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.
1
,
F
e
br
ua
r
y
202
0
,
pp.
301
~
31
0
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
K
A.
v18i1.
13130
301
Jou
r
n
al
h
omepage
:
ht
tp:
//
jour
nal.
uad
.
ac
.
id/
index
.
php/T
E
L
K
OM
N
I
K
A
I
nves
t
i
ga
t
i
on
on
E
M
radi
at
i
ons
f
rom
i
nt
erc
onnect
s
i
n
i
nt
egrat
ed
ci
rcu
i
t
s
L
ou
n
as
B
e
lh
im
e
r
,
Ar
e
z
k
i
B
e
n
f
d
il
a
,
A
h
c
e
n
e
L
ak
h
lef
Mi
cro
an
d
N
a
n
o
e
l
ect
r
o
n
i
cs
Res
ea
rch
G
ro
u
p
,
Facu
l
t
y
o
f
E
l
ec
t
ri
ca
l
E
n
g
i
n
eeri
n
g
a
n
d
Co
m
p
u
t
er
Sci
e
n
ces
,
U
n
i
v
er
s
i
t
y
Mo
u
l
o
u
d
Mammeri
,
T
i
z
i
-
Ouz
o
u
,
A
l
g
er
i
a
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
M
a
y
22,
2019
R
e
vis
e
d
J
ul
2,
2019
Ac
c
e
pted
J
ul
1
8
,
2019
Ch
aract
er
i
zat
i
o
n
an
d
e
s
t
i
mat
i
o
n
o
f
i
n
t
erc
o
n
n
ect
i
o
n
s
b
eh
av
i
o
r
i
n
i
n
t
e
g
rat
e
d
ci
rcu
i
t
s
d
es
i
g
n
b
efo
re
t
h
e
i
m
p
l
eme
n
t
a
t
i
o
n
p
h
as
e
i
s
o
f
p
a
ram
o
u
n
t
i
m
p
o
r
t
an
ce.
T
h
i
s
b
e
h
av
i
o
r
s
ee
n
as
mi
cro
s
t
r
i
p
an
t
en
n
as
g
et
s
co
mp
l
ex
as
t
h
e
i
n
t
ern
a
l
s
i
g
n
a
l
(s
q
u
are
o
r
s
i
n
e
w
av
e
s
)
freq
u
e
n
ci
e
s
i
n
cr
eas
e.
T
h
u
s
,
t
h
ey
b
eco
me
t
h
e
p
referred
p
at
h
fo
r
t
h
e
p
r
o
p
a
g
at
i
o
n
o
f
e
l
ect
r
o
mag
n
et
i
c
d
i
s
t
u
r
b
an
ces
.
In
t
h
i
s
w
o
rk
w
e
h
av
e
w
o
rk
e
d
o
u
t
t
h
e
n
u
mer
i
cal
m
o
d
e
l
i
n
g
o
f
t
h
e
e
l
ect
r
o
mag
n
e
t
i
c
i
n
t
er
act
i
o
n
s
ch
aract
er
i
zi
n
g
t
h
e
el
ec
t
ro
ma
g
n
e
t
i
c
c
o
mp
a
t
i
b
i
l
i
t
y
i
n
t
h
e
mi
cr
o
s
t
ri
p
t
ran
s
mi
s
s
i
o
n
l
i
n
es
.
T
h
e
e
ffec
t
o
f
t
h
es
e
el
ec
t
ro
ma
g
n
et
i
c
i
n
t
erac
t
i
o
n
s
i
n
d
i
ffere
n
t
s
t
r
u
ct
u
res
t
o
p
o
l
o
g
i
e
s
are
s
t
u
d
i
ed
t
h
r
o
u
g
h
t
h
e
an
a
l
y
s
i
s
o
f
t
h
e
i
n
fl
u
en
ce
o
f
t
h
e
s
u
p
p
l
y
s
i
g
n
al
s
freq
u
en
c
y
an
d
s
t
r
u
ct
u
res
.
T
h
e
s
p
aci
n
g
b
et
w
een
t
ra
n
s
m
i
s
s
i
o
n
l
i
n
e
t
rac
k
s
an
d
t
h
e
n
u
mb
er
o
f
t
r
ack
s
s
u
p
er
p
o
s
i
t
i
o
n
i
s
mo
d
e
l
ed
.
T
h
e
ev
o
l
u
t
i
o
n
a
n
d
v
ar
i
at
i
o
n
o
f
t
h
e
s
c
h
eme
p
aramet
ers
i
n
t
h
e
freq
u
en
c
y
d
o
mai
n
are
d
et
erm
i
n
e
d
.
T
h
e
t
ran
s
mi
s
s
i
o
n
l
i
n
e
s
are
co
n
s
i
d
ered
p
aral
l
el
o
f
eq
u
al
s
p
ac
i
n
g
an
d
s
u
p
erp
o
s
e
d
t
rac
k
s
o
f
eq
u
a
l
s
p
aci
n
g
a
n
d
t
h
i
ck
n
es
s
.
T
h
e
cap
ac
i
t
a
n
ce
an
d
i
n
d
u
c
t
an
ce
ma
t
ri
ce
s
are
co
mp
u
t
e
d
a
n
d
d
i
s
cu
s
s
e
d
.
T
h
e
res
u
l
t
s
are
fo
u
n
d
t
o
co
mp
l
y
w
i
t
h
cu
rre
n
t
res
earc
h
o
u
t
c
o
mes
.
K
e
y
w
o
r
d
s
:
C
a
pa
c
it
a
nc
e
E
lec
tr
omagne
ti
c
F
ini
te
e
leme
nt
method
I
nter
c
onne
c
t
M
ult
iconduc
tor
R
a
diations
T
r
a
ns
mi
s
s
ion
li
ne
s
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
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
:
Ar
e
z
ki
B
e
nf
dil
a
,
M
icr
o
a
nd
Na
noe
lec
tr
onics
R
e
s
e
a
r
c
h
Gr
oup,
F
a
c
ult
y
of
E
lec
tr
ica
l
E
nginee
r
ing
a
nd
C
omput
e
r
S
c
ienc
e
s
,
Unive
r
s
it
y
M
ouloud
M
a
mm
e
r
i
,
T
izi
-
Ouz
ou,
Alge
r
ia.
E
mail:
be
nf
di
la@u
m
mt
o.
dz
1.
I
NT
RODU
C
T
I
ON
Now
a
da
ys
,
int
e
gr
a
ted
c
ir
c
uit
s
e
lec
tr
omagne
ti
c
s
us
c
e
pti
bil
it
y
thr
e
s
hold
ge
ts
lowe
r
due
to
the
int
e
gr
a
ti
on
de
ns
it
ies
incr
e
a
s
ing
a
nd
highe
r
le
ve
ls
of
meta
ll
iza
ti
on
.
T
his
inc
r
e
a
s
e
d
vulner
a
bil
it
y
r
e
s
ult
s
f
r
om
thei
r
s
ize
s
hr
inki
ng
,
s
uppl
y
vo
lt
a
ge
a
nd
t
he
r
e
gula
r
inc
r
e
a
s
e
in
their
ope
r
a
ti
on
f
r
e
que
nc
i
e
s
[
1
,
2
]
.
Giga
he
r
tz
f
r
e
que
nc
ies
a
r
e
pa
r
ti
c
ular
ly
ha
r
m
f
ul
f
o
r
thes
e
e
lec
tr
onic
s
ys
tems
be
c
a
us
e
their
wa
ve
len
gths
a
r
e
li
ke
ly
to
ge
ne
r
a
te
r
e
s
ona
nc
e
phe
nomena
on
th
e
int
e
gr
a
ted
c
ir
c
uit
s
t
r
a
c
ks
,
th
us
incr
e
a
s
ing
the
s
ys
tem
dis
tur
ba
nc
e
r
is
ks
[
3
-
5]
.
As
mi
c
r
oe
lec
tr
onics
tec
hnology
pr
ogr
e
s
s
e
s
,
manu
f
a
c
tur
e
r
s
a
r
e
c
onti
nua
ll
y
s
tr
ivi
ng
to
buil
d
higher
de
ns
it
y
e
lec
tr
onic
s
ys
tem
s
int
e
gr
a
ti
on.
T
his
e
volut
ion
is
c
ha
r
a
c
ter
ize
d
by
a
r
e
gular
de
vice
s
hr
inki
ng
a
nd
a
mul
ti
leve
l
in
tegr
a
ti
on
[
6]
.
T
his
led
to
a
c
ompl
e
x
int
e
r
c
onne
c
ti
on
c
i
r
c
uit
r
y
c
ons
is
ti
ng
of
pa
r
a
ll
e
l
plane
s
of
e
quidi
s
tant
tr
a
ns
mi
s
s
ion
li
ne
s
.
T
oda
y
thi
s
be
c
o
mes
a
c
ompl
e
x
pr
oblem
f
a
c
e
d
in
the
im
pr
ove
ment
of
the
int
e
gr
a
ted
c
ir
c
uit
s
pe
r
f
or
manc
e
s
[
7]
.
W
he
n
de
s
igni
ng
a
n
d
im
pleme
nti
ng
a
n
e
lec
tr
onic
s
ys
tem,
the
pos
s
ibl
e
e
lec
tr
omagne
ti
c
int
e
r
a
c
ti
ons
s
hould
be
take
n
int
o
a
c
c
ount
a
nd
methods
s
hould
be
p
r
ovided
to
r
e
duc
e
their
in
f
luenc
e
s
uf
f
icie
ntl
y,
s
o
a
s
to
e
ns
ur
e
s
a
f
e
ope
r
a
ti
on
in
mos
t
c
a
s
e
s
[
8
,
9]
.
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
.
1
,
F
e
br
ua
r
y
2020
:
301
-
31
0
302
E
ns
ur
ing
e
lec
tr
o
magne
ti
c
c
ompatibi
li
ty
a
t
the
in
tegr
a
ted
c
ir
c
uit
leve
l
im
pl
ies
e
f
f
e
c
ti
ve
r
e
duc
ti
on
o
f
nois
e
s
our
c
e
s
a
nd
dis
tur
ba
nc
e
s
or
igi
ns
.
T
he
modeling
of
thes
e
f
a
c
ts
be
c
omes
manda
tor
y
t
o
e
ns
ur
e
a
pr
e
dictive
a
ppr
oa
c
h
to
the
r
is
ks
of
E
M
-
induce
d
dis
r
upti
on
[
10
,
11
]
.
T
h
is
r
e
qui
r
e
s
s
pe
c
if
ic
too
ls
,
mo
de
ls
a
nd
E
M
C
knowle
dge
[
12
,
13]
.
T
he
de
s
igner
of
in
tegr
a
ted
c
ir
c
uit
s
s
hould
c
ons
ider
the
c
a
pa
c
it
a
nc
e
s
a
nd
inducta
nc
e
s
that
we
r
e
not
c
ons
ider
e
d
in
e
a
r
li
e
r
ti
mes
,
be
c
a
us
e
of
the
int
e
r
c
onne
c
ti
on’
s
lengths
a
nd
th
e
higher
ope
r
a
ti
ng
f
r
e
que
n
c
ies
[
14
,
15]
.
T
he
s
tudy
of
e
l
e
c
tr
omagne
ti
c
r
a
diation
in
a
n
int
e
gr
a
ted
c
ir
c
uit
r
e
quir
e
s
knowle
dge
of
the
e
lec
tr
omagne
ti
c
f
ields
in
thi
s
de
vice
a
nd
ther
e
f
or
e
the
f
lux
va
lues
[
16]
.
T
he
c
a
lcul
a
ti
on
of
the
magne
ti
c
f
ield
r
e
quir
e
s
a
r
e
s
olut
ion
o
f
M
a
xw
e
ll
e
qua
ti
ons
.
T
his
is
a
c
hi
e
ve
d
by
s
e
ve
r
a
l
c
omput
a
ti
ona
l
methods
,
s
uc
h
a
s
the
M
e
thod
of
F
ini
te
E
leme
nt,
f
i
nit
e
dif
f
e
r
e
nc
e
s
a
nd
the
method
o
f
mom
e
nts
[
17
,
1
8]
.
I
n
or
de
r
to
f
u
r
ther
im
p
r
ove
the
int
e
gr
a
ted
c
ir
c
uit
s
e
ve
r
a
l
c
a
lcula
ti
on
models
ha
v
e
be
e
n
pr
opos
e
d
to
e
s
ti
mat
e
the
be
ha
vior
o
f
the
int
e
r
c
onne
c
ti
on’
s
l
in
e
s
,
a
s
it
wa
s
p
r
e
s
e
nted
in
[
19
.
20]
.
And
may
r
e
s
e
a
r
c
he
r
s
ha
ve
c
a
lcula
ted
a
nd
s
im
ulate
d
the
e
lec
tr
omagne
ti
c
pr
oblem
[
21
-
23]
.
I
n
thi
s
pa
pe
r
we
ha
ve
us
e
d
t
he
f
ini
te
e
leme
nt
method
to
de
ter
mi
ne
the
r
a
diation
a
nd
t
he
c
oupli
ng
be
twe
e
n
it
s
int
e
r
c
onne
c
ti
on
t
r
a
c
ks
in
or
de
r
to
int
e
gr
a
te
a
ll
the
li
ne
f
ields
s
ur
r
ounding
a
n
in
ter
c
onne
c
t
li
ne
.
W
e
ha
ve
o
r
ga
nize
d
the
pa
pe
r
a
s
f
ol
lows
:
in
the
s
e
c
onde
pa
r
t
we
ha
ve
given
the
de
f
ini
ti
on
of
t
he
f
ini
te
e
leme
nt
method,
in
the
thi
r
d
pa
r
t
a
math
e
matica
l
model
ha
s
be
e
n
de
ve
lopped
to
mi
nim
ize
e
lec
tr
omagne
ti
c
dis
tur
ba
nc
e
on
c
i
r
c
uit
s
int
e
r
c
onne
c
ts
,
a
nd
in
the
f
i
f
th
pa
r
t
the
c
i
r
c
uit
s
int
e
r
c
onne
c
t
ha
s
be
e
n
s
im
ulate
d
with
de
f
f
e
r
e
nts
pa
r
a
mete
r
s
in
or
de
r
to
a
c
hieve
a
n
int
e
r
c
onne
c
ti
on
s
t
r
uc
tur
e
wi
th
les
s
e
ne
r
gy
l
os
s
e
s
.
2.
T
HE
F
I
NI
T
E
E
L
E
M
E
NT
M
E
T
HO
D
T
he
f
ini
te
e
leme
nt
a
ppr
oa
c
h
is
ba
s
e
d
on
s
olvi
ng
p
a
r
ti
a
l
dif
f
e
r
e
nti
a
l
e
qua
ti
ons
knowing
the
bounda
r
y
c
ondit
ions
.
T
his
method
wa
s
ini
ti
a
ll
y
us
e
d
f
o
r
s
olvi
ng
pr
oblems
in
the
f
ield
of
f
r
a
c
tur
e
mec
ha
nics
a
nd
s
tr
uc
tur
a
l
de
s
ign
(
by
mec
ha
nics
)
.
T
he
method
w
a
s
f
ir
s
t
us
e
d
f
or
c
omput
ing
the
e
lec
tr
omagne
ti
c
f
ield
in
the
1970s
by
P
.
P
S
il
ve
s
ter
a
nd
M
.
V.
K
C
ha
r
i
.
I
n
m
os
t
c
a
s
e
s
,
it
is
int
e
gr
a
ted
with
C
.
A.
O
s
of
twa
r
e
s
a
nd
s
howe
d
gr
e
a
t
a
dva
ntage
f
or
the
de
s
igner
s
o
f
phys
ica
l
s
ys
te
ms
[
24]
.
T
he
ba
s
ic
a
ppr
oa
c
h
o
f
the
f
ini
te
e
leme
nt
metho
d
is
to
s
ubdivi
de
the
f
ield
of
s
tudy
int
o
f
ini
te
number
s
of
s
ubdomains
c
a
ll
e
d
e
leme
nts
a
s
s
how
in
F
igu
r
e
1
.
T
he
a
ppr
oxim
a
ti
on
o
f
the
unknown
va
lues
is
done
f
or
e
a
c
h
e
leme
nt
of
the
int
e
r
polation
f
unc
t
ions
.
T
his
f
unc
ti
on
is
de
f
ined
ba
s
e
d
on
the
ge
o
metr
y
of
the
e
leme
nt
that
is
c
hos
e
n
be
f
or
e
ha
nd
a
nd
f
it
s
wi
th
the
node
s
of
thi
s
e
leme
nt
wi
th
r
e
s
pe
c
t
to
the
u
nknown
va
lues
.
T
his
is
c
a
ll
e
d
noda
l
int
e
r
polation
[
25]
.
F
igur
e
1.
M
e
s
h
by
f
ini
te
e
leme
nt
3.
T
HE
M
AT
HE
M
A
T
I
CA
L
M
ODE
L
I
n
the
f
oll
owing
,
we
will
be
de
ve
lopi
ng
a
ma
thema
ti
c
a
l
model
that
gove
r
ns
e
lec
tr
omagne
ti
c
c
ompatibi
li
ty
p
r
oblems
of
the
magne
ti
z
a
ti
on
c
o
ns
e
r
va
ti
on.
Us
ing
the
M
a
xwe
ll
e
qua
ti
on
,
we
c
a
n
de
duc
e
the
r
e
lation
that
li
nks
the
magn
e
ti
c
induc
ti
on
to
the
mag
ne
ti
c
ve
c
tor
potential
a
s
:
∇
⃗
⃗
.
⃗
=
0
⇒
∃
/
⃗
=
∇
⃗
⃗
^
(
1)
i
ntr
oduc
ing
(
1
)
int
o
M
a
xwe
ll
F
a
r
a
da
y
e
qua
ti
on
we
will
ha
ve
:
∇
⃗
⃗
^
(
⃗
+
∂
∂
)
=
0
(
2)
s
ince
the
r
otational
of
a
gr
a
dient
is
null
,
we
c
a
n
de
duc
e
the
e
xis
tenc
e
of
a
n
e
lec
tr
ic
s
c
a
l
a
r
potential
V,
a
nd
then
we
wr
it
e
i
t
a
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
I
nv
e
s
ti
gati
on
on
E
M
r
adiat
ions
fr
om
int
e
r
c
onne
c
ts
in
int
e
gr
ated
c
ir
c
uit
s
(
L
ounas
B
e
lhi
me
r
)
303
∃
/
⃗
+
∂
∂
=
−
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
(
3)
w
e
ha
ve
:
⃗
=
−
∂
∂
−
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
(
4)
r
e
plac
ing
(
4)
in
the
e
xpr
e
s
s
ion
of
Ohm's
law
we
ge
t:
=
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
∂
∂
(
5)
w
e
ha
ve
⃗
⃗
=
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
(
6)
⃗
⃗
:
c
ur
r
e
nt
de
ns
i
ty
of
the
e
xc
it
a
ti
on
s
our
c
e
=
⃗
⃗
−
∂
∂
(
7)
by
int
r
oduc
ing
the
(
1
)
in
the
r
e
lation
of
magne
ti
c
medium
we
ge
t:
⃗
⃗
=
∇
⃗
⃗
^
(
8)
r
e
plac
ing
(
8)
in
the
M
a
xwe
ll
-
Ampe
r
e
e
qua
ti
on
a
nd
a
pplyi
ng
to
it
the
r
otational
we
will
ha
ve
:
∇
⃗
⃗
^
(
∇
⃗
⃗
^
)
=
⃗
⃗
−
∂
∂
+
∂
⃗
⃗
∂
(
9)
taking
int
o
a
c
c
ount
the
r
e
lation
of
a
diele
c
tr
ic
me
dium
a
nd
r
e
plac
ing
(
4)
in
(
9)
we
obtain
the
f
oll
o
wing
s
e
t
of
e
qua
ti
ons
:
∇
⃗
⃗
^
(
∇
⃗
⃗
^
)
=
⃗
⃗
−
∂
∂
+
∂
⃗
∂
(
10)
∇
⃗
⃗
^
(
∇
⃗
⃗
^
)
=
⃗
⃗
−
∂
∂
+
∂
∂
(
−
∂
∂
−
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
)
(
11)
∇
⃗
⃗
^
(
∇
⃗
⃗
^
)
=
⃗
⃗
−
∂
∂
+
∂
2
∂
2
−
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
∂
∂
(
12)
i
t
is
known
that:
∇
⃗
⃗
^
∇
⃗
⃗
^
=
−
∇
2
+
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
(
∇
⃗
⃗
.
⃗
⃗
⃗
)
(
13)
−
1
(
∇
2
)
=
⃗
⃗
−
∂
∂
−
∂
2
∂
2
−
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
(
∇
⃗
⃗
.
+
∂
⃗
∂
)
(
14)
to
c
ompl
e
tely
de
f
ine
the
magne
ti
c
potential
ve
c
tor
,
one
im
pos
e
s
the
c
ondit
ion
o
f
L
or
e
ntz:
∇
⃗
⃗
.
+
∂
⃗
∂
=
0
(
15)
T
he
n
(
14)
is
s
im
p
li
f
ied
a
s
given
b
e
low:
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
.
1
,
F
e
br
ua
r
y
2020
:
301
-
31
0
304
−
1
∇
2
+
∂
∂
+
∂
2
∂
2
=
⃗
⃗
(
16)
we
c
ons
ider
that
the
p
r
opa
ga
ti
on
is
done
in
a
C
a
r
tes
ian
c
oor
dinate
s
s
ys
tem
a
long
the
z
a
xis
,
a
nd
then
the
pr
opa
ga
ti
on
e
qua
ti
on
o
f
the
magne
ti
c
ve
c
tor
po
tential
wi
ll
be
:
−
1
[
∂
2
∂
2
+
∂
2
∂
2
]
+
∂
∂
+
∂
2
∂
2
=
(
17)
if
we
c
ons
ider
the
s
inus
oidal
ha
r
moni
c
r
e
gim
e
thi
s
lea
ds
to:
−
1
[
∂
2
∂
2
+
∂
2
∂
2
]
+
(
−
2
)
=
(
1
8)
A
z
,
J
z
:
a
r
e
r
e
s
pe
c
ti
ve
ly
the
c
omponent
of
the
mag
ne
ti
c
ve
c
tor
potential
a
nd
the
c
ur
r
e
nt
de
ns
it
y
s
our
c
e
a
long
the
z
a
xis
.
I
n
the
(
18)
c
ha
r
a
c
ter
ize
s
the
pr
opa
ga
ti
on
of
the
magne
ti
c
ve
c
tor
potential.
T
his
latter
will
be
c
ons
ider
e
d
in
the
f
oll
owing
pa
r
t
o
f
thi
s
wor
k
to
model
the
e
lec
tr
omagne
ti
c
int
e
r
a
c
ti
on
phe
no
mena
of
the
int
e
r
c
onne
c
ti
ons
in
a
n
in
tegr
a
ted
c
ir
c
uit
.
F
or
s
olvi
ng
the
po
tential
magne
ti
c
ve
c
tor
pr
op
a
ga
ti
on
e
qua
ti
on,
c
ons
ider
ing
the
f
in
it
e
e
leme
nt
f
or
mul
a
ti
on,
we
ha
ve
int
r
oduc
e
d
the
Ga
ler
kin
m
e
thod
[
14]
de
f
ined
in
a
C
a
r
tes
ian
c
oor
dinate
s
ys
tem.
T
he
pr
opa
ga
ti
on
is
c
ons
ider
e
d
a
c
c
or
ding
to
the
oz
a
xis
,
by
c
ons
ider
ing
the
phe
n
omenon
is
gove
r
ne
d
by
the
e
qua
ti
on:
−
1
[
∂
2
∂
2
+
∂
2
∂
2
]
+
(
−
2
)
−
=
0
(
19)
∬
(
(
−
1
[
∂
2
∂
2
+
∂
2
∂
2
]
+
(
−
2
)
)
−
)
Ω
=
0
(
20)
∬
(
−
1
[
∂
2
∂
2
+
∂
2
∂
2
]
)
Ω
Φ
+
∬
(
(
−
2
)
)
Ω
−
∬
Φ
=
0
Ω
(
21)
−
1
∬
∇
⃗
⃗
∇
⃗
⃗
+
∫
∂
∂
Γ
+
Γ
Ω
(
−
2
)
∬
=
Ω
∬
Ω
(
22)
us
ing
the
bounda
r
y
Di
r
ichle
t
c
ondit
ions
,
thi
s
lea
ds
to:
−
1
∬
∇
⃗
⃗
∇
⃗
⃗
+
Ω
(
−
2
)
∬
=
Ω
∬
Ω
(
24)
=
∑
=
1
(
25)
∑
[
−
1
∬
∇
⃗
⃗
∇
⃗
⃗
Ω
]
=
1
+
(
−
2
)
∑
[
∬
Ω
]
=
=
1
∬
Ω
(
26)
f
or
a
ll
mes
h
node
s
,
the
f
oll
owing
matr
ix
s
ys
tem
c
a
n
be
wr
it
ten:
[
]
[
]
+
(
−
2
)
[
]
[
]
=
[
]
(
27)
=
−
1
∬
∇
⃗
⃗
Ω
∇
⃗
⃗
(
28)
∫
∂
∂
Γ
Γ
=
0
(
23)
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
I
nv
e
s
ti
gati
on
on
E
M
r
adiat
ions
fr
om
int
e
r
c
onne
c
ts
in
int
e
gr
ated
c
ir
c
uit
s
(
L
ounas
B
e
lhi
me
r
)
305
=
∬
Ω
=
∬
Ω
(
29)
[
A]
a
nd
[
K]
a
r
e
r
e
s
pe
c
ti
ve
ly
the
unknown
ve
c
tor
a
nd
the
e
xc
it
a
ti
on
s
our
c
e
ve
c
tor
[
M
]
a
nd
[
L
]
a
r
e
two
matr
ice
s
that
de
pe
nd
on
the
m
e
s
h
s
tr
uc
t
ur
e
4.
P
AR
AM
E
T
E
RS
I
DE
NT
I
F
I
C
AT
I
ON
OF
T
HE
EQ
UI
VA
L
E
NT
CI
RC
UI
T
DI
AGRA
M
I
t
is
im
por
tant
f
o
r
a
n
int
e
gr
a
ted
c
ir
c
uit
de
s
igner
to
pr
e
dict
the
be
ha
vior
o
f
his
pr
oduc
t
in
a
n
e
lec
tr
omagne
ti
c
int
e
r
f
e
r
e
nc
e
e
nvir
onment.
I
nte
r
c
onne
c
ti
ons
a
r
e
of
ten
victim
s
of
thi
s
e
lec
tr
oma
gne
ti
c
poll
uti
on.
T
his
pa
r
t
c
ons
is
ts
of
a
numer
ica
l
mode
li
ng
of
the
e
lec
tr
omagne
ti
c
int
e
r
f
e
r
e
nc
e
s
.
W
e
will
a
na
lyze
the
inf
luenc
e
o
f
the
f
r
e
que
nc
y
pa
r
a
mete
r
s
of
the
s
u
pply
s
ignal
a
nd
s
pa
c
ing
be
twe
e
n
tr
a
c
k
a
nd
the
pe
r
mi
tt
ivi
ty
of
diele
c
tr
ic
on
the
e
volut
ion
of
the
pa
r
a
mete
r
s
o
f
the
e
quivale
nt
dia
gr
a
m
.
T
he
int
e
r
c
onne
c
ti
on
li
ne
s
c
a
n
be
modele
d
us
ing
their
dis
tr
ibut
e
d
c
ons
tants
,
the
e
qui
va
lent
diagr
a
ms
a
r
e
s
hown
in
F
igu
r
e
2
,
it
r
e
pr
e
s
e
nt
s
a
t
r
a
c
k
por
ti
on
in
the
f
or
m
o
f
a
n
e
lec
tr
ica
l
qua
dr
upole
th
a
t
li
nks
the
c
h
a
r
a
c
ter
is
ti
c
s
(
i,
v
)
of
the
pos
it
ion
(
z
+
dz
)
to
that
of
pos
it
ion
(
z
)
a
t
ti
me
(
t
)
.
v
(
z
,t
)
:
r
e
pr
e
s
e
nt
s
t
he
vol
ta
ge
a
t
po
s
it
io
n "
z
"
v
(
z
+dz
,t
)
:
r
e
pr
e
s
e
nt
s
t
he
vol
ta
ge
a
t
pos
it
io
n "
z
+
dz
"
F
igur
e
2
.
E
qu
ivale
nt
c
ir
c
uit
of
a
s
tr
ip
po
r
ti
on
T
he
pa
r
a
mete
r
s
of
t
he
e
quivale
nt
diagr
a
m
a
r
e
:
t
he
e
quivale
nt
inducta
nc
e
"
L
"
pe
r
unit
length,
it
c
ha
r
a
c
ter
ize
s
the
magne
ti
c
e
ne
r
gy
de
ns
it
y
s
tor
e
d
in
the
medium
,
the
e
quivale
nt
c
a
pa
c
it
a
nc
e
"
C
"
pe
r
unit
length,
i
t
c
ha
r
a
c
ter
ize
s
the
de
ns
it
y
o
f
diele
c
tr
ic
e
ne
r
g
y
s
tor
e
d
in
the
s
ub
s
tr
a
te,
the
r
e
s
is
tanc
e
s
e
r
ies
pe
r
unit
len
gth
"
R
"
,
it
c
ha
r
a
c
ter
ize
s
the
los
s
e
s
by
J
oule
e
f
f
e
c
t,
the
pa
r
a
ll
e
l
c
onduc
tanc
e
pe
r
unit
lengt
h
"
G"
,
it
c
ha
r
a
c
ter
ize
s
the
los
s
e
s
in
the
ins
ulation.
J
oules
l
os
s
e
s
we
r
e
us
e
d
to
e
va
luate
the
l
inea
r
r
e
s
is
tanc
e
given
by
the
f
oll
owing
r
e
lation:
=
2
[
Ω
/
m
]
(
30)
=
∭
2
d
v
(
31)
=
2*
2
[
H
/
m
]
(
32)
to
e
va
luate
the
inducta
nc
e
,
the
f
oll
owing
magne
ti
c
e
ne
r
gy
s
hould
be
us
e
d
:
=
∭
1
2
0
|
|
2
(
33)
=
2*
2
[
F
/
m
]
(
34)
the
diele
c
tr
ic
e
ne
r
gy
is
us
e
d
to
e
va
luate
the
l
inea
r
c
a
pa
c
it
a
nc
e
:
=
∭
0
|
|
2
(
35)
to
e
va
luate
the
c
onduc
tanc
e
of
the
s
ubs
tr
a
te,
we
wi
ll
us
e
a
f
o
r
mul
a
that
include
s
the
c
a
pa
c
it
y
:
=
*
*
[
S
/
m
]
(
36)
tan
δ
:
dis
s
ip
a
ti
on
f
a
c
tor
(
diele
c
tr
ic
los
s
a
ngle)
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
.
1
,
F
e
br
ua
r
y
2020
:
301
-
31
0
306
T
o
s
tudy
the
pa
r
a
mete
r
s
of
e
quivale
nt
diagr
a
ms
a
s
a
f
unc
ti
on
of
the
s
upply
f
r
e
que
nc
y,
the
dis
tanc
e
be
twe
e
n
the
t
r
a
c
k
a
nd
the
pe
r
mi
tt
ivi
ty,
we
ha
ve
e
lab
or
a
ted
the
f
lows
hr
t
s
hown
in
F
ig
ur
e
3
whic
h
h
a
s
be
e
n
us
e
d
to
de
s
ign
our
c
omput
a
ti
on
pr
og
r
a
ms
.
At
the
s
tar
t
o
f
ou
r
p
r
ogr
a
m
a
s
s
hown
in
F
ig
ur
e
3
we
i
ntr
oduc
e
ge
ometr
y
a
nd
phys
ica
l
c
ha
r
a
c
ter
is
ti
c
s
f
r
om
model
to
modele
d
.
Af
ter
ha
ving
mes
he
d
the
f
ield
of
s
t
udy,
we
will
s
olve
the
pa
r
t
ial
di
f
f
e
r
e
nti
a
l
e
qua
ti
on
a
t
e
a
c
h
mes
h
point
a
nd
identi
f
y
the
pa
r
a
mete
r
s
(
R
,
L
,
C
,
a
nd
G)
of
the
int
e
r
c
onne
c
ti
on
li
ne
f
or
a
given
f
r
e
que
nc
y
a
nd
dis
tanc
e
be
twe
e
n
t
r
a
c
ks
.
E
a
c
h
ti
me
the
f
r
e
que
nc
y
a
nd
the
dis
tanc
e
be
twe
e
n
tr
a
c
ks
a
r
e
incr
e
mente
d.
F
igur
e
3
.
F
lowc
ha
r
t
us
e
d
to
s
tudy
the
pa
r
a
mete
r
s
o
f
th
e
e
quivale
nt
c
ir
c
uit
a
s
a
f
unc
ti
on
of
s
upply
f
r
e
que
nc
y,
the
dis
tanc
e
be
twe
e
n
the
tr
a
c
k
a
nd
the
pe
r
m
it
ti
vit
y
5.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
5.
1.
Groun
d
p
lan
e
e
f
f
e
c
t
I
n
thi
s
pa
r
t
we
will
s
tudy
the
e
f
f
e
c
t
o
f
gr
oun
d
plane
on
the
im
pe
da
nc
e
of
the
int
e
r
c
onne
c
ts
.
W
e
c
ons
id
e
r
the
s
tr
uc
tur
e
s
in
F
igu
r
e
4
,
thi
s
mi
c
r
os
tr
ip
c
oupled
int
e
r
c
onne
c
t
ha
s
the
f
o
ll
owing
ge
o
metr
ica
l
pa
r
a
mete
r
s
w
=
2
μ
m
,
S
=
5
n
m,
h
=
1
μ
m,
H
=
3
μ
m
,
=
3.
9
I
n
th
is
c
a
s
e
we
note
a
s
igni
f
ica
nt
incr
e
a
s
e
in
the
c
a
pa
c
it
y
towa
r
ds
the
mas
s
whic
h
is
due
to
t
he
li
ne
s
o
f
f
ields
whic
h
r
e
f
oc
us
towa
r
ds
the
mas
s
a
s
s
how
in
F
igur
e
5.
5.
2.
I
n
f
lu
e
n
c
e
of
t
h
e
f
r
e
q
u
e
n
c
y
In
our
a
na
lys
is
w
e
ba
s
e
d
our
s
ys
tem
on
a
two
p
a
r
a
ll
e
l
tr
a
ns
mi
s
s
ion
li
ne
s
.
T
his
c
o
r
r
e
s
ponds
to
a
2
li
ne
s
of
a
n
n
li
ne
int
e
r
na
l
int
e
gr
a
ted
c
ir
c
ui
t
bus
.
T
he
thr
e
e
-
li
ne
c
onf
igur
a
ti
on
is
us
e
d
to
dis
c
us
s
the
int
e
r
de
pe
nda
nc
e
of
the
two
-
li
ne
T
r
a
ns
mi
s
s
ion
li
ne
s
.
T
his
mi
c
r
os
tr
ip
c
o
upled
int
e
r
c
onne
c
ts
ha
ve
the
f
oll
owing
ge
ometr
ica
l
pa
r
a
mete
r
s
:
w
=
2
μ
m
,
S
=
5
nm
,
h
=
1
μ
m
,
H
=
3
μ
m
,
=
3.
9
.
T
he
thr
e
e
mi
c
r
os
tr
ip
li
ne
s
a
s
s
hown
in
F
igur
e
6
a
r
e
e
quidi
s
tanc
e
a
nd
mount
e
d
on
a
oxide
gr
own
on
s
il
icon
s
ubs
tr
a
te.
W
e
s
i
mul
a
ted
a
nd
mode
led
the
int
e
r
c
onne
c
t
c
a
pa
c
it
a
nc
e
in
d
if
f
e
r
e
nt
s
it
ua
ti
on.
T
he
F
igur
e
s
7
s
ho
w
inducta
nc
e
a
nd
r
e
s
is
tanc
e
ve
r
s
u
s
f
r
e
que
nc
y.
T
he
incr
e
a
s
e
in
r
e
s
is
tanc
e
is
due
to
the
s
kin
e
f
f
e
c
t
whic
h
c
a
us
e
s
the
dis
tr
ibut
ion
of
the
c
ur
r
e
nt
de
ns
it
y
in
the
s
e
c
ti
on
of
the
tr
a
c
k
t
o
be
c
ome
non
-
unif
or
m
with
the
inc
r
e
a
s
e
of
the
f
r
e
que
nc
y
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
I
nv
e
s
ti
gati
on
on
E
M
r
adiat
ions
fr
om
int
e
r
c
onne
c
ts
in
int
e
gr
ated
c
ir
c
uit
s
(
L
ounas
B
e
lhi
me
r
)
307
a
nd
the
c
ur
r
e
nt
that
tr
a
ve
ls
the
tr
a
c
k
will
tend
to
c
i
r
c
ulate
on
thi
s
pe
r
ipher
y
in
a
s
e
c
ti
on
de
f
ined
by
a
t
hickne
s
s
c
a
ll
e
d
"
s
kin
thi
c
kne
s
s
"
.
T
he
r
e
f
or
e
,
the
a
c
ti
ve
s
e
c
ti
on
of
the
t
r
a
c
k
de
c
r
e
a
s
e
s
a
nd
ther
e
f
or
e
the
r
e
s
is
tanc
e
incr
e
a
s
e
s
.
W
e
a
ls
o
note
that
the
inducta
nc
e
of
the
t
r
a
c
k
d
e
c
r
e
a
s
e
s
a
s
the
f
r
e
que
nc
y
incr
e
a
s
e
s
a
s
s
hown
in
F
igur
e
8.
Ac
c
or
ding
to
the
r
e
lation
of
the
inducta
nc
e
it
is
unde
r
s
tood
that,
a
s
r
e
ga
r
ds
the
int
e
r
na
l
v
olum
e
of
the
c
onduc
tor
,
th
e
c
ontr
ibut
ion
to
the
int
e
gr
a
l
of
t
he
magne
ti
c
e
ne
r
gy
is
e
ve
n
s
maller
than
the
f
r
e
q
ue
nc
y
is
lar
ge
.
I
t
is
f
ound
that
the
c
a
pa
c
it
y
incr
e
a
s
e
s
with
t
he
incr
e
a
s
e
of
the
f
r
e
que
nc
y,
th
is
is
e
xplaine
d
a
s
much
a
s
the
f
r
e
que
nc
y
is
mo
r
e
im
po
r
tant
the
d
iele
c
tr
ic
e
ne
r
g
y
will
tend
incr
e
a
s
e
d
c
ons
e
que
ntl
y
the
c
a
pa
c
it
y
in
c
r
e
a
s
e
s
.
T
he
incr
e
a
s
e
in
c
onduc
tanc
e
a
s
s
how
in
F
igur
e
9
is
due
to
the
incr
e
a
s
e
in
c
a
pa
c
it
y,
Ac
c
or
ding
to
the
e
qua
ti
on
of
c
onduc
tanc
e
.
T
he
obtaine
d
r
e
s
ult
s
we
ll
mot
ivate
the
e
f
f
e
c
t
o
f
the
e
lec
tr
omagne
ti
c
int
e
r
a
c
ti
ons
on
the
e
lec
tr
ica
l
pa
r
a
mete
r
s
of
the
int
e
r
c
onne
c
t
s
,
notably
the
im
pe
da
nc
e
whic
h
ha
s
known
a
n
incr
e
a
s
e
c
ompar
e
d
to
that
obtaine
d
in
the
a
bs
e
nc
e
of
the
e
le
c
tr
omagne
ti
c
int
e
r
a
c
ti
ons
a
s
s
how
i
n
F
igu
r
e
10
.
F
igur
e
4
.
M
icr
os
tr
ip
c
oupled
int
e
r
c
onne
c
t
:
(
a
)
without
gr
ound
plane
,
(
b)
wi
th
gr
ound
plane
F
igur
e
5
.
P
a
r
a
s
it
ic
c
a
pa
c
it
a
nc
e
ve
r
s
us
f
r
e
que
nc
y
F
igur
e
6
.
S
ymm
e
t
r
ic
mi
c
r
os
tr
ip
c
oupled
int
e
r
c
onne
c
ts
F
igur
e
7
.
I
nduc
tanc
e
a
nd
r
e
s
is
tanc
e
ve
r
s
us
f
r
e
que
nc
y
F
igur
e
8
.
C
a
pa
c
i
tanc
e
ve
r
s
us
f
r
e
que
nc
y
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
.
1
,
F
e
br
ua
r
y
2020
:
301
-
31
0
308
F
igur
e
9
.
C
onduc
tanc
e
ve
r
s
us
f
r
e
que
nc
y
F
igur
e
10
.
S
umm
a
r
y
a
nd
da
ta
c
ompar
is
on
5
.
3
.
I
n
f
lu
e
n
c
e
of
t
h
e
d
iele
c
t
r
ic
p
e
r
m
i
t
t
ivi
t
y
W
e
va
r
ied
the
diele
c
tr
ic
pe
r
mi
tt
ivi
ty
a
nd
the
f
r
e
que
nc
y
is
f
ixed
we
c
a
lcula
te
the
ne
w
va
lues
of
the
pa
r
a
s
it
ic
c
a
pa
c
it
a
nc
e
s
.
T
he
pe
r
mi
tt
ivi
ty
is
d
ir
e
c
tl
y
r
e
late
d
to
the
diele
c
tr
ic
e
ne
r
gy
s
o
by
in
c
r
e
a
s
ing
the
pe
r
mi
tt
ivi
ty
the
diele
c
tr
ic
e
ne
r
gy
a
ls
o
incr
e
a
s
e
s
c
ons
e
que
ntl
y
the
pa
r
a
s
it
ic
c
a
pa
c
it
a
nc
e
incr
e
a
s
e
s
a
s
s
how
in
F
igur
e
11
a
nd
F
igur
e
12
.
F
igur
e
11
.
P
a
r
a
s
it
ic
c
a
pa
c
it
a
nc
e
ve
r
s
us
P
e
r
mi
tt
ivi
ty
F
igur
e
12
.
P
a
r
a
s
it
ic
c
a
pa
c
it
a
nc
e
ve
r
s
us
pe
r
mi
tt
ivi
ty
f
or
di
f
f
e
r
e
nt
S
va
l
ue
5
.
4
.
I
n
f
lu
e
n
c
e
of
t
h
e
d
is
t
an
c
e
in
t
e
r
t
r
ac
k
s
F
or
d
if
f
e
r
e
nt
va
lues
o
f
"
S
"
(
the
dis
t
a
nc
e
be
twe
e
n
two
int
e
r
c
onne
c
ti
on
tr
a
c
ks
)
,
it
s
e
ts
the
wor
king
f
r
e
que
nc
y
is
1
gigahe
tr
z
we
c
a
lcula
te
the
va
lue
o
f
the
c
a
pa
c
it
y
a
nd
inducta
nc
e
pe
r
unit
length.
As
s
how
in
the
F
igur
e
13
a
nd
F
igu
r
e
14,
the
c
a
pa
c
it
y
de
c
r
e
a
s
e
s
with
the
dis
tanc
e
be
twe
e
n
tr
a
c
ks
,
t
his
e
volut
io
n
c
a
n
be
e
xplaine
d
by
the
f
a
c
t
that
we
a
s
s
oc
iate
the
incr
e
a
s
e
in
the
dis
tanc
e
be
twe
e
n
t
r
a
c
ks
,
in
or
de
r
to
l
oc
a
te
a
n
opti
mal
laye
r
thi
c
kne
s
s
c
or
r
e
s
ponding
to
the
th
i
c
kne
s
s
f
or
whic
h
the
s
pur
ious
c
a
pa
c
it
a
nc
e
tr
a
c
k
r
a
ti
o
is
the
lowe
s
t
.
5
.
5
.
M
od
e
l
in
g
o
f
c
r
os
s
t
alk
Any
unwa
nted
volt
a
ge
or
c
ur
r
e
nt
a
nd
c
r
e
a
ted
by
c
oupli
ng
be
twe
e
n
two
tr
a
c
ks
of
a
n
int
e
r
c
onne
c
ti
on
ne
twor
k
is
c
ons
ider
e
d
to
be
c
r
os
s
talk.
I
n
wha
t
f
oll
ows
,
we
pr
opos
e
to
model
the
tens
ion
induce
d
by
a
tr
a
c
k
on
a
nother
tr
a
c
k
that
is
a
djac
e
nt
to
it
.
F
or
that
we
c
ons
ider
the
pr
e
c
inct
s
tr
uc
tur
e
.
Ac
c
or
ding
to
the
law
of
f
a
r
a
da
y,
the
c
oupli
ng
i
n
magne
ti
c
f
ield
induce
s
a
v
olt
a
ge
V
in
d
ir
e
c
tl
y
r
e
late
d
to
the
va
r
iations
of
the
magne
ti
c
f
lux
whic
h
c
r
os
s
e
s
the
c
ond
uc
tor
of
s
e
c
ti
on
"
s
"
a
nd
it
is
wr
it
ten
a
s
f
oll
ows
:
=
−
(
37)
⃗
=
∬
⃗
⃗
⃗
⃗
⃗
(
38)
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
I
nv
e
s
ti
gati
on
on
E
M
r
adiat
ions
fr
om
int
e
r
c
onne
c
ts
in
int
e
gr
ated
c
ir
c
uit
s
(
L
ounas
B
e
lhi
me
r
)
309
⃗
=
(
39)
I
n
thi
s
pa
r
t
a
lwa
ys
c
ons
ider
s
the
F
igur
e
6,
but
thi
s
ti
me
with
the
f
oll
owing
dim
e
ns
ions
:
w
=
20
μ
m,
S
=
20
μ
m,
h
=
5
μ
m
,
H
=
40
μ
m
,
=
3
.
9.
C
ons
ider
ing
a
s
upply
volt
a
ge
of
2
V,
with
a
tr
a
c
k
whi
c
h
ha
s
a
length
of
0.
5
m,
we
ge
t
the
f
oll
owing
s
im
ulation
r
e
s
ult
s
in
F
igur
e
15
a
nd
F
igur
e
16.
T
he
F
igur
e
15
r
e
pr
e
s
e
nts
the
r
e
s
ult
s
of
s
im
ulation
of
the
c
r
os
s
talk
a
s
a
f
u
nc
ti
on
of
the
f
r
e
que
nc
y
of
the
s
ignal
c
ompar
e
d
with
that
obtaine
d
in
[
4
]
.
W
e
s
e
e
that
ther
e
is
s
ome
a
g
r
e
e
ment
be
twe
e
n
the
two
r
e
s
ult
s
,
a
nd
a
r
e
latio
ns
hip
of
pr
opor
ti
on
a
li
ty
li
nks
the
c
r
os
s
talk
a
nd
the
f
r
e
que
n
c
y.
W
e
s
e
e
that
f
r
om
the
f
r
e
que
nc
y
10
Hz
the
volt
a
ge
dr
op
be
gins
to
be
f
e
lt
.
S
o,
the
s
ignal
inj
e
c
ted
a
t
the
be
gi
nn
ing
of
the
tr
a
c
k
unde
r
goe
s
a
tt
e
nua
ti
on
due
to
th
e
e
f
f
e
c
ts
of
high
f
r
e
que
nc
ies
a
nd
e
lec
tr
omagne
ti
c
int
e
r
a
c
ti
o
ns
.
F
igur
e
16
r
e
pr
e
s
e
nts
the
s
im
ulation
of
the
volt
a
ge
dr
op
in
the
int
e
r
c
o
nne
c
ti
on
li
ne
f
o
r
f
r
e
que
nc
ies
given
a
s
a
f
unc
ti
on
o
f
the
dis
tanc
e
be
twe
e
n
tr
a
c
ks
,
it
’
s
noted
that
the
volt
a
ge
dr
op
de
c
r
e
a
s
e
s
with
the
incr
e
a
s
e
in
the
dis
tanc
e
be
twe
e
n
tr
a
c
k
a
n
d
it
incr
e
a
s
e
s
with
incr
e
a
s
e
d
f
r
e
que
nc
y
Fi
gur
e
13
.
P
a
r
a
s
it
ic
c
a
pa
c
it
a
nc
e
ve
r
s
us
int
e
r
l
ine
d
is
tanc
e
F
igur
e
14
.
P
a
r
a
s
it
ic
c
a
pa
c
it
a
nc
e
ve
r
s
us
int
e
r
li
ne
d
is
tanc
e
f
or
di
f
f
e
r
e
nt
f
r
e
que
nc
y
F
igur
e
15
.
C
r
os
s
talk
ve
r
s
us
f
r
e
que
nc
y
F
igur
e
16
.
P
r
e
s
s
ur
e
dr
op
v
er
s
us
int
e
r
li
ne
dis
tanc
e
6.
CONC
L
USI
ON
T
he
main
c
onc
lus
ions
a
r
e
dr
a
w
n
f
o
r
the
s
tudy
of
the
inf
luenc
e
of
diele
c
tr
ic
width
a
nd
pe
r
mi
tt
iv
it
y.
T
he
tr
a
ns
mi
s
s
ion
li
ne
length
a
nd
ge
ometr
y
wa
s
a
l
s
o
s
tudi
e
d
a
nd
the
im
pe
da
nc
e
pe
r
uni
t
length
is
t
r
e
a
ted
in
or
de
r
to
e
s
ti
mate
the
los
s
e
s
a
nd
de
f
ine
the
li
mi
t
a
mpl
it
ude
o
f
the
dig
it
a
l
s
ig
na
l
in
us
e
.
W
e
de
mons
tr
a
ted
that
the
c
a
pa
c
it
a
nc
e
a
nd
r
e
s
is
tanc
e
incr
e
a
s
e
with
in
c
r
e
a
s
ing
f
r
e
que
nc
y
but
the
inducta
nc
e
de
c
r
e
a
s
e
a
nd
by
incr
e
a
s
ing
the
pe
r
mi
tt
ivi
ty
or
the
dis
tanc
e
be
twe
e
n
tr
a
c
ks
the
pa
r
a
s
it
ic
c
a
pa
c
it
a
n
c
e
de
c
r
e
a
s
e
.
Obta
ined
li
ter
a
tur
e
r
e
s
ult
s
a
nd
with
our
s
im
ulations
da
ta,
de
mons
tr
a
ted
that
the
c
r
os
s
talk
a
s
a
f
unc
ti
on
o
f
the
f
r
e
que
nc
y
of
the
s
ignal.
T
hr
ough
thes
e
r
e
s
ult
s
,
we
c
a
n
e
s
ti
mate
the
be
s
t
mate
r
ials
f
or
the
be
s
t
c
ir
c
ui
ts
int
e
r
c
onne
c
t
ge
ometr
y
to
e
ns
ur
e
the
b
e
s
t
pos
s
ibl
e
pe
r
f
or
manc
e
.
T
he
r
e
s
ult
s
a
r
e
f
ound
to
c
ompl
y
with
li
ter
a
tur
e
a
nd
e
nc
our
a
ging
f
or
f
ur
the
r
inves
ti
ga
ti
ons
on
diele
c
tr
ic
s
e
pa
r
a
ti
on.
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
.
1
,
F
e
br
ua
r
y
2020
:
301
-
31
0
310
RE
F
E
RE
NC
E
S
[1
]
E
.
Si
card
,
W
.
J
i
an
-
fei
,
L
.
J
.
Ch
en
g
.
“
Si
g
n
al
i
n
t
er
g
ri
t
y
an
d
E
MC
p
erfo
rma
n
ce
en
h
a
n
cemen
t
u
s
i
n
g
3
D
In
t
e
g
ra
t
ed
Ci
rcu
i
t
s
-
A
Cas
e
S
t
u
d
y
,
”
9
th
In
t
e
r
n
a
t
i
o
n
a
l
W
o
r
k
s
h
o
p
o
n
E
l
ec
t
r
o
m
a
g
n
et
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
o
f
In
t
eg
r
a
t
ed
C
i
r
c
u
i
t
s
(E
M
C
Co
m
p
o
)
,
N
ara
,
J
ap
a
n
,
p
p
.
10
-
14
,
15
-
18
D
ecemb
er
2
0
1
3
.
[2
]
B.
Z
h
u
,
J
.
L
u
,
M.
Z
h
u
.
“
Co
mp
u
t
a
t
i
o
n
a
l
E
l
ec
t
ro
ma
g
n
e
t
i
c
s
fo
r
E
MC
Pro
b
l
em
s
o
f
In
t
eg
r
at
e
d
Ci
rcu
i
t
s
,
”
10
th
In
t
e
r
n
a
t
i
o
n
a
l
S
ym
p
o
s
i
u
m
o
n
E
l
ect
r
o
m
a
g
n
e
t
i
c
C
o
m
p
a
t
i
b
i
l
i
t
y
,
Y
o
r
k
,
U
K
,
p
p
.
7
1
7
-
7
2
3
,
26
-
30
Sep
t
em
b
er
2
0
1
1
.
[3
]
Mat
h
i
as
Mag
d
o
v
w
s
k
i
,
Serg
y
e
K
o
c
h
et
o
v
an
d
Marco
n
L
eo
n
e
“
Mo
d
el
i
n
g
t
h
e
Sk
i
n
E
ffect
i
n
t
h
e
T
i
me
D
o
mai
n
fo
r
Si
mu
l
a
t
i
o
n
o
f
Ci
rc
u
i
t
In
t
erco
n
n
ec
t
,
”
IE
E
E
-
In
t
er
n
a
t
i
o
n
a
l
S
ym
p
o
s
i
u
m
o
n
E
l
ect
r
o
m
a
g
n
e
t
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
(
E
M
C
)
E
u
r
o
p
e,
2
0
0
8
.
[4
]
H
.
Y
meri
,
B.
N
au
w
el
aer
s
,
K
.
Maex
,
V
an
d
en
b
er,
an
d
D
.
D
e
Ro
es
t
,
an
d
V
an
d
en
b
er,
“N
ew
an
a
l
y
t
i
c
ex
p
res
s
i
o
n
fo
r
mu
t
u
al
i
n
d
u
ct
a
n
ce
an
d
res
i
s
t
an
ce
o
f
co
u
p
l
ed
i
n
t
erco
n
n
ect
s
o
n
l
o
s
s
y
s
i
l
i
c
o
n
s
u
b
s
t
rat
e
,
”
2
0
0
1
To
p
i
c
a
l
M
e
et
i
n
g
o
n
S
i
l
i
c
o
n
M
o
n
o
l
i
t
h
i
c
I
n
t
e
g
r
a
t
e
d
Ci
r
c
u
i
t
s
i
n
R
F
S
y
s
t
e
m
s
.
D
i
g
es
t
o
f
P
a
p
er
s
,
p
p
.
7
8
0
3
-
7
1
2
9
,
Sep
t
em
b
er
2
0
0
1
.
[5
]
M.
ramd
an
i
,
E
.
Si
card
,
A
.
b
o
y
er,
S.
Ben
D
h
i
a,
J
.
J
.
W
al
en
,
T
.
H
.
H
u
b
i
n
g
,
M.
Co
en
en
,
O
.
W
ad
a
“
T
h
e
el
ect
r
o
mag
n
et
i
c
co
mp
a
t
i
b
i
l
i
t
y
o
f
i
n
t
eg
ra
t
ed
ci
rcu
i
t
s
-
p
a
s
t
,
p
res
e
n
t
,
fu
t
u
re
,
”
IE
E
E
t
r
a
n
s
a
ct
i
o
n
o
n
E
l
ec
t
r
o
m
a
g
n
et
i
c
co
m
p
a
t
i
b
i
l
i
t
y
,
v
o
l
.
5
1
,
n
o
.
1,
p
p
.
7
8
-
1
0
0
,
Feb
ru
r
y
2
0
0
9
.
[6
]
H
.
N
.
L
i
n
,
C.
W
.
K
u
o
,
J
.
L
.
Ch
an
g
,
C.
K
.
Ch
en
.
“
St
at
i
s
t
i
ca
l
A
n
a
l
y
s
i
s
o
f
E
MI
N
o
i
s
e
Mea
s
u
reme
n
t
f
o
r
Fl
as
h
Memo
ry
,
”
8
th
W
o
r
k
s
h
o
p
o
n
E
l
ect
r
o
m
a
g
n
e
t
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
o
f
In
t
eg
r
a
t
ed
Ci
r
c
u
i
t
s
,
D
u
b
r
o
v
n
i
k
,
Cro
at
i
a
,
pp.
2
4
5
-
2
5
0
,
6
-
9
N
o
v
em
b
er
2
0
1
1
.
[7
]
M.
K
ach
o
u
t
,
J
.
Bel
h
ad
j
T
ah
ar
an
d
F.
Ch
o
u
b
a
n
i
,
“
M
o
d
el
i
n
g
o
f
mi
cro
s
t
ri
p
an
d
PCB
t
races
t
o
en
h
a
n
ce
cro
s
s
t
al
k
red
u
c
t
i
o
n
,
”
2
0
1
0
IE
E
E
R
eg
i
o
n
8
In
t
e
r
n
a
t
i
o
n
a
l
Co
n
f
e
r
en
ce
o
n
Co
m
p
u
t
a
t
i
o
n
a
l
Tech
n
o
l
o
g
i
es
i
n
E
l
ect
r
i
c
a
l
a
n
d
E
l
ec
t
r
o
n
i
cs
E
n
g
i
n
ee
r
i
n
g
(
S
IB
I
R
CO
N)
,
Irk
u
t
s
k
L
i
s
t
v
y
an
k
a
,
Ru
s
s
i
a,
pp.
5
9
4
-
5
9
7
,
11
-
15
J
u
l
y
,
2
0
1
0
.
[8
]
Rao
u
f
L
aw
ren
ce
K
h
an
an
d
G
eo
rg
e
I.
Co
s
t
ach
e
“Fi
n
i
t
e
E
l
eme
n
t
s
Met
h
o
d
A
p
p
l
i
ed
t
o
Mo
d
e
l
i
n
g
Cro
s
s
t
al
k
Pro
b
l
ems
o
n
Pri
n
t
e
d
Ci
rcu
i
t
Bo
ar
d
s
,
”
IE
E
E
t
r
a
n
s
a
ct
i
o
n
s
o
n
E
l
ect
r
o
m
a
g
n
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
,
v
o
l
.
3
1
,
n
o
.
1,
p
p
.
5
-
15,
Feb
r
u
ary
1
9
8
9
.
[9
]
F.
Med
i
n
a
an
d
M.
H
o
r
n
o
,
“Cap
aci
t
an
ce
an
d
i
n
d
u
c
t
an
ce
mat
r
i
ces
fo
r
mu
l
t
i
s
t
ri
p
s
t
r
u
ct
u
res
i
n
mu
l
t
i
l
ay
e
red
an
i
s
o
t
ro
p
i
c
,
”
IE
E
E
Tr
a
n
s
m
i
s
s
i
o
n
o
n
m
i
c
r
o
w
a
ve
t
h
e
o
r
y
a
n
d
t
ech
n
i
q
u
e
s
,
v
ol.
3
5
,
n
o
.
1
1
,
p
p
.
1
0
0
2
-
1
0
0
8
,
N
o
v
em
b
er
1
9
8
7
.
[1
0
]
J
.
G
u
o
,
F.
Rach
i
d
i
,
S.
V
.
T
k
ach
en
k
o
,
Y
.
Z
.
X
i
e
,
“Cal
cu
l
at
i
o
n
o
f
H
i
g
h
-
Fre
q
u
e
n
cy
E
l
e
ct
r
o
mag
n
et
i
c
Fi
el
d
Co
u
p
l
i
n
g
t
o
Ove
r
h
ead
T
ra
n
s
m
i
s
s
i
o
n
L
i
n
e
A
b
o
v
e
a
L
o
s
s
y
G
ro
u
n
d
an
d
T
ermi
n
at
e
d
w
i
t
h
a
N
o
n
l
i
n
ear
L
o
ad
,
”
IE
E
E
Tr
a
n
s
m
i
s
s
i
o
n
o
n
A
n
t
e
n
n
a
a
n
d
P
r
o
p
a
g
a
t
i
o
n
,
v
ol
.
6
7
,
n
o
6
,
pp
.
4
1
1
9
-
4
1
3
2
,
J
u
n
e
2
0
1
9
.
[1
1
]
J
.
G
u
o
,
Y
.
Z
.
X
i
e,
F.
Rach
i
d
i
,
“
Mo
d
e
l
i
n
g
o
f
E
MP
Co
u
p
l
i
n
g
t
o
L
o
s
s
l
e
s
s
MT
L
s
i
n
T
i
me
D
o
ma
i
n
Bas
e
d
o
n
A
n
al
y
t
i
ca
l
G
au
s
s
-
Se
i
d
e
l
It
erat
i
o
n
T
ech
n
i
q
u
e
,
”
IE
E
E
In
t
er
n
a
t
i
o
n
a
t
S
ym
p
o
s
i
u
m
o
n
E
l
ect
r
o
m
a
g
n
e
t
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
a
n
d
IE
E
E
A
s
i
a
-
P
a
c
i
f
i
c
S
ym
p
o
s
i
u
m
o
n
E
l
ect
r
o
m
a
g
n
e
t
i
c
C
o
m
p
a
t
i
b
i
l
i
t
y
,
p
p
.
8
9
7
-
9
0
2
,
2
0
1
8
.
[1
2
]
E
.
Si
card
an
d
A
.
B
o
y
er,
“E
n
h
an
c
i
n
g
E
n
g
i
n
eer
s
i
n
E
MC
o
f
In
t
e
g
rat
e
d
Ci
rc
u
i
t
s
,
”
E
M
C
Co
m
p
o
2
0
1
1
-
8
t
h
wo
r
ks
h
o
p
o
n
E
l
ect
r
o
m
a
g
n
e
t
i
c
C
o
m
p
a
t
i
b
i
l
i
t
y
o
n
i
n
t
eg
r
a
t
ed
Ci
r
cu
i
t
s
,
D
u
b
r
o
v
n
i
k
,
Cro
at
i
a
,
6
-
9
N
o
v
em
b
er
2
0
1
1
.
[1
3
]
Y
.
Bach
er,
N
.
Fro
i
d
ev
ea
u
x
,
P.
D
u
p
re,
H
.
Braq
u
e
t
,
G
.
J
acq
u
em
o
d
,
“
Res
o
n
a
n
ce
A
n
al
y
s
i
s
fo
r
E
MC
Imp
ro
v
emen
t
i
n
In
t
e
g
ra
t
e
d
Ci
rcu
i
t
s
,
”
10
th
In
t
er
n
a
t
i
o
n
a
l
W
o
r
ks
h
o
p
o
n
t
h
e
E
l
ec
t
r
o
m
a
g
n
et
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
o
f
In
t
eg
r
a
t
ed
C
i
r
c
u
i
t
s
,
pp.
56
-
60
,
N
o
v
emb
er
2
0
1
5
.
[1
4
]
M.
S.
U
l
l
a
h
an
d
M.
H
.
C
h
o
w
d
h
u
r
y
,
“A
n
al
y
t
i
cal
M
o
d
e
l
s
o
f
H
i
g
h
-
S
p
eed
RL
C
I
n
t
erc
o
n
n
ect
D
el
a
y
fo
r
Co
m
p
l
e
x
an
d
Real
Po
l
e
s
,
”
IE
E
E
Tr
a
n
s
a
c
t
i
o
n
o
n
ver
y
l
a
r
g
e
s
c
a
l
e
i
n
t
e
g
r
a
t
i
o
n
s
y
s
t
e
m
s
,
v
ol.
2
5
,
n
o.
6
,
p
p
.
1
8
3
1
-
1
8
4
1
,
J
u
n
e
2
0
1
7
.
[1
5
]
R.
Ian
co
n
e
s
cu
,
V
.
V
u
l
f
i
n
,
“Free
Sp
ace
T
E
M
T
ra
n
s
mi
s
s
i
o
n
L
i
n
es
Ra
d
i
a
t
i
o
n
L
o
s
s
es
,
”
[O
n
l
i
n
e]
,
A
v
a
i
l
a
b
l
e
:
h
t
t
p
:
/
/
v
i
x
ra.
o
r
g
/
a
b
s
/
1
6
0
9
.
0
4
2
0
,
2
0
1
6
.
[1
6
]
A
.
Bo
y
er,
E
.
Si
card
an
d
S.
Ben
D
h
i
a,
“
IC
-
E
MC,
a
D
emo
n
s
t
ra
t
i
o
n
Frew
are
fo
r
Pred
i
c
i
n
g
E
l
ec
t
ro
ma
g
n
et
i
c
Co
mp
a
t
i
b
i
l
i
t
y
I
n
t
e
g
rat
e
d
Ci
rc
u
i
t
s
,
”
19
th
In
t
er
n
a
t
i
o
n
a
l
Z
u
r
i
ch
S
ym
p
o
s
i
u
m
o
n
E
l
ec
t
r
o
m
a
g
n
et
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
,
May
2
0
0
8
.
[1
7
]
Y
ao
w
u
L
i
u
,
K
an
g
L
A
n
an
d
K
en
n
et
h
K.
Mei
,
“Cap
aci
t
a
n
ce
E
x
t
rac
t
i
o
n
f
o
r
E
l
ec
t
ro
s
t
a
t
i
c
Mu
l
t
i
co
n
d
u
ct
o
r
Pro
b
l
ems
b
y
On
-
Su
rface
ME
I
,
”
IE
E
E
t
r
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
.
2
3
,
n
o
.
3
,
p
p
.
1
5
2
1
-
3
3
2
3
,
A
u
g
u
s
t
2
0
0
0
.
[1
8
]
J
.
G
u
o
,
Y
.
Z
.
X
i
e
,
“A
n
E
ffi
ci
e
n
t
Mo
d
el
o
f
T
ra
n
s
i
en
t
E
l
ect
r
o
mag
n
et
i
c
Fi
el
d
Co
u
p
l
i
n
g
t
o
Mu
l
t
i
c
o
n
d
u
ct
o
r
T
ran
s
mi
s
s
i
o
n
L
i
n
e
s
Bas
e
d
o
n
A
n
a
l
y
t
i
ca
l
It
erac
t
i
v
e
T
ech
n
i
q
u
e
i
n
T
i
me
D
o
ma
i
n
,
”
I
E
E
E
t
r
a
n
s
a
c
t
i
o
n
s
o
n
M
i
cr
o
w
a
ve
Th
eo
r
y
a
n
d
t
ec
h
n
i
q
u
es
,
v
o
l
.
6
6
,
n
o
.
6
.
pp
.
2
6
6
3
-
2
6
7
3
,
2
0
1
8
.
[1
9
]
M.
S.
U
l
l
a
h
an
d
M.
H
.
Ch
o
w
d
h
u
ry
,
“
A
n
ew
p
o
l
e
d
el
a
y
mo
d
el
f
o
r
R
L
C
i
n
t
erco
n
n
ec
t
u
s
i
n
g
s
eco
n
d
o
rd
er
ap
p
r
o
x
i
mat
i
o
n
,
”
IE
E
E
5
7
th
In
t
er
n
a
t
i
o
n
a
l
M
i
d
wes
t
S
ym
p
o
s
i
u
m
o
n
Ci
r
cu
i
t
s
a
n
d
S
y
s
t
em
s
,
p
p
.
2
3
8
-
2
4
1
,
A
u
g
u
s
t
2
0
1
4
.
[2
0
]
V
.
R.
K
u
mar,
M.
K
.
Maj
u
md
er,
A
.
A
l
am,
N
.
R.
K
u
k
k
am
an
d
B.
K
.
K
au
s
h
i
k
,
“St
a
b
i
l
i
t
y
an
d
d
el
a
y
an
al
y
s
i
s
o
f
mu
l
t
i
-
l
ay
ere
d
G
N
R
an
d
ml
t
i
-
w
al
l
ed
CN
T
i
n
t
er
c
o
n
n
ect
s
,
”
J.
Co
m
p
u
t
.
E
l
ect
r
o
n
,
v
o
l
.
1
4
,
n
o
.
2
,
p
p
.
6
1
1
-
6
1
8
,
J
u
n
e
2
0
1
5
.
[2
1
]
B.
N
o
u
ri
,
M.
S.
N
ak
h
l
a,
R.
A
ch
ar,
“E
ffi
c
i
en
t
Si
mu
l
at
i
o
n
o
f
N
o
n
l
i
n
ear
T
ran
s
mi
s
s
i
o
n
L
i
n
es
v
i
a
Mo
d
e
l
-
O
r
d
er
Red
u
c
t
i
o
n
,
”
IE
E
E
Tr
a
n
s
a
c
t
i
o
n
s
o
n
M
i
c
r
o
w
a
ve
Th
e
o
r
y
a
n
d
Th
ec
h
n
i
q
u
es
,
v
o
l
.
6
5
,
no
.
3
,
p
p
.
6
7
3
-
9
8
3
,
Mar
c
h
2
0
1
7
.
[2
2
]
H
.
X
u
e,
A
.
A
met
a
n
i
,
J
.
Ma
h
s
ere
d
j
a
n
,
Y
.
Bab
a,
F.
Rach
i
d
i
,
I.
K
o
car,
“
T
ran
s
n
s
i
e
n
t
Re
s
p
o
n
s
es
o
f
O
v
erh
ea
d
Ca
b
l
e
s
D
u
e
t
o
Mo
d
e
T
ra
n
s
i
t
i
o
n
i
n
H
i
g
h
Freq
u
en
c
y
,
”
IE
E
E
T
r
a
n
s
a
ct
i
o
n
s
o
n
E
l
ect
r
o
m
a
g
n
e
t
i
c
C
o
m
p
a
t
i
b
i
l
i
t
y
,
v
o
l
.
6
0
,
n
o
.
3
,
p
p
.
7
8
5
-
7
9
4
,
J
u
n
e
2
0
1
8
.
[2
3
]
G
.
L
u
g
ri
n
,
S.
V
.
T
k
ach
en
k
o
,
F.
Rach
i
d
i
,
M.
Ru
b
i
n
t
ei
n
,
R.
Ch
erk
ao
u
i
,
“
H
i
g
h
-
freq
u
en
c
y
E
l
ect
r
o
mag
n
et
i
c
Co
u
p
l
i
n
g
t
o
Mu
l
t
i
co
n
d
u
ct
o
r
T
ran
s
mi
s
s
i
o
n
L
i
n
es
o
f
Fi
n
i
t
es
L
en
g
t
h
,
”
IE
E
E
Tr
a
n
s
a
c
t
i
o
n
s
o
n
E
l
ec
t
r
o
m
a
g
n
et
i
c
Co
m
p
a
t
i
b
i
l
i
t
y
,
v
o
l
.
5
7
,
n
o
. 6
,
p
p
.
1
7
1
4
-
1
7
2
3
,
D
ecemb
er
2
0
1
5
.
[2
4
]
G
o
u
ri
D
h
at
t
an
d
G
i
l
b
er
t
T
o
u
z
o
t
E
mma
n
u
e
l
L
e
Fran
co
i
s
“Fi
n
i
t
e
E
l
emen
t
Met
h
o
d
,
”
E
d
i
t
i
o
n
L
av
o
i
s
i
er
,
2
0
0
5
.
[2
5
]
G
o
u
ri
D
h
at
t
,
J
ean
-
L
u
i
s
Ba
t
oz
,
“
Mo
d
el
i
n
g
o
f
s
t
ru
c
t
u
re
s
w
i
d
h
fi
n
i
t
e
el
eme
n
t
,”
H
ermè
s
E
d
i
t
i
o
n
,
Pari
s
,
1
9
9
0
,
1
9
9
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.