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[
1
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a
n
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“
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”
[
2
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,
[
3
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(
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s
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d
[
4
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f
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[
5
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.
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[
6
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.
H
o
w
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s
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p
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[
7
]
,
[
8
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s
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g
n
i
f
i
c
a
n
t
l
y
r
e
d
u
c
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o
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s
e
s
.
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h
u
s
,
i
m
p
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o
v
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d
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c
o
n
v
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s
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f
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c
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n
c
y
w
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t
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l
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s
s
c
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m
p
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n
e
n
t
s
c
o
u
n
t
.
An
y
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p
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s
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m
o
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d
s
m
all
-
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ig
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m
o
d
el
[
9
]
.
T
h
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lar
g
e
-
s
ig
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al
an
aly
s
is
is
f
o
r
co
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p
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ts
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s
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s
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d
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p
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.
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s
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n
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ely
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c
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it
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er
a
g
in
g
[
1
0
]
-
[
1
7
]
,
s
tate
-
s
p
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e
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e
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ag
in
g
[
18]
-
[
2
3
]
an
d
cu
r
r
en
t
in
jecte
d
eq
u
i
v
alen
t
cir
c
u
it
ap
p
r
o
ac
h
[
2
1
]
,
[
2
2
].
I
n
cir
cu
it
av
er
ag
i
n
g
tec
h
n
iq
u
e,
th
e
av
er
ag
in
g
a
n
d
lin
ea
r
izatio
n
o
p
er
at
io
n
s
ar
e
p
er
f
o
r
m
e
d
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:
2
0
8
8
-
8
694
S
ma
ll
-
s
ig
n
a
l a
n
a
lysi
s
o
f a
s
in
g
le
-
s
ta
g
e
b
r
id
g
eless
b
o
o
s
t h
a
lf
-
b
r
id
g
e
…
(
Mo
h
a
ma
d
A
ffa
n
B
i
n
Mo
h
d
N
o
h
)
2359
d
ir
ec
tly
f
r
o
m
th
e
co
n
v
er
ter
cir
cu
it.
T
h
e
s
m
all
-
s
ig
n
al
eq
u
atio
n
is
d
er
iv
ed
f
r
o
m
th
e
s
tead
y
s
tate
o
p
er
atio
n
o
f
th
e
co
n
v
er
ter
cir
cu
it
.
T
h
e
s
tead
y
-
s
tate
eq
u
atio
n
is
d
er
iv
e
d
f
r
o
m
th
e
cir
cu
it
o
p
er
atio
n
an
d
w
av
ef
o
r
m
an
aly
s
is
in
o
n
e
s
witch
in
g
p
er
i
o
d
.
I
t
is
a
s
s
u
m
ed
th
at
th
e
co
m
p
o
n
e
n
ts
ar
e
l
o
s
s
less
an
d
id
ea
l.
T
h
is
is
to
s
im
p
lif
y
th
e
eq
u
atio
n
wh
ic
h
d
er
iv
e
f
r
o
m
s
tead
y
-
s
tate
an
d
s
m
all
-
s
ig
n
al
an
aly
s
is
.
I
n
th
is
p
ap
er
,
th
e
s
m
all
-
s
ig
n
al
o
f
a
b
r
id
g
eless
AC
/D
C
c
o
n
v
er
ter
with
b
id
ir
ec
tio
n
al
s
witch
es
a
s
d
ep
icted
in
Fig
u
r
e
1
is
p
r
esen
ted
.
T
h
e
f
u
ll
b
r
id
g
eless
o
f
th
e
p
r
o
p
o
s
ed
ci
r
cu
it
to
p
o
lo
g
y
eli
m
in
ated
th
e
b
r
id
g
e
r
ec
tifie
r
o
f
a
c
o
n
v
e
n
tio
n
al
c
ir
cu
it
to
p
o
lo
g
y
an
d
th
e
s
em
i
-
b
r
id
g
eless
d
io
d
es
[
7
]
,
[
8
]
in
a
co
n
v
e
n
tio
n
al
b
r
id
g
eless
cir
cu
it.
T
h
e
i
d
ea
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
v
er
te
r
is
b
a
s
ed
o
n
th
e
p
r
im
ar
y
s
id
e
[
18
]
b
u
t
with
o
u
t
d
io
d
es
p
r
esen
ted
wh
ich
f
u
r
th
er
elim
in
ate
th
e
lin
e
f
r
eq
u
en
cy
r
ec
ti
f
ier
lo
s
s
es
.
I
n
ad
d
itio
n
,
t
h
e
b
id
ir
ec
tio
n
al
s
witch
co
n
ce
p
t
is
d
er
iv
e
d
f
r
o
m
th
e
t
o
p
o
lo
g
ies
in
[
2
4
]
-
[
3
1
]
.
T
h
e
b
i
d
ir
ec
tio
n
al
s
witch
es
s
im
p
lify
th
e
m
o
d
e
o
f
cir
cu
it
o
p
er
atio
n
an
d
co
n
t
r
o
l
s
ig
n
al.
T
h
e
s
m
all
-
s
ig
n
al
m
o
d
el
is
d
ev
elo
p
u
s
in
g
th
e
s
im
ilar
p
r
o
ce
d
u
r
e
in
[
1
9
]
,
[
2
3
]
.
T
h
e
s
m
all
-
s
ig
n
al
m
o
d
el
is
th
en
u
s
ed
to
f
in
d
th
e
c
o
n
tr
o
l
-
to
-
o
u
tp
u
t
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
co
n
v
er
ter
.
T
h
en
,
th
e
d
er
iv
ed
t
r
an
s
f
er
f
u
n
ctio
n
o
f
t
h
e
p
r
o
p
o
s
ed
cir
cu
it
is
s
im
u
lated
in
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
e
b
o
d
e
p
l
o
t
o
b
tai
n
f
r
o
m
th
e
MA
T
L
AB
/Si
m
u
lin
k
is
th
en
v
er
if
ied
with
th
e
b
o
d
e
-
p
lo
t
o
b
tain
ed
f
r
o
m
th
e
lar
g
e
ci
r
cu
it
m
o
d
el
wh
ich
s
im
u
lated
with
PLE
C
S.
I
n
ad
d
itio
n
,
a
s
witch
lar
g
e
-
s
ig
n
al
m
o
d
el
is
p
r
o
p
o
s
ed
wh
ich
is
d
er
i
v
e
f
r
o
m
th
e
s
tead
y
-
s
tate
eq
u
ati
o
n
.
T
h
e
m
o
d
el
is
d
esig
n
ed
with
th
e
cir
cu
it
p
ar
am
eter
s
as st
ated
in
T
ab
le
1
.
T
h
e
cir
cu
it
lev
el
s
im
u
latio
n
a
n
d
e
x
p
er
im
e
n
tal
v
er
i
f
icatio
n
r
esu
lts
will
b
e
p
r
esen
ted
in
an
o
th
er
r
e
p
o
r
t.
T
h
is
r
ep
o
r
t w
ill o
n
ly
b
e
d
is
cu
s
s
ed
o
n
th
e
v
er
if
icatio
n
o
f
th
e
d
er
iv
ed
s
m
all
s
ig
n
al
eq
u
atio
n
with
MA
T
L
AB
an
d
PLE
C
S so
f
twar
e.
I
n
a
n
u
ts
h
ell,
th
is
wo
r
k
s
.
–
E
lim
in
ates
th
e
d
r
awb
ac
k
s
o
f
a
b
r
i
d
g
e
r
ec
tifie
r
in
co
n
v
en
tio
n
al
AC
/DC
co
n
v
er
ter
cir
c
u
it
an
d
a
s
em
i
-
b
r
id
g
eless
AC
/DC
co
n
v
en
tio
n
al
cir
cu
it
–
E
lim
in
ates th
e
cr
o
s
s
o
v
er
d
is
to
r
tio
n
o
f
in
p
u
t
c
u
r
r
e
n
t a
t h
ig
h
f
r
eq
u
en
cy
o
f
in
p
u
t su
p
p
ly
–
I
n
p
u
t c
u
r
r
en
t
h
ar
m
o
n
ic
wh
ich
co
m
p
ly
to
th
e
I
E
C
6
0
0
0
-
3
-
2
s
t
an
d
ar
d
–
I
m
p
r
o
v
e
in
p
u
t p
o
wer
f
ac
to
r
–
R
ed
u
ce
th
e
co
m
p
o
n
en
ts
co
u
n
t
–
Simp
lify
th
e
m
o
d
es o
f
cir
c
u
it o
p
er
atio
n
a
n
d
c
o
n
tr
o
l sig
n
al
I
n
s
ec
tio
n
2
,
th
e
d
etails
s
tead
y
s
tate
an
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
cir
cu
it
to
p
o
l
o
g
y
will
b
e
d
is
cu
s
s
ed
.
T
h
e
m
o
d
es
o
f
cir
c
u
it
o
p
e
r
atio
n
with
s
witch
in
g
wav
ef
o
r
m
s
a
r
e
illu
s
tr
ated
to
s
u
p
p
o
r
t
th
e
d
er
i
v
atio
n
o
f
r
elea
ted
eq
u
atio
n
s
.
Sectio
n
3
p
r
esen
ted
th
e
s
m
all
s
ig
n
al
an
aly
s
is
an
d
d
er
iv
atio
n
s
tep
s
to
o
b
tain
ed
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
;
co
n
tr
o
l
-
to
-
o
u
p
u
t,
o
u
tp
u
t
-
to
-
in
p
u
t,
an
d
im
p
e
d
an
ce
.
Nex
t,
th
e
co
n
v
er
ter
s
m
all
s
ig
n
al
b
lo
c
k
d
iag
r
am
in
Simu
lin
k
an
d
in
PECS
is
p
r
o
p
o
s
ed
.
Sectio
n
4
p
r
esen
ted
th
e
r
esu
lts
f
r
o
m
b
o
th
MA
T
L
AB
/Si
m
u
lin
k
an
d
PLE
C
S
f
o
r
v
er
if
icatio
n
.
I
n
ad
d
itio
n
,
th
e
lar
g
e
s
ig
n
al
s
witch
m
o
d
el
is
o
b
tain
ed
.
Fin
ally
,
s
ec
tio
n
5
g
iv
es
th
e
co
n
clu
s
io
n
.
Fig
u
r
e
1
.
Pro
p
o
s
ed
AC
-
DC
f
u
ll
b
r
id
g
eless
h
alf
-
b
r
i
d
g
e
with
b
id
ir
ec
tio
n
al
s
witch
T
ab
le
1
.
Pro
p
o
s
ed
cir
c
u
it p
ar
a
m
eter
s
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
I
n
p
u
t
v
o
l
t
a
g
e
,
1
1
5
V
r
ms
I
n
p
u
t
l
i
n
e
f
r
e
q
u
e
n
c
y
,
5
0
H
z
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
,
5
0
k
H
z
O
u
t
p
u
t
v
o
l
t
a
g
e
,
2
0
V
D
C
B
o
o
st
i
n
d
u
c
t
o
r
1
,
2
5
0
0
µ
H
I
n
d
u
c
t
o
r
1
0
0
µ
H
C
a
p
a
c
i
t
o
r
1
,
2
0
.
1
µ
F
C
a
p
a
c
i
t
o
r
1
0
mF
2.
ST
E
ADY
S
T
A
T
E
AN
AL
Y
S
I
S
I
n
th
is
an
aly
s
is
,
all
s
witch
es
a
n
d
co
m
p
o
n
e
n
ts
ar
e
ass
u
m
ed
t
o
b
e
id
ea
l
an
d
th
e
a
n
aly
s
is
o
n
ly
ca
r
r
ied
o
u
t
at
t
h
e
p
o
s
itiv
e
h
alf
lin
e
c
y
cle.
Fig
u
r
e
2
s
h
o
ws
th
e
f
o
u
r
m
o
d
e
o
f
cir
cu
it
o
p
er
atio
n
at
p
o
s
itiv
e
h
alf
c
y
cle
o
f
in
p
u
t v
o
ltag
e
.
At
M
o
d
e
1
,
th
e
Kir
ch
h
o
f
f
v
o
ltag
e
law
(
KVL
)
eq
u
atio
n
at
p
r
im
ar
y
s
id
e
is
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2358
–
23
71
2360
=
1
+
1
+
2
+
2
(
1
)
As
d
ep
icted
in
Fig
u
r
e
2
(
a)
,
ca
p
ac
ito
r
1
is
co
n
n
ec
ted
in
p
ar
allel
with
th
e
tr
an
s
f
o
r
m
er
p
r
im
ar
y
win
d
in
g
.
C
ap
ac
ito
r
1
d
is
ch
ar
g
e
d
to
p
r
im
ar
y
win
d
in
g
.
T
h
e
v
a
lu
e
o
f
ca
p
ac
ito
r
1
an
d
2
ar
e
also
eq
u
al,
an
d
ca
p
ac
ito
r
2
is
in
c
h
ar
g
i
n
g
m
o
d
e.
As
d
ep
icted
f
r
o
m
t
h
e
k
ey
wav
ef
o
r
m
,
th
e
ca
p
ac
ito
r
v
o
lt
ag
e
1
an
d
2
is
eq
u
al
to
th
e
d
if
f
er
e
n
ce
b
etwe
en
th
e
in
p
u
t
v
o
lta
g
e
an
d
th
e
b
o
o
s
t
in
d
u
cto
r
v
o
ltag
e
.
T
h
e
ca
p
ac
ito
r
v
o
lta
g
e
is
at
m
in
im
u
m
o
r
m
ax
im
u
m
at
s
tar
tin
g
o
f
ea
ch
s
witch
in
g
m
o
d
e.
T
h
is
is
d
u
e
to
th
e
ca
p
ac
ito
r
wh
ich
is
alm
o
s
t
f
u
ll
y
ch
ar
g
ed
o
r
f
u
ll
y
d
is
ch
ar
g
ed
at
th
e
en
d
o
f
s
witch
in
g
m
o
d
e.
T
h
u
s
,
ass
u
m
e
th
e
ca
p
ac
ito
r
2
v
o
ltag
e
;
2
≈
0
an
d
th
e
ca
p
ac
ito
r
1
v
o
ltag
e
;
1
e
q
u
al
to
tr
an
s
f
o
r
m
er
p
r
im
ar
y
v
o
ltag
e
.
T
h
e
v
al
u
e
o
f
t
h
e
in
d
u
c
to
r
1
an
d
2
ar
e
eq
u
al.
T
h
er
ef
o
r
e,
(
1
)
ca
n
b
e
s
im
p
lifie
d
as
.
=
2
+
+
2
(
2
)
T
h
e
tr
an
s
f
o
r
m
er
tu
r
n
r
atio
is
g
iv
en
b
y
:
=
=
=
(
3
)
wh
er
e
tr
an
s
f
o
r
m
er
win
d
in
g
n
u
m
b
er
o
f
tu
r
n
s
at
p
r
im
ar
y
s
id
e
an
d
s
ec
o
n
d
a
r
y
s
id
e
.
T
h
u
s
,
th
e
v
o
ltag
e
eq
u
atio
n
at
s
ec
o
n
d
ar
y
s
id
e
+
in
M
o
d
e
1
is
.
+
=
+
(
4
)
At
M
o
d
e
2
in
Fig
u
r
e
2
(
b)
,
th
e
KVL
eq
u
atio
n
at
p
r
im
ar
y
s
id
e
is
.
=
1
+
1
+
2
+
2
(
5
)
T
h
u
s
,
th
e
in
d
u
cto
r
v
o
ltag
e
ca
n
b
e
wr
itten
as:
=
1
2
(
−
1
−
2
)
(
6
)
Mo
d
e
3
in
Fig
u
r
e
2
(
c)
is
s
im
ilar
to
M
o
d
e
1
.
T
h
u
s
,
th
e
v
o
ltag
e
eq
u
atio
n
at
s
ec
o
n
d
ar
y
s
id
e
−
;
−
=
+
(
7
)
wh
er
e
is
v
o
ltag
e
d
r
o
p
at
o
u
p
u
t
in
d
u
cto
r
an
d
is
th
e
lo
ad
v
o
lta
g
e.
T
h
e
b
o
o
s
t
m
o
d
e
o
p
e
r
atio
n
at
p
r
im
ar
y
s
id
e
in
Mo
d
e
4
is
th
e
s
am
e
as
Mo
d
e
2
.
T
h
u
s
,
th
e
KVL
eq
u
atio
n
f
o
r
m
o
d
e
4
in
Fig
u
r
e
2
(
d
)
is
th
e
s
am
e
as (
5
)
.
T
h
e
v
o
ltag
e
d
r
o
p
eq
u
atio
n
at
o
u
tp
u
t in
d
u
cto
r
is
.
=
(
8
)
Su
b
s
titu
te
(
2
)
-
(
5
)
to
(
1
)
,
th
u
s
th
e
b
o
o
s
t
in
d
u
cto
r
v
o
ltag
e
is
;
=
1
2
(
−
(
)
+
−
2
)
(
9
)
T
h
e
av
er
a
g
e
v
o
ltag
e
ac
r
o
s
s
in
d
u
cto
r
with
in
ea
ch
s
witch
in
g
p
er
io
d
is
ze
r
o
.
T
h
u
s
,
it
ca
n
b
e
co
n
clu
d
e
d
in
(
8
)
th
at
f
o
r
ea
c
h
h
alf
lin
e
p
er
io
d
.
(
)
=
.
=
0
(
1
0
)
Hen
ce
,
(
7
)
ca
n
b
e
s
im
p
lifie
d
a
s
.
=
1
2
(
−
−
2
)
(
11
)
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:
2
0
8
8
-
8
694
S
ma
ll
-
s
ig
n
a
l a
n
a
lysi
s
o
f a
s
in
g
le
-
s
ta
g
e
b
r
id
g
eless
b
o
o
s
t h
a
lf
-
b
r
id
g
e
…
(
Mo
h
a
ma
d
A
ffa
n
B
i
n
Mo
h
d
N
o
h
)
2361
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
2
.
C
ir
cu
it
o
p
er
atio
n
at
p
o
s
itiv
e
h
alf
-
cy
cle
o
f
in
p
u
t v
o
ltag
e,
(
a)
Mo
d
e
1
,
(
b
)
M
o
d
e
2
,
(
c)
Mo
d
e
3
,
(
d
)
Mo
d
e
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2358
–
23
71
2362
T
h
e
b
o
o
s
t
in
d
u
cto
r
is
in
ch
a
r
g
in
g
in
Mo
d
e
1
a
n
d
3
a
n
d
d
is
ch
ar
g
e
at
Mo
d
e
2
an
d
4
o
f
th
e
s
witch
in
g
p
er
io
d
s
.
I
t
is
ass
u
m
ed
th
at
th
e
m
ag
n
itu
d
e
o
f
i
n
p
u
t
v
o
ltag
e
is
co
n
s
tan
t.
C
o
n
s
eq
u
en
tly
,
th
e
in
p
u
t
cu
r
r
en
t
als
o
ass
u
m
es
to
b
e
co
n
s
tan
t.
T
h
e
b
o
o
s
t
in
d
u
cto
r
cu
r
r
en
t
wo
r
k
s
in
co
n
tin
u
o
u
s
cu
r
r
e
n
t
m
o
d
e
.
T
h
er
ef
o
r
e,
b
ased
o
n
th
e
b
alan
ce
d
v
o
lt
-
s
ec
o
n
d
;
−
1
=
−
2
(
1
2
)
Hen
ce
,
b
y
(
12
),
th
e
r
elatio
n
s
h
ip
o
f
d
u
ty
c
y
cle
at
Mo
d
e
1
1
an
d
Mo
d
e
2
2
,
1
=
−
1
−
2
−
−
2
2
(
1
3
)
T
h
e
ca
p
ac
ito
r
v
o
ltag
e
in
o
n
e
s
witch
in
g
p
er
io
d
is
ze
r
o
v
o
lt.
T
h
er
ef
o
r
e
,
(
1
3
)
ca
n
b
e
s
im
p
lifie
d
as
.
1
=
−
2
(
1
4
)
T
h
e
to
tal
p
er
io
d
o
f
Mo
d
e
1
an
d
Mo
d
e
2
is
h
alf
o
f
th
e
s
witch
in
g
p
er
i
o
d
.
T
h
er
ef
o
r
e;
2
=
(
0
.
5
−
1
)
(
15
)
Su
b
s
titu
te
(
15
)
in
(
14
)
,
th
u
s
;
1
=
2
(
2
−
)
(
16
)
T
h
e
in
p
u
t
c
u
r
r
e
n
t
d
ir
ec
tly
f
l
o
w
s
to
th
e
b
o
o
s
t
in
d
u
cto
r
1
an
d
2
.
T
h
u
s
,
th
e
b
o
o
s
t
in
d
u
ct
o
r
cu
r
r
en
t
is
eq
u
al
to
in
p
u
t c
u
r
r
en
t
.
Ass
u
m
e
th
at
all
in
p
u
t p
o
wer
tr
an
s
f
er
r
e
d
to
o
u
tp
u
t.
T
h
u
s
,
th
e
i
n
p
u
t c
u
r
r
en
t
is
.
=
2
(
1
7
)
wh
er
e
is
p
o
wer
f
ac
to
r
an
g
le
a
n
d
is
lo
ad
r
esis
tan
ce
.
Hen
ce
,
th
e
b
o
o
s
t in
d
u
cto
r
is
ch
o
o
s
e
s
u
ch
th
at.
≥
(
−
)
1
2
2
(
1
8
)
wh
er
e
is
th
e
s
witch
in
g
f
r
eq
u
e
n
cy
As
d
ep
icted
f
r
o
m
s
witch
in
g
wav
ef
o
r
m
,
th
e
in
p
u
t
cu
r
r
en
t
f
lo
w
to
t
h
e
h
al
f
b
r
id
g
e
ca
p
a
cito
r
1
an
d
2
at
a
p
er
io
d
o
f
(
1
−
1
)
.
T
h
u
s
;
th
e
cu
r
r
en
t f
l
o
w
tr
o
u
g
h
ca
p
ac
ito
r
1
;
1
an
d
2
;
2
.
1
=
2
=
(
19
)
T
h
er
ef
o
r
e,
th
e
e
x
p
r
ess
io
n
o
f
h
alf
b
r
id
g
e
ca
p
ac
ito
r
is
.
1
=
2
=
2
(
1
−
1
)
(
20
)
wh
er
e
∆
is
th
e
m
in
im
u
m
to
m
ax
im
u
m
c
h
ar
g
in
g
v
o
ltag
e
o
f
h
alf
b
r
id
g
e
ca
p
ac
ito
r
.
As
d
ep
icted
f
r
o
m
Fig
u
r
e
3
,
ea
c
h
h
alf
b
r
id
g
e
ca
p
ac
ito
r
is
ch
ar
g
e
d
a
p
p
r
o
x
im
atel
y
f
r
o
m
ze
r
o
t
o
p
ea
k
s
u
p
p
ly
v
o
l
tag
e
.
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:
2
0
8
8
-
8
694
S
ma
ll
-
s
ig
n
a
l a
n
a
lysi
s
o
f a
s
in
g
le
-
s
ta
g
e
b
r
id
g
eless
b
o
o
s
t h
a
lf
-
b
r
id
g
e
…
(
Mo
h
a
ma
d
A
ffa
n
B
i
n
Mo
h
d
N
o
h
)
2363
Fig
u
r
e
3
.
Pro
p
o
s
ed
k
ey
wav
ef
o
r
m
T
h
er
e
is
n
o
co
n
n
ec
tio
n
b
etw
ee
n
th
e
in
p
u
t
b
o
o
s
t
cir
cu
it
to
o
u
tp
u
t
cir
c
u
it
at
Mo
d
e
2
an
d
Mo
d
e
4
.
T
h
er
ef
o
r
e,
n
o
en
er
g
y
t
r
an
s
f
er
r
ed
f
r
o
m
p
r
im
ar
y
s
id
e
to
s
ec
o
n
d
ar
y
s
id
e
o
f
th
e
tr
an
s
f
o
r
m
er
i
n
th
is
m
o
d
e
.
T
h
u
s
,
th
e
o
u
tp
u
t in
d
u
ct
o
r
an
d
o
u
tp
u
t c
ap
ac
ito
r
ar
e
d
is
ch
ar
g
e
d
to
t
h
e
lo
ad
.
T
h
er
ef
o
r
e
;
=
−
(
21
)
B
y
ass
u
m
in
g
th
e
o
u
tp
u
t c
ap
ac
i
to
r
is
f
u
lly
ch
ar
g
e,
t
h
e
o
u
t
p
u
t
in
d
u
cto
r
c
u
r
r
e
n
t is.
=
=
(
2
2
)
T
h
u
s
,
th
e
m
a
x
im
u
m
a
n
d
m
in
i
m
u
m
o
u
tp
u
t in
d
u
cto
r
c
u
r
r
e
n
t
,
an
d
,
ar
e.
2
,
m
a
x
,
2
os
o
L
d
T
L
L
a
v
e
r
a
g
e
i
ii
−
=+
(
2
3
)
,
m
a
x
2
o
oo
Ls
Lo
vv
i
d
T
RL
=+
(
24
)
,
m
i
n
2
o
oo
Ls
Lo
vv
i
d
T
RL
=−
(
2
5
)
T
h
u
s
,
th
e
o
u
tp
u
t in
d
u
cto
r
r
ip
p
l
e
∆
;
,m
a
x
.
m
i
n
o
o
o
L
L
L
i
i
i
=
−
(
2
6
)
I
n
o
r
d
er
to
e
n
s
u
r
e
o
u
tp
u
t in
d
u
cto
r
wo
r
k
in
g
in
c
o
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e;
m
i
n
2
o
L
s
L
R
d
T
(
2
7
)
Sin
ce
th
e
o
u
tp
u
t
ca
p
ac
ito
r
cu
r
r
en
t
wav
e
-
s
h
ap
e
s
am
e
as
o
u
tp
u
t
in
d
u
cto
r
c
u
r
r
en
t,
th
e
c
h
ar
g
e
in
o
u
tp
u
t
ca
p
ac
ito
r
is
eq
u
al
to
th
e
ar
ea
u
n
d
e
r
th
e
wav
e
-
s
h
ap
e.
T
h
u
s
,
th
e
∆
is
;
=
=
2
8
2
(
2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2358
–
23
71
2364
Hen
ce
,
th
e
o
u
tp
u
t v
o
ltag
e
r
ip
p
le,
is
;
2
2
8
o
o
o
o
s
v
d
r
v
C
L
f
==
(
2
9
)
B
y
ex
am
in
in
g
th
e
ab
o
v
e
wav
e
f
o
r
m
,
t
h
e
p
ea
k
in
d
u
ct
o
r
cu
r
r
en
t c
an
b
e
r
e
p
r
esen
ted
as.
−
=
1
2
(
−
−
1
)
1
(
3
0
)
B
ased
o
n
th
e
Kir
ch
h
o
f
f
c
u
r
r
en
t la
w,
th
e
cu
r
r
e
n
t a
t c
ap
ac
ito
r
1
is
.
1
=
−
(
3
1
)
B
y
s
u
b
s
titu
tin
g
(
2
)
an
d
(
3
0
)
in
(
3
1
)
.
T
h
u
s
;
1
−
=
(
−
2
−
2
−
1
2
)
1
(
3
2
)
At
1
,
th
e
o
u
tp
u
t
in
d
u
cto
r
is
co
n
n
ec
ted
to
th
e
tr
an
s
f
o
r
m
er
s
e
co
n
d
ar
y
win
d
in
g
th
r
o
u
g
h
th
e
r
ec
tifie
r
d
io
d
e.
T
h
er
ef
o
r
e,
o
u
tp
u
t
in
d
u
cto
r
c
u
r
r
en
t sam
e
as seco
n
d
ar
y
cu
r
r
e
n
t o
f
th
e
tr
a
n
s
f
o
r
m
er
.
T
h
u
s
,
−
=
(
)
1
(
3
3
)
I
n
ad
d
itio
n
,
th
e
o
u
tp
u
t c
a
p
ac
it
o
r
cu
r
r
en
t r
ip
p
le
is
.
−
=
(
−
)
1
(
3
4
)
An
d
at
2
−
=
1
2
(
−
1
−
2
)
2
(
3
5
)
At
2
,
s
in
ce
all
s
witch
es
ar
e
in
OFF
s
tate,
th
e
b
o
o
s
t
cir
cu
it
h
as
n
o
c
o
n
n
ec
tio
n
to
th
e
s
ec
o
n
d
ar
y
cir
c
u
it
lo
o
p
.
T
h
er
ef
o
r
e,
th
e
h
alf
b
r
i
d
g
e
ca
p
ac
ito
r
cu
r
r
e
n
t sam
e
as b
o
o
s
t in
d
u
cto
r
c
u
r
r
en
t.
T
h
u
s
,
1
=
(
3
6
)
As
d
ep
icted
f
r
o
m
th
e
ca
p
ac
ito
r
cu
r
r
e
n
t
wav
ef
o
r
m
,
ca
p
ac
ito
r
cu
r
r
en
t
is
co
n
s
tan
t
ac
r
o
s
s
th
e
p
er
io
d
o
f
(
1
−
1
)
.
T
h
u
s
.
1
−
=
(
3
(
−
1
)
2
−
2
−
2
)
(
1
−
1
)
(
3
7
)
At
2
,
b
ec
au
s
e
h
as n
o
e
n
er
g
y
tr
an
s
f
er
f
r
o
m
p
r
im
ar
y
cir
cu
it,
h
en
ce
.
−
2
=
−
(
)
2
(
3
8
)
−
2
=
−
(
)
1
(
3
9
)
T
h
is
d
er
iv
ed
e
q
u
atio
n
will f
u
r
t
h
er
ap
p
l
y
in
d
e
v
elo
p
m
e
n
t o
f
s
m
all
s
ig
n
al
an
d
s
tead
y
s
tate
m
o
d
ellin
g
.
3.
SM
A
L
L
-
S
I
G
NA
L
ANA
L
YS
I
S
Fo
r
th
e
p
r
o
p
o
s
ed
cir
cu
it
to
p
o
lo
g
y
,
t
h
e
cir
cu
it
av
er
a
g
in
g
an
d
av
er
a
g
e
s
witch
mode
l
a
r
e
u
s
ed
to
d
ev
elo
p
th
e
s
m
all
s
ig
n
al
m
o
d
e
l.
T
h
e
s
im
ilar
p
r
o
ce
d
u
r
e
[
1
0
]
ap
p
lied
to
d
ev
elo
p
th
e
s
m
all
s
ig
n
al
m
o
d
e
l.
T
h
e
s
m
all
-
s
ig
n
al
mode
l
is
th
en
u
s
e
d
to
f
in
d
t
h
e
co
n
tr
o
l
-
to
-
o
u
tp
u
t
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
co
n
v
e
r
ter
.
I
n
th
e
c
ase
o
f
th
e
p
r
o
p
o
s
ed
b
r
id
g
eless
co
n
v
er
ter
,
th
e
in
p
u
t
cu
r
r
en
t
is
th
e
s
am
e
cu
r
r
en
t
f
lo
w
to
th
e
in
d
u
cto
r
an
d
also
to
th
e
h
alf
b
r
id
g
e
ca
p
ac
ito
r
s
.
T
h
u
s
,
o
n
ly
in
d
u
cto
r
lo
o
p
an
d
o
u
tp
u
t c
ap
ac
ito
r
lo
o
p
ar
e
p
r
esen
ted
.
I
n
th
e
s
tead
y
s
tate,
th
e
av
er
ag
e
in
d
u
cto
r
v
o
ltag
e
is
ze
r
o
b
u
t
t
h
er
e
is
n
o
n
et
ch
an
g
e
in
in
d
u
c
to
r
cu
r
r
e
n
t
o
v
er
o
n
e
s
witch
in
g
p
er
io
d
.
Du
r
in
g
tr
an
s
ien
ts
o
r
ac
v
ar
iatio
n
s
,
th
e
av
er
ag
e
in
d
u
cto
r
v
o
ltag
e
is
n
o
t z
er
o
an
d
th
is
lead
s
to
n
et
v
ar
iatio
n
s
in
in
d
u
cto
r
cu
r
r
en
t.
T
h
e
n
et
ch
a
n
g
e
i
n
in
d
u
ct
o
r
cu
r
r
en
t
o
v
er
o
n
e
s
witch
in
g
p
er
io
d
is
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:
2
0
8
8
-
8
694
S
ma
ll
-
s
ig
n
a
l a
n
a
lysi
s
o
f a
s
in
g
le
-
s
ta
g
e
b
r
id
g
eless
b
o
o
s
t h
a
lf
-
b
r
id
g
e
…
(
Mo
h
a
ma
d
A
ffa
n
B
i
n
Mo
h
d
N
o
h
)
2365
ex
ac
tly
eq
u
al
to
in
d
u
cto
r
v
o
lt
ag
e.
I
t
ca
n
b
e
co
m
p
u
te
d
b
y
lin
ea
r
r
ip
p
le
ap
p
r
o
x
im
atio
n
.
T
h
u
s
,
th
e
wav
ef
o
r
m
s
n
o
w
will
b
e
r
e
p
lace
d
with
th
e
ir
lo
w
f
r
eq
u
e
n
cy
av
er
a
g
e
v
alu
e.
As
d
ep
icted
f
r
o
m
t
h
e
wa
v
ef
o
r
m
,
th
e
in
d
u
ct
o
r
cu
r
r
en
t
p
e
r
io
d
is
twice
o
f
s
witch
in
g
p
er
i
o
d
wh
ich
Mo
d
e
1
t
o
Mo
d
e
2
an
d
Mo
d
e
3
to
Mo
d
e
4.
T
h
er
e
f
o
r
e,
t
h
e
s
m
all
r
ip
p
le
ap
p
r
o
x
im
atio
n
eq
u
atio
n
at
Mo
d
e
1
in
ter
v
al
is
.
(
)
=
⟨
(
)
⟩
2
−
⟨
(
)
⟩
2
−
⟨
2
(
)
⟩
2
(
4
0
)
(
)
=
⟨
(
)
⟩
−
⟨
(
)
⟩
(
4
1
)
T
h
e
s
m
all
r
ip
p
le
ap
p
r
o
x
im
atio
n
eq
u
atio
n
at
Mo
d
e
2
in
ter
v
al
is
(
)
=
⟨
(
)
⟩
2
−
⟨
1
(
)
⟩
2
−
⟨
2
(
)
⟩
2
(
42
)
(
)
=
⟨
(
)
⟩
−
⟨
(
)
⟩
(
43
)
I
n
th
e
p
r
ev
io
u
s
s
tead
y
s
tate
an
aly
s
is
,
th
e
in
p
u
t
v
o
ltag
e
is
co
n
s
id
er
ed
to
b
e
co
n
s
tan
t.
Ho
we
v
er
,
in
th
e
n
ex
t
d
er
iv
atio
n
o
f
s
m
all
s
ig
n
al
mode
l,
th
e
s
in
u
s
o
id
al
in
p
u
t
v
o
ltag
e
will
b
e
u
s
ed
.
T
h
u
s
,
th
e
s
m
all
s
ig
n
al
eq
u
atio
n
d
escr
ib
es
o
n
h
o
w
t
h
e
lo
w
f
r
eq
u
e
n
cy
cir
cu
it
co
m
p
o
n
e
n
ts
wav
ef
o
r
m
ev
o
lv
e
in
tim
e.
T
h
e
in
p
u
t
s
in
u
s
o
id
al
ca
n
b
e
r
e
p
r
esen
ted
as
.
(
)
=
s
in
(
4
4
)
Su
b
s
titu
te
(
4
1
)
to
s
m
all
r
ip
p
le
ap
p
r
o
x
im
atio
n
e
q
u
atio
n
a
n
d
in
teg
r
ate
it
with
in
h
alf
c
y
c
le
o
f
in
p
u
t
v
o
ltag
e.
T
h
u
s
,
th
e
av
e
r
ag
e
in
d
u
cto
r
v
o
l
tag
e
ca
n
b
e
r
ep
r
esen
ted
as
.
⟨
(
)
⟩
=
(
⟨
(
)
⟩
−
⟨
(
)
⟩
2
−
2
(
)
2
)
1
(
)
+
(
(
)
−
1
(
)
2
−
2
(
)
2
)
2
(
)
(
45
)
T
h
e
av
er
a
g
e
ca
p
ac
ito
r
lo
o
p
eq
u
atio
n
ca
n
b
e
r
ep
r
esen
ted
as
.
⟨
(
)
⟩
=
(
⟨
(
)
⟩
−
⟨
(
)
⟩
)
1
(
)
+
(
−
⟨
(
)
⟩
)
2
(
)
(
46
)
B
o
th
(
42
)
an
d
(
43
)
is
n
o
n
-
lin
ea
r
d
if
f
e
r
en
tial
eq
u
atio
n
.
Nex
t,
ass
u
m
e
th
at
th
e
in
p
u
t
v
o
ltag
e,
d
u
ty
cy
cl
e,
d
e
p
en
d
e
n
t
v
o
ltag
es
an
d
cu
r
r
e
n
ts
ar
e
eq
u
al
to
s
o
m
e
q
u
iescen
t
v
alu
es
to
g
eth
er
with
s
u
p
er
im
p
o
s
ed
s
m
all
ac
v
ar
iatio
n
s
.
T
h
e
n
o
n
-
lin
ea
r
eq
u
atio
n
s
ca
n
b
e
lin
ea
r
ize
d
if
th
e
m
ag
n
itu
d
e
o
f
ac
v
a
r
iatio
n
s
ar
e
m
u
ch
s
m
aller
th
an
th
e
r
esp
ec
tiv
e
q
u
iescen
t
v
alu
es.
Hen
ce
,
in
s
er
t
th
e
p
er
t
u
r
b
ed
ex
p
r
ess
io
n
to
t
h
e
av
e
r
a
g
e
in
d
u
cto
r
v
o
ltag
e
eq
u
atio
n
an
d
ca
p
ac
ito
r
a
v
er
a
g
e
eq
u
atio
n
.
T
h
e
r
ef
o
r
e
,
th
e
r
e
ar
e
DC
ter
m
,
f
ir
s
t
o
r
d
er
ter
m
an
d
s
ec
o
n
d
o
r
d
e
r
ter
m
p
r
esen
t
in
th
e
in
d
u
cto
r
a
n
d
ca
p
ac
ito
r
av
er
a
g
e
lo
o
p
e
q
u
atio
n
s
.
Hen
ce
,
th
e
s
im
p
lifi
ed
f
ir
s
t
o
r
d
er
eq
u
atio
n
s
ar
e.
⟨
(
)
+
̂
(
)
⟩
=
(
⟨
(
)
+
̂
(
)
⟩
−
⟨
(
)
+
̂
(
)
⟩
2
−
⟨
2
(
)
+
̂
2
(
)
⟩
2
)
(
+
̂
1
(
)
)
+
(
⟨
(
)
+
̂
(
)
⟩
−
⟨
(
)
+
̂
(
)
⟩
2
−
⟨
2
(
)
+
̂
2
(
)
⟩
2
)
(
′
−
̂
1
(
)
)
(
4
7
)
⟨
+
̂
(
)
⟩
=
(
⟨
+
̂
(
)
⟩
−
⟨
+
̂
(
)
⟩
)
(
+
̂
1
(
)
)
+
(
−
⟨
+
̂
(
)
⟩
)
(
′
−
̂
1
(
)
)
(
4
8
)
DC
ter
m
s
o
n
ly
co
n
tain
in
g
DC
q
u
an
titi
es.
T
h
er
ef
o
r
e,
DC
ter
m
will
b
e
r
em
o
v
ed
i
n
o
r
d
er
to
g
et
s
m
all
s
ig
n
al
lin
ea
r
ize
eq
u
atio
n
.
T
h
e
s
ec
o
n
d
o
r
d
e
r
ac
ter
m
s
ar
e
n
o
n
lin
ea
r
b
ec
au
s
e
it
co
n
tain
s
th
e
p
r
o
d
u
ct
o
f
ac
q
u
an
titi
es.
On
t
h
e
o
th
er
h
an
d
,
th
e
s
ec
o
n
d
o
r
d
er
ac
te
r
m
s
ar
e
m
u
ch
s
m
aller
th
an
th
e
f
ir
s
t
o
r
d
er
f
o
r
m
.
T
h
er
ef
o
r
e,
th
e
s
ec
o
n
d
o
r
d
e
r
ter
m
s
will
b
e
n
eg
lecte
d
.
T
h
u
s
,
o
n
ly
f
ir
s
t
o
r
d
er
eq
u
atio
n
lef
t.
T
h
e
f
ir
s
t
o
r
d
er
ter
m
co
n
tain
s
a
s
in
g
le
ac
q
u
an
tity
wh
ich
m
o
s
tly
m
u
ltip
lied
b
y
a
co
n
s
tan
t
co
ef
f
icien
t
s
u
ch
as
DC
ter
m
.
T
h
ese
f
ir
s
t
o
r
d
er
e
q
u
atio
n
is
th
e
lin
ea
r
ize
eq
u
atio
n
wh
ic
h
d
escr
ib
es sm
all
s
ig
n
al
ac
v
ar
iatio
n
s
.
T
h
e
p
r
o
p
o
s
ed
cir
cu
it
av
er
ag
e
m
o
d
el
is
d
e
p
icted
in
Fig
u
r
e
4
(
a)
w
h
ich
d
er
iv
ed
f
r
o
m
t
h
e
o
f
(
4
7
)
a
n
d
(
4
8
)
.
T
h
e
av
er
a
g
e
s
witch
n
etwo
r
k
in
Fig
u
r
e
4
(
a)
also
ca
n
b
e
r
ep
r
esen
ted
as
a
tr
an
s
f
o
r
m
er
co
il
as
d
ep
icted
in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
2358
–
23
71
2366
Fig
u
r
e
4
(
b
)
.
Nex
t,
Fig
u
r
e
4
(
c)
is
th
e
eq
u
iv
alen
t
cir
c
u
it
av
er
ag
e
m
o
d
el
r
ef
er
r
ed
to
s
ec
o
n
d
ar
y
s
id
e
o
f
th
e
tr
an
s
f
o
r
m
er
.
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
Pro
p
o
s
ed
e
q
u
iv
alen
t
cir
cu
it o
f
s
m
all
s
ig
n
al
AC
,
(
a)
with
d
ep
en
d
e
n
t so
u
r
ce
s
,
(
b
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w
ith
id
ea
l D
C
tr
an
s
f
o
r
m
er
,
(
c)
r
ef
er
r
e
d
to
s
ec
o
n
d
ar
y
s
id
e
T
h
e
cir
cu
it
elem
en
ts
in
th
e
eq
u
iv
alen
t
cir
c
u
it
av
er
a
g
e
m
o
d
e
l
o
f
Fig
u
r
e
4
(
c)
is
t
h
en
co
n
v
er
ted
f
r
o
m
t
im
e
d
o
m
ai
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′
′
to
′
′
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o
m
ain
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T
h
e
v
o
ltag
e
s
o
u
r
ce
s
o
f
(
)
,
1
(
)
an
d
2
(
)
ar
e
s
et
eq
u
al
to
0
i
n
o
r
d
er
t
o
d
er
iv
e
th
e
co
n
tr
o
l
-
to
=
o
u
t
p
u
t
tr
an
s
f
er
f
u
n
ctio
n
(
)
(
)
.
On
th
e
o
th
er
h
an
d
,
th
e
(
)
,
1
(
)
an
d
2
(
)
is
eq
u
al
to
ze
r
o
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o
b
tain
t
h
e
li
n
e
to
o
u
tp
u
t
tr
an
s
f
er
f
u
n
ctio
n
(
)
(
)
.
T
h
e
o
u
tp
u
t
im
p
ed
an
ce
(
)
is
o
b
tain
ed
as
d
is
tu
r
b
an
ce
s
to
test
th
e
co
n
tr
o
l
to
o
u
tp
u
t tr
an
s
f
er
f
u
n
ctio
n
.
T
h
u
s
,
(
)
(
)
=
2
2
+
1
(
2
2
)
2
+
(
2
2
)
+
1
(
4
9
)
W
h
er
e;
=
2
(
1
−
)
(
5
0
)
(
)
(
)
=
×
1
(
2
2
)
2
+
(
2
2
)
+
1
(
5
1
)
W
h
er
e;
=
2
(
5
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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T
h
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mode
l
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Fig
u
r
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5
is
s
i
m
u
lated
with
co
n
tr
o
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d
esig
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MA
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B
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h
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r
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n
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eter
s
ar
e
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eter
m
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ed
b
ase
d
o
n
th
e
o
b
t
ain
ed
s
tead
y
s
tate
eq
u
atio
n
.
T
h
e
v
o
ltag
e
f
o
llo
wer
co
n
tr
o
l
m
eth
o
d
is
u
s
ed
to
v
er
if
y
th
e
o
p
e
r
atio
n
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
in
cir
c
u
it
s
im
u
lato
r
an
d
ex
p
er
im
en
tally
.
T
h
is
co
n
tr
o
l
m
eth
o
d
is
u
s
ed
to
r
e
g
u
late
th
e
o
u
tp
u
t
v
o
ltag
e
to
th
e
d
esire
d
v
alu
e
.
T
h
u
s
,
t
h
e
co
n
tr
o
ller
is
ex
p
ec
ted
to
p
r
o
v
i
d
e
th
e
ap
p
r
o
p
r
iate
d
u
t
y
cy
cle
f
o
r
an
y
lo
ad
ch
an
g
es.
T
h
is
clo
s
ed
lo
o
p
f
ee
d
b
ac
k
co
n
tr
o
ller
is
d
esig
n
e
d
u
s
in
g
th
e
co
n
tr
o
l
-
to
-
o
u
t
p
u
t tr
an
s
f
er
f
u
n
ctio
n
ex
p
r
ess
ed
b
y
(
49
)
.
It
is
th
en
co
m
p
ar
e
d
with
th
e
tr
an
s
f
er
f
u
n
ctio
n
th
at
o
b
tain
ed
f
r
o
m
th
e
s
witch
mode
l
in
PLE
C
S/
Simu
lin
k
.
T
h
is
is
to
p
r
o
v
e
th
at
th
e
d
er
iv
e
d
tr
an
s
f
er
f
u
n
ctio
n
(
49
)
is
co
r
r
ec
t.
T
h
e
s
in
u
s
o
id
al
wav
e
f
o
r
m
with
f
r
eq
u
en
c
y
o
f
1
0
-
1
0
0
0
Hz
an
d
am
p
litu
d
e
r
a
n
g
e
o
f
(
0
.
1
-
4
)
V
is
u
s
ed
to
p
er
tu
r
b
th
e
co
n
v
er
ter
d
u
ty
cy
cle
in
th
e
PLE
C
S
mode
l.
T
h
u
s
,
th
e
d
u
ty
cy
cle
th
at
d
r
iv
e
th
e
MO
SF
E
T
’
s
in
th
e
PLE
C
S
cir
cu
it
is
a
s
u
m
m
atio
n
o
f
1
an
d
th
e
p
er
t
u
r
b
ed
s
ig
n
al.
Fig
u
r
e
6
s
h
o
ws
th
e
b
lo
ck
d
iag
r
a
m
o
f
th
e
s
witch
Mo
d
e
l
with
p
er
tu
r
b
atio
n
o
f
d
u
t
y
cy
cle
in
th
e
PLE
C
S/S
im
u
lin
k
.
Fig
u
r
e
5
.
Pro
p
o
s
ed
c
o
n
v
er
te
r
s
m
all
s
ig
n
al
b
lo
ck
d
iag
r
am
in
Simu
lin
k
Fig
u
r
e
6.
Pro
p
o
s
ed
c
o
n
v
er
te
r
b
lo
ck
d
ia
g
r
am
in
PLE
C
S
4.
RE
SU
L
T
S
T
h
e
cir
c
u
it
m
o
d
el
in
PLE
C
S
is
u
s
ed
to
v
e
r
if
y
th
e
d
ev
elo
p
ed
tr
an
s
f
er
f
u
n
ctio
n
in
Simu
lin
k
.
T
h
e
b
o
d
e
-
p
lo
t
d
iag
r
am
o
b
tain
ed
f
r
o
m
th
e
m
ath
em
atica
l
ex
p
r
ess
io
n
is
co
m
p
ar
ed
with
th
e
b
o
d
e
-
p
l
o
t
d
iag
r
am
o
b
tain
e
d
in
t
h
e
PLE
C
S/S
im
u
lin
k
s
witch
m
o
d
el
as
d
ep
icte
d
in
Fig
u
r
e
7
.
T
h
e
p
lo
t
s
h
o
ws
th
e
s
am
e
m
ag
n
itu
d
e
an
d
Q
-
f
ac
to
r
o
b
tain
ed
f
r
o
m
th
e
m
ath
em
atic
al
ex
p
r
ess
io
n
an
d
PLE
C
S/S
im
u
lin
k
s
witch
mode
l.
Ho
wev
er
,
a
s
m
all
d
if
f
er
en
ce
o
f
co
r
n
e
r
f
r
eq
u
e
n
cy
ar
o
u
n
d
1
0
Hz
is
o
b
s
er
v
ed
.
T
h
is
d
u
e
to
id
ea
l
co
n
s
id
er
atio
n
i
n
d
ev
elo
p
in
g
th
e
m
ath
em
atica
l
ex
p
r
ess
io
n
.
T
h
u
s
,
th
e
r
esu
lts
s
h
o
w
g
o
o
d
ag
r
ee
m
en
t
b
etwe
en
th
e
m
ath
e
m
atica
l
ex
p
r
ess
io
n
co
n
tr
o
l
to
o
u
tp
u
t
tr
a
n
s
f
er
f
u
n
ctio
n
an
d
t
h
e
PLE
C
S/S
im
u
l
in
k
s
witch
mode
l.
T
h
er
e
f
o
r
e,
th
e
m
ath
em
ati
ca
l
ex
p
r
ess
io
n
(
49
)
w
h
ich
d
e
v
elo
p
ed
u
s
in
g
cir
cu
it
a
v
er
ag
in
g
te
ch
n
iq
u
es
is
v
alid
ated
.
I
n
th
is
wo
r
k
,
PI
co
n
tr
o
ller
is
u
s
ed
s
u
ch
th
at
th
e
o
u
tp
u
t v
o
lta
g
e
is
r
eg
u
lated
at
20
r
eg
ar
d
less
th
e
o
u
tp
u
t p
o
wer
co
n
d
itio
n
.
As
d
ep
icted
in
Fig
u
r
e
8
,
th
e
c
r
o
s
s
o
v
er
f
r
eq
u
e
n
cy
is
at
2
.
9
2
Hz
with
o
v
er
all
s
y
s
tem
p
h
as
e
m
ar
g
i
n
o
f
9
0
°.
T
a
b
le
2
s
h
o
ws
t
h
e
s
y
s
tem
p
er
f
o
r
m
an
ce
an
d
r
o
b
u
s
tn
ess
wh
ich
is
o
b
tain
ed
f
r
o
m
th
e
MA
T
L
AB
/S
im
u
lin
k
au
to
m
ate
d
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
ated
-
d
er
i
v
ate
(
PID
)
tu
n
in
g
ap
p
s
.
I
t
s
h
o
ws
th
at
th
e
s
y
s
te
m
m
ee
ts
th
e
Ny
q
u
is
t
s
tab
ilit
y
cr
iter
io
n
wh
er
e
b
y
th
e
s
y
s
tem
is
s
tab
le
if
th
e
p
h
ase
lag
at
th
e
c
r
o
s
s
o
v
er
f
r
e
q
u
en
c
y
is
less
th
an
1
8
0
°.
Ho
wev
er
,
a
n
o
v
er
s
h
o
o
t o
f
0
.
4
7
4
% o
cc
u
r
r
e
d
wh
ich
h
a
v
e
to
b
e
ac
ce
p
ted
.
T
h
e
s
m
all
-
s
ig
n
al
mode
l
ca
n
b
e
u
s
ed
to
d
eter
m
in
e
t
h
e
s
tab
ilit
y
o
f
t
h
e
p
r
o
p
o
s
e
s
y
s
tem
.
Ho
w
ev
er
,
th
er
e
s
till
h
av
e
s
o
m
e
lo
o
p
h
o
le
e
v
e
n
th
o
u
g
h
s
m
all
s
ig
n
al
m
o
d
e
l
ca
n
en
s
u
r
e
th
e
s
tab
ilit
y
o
f
t
h
e
s
y
s
tem
.
A
s
m
all
s
ig
n
al
mode
l
o
n
ly
co
n
s
id
er
e
d
a
s
m
all
v
ar
iatio
n
o
f
cir
cu
it
s
ig
n
al.
T
h
er
ef
o
r
e,
th
e
lar
g
e
s
ig
n
al
mode
l
is
im
p
o
r
tan
t
t
o
o
b
s
er
v
e
th
e
o
v
e
r
all
tim
e
r
esp
o
n
s
e
a
n
aly
s
is
eith
er
d
u
r
in
g
s
tead
y
-
s
tate
o
r
tr
an
s
ien
t.
T
h
e
lar
g
e
s
ig
n
al
af
f
ec
ts
th
e
o
p
er
atin
g
p
o
in
t
an
d
n
o
n
-
lin
ea
r
c
o
m
p
o
n
en
ts
.
I
n
th
is
wo
r
k
,
t
h
e
lar
g
e
-
s
ig
n
al
mode
l
as
d
ep
icted
in
Fig
u
r
e
9
is
d
ev
elo
p
e
d
b
y
c
o
n
s
id
er
in
g
th
e
cu
r
r
e
n
t
an
d
v
o
lta
g
e
wav
ef
o
r
m
s
d
u
r
in
g
l
o
ad
tr
a
n
s
ien
ts
an
d
s
tead
y
-
s
tate
co
n
d
itio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.