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p
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ar
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ap
p
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s
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s
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s
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im
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witch
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f
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eq
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cy
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T
h
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h
en
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m
e
n
o
n
p
r
ec
i
p
itates
au
d
ib
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m
ec
h
an
ical
n
o
is
e,
v
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ati
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s
,
a
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ag
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etic
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r
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o
f
elec
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o
m
ec
h
a
n
ical
s
y
s
t
em
s
[
1
]
.
A
p
leth
o
r
a
o
f
s
o
lu
tio
n
s
to
m
itig
ate
th
is
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s
u
e
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av
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b
ee
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p
r
o
p
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ed
b
y
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ar
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s
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esear
ch
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s
i
n
p
r
ec
ed
in
g
s
tu
d
ies.
T
h
e
ar
ticle
[
1
]
,
[
2
]
p
r
esen
ted
th
e
r
an
d
o
m
ca
r
r
ier
PW
M
(
R
C
P
W
M)
m
et
h
o
d
u
s
in
g
p
s
eu
d
o
-
r
an
d
o
m
b
it
s
eq
u
en
ce
(
PR
B
S).
T
h
e
r
an
d
o
m
r
ef
er
en
ce
PW
M
(
R
R
-
P
W
M)
an
d
r
a
n
d
o
m
r
e
f
er
en
ce
an
d
r
a
n
d
o
m
ca
r
r
ier
PW
M
(
R
R
R
C
-
PW
M)
m
eth
o
d
wi
th
th
e
r
an
d
o
m
n
ess
in
tr
o
d
u
ce
d
in
b
o
t
h
g
e
n
er
atio
n
o
f
m
o
d
u
latin
g
s
ig
n
al
a
n
d
s
elec
tio
n
o
f
ca
r
r
ie
r
s
ig
n
al
we
r
e
m
en
tio
n
ed
in
th
e
[
3
]
.
Nay
ee
m
u
d
d
i
n
et
a
l.
[
4
]
d
is
cu
s
s
es
th
e
im
p
lem
en
tatio
n
o
f
r
an
d
o
m
m
o
d
u
latin
g
-
ca
r
r
ier
P
W
M
alg
o
r
ith
m
f
o
r
ca
s
ca
d
ed
m
u
ltil
ev
el
i
n
v
er
ter
f
e
d
in
d
u
ctio
n
m
o
to
r
d
r
iv
e.
T
h
e
e
n
co
d
in
g
o
f
a
r
an
d
o
m
ca
r
r
ier
as
a
g
en
e,
th
e
r
an
d
o
m
ca
r
r
ier
s
eq
u
en
ce
co
r
r
esp
o
n
d
in
g
to
a
ch
r
o
m
o
s
o
m
e
,
an
d
th
e
f
i
tn
ess
f
u
n
ctio
n
as
th
e
r
ec
ip
r
o
c
al
o
f
th
e
m
ax
im
u
m
am
p
litu
d
e
o
f
th
e
h
ar
m
o
n
ic
s
p
e
ctr
u
m
f
o
r
R
C
PW
M
b
ased
o
n
t
h
e
g
en
etic
alg
o
r
ith
m
d
escr
ib
e
d
wer
e
p
r
o
p
o
s
ed
in
[
5
]
.
Oth
er
s
s
tr
ateg
ies
in
v
o
l
v
e
th
e
u
tili
za
tio
n
o
f
r
an
d
o
m
ize
d
ca
r
r
ier
f
r
eq
u
e
n
cy
m
o
d
u
lati
o
n
(
R
C
FM)
[
6
]
-
[
8
]
,
ch
ao
tic
ca
r
r
ier
r
a
n
d
o
m
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
C
C
R
P
W
M
)
[
9
]
an
d
r
an
d
o
m
ized
p
u
ls
e
p
o
s
itio
n
m
o
d
u
latio
n
(
R
PP
M)
as we
ll a
s
th
e
d
u
al
R
PW
M
m
eth
o
d
o
lo
g
y
,
wh
ich
a
m
alg
am
ates th
e
R
C
FM
an
d
R
PP
M
s
ch
em
es,
is
al
s
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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I
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N:
2088
-
8
6
9
4
Dev
elo
p
men
t o
f ra
n
d
o
m
p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tec
h
n
iq
u
e
fo
r
vo
lta
g
e
s
o
u
r
ce
…
(
Qu
o
c
Da
t
Lu
o
n
g
)
643
ap
p
lied
in
[
8
]
.
B
esid
es
th
at,
th
e
im
p
lem
e
n
tatio
n
o
f
th
e
r
an
d
o
m
s
p
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
R
SVP
W
M)
tech
n
iq
u
e
is
f
r
eq
u
en
tly
em
p
lo
y
e
d
as
an
ef
f
icac
io
u
s
s
o
lu
tio
n
f
o
r
th
e
g
en
er
atio
n
o
f
a
r
an
d
o
m
n
ess
ca
r
r
ier
[
1
0
]
-
[
1
4
]
.
Fu
r
t
h
er
m
o
r
e,
th
e
R
PW
M
alg
o
r
ith
m
ca
n
also
b
e
a
p
p
lied
i
n
p
h
o
to
v
o
ltaic
(
P
V)
in
v
er
ter
s
y
s
tem
s
f
o
r
d
o
m
esti
c
u
tili
za
tio
n
[
1
5
]
.
I
n
th
e
p
r
esen
t
s
tu
d
y
,
a
n
o
v
el
a
p
p
r
o
ac
h
f
o
r
th
e
d
e
v
elo
p
m
e
n
t o
f
R
PW
M
tech
n
iq
u
e
em
p
lo
y
e
d
in
s
in
g
le
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
in
v
er
te
r
(
VSI
)
will
b
e
in
v
esti
g
ated
.
T
h
e
c
o
n
f
ig
u
r
atio
n
o
f
ca
r
r
ie
r
s
tr
u
ctu
r
es
in
th
is
tech
n
iq
u
e
is
ch
ar
ac
ter
ized
b
y
a
1
6
-
b
it
b
i
n
ar
y
s
eq
u
e
n
ce
.
T
wo
d
if
f
er
en
t
m
eth
o
d
s
f
o
r
ca
r
r
ier
r
eg
u
latio
n
ar
e
p
r
o
p
o
s
ed
in
r
elatio
n
to
th
e
alg
o
r
ith
m
m
e
n
tio
n
ed
a
b
o
v
e
.
Su
b
s
eq
u
en
tly
,
t
h
e
g
en
etic
al
g
o
r
ith
m
(
GA
)
is
ap
p
lied
to
d
eter
m
in
e
th
e
o
p
tim
al
b
in
ar
y
s
eq
u
en
ce
s
o
l
u
tio
n
,
t
h
er
eb
y
allo
win
g
th
e
o
u
tp
u
t
v
o
ltag
e
s
ig
n
al
to
a
ttain
th
e
m
in
im
u
m
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
.
A
c
o
m
p
r
eh
en
s
iv
e
an
aly
s
is
o
f
th
e
h
a
r
m
o
n
ic
s
p
ec
tr
u
m
s
tr
u
ctu
r
e
o
f
th
e
o
u
tp
u
t v
o
ltag
e
s
ig
n
al
is
also
co
n
d
u
cted
th
r
o
u
g
h
th
e
ca
lc
u
latio
n
o
f
th
e
HSF.
2.
T
H
E
P
RO
P
O
SE
D
RP
W
M
T
E
CH
NIQU
E
S
W
ith
in
th
e
f
r
am
ewo
r
k
o
f
t
h
e
R
PW
M
tech
n
iq
u
e,
th
e
s
in
u
s
o
id
al
a
lter
n
atin
g
cu
r
r
en
t
(
AC
)
r
ef
er
e
n
ce
v
o
ltag
e
s
ig
n
al
is
co
m
p
ar
ed
wit
h
th
e
h
ig
h
-
f
r
eq
u
en
cy
r
an
d
o
m
t
r
ian
g
u
lar
ca
r
r
ier
s
ig
n
al
in
a
r
ea
l
-
tim
e
s
ettin
g
.
T
h
is
co
m
p
ar
is
o
n
is
in
s
tr
u
m
en
tal
in
ascer
tain
in
g
th
e
s
witch
in
g
s
tat
es
f
o
r
th
e
g
ates
o
f
th
e
I
GB
T
p
o
wer
m
o
d
u
les
with
in
s
in
g
le
-
p
h
ase
VSI
.
Fu
r
t
h
er
m
o
r
e,
th
e
lev
el
-
s
h
if
ted
a
p
p
r
o
ac
h
i
s
s
elec
ted
as
th
e
m
o
d
u
latio
n
s
ch
em
e
with
in
th
is
tech
n
iq
u
e.
Af
te
r
war
d
,
th
e
co
n
t
in
u
o
u
s
tr
ian
g
u
lar
ca
r
r
ier
s
co
r
r
esp
o
n
d
in
g
to
ea
ch
r
an
d
o
m
ly
g
en
er
ated
b
in
a
r
y
b
it
v
alu
e
ar
e
co
n
s
tr
u
cted
.
T
h
is
all
o
ws
f
o
r
th
e
ca
r
r
ier
s
h
ap
e
to
d
y
n
am
ically
a
d
ap
t
to
i
n
s
tan
tan
eo
u
s
b
in
a
r
y
v
alu
es,
th
er
eb
y
r
ed
u
cin
g
T
HD
in
c
o
m
p
ar
is
o
n
to
t
h
e
co
n
v
en
tio
n
al
SP
W
M
also
k
n
o
wn
as
f
ix
e
d
-
f
r
e
q
u
en
cy
PW
M
co
n
tr
o
l.
T
h
u
s
,
th
e
s
im
u
latio
n
e
x
p
er
im
e
n
ts
o
f
th
e
R
PW
M
ar
e
ca
r
r
ied
o
u
t th
r
o
u
g
h
two
d
is
tin
ct
alter
n
ativ
es:
˗
+
Op
tio
n
1
: Bi
n
ar
y
b
it v
alu
es o
f
0
an
d
1
ar
e
r
esp
ec
tiv
ely
ass
ig
n
ed
to
th
e
lo
wer
an
d
u
p
p
er
wav
ef
o
r
m
s
,
b
o
t
h
ex
h
ib
itin
g
id
e
n
tical
f
r
eq
u
en
cy
f
an
d
am
p
litu
d
e
A.
˗
+
Op
tio
n
2
is
c
o
n
s
tr
u
ed
as
an
ex
ten
s
io
n
o
f
th
e
wav
ef
o
r
m
s
e
s
tab
lis
h
ed
in
o
p
tio
n
1
:
A
b
in
a
r
y
b
it
v
alu
e
o
f
0
d
esig
n
ates
th
e
“sm
all”
wav
ef
o
r
m
(
with
a
f
r
eq
u
e
n
cy
2
f
an
d
am
p
litu
d
e
A)
,
wh
ile
a
b
in
ar
y
b
it
v
alu
e
o
f
1
d
esig
n
ates th
e
“lar
g
e”
wav
ef
o
r
m
(
with
a
f
r
eq
u
e
n
cy
f
a
n
d
am
p
litu
d
e
2
A)
.
E
m
p
l
o
y
i
n
g
v
a
l
u
e
s
w
h
e
r
e
t
h
e
a
m
p
l
i
t
u
d
e
A
i
s
s
e
t
t
o
0
.
2
5
a
n
d
t
h
e
f
r
e
q
u
e
n
c
y
f
i
s
e
s
t
a
b
l
is
h
ed
a
t
8
k
H
z
(8
k
H
z
i
s
n
o
t
t
o
o
h
i
g
h
t
o
a
v
o
id
g
e
n
e
r
a
t
i
n
g
e
x
c
e
s
s
i
v
e
t
h
e
r
m
al
l
o
s
s
e
s
i
n
t
h
e
s
e
m
i
c
o
n
d
u
c
t
o
r
s
w
it
c
h
e
s
d
u
r
i
n
g
t
h
e
o
p
e
r
a
t
i
o
n
o
f
t
h
i
s
i
n
v
e
r
t
e
r
)
.
T
h
e
f
r
e
q
u
e
n
c
y
o
f
t
h
e
r
e
f
e
r
e
n
c
e
s
i
n
u
s
o
i
d
a
l
w
a
v
e
i
s
d
et
e
r
m
in
e
d
t
o
b
e
5
0
H
z
.
C
o
n
s
e
q
u
e
n
t
l
y
,
t
h
e
r
e
t
e
n
ti
o
n
d
u
r
a
t
i
o
n
f
o
r
e
a
c
h
s
i
n
g
l
e
b
i
t
i
n
t
h
e
b
i
n
a
r
y
s
e
q
u
e
n
c
e
i
s
c
a
l
c
u
l
a
t
e
d
a
s
0
.
0
2
/
1
6
,
e
q
u
a
t
i
n
g
t
o
0
.
0
0
1
2
5
s
e
c
o
n
d
s
.
T
h
e
c
u
m
u
la
t
i
v
e
d
u
r
a
ti
o
n
f
o
r
e
a
c
h
b
i
n
a
r
y
s
e
q
u
e
n
c
e
is
d
e
te
r
m
i
n
e
d
t
o
b
e
1
/5
0
,
o
r
0
.
0
2
s
e
c
o
n
d
s
.
T
h
i
s
d
at
a
s
e
r
v
e
s
a
s
a
r
e
p
r
es
en
t
a
t
i
v
e
s
a
m
p
l
e
f
o
r
o
u
r
r
e
s
e
a
r
c
h
.
I
n
r
e
a
l
it
y
,
t
h
e
a
l
g
o
r
i
t
h
m
c
a
n
b
e
e
x
t
e
n
d
e
d
t
o
a
c
c
o
m
m
o
d
a
t
e
8
-
b
i
t
,
3
2
-
b
i
t
,
o
r
6
4
-
b
i
t
c
o
n
f
i
g
u
r
a
t
i
o
n
s
,
a
n
d
t
h
e
f
r
e
q
u
e
n
c
y
o
f
t
h
e
c
a
r
r
i
e
r
w
a
v
e
c
a
n
b
e
i
n
c
r
e
a
s
e
d
t
o
f
a
c
i
l
it
a
t
e
t
h
e
m
o
d
u
l
at
i
o
n
o
f
v
o
l
t
a
g
e
i
n
m
e
t
al
-
o
x
i
d
e
-
s
e
m
ic
o
n
d
u
c
t
o
r
f
i
e
l
d
-
e
f
f
e
c
t
t
r
a
n
s
is
t
o
r
(
MO
S
F
E
T
)
m
o
d
u
l
es
.
I
n
th
ese
2
p
r
o
p
o
s
ed
o
p
tio
n
s
,
a
s
y
s
tem
atic
s
h
if
t
o
f
b
in
ar
y
d
i
g
its
with
in
a
1
6
-
b
it
s
eq
u
e
n
ce
is
p
er
f
o
r
m
e
d
f
o
r
tr
an
s
itio
n
in
g
in
t
o
th
e
p
r
o
ce
s
s
o
r
f
r
o
m
th
e
least si
g
n
if
ican
t b
it (
L
SB
)
to
th
e
m
o
s
t sig
n
if
ica
n
t b
it (
MSB
)
.
T
h
is
p
r
o
ce
s
s
is
in
s
tr
u
m
en
tal
in
co
n
t
r
o
llin
g
th
e
s
elec
tio
n
o
f
ca
r
r
ier
s
,
as
s
h
o
wn
in
Fig
u
r
es
1
an
d
2
(
s
ee
A
p
p
en
d
ices
)
.
Su
b
s
eq
u
en
tly
,
th
is
s
p
ec
if
ic
1
6
-
b
it
s
eq
u
en
ce
is
r
eiter
ated
in
th
e
en
s
u
in
g
cy
cles
o
f
th
e
r
ef
er
en
ce
s
in
u
s
o
id
al
wav
e.
E
ac
h
ca
r
r
ier
s
ig
n
al
is
th
en
c
o
m
p
ar
ed
with
th
e
r
ef
er
e
n
ce
s
ig
n
al
to
g
en
e
r
ate
2
s
witch
in
g
s
ig
n
als
wh
ich
ar
e
co
m
p
lem
en
tar
y
f
o
r
co
n
t
r
o
llin
g
1
leg
o
f
th
e
VSI
.
I
n
ad
d
itio
n
to
th
e
e
x
is
tin
g
co
n
f
ig
u
r
atio
n
,
it
is
p
o
s
s
ib
le
to
cr
e
ate
s
eg
m
en
ts
ex
h
ib
itin
g
a
h
o
l
d
in
g
s
tate
in
to
th
e
ce
n
tr
o
id
o
f
th
e
s
elec
ted
wav
ef
o
r
m
i
n
th
e
r
eten
tio
n
d
u
r
atio
n
f
o
r
ea
ch
s
in
g
le
b
it
in
t
h
e
b
in
ar
y
s
eq
u
en
ce
,
as sh
o
wn
in
Fig
u
r
e
3
(
s
ee
A
p
p
en
d
ices
)
.
T
h
is
ap
p
r
o
ac
h
r
e
d
u
c
es th
e
n
u
m
b
er
o
f
s
witch
in
g
tim
es p
er
cy
cle
o
f
th
e
r
ef
er
en
ce
s
in
u
s
o
id
al
wav
e,
th
er
eb
y
r
ed
u
cin
g
s
witch
in
g
lo
s
s
es
o
n
s
em
ico
n
d
u
cto
r
s
witch
es
an
d
en
h
an
cin
g
th
e
ef
f
icien
cy
o
f
th
e
o
v
e
r
all
s
y
s
tem
.
Nev
er
th
eless
,
th
e
ap
p
licatio
n
s
o
f
th
is
p
r
o
p
o
s
a
l
in
th
e
d
o
m
ain
o
f
elec
tr
o
m
ec
h
an
ical
s
y
s
tem
c
o
n
tr
o
l
p
r
esen
t
ch
allen
g
es
d
u
e
to
th
e
n
o
n
-
lin
ea
r
ch
ar
ac
ter
i
s
tics
o
f
th
e
s
y
s
tem
p
r
o
p
er
ties
.
Mo
r
e
o
v
er
,
th
is
n
o
n
-
lin
ea
r
ity
co
m
p
licates
th
e
s
y
s
tem
’
s
r
esp
o
n
s
e
an
d
b
eh
av
io
r
,
th
u
s
p
o
s
in
g
d
if
f
icu
lties
in
c
o
n
tr
o
llin
g
t
h
em
ef
f
ec
tiv
ely
.
Hen
ce
,
in
th
e
f
o
ll
o
win
g
s
ec
tio
n
s
o
f
th
is
r
ese
ar
ch
,
o
u
r
p
r
im
ar
y
f
o
cu
s
will b
e
to
m
eticu
lo
u
s
ly
an
al
y
z
e
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
2
m
o
d
u
latio
n
tec
h
n
iq
u
es sh
o
w
n
in
Fig
u
r
es 1
an
d
2
.
3.
R
E
S
E
ARCH
M
E
T
H
O
D
-
O
P
T
I
M
I
Z
AT
I
O
N
O
F
O
UT
P
UT
VO
L
T
AG
E
T
H
D
I
N
RAND
O
M
M
O
DUL
AT
I
O
N
SCH
E
M
E
S
I
n
th
is
s
ec
tio
n
,
th
e
ap
p
licatio
n
o
f
GA
[
1
6
]
,
[
1
7
]
is
em
p
l
o
y
ed
to
d
eter
m
in
e
th
e
o
p
tim
al
b
it
s
eq
u
en
ce
cr
u
cial
f
o
r
co
n
tr
o
llin
g
t
h
e
ca
r
r
ier
s
ig
n
al
th
at
m
o
d
u
lates th
e
o
u
tp
u
t v
o
ltag
e
.
T
h
r
o
u
g
h
t
h
e
o
p
t
im
izatio
n
o
f
th
e
b
it
s
eq
u
en
ce
,
th
e
attain
m
e
n
t
o
f
a
n
o
u
tp
u
t
v
o
ltag
e
with
m
in
im
al
T
HD
is
ef
f
ec
tiv
ely
f
ac
ilit
ated
.
T
h
e
alg
o
r
ith
m
f
lo
wch
ar
t
p
r
esen
ted
in
Fig
u
r
e
4
d
escr
ib
es
th
e
e
v
o
lu
tio
n
p
r
o
ce
s
s
o
f
th
e
n
atu
r
al
p
o
p
u
latio
n
with
N
b
ein
g
th
e
n
u
m
b
er
o
f
in
d
iv
id
u
als
in
th
e
p
o
p
u
latio
n
,
th
r
o
u
g
h
th
e
p
r
o
c
ess
es
o
f
g
en
er
ate
p
o
p
u
latio
n
,
f
itn
ess
ev
alu
atio
n
,
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.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
64
2
-
65
6
644
s
elec
tio
n
,
cr
o
s
s
o
v
er
,
m
u
tatio
n
,
r
ep
lace
m
e
n
t,
a
n
d
te
r
m
in
atio
n
ch
ec
k
.
ea
c
h
o
f
th
ese
in
d
i
v
id
u
a
ls
is
a
1
6
-
b
it
b
i
n
ar
y
s
tr
in
g
th
at
ch
ar
ac
ter
izes th
e
c
o
n
f
ig
u
r
atio
n
o
f
ca
r
r
ier
s
tr
u
ct
u
r
e
to
r
eg
u
late
th
e
o
u
tp
u
t v
o
lta
g
e.
T
h
e
f
itn
ess
f
u
n
ctio
n
is
u
til
ized
to
ass
ess
th
e
q
u
ality
o
r
s
u
itab
ilit
y
o
f
in
d
i
v
id
u
als
with
in
a
p
o
p
u
latio
n
[
1
8
]
.
T
h
is
ass
ess
m
en
t
is
p
iv
o
tal
in
d
eter
m
in
in
g
t
h
e
r
ep
r
o
d
u
ctiv
e
s
u
cc
ess
o
f
ea
c
h
in
d
iv
i
d
u
al,
w
h
ich
is
in
h
er
en
tly
p
r
o
p
o
r
tio
n
al
to
t
h
eir
f
itn
ess
.
I
n
th
is
r
esear
ch
,
o
u
r
f
itn
ess
f
u
n
ctio
n
is
T
HD
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
ca
lcu
lated
u
p
to
3
0
k
Hz
as sh
o
wn
in
(
1
)
.
=
√
∑
600
=
2
1
(
1
)
W
h
er
e
,
is
th
e
am
p
litu
d
e
o
f
t
h
e
ℎ
h
ar
m
o
n
ic
v
o
ltag
e.
No
ta
b
ly
,
o
u
r
m
eth
o
d
o
lo
g
y
allo
ws
f
o
r
a
co
m
p
r
eh
en
s
iv
e
ex
ten
s
io
n
o
f
th
e
ca
lcu
late
d
f
r
eq
u
en
cy
r
an
g
e
to
e
v
en
h
ig
h
er
f
r
eq
u
e
n
cies.
T
h
is
ca
p
a
b
ilit
y
en
h
an
ce
s
th
e
s
co
p
e
p
r
o
v
id
i
n
g
a
m
o
r
e
v
er
s
atile
an
aly
tical
f
r
am
ewo
r
k
.
I
n
th
is
r
esear
ch
,
th
e
m
eth
o
d
o
f
r
ea
l
n
u
m
b
er
e
n
co
d
in
g
[
1
9
]
,
[
2
0
]
is
ap
p
lied
to
d
eter
m
in
e
t
h
e
o
p
tim
al
16
-
b
it
s
eq
u
en
ce
t
h
at
r
eg
u
lates
th
e
o
u
tp
u
t
v
o
ltag
e
with
m
in
im
al
T
HD.
No
tab
ly
,
th
e
r
ea
l
-
en
c
o
d
ed
v
alu
es
o
f
1
6
-
b
it
s
eq
u
en
ce
s
ar
e
d
is
cr
ete
i
n
teg
er
s
with
in
th
e
r
a
n
g
e
o
f
0
t
o
2
16
-
1
=
65535
.
T
h
is
ch
ar
ac
te
r
is
tic
s
ig
n
if
ican
tly
en
h
an
ce
s
th
e
ef
f
icien
c
y
o
f
t
h
e
GA
in
i
d
en
tify
in
g
th
e
o
p
tim
al
s
o
lu
tio
n
,
th
e
r
eb
y
ac
ce
l
er
atin
g
th
e
o
v
e
r
all
co
m
p
u
tatio
n
al
p
r
o
ce
s
s
.
Fig
u
r
e
4
.
T
h
e
p
r
o
ce
d
u
r
e
o
f
o
u
r
p
r
o
p
o
s
ed
GA
T
h
e
lin
ea
r
r
an
k
i
n
g
s
elec
tio
n
[
2
1
]
-
[
2
3
]
is
also
ap
p
lied
in
o
u
r
alg
o
r
ith
m
to
elim
in
ate
s
o
m
e
i
n
d
iv
id
u
als
with
lo
wer
ad
ap
tab
ilit
y
,
lead
in
g
to
a
r
ed
u
ctio
n
in
g
en
etic
d
iv
er
s
ity
in
th
e
p
o
p
u
latio
n
a
n
d
,
as
a
r
esu
lt,
ea
r
lier
co
n
v
er
g
en
ce
o
f
th
e
m
in
im
al
T
HD.
I
n
th
e
p
r
o
ce
s
s
o
f
o
p
ti
m
izin
g
ad
a
p
tab
ilit
y
,
in
d
iv
id
u
a
ls
ar
e
s
y
s
tem
atica
lly
o
r
g
an
ized
i
n
an
ascen
d
in
g
s
eq
u
en
ce
.
T
h
e
in
d
iv
id
u
al
e
x
h
ib
iti
n
g
th
e
h
ig
h
est
p
er
f
o
r
m
an
ce
is
co
n
f
er
r
e
d
with
th
e
r
an
k
o
f
N
,
wh
ile
th
e
o
n
e
d
em
o
n
s
tr
atin
g
th
e
least
p
er
f
o
r
m
an
ce
is
ass
ig
n
ed
th
e
r
an
k
o
f
1
.
I
t
is
n
o
tewo
r
th
y
th
at
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
Dev
elo
p
men
t o
f ra
n
d
o
m
p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tec
h
n
iq
u
e
fo
r
vo
lta
g
e
s
o
u
r
ce
…
(
Qu
o
c
Da
t
Lu
o
n
g
)
645
th
e
p
r
o
b
ab
ilit
y
o
f
s
elec
tio
n
f
o
r
ea
ch
in
d
iv
id
u
al
is
d
ir
ec
tly
c
o
m
m
en
s
u
r
ate
with
its
r
esp
ec
t
iv
e
r
an
k
[
2
4
]
.
T
h
e
s
elec
tio
n
p
r
o
b
a
b
ilit
y
o
f
ea
c
h
i
n
d
iv
id
u
al
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
its
r
an
k
as sh
o
wn
i
n
(
2
)
.
=
1
[
+
2
(
1
−
)
−
1
−
1
]
(
2
)
W
h
er
e,
=
1
.
.
̅
̅
̅
̅
̅
̅
an
d
0
<
<
1
.
I
n
a
d
d
itio
n
,
n
o
n
-
u
n
if
o
r
m
m
u
t
atio
n
is
u
s
ed
in
GA
to
r
an
d
o
m
ly
alter
o
n
e
o
r
m
o
r
e
g
en
e
s
o
f
ea
c
h
in
d
iv
id
u
al
to
in
cr
ea
s
e
s
tr
u
ctu
r
al
d
iv
er
s
ity
with
in
th
e
p
o
p
u
lati
o
n
.
T
h
e
m
u
tatio
n
o
p
er
atio
n
g
u
ar
an
tees
a
n
o
n
-
ze
r
o
p
r
o
b
a
b
ilit
y
o
f
r
ea
ch
i
n
g
an
y
p
o
in
t
in
th
e
s
ea
r
ch
s
p
ac
e.
W
e
d
ef
in
ed
=
〈
1
…
〉
is
a
ch
r
o
m
o
s
o
m
e
(
is
th
e
g
en
er
atio
n
n
u
m
b
er
)
a
n
d
th
e
elem
en
t
was
s
elec
ted
f
o
r
th
is
m
u
tatio
n
,
th
e
r
esu
lt
is
a
v
ec
to
r
+
1
=
〈
1
′
…
′
…
′
〉
,
with
′
ca
lcu
lated
ac
co
r
d
in
g
to
(
3
)
.
′
=
{
+
∆
(
,
−
)
if
a
r
an
d
o
m
d
ig
it is
0
−
∆
(
,
−
)
if
a
r
an
d
o
m
d
ig
it is
1
(
3
)
W
h
er
e
L
B
an
d
UB
ar
e
l
o
wer
a
n
d
u
p
p
er
d
o
m
ain
b
o
u
n
d
s
o
f
t
h
e
v
ar
iab
le
[
2
5
]
.
T
h
e
f
u
n
ctio
n
∆
(
,
)
r
etu
r
n
s
a
v
alu
e
in
t
h
e
r
a
n
g
e
[
0
,
]
s
u
ch
th
at
th
e
p
r
o
b
ab
ilit
y
o
f
∆
(
,
)
b
ein
g
cl
o
s
e
to
0
in
cr
ea
s
es
as
in
cr
ea
s
es.
T
h
e
∆
(
,
)
f
u
n
ctio
n
is
d
e
f
in
ed
b
y
th
e
m
ath
em
atica
l e
x
p
r
ess
io
n
as sh
o
w
n
in
(
4
)
.
∆
(
,
)
=
×
[
1
−
(
1
−
)
]
(
4
)
W
h
er
e
r
is
a
r
an
d
o
m
n
u
m
b
e
r
in
th
e
r
an
g
e
[
0
,
1
]
,
is
th
e
m
ax
im
al
g
en
er
atio
n
n
u
m
b
er
,
an
d
is
a
s
y
s
tem
p
ar
am
eter
d
eter
m
in
i
n
g
th
e
d
e
g
r
ee
o
f
d
ep
e
n
d
en
c
y
o
n
iter
atio
n
n
u
m
b
er
[
2
5
]
.
T
h
e
n
o
n
-
u
n
if
o
r
m
m
u
tatio
n
p
r
o
v
es
p
ar
ticu
lar
ly
well
-
s
u
ited
f
o
r
r
e
al
-
co
d
ed
GA
o
win
g
to
its
in
h
er
en
t
ch
ar
ac
ter
is
tic
wh
er
ein
t
h
e
in
f
lu
en
ce
o
f
t
h
e
m
u
tatio
n
p
r
o
ce
s
s
d
im
in
is
h
es o
v
er
an
e
x
ten
d
ed
r
u
n
tim
e
o
f
th
e
GA
[
2
6
]
.
Fin
ally
,
th
e
b
len
d
cr
o
s
s
o
v
er
(
B
L
X
-
α
)
tech
n
iq
u
e
[
2
7
]
-
[
2
9
]
is
ap
p
lied
as
a
GA
-
b
ased
m
eth
o
d
i
n
ex
p
lo
r
in
g
th
e
s
ea
r
ch
s
p
ac
e
b
y
g
en
er
atin
g
o
f
f
s
p
r
in
g
’
s
th
at
ar
e
a
b
len
d
o
f
th
e
p
ar
en
t
g
e
n
es
an
d
o
p
tim
izin
g
co
m
p
lex
m
u
lti
-
m
o
d
al
f
u
n
ctio
n
s
.
T
h
e
g
e
n
e
o
f
th
e
o
f
f
s
p
r
in
g
ch
r
o
m
o
s
o
m
e
is
r
a
n
d
o
m
l
y
s
elec
ted
with
in
th
e
clo
s
ed
in
ter
v
al
[
,
̅
]
as r
ep
r
esen
ted
in
(
5
)
.
=
r
a
n
dom
(
[
,
̅
]
)
with
=
min
(
,
)
−
‖
−
‖
an
d
̅
=
ma
x
(
,
)
+
‖
−
‖
(
5
)
T
h
e
B
L
X
-
c
r
o
s
s
o
v
e
r
o
p
e
r
a
t
i
o
n
(
e
s
p
e
c
i
al
l
y
i
n
t
h
e
c
a
s
e
o
f
=
0
.
5
)
a
n
d
l
i
n
e
a
r
c
r
o
s
s
o
v
e
r
a
r
e
m
o
s
t
s
u
i
t
a
b
le
f
o
r
r
e
a
l
-
e
n
c
o
d
e
d
G
A
.
T
h
e
s
e
o
p
e
r
a
t
i
o
n
s
h
a
v
e
t
h
e
a
b
i
li
t
y
t
o
g
e
n
e
r
a
t
e
o
f
f
s
p
r
i
n
g
o
u
t
s
i
d
e
t
h
e
d
o
m
a
i
n
[
min
(
,
)
,
ma
x
(
,
)
]
e
n
s
u
r
i
n
g
n
o
p
o
t
e
n
t
i
a
l
s
o
l
u
t
i
o
n
s
o
v
e
r
l
o
o
k
e
d
d
u
r
i
n
g
t
h
e
s
e
a
r
c
h
p
r
o
c
e
s
s
[
2
9
]
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
is
s
ec
tio
n
,
we
ap
p
ly
th
e
c
o
m
p
u
tatio
n
al
ca
p
ab
ilit
ies o
f
MA
T
L
AB
in
co
n
ju
n
ctio
n
with
th
e
PLE
C
S
B
L
OC
K
SET
p
ac
k
ag
es.
T
h
ese
to
o
ls
ar
e
u
tili
ze
d
to
ex
ec
u
te
th
e
GA
in
o
r
d
er
to
id
en
tify
th
e
o
p
tim
al
1
6
-
b
it
s
eq
u
en
ce
.
T
h
e
m
o
d
el
o
f
p
o
w
er
co
n
v
e
r
ter
b
u
ilt
in
th
e
PLE
C
S
B
L
OC
K
SET
is
d
escr
ib
ed
in
Fig
u
r
e
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I
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N
:
2
0
8
8
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8
6
9
4
I
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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
Dev
elo
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647
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m
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u
r
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.
R
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lts
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tain
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f
t
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tp
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ltag
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d
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b
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p
tim
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eq
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c)
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h
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m
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p
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tr
u
m
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.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
64
2
-
65
6
648
(
a)
(
b
)
(
c)
Fig
u
r
e
8
.
R
esu
lts
o
b
tain
ed
o
f
t
h
e
o
u
tp
u
t v
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ltag
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d
elin
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ted
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y
th
e
s
eq
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en
ce
with
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e
eq
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iv
alen
t r
ea
l
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co
d
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d
v
alu
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f
6
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2
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e
co
r
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t v
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m
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m
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.
1
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2
.
T
he
o
ptio
n 2
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
an
al
y
zin
g
th
e
o
u
tp
u
t
wav
e
f
o
r
m
o
f
th
e
o
p
tim
al
s
eq
u
en
ce
with
a
m
o
d
u
latio
n
in
d
ex
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f
0
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8
ar
e
s
h
o
wn
in
Fig
u
r
e
9
.
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n
Fig
u
r
e
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,
th
e
HSF
an
d
T
HD
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alu
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f
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h
ar
m
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s
p
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m
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1
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5
3
9
9
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d
4
8
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5
0
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esp
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tio
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2
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t h
ar
m
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p
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h
u
s
,
th
is
m
o
d
u
latio
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m
eth
o
d
is
n
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t
s
u
itab
le,
ev
en
th
o
u
g
h
t
h
e
T
HD
v
al
u
e
af
ter
o
p
tim
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n
b
y
GA
is
lo
we
r
th
an
th
at
o
f
th
e
f
ix
e
d
-
f
r
e
q
u
en
c
y
m
eth
o
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:
2088
-
8
6
9
4
Dev
elo
p
men
t o
f ra
n
d
o
m
p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tec
h
n
iq
u
e
fo
r
vo
lta
g
e
s
o
u
r
ce
…
(
Qu
o
c
Da
t
Lu
o
n
g
)
649
(
a)
(
b
)
(
c)
Fig
u
r
e
9
.
R
esu
lts
o
b
tain
ed
o
f
t
h
e
o
u
tp
u
t v
o
ltag
e
d
elin
ea
ted
b
y
th
e
o
p
tim
al
s
eq
u
en
ce
:
(
a
)
th
e
co
r
r
esp
o
n
d
in
g
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
,
(
b
)
th
e
r
ef
er
e
n
ce
s
in
u
s
o
id
al
wav
ef
o
r
m
an
d
th
e
ca
r
r
ier
wav
ef
o
r
m
,
an
d
(
c
)
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
4
.
1
.
3
.
Dis
cus
s
io
n
T
h
e
g
r
ap
h
d
escr
ib
in
g
t
h
e
v
ar
i
atio
n
o
f
T
HD
an
d
HSF,
as
in
f
l
u
en
ce
d
b
y
th
e
m
o
d
u
latio
n
in
d
ex
(
MI
)
,
is
s
h
o
wn
in
Fig
u
r
es
1
0
an
d
1
1
.
GA
-
o
p
tim
ized
R
PW
M
ex
h
ib
its
lo
wer
T
HD
co
m
p
ar
ed
to
co
n
v
en
tio
n
al
R
PW
M
an
d
ac
h
iev
es
b
etter
HSF,
in
d
ic
atin
g
im
p
r
o
v
ed
h
a
r
m
o
n
ic
s
u
p
p
r
ess
io
n
.
Op
tio
n
1
s
u
r
p
ass
es
o
p
tio
n
2
b
ec
a
u
s
e
th
er
e
ar
e
n
o
d
o
m
in
a
n
t
h
ar
m
o
n
ics
in
th
e
h
ig
h
-
f
r
eq
u
en
cy
r
eg
io
n
in
o
p
tio
n
1
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
wa
v
ef
o
r
m
o
f
o
p
tio
n
1
is
s
y
m
m
etr
ical
ab
o
u
t
th
e
h
o
r
izo
n
tal
ax
is
a
n
d
t
h
is
s
y
m
m
etr
ica
l
wav
ef
o
r
m
ch
a
r
ac
ter
is
tic
en
s
u
r
es
th
at
ze
r
o
-
o
r
d
er
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.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
64
2
-
65
6
650
h
ar
m
o
n
ics
(
also
k
n
o
w
n
as
DC
co
m
p
o
n
en
ts
)
ar
e
n
eg
lig
ib
le
in
t
h
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
.
Actu
ally
,
DC
co
m
p
o
n
en
ts
ca
n
s
atu
r
ate
in
p
o
wer
tr
an
s
f
o
r
m
er
s
an
d
it
ca
n
ca
u
s
e
v
ib
r
atio
n
an
d
a
u
d
ib
le
n
o
is
e
in
tr
an
s
f
o
r
m
er
s
.
T
h
u
s
,
in
th
e
h
ar
d
war
e
e
x
p
er
im
e
n
ts
in
ten
d
ed
to
v
alid
ate
th
e
e
f
f
icac
y
o
f
th
is
r
esear
ch
,
th
e
R
PW
M
m
eth
o
d
is
ex
clu
s
iv
ely
im
p
lem
en
ted
b
y
u
s
in
g
t
h
e
o
p
ti
o
n
1
.
Fo
r
th
e
r
ea
s
o
n
s
a
b
o
v
e,
th
e
alg
o
r
ith
m
o
f
o
p
tio
n
1
ca
n
b
e
co
m
p
letely
ap
p
lied
to
m
o
d
u
late
th
r
ee
-
p
h
as
e
v
o
ltag
e
f
o
r
th
e
co
n
tr
o
l
o
f
AC
m
o
to
r
s
.
Su
b
s
eq
u
e
n
tly
,
a
s
p
ee
d
co
n
tr
o
l
m
o
d
el
s
p
ec
if
ically
d
e
s
ig
n
ed
f
o
r
s
q
u
ir
r
el
-
ca
g
e
in
d
u
ctio
n
m
o
to
r
s
is
also
p
r
o
p
o
s
ed
.
Sp
ec
if
ic
ally
,
th
is
m
o
d
el
u
tili
ze
s
a
th
r
ee
-
p
h
ase
VSI
,
m
o
d
u
lated
b
y
GA
-
o
p
tim
ized
R
PW
M,
with
th
e
in
p
u
t
p
o
wer
f
o
r
th
is
s
y
s
tem
s
o
u
r
ce
d
f
r
o
m
th
e
s
o
lar
p
an
el
s
y
s
tem
.
T
h
is
is
o
n
e
o
f
th
e
im
p
o
r
tan
t a
p
p
licatio
n
s
o
f
t
h
is
alg
o
r
ith
m
f
o
r
s
elf
-
co
n
s
u
m
p
tio
n
o
f
PV r
en
ewa
b
le
en
er
g
y
.
4
.
2
.
H
a
rdwa
re
ex
perim
ent
s
T
h
e
h
ar
d
war
e
e
x
p
er
im
e
n
t
u
tili
ze
d
to
v
alid
ate
th
e
d
ev
elo
p
ed
co
n
tr
o
l
m
eth
o
d
is
s
h
o
wn
in
Fig
u
r
e
1
2
.
T
h
e
L
AUNCHXL
-
F2
8
3
7
9
D
Dev
elo
p
m
en
t
Kit
g
e
n
er
ates
co
n
tr
o
l
s
ig
n
als
PW
M_
T
OP1
an
d
PW
M_
B
OT
1
th
r
o
u
g
h
p
in
s
J
4
-
4
0
(
GPI
O0
)
an
d
J
4
-
3
9
(
GPI
O1
)
,
an
d
PW
M_
T
OP2
an
d
PW
M_
B
OT
2
t
h
r
o
u
g
h
p
in
s
J
4
-
38
(
GPI
O2
)
an
d
J
4
-
3
7
(
GPI
O3
)
,
s
u
p
p
ly
in
g
two
E
VAL
-
1
E
DI
6
0
I
1
2
AF
m
o
d
u
les
v
ia
X1
-
B
7
an
d
X1
-
B
8
.
T
h
e
F2
8
3
7
9
D
Kit
also
g
en
er
ates
G
ND
s
ig
n
als
th
r
o
u
g
h
J
2
-
2
0
a
n
d
J
1
0
-
GND
f
o
r
th
e
1
E
DI
6
0
I
1
2
AF
m
o
d
u
les
v
ia
t
h
e
R
E
SET
Sig
n
al
GN
D
p
in
,
p
r
o
v
id
es
a
3
.
3
V
E
NABLE
v
o
ltag
e
th
r
o
u
g
h
J
1
-
1
an
d
J
5
-
4
1
v
ia
X1
-
B
3
,
an
d
a
GND
v
o
ltag
e
th
r
o
u
g
h
J
7
-
6
2
an
d
J
1
0
-
GND
v
ia
X1
-
A1
6
.
(
a)
(
b
)
Fig
u
r
e
1
0
.
T
h
e
v
ar
iatio
n
o
f
(
a)
T
HD
an
d
(
b
)
HSF,
as in
f
lu
en
ce
d
b
y
t
h
e
m
o
d
u
latio
n
in
d
ex
(
MI
)
in
o
p
tio
n
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
Dev
elo
p
men
t o
f ra
n
d
o
m
p
u
ls
e
w
id
th
mo
d
u
la
tio
n
tec
h
n
iq
u
e
fo
r
vo
lta
g
e
s
o
u
r
ce
…
(
Qu
o
c
Da
t
Lu
o
n
g
)
651
(
a)
(
b
)
Fig
u
r
e
1
1
.
T
h
e
v
ar
iatio
n
o
f
(
a)
T
HD
an
d
(
b
)
HSF,
as in
f
lu
en
ce
d
b
y
t
h
e
m
o
d
u
latio
n
in
d
ex
(
MI
)
in
o
p
tio
n
2
Fig
u
r
e
1
2
.
E
x
p
e
r
im
en
tal
p
r
o
to
ty
p
e
o
f
t
h
e
o
p
tio
n
1
:
(
1
)
Oscill
o
s
co
p
e;
(
2
)
2
×
DC
r
eg
u
lated
p
o
wer
s
u
p
p
lies
;
(
3
)
R
-
L
lo
ad
s
(
4
m
H,
5
2
Ω
)
;
(
4
)
L
AUNCHXL
-
F2
8
3
7
9
D;
(
5
)
2
×
E
VAL
-
1
E
DI
6
0
I
1
2
AF m
o
d
u
les
Evaluation Warning : The document was created with Spire.PDF for Python.