o
f
h
alf
.
B
y
u
s
in
g
th
e
s
am
e
m
eth
o
d
,
th
e
o
u
tp
u
t
v
o
ltag
e
ex
p
r
ess
io
n
o
f
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
er
ter
with
th
e
s
ch
em
e
as sh
o
wn
in
Fig
u
r
e
6
ca
n
b
e
o
b
tain
e
d
as
;
̄
=
−
−
(
1
−
)
1
−
−
+
+
(
1
−
)
(
1
−
)
2
(
1
2
)
Fig
u
r
e
7
s
h
o
ws
th
e
p
lo
ts
o
f
v
o
ltag
e
d
r
o
p
ac
r
o
s
s
th
e
in
d
u
cto
r
r
esis
tan
ce
o
f
c
o
n
v
e
n
tio
n
al
b
o
o
s
t
an
d
p
r
o
p
o
s
ed
DC
-
DC
p
o
wer
co
n
v
er
ter
s
,
as
a
f
u
n
ctio
n
o
f
d
u
ty
c
y
cle.
T
h
is
f
ig
u
r
e
r
e
p
r
esen
ts
th
e
co
n
d
u
ctio
n
lo
s
s
es
wh
en
th
e
v
o
ltag
e
d
r
o
p
s
ac
r
o
s
s
th
e
s
witch
in
g
d
ev
ices
ar
e
n
eg
lecte
d
.
T
h
o
u
g
h
th
e
n
u
m
b
er
o
f
in
d
u
ct
o
r
is
d
o
u
b
le,
th
e
in
d
u
cto
r
lo
s
s
es
ar
e
lo
wer
co
m
p
ar
ed
t
o
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
co
n
v
er
ter
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
v
o
ltag
e
d
r
o
p
i
n
th
e
p
r
o
p
o
s
ed
s
tep
-
up
DC
-
DC
co
n
v
er
ter
is
lo
wer
th
a
n
th
e
c
o
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
co
n
v
er
ter
.
I
f
th
e
s
witch
in
g
lo
s
s
es c
an
b
e
n
e
g
lecte
d
,
t
h
e
co
n
d
u
ctio
n
l
o
s
s
es c
an
b
e
ca
lcu
lated
as
;
=
−
̄
(
1
3
)
T
h
e
in
p
u
t c
u
r
r
e
n
t is
=
̄
+
(
1
4
)
Su
b
s
titu
tin
g
(
8
)
in
t
o
(
1
4
)
th
e
f
o
llo
win
g
is
o
b
tain
ed
=
1
−
(
1
5
)
B
ased
o
n
(
1
0
-
1
3
)
an
d
(
1
5
)
,
th
e
lo
s
s
es o
f
co
n
v
er
ter
is
=
+
(
1
−
)
1
−
+
(
1
−
2
+
2
2
)
+
+
(
1
−
)
(
1
−
)
2
2
(
1
6
)
f
o
r
co
n
v
en
tio
n
al
an
d
m
o
d
if
ie
d
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
te
r
,
an
d
=
+
(
1
−
)
1
−
+
+
+
(
1
−
)
(
1
−
)
2
2
(
1
7
)
f
o
r
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
e
r
ter
.
As
it
h
as
b
ee
n
m
en
tio
n
e
d
b
e
f
o
r
e,
f
o
r
th
e
s
am
e
o
u
t
p
u
t
v
o
l
tag
es,
t
h
e
d
u
ty
c
y
cle
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
is
lo
wer
th
an
th
e
co
n
v
en
tio
n
al
o
n
e
.
T
h
u
s
,
th
e
lo
s
s
es
in
m
o
d
if
ied
C
u
k
DC
-
D
C
p
o
wer
co
n
v
er
ter
is
lo
wer
th
an
th
e
c
o
n
v
en
tio
n
al
o
n
es.
In
(
1
6
,
1
7
)
s
h
o
w
th
at
f
o
r
th
e
s
am
e
o
u
tp
u
t
v
o
ltag
es,
th
e
p
o
wer
lo
s
s
in
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
is
lo
wer
th
an
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
er
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
2
4
7
-
3
2
5
7
3252
T
h
e
r
ea
s
o
n
wh
y
th
e
in
d
u
cto
r
lo
s
s
es
in
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
ar
e
lo
wer
th
a
n
th
e
in
d
u
cto
r
lo
s
s
es
in
co
n
v
e
n
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
er
ter
ca
n
b
e
e
x
p
lai
n
ed
as f
o
llo
ws:
−
All so
u
r
ce
cu
r
r
e
n
t is f
lo
win
g
t
h
r
o
u
g
h
th
e
i
n
d
u
cto
r
o
f
b
o
o
s
t
DC
-
DC
co
n
v
er
ter
.
−
C
u
r
r
en
ts
th
r
o
u
g
h
i
n
d
u
cto
r
s
L
d
an
d
L
o
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
ar
e
lo
wer
th
an
th
e
in
d
u
cto
r
cu
r
r
en
t in
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
er
ter
.
L
oad
d
E
d
L
Q
D
o
C
d
i
L
v
L
I
Fig
u
r
e
6
.
C
o
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
er
ter
0
10
20
30
40
50
60
70
80
90
100
0
0
,
2
0
,
4
0
,
6
0
,
8
1
Ch
a
r
t
T
i
t
l
e
S
er
i
es1
S
er
i
es2
)
(
cyc
le
Dut
y
(
)
2
1
1
Bo
os
t
−
=
(
)
2
2
1
2
2
-
1
Pr
op
os
e
d
−
+
=
L
d
I
R
dro
p
vol
tage
Fig
u
r
e
7
.
Vo
ltag
e
d
r
o
p
co
m
p
a
r
is
o
n
4.
CURR
E
NT
R
I
P
P
L
E
ANA
L
YSI
S
I
n
th
e
f
o
llo
win
g
an
aly
s
is
,
it
is
ass
u
m
ed
th
at
th
e
in
d
u
cto
r
c
u
r
r
en
ts
ar
e
c
o
n
tin
u
o
u
s
.
Mo
r
e
o
v
er
,
it
is
ass
u
m
ed
th
at
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
ito
r
C
is
n
o
t
ch
a
n
g
in
g
s
o
m
u
c
h
i
n
o
n
e
s
witch
in
g
p
e
r
io
d
.
B
ased
o
n
Fig
u
r
e
4
(
a
)
,
th
e
f
o
llo
win
g
ca
n
b
e
o
b
tain
e
d
;
[
]
[
]
=
[
−
−
]
(
18)
wh
er
e
v
Q
an
d
v
D
ar
e
v
o
ltag
es
ac
r
o
s
s
tr
an
s
is
to
r
Q
d
an
d
io
d
e
D
,
r
esp
ec
tiv
ely
,
a
n
d
M
is
th
e
m
u
tu
al
in
d
u
ctan
ce
b
etwe
en
L
d
an
d
L
o
.
T
h
e
cu
r
r
en
ts
an
d
v
o
ltag
es
ca
n
b
e
d
iv
id
ed
in
to
th
e
av
e
r
ag
e
an
d
r
ip
p
le
co
m
p
o
n
en
ts
as
th
e
f
o
llo
win
g
s
:
d
d
d
i
I
i
~
+
=
(
19
)
o
o
o
i
I
i
~
+
=
(
20
)
Q
Q
Q
v
V
v
~
+
=
(
21
)
D
D
D
v
V
v
~
+
=
(
22
)
o
o
o
v
V
v
~
+
=
(
23
)
wh
er
e
b
ar
an
d
tild
e
in
d
icate
a
v
er
ag
e
an
d
r
ip
p
le
co
m
p
o
n
e
n
ts
,
r
esp
ec
tiv
ely
.
I
f
(
19
-
23
)
ar
e
s
u
b
s
titu
ted
in
to
(
18
)
th
en
th
e
cu
r
r
en
t r
i
p
p
le
co
m
p
o
n
en
ts
ca
n
b
e
o
b
tain
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
mo
d
ified
C
u
k
DC
-
DC
co
n
ve
r
ter fo
r
d
c
micro
g
r
id
s
ys
tems
(
A
n
d
r
ia
z
is
Da
h
o
n
o
)
3253
[
]
[
̃
̃
]
=
[
−
̃
̃
−
̃
]
(
24
)
B
ased
o
n
(
2
4
)
th
e
f
o
llo
win
g
s
ar
e
o
b
tain
ed
:
̃
=
∫
(
−
̃
)
−
∫
(
̃
−
̃
)
+
1
(
25
)
̃
=
∫
(
̃
−
̃
)
−
∫
(
−
̃
)
+
2
(
26
)
wh
er
e
C
1
an
d
C
2
co
n
s
tan
ts
o
f
i
n
teg
r
atio
n
.
I
f
it is
as
s
u
m
ed
th
at
th
e
r
ip
p
le
co
m
p
o
n
en
t o
f
s
witch
v
o
ltag
e
is
m
u
ch
h
ig
h
er
th
a
n
th
e
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
le,
o
D
v
v
~
~
(
27
)
T
h
en
(
25
)
a
n
d
(
26
)
ca
n
b
e
a
p
p
r
o
x
im
ated
as
;
̃
=
∫
(
−
̃
)
−
∫
̃
+
1
(
28
)
̃
=
∫
̃
2
−
∫
(
−
̃
1
)
+
2
(
29
)
B
ased
o
n
(
21
-
22
)
,
th
e
r
ip
p
le
v
o
ltag
es o
f
tr
an
s
is
to
r
ar
e
;
̃
1
=
1
−
1
(
30
)
̃
=
−
(
31
)
wh
er
e
,
=
(
32
=
=
1
−
(
33
)
wh
en
tr
an
s
is
to
r
Q
r
ec
eiv
es a
n
ON
s
ig
n
al
;
=
0
(
34
)
=
̄
=
1
−
(
35
)
T
hus
,
th
e
cu
r
r
en
t r
i
p
p
le
ex
p
r
ess
io
n
s
wh
en
tr
an
s
is
to
r
Q
r
ec
eiv
es a
n
ON
s
ig
n
al
ar
e
,
̃
=
−
∫
+
1
(
36
)
̃
=
−
∫
+
2
(
37
)
W
h
en
tr
an
s
is
to
r
Q
r
ec
eiv
es a
n
OFF s
ig
n
al,
th
e
tr
an
s
is
to
r
v
o
ltag
es a
r
e
,
=
̄
=
1
−
(
38
)
=
0
(
39
)
th
u
s
,
th
e
cu
r
r
en
t r
ip
p
le
ex
p
r
ess
io
n
s
wh
en
tr
an
s
is
to
r
Q
r
ec
eiv
es a
n
OFF s
ig
n
al
ar
e
,
̃
=
−
−
∫
1
−
+
3
(
40
)
̃
=
−
−
∫
1
−
+
4
(
41
)
wh
er
e
C
3
an
d
C
4
a
r
e
co
n
s
tan
ts
o
f
in
teg
r
atio
n
.
T
h
ese
co
n
s
tan
t
s
ca
n
b
e
d
eter
m
i
n
ed
b
ased
o
n
t
h
e
f
ac
ts
th
at:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
2
4
7
-
3
2
5
7
3254
−
Av
er
ag
e
v
alu
e
o
f
c
u
r
r
e
n
t r
ip
p
l
e
o
v
er
o
n
e
s
witch
in
g
p
er
io
d
is
ze
r
o
.
−
I
n
itial
v
alu
e
o
f
cu
r
r
e
n
t
r
i
p
p
le
d
u
r
in
g
ON
p
e
r
io
d
is
th
e
f
in
al
v
alu
e
o
f
th
e
cu
r
r
en
t
r
ip
p
le
d
u
r
in
g
OFF
p
er
io
d
.
Similar
ly
,
th
e
in
itial
v
alu
e
o
f
cu
r
r
en
t
r
ip
p
le
d
u
r
in
g
OFF
p
er
io
d
is
th
e
f
in
al
v
alu
e
o
f
c
u
r
r
e
n
t
r
ip
p
le
d
u
r
in
g
ON
p
er
io
d
.
B
ased
o
n
th
e
ab
o
v
e
an
aly
s
is
,
t
h
e
cu
r
r
e
n
t r
ip
p
le
e
x
p
r
ess
io
n
in
o
n
e
s
witch
in
g
p
e
r
io
d
ca
n
b
e
wr
itten
as
;
̃
=
(
−
)
{
−
2
+
(
−
)
f
o
r
≤
≤
2
1
−
2
−
1
−
(
−
2
)
f
o
r
2
≤
≤
4
(
42
)
̃
=
(
−
)
{
−
2
+
(
−
)
f
o
r
≤
≤
2
1
−
2
−
1
−
(
−
2
)
f
o
r
2
≤
≤
4
(
43
)
Fig
u
r
e
8
s
h
o
ws
th
e
cu
r
r
en
t
r
ip
p
les
o
v
er
o
n
e
s
witch
in
g
p
er
i
o
d
.
T
h
e
r
m
s
v
alu
es
o
f
cu
r
r
en
t
r
ip
p
le
ca
n
b
e
d
eter
m
in
ed
as
;
̃
=
[
1
∫
̃
2
+
]
1
/
2
(
44
)
̃
=
[
1
∫
̃
2
+
]
1
/
2
(
45
)
B
ased
o
n
(
4
4
,
4
5
)
th
e
f
o
llo
win
g
s
ar
e
o
b
tain
e
d
;
̃
=
−
2
√
3
(
46
)
̃
=
−
2
√
3
(
4
7
In
(
4
6
,
4
7
)
s
h
o
w
th
at
th
e
m
u
t
u
al
in
d
u
ctan
ce
b
etwe
en
th
e
t
wo
in
d
u
cto
r
s
ca
n
b
e
u
s
ed
to
r
ed
u
ce
th
e
in
d
u
ct
o
r
cu
r
r
en
t
r
i
p
p
les.
B
ased
o
n
th
e
c
ir
cu
it in
Fig
u
r
e
4
,
we
ca
n
o
b
ta
in
th
e
ca
p
ac
ito
r
cu
r
r
e
n
t a
s
;
=
{
−
f
o
r
≤
≤
+
f
o
r
+
≤
≤
+
(
4
8
)
t
t
o
t
1
t
2
t
3
t
4
t
s
T
0
0
d
i
~
C
i
Fig
u
r
e
8
.
C
o
n
v
er
ter
c
u
r
r
en
t
r
ip
p
les o
v
er
o
n
e
ca
r
r
ier
p
e
r
io
d
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
mo
d
ified
C
u
k
DC
-
DC
co
n
ve
r
ter fo
r
d
c
micro
g
r
id
s
ys
tems
(
A
n
d
r
ia
z
is
Da
h
o
n
o
)
3255
Fig
u
r
e
8
s
h
o
ws
th
e
ca
p
ac
ito
r
c
u
r
r
en
t
wav
ef
o
r
m
.
B
y
n
e
g
lectin
g
th
e
r
ip
p
le
co
m
p
o
n
en
ts
o
f
i
o
a
n
d
i
d
,
th
e
r
m
s
v
alu
e
o
f
ca
p
ac
ito
r
cu
r
r
e
n
t is
;
=
(
1
−
)
1
/
2
(
4
9
)
I
n
th
e
p
r
o
p
o
s
ed
c
o
n
v
e
r
ter
,
th
e
r
ef
o
r
e,
a
ca
p
ac
ito
r
with
a
la
r
g
e
cu
r
r
e
n
t
r
ip
p
le
r
atin
g
is
r
eq
u
i
r
ed
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
ca
p
ac
ito
r
c
u
r
r
e
n
t r
ip
p
l
e
ca
n
n
o
t
b
e
r
ed
u
ce
d
b
y
in
cr
ea
s
in
g
th
e
s
witch
in
g
f
r
e
q
u
en
c
y
.
5.
CO
M
P
ARA
T
I
V
E
E
VALU
A
T
I
O
N
I
n
o
r
d
er
to
k
n
o
w
th
e
ad
v
an
tag
es
an
d
d
is
ad
v
an
tag
es
o
f
th
e
p
r
o
p
o
s
ed
DC
-
DC
co
n
v
er
ter
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
is
co
m
p
ar
ed
to
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
c
o
n
v
e
r
ter
.
T
h
e
co
m
p
ar
is
o
n
is
s
u
m
m
a
r
ized
in
T
a
b
le
1
.
I
n
th
is
co
m
p
a
r
is
o
n
,
th
e
two
i
n
d
u
cto
r
s
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
a
r
e
ass
u
m
ed
eq
u
al
with
n
o
m
u
tu
al
c
o
u
p
lin
g
.
C
o
m
p
a
r
e
d
t
o
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
b
o
o
s
t
DC
-
D
C
p
o
w
e
r
c
o
n
v
e
r
te
r
,
t
h
e
p
r
o
p
o
s
e
d
c
o
n
v
e
r
t
e
r
h
a
s
t
h
e
l
o
w
e
s
t
c
o
n
d
u
c
t
i
o
n
l
o
s
s
es
a
n
d
l
o
w
es
t
o
u
t
p
u
t
c
a
p
a
c
i
t
o
r
c
u
r
r
e
n
t
r
i
p
p
l
e
.
T
h
e
r
e
a
s
o
n
w
h
y
t
h
e
i
n
d
u
c
t
o
r
l
o
s
s
es
o
f
m
o
f
i
d
i
e
d
C
u
k
DC
-
DC
p
o
we
r
c
o
n
v
e
r
t
e
r
a
r
e
l
o
w
e
r
t
h
a
n
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
b
o
o
s
t
DC
-
DC
p
o
w
e
r
c
o
n
v
e
r
t
er
c
a
n
b
e
s
e
e
n
f
r
o
m
t
h
e
i
n
d
u
c
t
o
r
c
u
r
r
e
n
t
e
x
p
r
e
s
s
i
o
n
s
i
n
T
a
b
l
e
1
.
T
h
e
i
n
d
u
c
t
o
r
c
u
r
r
e
n
t
s
o
f
m
o
d
i
f
i
e
d
C
u
k
DC
-
DC
p
o
w
e
r
c
o
n
v
e
r
t
e
r
a
r
e
lo
w
e
r
t
h
a
n
t
h
e
i
n
d
u
c
t
o
r
c
u
r
r
e
n
t
i
n
c
o
n
v
e
n
t
i
o
n
a
l
b
o
o
s
t
DC
-
DC
c
o
n
v
e
r
t
e
r
.
T
h
u
s
,
t
h
e
e
f
f
i
c
ien
c
y
o
f
t
h
e
p
r
o
p
o
s
e
d
c
o
n
v
e
r
t
e
r
i
s
t
h
e
h
i
g
h
e
s
t
as
t
h
e
s
w
i
t
c
h
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n
g
l
o
s
s
e
s
a
r
e
a
l
m
o
s
t
t
h
e
s
a
m
e
.
T
h
e
d
is
a
d
v
a
n
t
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g
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o
f
t
h
e
p
r
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p
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e
d
c
o
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s
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d
o
f
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c
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p
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c
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t
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a
h
i
g
h
c
u
r
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n
t
r
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p
p
l
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r
a
t
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g
.
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h
e
u
s
e
o
f
f
i
l
m
c
a
p
a
c
i
t
o
r
i
s
p
r
e
f
e
r
r
ed
i
n
t
h
i
s
a
p
p
l
i
c
a
t
i
o
n
.
T
h
e
t
w
o
i
n
d
u
c
t
o
r
s
c
a
n
b
e
i
n
t
e
g
r
a
t
e
d
i
n
o
n
e
c
o
r
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s
o
t
h
a
t
t
h
e
v
o
l
u
m
e
c
a
n
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e
m
i
n
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m
i
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e
d
.
I
t
s
h
o
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d
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e
n
o
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e
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t
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p
r
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p
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e
d
DC
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p
o
w
e
r
c
o
n
v
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t
e
r
i
s
a
f
o
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o
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d
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r
c
o
n
v
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r
t
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r
a
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d
,
t
h
e
r
e
f
o
r
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,
t
h
e
c
o
n
t
r
o
l
i
s
m
o
r
e
d
i
f
f
i
c
u
l
t
t
h
a
n
t
h
e
c
o
n
v
e
n
t
i
o
n
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l
b
o
o
s
t
DC
-
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C
p
o
w
e
r
c
o
n
v
e
r
t
e
r
.
V
a
r
i
o
u
s
c
o
n
t
r
o
l
m
et
h
o
d
s
f
o
r
h
i
g
h
-
o
r
d
e
r
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p
o
w
e
r
c
o
n
v
e
r
t
e
r
s
w
e
r
e
r
e
p
o
r
t
e
d
i
n
[
2
4
-
2
8
]
.
T
ab
le
1
.
Per
f
o
r
m
an
ce
co
m
p
a
r
is
o
n
M
o
d
i
f
i
e
d
C
u
k
C
o
n
v
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t
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l
B
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C
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C
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e
O
u
t
p
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t
v
o
l
t
a
g
e
̄
=
−
−
(
1
−
)
1
−
−
(
1
−
2
+
2
2
)
+
+
(
1
−
)
(
1
−
)
2
̄
=
−
−
(
1
−
)
1
−
−
+
+
(
1
−
)
(
1
−
)
2
S
o
u
r
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e
c
u
r
r
e
n
t
r
i
p
p
l
e
̃
=
1
2
√
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=
1
2
√
3
O
u
t
p
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t
c
a
p
a
c
i
t
o
r
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u
r
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l
e
̃
=
1
2
√
3
̃
=
(
1
−
)
1
/
2
Tr
a
n
sf
e
r
c
a
p
a
c
i
t
o
r
c
u
r
r
e
n
t
=
(
1
−
)
1
/
2
NA
A
v
e
r
a
g
e
i
n
p
u
t
i
n
d
u
c
t
o
r
c
u
r
r
e
n
t
=
1
−
=
1
−
A
v
e
r
a
g
e
o
u
t
p
u
t
i
n
d
u
c
t
o
r
c
u
r
r
e
n
t
=
NA
6.
E
XP
E
R
I
M
E
N
T
A
L
RE
SUL
T
S
A
s
m
all
ex
p
er
im
en
tal
s
y
s
tem
as
th
e
o
n
e
s
h
o
wn
in
Fig
u
r
e
4
(
b
)
was
co
n
s
tr
u
cted
.
I
n
th
is
ex
p
er
im
en
t,
two
p
o
wer
MO
SF
E
T
s
wer
e
u
s
ed
as
s
witch
in
g
d
ev
ices.
Un
co
u
p
led
two
eq
u
al
in
d
u
cto
r
s
o
f
2
.
2
m
H
wer
e
u
s
ed
as
L
d
an
d
L
o
.
T
h
e
s
witch
in
g
f
r
eq
u
en
cy
ca
n
b
e
v
a
r
ied
f
r
o
m
1
k
Hz
u
p
to
2
0
k
Hz.
T
h
e
ca
p
ac
it
an
ce
C
is
2
2
0
u
F
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
2
4
7
-
3
2
5
7
3256
th
e
ca
p
ac
itan
ce
C
o
is
3
3
0
u
F.
T
h
e
DC
s
o
u
r
ce
is
o
b
tain
ed
f
r
o
m
a
DC
p
o
wer
s
u
p
p
ly
th
at
is
m
ain
tain
ed
co
n
s
tan
t
at
3
6
Vd
c.
T
h
e
lo
ad
is
a
co
n
s
tan
t r
esis
tan
ce
o
f
1
0
0
Oh
m
.
Fig
u
r
e
9
s
h
o
ws
th
e
o
u
tp
u
t
v
o
ltag
e
as
th
e
f
u
n
ctio
n
o
f
d
u
ty
c
y
cle.
I
d
ea
l
cu
r
v
e
is
th
e
ca
lcu
l
ated
r
esu
lts
wh
en
th
e
v
o
ltag
e
d
r
o
p
s
ac
r
o
s
s
th
e
s
witch
in
g
d
ev
ices
an
d
in
d
u
cto
r
s
ar
e
n
e
g
lecte
d
.
T
h
e
n
o
n
id
ea
l
cu
r
v
e
is
ca
lcu
lated
r
esu
lts
wh
en
th
e
v
o
ltag
e
d
r
o
p
s
ar
e
tak
en
in
to
ac
co
u
n
t
as
g
iv
en
b
y
(
9
)
.
Me
asu
r
em
e
n
ts
wer
e
co
n
d
u
cted
u
n
d
er
two
s
witch
in
g
f
r
eq
u
en
ci
es.
Me
asu
r
em
en
t r
esu
lts
ar
e
in
d
icate
d
b
y
s
m
all
s
q
u
ar
e
an
d
ci
r
cle.
I
t c
an
b
e
s
ee
n
th
at
th
e
d
er
iv
e
d
ex
p
r
ess
io
n
is
ac
cu
r
ate
in
p
r
ed
ictin
g
th
e
o
u
tp
u
t v
o
ltag
e.
Fig
u
r
e
1
0
s
h
o
ws
th
e
ex
p
er
im
en
t
al
an
d
ca
lcu
lated
r
esu
lts
o
f
cu
r
r
e
n
t
r
ip
p
le
th
r
o
u
g
h
in
d
u
cto
r
L
o
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
.
Ver
y
g
o
o
d
ag
r
ee
m
en
t
b
etwe
en
ca
lcu
lated
an
d
ex
p
er
im
en
tal
r
esu
lts
ca
n
b
e
ap
p
r
ec
iated
.
Similar
r
esu
lt
s
ar
e
o
b
tain
ed
f
o
r
cu
r
r
en
t
r
ip
p
le
th
r
o
u
g
h
in
d
u
cto
r
L
d
.
Simi
lar
to
o
th
er
DC
-
D
C
p
o
wer
co
n
v
er
ter
s
,
th
e
cu
r
r
e
n
t
r
ip
p
le
ca
n
b
e
r
ed
u
ce
d
f
u
r
th
er
b
y
m
u
ltip
h
asin
g
tech
n
iq
u
e.
Fig
u
r
e
1
1
s
h
o
ws
th
e
ef
f
icien
cy
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
wh
e
n
th
e
d
u
ty
cy
cle
is
ch
an
g
ed
.
T
h
e
lo
ad
r
esis
tan
ce
d
u
r
in
g
th
is
ex
p
er
im
en
t
wa
s
co
n
s
tan
t.
As
it
is
p
r
ed
icte
d
,
th
e
ef
f
icien
cy
is
h
ig
h
er
wh
en
th
e
d
u
ty
cy
cle
is
s
m
all.
T
h
e
ef
f
icien
cy
ca
n
b
e
in
cr
ea
s
ed
b
y
r
ed
u
cin
g
th
e
r
esis
tan
ce
s
o
f
th
e
i
n
d
u
cto
r
s
.
I
t sh
o
u
ld
b
e
n
o
te
d
th
at
th
is
ef
f
i
cien
cy
is
h
ig
h
er
th
an
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
er
ter
.
Fig
u
r
e
9
.
Ou
t
p
u
t v
o
ltag
e
as a
f
u
n
ctio
n
o
f
d
u
ty
cy
cle
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
e
r
ter
Fig
u
r
e
1
0
.
I
n
d
u
cto
r
c
u
r
r
e
n
t r
ip
p
le
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
Fig
u
r
e
1
1
.
E
f
f
icien
c
y
o
f
m
o
d
if
ied
C
u
k
DC
-
DC
p
o
wer
co
n
v
e
r
ter
7.
CO
NCLU
SI
O
N
An
ef
f
icien
t
s
tep
-
u
p
DC
-
DC
p
o
wer
co
n
v
er
te
r
b
ased
o
n
t
h
e
m
o
d
if
icatio
n
o
f
C
u
k
DC
-
DC
p
o
wer
co
n
v
er
ter
th
at
is
s
u
itab
le
f
o
r
DC
m
icr
o
g
r
id
s
y
s
tem
s
h
as b
ee
n
p
r
o
p
o
s
ed
.
T
h
e
co
n
d
u
ctio
n
lo
s
s
es o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
ar
e
l
o
wer
th
a
n
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
DC
-
DC
p
o
wer
co
n
v
er
ter
.
An
aly
s
is
o
f
o
u
tp
u
t
v
o
ltag
e
a
n
d
in
d
u
cto
r
cu
r
r
en
t
r
ip
p
le
th
at
u
s
ef
u
l
in
co
n
v
er
ter
d
esig
n
i
s
p
r
esen
ted
.
E
x
p
er
im
e
n
tal
r
e
s
u
lts
h
av
e
v
er
if
ied
th
e
an
aly
s
is
g
iv
en
in
th
is
p
ap
e
r
.
Pra
ctica
l
in
d
u
s
tr
ial
p
r
o
to
ty
p
e
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
is
in
p
r
o
g
r
ess
an
d
will
b
e
r
ep
o
r
ted
in
t
h
e
f
u
tu
r
e
o
cc
as
io
n
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
s
wis
h
to
th
an
k
PT.
L
E
N
(
Per
s
er
o
)
an
d
L
PDP
f
o
r
p
r
o
v
id
i
n
g
r
esear
ch
f
u
n
d
s
o
f
th
is
wo
r
k
.
T
h
is
p
ap
er
is
d
ed
icate
d
to
th
e
an
n
iv
er
s
ar
y
o
f
1
0
0
-
y
ea
r
e
n
g
in
ee
r
in
g
ed
u
ca
tio
n
in
I
n
d
o
n
esia.
Evaluation Warning : The document was created with Spire.PDF for Python.