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f
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el
ce
ll is
i
ts
m
ain
co
n
s
tr
ai
n
t [
1
]
-
[
2
]
.
Fu
el
ce
ll
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s
a
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m
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in
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at
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r
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[
3
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lated
Fu
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.
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Fi
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1
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ed
an
d
th
er
ef
o
r
e
th
e
s
en
s
in
g
d
ev
ice
s
n
ee
d
ed
ar
e
m
o
r
e.
I
n
n
o
n
-
lin
ea
r
ca
r
r
ier
cu
r
r
en
t
co
n
tr
o
l
(
NL
C
)
th
r
ee
r
eset
in
te
g
r
ato
r
s
ar
e
n
ee
d
ed
to
g
en
er
ate
th
e
ca
r
r
ier
w
av
e
f
o
r
m
.
T
h
e
NL
C
co
n
tr
o
lled
co
n
v
er
ter
r
esu
lts
i
n
d
is
t
o
r
ted
in
p
u
t
cu
r
r
en
t
w
a
v
e
f
o
r
m
in
d
i
s
co
n
ti
n
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
o
f
o
p
er
atio
n
.
T
o
o
v
er
co
m
e
t
h
e
p
r
o
b
lem
s
i
n
L
P
C
M
a
n
d
NL
C
co
n
tr
o
lle
r
s
an
o
th
er
co
n
tr
o
l
k
n
o
w
n
a
s
P
r
e
d
ictiv
e
s
w
itc
h
in
g
m
o
d
u
lato
r
co
n
tr
o
l
(
P
SM)
[
1
2
]
,
[
1
3
]
is
p
r
o
p
o
s
ed
w
h
er
e
o
n
l
y
t
w
o
r
eset
i
n
te
g
r
at
o
r
s
ar
e
u
s
ed
w
h
e
n
co
m
p
ar
ed
to
NL
C
.
A
ls
o
P
SM
co
n
tr
o
l
ex
ten
d
s
th
e
r
a
n
g
e
o
f
co
n
tin
u
o
u
s
co
n
d
u
ct
io
n
m
o
d
e
as
p
r
ed
ictio
n
o
f
o
f
f
s
tate
r
ip
p
le
cu
r
r
en
t is p
o
s
s
ib
le
w
h
ic
h
is
ad
d
ed
to
o
n
s
tate
ac
tu
al
cu
r
r
en
t a
t t
h
e
en
d
o
f
s
w
i
tch
i
n
g
p
er
io
d
.
I
n
th
is
p
ap
er
an
is
o
lated
f
u
ll
b
r
id
g
e
b
o
o
s
t
d
c
-
d
c
co
n
v
er
te
r
to
p
o
lo
g
y
is
tak
e
n
a
n
d
f
ir
s
t
o
p
en
lo
o
p
co
n
f
i
g
u
r
atio
n
s
i
m
u
la
tio
n
is
d
o
n
e
u
s
i
n
g
s
i
m
u
li
n
k
.
Nex
t
th
r
ee
t
y
p
es
o
f
co
n
tr
o
ller
s
li
n
ea
r
p
ea
k
c
u
r
r
en
t
m
o
d
e
co
n
tr
o
l (
L
P
C
M)
,
No
n
L
i
n
ea
r
C
ar
r
ier
co
n
tr
o
l (
NL
C
)
an
d
P
r
ed
ictiv
e
s
w
i
tch
in
g
m
o
d
e
co
n
tr
o
l (
P
SM)
ar
e
ap
p
lied
to
th
e
co
n
v
er
ter
to
p
o
lo
g
y
.
Fi
n
all
y
th
e
s
i
m
u
lated
r
esu
lt
s
o
f
all
t
h
e
t
h
r
ee
co
n
tr
o
ller
s
ar
e
an
al
y
s
ed
an
d
t
h
e
p
r
o
p
o
s
ed
P
SM
co
n
tr
o
l is co
m
p
ar
e
d
w
it
h
e
x
is
ti
n
g
L
P
C
M
an
d
NL
C
co
n
tr
o
ller
s
.
2.
I
SO
L
A
T
E
D
F
UL
L
B
RID
G
E
B
O
O
ST
CO
NVER
T
E
R
T
O
P
O
L
O
G
Y
(
I
F
B
C)
2
.
1
.
B
a
s
ic
Co
nv
er
t
er
O
p
er
a
t
i
o
n
I
n
th
i
s
s
ec
tio
n
co
m
p
lete
w
o
r
k
i
n
g
o
f
th
e
co
n
v
er
ter
i
s
p
r
esen
te
d
.
Fig
u
r
e
2
s
h
o
w
s
t
h
e
cir
cu
i
t
d
iag
r
a
m
o
f
th
e
ch
o
s
e
n
co
n
v
er
ter
to
p
o
lo
g
y
an
d
F
ig
u
r
e
3
s
h
o
w
s
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
co
n
v
er
ter
ac
co
r
d
in
g
to
th
e
m
o
d
es
o
f
o
p
er
atio
n
.
Fig
u
r
e
2
.
C
ir
cu
it
d
ia
g
r
a
m
o
f
i
s
o
lated
Fu
ll B
r
id
g
e
B
o
o
s
t Co
n
v
er
ter
T
o
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o
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
694
I
n
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P
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w
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lec
&
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S
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s
t
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
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–
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6
5
6
1646
Fig
u
r
e
3
.
B
asic
o
p
er
atin
g
w
a
v
ef
o
r
m
s
o
f
I
FB
C
T
h
e
s
w
itc
h
es
M1
-
M4
ar
e
r
u
n
in
p
air
s
(
i)
M1
-
M2
an
d
(
ii)
M
3
-
M4
r
esp
ec
tiv
el
y
.
S
w
itc
h
in
g
p
u
ls
es
ar
e
1
8
0
d
eg
r
ee
s
p
h
ase
s
h
if
ted
.
S
witch
M
OSFET
d
u
t
y
c
y
cle
i
s
c
h
o
s
en
b
et
w
ee
n
0
.
5
an
d
1
to
e
n
s
u
r
e
o
v
er
lap
p
in
g
o
f
s
w
itc
h
es.
M
o
de1
:
Du
r
in
g
th
i
s
p
er
io
d
en
er
g
y
s
tar
ts
to
d
i
s
tr
ib
u
te.
S
w
itc
h
es M
1
-
M4
ar
e
in
co
n
d
u
ctio
n
.
I
n
p
u
t i
n
d
u
c
to
r
L
i
s
ch
ar
g
ed
b
y
i
n
p
u
t p
o
w
er
a
n
d
tr
an
s
f
o
r
m
er
s
ec
o
n
d
ar
y
v
o
lta
g
e
i
s
ze
r
o
.
Seco
n
d
ar
y
d
io
d
es a
r
e
all
in
o
f
f
s
ta
te.
M
o
de2
:
I
n
th
is
i
n
ter
v
al
M1
-
M2
ar
e
in
co
n
d
u
ctio
n
a
n
d
M3
-
M4
ar
e
in
o
f
f
s
tate.
I
n
p
u
t
p
o
w
er
i
s
allo
w
ed
th
r
o
u
g
h
M1
-
M2
an
d
s
to
r
ed
in
d
u
cto
r
en
er
g
y
i
s
tr
an
s
f
er
r
ed
to
s
ec
o
n
d
ar
y
s
id
e
o
f
tr
an
s
f
o
r
m
er
.
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o
ad
p
o
w
er
is
ac
h
iev
ed
b
y
co
n
d
u
ctio
n
o
f
d
io
d
es D1
-
D2
.
M
o
de3
:
T
h
is
m
o
d
e
is
s
a
m
e
as
m
o
d
e1
.
All
s
w
i
tch
e
s
ar
e
i
n
co
n
d
u
c
tio
n
a
n
d
s
o
u
r
ce
i
n
d
u
cto
r
cu
r
r
en
t
r
i
s
e
s
g
r
ad
u
all
y
.
M
o
de4
:
R
ev
er
s
e
c
y
cle
p
er
io
d
s
tar
ts
h
er
e.
S
w
i
tch
e
s
M3
-
M4
ar
e
in
co
n
d
u
ctio
n
a
n
d
M1
-
M2
ar
e
in
o
f
f
s
ta
te.
Dis
ch
ar
g
i
n
g
o
f
s
o
u
r
ce
in
d
u
c
to
r
en
er
g
y
a
n
d
p
r
i
m
ar
y
c
u
r
r
en
t
tr
a
n
s
f
er
ta
k
es
p
lace
t
h
r
o
u
g
h
M3
-
M4
a
n
d
tr
an
s
f
o
r
m
er
T
1
.
Seco
n
d
ar
y
cu
r
r
en
t f
lo
w
i
s
ac
h
ie
v
ed
b
y
co
n
d
u
ctio
n
o
f
d
io
d
es D3
an
d
D4
.
2
.
2
.
S
m
a
ll Sig
na
l M
o
dellin
g
o
f
I
F
B
C
Usi
ng
Av
er
a
g
e
Sta
t
e
Sp
a
ce
Ma
n
y
m
o
d
elli
n
g
tec
h
n
iq
u
e
s
f
o
r
th
e
D
C
-
DC
co
n
v
er
ter
s
ar
e
s
u
g
g
e
s
ted
i
n
[
1
4
]
-
[
1
8
]
.
T
h
e
co
n
v
er
ter
ca
n
b
e
m
o
d
elled
b
y
s
tate
s
p
ac
e
av
er
ag
in
g
tec
h
n
iq
u
e
u
s
in
g
f
o
llo
w
i
n
g
s
tep
s
:
Ob
tain
s
tate
eq
u
atio
n
s
f
o
r
ea
ch
s
tate
(
s
w
i
tch
clo
s
ed
/o
p
en
)
.
Av
er
ag
e
t
h
e
s
tate
eq
u
atio
n
s
in
o
n
e
s
w
itc
h
in
g
p
er
io
d
.
T
h
e
av
er
ag
e
eq
u
atio
n
s
th
u
s
o
b
tain
ed
ar
e
p
er
tu
r
b
ed
th
er
eb
y
t
h
e
v
ar
iab
les h
a
v
e
a
DC
a
n
d
AC
co
m
p
o
n
e
n
t.
Nex
t b
y
ap
p
l
y
i
n
g
L
ap
lace
T
r
a
n
s
f
o
r
m
a
n
d
ex
cl
u
d
in
g
ad
d
itio
n
al
AC
an
d
D
C
ter
m
s
(
o
n
l
y
t
h
e
f
ir
s
t o
r
d
er
AC
ter
m
s
)
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
s
n
ee
d
ed
ca
n
b
e
ac
h
iev
ed
.
T
h
e
m
o
d
elled
eq
u
atio
n
s
ar
e
s
i
m
p
li
f
ied
b
y
tak
i
n
g
s
o
m
e
p
r
es
u
m
p
tio
n
s
I
d
ea
l s
w
itc
h
es
h
a
v
in
g
n
o
p
ar
asit
ic
ef
f
ec
t.
No
r
esis
tan
ce
f
o
r
in
d
u
cto
r
I
s
o
lated
tr
an
s
f
o
r
m
er
u
s
ed
is
id
ea
l a
n
d
h
as
n
o
leak
a
g
e,
m
a
g
n
e
tizin
g
in
d
u
cta
n
ce
.
Fil
ter
ca
p
ac
ito
r
in
o
u
tp
u
t
h
av
i
n
g
le
s
s
eq
u
iv
ale
n
t ser
ie
s
r
esis
t
an
ce
is
as
s
u
m
ed
an
d
it c
a
n
b
e
d
is
r
eg
ar
d
ed
.
C
o
n
s
tan
t lo
ad
Star
tin
g
co
n
d
itio
n
s
ar
e
tak
e
n
a
s
ze
r
o
at
th
e
ti
m
e
o
f
o
p
er
atio
n
.
2
.
3
.
Sta
t
e
E
qu
a
t
io
ns
As
s
ee
n
i
n
p
r
ev
io
u
s
s
ec
tio
n
o
p
er
atio
n
o
f
I
FB
C
h
as
t
w
o
m
ai
n
in
ter
v
als
a
n
d
th
eir
id
en
tical
cir
cu
i
t
d
iag
r
a
m
s
ar
e
as
s
h
o
w
n
in
F
ig
u
r
e
4
.
d
-
L
L
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
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C
o
mp
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r
a
tive
S
tu
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f Co
n
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fo
r
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I
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F
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ll B
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ter
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(
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ija
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vi)
1647
I
n
ter
v
al
1
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n
ter
v
al
2
Fig
u
r
e
4
.
E
q
u
iv
ale
n
t c
ir
cu
it
w
i
th
all
s
w
i
tch
e
s
an
d
t
w
o
d
iag
o
n
al
s
w
itc
h
es c
o
n
d
u
c
tin
g
I
nte
rv
a
l
1
:
Her
e
all
th
e
f
o
u
r
s
w
itc
h
e
s
M1
-
M4
co
n
d
u
ct.
T
h
e
d
if
f
er
e
n
tial
eq
u
at
io
n
s
f
o
r
th
is
i
n
ter
v
al
ar
e
w
r
itte
n
as b
elo
w
=
→
=
1
(
1
)
+
=
0
→
=
−
1
(
2
)
[
]
=
[
0
0
0
−
1
]
[
]
+
[
1
0
]
(
3
)
T
h
is
in
ter
v
a
l
co
n
ti
n
u
e
s
f
o
r
(
d
-
0
.
5
)
T
w
h
er
e
T
=1
/f
is
t
h
e
o
n
p
er
io
d
an
d
d
=
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th
e
ef
f
ec
t
u
al
d
u
t
y
r
atio
an
d
n
is
th
e
t
u
r
n
s
r
atio
o
f
th
e
is
o
lated
tr
an
s
f
o
r
m
er
.
I
nte
rv
a
l
2
:
I
n
th
is
th
e
s
w
itc
h
es
M1
an
d
M2
ar
e
o
n
.
T
h
e
d
if
f
er
en
tial
r
elatio
n
s
o
f
s
tate
v
ar
iab
les
f
o
r
th
i
s
in
ter
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I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
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9
,
No
.
4
,
Dec
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b
er
2
0
1
8
:
1644
–
1
6
5
6
1650
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e
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[
1
9
]
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[
2
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]
b
u
t th
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s
it in
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s
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s
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u
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atic
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Fig
u
r
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1
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.
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r
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o
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ller
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o
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1
2
3
4
i
-
Evaluation Warning : The document was created with Spire.PDF for Python.
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3
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Desig
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ntr
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th
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s
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a
clo
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p
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tr
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th
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m
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(
2
7
)
.
T
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m
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r
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1
4
.
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ig
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r
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1
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Diag
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p
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v
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q
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(
1
8
)
(
)
=
+
+
(
2
8
)
w
h
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e
=
1
1
1
,
=
1
2
1
,
=
1
+
2
2
2
1
w
h
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A
i
s
p
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itiv
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s
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p
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ig
in
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ase
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(
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s
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ts
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9
0
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.
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f
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ater
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Fin
all
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e
p
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e
p
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ase
an
g
le
o
f
(
)
to
co
m
e
b
ac
k
d
o
w
n
to
-
9
0
º
.
Evaluation Warning : The document was created with Spire.PDF for Python.