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th
e
f
o
u
n
d
elec
tr
ica
l
p
ar
am
eter
s
m
a
k
e
it
p
o
s
s
ib
le
t
o
d
ed
u
ce
b
o
th
th
e
m
i
n
o
r
it
y
c
ar
r
ier
’
s
lif
e
ti
m
e
an
d
d
if
f
u
s
io
n
len
g
t
h
s
u
s
in
g
t
h
e
an
al
y
tical
m
eth
o
d
.
2.
SO
L
AR
C
E
L
L
M
O
DE
L
I
N
G
2
.
1
.
E
lect
rica
l
mo
del o
f
do
ub
le
di
o
de
T
h
e
p
h
o
to
v
o
ltaic
ce
lls
ca
n
b
e
r
ep
r
esen
ted
b
y
t
h
e
S
h
o
ck
le
y
d
o
u
b
le
d
io
d
e
m
o
d
el
an
d
h
is
eq
u
iv
ale
n
t
elec
tr
ical
cir
cu
it
i
s
d
escr
ib
ed
b
y
t
h
e
d
ia
g
r
a
m
o
f
Fi
g
u
r
e
1
[
1
2
]
.
T
h
e
an
al
y
t
ical
r
elatio
n
s
h
ip
b
et
w
ee
n
th
e
c
u
r
r
en
t
I
an
d
th
e
v
o
lta
g
e
V
o
f
t
h
is
m
o
d
el
is
:
(
(
(
⁄
(
(
(
⁄
(
⁄
(
1
)
T
h
e
elec
tr
ical
ter
m
s
o
f
th
i
s
eq
u
atio
n
ar
e
th
e
p
h
o
to
cu
r
r
en
t
,
th
e
d
if
f
u
s
io
n
r
e
v
er
s
e
s
a
tu
r
atio
n
cu
r
r
en
t
,
th
e
r
ec
o
m
b
i
n
atio
n
r
ev
er
s
e
s
atu
r
atio
n
c
u
r
r
en
t
,
th
e
id
ea
lit
y
f
ac
to
r
s
o
f
th
e
t
w
o
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io
d
e
s
(
,
th
e
s
er
ies
r
esis
ta
n
ce
,
th
e
p
ar
allel
r
esis
ta
n
ce
(
o
r
s
h
u
n
t)
.
T
h
e
th
er
m
al
v
o
ltag
e
(
⁄
o
f
th
e
P
VC
is
eq
u
al
ap
p
r
o
x
i
m
atel
y
to
at
,
(
q
)
is
t
h
e
ele
m
en
tar
y
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t
r
o
n
ch
ar
g
e,
(
K)
is
th
e
B
o
ltz
m
an
n
's
co
n
s
ta
n
t,
an
d
(
T
)
is
th
e
ab
s
o
lu
te
ce
ll te
m
p
er
atu
r
e.
Fig
u
r
e
1
.
T
h
e
d
o
u
b
le
-
d
io
d
e
e
q
u
iv
a
len
t c
ir
c
u
it
m
o
d
el
2
.
2
.
M
ino
it
y
ca
rr
ier
life
t
im
e
m
ea
s
ure
m
e
nt
As
cited
p
r
ev
io
u
s
l
y
,
t
h
e
m
i
n
o
r
it
y
ca
r
r
ier
r
ec
o
m
b
in
atio
n
is
q
u
a
n
ti
f
ied
b
y
th
e
ir
lif
e
t
i
m
es.
T
h
e
d
o
m
i
n
a
n
t
t
y
p
e
o
f
r
ec
o
m
b
i
n
ati
o
n
i
n
t
h
e
s
ilico
n
i
s
t
h
e
Sh
o
c
k
l
e
y
–
R
ea
d
–
Hall
(
S
R
H)
m
ec
h
an
is
m
.
I
n
th
is
last
,
th
e
r
ec
o
m
b
i
n
atio
n
o
f
t
h
e
elec
tr
o
n
d
o
es
n
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t
f
o
llo
w
a
d
ir
ec
t
tr
an
s
iti
o
n
f
r
o
m
t
h
e
co
n
d
u
ct
io
n
to
th
e
v
alen
ce
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an
d
s
,
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u
t
it
f
o
llo
w
s
a
n
i
n
d
ir
ec
t
tr
an
s
itio
n
v
ia
t
h
e
r
ec
o
m
b
i
n
atio
n
zo
n
e
s
w
h
ich
h
i
s
e
n
er
g
y
le
v
el
is
lo
ca
ted
in
f
o
r
b
id
d
en
b
an
d
g
ap
.
A
l
s
o
,
th
e
b
u
l
k
r
ec
o
m
b
in
at
io
n
li
f
eti
m
e
o
f
m
i
n
o
r
ity
ca
r
r
ier
s
is
h
i
g
h
l
y
d
ep
en
d
i
n
g
o
n
t
h
e
d
en
s
it
y
an
d
th
e
p
o
s
itio
n
o
f
th
e
s
e
tr
ap
s
.
T
h
e
(
is
id
en
ti
f
ied
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
[
1
3
]
:
⁄
(
2
)
W
h
er
e
(
th
e
e
x
ce
s
s
o
f
t
h
e
ch
ar
g
e
ca
r
r
ier
s
is
r
elate
d
to
th
e
eq
u
ilib
r
iu
m
,
an
d
(
is
t
h
e
r
ec
o
m
b
i
n
atio
n
r
ate
S
R
H
in
t
h
e
P
VC
.
T
h
is
lif
eti
m
e
i
n
th
e
j
u
n
ctio
n
ca
n
id
e
n
ti
f
y
t
h
e
d
if
f
u
s
io
n
le
n
g
th
o
f
th
e
m
i
n
o
r
it
y
ca
r
r
ier
.
T
h
is
last
r
ep
r
esen
t
s
th
e
av
er
a
g
e
d
is
ta
n
ce
th
at
a
p
h
o
to
-
g
en
er
ated
ca
r
r
ier
ca
n
cr
o
s
s
b
ef
o
r
e
it
is
r
ec
o
m
b
i
n
ed
.
T
h
e
r
elatio
n
s
h
ip
b
et
w
ee
n
an
d
(
is
d
ef
i
n
ed
b
y
th
e
f
o
llo
w
in
g
f
o
r
m
u
la
[
1
3
]
:
√
(
3
)
W
ith
(
is
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d
if
f
u
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io
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icien
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li
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o
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th
e
d
e
f
ec
ts
le
v
el
i
n
th
e
j
u
n
ctio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
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I
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N:
2252
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8792
A
F
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105
3.
P
RO
P
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D
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C
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RIC
AL
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itate
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r
E
q
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atio
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(
1
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,
w
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i
s
d
i
f
f
ic
u
lt
to
o
b
tain
an
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w
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et
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o
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s
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t
h
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tu
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n
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u
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ical
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h
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tr
ac
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p
ar
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m
eter
s
is
p
r
esen
ted
u
s
i
n
g
t
w
o
s
t
ep
s
.
T
h
e
b
est
ch
o
ice
o
f
in
itial
p
a
r
a
m
eter
s
ca
n
ac
ce
ler
ate
t
h
e
alg
o
r
ith
m
co
n
v
er
g
e
n
ce
.
C
o
n
t
r
ar
y
,
p
o
o
r
in
itial
v
alu
e
s
in
cr
ea
s
e
t
h
e
iter
atio
n
s
n
u
m
b
er
an
d
ca
n
af
f
ec
t
o
n
th
e
o
p
ti
m
izatio
n
al
g
o
r
ith
m
.
I
n
liter
atu
r
e
m
a
n
y
tech
n
iq
u
es
ca
n
d
eter
m
i
n
e
t
h
e
in
it
ial
p
ar
a
m
eter
s
o
f
P
VC
u
s
ed
to
s
tar
t
th
e
Ne
w
to
n
R
ap
h
s
o
n
’
s
m
et
h
o
d
[
1
4
]
,
[
1
5
]
.
3.
1
.
Resis
t
a
nces
v
a
lues
o
f
R
s
a
nd
R
sh
T
h
e
in
itial e
s
ti
m
at
io
n
o
f
t
h
ese
r
esis
ta
n
ce
s
an
d
,
ca
n
b
e
ca
lcu
lated
b
y
g
r
ap
h
ical
m
eth
o
d
[
1
6
]
.
I
n
th
e
s
m
all
v
o
lta
g
e
v
al
u
e
s
,
t
h
e
I
=
f
(
V)
cu
r
v
e
is
li
n
ea
r
:
(
(
4
)
T
h
is
eq
u
atio
n
ca
n
b
e
w
r
itte
n
:
(
5
)
W
ith
(
⁄
an
d
(
⁄
T
h
u
s
,
is
th
e
r
ig
h
t
s
lo
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e
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v
alu
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.
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o
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u
n
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er
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n
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li
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w
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6
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I
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ig
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o
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h
e
cu
r
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V)
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e
cu
r
r
e
n
t t
h
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o
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t
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ce
ll is
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en
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y
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(
⁄
(
7
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T
o
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eter
m
in
e
th
e
s
er
ies
r
esis
tan
ce
,
th
e
v
o
ltag
e
is
w
r
itte
n
as
in
d
ep
en
d
en
t
v
ar
iab
le
in
E
q
u
atio
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(
7
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t
o
g
iv
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th
e
f
o
llo
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n
g
eq
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atio
n
:
(
⁄
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(
⁄
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(
8
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T
h
e
(
is
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e
o
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i
s
eq
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ati
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o
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n
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e
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r
itte
n
as:
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(
⁄
⁄
(
9
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T
h
e
in
itial v
al
u
e
o
f
p
h
o
to
cu
r
r
en
t
ca
n
b
e
d
ed
u
ce
d
f
r
o
m
,
an
d
as:
(
⁄
(
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0
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3
.
2
.
Dio
de
idea
lity
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a
ct
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rs
I
n
eq
u
atio
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(
1
)
,
th
e
f
ir
s
t
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io
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(
r
ep
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if
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u
s
io
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io
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(
r
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p
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ca
r
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o
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b
i
n
atio
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i
n
th
e
s
p
ac
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ch
ar
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eg
io
n
.
Sev
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t
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u
s
e
th
e
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f
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to
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s
(
in
id
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ce
ll
b
u
t
th
ese
v
alu
es
b
ec
o
m
e
u
n
s
u
itab
le
f
o
r
a
r
ea
l
d
io
d
e
[
1
7
]
,
[
1
8
]
.
T
o
in
itial
ize
th
e
s
e
f
ac
to
r
s
(
w
e
c
h
o
o
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e
th
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in
itial
v
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e
s
o
f
id
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lit
y
f
ac
to
r
s
eq
u
a
l to
(
1
,
2
)
r
esp
ec
tiv
el
y
.
3.
3
. S
a
t
ura
t
io
n
c
urre
nt
I
s
1
a
nd
I
s
2
T
h
e
s
atu
r
atio
n
cu
r
r
en
ts
an
d
ar
e
d
eter
m
i
n
ed
f
r
o
m
th
e
E
q
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atio
n
(
1
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at
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ts
(
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(
.
A
s
y
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te
m
o
f
t
w
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n
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was o
b
tain
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an
d
s
o
lv
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w
it
h
C
r
a
m
er
’
s
m
et
h
o
d
[
1
9
]
.
[
(
(
⁄
]
[
(
(
⁄
]
⁄
(
1
1
)
[
(
(
(
⁄
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[
(
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⁄
(
1
2
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Usi
n
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t
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e
m
a
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o
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n
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t
h
is
eq
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n
s
y
s
te
m
ca
n
b
e
w
r
itte
n
as:
(
⁄
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
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Vo
l.
6
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No
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2
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W
ith
,
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as
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s
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2
0
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1
5
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et
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atr
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ith
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ay
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en
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tr
ical
p
ar
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eter
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o
f
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h
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a
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s
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e,
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tain
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atr
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ated
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R
ap
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n
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et
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[
2
1
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[
]
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]
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1
9
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W
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ai
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i
g
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r
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2.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
5
.1
.
Det
er
m
i
na
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io
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o
f
elec
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rica
l pa
ra
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et
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f
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VC
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h
e
u
s
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atab
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t
h
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y
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n
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6
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6
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f
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ea
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h
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ex
p
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tal
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-
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7
6
4
A
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to
(
0
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5
9
V,
-
0
.
2
1
A
)
[
2
2
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[
2
3
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
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8792
A
F
a
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u
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ith
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An
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e
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s
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t
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ir
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1
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ig
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3
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h
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ef
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ed
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0
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e
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u
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.
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o
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t
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ltag
e
m
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t b
e
s
m
al
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
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Vo
l.
6
,
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2
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A
u
g
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s
t
2
0
1
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:
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0
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–
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1
2
108
Fig
u
r
e
3
.
(
a)
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-
V
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(
b
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V
ch
ar
ac
ter
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tics
o
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ca
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d
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p
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ea
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r
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m
en
t
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an
d
(
c)
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v
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iat
io
n
o
f
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s
o
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u
te
cu
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r
e
n
t e
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r
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w
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g
e
Usi
n
g
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ev
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et
h
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d
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t
h
e
in
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tial
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e
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ar
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eter
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ted
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T
ab
le
1
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n
t
h
is
tab
le,
s
o
m
e
r
e
f
er
en
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alu
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p
r
esen
ted
to
b
e
co
m
p
ar
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d
w
it
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t
h
e
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i
n
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l
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2
4
]
.
I
t’
s
n
o
ted
t
h
at
th
e
i
n
itial
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d
f
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l
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s
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o
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t
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ce
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o
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ith
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o
f
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p
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o
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iq
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a
n
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tati
s
tical
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ter
p
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eted
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icato
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n
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R
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e
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r
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MB
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,
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d
th
e
"
t
-
s
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tic
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"
.
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h
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al
y
tical
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x
p
r
ess
io
n
s
ar
e
d
ef
in
ed
as
f
o
llo
w
s
[
8
,
2
4
]
:
√
∑
(
,
√
∑
(
,
√
∑
(
,
√
(
(
⁄
(
2
1
)
T
ab
le
1
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x
tr
ac
ted
E
lectr
ical
Par
a
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r
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-
Si s
o
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C
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ll
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R
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f
er
e
n
ce
[
2
4
]
an
d
in
th
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W
o
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k
El
e
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t
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i
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p
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i
t
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a
l
v
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s
F
i
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n
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e
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e
[
2
4
]
I
ph
(
A
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0
.
7
6
7
5
0
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7
6
4
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0
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7
6
0
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2
.
7
7
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.
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4
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2
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.
1
3
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.
3
9
7
5
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9
.
8
8
9
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1
0
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7
N
1
1
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I
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N:
2252
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8792
A
F
a
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e
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lectrica
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109
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ical
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
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8792
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ased
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ased
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5
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6
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.
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7
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.
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.
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E.
R.
F
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,
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8
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p
.
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–
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0
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b
.
[1
9
]
J.
A
p
p
e
lb
a
u
m
,
A
.
P
e
led
,
"
P
a
ra
m
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.
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In
:
3
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In
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1
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