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I
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8
7
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tr
u
ctu
r
ed
as
f
o
llo
ws
:
i)
s
ec
tio
n
2
p
r
esen
ts
th
e
p
r
o
p
o
s
ed
cir
c
u
it
an
d
its
p
er
f
o
r
m
an
ce
an
aly
s
is
in
b
o
th
s
y
m
m
etr
ic
an
d
asy
m
m
etr
ic
c
o
n
f
ig
u
r
atio
n
s
;
ii)
S
ec
tio
n
3
,
c
o
m
p
ar
is
o
n
an
al
y
s
es
o
f
th
e
s
u
g
g
ested
an
d
o
th
er
m
o
d
er
n
to
p
o
l
o
g
ies
ar
e
also
d
is
cu
s
s
ed
;
iii)
T
h
e
s
im
u
latio
n
r
esu
lts
u
s
in
g
th
e
m
o
d
if
ied
s
witch
in
g
s
ch
em
e
ar
e
d
is
cu
s
s
ed
in
s
ec
tio
n
4
;
an
d
iv
)
F
o
llo
wed
b
y
c
o
n
clu
s
io
n
in
s
ec
tio
n
5
,
an
d
th
e
r
ef
er
en
ce
s
ar
e
lis
ted
af
ter
t
h
at.
2.
P
RO
P
O
SE
D
CIR
CUI
T
T
h
e
to
p
o
lo
g
y
co
n
s
is
ts
o
f
s
er
i
es
co
n
n
ec
tio
n
b
asic
ce
lls
,
6
d
ev
ices
an
d
n
-
DC
v
o
ltag
e
(
as
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
.
T
h
e
b
asic
ce
ll
co
n
s
is
ts
o
f
2
DC
s
u
p
p
lies
an
d
2
d
ev
ices
(
S
1
an
d
S
1
’
)
as
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
.
T
h
e
d
ev
ices
S
1
an
d
S
1
’
ar
e
wo
r
k
e
d
in
a
o
p
p
o
s
ite
m
an
n
er
to
a
v
o
id
a
f
au
lt.
T
h
e
m
a
g
n
itu
d
e
o
f
DC
s
u
p
p
lies
f
o
r
a
b
asic
ce
ll
is
s
am
e;
it
is
s
y
n
th
esis
ze
r
o
an
d
2
V
dc
g
iv
en
in
T
a
b
le
1
.
R
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
in
clu
d
in
g
s
o
lar
ce
lls
,
f
u
el
ce
lls
with
en
er
g
y
s
to
r
ag
e
d
ev
ices
lik
e
b
atter
ies,
an
d
b
r
id
g
e
r
ec
tifie
r
s
with
is
o
latio
n
tr
an
s
f
o
r
m
e
r
s
,
ca
n
p
r
o
v
id
e
th
e
DC
v
o
ltag
e
s
o
u
r
ce
s
.
(
a)
(
b
)
Fig
u
r
e
1
.
Su
g
g
ested
c
ir
cu
it
: (
a
)
m
ain
cir
cu
it
a
n
d
(
b
)
b
asic u
n
it
T
ab
le
1
.
Switch
in
g
s
tates o
f
b
asic c
ell
S
t
a
t
e
S
1
O
u
t
p
u
t
v
o
l
t
a
g
e
F
i
r
st
ON
Ze
r
o
S
e
c
o
n
d
O
F
F
2V
dc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dec
em
b
er
20
2
4
:
7
9
8
-
807
800
2
.
1
.
Sy
m
m
e
t
ric
M
L
I
All
th
e
DC
v
o
ltag
e
s
o
u
r
ce
s
(
V
dc
)
h
av
in
g
s
am
e
v
al
u
es,
ca
lled
s
y
m
m
etr
ic
s
o
u
r
ce
ML
I
.
T
h
e
n
ec
ess
ar
y
co
u
n
t
o
f
DC
s
o
u
r
ce
s
(
n
)
,
n
u
m
b
er
o
f
lev
els
(
N
level
)
,
an
d
t
h
e
m
ax
im
u
m
o
b
tain
ed
o
u
t
p
u
t
v
o
ltag
e
(
V
0,
max
)
is
wr
itten
as
(
1
)
-
(
3
)
.
,
=
∑
=
=
1
(
1
)
=
(
−
1
)
/
2
(
2
)
=
2
+
1
(
3
)
Sep
ar
ate
DC
s
u
p
p
lies
ar
e
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
with
ar
r
o
w
m
ar
k
s
ac
co
r
d
in
g
to
th
e
o
u
tp
u
t
v
o
lta
g
e
lev
els.
T
h
e
s
u
g
g
ested
in
v
er
t
er
co
n
f
ig
u
r
atio
n
ca
n
b
e
d
is
r
eg
ar
d
ed
.
T
o
g
e
n
er
ate
a
f
if
te
en
-
lev
el
o
u
tp
u
t,
f
o
r
in
s
tan
ce
,
th
e
cir
cu
it
r
e
q
u
ir
es
7
in
p
u
t
s
u
p
p
lies
,
s
o
th
e
s
ep
ar
at
ed
DC
s
o
u
r
ce
is
o
m
itted
.
An
o
th
er
s
ce
n
ar
io
f
o
r
a
s
ev
en
teen
-
lev
el
ML
I
ca
lls
f
o
r
8
s
ep
ar
ate
DC
s
o
u
r
ce
s
,
ea
ch
o
f
wh
ich
is
s
et
to
b
e
(
V
dc
).
Hig
h
er
v
o
ltag
e
lev
els ar
e
s
y
n
t
h
esized
u
s
in
g
th
e
f
u
n
d
am
en
tal
u
n
its
.
Acc
o
r
d
in
g
to
(
4
)
,
wh
ic
h
d
escr
ib
es
th
e
co
r
r
elatio
n
b
etwe
en
p
an
d
n
,
th
e
n
u
m
b
er
o
f
b
asic u
n
its
s
h
o
u
ld
b
e
an
in
te
g
er
.
W
ith
th
e
v
alu
e
o
f
p
,
th
e
v
al
u
e
o
f
n
will b
e
u
p
d
ated
.
(
5
)
is
u
s
ed
to
d
eter
m
i
n
e
th
e
q
u
an
tity
o
f
p
o
wer
s
witch
es.
=
{
2
+
2
ℎ
2
+
1
ℎ
;
=
1
,
2
,
.
.
,
(
4
)
ℎ
=
{
(
+
4
)
ℎ
(
+
5
)
ℎ
(
5
)
Fo
r
in
s
tan
ce
,
ea
c
h
p
o
wer
s
em
ico
n
d
u
cto
r
d
e
v
ice
g
e
n
er
ates
a
n
u
n
n
ec
ess
ar
y
v
o
ltag
e
d
r
o
p
t
h
at
ca
u
s
es
th
e
s
witch
to
lo
s
e
p
o
wer
b
o
th
wh
en
it
co
n
d
u
cts
an
d
wh
en
it
ch
a
n
g
es
f
r
o
m
th
e
ON
to
th
e
OFF
s
tate.
C
o
n
d
u
ctio
n
a
n
d
s
witch
in
g
lo
s
s
es
ar
e
th
er
ef
o
r
e
p
r
ed
o
m
in
ate
ly
d
o
m
in
a
n
t.
I
n
th
e
s
u
g
g
ested
cir
cu
it,
h
alf
o
f
th
e
d
ev
ices
m
u
s
t
b
e
in
a
co
n
d
u
cti
n
g
s
tate
f
o
r
an
y
v
o
ltag
e
to
b
e
p
r
esen
t
at
th
e
o
u
tp
u
t
ter
m
in
al.
T
h
e
m
ag
n
itu
d
e
o
f
th
e
v
o
ltag
e
d
r
o
p
s
(
Vd
p
)
,
wh
ic
h
o
cc
u
r
s
wh
ile
s
witch
es a
r
e
o
p
er
atin
g
,
is
u
s
ed
in
(
6
)
.
W
h
en
lo
s
s
es a
r
e
tak
en
in
to
ac
co
u
n
t,
th
e
p
ea
k
o
u
tp
u
t v
o
lta
g
e
is
ca
lcu
lated
u
s
in
g
(
6
)
.
,
=
∑
−
{
2
}
=
1
(
6
)
2
.
2
.
Asy
m
m
et
ric
c
o
nfig
ura
t
i
o
n
T
h
e
v
alu
e
o
f
is
o
lated
DC
s
o
u
r
ce
s
f
r
o
m
d
i
f
f
er
en
t
b
asic
u
n
it
s
is
n
o
t
eq
u
al
in
asy
m
m
etr
ical
ML
I
.
Fo
r
in
s
tan
ce
,
th
e
p
er
f
o
r
m
an
ce
o
f
ML
I
is
im
p
r
o
v
ed
b
y
v
ar
y
in
g
th
e
v
alu
es
o
f
th
e
DC
v
o
ltag
e
s
o
u
r
ce
s
f
o
r
b
asic
u
n
its
.
As
a
r
esu
lt,
s
elec
tin
g
DC
v
o
ltag
e
s
o
u
r
ce
s
is
cr
u
cial.
T
o
ca
lcu
late
t
h
e
v
alu
e
o
f
DC
v
o
ltag
e,
f
o
u
r
d
if
f
e
r
en
t
m
eth
o
d
s
(
M1
,
M2
,
M3
,
an
d
M4
)
ar
e
s
u
g
g
ested
.
T
h
e
s
p
ec
if
ic
atio
n
s
f
o
r
ea
ch
m
eth
o
d
ar
e
lis
ted
in
T
ab
le
2
.
T
ab
le
2
.
Var
io
u
s
co
n
s
tr
ain
ts
o
f
th
e
s
u
g
g
ested
asy
m
m
etr
ical
ML
I
C
o
n
st
r
a
i
n
t
s
M
e
t
h
o
d
(
M
1
)
M
e
t
h
o
d
(
M
2
)
M
e
t
h
o
d
(
M
3
)
M
e
t
h
o
d
(
M
4
)
S
e
p
a
r
a
t
e
D
C
so
u
r
c
e
(
V
S,
dc
)
0
1
1
2
B
a
si
c
u
n
i
t
(
p
)
(n
-
1
)
/
2
(n
-
2
)
/
2
(n
-
2
)
/
2
(n
-
2
)
/
2
N
s
w
i
t
c
h
n
+
5
n
+
4
n
+
6
n
+
5
N
l
e
ve
l
2
(n+
3/
2)
−
1
2
(n+
2/
2)
−
1
3
×
2
(n/
2)
−
1
2
×
2
(n
+
3/
2)
−1
M
a
g
n
i
t
u
d
e
o
f
D
C
s
o
u
r
c
e
V
1,
1
=
V
2,
1
= V
dc
V
1,
j
=
V
2,
j
=
2
j
-
1
V
dc
j
=
2
,
3
,
…p
V
1,
1
=
V
2,
1
= V
dc
V
1,
j
=
V
2,
j
=
2
j
-
1
V
dc
j
=
2
,
3
,
…p
V
1,
1
=
V
2,
1
=
1
.
5
V
dc
V
1,
j
=
V
2,
j
=
2
j
-
1
V
dc
j
=
2
,
3
,
…p
V
1,
1
=
V
2,
1
=
2
V
dc
V
1,
j
=
V
2,
j
=
2
j
-
1
V
dc
j
=
2
,
3
,
…p
I
t
is
im
p
o
r
tan
t
to
n
o
te
th
at
ea
c
h
u
n
it'
s
in
p
u
t
DC
s
u
p
p
ly
v
alu
e
s
ar
e
d
if
f
er
e
n
t
f
o
r
ea
c
h
o
f
th
e
s
u
g
g
ested
m
eth
o
d
s
.
B
y
a
d
d
in
g
two
ad
d
itio
n
al
s
witch
es
to
d
iv
id
e
th
e
DC
v
o
ltag
e
s
o
u
r
ce
,
t
h
e
p
r
o
p
o
s
ed
in
v
er
ter
ca
n
in
cr
ea
s
e
v
o
ltag
e
lev
els
in
s
o
m
e
s
o
lu
tio
n
s
f
o
r
asy
m
m
etr
ic
s
tr
u
ctu
r
es.
T
h
is
s
witch
's
n
ew
co
n
f
ig
u
r
atio
n
with
a
s
ep
ar
ate
DC
s
o
u
r
ce
is
d
ep
ict
ed
in
Fig
u
r
e
2
.
T
h
e
M3
a
n
d
M4
m
eth
o
d
s
r
e
q
u
ir
e
t
h
is
r
ea
r
r
an
g
em
en
t.
C
ir
cu
it
r
ec
o
n
f
ig
u
r
atio
n
is
n
o
t r
eq
u
ir
ed
in
s
u
ch
a
ca
s
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Min
imi
z
a
tio
n
o
f th
e
circu
it c
o
mp
o
n
en
ts
w
ith
mo
d
ified
ca
s
ca
d
ed
mu
ltil
ev
el
…
(
R
a
g
h
ve
n
d
r
a
P
r
a
ta
p
S
in
g
h
)
801
Fig
u
r
e
2
.
Gen
e
r
alize
d
to
p
o
lo
g
i
es
f
o
r
asy
m
m
etr
ical
ML
I
3.
CO
M
P
ARA
T
I
V
E
ANA
L
YS
I
S
T
o
v
er
if
y
th
e
ef
f
ec
tiv
en
ess
o
f
s
u
g
g
ested
ML
I
b
ased
o
n
b
o
t
h
s
y
m
m
etr
ical
an
d
asy
m
m
etr
ical
cir
cu
its
,
we
p
r
o
p
o
s
e
f
o
u
r
alg
o
r
ith
m
s
t
o
d
eter
m
in
e
th
e
v
alu
e
o
f
i
n
p
u
t
DC
s
o
u
r
ce
s
,
wh
ich
ar
e
co
m
p
ar
ed
with
s
ev
er
al
asy
m
m
etr
ical
s
o
u
r
ce
ML
I
s
in
[
2
4
]
-
[
3
0
]
in
clu
d
in
g
class
ical
ca
s
ca
d
e
H
-
b
r
id
g
e
tr
i
n
ar
y
ci
r
c
u
it.
Als
o
,
r
elate
th
e
to
p
o
lo
g
ies
p
r
esen
ted
i
n
th
e
liter
atu
r
e
[
1
2
]
,
[
1
8
]
-
[
2
3
]
with
s
u
g
g
ested
s
y
m
m
etr
ical
co
n
f
ig
u
r
atio
n
s
(
with
an
d
with
o
u
t
s
ep
ar
ate
DC
s
o
u
r
ce
)
d
ep
icted
in
Fig
u
r
e
3
(
a
)
.
As
c
o
m
p
lete
f
r
o
m
f
ig
u
r
e
s
u
g
g
ested
cir
cu
it
with
(
P4
)
m
eth
o
d
o
f
f
er
s
f
ewe
r
s
witch
es
as c
o
m
p
ar
ed
t
o
o
th
er
m
en
tio
n
ed
ML
I
s
[
1
2
]
,
[
1
8
]
-
[
3
0
]
.
T
h
e
o
n
-
s
tate
d
ev
ices
in
ML
I
lead
to
u
n
wan
ted
d
r
o
p
s
th
at
r
ea
s
o
n
t
h
e
o
cc
u
r
r
en
ce
o
f
p
o
wer
lo
s
s
.
T
h
e
co
n
d
u
ctin
g
s
witch
es
co
u
n
t
is
f
ewe
r
in
th
e
s
u
g
g
ested
cir
c
u
it
as
co
m
p
ar
ed
to
co
n
tem
p
o
r
ar
y
to
p
o
lo
g
ies
as
s
h
o
wn
in
Fig
u
r
e
3
(
b
)
.
T
h
er
e
f
o
r
e,
th
e
to
tal
p
o
wer
lo
s
s
es
ar
e
m
in
im
ized
,
an
d
h
e
n
ce
th
e
ef
f
icien
cy
o
f
th
e
in
v
er
ter
is
im
p
r
o
v
e
d
.
th
e
n
u
m
b
er
o
f
DC
s
u
p
p
lies
in
d
if
f
er
e
n
t
co
n
f
ig
u
r
atio
n
s
is
s
h
o
wn
in
Fig
u
r
e
3
(
c
)
as
s
ee
n
f
r
o
m
co
m
p
ar
ativ
e
an
aly
s
is
th
e
s
u
g
g
ested
asy
m
m
etr
ical
co
n
f
ig
u
r
atio
n
-
b
ased
f
o
r
th
m
et
h
o
d
r
eq
u
ir
es
lo
wer
DC
s
o
u
r
ce
co
u
n
ts
th
an
[
1
2
]
,
[
1
8
]
-
[
3
0
]
.
Ho
wev
er
,
th
e
s
ec
o
n
d
an
d
th
ir
d
m
eth
o
d
s
o
f
p
r
o
p
o
s
ed
co
n
f
ig
u
r
atio
n
s
r
eq
u
ir
e
alm
o
s
t
th
e
s
am
e
n
u
m
b
er
o
f
DC
s
o
u
r
ce
s
as [
2
7
]
,
[
3
0
]
.
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
C
o
m
p
a
r
ativ
e
g
r
ap
h
s
:
(
a)
n
o
.
o
f
s
witch
es a
g
ain
s
t n
o
.
o
f
lev
els
,
(
b
)
n
o
.
o
f
o
n
-
s
tate
s
witch
er
s
ag
ain
s
t
n
o
.
o
f
lev
els
,
an
d
(
c)
n
u
m
b
e
r
o
f
DC
s
o
u
r
ce
s
ag
ain
s
t n
u
m
b
e
r
o
f
v
o
ltag
e
lev
els
0
50
100
150
200
0
10
20
30
40
50
60
70
80
N
u
m
b
e
r
o
f
o
u
t
p
u
t
v
o
l
t
a
g
e
l
e
v
e
l
s
N
u
n
m
b
e
r
o
f
s
w
i
t
c
h
e
s
[
C
H
B
]
[
2
2
]
[
2
9
]
[
1
2
]
[
1
9
-
2
1
,
2
3
]
[
1
8
]
[
2
8
]
P
r
o
p
o
s
e
d
s
y
m
m
e
t
r
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
[
2
4
,
2
5
]
C
H
B
t
r
i
n
a
r
y
c
o
n
f
i
g
u
r
a
t
i
o
n
[
3
0
,
P
3
]
[
2
7
,
P
1
]
[
2
6
,
P
2
]
P
r
o
p
o
s
e
d
a
s
y
m
m
e
t
r
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
[
P
4
]
0
50
100
150
200
0
10
20
30
40
0
10
20
30
N
u
m
b
e
r
o
f
o
u
t
p
u
t
v
o
l
t
a
g
e
l
e
v
e
l
s
N
u
n
m
b
e
r
o
f
O
N
-
s
t
a
t
e
s
w
i
t
c
h
e
s
[
2
6
]
[
C
H
B
]
[
2
2
]
[
1
9
-
2
1
,
2
3
]
[
1
8
]
[
2
8
]
P
r
o
p
o
s
e
d
s
y
m
m
e
t
r
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
[
3
0
]
[
2
4
,
2
5
]
[
2
7
]
C
H
B
t
r
i
n
a
r
y
c
o
n
f
i
g
u
r
a
t
i
o
n
[
1
2
]
[
2
9
]
[
P
4
]
P
r
o
p
o
s
e
d
a
s
y
m
m
e
t
r
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
0
10
20
30
40
50
60
70
80
0
10
20
30
40
0
10
20
30
N
u
m
b
e
r
o
f
o
u
t
p
u
t
v
o
l
t
a
g
e
l
e
v
e
l
s
N
u
n
m
b
e
r
o
f
d
c
s
o
u
r
c
e
s
C
H
B
t
r
i
n
a
r
y
c
o
n
f
i
g
u
r
a
t
i
o
n
[
1
8
]
[
2
8
]
P
r
o
p
o
s
e
d
s
y
m
m
e
t
r
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
[
2
4
,
2
5
]
[
3
0
]
[
2
7
]
[
2
6
]
[
1
2
]
[
C
H
B
]
[
2
9
]
[
2
2
]
[
1
9
-
2
1
,
2
3
]
[
P
4
]
P
r
o
p
o
s
e
d
a
s
y
m
m
e
t
r
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
3
,
No
.
4
,
Dec
em
b
er
20
2
4
:
7
9
8
-
807
802
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
M
o
du
la
t
io
n
t
ec
hn
iqu
es
f
o
r
s
wit
ches
T
h
e
s
u
g
g
ested
cir
cu
it
s
witch
e
s
ca
n
o
p
er
ate
b
o
th
,
at
th
e
f
u
n
d
am
en
tal
an
d
h
ig
h
er
s
witch
in
g
f
r
eq
u
e
n
cy
.
T
h
eir
d
if
f
er
en
t
m
o
d
u
latio
n
te
ch
n
iq
u
es
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
i
n
v
er
ter
s
lik
e
n
ea
r
est
lev
el
co
n
tr
o
l,
ca
r
r
ier
-
b
ased
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SP
W
M
)
[
3
1
]
,
[
3
2
]
,
an
d
s
elec
tiv
e
h
ar
m
o
n
ic
elim
in
atio
n
(
SHE)
m
o
d
u
latio
n
tech
n
iq
u
e
[
3
3
]
-
[
3
5
]
,
t
h
e
in
tr
icac
y
o
f
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
tech
n
i
q
u
e
f
o
r
h
ig
h
e
r
lev
els.
L
ik
ewise,
SHE
f
o
r
th
e
lar
g
e
v
o
ltag
e
lev
els in
th
e
s
u
g
g
ested
cir
cu
it is
n
o
t e
asy
as
it r
eq
u
ir
es d
eter
m
in
in
g
m
an
y
s
witch
in
g
an
g
les.
T
h
er
ef
o
r
e,
a
m
u
lticar
r
ier
-
b
ased
s
ch
e
m
e
with
a
ca
r
r
ier
f
r
e
q
u
en
c
y
o
f
1
k
Hz
is
tak
en
.
A
s
in
ewa
v
e
o
f
5
0
Hz
f
r
e
q
u
e
n
cy
is
ch
o
s
en
as
a
r
ef
er
en
ce
s
ig
n
al.
I
n
a
m
u
lticar
r
ier
-
b
ase
d
s
ch
em
e
(N
level
-
1)
ca
r
r
ier
s
ar
e
c
o
m
p
ar
e
d
with
r
e
f
er
en
ce
wav
e
f
o
r
m
an
d
s
witch
in
g
s
ig
n
al
o
b
tain
ed
u
s
in
g
l
o
g
ic
o
p
er
atio
n
s
.
T
h
e
co
r
r
esp
o
n
d
in
g
s
ig
n
als f
o
r
th
e
23
-
lev
el
in
v
er
ter
ar
e
illu
s
tr
ated
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
C
o
r
r
esp
o
n
d
i
n
g
s
ig
n
a
l f
o
r
2
3
-
lev
el
in
v
er
ter
4
.
2
.
Sim
ula
t
i
o
n
r
esu
lt
s
T
h
e
MA
T
L
AB
/Si
m
u
lin
k
s
o
f
t
war
e
h
as
b
ee
n
u
s
ed
to
a
n
aly
ze
s
im
u
latio
n
s
tu
d
ies
to
ass
ess
t
h
e
v
iab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
co
n
ce
p
t
o
f
ML
I
.
T
h
e
1
5
-
lev
el
an
d
1
7
-
le
v
el
in
v
er
ter
s
th
at
wer
e
s
u
g
g
ested
as
s
y
m
m
etr
ical
s
tr
u
ctu
r
es
ar
e
u
s
ed
.
T
h
e
s
ev
e
n
id
en
tically
s
ized
DC
s
u
p
p
lies
m
ak
e
u
p
th
e
1
5
-
lev
el
in
v
e
r
ter
cir
cu
it.
T
welv
e
p
o
wer
s
witch
es,
th
r
ee
b
asic
ce
lls
ex
clu
d
in
g
a
s
ep
ar
ate
DC
s
u
p
p
ly
,
an
d
ten
v
o
ltag
es
o
f
1
0
V
ea
ch
.
A
s
er
ies
R
L
b
r
an
ch
(
R
=
1
8
Ω
an
d
2
5
m
H)
is
tak
en
f
o
r
o
u
tp
u
t
ter
m
i
n
als.
I
n
co
n
tr
ast,
a
s
ec
o
n
d
in
d
e
p
e
n
d
en
t
DC
s
o
u
r
ce
is
ad
d
ed
to
th
e
1
7
-
lev
el
in
v
e
r
ter
,
as sh
o
wn
in
Fig
u
r
e
5
(
a
)
.
T
h
e
ML
I
cir
cu
it
with
2
3
an
d
3
1
lev
els
ar
e
u
s
ed
in
th
e
p
r
o
p
o
s
ed
asy
m
m
etr
ical
s
o
u
r
ce
co
n
f
ig
u
r
atio
n
s
as
s
h
o
wn
in
Fig
u
r
e
5
(
b
)
,
th
e
eq
u
iv
alen
t
ci
r
cu
its
o
f
th
e
3
1
-
lev
el
an
d
2
3
-
lev
el
i
n
v
er
ter
s
a
r
e
s
im
u
lated
u
s
in
g
m
eth
o
d
s
P1
an
d
P2
,
r
esp
ec
tiv
ely
,
b
ased
o
n
th
e
p
ar
a
m
eter
s
lis
ted
in
T
ab
le
2
.
T
ab
le
3
s
h
o
ws
th
e
s
witch
in
g
s
eq
u
en
ce
s
f
o
r
t
h
e
2
3
-
lev
el
an
d
3
1
-
le
v
el,
r
esp
ec
tiv
ely
.
Dif
f
e
r
en
t
lev
el
in
v
e
r
ter
s
with
1
5
,
1
7
,
2
3
,
an
d
3
1
le
v
els
ar
e
d
ep
icted
i
n
Fig
u
r
es
6
(
a
)
-
6(
d
)
r
esp
ec
tiv
ely
.
Vo
ltag
e
T
H
D
s
p
ec
tr
u
m
f
o
r
lev
els
1
5
,
1
7
,
2
3
,
a
n
d
3
1
ar
e
also
s
h
o
wn
alo
n
g
with
th
e
v
o
lta
g
e
wav
ef
o
r
m
in
Fig
u
r
es
6
(
b
)
-
6(
d
)
.
T
h
e
v
o
ltag
e
wav
e
f
o
r
m
'
s
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
was
r
ec
o
r
d
e
d
as
4
.
2
5
,
3
.
4
5
,
2
.
5
9
,
an
d
2
.
1
5
p
er
ce
n
t
f
o
r
th
e
1
5
,
1
7
,
2
3
,
a
n
d
3
1
-
lev
el
v
o
ltag
e
lev
els,
r
esp
ec
tiv
ely
.
T
h
is
s
tu
d
y
d
em
o
n
s
tr
ates th
at
m
o
r
e
v
o
ltag
e
lev
els p
r
o
d
u
ce
an
d
b
etter
T
HD
p
er
f
o
r
m
a
n
ce
.
I
n
o
r
d
er
to
v
er
if
y
th
e
r
o
b
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2
0
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n
d
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9
.
Dr.
T
h
a
k
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p
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b
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d
m
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tern
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ti
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c
o
n
fe
re
n
c
e
p
ro
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d
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n
g
s
(S
CI,
S
COPUS
,
a
n
d
Web
o
f
S
c
i
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n
c
e
).
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is
a
n
Ac
ti
v
e
Re
v
iew
e
r
o
f
IEE
E
Tra
n
sa
c
ti
o
n
s,
IET
Jo
u
rn
a
ls,
ITE
E
S
Wi
ley
IJE
(Tay
lo
r
a
n
d
F
ra
n
c
is)
a
n
d
s
o
m
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re
n
o
wn
e
d
jo
u
rn
a
ls
o
f
El
se
v
ie
r
p
u
b
li
c
a
ti
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n
(Re
n
e
wa
b
le
En
e
rg
y
,
I
JEP
ES
,
EP
S
R,
a
n
d
IAE
S
Jo
u
r
n
a
l
).
No
w,
h
e
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wo
rk
i
n
g
a
s
a
n
As
so
c
iate
P
ro
fe
ss
o
r
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n
Ra
b
i
n
d
r
a
n
a
th
Tag
o
re
Un
iv
e
rsity
Bh
o
p
a
l.
His
re
se
a
rc
h
in
tere
sts
in
m
u
lt
il
e
v
e
l
i
n
v
e
rters
e
sp
e
c
ially
in
th
e
t
o
p
o
l
o
g
y
a
n
a
ly
sis
a
n
d
m
o
d
e
ll
in
g
o
f
p
o
we
r
e
lec
tro
n
ic
s
c
o
n
v
e
rters
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
k
th
a
k
re
.
e
e
@g
m
a
il
.
c
o
m
.
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