I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t
201
9
,
p
p
.
2
9
1
8
~2
9
3
1
I
SS
N:
2088
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v9
i
4
.
p
p
2
9
1
8
-
2931
2918
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e
.
co
m/
jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JE
C
E
Ana
ly
sis
of t
he
i
mpa
ct
o
f
m
e
tal
t
hi
c
k
n
ess
and
g
eo
m
et
ric
p
a
ra
m
et
ers o
n
th
e
q
ua
lity
f
a
c
tor
-
Q
in
i
nt
eg
ra
ted
s
pi
r
a
l
i
nductors
by
m
ea
ns o
f
a
rti
ficial
b
ee
c
o
lo
ny
t
echniq
ue
H
a
m
id B
o
uy
g
hf
1
,
B
a
chir
B
e
nh
a
la
2
,
Abdelh
a
d
i R
a
iha
ni
3
1
,3
L
S
S
DIA
,
ENS
ET
M
o
h
a
m
m
e
d
ia,
Un
iv
e
rs
it
y
o
f
Ha
ss
a
n
II
Ca
sa
b
lan
c
a
,
BP
1
5
9
B
d
Ha
ss
a
n
II
-
M
o
h
a
m
m
e
d
ia
-
M
o
ro
c
c
o
2
BA
B
A
T
e
a
m
,
L
E
A
B,
F
a
c
u
lt
y
o
f
S
c
ien
c
e
s,
Un
iv
e
rsit
y
M
o
u
lay
Is
m
a
il
,
B
P
1
1
2
0
1
,
Zi
to
u
n
e
,
M
e
k
n
e
s
-
M
o
ro
c
c
o
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Oct
10
,
2
0
1
8
R
ev
i
s
ed
Mar
2
9
,
2
0
1
9
Ac
ce
p
ted
A
p
r
3
,
2
0
1
9
T
h
e
g
o
a
l
o
f
th
is
p
re
se
n
t
p
a
p
e
r
is
to
d
e
sig
n
,
a
n
a
ly
sis
th
e
in
f
lu
e
n
c
e
o
f
th
e
in
d
u
c
to
r
g
e
o
m
e
tri
c
a
l
p
a
ra
m
e
ter
s
a
n
d
t
h
e
e
ff
e
c
t
o
f
th
e
m
e
tal
th
ick
n
e
ss
o
n
th
e
q
u
a
li
ty
fa
c
to
r
-
Q
in
in
teg
ra
ted
sq
u
a
re
sp
iral
in
d
u
c
to
r
u
sin
g
a
n
e
ff
icie
n
t
a
p
p
li
c
a
ti
o
n
of
th
e
a
rti
f
icia
l
b
e
e
c
o
lo
n
y
(
A
BC)
a
lg
o
rit
h
m
.
T
h
e
in
d
u
c
to
rs
w
e
re
o
p
ti
m
ize
d
a
t
2
.
4
G
Hz
to
d
e
ter
m
in
a
te
th
e
ir
m
a
jo
r
g
e
o
m
e
tri
c
a
l
d
i
m
e
n
sio
n
s
(
sp
,
w
,
d
in
…
)
a
n
d
th
e
ir
n
u
m
b
e
r
o
f
tu
rn
s,
f
o
r
u
se
s
in
ra
d
io
-
f
re
q
u
e
n
c
y
in
teg
ra
ted
c
ircu
it
s
(RF
ICs).
T
h
e
o
p
t
im
iza
ti
o
n
re
s
u
lt
s
a
re
v
a
li
d
a
ted
b
y
th
e
sim
u
latio
n
u
sin
g
a
n
e
lec
tro
m
a
g
n
e
ti
c
si
m
u
lato
r
(A
DS
-
M
o
m
e
n
tu
m
).
Us
i
n
g
m
a
tl
a
b
so
f
t
w
a
re
,
th
e
stu
d
y
o
n
th
e
im
p
a
c
t
o
f
th
e
e
ff
e
c
t
o
f
g
e
o
m
e
tri
c
a
l
p
a
ra
m
e
ters
a
n
d
th
e
e
ff
e
c
t
o
f
m
e
tal
th
ick
n
e
ss
,
o
n
th
e
f
a
c
to
r
o
f
q
u
a
li
t
y
-
Q
o
f
sp
iral
in
d
u
c
to
rs
,
is
sh
o
w
n
.
W
e
f
irst
re
p
o
rted
th
a
t
it
is
p
o
ss
ib
le
to
im
p
ro
v
e
Q
-
f
a
c
to
rs
f
u
rth
e
r
b
y
in
c
re
a
sin
g
th
e
m
e
tal
th
ick
n
e
ss
,
a
n
d
i
n
th
e
d
e
sig
n
o
f
in
d
u
c
to
r;
a
c
o
m
p
ro
m
is
e
m
u
st
b
e
re
a
c
h
e
d
b
e
tw
e
e
n
th
e
v
a
lu
e
o
f
w
,
n
,
sp
a
n
d
d
in
to
a
c
h
iev
e
th
e
d
e
sire
d
q
u
a
li
ty
f
a
c
to
r
-
Q
a
n
d
o
th
e
r
e
lec
tri
c
a
l
p
a
ra
m
e
ters
.
K
ey
w
o
r
d
s
:
A
B
C
al
g
o
r
ith
m
Me
tal
th
ic
k
n
ess
Op
ti
m
izatio
n
Qu
alit
y
f
ac
to
r
-
Q
R
FIC
s
Sp
ir
al
in
d
u
cto
r
Co
p
y
rig
h
t
©
2
0
1
9
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ha
m
id
B
o
u
y
g
h
f
,
L
S
SD
I
A
,
E
NSET
Mo
h
a
m
m
ed
ia,
Un
i
v
er
s
it
y
o
f
Ha
s
s
a
n
I
I
C
asab
lan
ca
,
B
P
1
5
9
B
d
Hass
an
I
I
-
Mo
h
a
m
m
ed
ia
-
Mo
r
o
cc
o
.
E
m
ail:
h
a
m
id
.
b
o
u
y
g
h
f
@
g
m
ail
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
P
lan
ar
s
p
ir
al
C
MO
S
i
n
d
u
cto
r
s
h
a
v
e
b
ec
o
m
e
s
i
g
n
if
ica
n
t
ele
m
en
t
an
d
i
m
p
o
r
ta
n
t
p
ass
i
v
e
c
o
m
p
o
n
en
t
s
in
m
a
n
y
cir
cu
it
b
lo
ck
s
u
s
ed
in
telec
o
m
m
u
n
icatio
n
ap
p
li
ca
tio
n
s
an
d
r
ad
io
f
r
eq
u
e
n
c
y
(
R
F)
tr
an
s
ce
i
v
er
s
.
T
h
e
s
q
u
ar
e
s
p
ir
al
i
n
d
u
cto
r
d
esig
n
s
p
ac
e
is
co
m
p
lex
,
a
n
d
n
e
w
o
p
ti
m
izatio
n
a
n
d
s
y
n
t
h
esis
tec
h
n
iq
u
e
s
ar
e
r
eq
u
ir
ed
to
r
ea
lize
p
r
ac
tical
d
esig
n
s
an
d
la
y
o
u
ts
[
1
]
.
Ma
j
o
r
an
alo
g
/
R
F
cir
cu
its
li
k
e
Vo
ltag
e
C
o
n
tr
o
lled
Oscill
ato
r
s
(
V
C
O)
,
Mix
er
s
,
F
ilter
s
,
R
F
Am
p
li
f
ier
s
a
n
d
L
o
w
No
i
s
e
Am
p
li
f
ier
s
(
L
N
As),
s
tr
o
n
g
l
y
d
ep
en
d
o
n
in
d
u
cto
r
s
w
it
h
o
p
ti
m
ized
d
esi
g
n
p
ar
a
m
eter
s
.
C
o
n
s
eq
u
en
tl
y
,
th
e
ef
f
icien
t
o
p
ti
m
izatio
n
m
e
th
o
d
o
lo
g
y
o
f
s
p
ir
al
in
d
u
cto
r
s
i
s
cr
itical
to
th
e
s
u
cc
ess
f
u
l r
ea
lizat
io
n
o
f
telec
o
m
m
u
n
ica
tio
n
s
y
s
te
m
s
.
His
to
r
icall
y
,
m
o
s
t
o
f
r
esear
ch
an
d
p
ap
er
s
o
n
s
p
ir
al
i
n
d
u
cto
r
o
p
ti
m
izatio
n
tec
h
n
i
q
u
es
h
a
v
e
co
n
ce
n
tr
ated
o
n
t
h
e
m
a
x
i
m
izi
n
g
t
h
e
i
n
d
u
cto
r
’
s
q
u
alit
y
f
ac
to
r
(
Q)
f
o
r
a
f
ix
ed
o
p
er
atin
g
f
r
e
q
u
en
c
y
a
n
d
d
esire
d
in
d
u
cta
n
ce
v
alu
e.
T
o
ef
f
icie
n
tl
y
r
eso
l
v
e
th
i
s
is
s
u
e,
s
o
m
e
s
w
ar
m
in
telli
g
e
n
ce
al
g
o
r
ith
m
s
w
er
e
p
r
o
p
o
s
ed
i
n
th
e
liter
atu
r
e
[
2
,
3
]
an
d
ar
e
u
s
ed
b
y
th
e
an
alo
g
/R
F
en
g
in
ee
r
s
.
T
h
ese
alg
o
r
ith
m
s
f
o
cu
s
o
n
s
w
ar
m
o
r
g
r
o
u
p
o
f
an
i
m
al
b
eh
a
v
io
r
in
o
r
d
er
to
d
e
v
elo
p
s
o
m
e
m
eta
-
h
eu
r
i
s
tics
wh
ich
ca
n
m
i
m
ic
t
h
eir
p
r
o
b
le
m
r
eso
lu
tio
n
ab
ili
ties
,
s
u
c
h
as
P
ar
ticle
S
w
ar
m
Op
t
i
m
izatio
n
(
P
SO)
[
4
]
,
A
n
t
C
o
lo
n
y
Op
ti
m
izatio
n
(
AC
O)
[
5
-
7
]
an
d
,
r
ec
en
tl
y
,
A
r
ti
f
icial
B
ee
C
o
lo
n
y
(
A
B
C
)
[
8
-
1
0
]
.
A
r
tif
icia
l
B
ee
C
o
lo
n
y
(
A
B
C
)
is
a
n
e
w
o
p
ti
m
izati
o
n
tech
n
i
q
u
e
p
r
o
p
o
s
e
d
b
y
(
Ka
r
a
b
o
g
a)
in
2
0
0
5
[
1
1
]
.
I
t
is
a
p
o
p
u
l
ati
o
n
b
ase
d
s
to
c
h
asti
c
o
p
t
im
izati
o
n
alg
o
r
ith
m
in
s
p
ir
ed
b
y
th
e
in
tellig
en
t
co
l
le
ctiv
e
f
o
r
ag
in
g
b
eh
av
i
o
r
o
b
s
e
r
v
e
d
in
th
e
b
e
e
co
l
o
n
y
.
I
t
h
as
in
s
p
ir
e
d
f
r
o
m
th
e
o
r
g
an
iza
ti
o
n
al
n
atu
r
e
an
d
f
o
r
ag
in
g
b
eh
av
io
r
o
f
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:
2
0
8
8
-
8708
A
n
a
lysi
s
o
f th
e
imp
a
ct
o
f m
eta
l th
ickn
ess
a
n
d
g
e
o
metric p
a
r
a
mete
r
s
o
n
th
e
q
u
a
li
ty
.
.
.
(
Ha
mid
B
o
u
yg
h
f)
2919
h
o
n
ey
b
ee
s
w
ar
m
s
.
Su
b
s
e
q
u
en
t
ly
,
w
e
f
o
cu
s
o
n
th
e
u
s
e
o
f
an
A
r
tif
icia
l
B
e
e
C
o
l
o
n
y
(
A
B
C
)
t
o
th
e
o
p
tim
al
s
iz
in
g
o
f
R
F
C
MO
S
s
p
ir
al
in
d
u
ct
o
r
s
.
I
n
th
is
p
a
p
e
r
,
s
p
i
r
a
l
in
d
u
ct
o
r
is
o
p
tim
ize
d
an
d
s
im
u
lated
u
s
i
n
g
A
B
C
alg
o
r
ith
m
an
d
A
DS
-
M
o
m
en
tu
m
s
o
f
t
w
ar
e
,
r
es
p
ec
t
iv
ely
.
W
e
h
av
e
a
ls
o
s
tu
d
ie
d
th
e
in
f
lu
en
ce
o
f
th
e
ef
f
e
ct
o
f
th
e
g
eo
m
etr
ic
p
a
r
am
ete
r
s
an
d
th
e
m
etal
th
ick
n
ess
o
n
th
e
q
u
ali
ty
f
ac
to
r
-
Q
.
2.
O
VE
RVI
E
W
OF
A
R
T
I
F
I
CI
AL
B
EE
C
O
L
O
NT
(
AB
C)
A
L
G
O
R
I
T
H
M
T
h
e
A
B
C
h
a
s
i
n
s
p
ir
ed
f
r
o
m
th
e
o
r
g
a
n
izatio
n
al
n
at
u
r
e
a
n
d
f
o
r
ag
i
n
g
b
eh
a
v
io
r
o
f
h
o
n
e
y
b
ee
s
[
1
1
]
.
I
n
th
e
A
B
C
al
g
o
r
ith
m
,
th
e
b
ee
co
lo
n
y
co
m
p
r
i
s
es
t
h
r
ee
k
in
d
s
o
f
b
ee
s
:
e
m
p
lo
y
ed
b
ee
s
,
o
n
lo
o
k
er
b
ee
s
,
an
d
s
co
u
t
b
ee
s
.
E
ac
h
b
ee
h
as
a
s
p
ec
ialized
task
in
th
e
co
lo
n
y
to
m
a
x
i
m
ize
t
h
e
n
ec
tar
a
m
o
u
n
t
t
h
at
is
s
to
r
ed
in
th
e
h
iv
e.
I
n
A
B
C
,
ea
ch
f
o
o
d
s
o
u
r
ce
is
p
lace
d
in
t
h
e
D
-
d
i
m
en
s
io
n
al
s
ea
r
ch
s
p
ac
e
an
d
r
ep
r
esen
ts
a
p
o
ten
tial
s
o
lu
tio
n
to
t
h
e
o
p
ti
m
izatio
n
p
r
o
b
lem
.
T
h
e
a
m
o
u
n
t
o
f
n
ec
tar
in
t
h
e
f
o
o
d
s
o
u
r
ce
i
s
a
s
s
u
m
e
d
to
b
e
th
e
f
itn
e
s
s
v
alu
e
o
f
a
f
o
o
d
s
o
u
r
ce
.
Gen
er
all
y
,
th
e
n
u
m
b
er
o
f
e
m
p
lo
y
ed
an
d
o
n
lo
o
k
e
r
b
ee
s
is
th
e
s
a
m
e
an
d
eq
u
al
to
th
e
n
u
m
b
er
o
f
f
o
o
d
s
o
u
r
ce
s
.
E
ac
h
e
m
p
lo
y
ed
b
ee
b
elo
n
g
s
to
a
f
o
o
d
s
o
u
r
c
e
a
n
d
is
r
esp
o
n
s
ib
le
f
o
r
m
i
n
i
n
g
th
e
co
r
r
esp
o
n
d
in
g
f
o
o
d
s
o
u
r
ce
.
T
h
en
,
e
m
p
lo
y
ed
b
ee
s
p
a
s
s
t
h
e
n
ec
tar
i
n
f
o
r
m
atio
n
to
o
n
lo
o
k
er
b
ee
s
in
th
e
“
d
an
ce
ar
ea
.
”
On
lo
o
k
er
b
ee
s
w
ait
in
th
e
h
i
v
e
a
n
d
s
elec
t
a
f
o
o
d
s
o
u
r
ce
to
m
i
n
e
b
ased
o
n
t
h
e
i
n
f
o
r
m
atio
n
co
m
in
g
f
r
o
m
th
e
e
m
p
lo
y
ed
b
e
es.
Her
e,
m
o
r
e
b
en
e
f
icial
f
o
o
d
s
o
u
r
ce
s
w
il
l
h
av
e
h
i
g
h
er
s
el
ec
tio
n
p
r
o
b
ab
ilit
ies
to
b
e
s
elec
ted
b
y
o
n
lo
o
k
er
b
ee
s
.
I
n
A
B
C
,
i
n
o
r
d
er
to
d
ec
i
d
e
if
a
f
o
o
d
s
o
u
r
ce
is
ab
an
d
o
n
ed
o
r
n
o
t,
tr
ial
co
u
n
ter
s
an
d
a
p
r
ed
eter
m
i
n
ed
li
m
it
p
ar
a
m
eter
ar
e
u
s
ed
.
I
f
a
s
o
lu
t
io
n
r
ep
r
esen
ted
b
y
a
f
o
o
d
s
o
u
r
ce
d
o
es
n
o
t
i
m
p
r
o
v
e
d
u
r
in
g
a
n
u
m
b
er
o
f
tr
ials
(
li
m
it),
t
h
e
f
o
o
d
s
o
u
r
ce
i
s
ab
an
d
o
n
ed
.
W
h
e
n
th
e
f
o
o
d
s
o
u
r
ce
is
ab
an
d
o
n
ed
,
t
h
e
co
r
r
es
p
o
n
d
in
g
e
m
p
lo
y
ed
b
ee
s
w
ill
b
ec
o
m
e
s
co
u
t
b
ee
s
an
d
r
an
d
o
m
l
y
g
e
n
er
ate
a
n
e
w
f
o
o
d
s
o
u
r
ce
a
n
d
r
ep
lace
it
with
t
h
e
ab
a
n
d
o
n
ed
o
n
e.
T
h
e
o
n
lo
o
k
er
b
ee
s
ev
alu
a
te
t
h
e
n
ec
tar
i
n
f
o
r
m
ati
o
n
an
d
ch
o
o
s
e
a
f
o
o
d
s
o
u
r
ce
d
ep
en
d
in
g
o
n
th
e
p
r
o
b
ab
ilit
y
v
al
u
e
ass
o
c
iate
d
w
it
h
th
at
f
o
o
d
s
o
u
r
ce
u
s
in
g
t
h
e
E
q
u
atio
n
(
1
)
[
1
2
]
:
(
1
)
w
h
er
e
i
f
i
t
is
t
h
e
s
o
lu
tio
n
'
s
f
i
tn
e
s
s
v
alu
e
i,
w
h
ic
h
i
n
tu
r
n
i
s
p
r
o
p
o
r
tio
n
al
to
t
h
e
a
m
o
u
n
t
o
f
n
ec
ta
r
o
f
t
h
e
s
o
u
r
ce
o
f
f
o
o
d
in
t
h
e
p
o
s
itio
n
i a
n
d
S
N
is
t
h
e
n
u
m
b
er
o
f
f
o
o
d
s
o
u
r
c
es
w
h
ic
h
i
s
eq
u
al
to
th
e
n
u
m
b
er
o
f
e
m
p
lo
y
ed
b
ee
s
in
t
h
e
co
lo
n
y
[
1
2
]
.
On
th
eir
tu
r
n
,
t
h
e
o
n
lo
o
k
er
b
ee
s
also
e
m
p
lo
y
t
h
e
s
a
m
e
p
r
o
ce
s
s
o
f
m
o
d
i
f
icatio
n
an
d
s
elec
tio
n
o
f
t
h
e
f
o
o
d
p
o
s
itio
n
s
as th
e
e
m
p
lo
y
ed
b
ee
s
d
o
.
T
h
is
ca
n
b
e
d
e
m
o
n
s
tr
ated
b
y
t
h
e
E
q
u
atio
n
(
2
)
.
(
2
)
w
h
er
e
j
is
a
r
an
d
o
m
l
y
s
elec
ted
in
d
ex
j
∈
{1
,
2
…
D
}
an
d
k
∈
{1
,
2
…
SN
}
is
a
r
an
d
o
m
l
y
ch
o
s
en
f
o
o
d
s
o
u
r
ce
th
a
t
is
n
o
t
eq
u
al
to
i
;
t
h
at
is
,
(
k
≠
i
)
.
ϕ
i
,
j
is
a
r
a
n
d
o
m
n
u
m
b
er
with
i
n
t
h
e
r
an
g
e
[
−1
,
1
]
g
e
n
er
a
ted
s
p
ec
if
ica
ll
y
f
o
r
ea
ch
i
an
d
j
co
m
b
i
n
atio
n
.
T
h
i
s
co
n
tr
o
ls
th
e
g
e
n
er
atio
n
o
f
t
h
e
n
eig
h
b
o
r
h
o
o
d
f
o
o
d
s
o
u
r
ce
s
.
A
g
r
ee
d
y
s
elec
tio
n
is
ap
p
lied
b
etw
ee
n
X
i
an
d
V
i
b
y
s
elec
ti
n
g
t
h
e
b
etter
o
n
e.
W
h
en
th
e
f
o
o
d
-
s
o
u
r
ce
p
o
s
itio
n
h
a
s
b
ee
n
ab
an
d
o
n
ed
,
th
e
e
m
p
lo
y
ed
b
ee
as
s
o
ciate
d
w
it
h
it
b
ec
o
m
es
a
s
co
u
t.
T
h
e
s
co
u
t
p
r
o
d
u
ce
s
a
co
m
p
letel
y
n
e
w
f
o
o
d
s
o
u
r
ce
p
o
s
itio
n
as
u
s
i
n
g
E
q
u
a
tio
n
(
2
)
.
Gen
er
all
y
,
th
e
A
B
C
al
g
o
r
ith
m
s
tep
s
ca
n
b
e
s
u
m
m
a
r
ized
as
s
h
o
w
n
i
n
Fig
u
r
e
1
[
1
3
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
9
1
8
-
2931
2920
Fig
u
r
e
1
.
A
r
ti
f
icial
b
ee
co
lo
n
y
alg
o
r
ith
m
f
lo
w
c
h
ar
t
I
t
is
clea
r
,
f
r
o
m
t
h
e
ab
o
v
e
e
x
p
lan
atio
n
,
th
at
i
n
th
e
A
B
C
al
g
o
r
ith
m
,
th
er
e
ar
e
f
o
u
r
co
n
tr
o
l
p
ar
a
m
eter
s
u
s
ed
:
T
h
e
n
u
m
b
er
o
f
t
h
e
f
o
o
d
s
o
u
r
ce
s
t
h
at
i
s
eq
u
al
to
th
e
n
u
m
b
er
o
f
e
m
p
lo
y
ed
o
r
o
n
lo
o
k
er
b
ee
s
(
SN)
,
th
e
v
al
u
e
o
f
l
i
m
it
an
d
th
e
m
a
x
i
m
u
m
c
y
cle
n
u
m
b
er
(
MCN)
.
3.
ANALY
SI
S
OF
T
H
E
RF
I
C
SPIRA
L
I
NDU
CT
O
R
S
3
.
1
.
L
a
y
o
ut
v
a
ria
bles
f
o
r
o
pti
m
iz
a
t
io
n
Fig
u
r
e
2
s
h
o
w
s
th
e
la
y
o
u
t
o
f
s
q
u
ar
e
s
p
ir
al
i
n
d
u
cto
r
.
T
h
e
g
eo
m
etr
y
p
ar
a
m
eter
s
c
h
a
r
ac
ter
izin
g
th
e
s
p
ir
al
in
d
u
cto
r
ar
e
th
e
n
u
m
b
er
o
f
t
u
r
n
s
(
n
)
,
th
e
tr
ac
e
w
id
t
h
(
w
)
,
th
e
t
u
r
n
s
p
ac
in
g
(
s
p
)
,
an
d
th
e
in
n
er
d
ia
m
eter
(
d
in
).
(d
out)
is
o
u
ter
d
ia
m
eter
.
Fig
u
r
e
2
.
T
h
e
g
eo
m
etr
y
p
ar
a
m
eter
s
o
f
a
s
q
u
ar
e
s
p
ir
al
in
d
u
cto
r
I
n
o
u
r
s
tu
d
y
ca
s
e,
w
e
f
o
cu
s
o
n
t
h
e
ap
p
licatio
n
o
f
A
B
C
al
g
o
r
ith
m
f
o
r
o
p
ti
m
iza
tio
n
th
e
g
eo
m
etr
ic
p
ar
am
eter
s
o
f
s
p
ir
al
in
d
u
cto
r
s
.
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:
2
0
8
8
-
8708
A
n
a
lysi
s
o
f th
e
imp
a
ct
o
f m
eta
l th
ickn
ess
a
n
d
g
e
o
metric p
a
r
a
mete
r
s
o
n
th
e
q
u
a
li
ty
.
.
.
(
Ha
mid
B
o
u
yg
h
f)
2921
3
.
2
.
A
na
ly
s
is
o
f
t
he
s
pira
l in
du
ct
o
r
m
o
del
T
h
e
p
h
y
s
ical
m
o
d
el
o
f
s
p
ir
al
i
n
d
u
cto
r
o
n
s
ilico
n
i
s
a
v
er
y
p
o
p
u
lar
m
o
d
el
u
s
ed
in
m
icr
o
elec
tr
o
n
ic
R
F
d
esig
n
[
1
4
]
.
I
ts
m
o
d
el
p
ar
a
m
e
ter
v
alu
e
s
ca
n
b
e
ex
p
r
ess
ed
d
i
r
ec
tl
y
u
s
i
n
g
th
e
g
eo
m
etr
y
o
f
t
h
e
s
p
ir
al
i
n
d
u
cto
r
.
An
ap
p
r
o
ac
h
is
d
ev
elo
p
ed
in
[
1
5
]
to
d
ir
ec
t
p
ar
am
eter
e
x
tr
ac
tio
n
b
ased
o
n
th
e
m
ea
s
u
r
ed
t
w
o
-
p
o
r
t
S
-
p
ar
a
m
eter
s
.
Fig
u
r
e
3
p
r
esen
t
s
t
h
e
eq
u
iv
ale
n
t
cir
c
u
it
m
o
d
el
o
f
th
e
in
d
u
cto
r
,
th
e
m
o
d
el
p
ar
a
m
eter
s
ar
e
Rs
,
R
s
i
,
Cs
,
C
o
x
,
Csi
an
d
Ls
.
W
h
er
e
L
s
is
th
e
in
d
u
ctan
ce
o
f
t
h
e
s
p
ir
al,
C
o
x
r
ep
r
esen
ts
th
e
ca
p
ac
itan
ce
b
et
w
ee
n
th
e
s
p
ir
al
an
d
t
h
e
s
ilico
n
s
u
b
s
tr
ate.
R
s
i
an
d
C
s
i
m
o
d
el
t
h
e
r
esi
s
ta
n
ce
an
d
t
h
e
ca
p
ac
ita
n
ce
o
f
t
h
e
s
u
b
s
tr
ate
r
esp
ec
tiv
el
y
,
an
d
C
s
m
o
d
el
s
t
h
e
p
ar
allel
-
p
late
ca
p
ac
itan
ce
b
et
w
ee
n
t
h
e
s
p
ir
al
an
d
t
h
e
ce
n
ter
tap
u
n
d
er
p
ass
.
Ho
w
ev
er
,
w
e
h
a
v
e
co
n
s
id
er
ed
th
e
s
i
m
p
lif
ie
d
eq
u
i
v
ale
n
t
cir
c
u
it
s
h
o
wn
in
Fi
g
u
r
e
4
to
ca
lcu
late
th
e
in
d
u
cta
n
ce
v
alu
e
.
T
h
er
ef
o
r
e,
th
e
in
d
u
cta
n
ce
v
al
u
e
f
o
r
a
g
iv
e
n
f
r
eq
u
e
n
c
y
(
f
)
is
d
eter
m
i
n
ed
b
y
E
q
u
a
tio
n
(
3
)
[
1
6
]
:
(
3
)
T
h
er
ea
f
ter
,
w
e
w
ill
u
s
e
t
h
is
eq
u
atio
n
to
ca
lc
u
late
t
h
e
i
n
d
u
ctan
ce
u
s
i
n
g
Y
-
p
ar
a
m
e
ter
o
b
tain
ed
f
r
o
m
A
D
S
Mo
m
en
t
u
m
s
o
f
t
w
ar
e.
Fig
u
r
e
3
.
P
h
y
s
ical
m
o
d
el
o
f
a
s
p
ir
al
in
d
u
cto
r
[
1
7
,
1
8
]
Fig
u
r
e
4
.
Si
m
p
li
f
ied
eq
u
i
v
alen
t c
ir
cu
it f
o
r
ca
lcu
lati
n
g
in
d
u
cta
n
ce
v
a
lu
e
w
h
er
e
C
s
u
b
1
=C
s
u
b
2
= Cs
i
an
d
R
s
u
b
1
=R
s
u
b
2
= R
s
i
T
h
e
p
ar
am
eter
s
R
s
,
R
s
i,
C
s
,
C
o
x
a
n
d
Csi
ar
e
d
ef
in
ed
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
s
[
1
4
]
:
(
4
)
(
5
)
(
6
)
(
7
)
(
8
)
(
9)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
9
1
8
-
2931
2922
w
h
er
e
σ
is
th
e
m
etal
co
n
d
u
cti
v
it
y
at
d
c,
δ
is
th
e
m
etal
s
k
i
n
d
ep
th
,
t
is
th
e
m
etal
t
h
ic
k
n
e
s
s
,
t
oxM1
-
M2
is
t
h
e
o
x
id
e
th
ic
k
n
e
s
s
b
et
w
ee
n
s
p
ir
al
an
d
ce
n
ter
tap
,
t
ox
i
s
th
e
o
x
id
e
th
ic
k
n
e
s
s
b
et
w
ee
n
s
p
ir
al
an
d
s
u
b
s
tr
ate,
l
is
th
e
o
v
er
all
len
g
th
o
f
s
p
ir
al,
w
i
s
t
h
e
l
in
e
w
id
t
h
,
G
sub
is
th
e
s
u
b
s
tr
ate
co
n
d
u
cta
n
ce
p
er
u
n
it
ar
ea
,
an
d
C
sub
is
t
h
e
s
u
b
s
tr
at
e
ca
p
ac
itan
ce
p
er
u
n
it a
r
ea
.
T
h
e
p
a
r
allel
eq
u
iv
alen
t
cir
cu
it
o
f
s
p
ir
al
in
d
u
c
to
r
s
h
o
w
n
in
Fi
g
u
r
e
5
is
u
s
ed
f
o
r
ca
lcu
latio
n
t
h
e
q
u
alit
y
f
ac
to
r
(
Q)
o
f
th
e
in
d
u
cto
r
[
1
8
]
:
Fig
u
r
e
5
.
T
h
e
p
ar
allel
eq
u
iv
alen
t c
ir
cu
i
t o
f
th
e
s
p
ir
al
in
d
u
c
t
o
r
[
1
8
]
T
h
e
q
u
alit
y
f
ac
to
r
(
Q)
ca
n
b
e
ex
p
r
ess
ed
as [
1
8
]
:
(
1
0
)
w
h
er
e
(
1
1
)
(
1
2
)
T
h
e
q
u
alit
y
f
ac
to
r
ca
n
also
b
e
ca
lcu
lated
f
r
o
m
th
e
Y
-
p
ar
a
m
et
er
s
as [
1
6
]
:
(
1
3
)
W
e
w
ill
u
s
e
(
1
3
)
to
ca
lcu
late
th
e
q
u
a
lit
y
f
ac
to
r
u
s
i
n
g
th
e
Y
-
p
ar
a
m
eter
o
b
tain
ed
f
r
o
m
A
D
S
Mo
m
en
t
u
m
s
o
f
t
w
ar
e.
T
h
e
in
d
u
ctan
ce
L
s
is
m
o
d
eled
b
y
t
h
e
f
o
llo
w
i
n
g
m
o
n
o
m
ial
e
x
p
r
ess
io
n
[
1
7
,
1
8
]
:
(
1
4
)
w
h
er
e
(
1
5
)
(
1
6
)
an
d
i
(
i=1
,
2
…
5
)
ar
e
t
h
e
co
ef
f
icien
t
s
d
ep
en
d
o
n
th
e
in
d
u
c
to
r
to
p
o
lo
g
y
.
T
h
e
co
ef
f
icie
n
ts
f
o
r
s
q
u
ar
e
in
d
u
cto
r
ar
e
[
1
9
]
:
=
1.62e
-
3,
1
=
-
1.21,
2
=
-
0.
147,
3
=
2.4,
4
=
1.7
8,
5
=
-
0.03
Rs
Ls
Cs
Rp
Cp
P1
P2
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:
2
0
8
8
-
8708
A
n
a
lysi
s
o
f th
e
imp
a
ct
o
f m
eta
l th
ickn
ess
a
n
d
g
e
o
metric p
a
r
a
mete
r
s
o
n
th
e
q
u
a
li
ty
.
.
.
(
Ha
mid
B
o
u
yg
h
f)
2923
4.
O
P
T
I
M
I
Z
AT
I
O
N
M
E
T
H
O
DO
L
O
G
Y
F
O
R
I
NDUC
T
O
R
DE
S
I
G
N
4
.
1
.
P
ro
ble
m
f
o
r
m
u
la
t
io
n
T
h
e
A
B
C
o
p
ti
m
izatio
n
m
et
h
o
d
is
ex
ec
u
ted
o
n
a
v
ec
to
r
o
f
d
esig
n
v
ar
iab
les
o
f
R
F
cir
cu
it.
I
n
f
ac
t,
th
e
b
ee
p
o
s
itio
n
v
ec
to
r
is
t
h
e
x
1
,
x
2
,
…x
d
d
e
s
ig
n
v
ar
iab
les
o
f
cir
cu
it.
At
f
ir
s
t,
ea
ch
b
ee
(
i
-
th
b
ee
)
p
o
s
itio
n
v
ec
to
r
is
r
an
d
o
m
l
y
in
i
tialized
.
I
n
ea
ch
iter
atio
n
,
t
h
e
A
B
C
alg
o
r
ith
m
r
u
n
s
t
h
e
p
r
o
g
r
a
m
m
e
f
o
r
ea
ch
b
ee
an
d
ev
alu
a
tes
a
C
o
s
t
F
u
n
c
tio
n
(
C
F),
d
escr
ib
ed
in
t
h
e
f
o
r
m
o
f
a
p
o
s
y
n
o
m
ial
f
u
n
ctio
n
w
it
h
i
n
eq
u
alit
y
co
n
s
tr
ain
t
s
ex
p
r
ess
ed
as p
o
s
y
n
o
m
ia
l f
u
n
ct
io
n
s
an
d
eq
u
al
it
y
co
n
s
tr
ai
n
ts
a
s
m
o
n
o
m
ial
f
u
n
ctio
n
s
[
2
0
]
:
A
m
o
n
o
m
ia
l
f
u
n
ctio
n
h
as t
h
e
f
o
llo
w
i
n
g
f
o
r
m
:
(
1
7
)
w
h
er
e
B
is
a
p
o
s
itiv
e
co
n
s
ta
n
t
(
B
>
0
)
,
x
1
,
x
2
…a
n
d
x
n
ar
e
r
ea
l
p
o
s
itiv
e
v
ar
iab
les:
a
1
,
a
2
.
.
.
an
d
a
n
ar
e
co
n
s
tan
t
s
k
n
o
w
n
a
s
t
h
e
e
x
p
o
n
e
n
ts
o
f
t
h
e
m
o
n
o
m
ial.
An
y
p
o
s
iti
v
e
co
n
s
tan
t
is
a
m
o
n
o
m
ial.
Mo
n
o
m
i
als
ar
e
clo
s
ed
u
n
d
er
m
u
ltip
licatio
n
a
n
d
d
iv
i
s
io
n
.
A
p
o
s
y
n
o
m
ial
f
u
n
ctio
n
is
a
s
u
m
o
f
o
n
e
o
r
m
o
r
e
m
o
n
o
m
ial
f
u
n
ctio
n
s
a
s
s
h
o
w
n
i
n
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
(
C
F o
b
tain
ed
b
y
eq
u
i
v
ale
n
t c
ir
cu
it a
n
al
y
s
i
s
o
f
R
F c
ir
cu
i
t)
:
(
1
8
)
So
,
th
e
d
esig
n
p
r
o
b
lem
o
f
th
e
s
p
ir
al
in
d
u
cto
r
ca
n
b
e
f
o
r
m
u
la
ted
as:
Ma
x
i
m
ize
o
f
Q
-
q
u
al
it
y
f
ac
to
r
(
Min
i
m
ize
Q
req
):
[
C
o
s
t
Fu
n
cti
o
n
(
C
F)
is
d
o
n
e
b
y
(
1
0
)
]
Su
b
j
ec
t to
: Req
u
ir
ed
in
d
u
c
tan
ce
I
n
d
ep
en
d
en
t g
eo
m
etr
y
p
ar
a
m
e
ter
s
co
n
s
tr
ai
n
ts
m
a
y
b
e
ad
d
ed
s
u
c
h
as:
a.
Nu
m
b
er
o
f
t
u
r
n
:
n
≤
4
b.
Min
i
m
u
m
v
al
u
e
o
f
t
h
e
tr
ac
k
wid
th
:
w
≤
1
2
µm
c.
Min
i
m
u
m
o
f
s
p
ac
in
g
: sp
=
2
.
5
µ
m
d.
Ou
ter
d
ia
m
eter
: d
in
≤
1
4
5
µm
Fo
r
r
ed
u
cin
g
t
h
e
p
ar
asit
ic
e
f
f
ec
t
d
u
e
to
th
e
p
r
o
x
i
m
it
y
p
r
o
b
lem
[
2
1
]
,
w
e
w
ill
r
esp
ec
t
th
is
ad
d
co
n
s
tr
ain
t:
(
1
9
)
T
h
e
o
b
j
ec
t f
u
n
ctio
n
f
i
n
d
s
t
h
e
g
lo
b
al
m
i
n
i
m
u
m
C
F
f
o
r
its
ex
p
r
ess
io
n
:
(
2
0
)
w
h
er
e
Q
req
=1
/Q,
P
en
al
t
y
:
P
en
alt
y
o
f
ea
ch
co
n
s
tr
ai
n
t
v
io
latio
n
,
S
u
m
(
C
t)
:
So
m
e
o
f
all
co
n
s
tr
ai
n
ts
(
C
t
(
1
)
,
C
t
(
2
)
…)
.
E
q
u
atio
n
(
2
0
)
is
th
e
m
in
i
m
u
m
v
alu
e
o
f
Ob
j
Val
(
C
F)
g
u
ar
a
n
tees
th
e
m
ax
i
m
a
l
v
al
u
e
f
o
r
Q
-
f
ac
to
r
f
o
r
L
s
r
eq
=
4
n
H
an
d
F
req
=f
s
=
2
.
4
GHz
.
T
h
e
tech
n
o
lo
g
ical
p
ar
a
m
eter
s
ar
e
s
u
m
m
ar
ized
in
T
ab
le
1
f
o
r
UM
C
1
3
0
n
m
C
MO
S tec
h
n
o
lo
g
y
.
A
l
g
o
r
ith
m
co
n
tr
o
l
p
ar
am
eter
s
ar
e
g
iv
e
n
in
T
ab
le
2
.
T
h
e
n
u
m
b
er
o
f
iter
atio
n
s
is
eq
u
al
to
1
0
0
0
.
Fo
r
th
e
s
p
ir
al
i
n
d
u
cto
r
d
esig
n
,
t
h
e
A
B
C
al
g
o
r
ith
m
s
tar
ts
w
it
h
cr
e
atio
n
o
f
t
h
e
in
itial
b
ee
s
b
y
r
an
d
o
m
izat
io
n
,
w
h
er
e
ea
ch
b
ee
is
co
m
p
o
s
ed
b
y
f
o
u
r
d
esig
n
v
ar
iab
les
[
d
in
=B
ee
(
:,1
)
,
w
=B
ee
(
:,2
)
,
s
p
=B
ee
(
:,3
)
,
n
=
B
ee
(
:,4
)
]
,
r
ep
r
esen
tin
g
th
e
la
y
o
u
t
g
eo
m
etr
y
p
ar
a
m
eter
s
,
an
d
m
u
s
t
o
b
ey
to
v
ar
iab
le
b
o
u
n
d
ar
ies
(
u
p
p
er
an
d
lo
w
e
r
b
o
u
n
d
ar
ies).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
9
1
8
-
2931
2924
T
ab
le
1
.
T
ec
h
n
o
lo
g
ical
p
ar
a
m
eter
s
f
o
r
in
d
u
cto
r
d
esi
g
n
N
a
me
S
y
mb
o
l
V
a
l
u
e
M
e
t
a
l
t
h
i
c
k
n
e
ss
T
h
i
c
k
n
e
ss o
f
t
h
e
o
x
i
d
e
i
n
s
u
l
a
t
o
r
b
e
t
w
e
e
n
t
h
e
sp
i
r
a
l
a
n
d
u
n
d
e
r
p
a
ss
t
M1
-
M2
T
h
i
c
k
n
e
ss o
f
t
h
e
o
x
i
d
e
M
e
t
a
l
c
o
n
d
u
c
t
i
v
i
t
y
S
u
b
s
t
r
a
t
e
c
o
n
d
u
c
t
a
n
c
e
G
su
b
P
e
r
mi
t
i
v
i
t
y
o
f
t
h
e
o
x
i
d
e
S
u
b
s
t
r
a
t
e
t
h
i
c
k
n
e
ss
S
u
b
s
t
r
a
t
e
r
e
si
st
i
v
i
t
y
S
u
b
s
t
r
a
t
e
p
e
r
mi
t
i
v
i
t
y
M
a
g
n
e
t
i
c
P
e
r
me
a
b
i
l
i
t
y
o
f
t
h
e
f
r
e
e
sp
a
c
e
t
t
o
xM
1M
2
t
ox
σ
G
s
ub
E
ox
t
s
ub
ρ
ε
r
u
(
mj
u
)
2
.
8
e
-
6
0
.
4
e
-
6
5
.
4
2
e
-
6
1
/
2
.
6
5
e
-
8
2
.
4
3
e
5
3
.
4
5
3
e
-
11
7
0
0
e
-
6
2
8
Ω
.
c
m
1
1
.
9
1
.
2
5
6
e
-
6
T
ab
le
2
.
A
B
C
co
n
tr
o
l
p
ar
am
et
er
s
f
o
r
in
d
u
cto
r
d
esi
g
n
P
a
r
a
me
t
e
r
n
a
me
V
a
l
u
e
C
o
l
o
n
y
si
z
e
(
C
S
)
N
u
mb
e
r
o
f
O
n
l
o
o
k
e
r
s b
e
e
s
N
u
mb
e
r
o
f
Em
p
l
o
y
e
d
b
e
e
s
N
u
mb
e
r
o
f
F
o
o
d
so
u
r
c
e
s
1
0
0
5
0
%
o
f
T
h
e
sw
a
r
m
5
0
%
o
f
T
h
e
sw
a
r
m
C
S
/
2
4
.
2
.
O
pti
m
iza
t
io
n r
esu
lt
s
T
h
e
d
esig
n
a
n
d
s
i
m
u
l
atio
n
r
esu
lt
s
o
f
4
n
H
in
d
u
cto
r
f
o
r
an
o
p
er
atio
n
f
r
eq
u
e
n
c
y
o
f
2
.
4
GHz
ar
e
ad
d
r
ess
ed
u
s
in
g
UM
C
1
3
0
n
m
C
MO
S
tech
n
o
lo
g
y
p
ar
a
m
eter
s
s
h
o
w
n
i
n
T
ab
le
1
.
T
h
e
A
B
C
o
p
ti
m
izat
io
n
r
esu
lt
s
ar
e
d
o
n
e
an
d
v
er
if
ied
w
it
h
u
s
i
n
g
an
E
M
s
i
m
u
lato
r
(
Mo
m
en
t
u
m
-
ADS)
[
2
2
]
.
A
m
a
x
i
m
u
m
to
l
er
an
ce
δ
an
d
r
elativ
e
er
r
o
r
o
f
4
%
r
esp
e
ctiv
el
y
ar
e
as
s
u
m
ed
an
d
ac
ce
p
ted
.
T
ab
le
3
g
iv
es
th
e
r
es
u
lts
o
b
tain
ed
b
y
A
B
C
.
Fig
u
r
e
6
g
iv
e
s
th
e
co
s
t
f
u
n
ctio
n
v
er
s
u
s
n
u
m
b
er
o
f
iter
atio
n
s
.
Fig
u
r
e
7
s
h
o
w
s
t
h
e
Mo
m
en
tu
m
-
ADS
s
i
m
u
lat
io
n
r
esu
lt
s
(
Q
a
n
d
L
)
u
s
in
g
t
h
e
o
b
tain
ed
o
p
ti
m
al
v
al
u
es
b
y
A
B
C
-
b
ased
m
et
h
o
d
[
8
]
f
o
r
R
F
C
MO
S
s
q
u
ar
e
s
p
ir
al
in
d
u
cto
r
.
T
ab
le
3
.
Op
tim
izatio
n
r
esu
l
ts
o
b
tain
ed
b
y
A
B
C
al
g
o
r
ith
m
s
p
(
µ
m)
d
in
(
µ
m)
w
(
µ
m)
n
d
o
ut
(
µ
m)
L
r
e
q
(
n
H
)
L
A
B
C
(
n
H
)
δ
(
%)
Q
A
B
C
2
.
5
1
4
0
.
4
5
1
1
.
15
3
.
5
2
3
1
4
3
.
9
6
1
1
2
.
7
1
F
ig
u
r
e
6
.
C
o
s
t f
u
n
ctio
n
o
f
t
h
e
s
p
ir
al
in
d
u
cto
r
v
er
s
u
s
I
ter
atio
n
s
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:
2
0
8
8
-
8708
A
n
a
lysi
s
o
f th
e
imp
a
ct
o
f m
eta
l th
ickn
ess
a
n
d
g
e
o
metric p
a
r
a
mete
r
s
o
n
th
e
q
u
a
li
ty
.
.
.
(
Ha
mid
B
o
u
yg
h
f)
2925
Fig
u
r
e
7
.
Mo
m
e
n
t
u
m
-
ADS
s
i
m
u
latio
n
s
f
o
r
L
a
n
d
Q
W
e
n
o
tice
th
at
th
e
s
i
m
u
lat
io
n
r
esu
l
ts
ar
e
in
g
o
o
d
ag
r
ee
m
en
t
w
it
h
th
o
s
e
o
b
tain
ed
u
s
i
n
g
th
e
A
B
C
tech
n
iq
u
e.
T
ab
le
4
s
h
o
w
s
t
h
e
co
m
p
ar
is
o
n
o
f
r
esu
lts
b
et
w
e
en
ev
a
lu
ated
a
n
d
s
i
m
u
lated
with
elec
tr
o
m
ag
n
etic
s
i
m
u
lato
r
.
T
ab
le
4
.
C
o
m
p
ar
is
o
n
o
f
o
p
ti
m
ized
an
d
s
i
m
u
lated
r
es
u
lts
L
A
B
C
(
n
H
)
L
M
o
m
.
*
(
n
H
)
Er
r
o
r
(L
)
(
%)
Q
A
B
C
Q
M
o
m
.
*
Er
r
o
r
(Q
)
(
%)
3
.
9
6
3
.
9
5
0
.
2
5
1
2
.
7
1
1
2
.
2
5
3
.
7
5
*
M
o
me
n
t
u
m
-
E
M
S
i
mu
l
a
t
o
r
5.
I
NF
L
U
E
NC
E
O
F
T
H
E
G
E
O
M
E
T
RIC
P
ARAM
E
T
E
R
S
AND
M
E
T
A
L
T
H
I
CK
N
E
SS
O
N
T
H
E
Q
UA
L
I
T
Y
F
AC
T
O
R
-
Q
T
h
is
s
ec
tio
n
w
ill
s
t
u
d
y
t
h
e
i
m
p
ac
t
o
f
g
eo
m
etr
ic
p
ar
am
e
ter
s
an
d
m
etal
th
ick
n
es
s
o
f
in
d
u
cto
r
s
,
o
n
th
e
f
ac
to
r
o
f
q
u
alit
y
b
y
t
h
e
ex
p
lo
itin
g
o
f
t
h
e
o
p
ti
m
ized
r
esu
lt
o
b
tain
ed
as
s
h
o
w
n
in
T
ab
le
3
.
Fo
r
th
e
s
tu
d
y
o
f
ea
ch
o
n
e
,
t
h
e
p
ar
a
m
eter
to
b
e
s
tu
d
ied
h
as b
ee
n
v
ar
ied
.
5
.
1
.
I
m
pa
ct
o
f
t
he
g
eo
m
et
ric
pa
r
a
m
et
er
s
o
f
ind
uct
o
r
o
n t
he
f
a
ct
o
r
o
f
qu
a
lity
I
n
o
r
d
er
to
an
al
y
ze
t
h
e
i
n
f
l
u
en
ce
th
at
t
h
e
g
eo
m
etr
ic
p
ar
a
m
et
er
s
o
f
th
e
i
n
d
u
cto
r
h
av
e
o
n
t
h
e
q
u
a
lit
y
f
ac
to
r
-
Q
b
e
h
av
io
r
,
w
e
u
s
e
m
a
tlab
s
o
f
t
w
ar
e
f
o
r
s
i
m
u
lat
io
n
s
w
it
h
e
x
p
lo
itin
g
o
f
th
e
o
p
ti
m
iz
atio
n
r
esu
lts
s
h
o
w
n
in
T
ab
le
3
.
W
h
ile
v
ar
y
i
n
g
n
u
m
b
er
o
f
t
u
r
n
s
(
n
)
,
th
e
tr
ac
e
w
i
d
th
(
w
)
,
s
p
ac
in
g
b
et
w
ee
n
tr
ac
k
s
(
s
p
)
,
an
d
th
e
in
n
er
d
ia
m
eter
(
d
in
)
,
r
ea
s
o
n
s
o
f
ch
a
n
g
e
s
in
t
h
e
q
u
a
lit
y
f
ac
to
r
-
Q
b
eh
av
io
r
o
f
i
n
d
u
cto
r
ar
e
an
al
y
z
ed
in
d
etail
f
o
r
ea
ch
ca
s
e.
T
h
e
m
a
x
i
m
u
m
Q
(
Q
m
ax
)
an
d
s
elf
-
r
eso
n
a
n
ce
f
r
eq
u
e
n
c
y
(
SF
R
)
ar
e
ea
s
il
y
ex
tr
ac
ted
f
r
o
m
t
h
e
cu
r
v
e
o
f
Q
v
er
s
u
s
f
r
eq
u
en
c
y
.
5
.
1
.
1
.
Sepa
ra
t
io
n bet
w
ee
n t
ra
ck
s
:
s
p
T
o
an
al
y
s
i
s
th
e
v
ar
iatio
n
o
f
t
h
is
p
ar
am
e
ter
o
n
th
e
f
ac
to
r
o
f
q
u
alit
y
,
s
i
x
in
d
u
cto
r
t
y
p
es
ar
e
c
h
o
s
en
f
o
r
s
i
m
u
lat
io
n
,
all
t
h
ese
i
n
d
u
cto
r
s
h
a
v
e
th
e
s
a
m
e
g
eo
m
e
tr
ical
p
ar
am
eter
s
ex
ce
p
t
f
o
r
s
ep
ar
atio
n
b
et
w
ee
n
tr
ac
k
s
(
s
p
)
.
T
h
e
w
=1
1
.
1
5
u
m
,
d
in
=1
4
0
.
4
5
u
m
,
an
d
t
h
e
n
u
m
b
er
o
f
t
u
r
n
s
n
=3
.
5
.
A
s
t
h
e
s
p
ac
in
g
b
et
w
ee
n
tr
ac
k
s
v
ar
y
i
n
g
f
r
o
m
1
.
5
to
4
u
m
,
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
s
p
ir
al
in
d
u
cto
r
s
is
s
h
o
w
n
in
F
ig
u
r
e
8
an
d
T
ab
le
5
.
Fig
u
r
e
8
an
d
T
a
b
le
5
s
h
o
w
t
h
at
th
e
m
a
x
i
m
u
m
q
u
ali
t
y
f
ac
t
o
r
-
Q
m
a
x
d
ec
r
ea
s
es
w
it
h
th
e
i
n
cr
ea
s
e
o
f
th
e
s
p
ac
i
n
g
s
p
.
A
s
th
e
s
p
d
ec
r
ea
s
es,
th
e
s
u
b
s
tr
ate
co
u
p
li
n
g
h
a
s
n
o
clea
r
ch
a
n
g
e,
s
o
t
h
e
ch
an
g
e
s
o
f
Fre
q
(
Q
m
ax
)
a
n
d
SR
F a
r
e
n
o
t c
lear
.
T
h
e
r
ea
s
o
n
f
o
r
th
e
d
ec
r
ea
s
e
o
f
Q
m
ax
i
n
t
h
at
t
h
e
in
cr
ea
s
e
o
f
t
h
e
s
p
ac
i
n
g
b
et
w
ee
n
ad
j
ac
en
t m
eta
l
tr
ac
es lo
w
er
s
t
h
e
m
a
g
n
etic
co
u
p
li
n
g
o
f
th
e
m
etal
tr
ac
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
9
1
8
-
2931
2926
Fig
u
r
e
8
.
Si
m
u
latio
n
r
esu
l
ts
o
f
q
u
alit
y
f
ac
to
r
f
o
r
d
if
f
er
en
t
v
al
u
es o
f
s
p
T
ab
le
5
. R
esu
lts
o
f
s
i
m
u
latio
n
f
o
r
d
if
f
er
e
n
t v
a
lu
e
s
o
f
s
p
I
n
d
u
c
t
o
r
S
p
(
u
m)
Q
max
F
r
e
q
/
Q
max
(
G
H
z
)
S
R
F
(
G
H
z
)
1
2
3
4
5
6
1
.
5
2
2
.
5
3
3
.
5
4
1
8
.
9
8
1
8
.
7
9
1
8
.
6
2
1
8
.
4
6
1
8
.
3
1
1
8
.
1
8
6
.
2
6
.
2
6
.
2
6
.
2
6
.
2
6
.
5
1
2
.
6
2
1
2
.
7
9
1
2
.
9
6
1
3
.
0
7
1
3
.
2
1
3
.
3
5
5
.
1
.
2
.
T
ra
ce
w
idth:
w
I
n
th
i
s
s
tu
d
y
,
w
e
i
n
ten
d
to
c
o
m
p
ar
e
t
h
e
e
f
f
ec
t
o
f
t
h
e
v
ar
i
atio
n
o
f
t
h
e
tr
ac
k
w
id
t
h
f
o
r
s
ix
i
n
d
u
cto
r
t
y
p
es
w
it
h
th
e
w
p
ar
a
m
eter
ta
k
in
g
v
alu
e
s
f
r
o
m
6
.
1
5
to
1
1
.
1
5
μ
m
.
T
h
e
s
p
=2
.
5
u
m
,
n
=3
.
5
,
an
d
d
in
=1
4
0
.
4
5
u
m
.
Fig
u
r
e
9
an
d
T
a
b
le
6
illu
s
tr
at
e
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
s
p
ir
al
in
d
u
cto
r
s
f
o
r
d
if
f
er
en
t
tr
ac
e
w
id
t
h
s
.
Fi
g
u
r
e
9
s
h
o
w
s
th
at,
f
o
r
th
e
s
i
m
u
lated
in
d
u
cto
r
,
as
i
n
cr
ea
s
e
s
th
e
w
i
d
th
o
f
t
h
e
tr
ac
k
o
f
t
h
e
s
p
ir
al,
th
e
q
u
al
it
y
f
ac
to
r
in
cr
ea
s
es
it
s
v
al
u
e.
Ho
w
ev
er
,
it
is
ap
p
r
ec
iated
th
at
th
e
i
n
d
u
ctan
ce
i
s
r
ed
u
ce
d
,
s
i
n
ce
t
h
e
e
n
clo
s
ed
ar
ea
i
n
th
e
s
p
ir
al
is
s
m
a
ller
.
I
n
ad
d
itio
n
,
th
e
r
eso
n
a
n
ce
f
r
eq
u
e
n
c
y
d
ec
r
ea
s
es
d
u
e
to
ev
id
en
t
in
cr
ea
s
e
in
p
ar
asit
ic
ca
p
ac
ities
.
Fig
u
r
e
9
.
Si
m
u
latio
n
r
esu
l
ts
o
f
q
u
alit
y
f
ac
to
r
f
o
r
d
if
f
er
en
t
v
al
u
es o
f
w
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:
2
0
8
8
-
8708
A
n
a
lysi
s
o
f th
e
imp
a
ct
o
f m
eta
l th
ickn
ess
a
n
d
g
e
o
metric p
a
r
a
mete
r
s
o
n
th
e
q
u
a
li
ty
.
.
.
(
Ha
mid
B
o
u
yg
h
f)
2927
T
ab
le
6
.
R
esu
lts
o
f
s
i
m
u
latio
n
f
o
r
d
if
f
er
e
n
t v
a
lu
e
s
o
f
w
I
n
d
u
c
t
o
r
w
(
u
m)
Q
max
F
r
e
q
/
Q
max
(
G
H
z
)
S
R
F
(
G
H
z
)
1
2
3
4
5
6
6
.
1
5
7
.
1
5
8
.
1
5
9
.
1
5
1
0
.
1
5
1
1
.
1
5
1
6
.
2
1
6
.
8
4
1
7
.
5
1
7
.
9
4
1
8
.
2
7
1
8
.
6
2
9
.
5
8
.
3
7
.
4
6
.
8
6
.
5
6
.
2
20
1
7
.
8
1
6
.
1
1
4
.
8
5
1
3
.
8
1
2
.
9
6
5
.
1
.
3
.
Nu
m
ber
o
f
t
urns
:
n
T
h
e
s
ix
in
d
u
cto
r
t
y
p
es
h
av
e
b
ee
n
s
i
m
u
la
ted
f
o
r
a
v
alu
e
o
f
n
u
m
b
er
o
f
tu
r
n
s
(
n
)
v
ar
y
in
g
f
r
o
m
1
.
5
to
4
w
it
h
s
tep
eq
u
al
to
0
.
5
.
T
h
e
d
in
=1
4
0
.
4
5
u
m
,
s
p
=2
.
5
u
m
a
n
d
w
=1
1
.
1
5
u
m
.
Fi
g
u
r
e
1
0
an
d
T
ab
le
7
illu
s
tr
ates
th
e
p
er
f
o
r
m
a
n
ce
o
f
s
p
ir
al
in
d
u
cto
r
s
f
o
r
d
if
f
er
e
n
t
v
al
u
e
s
o
f
n
u
m
b
er
o
f
t
u
r
n
s
(
n
)
.
W
e
ca
n
s
ee
cle
ar
l
y
t
h
at,
f
o
r
in
cr
ea
s
i
n
g
t
h
e
n
u
m
b
er
o
f
tu
r
n
s
,
th
e
SR
F
a
n
d
Q
m
a
x
d
ec
r
ea
s
es.
W
h
en
th
e
n
u
m
b
er
o
f
tu
r
n
s
i
n
cr
ea
s
e
s
,
th
en
m
etal
lo
s
s
an
d
s
u
b
s
tr
ate
c
o
u
p
lin
g
in
cr
ea
s
ed
,
t
h
is
i
s
th
e
r
ea
s
o
n
f
o
r
th
e
d
ec
r
ea
s
e
o
f
Q
m
a
x
an
d
S
R
F.
Fig
u
r
e
1
0
.
Si
m
u
latio
n
r
es
u
lt
s
o
f
q
u
al
it
y
f
ac
to
r
f
o
r
d
if
f
er
en
t v
alu
e
s
o
f
n
T
ab
le
7
. R
esu
lts
o
f
s
i
m
u
l
atio
n
f
o
r
d
if
f
er
e
n
t v
a
lu
e
s
o
f
n
I
n
d
u
c
t
o
r
n
Q
max
F
r
e
q
/
Q
max
(
G
H
z
)
S
R
F
(
G
H
z
)
1
2
3
4
5
6
1
.
5
2
2
.
5
3
3
.
5
4
2
0
.
5
2
2
0
.
1
9
1
9
.
7
3
1
9
.
1
5
1
8
.
6
2
18
1
6
.
1
11
8
.
6
7
.
7
6
.
2
5
.
6
3
5
.
4
2
4
.
8
1
8
.
6
1
5
.
1
1
2
.
9
6
1
1
.
1
5
.
1
.
4
.
Va
ria
t
io
n o
f
inn
er
dia
m
et
er
:
d
in
T
h
e
s
ix
-
in
d
u
cto
r
t
y
p
es
h
av
e
b
ee
n
s
i
m
u
lated
w
ith
d
i
f
f
er
en
t
d
in
v
alu
e
s
.
T
h
e
s
p
=2
.
5
u
m
,
w=
1
1
.
1
5
u
m
an
d
n
=3
.
5
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
i
n
teg
r
ated
s
p
ir
al
in
d
u
cto
r
s
f
o
r
d
in
f
r
o
m
1
4
0
.
4
5
u
m
to
1
9
0
.
4
5
u
m
w
it
h
s
tep
eq
u
a
l
to
1
0
u
m
i
s
ill
u
s
t
r
ated
i
n
F
i
g
u
r
e
1
1
an
d
T
ab
le
8
.
I
n
n
er
d
ia
m
eter
(
d
in
)
h
as
b
ee
n
v
ar
ied
f
r
o
m
1
4
0
.
4
5
t
o
1
9
0
.
4
5
µm
.
A
s
t
h
e
I
n
n
er
d
ia
m
ete
r
o
f
s
p
ir
al
in
d
u
cto
r
s
is
i
n
cr
ea
s
ed
,
s
elf
-
r
eso
n
an
t
f
r
eq
u
e
n
c
y
o
f
i
n
d
u
ct
o
r
d
ec
r
ea
s
es
s
ig
n
i
f
ican
tl
y
.
As
th
e
d
in
d
ec
r
ea
s
es
,
th
e
p
r
o
x
i
m
it
y
e
f
f
ec
t
b
ec
o
m
es
s
i
g
n
if
ican
t
en
o
u
g
h
to
i
n
tr
o
d
u
ce
an
ed
d
y
c
u
r
r
en
t
i
n
th
e
m
etal
tr
ac
es,
co
n
s
eq
u
e
n
tl
y
in
cr
e
a
s
in
g
t
h
e
s
e
r
ies r
esis
ta
n
ce
[
2
3
,
2
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.