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C
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Un
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jp
1.
I
NT
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UCT
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N
T
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elec
tr
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s
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s
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itio
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ch
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tech
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d
v
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ce
s
.
W
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f
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(
W
PT)
is
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ativ
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s
m
itter
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lo
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Usi
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o
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ag
n
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d
u
ctio
n
p
r
in
cip
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e
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tem
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n
elim
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ate
tr
ad
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ca
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le
co
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tio
n
s
,
p
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v
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eq
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s
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f
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wh
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r
esis
tin
g
d
y
n
am
ic
en
v
ir
o
n
m
en
ts
[
1
]
,
[
2
]
.
T
h
is
tech
n
o
lo
g
y
is
u
tili
ze
d
in
v
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io
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s
p
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ac
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in
ev
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d
ay
life
,
s
u
ch
as
elec
tr
ic
v
eh
icles
[
3
]
–
[
5
]
,
b
io
m
ed
ical
d
ev
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[
6
]
,
[
7
]
,
d
ig
ital
h
o
u
s
eh
o
ld
ap
p
lian
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s
[
8
]
,
[
9
]
,
an
d
in
d
u
s
tr
ial
elec
tr
icity
[
1
0
]
.
I
n
its
ap
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licatio
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en
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f
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[
1
1
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–
[
1
5
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.
So
m
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m
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co
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p
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T
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m
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im
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co
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to
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I
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I
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N:
2088
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8
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Lu
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)
2557
p
o
wer
-
tr
an
s
f
er
r
ed
.
Sh
ev
ch
e
n
k
o
et
a
l.
[
1
6
]
h
as
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p
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ted
a
co
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p
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n
s
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an
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tical
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ev
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s
f
o
r
s
o
m
e
to
p
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g
ies.
Dai
et
a
l.
[
1
7
]
d
is
cu
s
s
es
a
to
p
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lo
g
y
s
elec
tio
n
m
eth
o
d
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ased
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Sag
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[
1
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a
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th
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ly
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Mo
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Me
r
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s
[
1
9
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s
tated
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S
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d
c
o
u
p
lin
g
c
o
ef
f
icien
ts
ca
n
v
ar
y
th
o
u
g
h
d
eliv
er
m
ax
im
u
m
ef
f
icien
c
y
.
Detk
a
an
d
Gó
r
ec
k
i
[
2
0
]
p
r
esen
ts
th
e
g
en
er
al
ch
ar
ac
ter
is
tics
o
f
W
P
T
,
esp
ec
ially
th
e
en
er
g
y
tr
an
s
m
is
s
io
n
m
ec
h
an
is
m
,
d
is
cu
s
s
es
i
ts
ad
v
an
tag
es
an
d
d
is
ad
v
an
tag
es,
an
d
also
d
is
c
u
s
s
es
it
s
ap
p
licatio
n
in
ce
r
tain
in
d
u
s
tr
ial
f
ield
s
.
Ma
h
esh
et
a
l.
[
2
1
]
d
escr
ib
es
s
ev
er
al
to
p
o
lo
g
ies
in
g
en
er
a
l
with
o
u
t
e
x
p
lain
in
g
h
o
w
t
o
ch
o
o
s
e
th
e
co
r
r
ec
t
to
p
o
lo
g
y
f
o
r
a
n
ap
p
licatio
n
.
R
eh
m
an
et
a
l.
[
2
2
]
in
v
esti
g
ated
two
b
asic
to
p
o
lo
g
ies,
S
-
S
an
d
S
-
P,
f
o
r
u
n
s
y
m
m
etr
ical
an
d
s
y
m
m
etr
ical
co
ils
an
d
ca
lcu
lated
s
y
s
tem
ef
f
icien
cy
.
Usi
n
g
f
u
n
d
am
en
tal
to
p
o
lo
g
y
,
W
an
g
et
a
l.
[
2
3
]
p
r
o
p
o
s
ed
a
m
eth
o
d
to
ev
alu
ate
p
o
wer
tr
an
s
f
er
ca
p
a
b
ilit
y
an
d
an
aly
ze
b
if
u
r
ca
tio
n
p
h
en
o
m
en
a.
Ven
k
atesan
et
a
l.
[
2
4
]
in
v
esti
g
ated
th
e
b
asic
to
p
o
l
o
g
y
an
d
its
d
ev
el
o
p
m
e
n
t,
esp
ec
ially
th
e
tr
an
s
m
itter
s
id
e
an
d
o
u
tp
u
t
c
h
ar
ac
ter
is
tics
.
Fro
m
th
is
v
alu
a
b
le
r
esear
ch
,
t
o
p
o
lo
g
y
s
elec
tio
n
is
o
n
e
o
f
th
e
m
o
s
t
ch
allen
g
in
g
asp
ec
ts
o
f
b
u
ild
in
g
a
W
PT
s
y
s
tem
.
I
n
o
r
d
er
to
m
ak
e
a
p
r
ef
er
e
n
ce
o
f
th
e
to
p
o
lo
g
y
b
ased
o
n
th
e
u
n
k
n
o
wn
m
ax
im
u
m
p
o
wer
d
i
s
tr
ib
u
tio
n
,
we
h
av
e
to
co
m
p
ar
e
ea
ch
to
p
o
lo
g
y
an
d
its
c
h
ar
ac
ter
is
tics
in
ter
m
s
o
f
p
o
wer
q
u
an
tity
.
I
n
ac
tu
al
co
n
d
itio
n
s
,
it
m
ay
n
o
t
b
e
ea
s
y
to
ac
h
ie
v
e
th
e
m
a
x
im
u
m
p
o
wer
,
p
ar
ticu
lar
l
y
if
th
e
co
ils
f
o
r
p
o
wer
tr
a
n
s
f
er
ar
e
n
o
t
p
r
o
p
e
r
ly
alig
n
e
d
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
s
y
m
b
o
lic
im
p
e
d
an
ce
m
atch
in
g
m
et
h
o
d
to
ad
ap
t
to
d
y
n
am
ically
m
o
v
in
g
co
ils
f
o
r
b
asic
to
p
o
lo
g
ies.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
is
d
e
m
o
n
s
tr
ated
b
y
two
p
ar
am
eter
s
th
at
g
r
ea
tly
in
f
l
u
en
ce
th
e
r
ea
ch
i
n
g
o
f
m
a
x
im
u
m
p
o
wer
tr
an
s
f
er
:
t
h
e
p
o
wer
s
u
p
p
ly
f
r
eq
u
en
cy
an
d
a
co
u
p
lin
g
co
ef
f
icien
t.
T
h
e
o
p
er
atin
g
f
r
e
q
u
en
c
y
ca
n
b
e
ad
ju
s
te
d
m
o
r
e
q
u
ick
ly
f
r
o
m
a
tech
n
ic
al
p
er
s
p
ec
tiv
e,
a
n
d
th
e
co
u
p
lin
g
co
ef
f
icien
t
r
e
p
r
e
s
en
ts
th
e
co
il
m
is
alig
n
m
en
t
i
n
th
e
p
o
wer
tr
an
s
f
er
r
ed
o
f
th
e
W
PT
s
y
s
tem
.
T
h
is
in
v
esti
g
atio
n
is
in
ten
d
ed
to
p
r
o
v
id
e
a
co
m
p
r
eh
e
n
s
iv
e
an
d
s
tr
aig
h
tf
o
r
war
d
o
v
er
v
iew
o
f
p
o
wer
tr
an
s
f
er
,
g
iv
e
n
a
g
en
er
al
co
m
p
a
r
is
o
n
o
f
s
im
u
lat
io
n
r
esu
lts
.
T
h
is
ap
p
r
o
ac
h
is
also
ap
p
lied
to
s
o
m
e
to
p
o
lo
g
ies
in
o
r
d
er
to
d
eliv
er
m
ax
im
u
m
p
o
wer
to
t
h
e
lo
ad
,
wh
ich
is
th
e
m
ain
o
b
jectiv
e
o
f
th
e
W
PT
s
y
s
tem
.
2.
M
E
T
H
O
D
T
h
is
r
esear
ch
em
p
lo
y
s
a
f
u
n
d
am
en
tal
W
PT
cir
cu
it
co
m
b
in
ed
with
im
p
ed
an
ce
m
atch
in
g
.
I
m
p
ed
an
ce
m
atch
in
g
p
lay
s
a
k
ey
r
o
le
in
m
ax
im
izin
g
p
o
wer
tr
an
s
f
er
ef
f
icien
cy
.
I
t
en
s
u
r
es
th
at
th
e
in
p
u
t
im
p
ed
an
ce
,
in
clu
d
in
g
t
h
e
v
o
ltag
e
s
o
u
r
ce
,
alig
n
s
with
th
e
o
u
tp
u
t
im
p
e
d
an
ce
,
r
e
p
r
esen
tin
g
th
e
lo
ad
.
Sig
n
if
ican
t
p
o
wer
lo
s
s
es c
an
o
cc
u
r
with
o
u
t p
r
o
p
er
im
p
ed
an
ce
m
atch
in
g
,
d
ec
r
e
asin
g
s
y
s
tem
p
er
f
o
r
m
an
ce
.
2
.
1
.
Wirele
s
s
po
wer
t
ra
ns
f
er
Pair
ed
in
d
u
cto
r
s
ac
t
as
th
e
co
r
e
o
f
th
e
s
y
s
tem
W
PT
an
d
ar
e
f
u
n
d
am
e
n
tal
to
wir
eless
p
o
we
r
s
y
s
tem
s
.
Am
p
èr
e'
s
law
s
tate
s
th
at
th
e
c
u
r
r
en
t
f
lo
w
th
r
o
u
g
h
an
in
d
u
cto
r
g
e
n
er
ates
a
m
a
g
n
etic
f
ield
.
I
t
in
d
icate
s
th
at
a
s
tab
le
cu
r
r
en
t
in
d
u
ce
s
a
s
tab
le
m
ag
n
etic
f
ield
,
a
n
d
a
d
y
n
a
m
ic
cu
r
r
en
t
i
n
d
u
ce
s
a
d
y
n
am
i
c
m
ag
n
etic
f
ield
.
A
t
th
e
s
am
e
tim
e,
th
e
i
n
d
u
cto
r
p
air
will
p
r
o
d
u
ce
a
c
u
r
r
e
n
t
wh
en
v
ar
y
in
g
m
ag
n
etic
f
lu
x
p
en
etr
ates
th
e
in
d
u
cto
r
.
T
h
e
b
asic
elec
tr
ical
cir
cu
it
u
s
ed
in
th
is
m
o
d
el
co
m
p
r
is
es
two
clo
s
ed
lo
o
p
s
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
A
p
ar
tic
u
lar
co
il
h
as
s
elf
-
in
d
u
ctan
ce
1
an
d
2
co
m
b
i
n
ed
with
m
u
tu
al
in
d
u
ct
an
ce
,
wh
er
e
th
is
m
u
tu
al
in
d
u
ctan
ce
is
a
n
in
d
u
ctiv
e
c
o
u
p
lin
g
t
h
at
tak
es
i
n
to
in
ter
p
r
etatio
n
th
e
c
h
ar
ac
te
r
o
f
th
e
co
il
a
n
d
t
h
e
d
is
tan
ce
b
etwe
en
th
em
.
is
th
e
r
esis
tan
ce
with
in
a
p
o
wer
s
o
u
r
ce
,
an
d
is
th
e
lo
ad
r
esis
tan
ce
u
s
ed
in
t
h
e
s
y
s
tem
.
1
an
d
2
r
ef
er
s
t
o
ca
p
ac
ito
r
s
co
m
b
in
e
d
with
in
d
u
cto
r
s
in
s
er
ies
o
r
p
ar
allel
t
o
cr
ea
te
r
eso
n
an
ce
.
T
h
e
p
o
w
er
s
o
u
r
ce
,
,
is
an
alter
n
atin
g
cu
r
r
en
t
(
AC
)
s
u
p
p
ly
.
T
h
e
f
o
llo
win
g
eq
u
atio
n
r
ep
r
esen
ts
th
e
v
o
ltag
es
ac
r
o
s
s
th
e
in
d
u
ct
o
r
an
d
ca
p
ac
ito
r
,
r
esp
ec
tiv
ely
.
1
=
ω
1
1
+
ω
2
2
=
ω
1
+
ω
2
2
1
=
1
ω
2
2
=
2
ω
2
an
d
is
d
ef
in
ed
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
5
5
6
-
2
5
6
6
2558
=
√
1
2
I
n
g
en
e
r
al,
th
e
W
PT
cir
cu
it
co
n
s
is
ts
o
f
r
esis
to
r
s
,
in
d
u
cto
r
s
,
ca
p
ac
ito
r
s
,
an
d
v
o
ltag
e
s
o
u
r
ce
s
,
wh
ich
h
av
e
a
s
im
p
le
co
n
f
ig
u
r
atio
n
wh
o
s
e
b
eh
av
io
r
is
r
e
p
r
esen
ted
b
y
K
ir
ch
h
o
f
f
'
s
L
aw
(
v
o
ltag
e
an
d
cu
r
r
en
t)
an
d
Oh
m
'
s
L
aw.
B
ased
o
n
th
ese
laws,
th
e
eq
u
atio
n
f
o
r
ea
c
h
co
n
f
ig
u
r
atio
n
is
d
er
iv
e
d
in
th
e
f
o
llo
win
g
.
2
.
1
.
1
.
Series
-
s
er
ies (
S
-
S)
A
s
er
ies
-
s
er
ie
s
to
p
o
lo
g
y
u
s
es
two
ca
p
ac
ito
r
s
,
wh
ich
ar
e
in
s
er
ies
with
ea
ch
co
il,
as
illu
s
tr
ated
in
Fig
u
r
e
1
(
a)
.
T
h
is
to
p
o
l
o
g
y
is
th
e
s
im
p
lest
co
n
f
ig
u
r
atio
n
in
t
h
e
b
asic
W
PT
to
p
o
lo
g
y
.
T
h
e
cu
r
r
en
t
th
r
o
u
g
h
th
e
tr
an
s
m
itter
cir
cu
it
h
as
th
e
s
a
m
e
v
alu
e
f
o
r
ea
ch
co
m
p
o
n
e
n
t
(
=
1
=
1
)
,
an
d
th
e
r
ec
eiv
er
h
as
th
e
s
am
e
co
n
d
itio
n
(
=
2
=
2
)
.
r
ep
r
esen
ts
th
e
tr
an
s
m
itter
lo
o
p
cu
r
r
e
n
t,
wh
ich
s
tar
ted
f
r
o
m
th
e
v
o
ltag
e
s
o
u
r
c
e
th
r
o
u
g
h
th
e
ca
p
ac
ito
r
an
d
th
e
co
il,
wh
ile
h
as
th
e
o
p
p
o
s
ite
d
ir
ec
tio
n
f
r
o
m
th
e
tr
an
s
m
itter
s
id
e;
it
b
eg
i
n
s
f
r
o
m
t
h
e
lo
ad
to
t
h
e
co
il
i
n
a
co
u
n
ter
clo
ck
wis
e
d
ir
ec
tio
n
.
B
ased
o
n
th
ese
laws,
th
e
eq
u
atio
n
f
o
r
ea
ch
p
h
en
o
m
en
o
n
o
f
s
er
ies
-
s
er
ies to
p
o
lo
g
y
is
d
er
iv
e
d
as.
=
+
1
1
1
+
1
1
+
2
0
=
+
1
2
2
+
2
2
+
1
B
y
s
ep
ar
ati
n
g
th
e
e
q
u
ati
o
n
b
as
ed
o
n
v
o
lta
g
e
a
n
d
c
u
r
r
e
n
t
,
t
h
e
i
m
p
e
d
a
n
c
e
is
o
b
tai
n
ed
as
f
o
ll
o
win
g
e
q
u
ati
o
n
[
2
1
]
.
=
[
−
1
+
1
+
−
2
+
+
2
]
2
.
1
.
2
.
Series
-
pa
ra
llel
(S
-
P)
Fig
u
r
e
1
(
b
)
s
h
o
ws
th
at
th
e
c
o
il
in
th
e
tr
a
n
s
m
itter
is
p
air
ed
with
a
ca
p
ac
ito
r
as
a
p
r
e
v
io
u
s
to
p
o
lo
g
y
,
wh
er
ea
s
th
e
r
ec
eiv
in
g
co
il
is
p
air
ed
with
a
ca
p
ac
ito
r
in
p
ar
allel.
T
h
is
co
n
f
ig
u
r
atio
n
is
ca
l
led
a
s
er
ies
-
p
ar
allel
to
p
o
lo
g
y
.
On
t
h
e
tr
an
s
m
itter
s
id
e,
th
e
cu
r
r
e
n
t
f
o
r
ea
ch
c
o
m
p
o
n
e
n
t
is
th
e
s
am
e,
b
u
t
o
n
t
h
e
r
ec
eiv
er
s
id
e,
th
e
cu
r
r
en
t is d
if
f
e
r
en
t f
o
r
ea
ch
elem
en
t.
T
h
e
f
o
llo
win
g
is
th
e
ci
r
cu
it e
q
u
atio
n
s
.
=
+
1
1
1
+
1
1
+
2
0
=
+
2
2
+
1
=
2
+
2
T
h
e
im
p
ed
a
n
ce
Z
o
f
s
er
ies
-
p
ar
allel
is
,
=
[
3
2
1
2
−
2
3
2
−
1
2
2
2
−
1
−
2
2
1
(
2
2
2
−
1
)
+
1
(
2
2
2
−
1
)
+
−
2
2
2
−
1
−
2
2
2
−
1
−
2
2
2
2
−
1
]
2
.
1
.
3
.
P
a
r
a
llel
-
s
er
ies
(P
-
S)
I
n
a
p
a
r
allel
-
s
er
ies
cir
cu
it,
illu
s
tr
ated
in
Fig
u
r
e
1
(
c)
,
t
h
e
cir
cu
it
co
n
f
ig
u
r
atio
n
is
o
p
p
o
s
ite
to
th
e
p
r
ev
io
u
s
ci
r
cu
it.
T
h
e
cu
r
r
en
t
g
en
er
ated
f
r
o
m
th
e
s
o
u
r
ce
will
b
e
d
i
r
ec
tly
s
p
lit
in
to
th
e
c
ap
ac
ito
r
an
d
in
d
u
cto
r
.
T
h
e
cir
cu
it e
q
u
atio
n
s
ar
e:
=
+
1
1
+
2
=
1
+
1
0
=
+
1
2
2
+
2
2
+
1
T
h
e
im
p
ed
a
n
ce
Z
o
f
p
ar
allel
-
s
er
ies is
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
I
mp
ed
a
n
ce
ma
tch
in
g
a
n
d
p
o
w
er reco
ve
r
y
in
r
esp
o
n
s
e
to
co
il misa
lig
n
men
t
…
(
Lu
n
d
e
A
r
d
h
en
ta
)
2559
=
[
−
1
2
1
1
−
1
−
2
1
1
−
1
−
2
1
1
−
1
3
1
1
2
−
2
3
1
−
2
2
1
1
−
1
−
1
1
2
(
2
1
1
−
1
)
+
2
(
2
1
1
−
1
)
+
]
2
.
1
.
4
.
P
a
ra
llel
-
pa
r
a
llel
(P
-
P)
T
h
e
last
b
asic
to
p
o
lo
g
y
th
a
t
will
b
e
o
b
s
er
v
ed
is
p
ar
allel
-
p
ar
allel,
wh
er
e
th
e
c
u
r
r
en
t
in
ea
c
h
co
m
p
o
n
en
t
will
b
e
d
if
f
er
en
t,
b
u
t
th
e
v
o
ltag
e
will
b
e
th
e
s
am
e
in
ea
ch
co
m
p
o
n
en
t.
T
h
e
e
q
u
atio
n
s
b
elo
w
ar
e
d
er
iv
ed
f
r
o
m
t
h
e
cir
cu
it d
ia
g
r
a
m
s
h
o
wn
in
Fig
u
r
e
1
(
d
)
.
=
+
1
1
+
2
=
1
+
1
0
=
+
2
2
+
1
=
2
+
2
T
h
e
im
p
ed
a
n
ce
Z
o
f
p
ar
allel
-
p
ar
allel
is
,
=
[
1
+
2
3
2
+
3
2
1
2
+
−
3
1
1
2
−
2
−
2
3
1
+
]
wh
er
e,
=
4
1
2
1
2
−
2
1
1
−
2
2
2
−
2
4
1
2
+
1
=
−
4
1
2
1
2
+
2
1
1
+
2
2
2
+
2
4
1
2
−
1
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
.
W
PT
s
y
s
tem
in
(
a)
s
er
ies
-
s
er
ies to
p
o
lo
g
y
,
(
b
)
s
er
ie
s
-
p
ar
allel
to
p
o
lo
g
y
,
(
c
)
p
ar
alle
l
-
s
er
ies to
p
o
lo
g
y
,
an
d
(
d
)
p
ar
allel
-
p
ar
allel
to
p
o
l
o
g
y
2
.
2
.
I
m
peda
nce
m
a
t
ching
us
ing
s
y
m
bo
lic
co
nd
it
io
n
R
esear
ch
in
W
PT
p
r
im
a
r
ily
f
o
cu
s
es
o
n
ac
h
iev
in
g
m
ax
im
u
m
p
o
we
r
tr
a
n
s
f
er
.
On
e
r
eq
u
ir
em
en
t
f
o
r
r
ea
lizin
g
m
ax
im
u
m
p
o
wer
tr
a
n
s
f
er
is
co
n
s
id
er
in
g
s
y
s
tem
’
s
i
m
p
ed
an
ce
as a
m
a
x
im
u
m
p
o
w
er
tr
an
s
f
er
th
eo
r
em
.
T
h
er
ef
o
r
e,
th
e
im
p
e
d
an
ce
b
et
wee
n
s
o
u
r
ce
an
d
l
o
ad
is
d
et
er
m
in
ed
b
y
th
e
im
p
e
d
an
ce
m
atch
in
g
m
eth
o
d
in
v
ar
io
u
s
W
PT
s
ce
n
ar
io
s
.
T
y
p
i
ca
lly
,
th
e
im
p
ed
an
ce
m
atch
in
g
p
r
o
ce
s
s
in
a
W
PT
s
y
s
tem
co
v
er
s
two
p
ar
ts
,
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
5
5
6
-
2
5
6
6
2560
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
f
ir
s
t
p
ar
t
is
th
e
p
o
wer
s
o
u
r
ce
alo
n
g
with
its
im
p
ed
an
ce
,
wh
ile
th
e
s
ec
o
n
d
is
th
e
lo
ad
'
s
im
p
ed
an
ce
as
illu
s
tr
ated
in
eq
u
iv
alen
t
cir
cu
it.
Ma
x
im
u
m
p
o
wer
tr
an
s
f
er
is
o
b
tain
ed
w
h
en
th
e
two
p
ar
ts
h
av
e
th
e
s
am
e
v
alu
e
o
r
a
r
e
p
e
r
f
ec
tl
y
m
atch
ed
.
T
h
e
1
is
s
tated
as
im
p
ed
an
ce
o
f
t
h
e
in
p
u
t
s
id
e
(
v
o
ltag
e
s
o
u
r
ce
)
an
d
th
e
im
p
ed
an
ce
o
f
th
e
lo
ad
is
2
,
it d
eliv
er
s
th
e
m
ax
im
u
m
p
o
wer
to
th
e
lo
ad
if
1
=
2
̅
̅
̅
[
2
3
]
.
Fig
u
r
e
2
.
I
m
p
ed
a
n
ce
s
ettin
g
f
o
r
ev
er
y
to
p
o
l
o
g
y
T
h
e
2
im
p
ed
an
ce
is
an
im
p
e
d
a
n
ce
eq
u
atio
n
f
o
r
ea
ch
t
o
p
o
lo
g
y
as
in
Fig
u
r
e
2
,
wh
er
e
th
e
1
v
alu
e
m
u
s
t
b
e
th
e
s
am
e
as
th
e
co
n
ju
g
ate
v
alu
e
o
f
2
an
d
1
(
th
e
s
o
u
r
ce
im
p
ed
an
ce
)
is
ass
u
m
ed
to
b
e
a
p
u
r
ely
r
esis
tiv
e
lo
ad
.
I
n
o
r
d
er
to
s
im
p
lify
th
e
ca
lcu
latio
n
s
an
d
co
n
s
id
er
th
e
ca
s
es
o
f
ac
tu
al
co
n
d
itio
n
s
wh
er
e
p
ar
am
eter
s
ar
e
n
o
t a
lway
s
g
iv
en
an
d
k
ep
t c
o
n
s
tan
t,
th
e
f
o
llo
win
g
eq
u
atio
n
is
u
s
ed
,
1
=
1
√
1
1
,
2
=
1
√
2
2
,
1
=
1
√
1
1
,
2
=
1
√
2
2
T
h
e
f
o
llo
win
g
e
q
u
atio
n
s
s
h
o
w
th
at
th
e
s
o
u
r
ce
an
d
lo
a
d
i
m
p
ed
an
ce
e
q
u
ality
ar
e
s
ep
ar
a
ted
in
to
th
e
r
esis
tiv
e
an
d
r
ea
ctiv
e
c
o
m
p
o
n
en
ts
.
T
a
b
le
1
s
h
o
ws
two
e
q
u
atio
n
s
f
o
r
ea
ch
to
p
o
lo
g
y
i
n
im
p
ed
an
ce
m
atch
in
g
co
n
d
itio
n
s
wh
er
e
th
e
v
alu
e
eq
u
als 0
a
n
d
t
h
e
n
u
m
b
er
o
f
p
ar
a
m
eter
s
is
r
ed
u
ce
d
.
T
ab
le
1
.
I
m
p
ed
a
n
ce
m
atch
in
g
co
n
d
itio
n
f
o
r
ea
c
h
to
p
o
lo
g
y
To
p
o
l
o
g
y
I
mp
e
d
a
n
c
e
ma
t
c
h
i
n
g
c
o
n
d
i
t
i
o
n
S
-
S
0
=
2
4
1
2
−
4
1
2
+
2
1
2
1
2
+
2
1
2
2
2
−
1
2
1
2
2
2
−
2
1
2
0
=
−
2
2
1
+
1
2
2
+
2
1
2
2
−
1
1
2
2
S
-
P
0
=
−
2
2
1
2
2
+
2
1
2
2
−
1
2
1
2
2
+
2
(
−
1
)
+
1
2
2
0
=
−
2
4
1
+
4
1
−
2
1
1
2
−
2
1
2
2
+
2
2
1
2
+
1
1
2
2
2
P
-
S
0
=
−
2
2
1
2
1
+
2
1
2
1
−
1
2
1
2
2
−
2
2
+
1
2
2
0
=
2
4
2
−
4
2
+
2
2
1
2
+
2
2
2
2
−
2
1
1
2
−
2
1
2
2
2
P
-
P
0
=
−
2
2
1
2
1
2
−
2
4
+
2
1
2
1
2
+
4
−
2
1
2
−
2
2
2
+
1
2
2
2
0
=
2
1
1
−
2
2
2
2
−
2
1
1
+
2
2
2
+
1
1
2
2
−
2
1
2
2
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
wir
eless
p
o
wer
tr
an
s
f
er
s
y
s
tem
co
m
p
r
is
es
r
esis
to
r
s
,
in
d
u
cto
r
s
,
ca
p
ac
ito
r
s
,
an
d
v
o
ltag
e
s
o
u
r
ce
s
.
T
ab
le
2
s
h
o
ws th
e
n
o
tatio
n
u
s
ed
in
th
e
cir
cu
it.
I
n
d
esig
n
in
g
a
W
PT,
k
n
o
win
g
th
e
v
alu
es o
f
th
ese
p
ar
am
eter
s
is
r
eq
u
ir
ed
to
f
u
lf
ill
m
a
x
im
u
m
p
o
wer
.
T
h
is
p
ap
e
r
aim
s
to
h
elp
p
r
o
v
id
e
c
o
n
s
id
er
atio
n
s
f
o
r
d
eter
m
in
i
n
g
t
h
e
co
m
p
o
n
en
t v
alu
e
b
ased
o
n
th
e
im
p
ed
an
ce
m
atch
in
g
m
eth
o
d
.
B
ased
o
n
s
im
p
lifie
d
eq
u
atio
n
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
,
we
ca
n
s
im
p
lify
th
e
eq
u
atio
n
b
y
s
u
b
s
titu
tin
g
s
ev
er
al
v
ar
iab
les,
s
u
ch
as
1
,
2
,
1
,
an
d
2
.
Ma
n
y
o
th
e
r
p
a
p
er
s
s
tate
th
at
th
e
v
alu
es
o
f
th
ese
p
ar
a
m
eter
s
ar
e
d
eter
m
in
ed
to
b
e
th
e
s
am
e
to
m
ak
e
ca
lcu
latio
n
s
m
o
r
e
s
tr
aig
h
tf
o
r
war
d
.
Sti
ll,
s
elec
tin
g
th
e
co
m
p
o
n
en
t
v
alu
es
th
at
ar
e
p
r
ec
is
ely
th
e
s
am
e
wo
u
ld
b
e
to
u
g
h
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
th
e
s
p
ec
if
ic
co
n
d
itio
n
s
f
o
r
th
e
im
p
ed
a
n
ce
m
atch
in
g
co
n
d
itio
n
,
wh
ich
a
r
e
1
=
2
=
0
an
d
1
=
2
=
0
.
T
h
is
eq
u
ality
is
ar
r
an
g
ed
to
s
im
p
lify
th
e
eq
u
atio
n
b
y
m
in
im
izin
g
th
e
n
u
m
b
er
o
f
v
ar
iab
les ad
d
r
ess
ed
in
th
e
p
r
ev
i
o
u
s
s
ec
tio
n
,
as sh
o
w
n
in
T
ab
le
3
.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
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m
p
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g
I
SS
N:
2088
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T
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m
ax
im
u
m
p
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atch
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th
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ig
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5
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wh
ile
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p
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allel
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u
r
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3
(
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,
th
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Fro
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m
th
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m
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n
th
is
co
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n
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t
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m
ai
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tain
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o
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tim
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n
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g
h
th
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f
r
eq
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ad
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s
ted
ad
ap
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
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g
,
Vo
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15
,
No
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3
,
J
u
n
e
20
25
:
2
5
5
6
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2
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6
6
2562
I
n
co
n
tr
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m
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u
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3
.
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s
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tain
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th
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ased
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atch
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atch
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c
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ig
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r
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at
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e
ch
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e
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r
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en
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n
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m
m
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im
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m
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wer
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as
in
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u
r
e
3
(
b
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.
T
h
e
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d
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S
to
p
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ies
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e
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tp
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t
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ter
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e
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e
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k
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z,
as
in
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u
r
e
3
(
d
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an
d
3
(
f
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.
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n
Fig
u
r
e
3
(
h
)
,
th
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h
as
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m
p
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at
a
f
r
eq
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cy
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f
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(
a)
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(
b
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(
c)
(
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d
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(
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u
r
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atch
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atch
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f
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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C
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I
SS
N:
2088
-
8
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2563
T
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1
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u
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p
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u
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4
(
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ely
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Fig
u
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s
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Fi
g
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an
s
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r
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(
a)
(
b
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(
c)
Fig
u
r
e
4
.
C
o
m
p
a
r
is
o
n
o
f
th
e
a
v
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ag
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d
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e
to
c
o
m
p
o
n
e
n
t to
ler
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ce
s
(
a)
1
%,
(
b
)
5
%,
a
n
d
(
c)
10%
T
h
is
p
ap
er
d
em
o
n
s
tr
ates
s
ev
er
al
cr
u
cial
p
o
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ts
:
th
e
o
p
ti
m
al
f
r
eq
u
en
cy
an
d
d
is
tan
ce
o
f
wir
eless
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s
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ased
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s
y
m
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n
d
itio
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.
B
y
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co
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p
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r
atin
g
th
ese
s
y
m
b
o
lic
co
n
d
itio
n
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,
it
b
ec
o
m
es
p
o
s
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ib
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in
e
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m
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s
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is
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io
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n
d
er
d
if
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er
en
t
o
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e
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th
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u
s
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ap
p
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,
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ich
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s
ts
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s
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e
d
is
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s
h
av
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g
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ter
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a
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ce
,
w
h
ich
allo
ws
th
em
to
ad
ap
t e
f
f
ec
tiv
ely
to
d
y
n
am
ic
e
n
v
ir
o
n
m
en
tal
ch
an
g
es,
s
u
ch
as
in
co
n
s
is
ten
t o
b
s
tacle
s
o
r
in
ter
f
er
en
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
5
5
6
-
2
5
6
6
2564
4.
CO
NCLU
SI
O
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y
u
s
in
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f
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r
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tim
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s
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atch
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at
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b
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atch
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wh
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m
ax
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g
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f
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v
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p
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ased
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s
p
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co
n
d
itio
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f
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th
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f
f
icien
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f
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en
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ality
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.
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m
ea
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at
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n
m
ax
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ize
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n
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itter
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co
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.
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wo
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F
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in
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rre
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tl
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lan
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c
a
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tac
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a
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m
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jp
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ro
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g
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ri
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g
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t
Na
g
o
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a
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i
v
e
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in
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a
rc
h
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lete
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ra
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ra
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ro
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h
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m
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c
.
j
p
.
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