T
E
L
KO
M
N
I
KA
T
e
lec
om
m
u
n
icat
ion
,
Com
p
u
t
i
n
g,
E
lec
t
r
on
ics
an
d
Cont
r
ol
Vol.
18
,
No.
4
,
Augus
t
2020
,
pp.
1746
~
1753
I
S
S
N:
1693
-
6930,
a
c
c
r
e
dit
e
d
F
ir
s
t
G
r
a
de
by
Ke
me
nr
is
tekdikti
,
De
c
r
e
e
No:
21/E
/KP
T
/2018
DO
I
:
10.
12928/
T
E
L
KO
M
NI
KA
.
v18i4.
12139
1746
Jou
r
n
al
h
omepage
:
ht
tp:
//
jour
nal.
uad
.
ac
.
id/
index
.
php/T
E
L
K
OM
N
I
K
A
D
e
si
gn
an
d
m
o
d
e
li
n
g o
f
sol
e
n
oi
d
i
n
d
u
c
t
o
r
i
n
t
e
g
r
at
e
d
w
ith
Fe
N
iCo in
h
ig
h
f
r
e
q
u
e
n
c
y
Abd
e
lh
ad
i
Nam
o
u
n
e
1
,
Rac
h
i
d
T
aleb
2
,
Noure
d
d
i
n
e
M
an
s
ou
r
3
1
E
l
ec
t
ri
ca
l
E
n
g
i
n
eeri
n
g
D
ep
ar
t
men
t
,
In
s
t
i
t
u
t
e
o
f
Sci
e
n
ce
s
an
d
T
ech
n
o
l
o
g
y
,
A
h
med
Z
ab
an
a
U
n
i
v
er
s
i
t
y
Cen
t
re,
A
l
g
eri
a
2
E
l
ec
t
ri
ca
l
E
n
g
i
n
eeri
n
g
D
ep
ar
t
men
t
,
H
as
s
i
b
a
Ben
b
o
u
al
i
U
n
i
v
er
s
i
t
y
,
A
l
g
er
i
a
2
L
ab
o
rat
o
i
re
G
én
i
e
E
l
ec
t
ri
q
u
e
e
t
E
n
er
g
i
e
s
Ren
o
u
v
el
a
b
l
e
s
(L
G
E
E
R),
A
l
g
er
i
a
3
Co
l
l
eg
e
o
f
E
n
g
i
n
eeri
n
g
,
U
n
i
v
ers
i
t
y
o
f
Bah
ra
i
n
,
Bah
ra
i
n
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
De
c
27,
2018
R
e
vis
e
d
Apr
8,
2020
Ac
c
e
pted
Apr
20,
2020
In
t
h
i
s
w
o
r
k
,
t
h
e
d
es
i
g
n
an
d
mo
d
e
l
i
n
g
o
f
t
h
e
s
o
l
en
o
i
d
i
n
d
u
c
t
o
r
are
d
i
s
c
u
s
s
ed
.
T
h
e
l
a
y
o
u
t
o
f
i
n
t
eg
rat
e
d
i
n
d
u
c
t
o
r
s
w
i
t
h
mag
n
et
i
c
co
res
an
d
t
h
ei
r
g
eo
me
t
ri
ca
l
p
aramet
er
s
are
d
ev
e
l
o
p
ed
.
T
h
e
q
u
al
i
t
y
fact
o
r
Q
an
d
i
n
d
u
c
t
an
ce
v
a
l
u
e
L
are
d
eri
v
ed
fr
o
m
t
h
e
S
-
p
arame
t
e
rs
a
n
d
p
l
o
t
t
ed
v
ers
u
s
fr
eq
u
e
n
cy
.
T
h
e
effec
t
o
f
s
o
l
e
n
o
i
d
i
n
d
u
c
t
o
r
g
eo
me
t
ry
o
n
i
n
d
u
c
t
an
c
e
an
d
q
u
al
i
t
y
fac
t
o
r
are
s
t
u
d
i
ed
v
i
a
s
i
mu
l
at
i
o
n
u
s
i
n
g
MA
T
L
A
B.
T
h
e
s
o
l
en
o
i
d
i
n
d
u
c
t
o
r
g
eo
me
t
ry
p
arame
t
ers
co
n
s
i
d
ered
are
t
h
e
t
u
rn
’
s
n
u
m
b
er
,
t
h
e
mag
n
e
t
i
c
c
o
r
e
l
en
g
t
h
,
t
h
e
w
i
d
t
h
o
f
a
mag
n
et
i
c
co
r
e,
t
h
e
g
a
p
b
e
t
w
ee
n
t
u
rn
s
,
t
h
e
mag
n
et
i
c
co
re
t
h
i
ck
n
es
s
,
t
h
e
co
i
l
t
h
i
ck
n
es
s
,
an
d
s
o
l
en
o
i
d
i
n
d
u
ct
o
r
o
x
i
d
e
t
h
i
ck
n
e
s
s
.
T
h
e
p
erf
o
rman
ce
o
f
t
h
e
p
r
o
p
o
s
e
d
s
o
l
e
n
o
i
d
i
n
d
u
c
t
o
r
i
n
t
e
g
rat
e
d
w
i
t
h
FeN
i
Co
i
s
co
m
p
ared
w
i
t
h
o
t
h
er
s
o
l
en
o
i
d
i
n
d
u
ct
o
rs
.
K
e
y
w
o
r
d
s
:
High
f
r
e
que
nc
y
I
ntegr
a
ted
M
a
gne
ti
c
c
or
e
S
olenoid
inductor
Th
i
s
i
s
a
n
o
p
en
-
a
cces
s
a
r
t
i
cl
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e
.
C
or
r
e
s
pon
din
g
A
u
th
or
:
Abde
lhadi
Na
moune
,
E
lec
tr
ica
l
E
ng
inee
r
ing
De
pa
r
tm
e
nt
,
I
ns
ti
t
ute
of
S
c
ienc
e
s
a
nd
T
e
c
hnology
,
Ahme
d
Z
a
ba
na
Unive
r
s
it
y
C
e
ntr
e
,
R
e
li
z
a
ne
,
Alge
r
ia
.
E
mail:
na
moune.
a
bde
lhadi@gmail
.
c
om
1.
I
NT
RODU
C
T
I
ON
T
he
high
de
mand
f
or
de
c
r
e
a
s
ing
the
s
ize
a
nd
we
i
ght
of
c
omm
unica
ti
on
de
vice
s
ha
s
be
e
n
a
s
tr
ong
ince
nti
ve
f
or
r
e
s
e
a
r
c
h
e
r
s
to
im
pr
ove
monol
it
hic
in
duc
tor
s
[
1,
2]
.
T
he
inductor
is
the
lea
s
t
c
ompatibl
e
pa
s
s
ive
de
vice
with
s
il
icon
int
e
gr
a
ti
on
a
nd
s
ubs
e
que
nt
s
c
a
li
ng
[
3]
a
nd
is
of
ten
us
e
d
in
R
F
(
r
a
dio
f
r
e
q
ue
nc
ies
)
a
ppli
c
a
ti
ons
a
s
a
dis
c
r
e
te
de
vice
r
a
the
r
than
a
n
in
tegr
a
ted
c
ir
c
uit
int
o
the
s
il
icon
c
hi
p
[
4]
.
T
he
bulk
ines
s
of
the
dis
c
r
e
te
inductor
s
ha
s
be
e
n
a
dis
a
dva
ntage
f
o
r
us
e
in
por
table
e
lec
tr
onic
de
vice
s
,
a
nd
he
nc
e
induc
tor
s
that
incor
por
a
te
magne
ti
c
f
il
ms
to
boos
t
inducta
nc
e
d
e
ns
it
ies
ha
ve
r
e
s
e
a
r
c
he
d
r
e
c
e
ntl
y
[
4]
.
T
he
us
e
of
magne
ti
c
f
il
ms
s
hows
potential
f
or
c
ompl
e
tely
int
e
g
r
a
ted
i
nduc
tor
s
that
ha
ve
s
igni
f
ica
ntl
y
highe
r
inducta
nc
e
de
ns
it
y
a
nd
thus
take
up
les
s
s
pa
c
e
,
idea
l
f
o
r
por
table
e
le
c
tr
onics
[
5]
.
High
-
f
r
e
que
nc
y
mea
s
ur
e
ments
of
the
on
-
c
hip
int
e
gr
a
ted
inductor
s
ha
ve
be
e
n
im
pleme
nted,
f
r
om
whic
h
the
inducta
nc
e
,
the
r
e
s
is
tanc
e
a
nd
qua
li
ty
f
a
c
tor
of
the
magne
ti
c
a
nd
a
ir
-
c
or
e
inductor
c
a
n
be
e
xt
r
a
c
ted
a
c
c
or
ding
to
a
two
-
por
t
c
ir
c
uit
model.
I
nduc
tor
s
play
a
n
im
por
tant
r
ole
in
R
F
I
C
s
(
r
a
di
o
f
r
e
que
nc
ies
int
e
gr
a
ted
c
i
r
c
uit
s
)
.
T
his
va
luable
dis
ti
nc
ti
on
pa
ve
s
the
wa
y
f
o
r
r
e
s
e
a
r
c
he
r
s
to
w
or
k
on
their
s
tr
uc
tu
r
e
s
e
nha
nc
e
ment
to
r
e
a
c
h
o
pti
mi
z
e
d
pe
r
f
or
manc
e
.
T
he
us
e
o
f
on
-
c
hip
inductor
s
f
o
r
the
de
s
ign
of
int
e
gr
a
ted
wir
e
les
s
c
omm
unica
ti
on
s
ys
tems
e
a
s
e
the
s
ys
tem
int
e
gr
a
ti
on
a
nd
mi
niatur
iza
ti
on
a
nd
a
void
pa
r
a
s
it
e
int
r
oduc
ti
on
.
T
he
s
e
f
e
a
tur
e
s
a
r
e
,
how
e
ve
r
,
dif
f
icult
to
a
c
hieve
whe
n
us
ing
dis
c
r
e
te
c
omponent
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
De
s
ign
and
mode
li
ng
of
s
olenoid
inductor
int
e
gr
ated
w
it
h
F
e
N
iC
o
…
(
A
bde
lhadi
N
amoune
)
1747
P
r
e
vious
wor
k
[
6
]
p
r
opos
e
d
s
olenoid
inductor
s
tr
uc
tur
e
s
,
the
ir
f
indi
ngs
s
how
ed
e
nha
nc
e
ment
in
the
qua
li
ty
f
a
c
tor
a
nd
inducta
nc
e
a
s
e
va
luate
d
us
i
ng
ge
ometr
ica
l
pa
r
a
mete
r
s
.
R
e
c
e
ntl
y
,
i
nteg
r
a
ted
i
nduc
tor
s
f
a
br
ica
ted
us
ing
thi
n
f
il
ms
a
nd
magne
ti
c
c
or
e
s
[
7]
a
r
e
de
ve
loped
.
T
h
is
de
s
ign
tec
hnology
e
xhibi
ted
10
ti
mes
mor
e
pe
r
f
or
manc
e
e
nha
nc
e
ment
than
that
of
a
n
a
ir
-
c
or
e
inductor
of
identica
l
ge
ometr
y
.
I
n
t
his
wor
k,
we
p
ro
po
se
d
a
ne
w
magne
ti
c
mate
r
ial
made
of
F
e
NiC
o,
whic
h
c
a
n
a
c
hieve
opti
mi
s
ti
c
pe
r
mea
bil
it
y
o
f
100.
I
n
thi
s
pa
pe
r
,
a
n
on
-
c
hip
s
olenoid
inductor
ha
s
be
e
n
s
tudi
e
d.
T
he
f
i
r
s
t
pa
r
t
a
dd
r
e
s
s
e
s
,
the
modeling
of
the
s
olenoid
inductor
a
nd
de
r
ivation
of
the
r
e
la
ti
ons
hip
s
be
twe
e
n
ge
ometr
ica
l
pa
r
a
mete
r
s
a
nd
the
pr
oc
e
s
s
pa
r
a
mete
r
s
(
inducta
nc
e
a
nd
qua
li
ty
f
a
c
tor
)
.
T
he
s
e
c
ond
pa
r
t
dis
c
us
s
e
s
the
s
im
ulation
of
the
s
olenoid
inductor
int
e
gr
a
ted
with
F
e
NiC
o.
I
n
thi
s
pa
r
t,
the
in
f
luenc
e
of
va
r
ious
pa
r
a
mete
r
s
s
uc
h
a
s
the
ope
r
a
ti
ng
f
r
e
que
nc
y,
t
he
s
pa
c
ing
be
twe
e
n
the
c
oil
s
,
the
number
o
f
c
oil
s
,
a
nd
the
thi
c
kne
s
s
of
the
magne
ti
c
c
or
e
a
r
e
a
na
lyze
d
in
de
tail
by
s
im
ulation
with
M
AT
L
AB
s
of
twa
r
e
.
F
i
na
ll
y,
the
s
im
ulation
r
e
s
ult
s
a
r
e
c
ompar
e
d
with
p
ubli
s
he
d
r
e
s
ult
s
of
inductor
de
s
igns
.
2.
DE
S
I
GN
OF
S
OL
E
NOI
D
I
ND
UC
T
OR
F
i
gu
r
e
1
i
ll
us
tr
a
t
e
s
t
he
t
op
a
n
d
c
r
os
s
-
s
e
c
t
io
n
v
ie
ws
o
f
t
he
s
c
he
m
a
t
ic
de
s
i
gn
di
a
g
r
a
m
o
f
the
s
o
le
no
id
r
e
c
ta
ng
ul
a
r
mi
c
r
o
-
i
nd
uc
to
r
[
8
]
.
T
h
e
c
op
pe
r
wi
nd
i
ng
s
e
ts
up
t
he
bo
tt
o
m
c
op
pe
r
t
r
a
c
ks
a
n
d
t
he
t
op
c
o
pp
e
r
tr
a
c
k
s
a
r
e
c
on
ne
c
te
d
th
r
o
ug
h
vi
a
s
[
9
]
.
T
he
us
e
o
f
m
a
gn
e
t
ic
c
o
r
e
s
f
a
c
i
li
ta
te
t
he
s
ha
pe
mi
n
ia
tu
r
i
z
a
ti
on
a
n
d
ke
e
ps
t
he
s
tr
a
y
f
ie
l
ds
w
i
th
in
l
i
mi
ts
be
tt
e
r
t
ha
n
a
i
r
-
c
o
r
e
c
o
il
i
n
duc
to
r
s
.
T
h
e
ob
jec
t
ive
o
f
t
his
w
o
r
k
is
t
o
a
c
hi
e
ve
a
f
e
r
r
om
a
g
ne
ti
c
r
e
s
ona
nc
e
f
r
e
q
ue
n
c
y
o
f
4
.
7
GH
z
w
i
th
t
h
e
F
e
N
iC
o
m
a
g
ne
ti
c
c
or
e
a
s
a
h
a
r
d
a
x
is
a
nd
h
a
v
ing
a
pe
r
mea
bi
l
it
y
o
f
1
00
.
B
a
s
e
d
on
the
tar
ge
t
s
pe
c
if
ica
ti
ons
of
the
s
oleno
id
inductor
,
t
he
de
s
ign
wa
s
made
by
a
djus
ti
ng
pa
r
a
mete
r
s
of
the
c
or
e
a
nd
winding
d
im
e
ns
ions
[
9]
.
T
he
ge
ometr
ica
l
input
pa
r
a
mete
r
s
a
r
e
:
the
s
ize
o
f
vias
s
V
,
ga
p
s
ur
r
ounding
the
vias
g
V
,
the
ga
p
be
twe
e
n
two
a
djac
e
nt
tu
r
ns
g
,
the
thi
c
kne
s
s
of
c
oil
t
C
,
length
o
f
c
oil
l
C
,
the
width
of
c
oil
w
C
(
w
V
)
,
magne
ti
c
c
or
e
thi
c
kne
s
s
t
M
,
magne
ti
c
c
o
r
e
width
w
M
,
magne
ti
c
f
il
m
leng
th
l
A
(
l
M
)
,
a
ir
-
c
or
e
width
w
A
,
the
thi
c
kne
s
s
of
the
ga
p
be
twe
e
n
top
a
nd
bot
tom
c
onduc
tor
t
A
a
nd
number
of
tur
ns
N
.
T
he
output
pa
r
a
mete
r
s
a
r
e
the
DC
a
nd
AC
r
e
s
is
tanc
e
,
the
tot
a
l
inducta
nc
e
a
nd
maximum
magne
ti
c
i
nduc
ti
on
de
s
c
r
ibed
in
[
10]
.
(
a
)
(
b)
F
ig
ur
e
1
.
S
c
he
matic
de
s
ign
o
f
s
olenoid
mi
c
r
o
-
indu
c
tor
s
:
(
a
)
top
view
a
nd
(
b)
c
r
os
s
-
s
e
c
ti
on
view
T
he
r
e
lation
f
or
the
inducta
nc
e
of
the
in
tegr
a
ted
s
o
lenoid
inductor
wi
th
a
ir
c
or
e
c
a
n
be
e
xpr
e
s
s
e
d
a
s
:
L
AC
=
L
P
a
r
a
s
i
t
i
c
+
L
W
i
nd
i
ng
(
1)
w
he
r
e
the
winding
inducta
nc
e
L
W
i
n
d
i
n
g
c
a
n
be
de
s
c
r
ibed
by
the
c
las
s
ica
l
W
he
e
ler
f
or
mu
la
[
11
]
:
L
W
i
nd
i
ng
=
10
.
π
.
μ
0
.
N
2
.
a
2
9a
+
10
l
A
,
a
=
√
(
w
A
+
2
s
V
)
.
(
t
A
+
2
t
C
)
π
(
2)
T
he
pa
r
a
s
it
ic
inducta
n
c
e
L
P
a
r
a
s
i
t
i
c
de
s
c
r
ibes
the
e
f
f
e
c
ts
of
the
pa
r
a
s
it
ic
a
t
the
po
r
ts
.
I
f
the
magne
ti
c
c
or
e
is
include
d
,
it
c
a
n
be
s
hown
that
the
inducta
nc
e
[
1
2,
13]
a
nd
s
e
r
ies
r
e
s
is
tanc
e
[
14,
15]
c
a
n
be
a
ppr
oxim
a
ted
r
e
s
pe
c
ti
ve
ly
by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
4
,
Augus
t
2020
:
1746
-
1753
1748
L
=
μ
0
.
μ
r
.
N
2
.
w
M
.
t
M
l
M
(
3)
R
=
2N
.
w
M
.
ρ
C
w
C
.
δ
C
.
(
1
−
e
−
(
t
C
/
δ
C
)
(
4)
w
he
r
e
δ
C
is
the
wir
e
s
kin
de
pth
e
xpr
e
s
s
e
d
a
s
[
16]
:
δ
C
=
√
ρ
C
(
π
.
μ
0
.
μ
rC
.
f
)
(
5)
w
he
r
e
0
=
4.
.
10
-
7
[
H/m]
a
nd
μ
rC
is
the
r
e
lative
magne
ti
c
pe
r
mea
bil
it
y
of
the
wir
e
.
F
o
r
a
c
oppe
r
c
onduc
tor
c
a
s
e
,
μ
rC
=
1
a
nd
ρ
C
=
17
.
24×
10
-
9
[
Ω
.
m]
a
t
20
°C
.
S
ince
the
qua
li
ty
f
a
c
tor
,
Q
,
inducta
nc
e
,
L
,
a
nd
r
e
s
is
tanc
e
,
R
,
a
r
e
r
e
late
d
a
s
f
oll
ows
:
=
(
6)
He
nc
e
,
the
qua
li
ty
f
a
c
tor
c
a
n
be
c
omput
e
d
by
r
e
pla
c
ing
(
3)
a
nd
(
4
)
in
(
6)
:
Q
=
ω
μ
0
.
μ
r
.
N
.
t
M
.
w
C
.
(
1
−
e
−
(
t
C
/
δ
C
)
)
2
l
M
.
ρ
C
(
7
)
2
.
1.
P
ar
a
m
e
t
e
r
e
xt
r
ac
t
ion
I
n
a
typ
ica
l
two
-
por
t
c
i
r
c
uit
model
s
hown
in
F
ig
ur
e
2,
the
S
-
pa
r
a
mete
r
s
pr
ovide
a
c
lea
r
phys
ica
l
int
e
r
pr
e
tation
of
the
t
r
a
ns
mi
s
s
ion
a
nd
r
e
f
lec
ti
on
pe
r
f
or
manc
e
of
the
de
vice
[
17]
.
I
t
c
a
n
be
de
s
c
r
ibed
in
ter
ms
of
the
s
c
a
tt
e
r
ing
pa
r
a
mete
r
s
a
s
:
[
z
1
z
2
]
=
[
S
11
S
12
S
21
S
22
]
.
[
x
1
x
2
]
(
8
)
or
in
ter
ms
of
the
a
dmi
tt
a
nc
e
pa
r
a
mete
r
s
a
s
:
[
I
1
I
2
]
=
[
Y
11
Y
12
Y
21
Y
22
]
.
[
V
1
V
2
]
(
9
)
T
h
e
c
i
r
c
ui
t
o
f
t
he
in
te
g
r
a
ted
s
o
le
no
i
d
in
duc
t
or
in
t
his
wo
r
k
is
r
e
c
ip
r
o
c
a
l
,
s
o
Y
11
=Y
22
a
nd
Y
12
=Y
21
.
T
he
n
w
e
ha
ve
t
he
f
ol
lo
wi
ng
e
q
ua
ti
ons
to
c
o
mp
u
te
t
he
f
r
e
qu
e
nc
y
de
pe
nde
nc
e
o
f
the
in
du
c
t
a
nc
e
a
nd
qua
l
it
y
f
a
c
to
r
.
(
a
)
(
b)
F
ig
ur
e
2
.
T
he
e
quivale
nt
c
ir
c
uit
of
(
a
)
the
two
-
por
t
model
f
or
inductor
s
a
nd
(
b)
i
ts
ne
t
wor
k
of
S
-
pa
r
a
mete
r
s
.
S
21
S
2
2
S
12
S
11
x
1
x
2
z
2
z
1
S
21
S
2
2
S
12
S
11
x
1
x
2
z
2
z
1
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
De
s
ign
and
mode
li
ng
of
s
olenoid
inductor
int
e
gr
ated
w
it
h
F
e
N
iC
o
…
(
A
bde
lhadi
N
amoune
)
1749
L
=
Im
(
1
−
Y
12
)
2π
f
(
10
)
Q
=
−
Im
(
1
Y
12
)
Re
(
1
Y
12
)
(1
1
)
3.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
3.
1.
I
n
f
lu
e
n
c
e
of
t
h
e
n
u
m
b
e
r
of
t
u
r
n
s
R
e
s
ult
s
of
inducta
nc
e
a
nd
qua
li
ty
f
a
c
tor
va
r
iati
on
ve
r
s
us
f
r
e
que
nc
y
f
or
th
r
e
e
di
f
f
e
r
e
nt
number
s
of
tur
n
s
a
r
e
s
hown
in
F
ig
ur
e
3
.
As
s
hown
in
F
ig
ur
e
3
(
a
)
,
a
n
incr
e
a
s
e
in
tur
ns
number
lea
ds
to
a
n
incr
e
a
s
e
of
inducta
nc
e
f
r
om
15
to
24
nH
a
t
a
f
r
e
que
nc
y
of
1.
5
GH
z
.
How
e
ve
r
,
F
igur
e
3
(
b
)
s
hows
that
s
olenoid
inductor
with
a
lowe
r
number
o
f
tur
ns
ha
s
the
highes
t
qua
li
ty
f
a
c
tor
.
T
his
is
be
c
a
us
e
the
incr
e
a
s
e
of
N
e
nlar
ge
s
the
tot
a
l
length
a
n
d
r
e
duc
e
s
the
c
r
os
s
-
s
e
c
t
ion
of
the
c
oil
[
18
].
(
a
)
(
b)
F
ig
ur
e
3
.
I
l
lus
tr
a
te
(
a
)
the
inducta
nc
e
a
nd
(
b)
the
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
f
or
th
r
e
e
dif
f
e
r
e
nt
number
s
o
f
tu
r
ns
3.
2
.
I
n
f
lu
e
n
c
e
o
f
t
h
e
m
agn
e
t
ic
c
or
e
leng
t
h
F
igur
e
4
s
hows
the
p
lot
s
of
the
inducta
nc
e
a
nd
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
f
o
r
thr
e
e
d
if
f
e
r
e
nt
lengths
of
the
magne
ti
c
c
or
e
,
whic
h
a
r
e
300
,
40
0
a
nd
500
μ
m.
As
s
hown
in
F
igu
r
e
4
(
a
)
,
t
he
in
duc
tanc
e
de
c
r
e
a
s
e
s
f
or
high
length
.
How
e
ve
r
,
a
s
il
lus
tr
a
te
d
in
F
igur
e
4
(
b)
,
the
qua
li
ty
f
a
c
tor
tr
e
nd
is
the
oppos
it
e
f
or
high
length.
T
his
c
a
n
be
e
xplaine
d
by
the
f
a
c
t
an
incr
e
a
s
e
in
magne
ti
c
c
or
e
length
with
tur
n
number
a
nd
ga
p
be
twe
e
n
the
two
ne
ighbor
ing
windings
unc
ha
nge
d
,
r
e
s
ult
s
in
the
wide
r
win
ding
.
T
his
latter
will
lea
d
to
a
lowe
r
r
e
s
is
tanc
e
los
s
a
nd
he
nc
e
to
higher
qua
li
ty
f
a
c
tor
[
19]
.
3.
3
.
I
n
f
lu
e
n
c
e
o
f
t
h
e
m
agn
e
t
ic
c
or
e
wid
t
h
F
igur
e
5
il
lus
tr
a
tes
the
inducta
nc
e
a
nd
qua
li
ty
f
a
c
tor
a
s
a
f
unc
ti
on
of
the
f
r
e
que
nc
y
f
o
r
two
dif
f
e
r
e
nt
widths
of
the
magne
ti
c
c
or
e
,
whic
h
a
r
e
3
10
a
nd
420μ
m.
T
he
inducta
nc
e
incr
e
a
s
e
s
f
r
om
15
to
21
nH
a
t
a
f
r
e
que
nc
y
of
1
.
5
GH
z
f
o
r
a
n
incr
e
a
s
e
d
wi
dth,
while
the
qua
li
ty
f
a
c
tor
is
not
too
much
in
f
luenc
e
d
by
c
ha
nge
s
in
the
width
.
I
de
a
ll
y
,
with
a
s
t
a
ble
nu
mber
o
f
tur
n
a
nd
the
s
a
me
ga
p
be
twe
e
n
the
two
a
djoi
ning
c
oil
s
,
the
e
nlar
ge
d
magne
ti
c
c
or
e
width
r
e
s
ult
s
in
longer
c
oil
s
,
lea
ding
to
a
higher
r
e
s
is
tanc
e
los
s
a
nd
dim
ini
s
h
qua
li
ty
f
a
c
tor
[
20]
.
3.
4
.
I
n
f
lu
e
n
c
e
o
f
t
h
e
gap
b
e
t
we
e
n
t
u
r
n
s
F
igur
e
6
s
hows
t
he
plot
s
of
qua
li
ty
f
a
c
to
r
a
nd
inducta
nc
e
va
r
iation
ve
r
s
us
f
r
e
que
nc
y
f
or
ga
ps
be
twe
e
n
the
ne
ighbor
ing
wind
ing
e
qua
l
to
20
μ
m
a
nd
15
μm
.
T
he
r
e
s
ult
s
s
how
that
a
n
incr
e
a
s
e
o
f
a
bout
33%
of
the
ga
p
d
id
not
le
a
d
to
s
igni
f
ica
nt
c
ha
nge
s
.
I
n
thi
s
s
im
ulation,
we
only
obs
e
r
ve
d
a
16%
inc
r
e
a
s
e
in
the
inducta
nc
e
a
nd
a
7
%
de
c
r
e
a
s
e
in
the
pe
a
k
qua
l
it
y
f
a
c
to
r
a
t
a
f
r
e
que
nc
y
of
a
bout
2.
3
GH
z
.
T
his
r
e
s
ult
a
ls
o
il
lus
tr
a
t
es
that
a
n
incr
e
a
s
e
in
the
ga
p
be
twe
e
n
the
ne
ighbor
i
ng
windings
with
a
f
ixed
magne
ti
c
c
or
e
length
r
e
duc
e
s
the
width
of
windings
,
whic
h
lea
ds
to
a
n
i
nc
r
e
a
s
e
in
r
e
s
is
tanc
e
los
s
[
21]
.
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
N
=
5
t
u
r
n
s
N
=
4
t
u
r
n
s
N
=
3
t
u
r
n
s
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
18
20
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
N
=
5
t
u
r
n
s
N
=
4
t
u
r
n
s
N
=
3
t
u
r
n
s
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
N
=
5
t
u
r
n
s
N
=
4
t
u
r
n
s
N
=
3
t
u
r
n
s
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
18
20
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
N
=
5
t
u
r
n
s
N
=
4
t
u
r
n
s
N
=
3
t
u
r
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
4
,
Augus
t
2020
:
1746
-
1753
1750
(
a
)
(
b)
F
ig
ur
e
4.
I
l
lus
tr
a
te
(
a
)
the
inducta
nc
e
a
nd
(
b)
the
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
f
or
th
r
e
e
dif
f
e
r
e
nt
lengths
o
f
magne
ti
c
c
or
e
(
a
)
(
b)
F
ig
ur
e
5.
I
l
lus
tr
a
te
(
a
)
the
inducta
nc
e
a
nd
(
b)
the
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
f
or
two
dif
f
e
r
e
nt
widths
o
f
magne
ti
c
c
or
e
(
a
)
(
b)
F
ig
ur
e
6.
I
l
lus
tr
a
te
(
a
)
the
inducta
nc
e
a
nd
(
b)
the
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
f
or
two
dif
f
e
r
e
nt
ga
ps
be
twe
e
n
tur
ns
.
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
3
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
4
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
5
0
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
18
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
3
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
4
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
5
0
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
3
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
4
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
5
0
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
18
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
3
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
4
0
0
µ
m
l
e
n
g
th
o
f
m
a
g
n
e
tic co
r
e
=
5
0
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
3
1
0
µ
m
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
4
2
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
3
1
0
µ
m
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
4
2
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
3
1
0
µ
m
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
4
2
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
3
1
0
µ
m
w
i
d
th
o
f
m
a
g
n
e
tic co
r
e
=
4
2
0
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
g
a
p
b
e
twe
e
n
t
u
r
n
s =
2
0
µ
m
g
a
p
b
e
twe
e
n
t
u
r
n
s =
1
5
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
g
a
p
b
e
twe
e
n
t
u
r
n
s =
2
0
µ
m
g
a
p
b
e
twe
e
n
t
u
r
n
s =
1
5
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
g
a
p
b
e
twe
e
n
t
u
r
n
s =
2
0
µ
m
g
a
p
b
e
twe
e
n
t
u
r
n
s =
1
5
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
g
a
p
b
e
twe
e
n
t
u
r
n
s =
2
0
µ
m
g
a
p
b
e
twe
e
n
t
u
r
n
s =
1
5
µ
m
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
De
s
ign
and
mode
li
ng
of
s
olenoid
inductor
int
e
gr
ated
w
it
h
F
e
N
iC
o
…
(
A
bde
lhadi
N
amoune
)
1751
3.
5
.
I
n
f
lu
e
n
c
e
o
f
t
h
e
t
h
ickn
e
s
s
of
t
h
e
m
ag
n
e
t
ic
c
or
e
F
i
gu
r
e
7
d
is
p
la
ys
the
i
nd
uc
tan
c
e
a
n
d
q
ua
li
t
y
f
a
c
to
r
o
f
th
e
s
o
le
no
id
i
nd
uc
to
r
f
o
r
t
wo
d
i
f
f
e
r
e
n
t
t
h
ic
kne
s
s
e
s
o
f
th
e
m
a
g
ne
ti
c
c
or
e
.
T
h
e
r
e
s
u
l
ts
s
h
ow
t
h
a
t
by
i
n
c
r
e
a
s
in
g
the
t
hi
c
k
ne
s
s
of
t
he
mag
ne
t
ic
c
o
r
e
f
r
o
m
1
µ
m
t
o
2
µ
m
i
mp
r
ov
e
s
b
ot
h
t
he
in
du
c
ta
nc
e
va
l
ue
a
nd
q
ua
l
i
ty
f
a
c
t
o
r
.
(
a
)
(
b)
F
ig
ur
e
7.
I
l
lus
tr
a
te
(
a
)
the
inducta
nc
e
a
nd
(
b)
the
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
f
or
two
dif
f
e
r
e
nt
thi
c
kne
s
s
of
the
magne
ti
c
c
or
e
3.
6
.
I
n
f
lu
e
n
c
e
o
f
t
h
e
t
h
ickn
e
s
s
of
t
h
e
c
oil
F
i
gu
r
e
8
s
h
ows
t
he
in
duc
ta
nc
e
a
nd
qua
l
it
y
f
a
c
to
r
p
lo
t
te
d
ov
e
r
a
r
a
ng
e
o
f
f
r
e
q
ue
n
c
i
e
s
f
o
r
t
hr
e
e
d
i
f
f
e
r
e
nt
t
h
ic
kne
s
s
e
s
of
t
he
c
o
il
s
(
i
.
e
.
2
µ
m
–
3
µ
m
–
4µ
m
)
.
As
s
ho
wn
i
n
F
i
gu
r
e
8
(
a
)
,
t
he
i
nd
uc
tan
c
e
va
lue
f
o
r
th
e
t
h
ic
ke
r
c
o
il
i
s
mo
r
e
to
tha
t
o
f
t
he
t
hi
nn
e
r
c
o
il
.
I
t
c
a
n
b
e
no
ti
c
e
d
f
r
o
m
F
ig
u
r
e
8
(
b
)
t
ha
t
t
h
e
pe
a
k
o
f
t
he
q
ua
l
i
ty
f
a
c
to
r
ha
s
a
ls
o
i
m
p
r
o
ve
d
wi
th
a
n
in
c
r
e
a
s
e
i
n
t
he
th
ic
kne
s
s
o
f
t
he
c
oi
ls
.
(
a
)
(
b)
F
ig
ur
e
8.
I
l
lus
tr
a
te
(
a
)
the
inducta
nc
e
a
nd
(
b)
the
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
f
or
th
r
e
e
dif
f
e
r
e
nt
thi
c
kne
s
s
e
s
of
c
oil
s
3.
7
.
I
n
f
lu
e
n
c
e
o
f
t
h
e
in
s
u
la
t
or
t
h
ickn
e
s
s
T
he
e
f
f
e
c
t
of
the
oxide
thi
c
kne
s
s
on
the
inducta
n
c
e
is
s
hown
in
F
ig
ur
e
9
(
a
)
.
T
he
e
nha
nc
e
d
s
il
icon
dioxi
de
s
tr
uc
tur
e
s
hows
a
boos
t
ed
inducta
nc
e
va
l
ue
c
ompar
ed
with
that
of
c
onve
nti
ona
l
s
il
icon
di
oxide
a
t
a
bout
3
M
Hz
f
r
e
que
nc
y
.
F
ig
u
r
e
9
(
b)
il
lus
tr
a
tes
that
the
qua
li
ty
f
a
c
tor
e
xhibi
ts
lar
ge
r
va
lues
wi
th
oxide
thi
c
kne
s
s
.
T
his
latter
oc
c
ur
s
be
c
a
us
e
s
tr
uc
tur
e
with
thi
c
ke
r
s
il
icon
diox
ide
laye
r
wi
ll
e
xhibi
t
les
s
los
s
.
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
2
µ
m
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
1
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
2
µ
m
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
1
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
2
µ
m
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
1
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
2
µ
m
th
i
ckn
e
ss o
f
m
a
g
n
e
tic co
r
e
=
1
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
4
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
3
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
2
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
18
20
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
4
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
3
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
2
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
4
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
3
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
2
µ
m
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
18
20
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
4
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
3
µ
m
th
i
ckn
e
ss o
f
t
h
e
co
i
l
=
2
µ
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
4
,
Augus
t
2020
:
1746
-
1753
1752
(
a
)
(
b)
F
ig
ur
e
9.
I
l
lus
tr
a
te
(
a
)
the
inducta
nc
e
a
nd
(
b)
the
q
ua
li
ty
f
a
c
tor
ve
r
s
us
f
r
e
que
nc
y
with
a
nd
without
oxide
thi
c
kne
s
s
3.
8
.
Com
p
ar
is
on
of
s
olenoi
d
in
d
u
c
t
or
wit
h
ot
h
e
r
in
d
u
c
t
or
s
T
he
pe
r
f
or
manc
e
of
the
s
olenoid
inductor
is
c
ompar
e
d
with
other
inductor
s
int
e
gr
a
ted
wit
h
magne
ti
c
c
or
e
s
a
s
indi
c
a
ted
in
T
a
b
le
1.
T
he
va
lues
ment
ioned
in
the
table
unde
r
‘
thi
s
wo
r
k
’
a
r
e
the
m
a
xim
um
inducta
nc
e
,
maximum
qua
li
ty
f
a
c
to
r
,
s
e
lf
-
r
e
s
ona
nt
f
r
e
que
nc
y
a
nd
dif
f
e
r
e
nt
magne
ti
c
mate
r
ials
obta
ined
by
the
pa
r
a
metr
ic
a
na
lys
is
.
T
he
r
e
s
ult
s
s
how
that
with
our
de
s
ign
pr
opos
a
l,
we
c
a
n
a
c
hieve
s
im
ult
a
ne
ous
ly
s
a
ti
s
f
a
c
tor
y
e
nha
nc
e
d
inducta
nc
e
a
nd
qua
li
ty
f
a
c
to
r
s
a
t
GH
z
f
r
e
que
nc
ies
.
T
a
ble
1
.
C
ompar
is
on
of
int
e
gr
a
ted
s
olenoid
induct
or
c
ha
r
a
c
ter
is
ti
c
be
twe
e
n
‘
thi
s
wor
k’
a
nd
other
publi
s
he
d
r
e
s
ult
s
.
I
nduc
to
r
de
s
ig
ns
M
a
gne
ti
c
M
a
te
r
ia
ls
F
r
e
que
nc
y (
H
z
)
L
(
nH
)
Q
ma
x
R
e
f
S
ol
e
noi
d
C
oT
a
Z
r
10 .10
6
219
4
[
22]
S
ol
e
noi
d
F
e
C
oB
/Al
2
O
3
M
ul
ti
la
ye
r
50.10
6
13
8
[
23, 24]
S
ol
e
noi
d O
n P
C
B
C
oF
e
H
f
O
200.10
6
1
23
[
25]
S
ol
e
noi
d
F
e
G
a
B
/Al
2
O
3
M
ul
ti
la
ye
r
1200.10
6
15
20
[
26]
S
ol
e
noi
d
F
e
N
iC
o
(
1
-
4)
.10
9
20
17
T
hi
s
w
or
k
4.
CONC
L
USI
ON
I
n
t
his
pa
pe
r
,
we
ha
v
e
p
r
e
s
e
n
te
d
th
e
d
e
s
i
gn
a
n
d
mod
e
l
i
ng
o
f
a
s
ol
e
n
oi
d
in
du
c
t
o
r
.
T
he
m
os
t
c
h
a
l
le
ng
in
g
t
a
s
k
e
nc
ou
n
te
r
e
d
is
t
o
d
e
t
e
r
m
ine
th
e
a
p
p
r
o
p
r
ia
te
e
lec
t
r
i
c
a
l
pa
r
a
me
te
r
s
(
i
.
e
.
i
nd
uc
tan
c
e
a
nd
qua
l
it
y
f
a
c
tor
)
.
Ne
xt
,
t
he
op
ti
m
iza
ti
on
o
f
th
e
q
ua
l
i
ty
f
a
c
t
or
o
f
a
s
o
len
oi
d
i
n
duc
t
or
in
te
g
r
a
t
e
d
w
i
th
F
e
N
iC
o
r
e
qu
i
r
e
s
a
we
a
kl
y
w
i
dt
h
of
t
he
ma
gn
e
t
ic
c
o
r
e
,
t
he
g
a
p
be
tw
e
e
n
t
ur
ns
a
nd
s
t
r
o
ng
nu
mb
e
r
s
o
f
tu
r
ns
,
l
e
n
gt
h
o
f
th
e
m
a
g
ne
t
ic
c
o
r
e
,
t
he
t
hi
c
k
ne
s
s
o
f
th
e
m
a
g
ne
ti
c
c
o
r
e
,
t
he
th
ic
kn
e
s
s
o
f
t
he
c
oi
l
a
nd
ox
i
de
th
ick
ne
s
s
.
Ou
r
r
e
s
u
lt
s
de
m
o
ns
t
r
a
te
c
ut
t
in
g
-
e
d
ge
h
ig
h
-
f
r
e
q
ue
nc
y
(
o
ne
–
f
o
ur
G
Hz
)
pe
r
f
o
r
ma
nc
e
f
o
r
a
c
om
bi
na
ti
on
o
f
h
i
gh
-
q
ua
li
t
y
f
a
c
t
o
r
s
a
n
d
i
n
duc
ta
nc
e
va
lu
e
s
.
W
e
c
o
nc
lu
de
f
r
o
m
th
e
r
e
s
u
l
ts
o
bt
a
ine
d
in
th
is
w
o
r
k
,
th
a
t
t
he
r
e
is
s
ti
ll
a
p
os
s
ib
il
i
ty
to
i
m
p
r
o
ve
e
xis
t
in
g
i
nd
uc
to
r
s
t
r
u
c
t
u
r
e
to
r
e
a
li
z
e
s
tab
le
a
n
d
b
e
tt
e
r
r
e
s
ul
ts
ove
r
a
w
id
e
h
ig
h
-
f
r
e
q
ue
nc
y
r
a
n
ge
.
W
e
c
on
c
l
ud
e
a
ls
o
t
ha
t
us
e
o
f
in
du
c
t
o
r
s
i
m
ula
t
io
n
t
o
a
na
ly
z
e
a
nd
un
de
r
s
t
a
n
d
f
a
c
to
r
s
th
a
t
a
f
f
e
c
t
s
ys
te
m
pa
r
a
me
te
r
s
(
i
.
e
.
qu
a
l
i
ty
f
a
c
t
or
a
n
d
in
du
c
t
a
nc
e
)
a
n
d
c
o
mp
a
r
e
t
he
m
wi
t
h
e
xp
e
c
te
d
de
s
i
r
e
d
r
e
s
u
lt
s
is
p
r
e
-
r
e
qu
is
i
te
b
e
f
o
r
e
th
e
de
s
ig
n
o
f
m
o
r
e
r
ob
us
t
in
du
c
t
o
r
.
RE
F
E
RE
NC
E
S
[1
]
H
u
A
.
,
Ren
Z
.
,
Z
h
an
g
K
.
,
L
i
u
L
.
,
Ch
en
X
.
,
L
i
u
D
.
,
Z
o
u
X
.
,
“
L
o
w
-
p
h
as
e
-
n
o
i
s
e
w
i
d
e
b
an
d
V
CO
w
i
t
h
an
o
p
t
i
mi
zed
sub
-
n
H
i
n
d
u
c
t
o
r,
”
E
l
ect
r
o
n
i
c
s
Let
t
er
s
,
v
o
l
.
51
,
n
o
.
15
,
p
p
.
1
2
0
9
-
1
2
1
1
,
2
0
1
5
.
[2
]
O
u
ra
k
L
.
,
G
h
an
n
am
A
.
,
Bo
u
rri
er
D
.
,
V
i
a
l
l
o
n
C
.
,
P
arra
T
.
,
“
So
l
e
n
o
i
d
a
l
t
ra
n
s
f
o
rmers
f
o
r
mag
n
et
i
c
mat
e
ri
al
s
i
n
t
eg
ra
t
i
o
n
,”
P
r
o
cee
d
i
n
g
s
M
i
c
r
o
w
a
ve
Co
n
f
e
r
en
ce
(
A
P
M
C)
,
pp.
854
-
8
5
6
,
2
0
1
2
.
[3
]
Ben
h
a
d
d
a
Y
.
,
H
ami
d
A
.
,
L
eb
ey
T
.
,
A
l
l
a
o
u
i
A
.
,
D
erk
ao
u
i
M
.
,
Mel
at
i
R.
,
“
T
h
ermal
Beh
a
v
i
o
r
o
f
an
In
t
eg
ra
t
e
d
Sq
u
are
Sp
i
ra
l
Mi
cro
Co
i
l
,”
TE
LKO
M
NIK
A
Tel
eco
m
m
u
n
i
c
a
t
i
o
n
Co
m
p
u
t
i
n
g
E
l
ec
t
r
o
n
i
cs
a
n
d
Co
n
t
r
o
l
,
v
o
l
.
14
,
n
o
.
2
,
pp.
2
5
0
-
2
6
5
,
2
0
1
5
.
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
w
i
th
o
x
i
d
e
t
h
i
ckn
e
ss
w
i
th
o
u
t
o
x
i
d
e
t
h
i
ckn
e
ss
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
w
i
th
o
x
i
d
e
t
h
i
ckn
e
ss
w
i
th
o
u
t
o
x
i
d
e
t
h
i
ckn
e
ss
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
-4
-2
0
2
4
6
x
1
0
-8
F
r
e
q
u
e
n
cy
F
(
H
z
)
In
d
u
cta
n
ce
L
(
H
)
w
i
th
o
x
i
d
e
t
h
i
ckn
e
ss
w
i
th
o
u
t
o
x
i
d
e
t
h
i
ckn
e
ss
1
1
.5
2
2
.5
3
3
.5
4
x
1
0
9
2
4
6
8
10
12
14
16
F
r
e
q
u
e
n
cy
F
(
H
z
)
Qu
a
l
i
ty
F
a
cto
r
Q
w
i
th
o
x
i
d
e
t
h
i
ckn
e
ss
w
i
th
o
u
t
o
x
i
d
e
t
h
i
ckn
e
ss
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
De
s
ign
and
mode
li
ng
of
s
olenoid
inductor
int
e
gr
ated
w
it
h
F
e
N
iC
o
…
(
A
bde
lhadi
N
amoune
)
1753
[4
]
D
erk
a
o
u
i
M
.
,
H
ami
d
A
.
,
L
eb
ey
T
.
,
Mel
a
t
i
R.
,
“
D
e
s
i
g
n
an
d
Mo
d
el
i
n
g
o
f
a
n
In
t
eg
ra
t
ed
M
i
cro
-
T
ran
s
fo
r
mer
i
n
a
F
l
y
b
ack
Co
n
v
er
t
er
,”
TE
LK
O
M
NIK
A
Tel
ec
o
m
m
u
n
i
ca
t
i
o
n
Co
m
p
u
t
i
n
g
E
l
ect
r
o
n
i
c
s
a
n
d
Co
n
t
r
o
l
,
v
o
l
.
11
,
n
o
.
4
,
pp.
6
6
9
-
6
8
2
,
2
0
1
3
.
[5
]
N
amo
u
n
e
A
.
,
H
ami
d
A
.
,
T
al
e
b
R.
,
“
T
h
e
Perfo
rman
c
e
o
f
t
h
e
T
ra
n
s
f
o
rmer
fo
r
an
Is
o
l
a
t
ed
D
C/
D
C
C
o
n
v
ert
er
,”
TE
LKO
M
NIK
A
Tel
ec
o
m
m
u
n
i
c
a
t
i
o
n
Co
m
p
u
t
i
n
g
E
l
ec
t
r
o
n
i
c
s
a
n
d
Co
n
t
r
o
l
,
v
o
l
.
15
,
n
o
.
3
,
p
p
.
1
0
3
1
-
1
0
3
9
,
2
0
1
7
.
[6
]
L
i
u
W
.
Y
.
,
Su
ry
an
ar
ay
a
n
an
J
.
,
N
a
t
h
J
.
,
Mo
h
amma
d
i
S
.
,
K
at
eh
i
L
.
P
.
B
.
,
St
eer
M
.
B.
,
“
T
o
ro
i
d
al
I
n
d
u
ct
o
r
s
fo
r
Rad
i
o
-
Freq
u
en
c
y
In
t
eg
ra
t
ed
C
i
rcu
i
t
s
,”
IE
E
E
Tr
a
n
s
.
M
i
cr
o
wa
ve
Th
e
o
r
y
a
n
d
Tech
n
i
q
u
e
s
,
v
o
l
.
52
,
n
o
.
2
,
pp.
6
4
6
-
6
5
4
,
2
0
0
4
.
[7
]
L
ee
W
.
D
.
,
H
w
an
g
K
.
P
.
,
Sh
an
X
.
W.
,
“
Fab
r
i
cat
i
o
n
an
d
A
n
al
y
s
i
s
o
f
H
i
g
h
-
Perf
o
rma
n
ce
In
t
e
g
ra
t
ed
So
l
en
o
i
d
In
d
u
ct
o
r
w
i
t
h
Ma
g
n
e
t
i
c
Co
re
,”
IE
E
E
T
r
a
n
s
a
ct
i
o
n
s
o
n
M
a
g
n
et
i
cs
,
v
o
l
.
44
,
n
o
.
11
,
p
p
.
4
0
8
9
-
4
0
9
5
,
2
0
0
8
.
[8
]
G
ard
n
er
D
.
,
G
erh
ard
Sc
h
ro
m
S
.
,
Pai
l
l
et
F
.
,
J
am
i
es
o
n
B
.
,
K
arn
i
k
T
.
,
Bo
r
k
ar
S.
,
“
Rev
i
ew
o
f
On
-
Ch
i
p
In
d
u
ct
o
r
St
ru
c
t
u
re
s
w
i
t
h
Ma
g
n
e
t
i
c
Fi
l
ms
,
”
IE
E
E
T
r
a
n
s
a
ct
i
o
n
s
o
n
M
a
g
n
e
t
i
c
s
,
v
o
l
.
45
,
n
o
.
10
,
p
p
.
4
7
6
0
-
4
7
6
6
,
2
0
0
9
.
[9
]
Z
h
u
an
g
Y
.
,
V
ro
u
b
e
l
M
.
,
Rej
aei
B
.
,
Bu
rg
h
art
z
J
.
N.
,
“
In
t
e
g
rat
e
d
RF
i
n
d
u
c
t
o
r
s
w
i
t
h
mi
cro
-
p
at
t
ern
e
d
N
i
Fe
co
re
,”
S
o
l
i
d
-
S
t
a
t
e
E
l
ec
t
r
o
n
i
cs
, v
ol.
51
,
n
o
.
3
,
p
p
.
4
0
5
-
4
1
3
,
2
0
0
7
.
[1
0
]
H
o
mn
aw
a
n
g
N
.
,
“
Su
rface
Mi
cr
o
mach
i
n
e
d
A
rch
-
S
h
a
p
e
On
-
C
h
i
p
3
-
D
So
l
en
o
i
d
In
d
u
c
t
o
r
s
f
o
r
H
i
g
h
-
freq
u
en
cy
ap
p
l
i
ca
t
i
o
n
s
,”
Jo
u
r
n
a
l
o
f
M
i
cr
o
Na
n
o
l
i
t
h
o
g
r
a
p
h
y
,
v
o
l
.
2
,
n
o
.
4
,
p
p
.
2
7
5
-
2
8
1
,
2
0
0
3
.
[1
1
]
L
ee
T
.
H.
,
“
T
h
e
D
e
s
i
g
n
o
f
CM
O
S
Rad
i
o
-
Fre
q
u
e
n
cy
I
n
t
e
g
rat
e
d
Ci
rc
u
i
t
s
,”
2
n
d
E
d
.
Camb
r
i
d
g
e
U
n
i
v
ers
i
t
y
Pr
es
s
,
N
ew
Y
o
rk
,
2
0
0
4
.
[1
2
]
L
ei
C.
,
“
Fab
ri
cat
i
o
n
o
f
a
s
o
l
en
o
i
d
-
t
y
p
e
i
n
d
u
ct
o
r
w
i
t
h
Fe
-
b
as
ed
s
o
ft
mag
n
et
i
c
co
re
,”
J.
M
a
g
n
.
M
a
g
n
.
M
a
t
er
.
,
v
o
l
.
3
0
8
,
n
o
.
2
,
p
p
.
2
8
4
-
2
8
8
,
2
0
0
7
.
[1
3
]
G
ard
n
er
D
.
,
Sch
ro
m
G
.
,
Pai
l
l
et
F
.
,
J
ami
e
s
o
n
B
.
,
K
arn
i
k
T
.
,
Bo
rk
ar
S.
,
“
Rev
i
ew
o
f
o
n
-
ch
i
p
i
n
d
u
c
t
o
r
s
t
ru
c
t
u
re
s
w
i
t
h
mag
n
e
t
i
c
fi
l
ms
,”
IE
E
E
T
r
a
n
s
.
M
a
g
n
.
,
v
o
l
.
45
,
n
o
.
10
,
p
p
.
4760
-
4
7
6
6
,
2
0
0
9
.
[1
4
]
G
o
l
mak
a
n
i
A
.
,
Mafi
zej
a
d
K
.
,
Razza
g
h
p
o
u
r
M
.
,
K
o
u
zan
i
A
.
,
“
Mo
d
e
l
i
n
g
a
nd
o
p
t
i
m
i
zat
i
o
n
o
f
a
s
o
l
e
n
o
i
d
a
l
i
n
t
e
g
ra
t
ed
i
n
d
u
c
t
o
r
f
o
r
RF
I
c
s
,”
In
t
er
n
a
t
i
o
n
a
l
Jo
u
r
n
a
l
o
f
R
F
a
n
d
M
i
cr
o
w
a
ve
Co
m
p
u
t
er
-
A
i
d
e
d
E
n
g
i
n
e
er
i
n
g
,
v
o
l
.
20
,
n
o
.
2
,
p
p
.
1
8
2
-
1
8
9
,
2
0
1
0
.
[1
5
]
T
ai
C
.
M
.
,
L
i
ao
C
.
N
.
,
N
at
T
.
H
.
,
H
s
i
n
c
h
u
U
.
,
“
A
P
h
y
s
i
ca
l
Mo
d
e
l
o
f
S
o
l
e
n
o
i
d
I
n
d
u
ct
o
rs
o
n
S
i
l
i
co
n
Su
b
s
t
ra
t
e
s
,”
IE
E
E
Tr
a
n
s
a
ct
i
o
n
o
n
M
i
c
r
o
w
a
ve
Th
e
o
r
y
a
n
d
Tec
h
n
i
q
u
e
,
v
o
l
.
55
,
n
o
.
12
,
p
p
.
2
5
7
9
-
2
5
8
5
,
2
0
0
7
.
[1
6
]
Y
o
o
k
J
.
M
.
,
“
High
-
q
u
a
l
i
t
y
s
o
l
en
o
i
d
i
n
d
u
c
t
o
r
u
s
i
n
g
d
i
el
ect
r
i
c
fi
l
m
fo
r
mu
l
t
i
ch
i
p
mo
d
u
l
es
,”
IE
E
E
Tr
a
n
s
a
c
t
i
o
n
s
M
i
c
r
o
w
a
ve
Th
eo
r
y
a
n
d
Tech
n
i
q
u
e
s
,
v
o
l
.
53
,
n
o
.
6
,
p
p
.
2
2
3
0
-
2
2
3
4
,
2
0
0
5
.
[1
7
]
G
ran
d
i
G
.
,
K
azi
mi
ercz
u
k
M
.
K
.
,
Mas
s
ar
i
n
i
A
.
,
Reg
g
i
a
n
i
U
.
,
San
c
i
n
e
t
o
G
.
,
“
Mo
d
el
o
f
L
ami
n
a
t
ed
Iro
n
-
Co
re
In
d
u
ct
o
rs
fo
r
H
i
g
h
Freq
u
en
c
i
es
,”
IE
E
E
T
r
a
n
s
a
ct
i
o
n
s
o
n
M
a
g
n
e
t
i
c
s
,
v
o
l
.
40
,
n
o
.
4
,
p
p
.
1
8
3
9
-
1
8
4
5
,
2
0
0
4
.
[1
8
]
Fl
y
n
n
D
.
,
Su
d
an
N
.
S
.
,
T
o
o
n
A
.
,
D
es
mu
l
l
i
ez
M
.
P
.
Y.
,
“
Fab
ri
ca
t
i
o
n
p
ro
ce
s
s
o
f
a
mi
cro
i
n
d
u
c
t
o
r
u
t
i
l
i
z
i
n
g
a
mag
n
et
i
c
t
h
i
n
fi
l
m
co
re
,
”
M
i
cr
o
s
y
s
t
.
Tech
n
o
l
.
,
vol.
12
,
n
o
.
10
–
11
,
p
p
.
9
2
3
-
9
3
3
,
2
0
0
6
.
[1
9
]
Fro
mmb
er
g
er
M
.,
et
al
.
“
In
t
e
g
rat
i
o
n
o
f
cr
o
s
s
ed
a
n
i
s
o
t
r
o
p
y
mag
n
e
t
i
c
c
o
re
i
n
t
o
t
o
ro
i
d
a
l
t
h
i
n
-
fi
l
m
i
n
d
u
ct
o
rs
,”
IE
E
E
Tr
a
n
s
.
M
i
cr
o
w.
Th
eo
r
y
Tech
.
,
v
o
l
.
53
,
n
o
.
6
,
p
p
.
2
0
9
6
-
2
1
0
0
,
2
0
0
5
.
[2
0
]
Fan
g
D
.
M
.
,
W
an
g
X
.
N
.
,
Z
h
o
u
Y
.
,
Z
h
ao
X
.
L.
,
Fab
ri
cat
i
o
n
an
d
p
erfo
rma
n
ce
o
f
a
mi
cro
mac
h
i
n
ed
3
-
D
s
o
l
e
n
o
i
d
i
n
d
u
c
t
o
r
,”
J.
M
i
c
r
o
e
l
ect
r
o
n
.
,
v
o
l
.
37
,
n
o
.
9
,
p
p
.
9
4
8
-
9
5
1
,
2
0
0
6
.
[2
1
]
G
u
L
.
,
L
i
X
.
,
“
High
-
Q
So
l
e
n
o
i
d
I
n
d
u
ct
o
rs
w
i
t
h
a
CMO
S
-
Co
mp
a
t
i
b
l
e
Co
n
ca
v
e
-
Su
s
p
e
n
d
i
n
g
ME
MS
Pro
ce
s
s
,”
Jo
u
r
n
a
l
o
f
M
i
cr
o
el
ec
t
r
o
m
ec
h
a
n
i
c
a
l
S
y
s
t
e
m
s
,
v
o
l
.
16
,
n
o
.
5
,
p
p
.
1
1
6
2
-
1
1
7
2
,
2
0
0
7
.
[2
2
]
W
u
H
.
,
G
ard
n
er
D
.
S
.
,
X
u
W
.
,
Y
u
H
.
B.
,
In
t
e
g
rat
e
d
RF
O
n
-
Ch
i
p
i
n
d
u
c
t
o
r
s
w
i
t
h
p
at
t
ern
e
d
Co
-
Zr
-
Ta
-
B
fi
l
ms
,”
IE
E
E
Tr
a
n
s
a
ct
i
o
n
s
o
n
M
a
g
n
et
i
cs
,
v
o
l
.
48
,
n
o
.
11
,
p
p
.
4
1
2
3
-
4
1
2
6
,
2
0
1
2
.
[2
3
]
X
i
n
g
X
.
,
et
al
.
“
RF
mag
n
e
t
i
c
p
r
o
p
er
t
i
e
s
o
f
FeCo
B/
A
l
2
O
3
/
FeC
o
B
s
t
ru
c
t
u
re
w
i
t
h
v
ar
i
ed
A
l
2
O
3
t
h
i
c
k
n
e
s
s
,”
IE
E
E
Tr
a
n
s
a
ct
i
o
n
s
o
n
M
a
g
n
et
i
cs
,
v
o
l
.
47
,
n
o
.
10
,
p
p
.
3
1
0
4
-
3
1
0
7
,
2
0
1
1
.
[2
4
]
X
i
n
g
X
.
,
Su
n
N
,
X
.
,
Ch
en
B
.
X.
,
“
H
i
g
h
-
b
a
n
d
w
i
d
t
h
l
o
w
-
i
n
s
ert
i
o
n
l
o
s
s
s
o
l
e
n
o
i
d
t
ra
n
s
f
o
rmer
s
u
s
i
n
g
FeCo
B
mu
l
t
i
l
ay
er
s
,”
IE
E
E
Tr
a
n
s
a
ct
i
o
n
s
o
n
P
o
wer
E
l
ec
t
r
o
n
i
cs
,
v
o
l
.
28
,
n
o
.
9
,
p
p
.
4
3
9
5
-
4
4
0
1
,
2
0
1
3
.
[2
5
]
L
i
L
.
L.
,
“
Smal
l
-
res
i
s
t
an
ce
an
d
h
i
g
h
-
q
u
al
i
t
y
-
fact
o
r
mag
n
e
t
i
c
i
n
t
e
g
rat
e
d
i
n
d
u
c
t
o
r
s
o
n
PCB
,”
IE
E
E
Tr
a
n
s
a
ct
i
o
n
s
o
n
A
d
va
n
ced
P
a
ck
a
g
i
n
g
,
v
o
l
.
32
,
n
o
.
4
,
p
p
.
7
8
0
-
7
8
7
,
2
0
0
9
.
[2
6
]
G
ao
Y
.
,
Z
are
S
.
,
Y
an
g
X
.
,
N
an
T
.
X
.
,
Z
h
o
u
Z
.
Y
.
,
O
n
ab
aj
o
M
.
,
L
i
u
M
.
,
A
r
o
n
o
w
A
.
,
Mah
al
i
n
g
am
K
.
,
H
o
w
e
B
.
M
.
,
Bro
w
n
G
.
J
.
,
Su
n
N
.
X
.
,
“
Si
g
n
i
f
i
can
t
l
y
en
h
a
n
ced
i
n
d
u
ct
a
n
ce
an
d
q
u
al
i
t
y
fact
o
r
o
f
G
H
z
i
n
t
eg
ra
t
ed
ma
g
n
e
t
i
c
s
o
l
e
n
o
i
d
i
n
d
u
c
t
o
r
s
w
i
t
h
FeG
aB/
A
l
2
O
3
mu
l
t
i
l
ay
er
fi
l
m
s
,”
IE
E
E
Tr
a
n
s
a
ct
i
o
n
s
o
n
E
l
ec
t
r
o
n
D
e
vi
ce
s
,
v
o
l
.
61
,
n
o
.
2
,
pp.
1
4
7
0
-
1
4
7
6
,
2
0
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.