Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 5
,
O
c
tob
e
r
201
6, p
p
. 2
369
~237
8
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
5.1
163
5
2
369
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Circuit Models of Lossy Multic
onductor Transmission Lines:
Incident Plane W
a
ve E
f
f
e
ct
Saih Moh
a
me
d
1
, R
o
ui
ja
a
Hi
cham
2
, Gha
m
ma
z Abdelilah
1
1
Labor
ator
y
of
Electrical S
y
stems a
nd Telecom
m
unications, Department of
P
h
ys
ics
,
F
acu
lt
y of S
c
ienc
es
and
Techno
log
y
, Cadi A
y
y
a
d un
iver
sity
, Marr
akesh,
Morocco.
2
Labor
ator
y
for
S
y
stems Analy
s
is and Info
rmatio
n Processing, Department of
App
lied
Ph
y
s
i
c
s, Fa
c
u
lt
y of
Scien
ces
and
Techno
log
y
, Hassan I university
,
Settat, Morocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 25, 2016
Rev
i
sed
Ju
l 28
,
20
16
Accepted Aug 15, 2016
In this
p
a
per
,
w
e
con
centr
at
e on
the
vari
et
y
im
pacts
of
in
cident plane
wave
on m
u
lticonduct
o
r transm
ission
lines, uti
l
i
z
ing
Branin’s m
e
thod, which is
allud
e
d to as th
e method of characteris
tics. Th
e model can be d
i
rectly
used
for the time-domain and fre
quency
-
domain analy
s
es,
Moreover
,
it had the
advantage of being used wit
hout the need of setting the preconditions of the
charges appli
e
d
to its ends; t
h
is
permits it to be effortlessly
embedded in
circu
it s
i
m
u
la
tor
s
, for ex
am
ple S
p
ice
,
S
a
be
r,
and
Es
acap
.
This
m
odel v
a
lid
i
t
y
is affirmed b
y
contrasting ou
r
simulation results under ES
ACAP and
differen
t
results, and we will talk about
vari
et
y im
pacts of inci
dent plan
e
wave.
Keyword:
Bran
in’s m
e
th
o
d
ESAC
AP
Inci
dent
pl
ane
wave
Mu
ltico
n
d
u
c
t
o
r tran
sm
issi
o
n
lin
es
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Sai
h
M
oham
e
d,
Lab
o
rat
o
ry
of
El
ect
ri
cal
Sy
st
em
s and
Tel
e
c
o
m
m
uni
cat
i
ons, De
pa
rt
m
e
nt
of
Phy
s
i
c
s
,
Facul
t
y
o
f
Sci
e
nces a
n
d Tec
h
nol
ogy
,
C
a
di
A
y
y
a
d u
n
i
v
e
r
si
t
y
,
M
a
rra
kesh
, M
o
r
o
cc
o.
Em
a
il: saih
.
m
o
h
a
m
e
d
@
g
m
ail.
co
m
1.
INTRODUCTION
A
significant perce
n
tage of electric
and
el
ectro
ni
c sy
st
em
s com
m
uni
cat
e
t
h
ro
u
gh i
n
t
e
rco
n
n
ect
i
n
g
wiring
harness
e
s that can be
vulner
ab
le to
ex
tern
al electro
m
a
g
n
e
tic (EM) in
terferen
ce. Con
s
eq
u
e
n
tly, it is
th
u
s
ly
p
r
o
f
ou
nd
ly v
ital fo
r El
ectro
m
a
g
n
e
tic Co
m
p
atib
ili
t
y
(EM
C
) st
udi
es
t
o
dev
e
l
o
p s
o
ft
ware
t
o
ol
s ca
pabl
e
of predicting i
n
duce
d e
ffects
in
cables
confi
g
urations
[1],[2].
The foreca
st of these disturba
nces,
whic
h are typica
l
l
y
im
p
e
l
l
e
d by
out
si
d
e
fi
el
ds o
r
l
u
m
p
ed s
o
urces
,
is an
estab
lished
issu
e
wh
ich can
b
e
m
a
n
a
ged
in
an
assortmen
t
o
f
ways.
Hen
c
efo
r
th, it can
b
e
d
ealt with
in
th
e freq
u
e
n
c
y
do
m
a
in
, and
therefore t
h
e i
n
du
ced
respo
n
s
es o
f
cab
les
are fath
o
m
ed
b
y
utilizin
g
Mu
ltico
n
d
u
c
t
o
r tran
sm
issio
n
lin
e (MTL) th
eo
ry
[3
],[4
].
In a pi
onee
r
i
n
g w
o
r
k
, Tay
l
o
r
[5]
expl
oi
t
e
d t
h
e t
r
an
sm
issio
n
lin
e (TL) th
eo
ry to
pred
ict t
h
e resp
on
se
of a TL
e
x
cited
by a
n
e
x
ternal electrom
a
gnetic fiel
d. T
h
e
case st
udie
d
was a
two-wire line system
in
free
space excited
by a plane wa
ve field.
Since
then, m
a
ny o
t
her aut
h
ors cont
ributed to the refi
nem
e
nt
of the
m
e
t
hod.
I
n
pa
r
t
i
c
ul
ar, Pa
ul
[
6
]
ext
e
nde
d
t
h
e w
o
r
k
o
f
Tay
l
or t
o
t
h
e
case
o
f
(M
TLs)
a
n
d l
a
t
e
r,
A
g
raw
a
l
[7]
fo
rm
ul
at
ed fi
el
d-t
o
-
w
i
r
e c
o
up
l
i
ng i
n
term
s of the electric
field only.
As of late, a consi
d
era
b
le m
e
asure
of
researches
ha
ve
bee
n
d
o
n
e o
n
t
h
e
adva
ncem
ent
of si
m
u
l
a
ti
on
pr
o
g
ram
wi
t
h
i
n
t
e
grat
e
d
ci
rc
ui
t
em
phasi
s (
SPIC
E
) e
qual
ci
rcui
t
m
odel
s
f
o
r
M
TL e
n
e
r
gi
ze
d
by
an
e
p
i
s
o
d
e
electrom
a
gnetic field
[8]. In any cas
e
,
t
h
e
pr
o
p
o
s
ed
m
odel
s
depe
n
d
o
n
one
su
p
p
o
s
i
t
i
on t
h
at
t
h
e
T
L
s are
l
o
ssl
ess.
Aft
e
r
t
h
en
, s
o
m
e
lossl
ess m
odel
s
ha
ve
been
pr
o
pose
d
t
o
c
onsi
d
er
t
h
e
va
ri
et
y
im
pact
s of t
h
e
occu
rre
nce
pl
a
n
e
wav
e
on
a
M
TL
[9]
.
T
h
e
s
e m
odel
s
can
be
i
m
pl
em
ent
e
d t
o
c
o
m
put
e t
r
ansi
e
n
t
resp
ons
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
236
9
–
23
78
2
370
wi
t
h
o
u
t
t
h
e i
nve
rse F
o
uri
e
r Tra
n
s
f
o
r
m
(IFT
)
, a
nd
di
rectly connecte
d
to
nonlinea
r and tim
e-varying
termin
ato
r
s
with
th
e m
o
d
e
ls alread
y av
ailab
l
e in
SPICE.
In
th
is p
a
p
e
r, an
equ
i
v
a
len
t
circu
it
m
o
d
e
l for th
e an
alyses o
f
th
e rad
i
ated
su
scep
tib
ility o
f
lo
ssy
MTL, th
e m
o
d
e
l is sub
s
tantial in
th
e ti
me an
d fr
eq
ue
n
c
y
dom
ai
n wi
t
h
l
i
n
ear a
n
d
no
nl
i
n
ea
r l
o
a
d
s an
d
effo
rtlessly brou
gh
t i
n
to
t
h
e circu
it sim
u
lato
rs,
su
ch
as
Spi
ce and
ESACAP
[10],[11].
The va
riation
e
ffect of
i
n
ci
dent
pl
ane
wave
o
n
coa
x
i
a
l
cabl
e
i
s
st
udi
ed
wi
t
h
t
h
e pr
op
ose
d
m
odel
.
The m
e
tho
d
i
s
val
i
d
at
ed
b
y
com
p
ari
n
g
res
u
l
t
s
wi
t
h
ot
her
m
e
t
hods
.
2.
DESC
RIPTI
O
N OF MTL
2.
1.
Mo
del o
f
MT
L
The Tel
e
gra
p
h
e
r’s
e
quat
i
o
ns
f
o
r
a MT
L in the
prese
n
ce
of e
x
ternal
el
ectrom
a
gnetic ra
diation,
su
ch
as tho
s
e
rad
i
ated
b
y
the p
l
an
e wav
e
are
written
as
(,
)
(
,
)
(,
)
(
,
)
(,
)
(
,
)
Vz
t
I
z
t
R
Iz
t
L
V
z
t
f
zt
IV
G
V
zt
C
I
zt
f
zt
(
1
)
Whe
r
e
12
(
,
)
(
,
)
,
(
,
),
...,
(
,
)
T
N
V
z
t
V
zt
V
z
t
V
zt
and
12
(
,
)
(
,
)
,
(
,
),
...,
(
,
)
T
N
I
z
t
I
zt
I
z
t
I
zt
represent the
v
o
ltag
e
(with
resp
ect to th
e groun
d)
a
n
d c
u
rrent
vectors
of
the line, and
L
,
C
,
R
a
n
d
G
are th
e
p
e
r-un
it-
lenght (p.u.l) i
n
ductance
, ca
pacita
nce, re
sistance, a
n
d c
o
nductance m
a
tr
ices of th
e lin
e, resp
ectiv
ely.
The
n
x
1
ve
ct
ors,
(,
)
f
Vz
t
and
(,
)
f
I
zt
,
are
distributed s
o
urces t
h
a
t
represe
n
t
external
ex
citatio
n
o
f
th
e tran
sm
issi
o
n
lin
e and
are reso
lv
ed
utilizin
g
a p
r
op
er cou
p
ling
m
o
d
e
l. Th
ere
are a
few altern
atively eq
u
i
v
a
len
t
, u
s
u
a
lly u
tiliz
ed
coup
lin
g
m
o
d
e
ls created
by Taylo
r
et al
. [5
],
Agrawal et al.
[7
], and
Rach
i
d
i [1
2
]
. In
th
is p
a
p
e
r,
we are u
tilizin
g
th
e ex
ten
d
e
d
v
e
rsio
n
of th
e form
u
l
a
tio
n
d
e
v
e
lo
p
e
d
by
Tay
l
or,
Sa
t
t
e
rwhi
t
e
, a
nd
Har
r
i
s
o
n
.
In t
h
i
s
m
odel
,
t
h
e
di
spe
r
se
d exci
t
a
t
i
on s
o
u
r
ces
are de
pi
ct
ed as
far as
t
h
e ve
rt
i
cal
and
h
o
r
i
z
o
n
t
a
l
com
pone
nt
of
t
h
e i
n
ci
de
nt
el
ect
ri
c fi
el
d.
For
M
TL, a
s
a
ppea
r
e
d
i
n
Fi
g
u
re
1
.
We have:
0
(,
,
)
(
0
,
,
)
(
,
,
)
h
in
c
i
n
c
inc
fz
z
x
V
E
h
z
t
E
zt
E
x
zt
d
x
z
(
2
)
0
(,
,
)
h
inc
fx
I
CE
x
z
t
d
x
t
(
3
)
Wh
ere
h
is t
h
e
h
e
igh
t
of
th
e lin
e,
and
(,
,
)
in
c
z
E
hz
t
and
(,
,
)
in
c
x
E
xz
t
are t
h
e horiz
ontal
and
ve
rt
i
cal
com
pone
nt
s o
f
t
h
e i
n
ci
de
nt
el
ect
ri
c fi
el
d,
respect
i
v
el
y
.
T
h
e i
n
ci
de
nt
fi
el
d, i
n
t
h
e ab
sen
ce of
th
e lin
e,
as sh
own in
Figu
re 2, can
b
e
written
in
th
e fo
llowing
freq
u
e
n
c
y
form
0
(,
,
,
)
(
)
y
x
z
jy
jx
jz
inc
xx
y
y
z
z
Ex
y
z
E
e
a
e
a
e
a
e
e
e
(4)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Circu
it Mod
e
ls o
f
Lo
ssy Mu
ltico
ndu
cto
r
Tran
smissi
o
n
Lines: In
ci
d
e
n
t
Pl
an
e Wa
ve Effect
(S
a
i
h
Mo
hamed
)
2
371
Fig
u
re
1
.
A Mu
ltico
n
d
u
c
t
o
r tran
sm
issio
n
line ov
er an in
fi
n
i
te an
d p
e
rfectly co
ndu
ctin
g groun
d
Fi
gu
re
2.
De
fi
n
i
t
i
ons
of t
h
e
pa
ram
e
t
e
rs chara
c
t
e
ri
zi
ng t
h
e i
n
ci
dent
fi
el
d as
a u
n
i
f
orm
pl
an
e wa
ve
Whe
r
e
x
e
,
y
e
and
z
e
are
t
h
ree
u
n
i
t
vect
ors
i
n
t
h
e C
a
rt
e
s
i
a
n c
o
o
r
di
nat
e
sy
st
em
gi
ven
by
:
si
n
s
i
n
s
i
n
c
os
c
o
s
c
os
s
i
n
si
n
c
o
s
si
n
c
os
c
o
s
1
xE
P
yE
P
P
E
p
zE
P
P
E
P
xy
z
e
e
e
ee
e
(5)
The angle
E
d
e
fi
n
e
s th
e po
larizatio
n
typ
e
. Th
e p
o
l
arization
is h
o
r
izon
tal if
E
is eq
u
a
l to
zero an
d
v
e
rtical if it is eq
u
a
l t
o
90
°. Th
e an
g
l
e
p
determin
es th
e
elev
atio
n
relativ
e to
t
h
e gro
u
n
d
. Th
is ang
l
e is
comm
only called the
inci
dent
angle. T
h
e a
n
gle
p
g
i
v
e
s th
e pro
p
a
g
a
tion
d
i
rectio
n
relativ
e to
th
e ax
is
Oz
.
The c
o
m
pone
n
t
s of
t
h
e
p
h
ase
con
s
t
a
nt
al
o
n
g
t
hose
co
or
di
nat
e
axes
are:
cos
sin
c
os
sin
s
in
xP
yP
P
zP
P
(6)
Th
e
ph
ase co
nstan
t
is related
to
th
e
frequ
ency an
d pro
p
e
rties of th
e m
e
d
i
u
m
as:
0
1
rr
v
(
7
)
Whe
r
e
0
00
1
v
is the
phase
velocity in th
e
space a
n
d the m
e
dium
is
cha
r
acterized
by the
pe
rm
ea
bility
0
r
and
p
e
rm
i
ttiv
i
t
y
0
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
236
9
–
23
78
2
372
Fo
r
th
e
situ
ation
wh
ere
th
e
lin
e
is
situated over
a ground plane,
as a
p
pea
r
ed i
n
Fi
gu
re
3, t
h
e
co
nn
ected field tu
rn
s i
n
to
t
h
e t
o
tal of th
e in
ci
dent
field a
n
d t
h
e
ground-refl
ected field
in
c
i
nc
ref
tota
le
E
EE
(8
)
These
fi
el
d c
o
m
ponent
s a
r
e a
s
f
o
l
l
o
ws:
0
(,
,
,
)
(
)
y
x
z
jy
jx
jz
inc
xx
y
y
z
z
Ex
y
z
E
e
a
e
a
e
a
e
e
e
(
9
)
0
(,
,
,
)
(
)
y
x
z
jy
jx
j
z
re
f
xx
y
y
z
z
Ex
y
z
E
e
a
e
a
e
a
e
e
e
(10)
Fi
gu
re 3.
C
o
nfi
g
u
r
at
i
o
n wi
t
h
t
h
e prese
n
ce o
f
a
pe
rfect
l
y
co
n
duct
i
n
g g
r
o
u
n
d
pl
ane
The t
o
t
a
l
fi
el
d
i
s
defi
ned
by
:
xy
z
i
n
c
i
nc
r
e
f
i
nc
i
n
c
i
nc
to
ta
l
e
t
o
t
a
l
e
x
t
o
t
a
l
e
y
to
ta
le
z
E
EE
E
a
E
a
E
a
(1
1)
0
2c
o
s
(
)
y
z
x
jy
jz
inc
totale
x
x
EE
e
x
e
e
(
1
2)
0
2s
i
n
(
)
y
z
y
jy
j
z
in
c
tota
le
y
x
Ej
E
e
x
e
e
(
1
3)
0
2s
i
n
(
)
y
z
z
jy
jz
inc
t
o
ta
le
z
x
Ej
E
e
x
e
e
(
1
4)
2.
2.
Equiv
a
l
ent Ci
rcuit Model
for
Lo
ssy
MTL
Th
e equ
a
tion
s
in
(1) are co
up
led
sets of p
a
rtial
di
ffere
nt
i
a
l
equat
i
o
ns. T
o
dec
o
upl
e t
h
e
m
a sim
i
l
a
r
t
r
ans
f
o
r
m
a
ti
on
i
s
req
u
i
r
e
d
[3]
,
[1
3]
. C
h
aract
er
i
z
i
ng t
h
e
c
h
an
g
e
t
o
m
ode am
ount
s
as
Vm
Im
VT
V
IT
I
(
1
5)
Sub
s
titu
tin
g (15
)
in
to (1
) g
i
v
e
s, th
e system
o
f
eq
u
a
tion
s
fo
r
th
e inn
e
r condu
ctors
b
eco
m
e
s
(,
)
(,
)
(
,
)
(,
)
(,
)
(
,
)
m
mm
m
m
f
m
m
mm
m
m
f
m
Iz
t
VR
I
z
t
L
V
z
t
zt
Vz
t
I
GV
z
t
C
I
z
t
zt
(16)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Circu
it Mod
e
ls o
f
Lo
ssy Mu
ltico
ndu
cto
r
Tran
smissi
o
n
Lines: In
ci
d
e
n
t
Pl
an
e Wa
ve Effect
(S
a
i
h
Mo
hamed
)
2
373
Whe
r
e
1
mV
I
L
TL
T
(17.a
)
1
mI
V
CT
C
T
(17.
b)
1
mV
I
R
TR
T
(17.c
)
1
mI
V
GT
G
T
(17.
d)
1
f
mV
f
VT
V
(17.e
)
1
f
mI
f
I
TI
(17.
f)
Bo
th
m
L
and
m
C
are diagonal m
a
trices of dim
e
nsion
N
x
N
,
V
T
and
I
T
are selected so that th
e
matrices
m
L
and
m
C
are dia
g
onals
.
Afte
r calcul
a
ting
m
L
,
m
C
and
m
R
matrices, we cal
culate the m
o
d
e
ch
aracteristic im
p
e
d
a
n
ce,
u
tilizin
g
th
e prim
a
r
y te
rm
o
f
th
e
Taylo
r
series ex
p
a
n
s
i
o
n,
we
get
1
, R
ii
i
i
ii
i
i
i
i
i
ii
i
mm
cm
cm
m
m
mm
f
RL
ZR
L
Cj
C
1
...
iN
(18)
Whe
r
e
ii
i
ii
m
cm
m
L
R
C
(19)
The c
h
a
r
acteri
s
tic im
pedanc
e in t
h
is case, is
prese
n
ted
as a c
h
aracte
r
istic resistance
i
cm
R
a
n
d capacity
2
ii
i
ii
i
m
mf
mc
m
L
C
R
R
, as s
h
ow
n i
n
F
i
gu
re
4.
Wi
t
h
t
h
e sam
e
app
r
o
x
i
m
at
i
on, t
h
e c
onst
a
nt
of
p
r
o
p
a
gat
i
o
n
be
com
e
s:
2
ii
ii
i
i
i
i
i
i
m
mm
m
m
m
cm
R
j
jL
C
R
(20)
The
s
o
l
u
t
i
o
n o
f
(
1
6
)
i
n
t
h
e fre
que
ncy
dom
ai
n
can be f
o
u
n
d
i
n
[1
1]
,[
1
4
]
.
A
n
d
i
s
gi
ve
n by
11
12
21
22
()
()
(
0
)
(
0
)
I
(
0
)
()
I(
)
(
)
(
0
)
(
0
)
I
(
0
)
(
)
m
m
m
m
m
ftm
mm
m
m
m
f
t
m
VL
L
V
V
L
LL
V
I
L
(21)
Whe
r
e t
h
e m
odal chai
n-pa
ra
meter subm
atrices bec
o
m
e
11
1
()
(
)
2
mm
LL
m
ze
e
(
2
2.a)
12
1
()
(
)
2
mm
LL
mc
m
zZ
e
e
(
2
2.b)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
236
9
–
23
78
2
374
1
21
1
()
(
)
2
mm
LL
mc
m
zZ
e
e
(
2
2.c)
22
1
()
(
)
2
mm
LL
m
ze
e
(
2
2.d)
()
ft
m
VL
and
()
ftm
I
L
are t
h
e
t
o
t
a
l
m
odal
f
o
r
c
i
n
g
fu
nct
i
o
ns
du
e t
o
t
h
e
i
n
ci
den
t
fi
el
d, a
n
d a
r
e
gi
ve
n
by
11
12
0
(
)
()
(
)
()
(
)
L
ft
m
m
f
m
m
f
m
VL
L
V
L
I
d
(
2
3.a)
21
22
0
(
)
()
(
)
()
(
)
L
ftm
m
f
m
m
f
m
I
LL
V
L
I
d
(23.
b)
Sub
s
titu
tin
g (22
)
in
to (2
1)
g
i
ves
0
(0
)
I
(0
)
[
(
)
I
(
)
]
(
)
()
I
(
)
[
(
0
)
I
(
0
)
]
()
m
m
L
m
c
mm
m
c
mm
L
mc
m
m
m
c
m
m
L
VZ
e
V
L
Z
L
E
L
VL
Z
L
e
V
Z
E
L
(24)
Whe
r
e
0
()
()
()
()
()
(
)
m
L
ft
m
c
m
f
tm
L
f
tm
cm
ft
m
E
Le
V
L
Z
I
L
EL
V
L
Z
I
L
(25)
Reco
gn
izing
the b
a
sic tim
e-d
e
lay tran
sfo
r
m
a
tio
n
:
()
(
)
jT
eF
t
T
F
(26)
These
bec
o
m
e
, in the
tim
e domain,
0
(0
,
)
(0
,
)
[
(
,
)
(
,
)
]
+
(
)
(
,
)(
,
)
[
(
0
,
)(
0
,
)
]
(
)
m
m
L
mc
m
m
m
m
c
m
w
m
L
m
c
m
m
mm
c
m
mm
L
V
t
ZI
t
e
V
L
t
T
ZI
L
t
T
E
t
VL
t
Z
I
L
t
e
V
t
T
Z
I
t
T
E
t
(
2
7)
Were
T
m
i
s
t
h
e
one
-
w
ay
del
a
y
of
t
h
e
wi
res
,
a
n
d
i
s
den
o
e
d
b
y
mm
m
TL
L
C
. Th
e ad
d
ition
a
l so
urces are
0
()
(
,
)
(
,
)
()
(
,
)
(
,
)
m
L
ftm
m
c
m
ftm
m
L
ftm
cm
ftm
E
te
V
L
t
T
Z
I
L
t
T
Et
V
L
t
Z
I
L
t
(2
8)
The t
e
rm
s of
t
h
e '
c
ont
r
o
l
l
e
d'
g
e
nerat
o
rs
o
f
vo
l
t
a
ge an
d c
u
rre
n
t place
d i
n
ea
ch c
o
nductor
of the
cell are:
1
(,
)
(
,
)
k
N
iV
m
ik
k
Vz
t
T
V
z
t
(2
9.a
)
1
1
(,
)
(
,
)
i
N
mI
k
ik
k
I
zt
T
I
zt
(
2
9.b)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Circu
it Mod
e
ls o
f
Lo
ssy Mu
ltico
ndu
cto
r
Tran
smissi
o
n
Lines: In
ci
d
e
n
t
Pl
an
e Wa
ve Effect
(S
a
i
h
Mo
hamed
)
2
375
Fig
u
re
4
.
Circuit
m
o
d
e
l of lossy m
u
lt
ico
n
d
u
c
to
r tran
sm
issio
n
lin
e
3.
SIMULATION RESULTS
AN
D V
A
LID
A
TIO
N
3.
1.
Radiated Susc
eptibility
Anal
ysis
of T
h
ree c
o
nductors
The a
n
alysis of the ra
diated imm
uni
t
y
i
s
car
ri
ed
out
on t
h
r
ee con
d
u
ct
o
r
s
exci
t
e
d by
a
n
i
n
ci
de
nt
pl
a
n
e
wave as
sh
ow
n i
n
Fi
gu
re 5
.
The l
e
n
g
t
h
L a
nd t
h
e ra
di
us
r
of t
h
e l
i
n
e
s
ar
e 0.
2m
m
and 2
m
, respect
i
v
el
y
.
The
distance d bet
w
een the two wires is 1.27mm,
the diel
ectric thickness
es t is
0.25mm
,
and the dielectric
constant
ε
r
i
s
3.5. T
h
e l
o
ads
R
1
, R
2
, R
3
, and R
4
of the lines are 500
Ω
. The external field, orie
nted along
x
and
pr
o
p
agat
i
n
g al
o
ng z a
x
i
s
(
E
x
–K
z
). T
h
e va
ri
at
i
on o
f
t
h
e e
l
ect
ri
c fi
el
d i
s
defi
ned
by
a ra
m
p
ri
se t
i
m
e
t
r
=
1ns
and the am
plitude
E
0
=
1V
/
m
, as sh
ow
n in Figu
r
e
6.
Fi
gu
re
5.
(a
)
G
e
om
et
ri
cal
cross-sect
i
o
n
of
wi
res.
(
b
) C
o
nfi
g
urat
i
o
n
of
t
h
e
s
i
m
u
l
a
t
i
on f
o
r
r
a
di
at
ed a
n
al
y
s
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
JECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
236
9
–
23
78
2
376
Fi
gu
re
6.
El
ect
ri
c fi
el
d
va
ri
at
i
o
n
i
s
defi
ne
d
b
y
ram
p
ri
se t
i
m
e
t
r
=1ns
Th
e near-end
vo
ltag
e
of th
e lin
e ob
tain
ed
b
y
th
e p
r
op
osed
m
o
d
e
l is sh
o
w
n
in
Fi
g
u
re 7b
to
g
e
th
er
wit
h
the res
u
lt de
rived
by the FDT
D
[1],
whe
r
e t
h
e “FDT
D”
imp
lies th
e fi
n
ite d
i
fferen
ce tim
e
do
m
a
in
so
lu
tio
n to
th
e tran
sm
issio
n
-lin
e equ
a
tions of th
e cab
le.
Th
e
d
i
fferen
t so
lu
tion
s
are i
n
a ve
ry good agreem
ent.
Fi
gu
re 7a dem
onst
r
at
es t
h
e m
a
gni
t
ude
of t
h
e fre
q
u
ency
r
e
sp
onses
of t
h
e near-e
n
d
v
o
l
t
a
ge acqui
re
d
by
t
h
e
pr
o
pose
d
m
odel
.
T
h
e
o
u
t
c
om
es acqui
r
e
d
by
t
h
e ES
A
C
AP t
e
st
sy
st
em
are i
n
great
conc
u
rre
nce
w
i
t
h
t
h
e
analytical solution
[13].
3.
2.
Radiated Susc
eptibility
Anal
ysis
of T
h
ree c
o
nductors
Th
e configu
r
at
io
n
u
s
ed
for the rad
i
ated
su
scep
tib
ility
an
aly
s
is is sh
own
i
n
Fig
u
re 8. Th
e
h
e
igh
t
h
and
th
e leng
th
L are 2
c
m
an
d
1
m
, resp
ectiv
ely. Th
e
wire rad
i
us r is 0.25
mm
,
an
d th
e
relativ
e perm
it
tiv
ity
r
is
2
.
2
5
. th
e li
n
e
is term
in
ated
with
sho
r
t circu
it at th
e far-end
(
b
Z
= 0.
5
Ω
)
.
T
h
e
per
-
uni
t
-
l
e
ngt
h
dc resi
st
a
n
ce
of
th
e wi
re is
r
dc
=1.3
Ω
/m
. The norm
alized incident
field
E =
1V/m
.
The
A
n
al
y
s
i
s
p
e
rf
orm
e
d f
o
r
t
h
ree re
fere
nce
fi
el
d di
rect
i
o
n
s
a
s
desc
ri
be
d i
n
Fi
gu
re
8 a
r
e as
f
o
l
l
o
w:
a)
Ex, Kz
is the
vertical electric field (pa
r
allel to
t
e
rm
i
n
at
i
ons)
an
d
pr
o
p
agat
i
o
n vect
or along the
line.
b)
Ex, Ky is t
h
e
vertical electric fi
el
d a
n
d
pr
op
agat
i
o
n
ve
ct
or
ho
ri
zo
nt
al
an
d
ort
h
o
g
onal
t
o
t
h
e l
i
n
e
c)
Ez,
Kx is the
horiz
ontal electric field ( parallel to
l
i
n
e)
an
d pr
o
p
agat
i
o
n ve
ct
or vert
i
cal
t
o
GN
D-
pl
an
e
Fi
gu
re
9
dem
onst
r
at
es t
h
at
t
h
e v
o
l
t
a
ge
react
i
on at
t
h
e ca
ble ends in the
freque
ncy analy
s
is with t
h
e
in
cid
e
n
t
wav
e
. Fo
r all cases,
wh
en
th
e lin
e
is en
d
e
d
with
short circuit at the far-en
d and ope
n
circuit
at the
near
-en
d
(Z
1
=5.10
8
Ω
and Z
2
=0.5
Ω
), t
h
e line
res
o
nates at
8
4
fn
3
1
0
.
, n
=
1,
3,
5…
(f
1
=7
5MH
z
,
f
2
=2
25M
Hz, f
3
=3
75
MHz…).
Th
e co
nf
igu
r
at
io
n
w
ith
b
o
t
h
sid
e
s asso
ciated w
ith
th
e gr
ound
(Z
1
=Z
2
=0.5
Ω
), f
o
r
cases (a) and (c), elim
inates
practica
l
l
y
al
l
reso
na
nce, an
d
t
h
e im
m
uni
ty
i
s
enhance
d
m
o
re t
h
a
n
5
0
d
B
. For
case (b), the
resonance
s
are located a
t
8
2
fn
3
1
0
.
, n=1,
3,
5…
(f
1
=1
50
MH
z,
f
2
=4
50M
Hz.
..)
.
The
sim
u
l
a
t
i
ons h
a
ve a
ffi
rm
ed t
h
a
t
t
h
e pe
rfe
ct
co
nfi
g
u
r
at
i
o
n
re
q
u
est
s
t
h
e
est
a
bl
i
s
hi
n
g
of t
h
e l
i
ne at
bot
h si
de
s.
Fig
u
r
e
7b
. Vo
ltag
e
r
e
spon
ses at
th
e
n
e
ar-
e
nd
in
th
e tran
sien
t analysis wh
en
the in
cid
e
n
t
wave
propagates al
ong the
z-ax
is ob
tain
ed b
y
diffe
re
nt
m
e
t
h
ods
Fig
u
re
7
a
. Vo
ltag
e
respon
ses
at th
e n
e
ar-end in
th
e
fre
que
ncy
a
n
al
y
s
i
s
whe
n
t
h
e i
n
ci
de
nt
wa
ve
propagates al
ong the z
-
ax
is ob
tain
ed b
y
di
ffe
re
nt
m
e
t
h
ods
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Circu
it Mod
e
ls o
f
Lo
ssy Mu
ltico
ndu
cto
r
Tran
smissi
o
n
Lines: In
ci
d
e
n
t
Pl
an
e Wa
ve Effect
(S
a
i
h
Mo
hamed
)
2
377
4.
CO
NCL
USI
O
N
Circu
it m
o
d
e
ls for th
e
ex
am
i
n
atio
n of th
e
rad
i
ated
an
d
con
d
u
c
ted suscep
tib
ilities fo
r l
o
ssy MTL
h
a
v
e
b
e
en
exhib
ited
.
The prin
cip
l
e po
in
t
o
f
in
terest o
f
these
m
o
d
e
ls co
mp
rises in
t
h
e lik
elih
ood
of u
t
i
lizin
g
th
em
as
a p
a
rt o
f
frequ
e
n
c
y an
d
tim
e d
o
main
s, with
lin
ear and
no
n
linear lo
ads in
d
i
v
i
du
ally. A d
e
tailed
descri
pt
i
o
n
of
M
TL ha
s
bee
n
pres
ent
e
d.
T
h
e l
e
gi
t
i
m
acy
per
f
o
r
m
e
d by
cont
rast
i
n
g
t
h
e
ci
rcui
t
t
e
st
sy
st
em
resul
t
s
a
n
d t
h
e
arra
ngem
e
nt
s i
n
fe
rre
d
by
al
t
e
rnat
e t
e
c
hni
que
s has
u
n
c
ove
re
d a
n
a
g
reea
bl
e
preci
si
o
n
.
For the
variation
effects of
the incide
nt a
ngl
e
on a MT
L line, a m
o
del of a t
r
ansm
ission line
refe
rence
d
to
a ground pla
n
e excited by
an exte
rnal
pl
ane wa
ve is s
t
udied.
W
e
ca
n find that the best
arra
ngem
e
nt
reque
st
s t
h
e g
r
o
u
ndi
ng
of t
h
e l
i
n
e at
bo
t
h
si
des. It
i
s
easy
t
o
ext
e
nd t
h
e m
ode
l
s
t
o
Mu
ltico
n
d
u
c
t
o
r sh
ield
ed
cab
l
es ex
cited b
y
a un
ifo
r
m
an
d no
n-u
n
i
form
i
n
cid
e
n
t
wav
e
.
Th
is inqu
iry
will b
e
talk
ed
ab
ou
t i
n
a fu
rt
h
e
r stud
y.
REFERE
NC
ES
[1]
N. Ghaffarzadeh, “A New Method for Recog
n
ition of Ar
cin
g
Faults in T
r
ansm
i
ssion Lines using Wavelet
Trans
f
orm
and
Correla
tion Co
ef
fici
ent,
”
Indon
es. J.
Electr. Eng
.
Inform. IJEEI
, v
o
l/issue: 1
(
1), 20
13.
[2]
A.
Narwan,
et
al.
, “Backprop
agation Neural Network Modeling fo
r
Fault Lo
cation
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Indones.
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Inform. I
J
EEI
, vo
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[3]
C. R. Paul, “Analy
sis of
multicon
ductor
tr
a
n
smission line
s
,
”
Ne
w
York, Wiley
,
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94.
Fig
u
re
9
a
. Case 1-
Vo
ltag
e
resp
on
ses at th
e
cab
le
en
ds in th
e
freq
u
e
n
c
y an
alysis with th
e i
n
ciden
t
wav
e
with
90
,
90
and
90
pp
E
Fig
u
re
9b
. Case 2-
Vo
ltag
e
resp
on
ses at th
e
cab
le
en
ds in th
e
freq
u
e
n
c
y an
alysis with th
e i
n
ciden
t
wave
with
0
,
90
an
d
9
0
pp
E
Fig
u
re
9
c
. Case 3-
Vo
ltag
e
resp
on
ses at th
e
cab
le
en
ds in th
e
freq
u
e
n
c
y an
alysis with th
e i
n
ciden
t
wave
with
0
,
0
a
nd
0
pp
E
x
E
z
H
y
k
Fi
gu
re
8.
Si
n
g
l
e
l
i
n
e o
v
e
r
a
n
i
n
fi
ni
t
e
an
d
per
f
ect
l
y
co
nd
uct
i
n
g
g
r
ou
n
d
exci
t
e
d
by
a
n
i
n
ci
dent
pl
a
n
e
x
z
y
Z
b
Z
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 5
,
O
c
tob
e
r
20
16
:
236
9
–
23
78
2
378
[4]
C. R. Paul, “Efficient Numerical Co
mputation of the Frequency
R
e
spons
e of Cables Illuminated b
y
an
Electromagnetic Fiel
d (Short Pap
e
rs),”
IEE
E
T
r
ans
. Micr
ow
. T
h
eo
r
y
T
ech.
, vo
l/iss
u
e: 22(4)
, pp
. 45
4–457, 1974
.
[5]
C. Tay
l
or
,
et al.
, “The r
e
sponse of a ter
m
inated
two-wire
tr
ansmission line ex
cited
b
y
a nonun
ifor
m
e
l
ec
t
r
oma
gne
ti
c fi
e
l
d,
”
IEEE Trans. Antennas Pr
opag.
, vol/issue: 13(6), pp. 987–
989, 1965
.
[6]
C. Paul, “Frequency
Response of Multic
onduct
o
r Transm
ission Lines Illum
i
nat
e
d b
y
an
Electr
om
agnetic Field
,
”
IEEE Trans. Electromagn. Comp
at
, vo
l/issue: EMC-18(4), pp. 1
83–190, 1976
.
[7]
A.
Agrawal,
et
al
., “Transien
t
response of
m
u
lticonductor tr
ansm
ission lines excit
e
d b
y
a nonuniform
electromagnetic
field
,
” vol. 18, p
p
. 432–435
, 198
0.
[8]
H.
Xie,
et al.
, “A Hy
br
id FDTD-SPICE Method for Transmission
Lines Excited
b
y
a Nonunifor
m
Incident Wave,”
IEEE Trans. Electromagn. Comp
at
, vo
l/issue: 51(
3), pp
. 811–817
, 2009.
[9]
Y. Mejdoub,
et al.
, “Variation
effect o
f
plane-wave in
cide
n
c
e on multicondu
ctor
transmission lines
,”
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t. J.
Microw. W
i
rel.
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, pp
. 1–
8, 2015
.
[10]
Y. Mejdoub,
et al.
, “
O
ptim
iza
t
i
on circui
t m
odel of a m
u
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ission line
,
”
Int. J. Microw. Wirel.
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, vo
l/iss
u
e: 6(06)
, pp
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.
[11]
M.
Sa
ih,
et a
l
.
, “Circuit Models f
o
r Conducted
Susceptibility
An
aly
s
es of Mult
icon
ductor Shielded
Cables,”
Int. J.
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.
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[12]
F. Rachid
i, “Formulation of th
e f
i
eld-to
-transmission lin
e
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m
s of
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IEEE Trans. Electromagn. Comp
at
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l/issue: 35(
3), pp
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[13]
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Sa
ih,
et al.
, “Circuit m
odels of m
u
lticonductor shield
ed
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ane wave eff
e
ct
,”
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.
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. Devices
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, vol/issue: 29(2), pp. 243–
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.
[14]
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Ca
niggia
a
n
d F.
Ma
ra
de
i,
“SPICE
-L
ike Mod
e
ls for the Analy
s
is of
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ducted
and R
a
diated
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es,
”
IEEE Trans. Elec
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, vol/issue:
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16, 2004
.
BIOGRAP
HI
ES OF
AUTH
ORS
M
oham
e
d S
A
IH rece
ived th
e En
gineer Dip
l
om
a in Ele
c
tr
ica
l
S
y
s
t
em
s
and Tel
eco
m
m
unications
in 2011 from
Cadi A
y
y
a
d University
, M
a
rrak
ech Morocco
,
where he is cu
rrently
working
toward the Ph.
D
degree at th
e Departm
e
nt
of Applied Physics
,
Ele
c
tr
ica
l
Sy
st
em
s and
Tel
ecom
m
unicat
ions
Labor
ator
y,
Cadi A
y
ya
d Un
ivers
i
t
y
o
f
M
a
rr
akech
, M
o
roc
c
o.
His
res
ear
ch
inter
e
sts includ
e electrom
agneti
c com
p
atib
il
i
t
y
, m
u
lticonductor
transm
ission li
nes, num
erical
electromagnetic methods
and
antenna d
e
signs.
Hicham
ROUIJAA is
a P
r
ofes
sor of ph
y
s
i
c
s
,
a
tta
ched to C
a
di
A
yyad Univ
ers
i
t
y
, M
a
rr
akes
h
Morocco. He is obtain
e
d his Ph
D Thesis on \"
Modeling of Multicondu
ctor Tr
ansm
ission Lines
using Pade approximant
method: Circuit model
\", in 2004,
fro
m Aix
Marseille University
-
F
r
ance.
He is
a
s
s
o
ciate m
e
m
b
e
r
of El
ectr
i
c
a
l
S
y
s
t
em
s
and T
e
le
com
m
unicati
ons
Laborato
r
y
LS
ET at th
e Cadi A
yya
d Univers
i
t
y
. His
cur
r
ent res
e
arch in
teres
t
s
conc
ern
ele
c
trom
agnet
i
c
com
p
atibil
it
y
an
d m
u
lticondu
cto
r
transm
ission li
nes.
Abdelil
ah GHAM
M
A
Z received
the Doctor of E
l
ec
tronic d
e
gree
from
the Nation
a
l pol
yt
echni
c
Institut (ENSEE
IHT) of Toulou
se, France, in
1
993. In 1994 he went back
to
Cadi A
y
y
a
d
University
of
Marrakech
– M
o
rroco. Sin
ce 2
003, he h
a
s been a Professor at the Faculty
of
Sciences and
technolog
y
,
Marr
akech
, Morroco
.
He is
a member of
ELectr
i
cal S
y
stems and
Telecommunications Labor
at
or
y
LSET
at
the
Ca
di A
yya
d Univ
e
r
sit
y
. His r
e
sear
ch in
terests
in
the f
i
eld
of
electromagnetic com
p
atibi
lity
,
multiconductor
transmission lines.
Evaluation Warning : The document was created with Spire.PDF for Python.