TELKOM
NIKA
, Vol.14, No
.4, Dece
mbe
r
2016, pp. 13
56~136
1
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i4.4019
1356
Re
cei
v
ed Ma
y 19, 201
6; Revi
sed
No
ve
m
ber 11, 201
6; Acce
pted
No
vem
ber 2
6
, 2016
Least Mean Error Algorithm for Determining the
Radome Dimension of Planar Antenna
Ad
y
a
Pramu
d
ita*
1
, Yu
y
u
Wahy
u
2
1
T
e
lecommu
ni
cation R
e
se
arch Group, Electr
ical En
gin
eeri
n
g Dep
a
rtment Atma Ja
ya Uni
v
ersit
y
,
Jl. Sudirma
n 5
1
, Jakarta, 021
-570
882
6.
2
Pusat Penel
iti
an Elektro
n
ika
dan T
e
lekomu
nikasi, L
e
mba
g
a
Ilmu Peng
eta
hua
n Indo
nesi
a
Jl. Sangkur
ian
g
-Komp
l
ek LIP
I, Bandun
g, 02
2-25
046
60
*Corres
p
e
ndi
n
g
author, e-ma
i
l
: pramud
itaad
ya
@gma
il.com
A
b
st
r
a
ct
Antenn
as are gen
eral
ly
co
ntr
u
cted
fr
o
m
met
a
llic
materi
als;
therefore
it is
p
r
one
to corr
osi
on w
h
e
n
install
ed
outd
o
o
rs. Rad
o
m
e
i
s
an i
m
porta
nt part of a
n
o
u
td
oor a
n
ten
na th
at serves to
pr
otect the a
n
ten
n
a
from env
iro
n
m
ental co
nditi
on
s. Rado
me
str
u
cture is not e
x
pected to h
a
v
e
a sign
ificant
influ
ence o
n
th
e
character
i
stics
of the ante
n
na. Pa
ra
metric
study is ge
n
e
raly a
p
p
lie
d i
n
findi
ng th
e
opti
m
u
m
a
n
te
nna
di
me
nssio
n
inc
l
ud
ed ra
do
me.
A metho
d
for
guid
i
n
g
a par
ametric study
proses i
n
find
i
ng the o
p
ti
mu
m
anten
na
di
me
n
s
ions h
a
s i
n
ve
stigated
and
pr
opos
ed i
n
this
pap
er. In this study, a metho
d
for deter
min
i
n
g
the o
p
ti
mu
m r
a
do
me
di
mensi
o
n for
pla
nar
an
tenna
by
ap
plyi
ng th
e
alg
o
rith
m
Le
ast Mea
n
Error (LME)
ha
s
investi
gate
d
. L
M
E alg
o
rith
m i
s
used to fi
nd t
he o
p
ti
mu
m d
i
me
nsi
ons of th
e rad
o
m
e. T
h
e
simulati
on r
e
s
u
lts
show
that the propos
ed
meth
o
d
c
an be
app
lie
d to deter
min
e
the di
me
nsio
ns
of a plan
ar ant
enn
a.
Ke
y
w
ords
: rad
o
me, di
me
nsio
n, plan
ar, ante
nna
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Antenna
s
are ge
ne
rally
comp
osed
of
metalli
c m
a
terials that
n
eed to
b
e
p
r
otecte
d
again
s
t
corro
s
ion
process wh
en the
a
n
tenna
is
op
erated
a
s
a
n
outdo
or
ant
enna
[1-3]. T
he
addition of
rado
me st
ru
cture i
s
not
expec
ted t
o
have a
signifi
cant in
fluence on
the
cha
r
a
c
teri
stics of th
e a
n
te
nna, the
r
efo
r
e its
nee
d
to
be ta
ken
into
co
nsi
deratio
n at the
ante
nna
desi
gn. Ra
d
o
me is al
so
expected to
have a
sim
p
le structu
r
e
and provide
minimum final
dimen
s
ion
s
o
f
the antenna
. For the plan
ar anten
na,
the simpl
e
st radome
stru
ct
ure is the
cub
i
cal
st
ru
ct
ur
e.
On
most
su
rf
ac
es of
cubi
cal
st
ruct
u
r
e, ra
dome ante
n
n
a
position i
s
parallel to the
antenn
a su
rface a
nd futher more the wave prop
a
g
a
tion model i
n
layered me
dium is pote
n
t
ialy
be u
s
e
d
a
s
a theo
retical
approa
ch. Se
veral te
chni
q
ues for analy
z
ing
ra
dom
e
that have
be
en
studie
d
incl
ud
e a combi
nati
on of several nume
r
ical me
thods
with co
mplex com
p
u
t
ing [4-6].
Paramet
r
ic st
udie
s
often
u
s
ed
in
de
sign
ing the
ante
n
na in
o
r
de
r t
o
dete
r
min
e
t
he b
e
st
dimen
s
ion
s
o
f
the antenna
[7, 8]. Problem that
addre
s
sed in this p
aper i
s
determined du
e to the
fact that determini
ng the
antenna'
s o
p
timum di
me
nssion by p
e
rformi
ng se
veral pa
rame
tric
studie
s
may
time consu
m
ing and n
eed a larger
computatio
n
reso
urce
s. To improve
the
effectivene
ss of desig
n proce
s
s in dete
r
minin
g
t
he b
e
st dime
nsi
o
ns of the a
n
tenna, a
sea
r
chin
g
algorith
m
is
studie
d
and
prop
osed to
be appli
ed
i
n
the pa
ram
e
tric
study. In the previo
us
resea
r
ch, a
determi
nisti
c
app
roa
c
h
wa
s p
r
opo
se
d for o
p
tima
l synthe
sis
of linea
r ph
ase
reconfigu
r
a
b
le isotropi
c sp
arse
array. T
he optimi
z
ati
on step
of
synthesi
s
p
r
o
c
e
dure i
s
ba
se
d
on
minimum
sq
u
a
re
error bet
wee
n
refere
n
c
e a
nd
actu
a
l
radi
ation p
a
ttern [9]. Lea
st Mea
n
Erro
r
(LME) alg
o
rit
h
m is sea
r
chi
ng algo
rithm that freque
ntly used an
d ha
s simpl
e
com
putation. In this
resea
r
ch, implementatio
n of LME algori
t
hm in
determining the ra
dome dime
nsions of a pla
nar
antenn
a has investigated
. In this research,
a method of determining dime
nsio
ns of pl
ana
r
antenn
a ra
d
o
me ha
s in
vestigated
b
y
using
a case
study o
n
a tria
ngul
ar-sh
ape
d pl
ana
r
monop
ole an
tenna whi
c
h
is studie
d
in
the previo
u
s
re
sea
r
ch a
s
an anten
n
a
for digital TV
broa
dcast sy
stem [10].
This
pap
er i
s
org
ani
zed
a
s
follo
ws: th
e
fi
rst chapte
r
describe
s
th
e ba
ckgroun
d of the
resea
r
ch. In chapter II discusse
s
the cal
c
ulatio
n meth
od that asso
ciated with the
implementati
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Lea
st Mean
Erro
r Algorith
m
for Determ
ining the Rad
o
m
e
Dim
ensi
on of… (Ad
y
a
Pram
udita)
1357
of the LMS algorithm. Chapter III contains the
result
s and di
scussion of
the result
s that have
been o
b
taine
d
and in chap
ter IV is the concl
u
si
on.
2. Rese
arch
Metho
d
Rad
o
me is a
stru
cture use
d
to protect p
a
rts
of the an
tenna that se
rves a
s
a rad
i
ator to
the effects of
environm
ent
al con
d
ition
s
[1-3].
Rad
o
m
e structu
r
e
is gen
erally
comp
osed b
y
a
diele
c
tric m
a
terial an
d mat
e
rial
s that are
o
ften used to
manufact
u
re
the antenna
rado
me in
clu
d
e
Polyester, Ep
oxy, cyanate ester, polyi
mide, PTFE
,
polyca
r
bo
nat
e, fibergla
ss
[11]. In a certain
appli
c
ation
such
as
ro
cke
t
and ra
da
r, the sele
ct
ion
of rado
me m
a
terial
s mu
st
also
co
nsi
d
e
r
ed
environ
menta
l
conditio
n
s th
at are mo
re e
x
treme [4].
Figure 1. Modelling of the
rado
me effect
to the planar
antenn
a
Rad
o
me
stru
cture
s
an
d it
s m
a
terial
s
potentia
lly af
fec
t
to the
charac
teris
t
ic
s of the
antenn
a
su
ch
as radiatio
n
pattern
an
d t
he in
put
im
pe
dan
ce
of the
antenn
a [5, 6
]
so
the
pro
c
ess
of desig
ning the sh
ape of the rad
o
me a
nd ch
oo
sing the rad
o
me m
a
terial
s nee
d
to consi
der i
t
s
effect on th
e
antenn
a cha
r
acteri
stics.
Radome
in
flue
nce
on th
e el
ectro
m
ag
neti
c
wave
s radi
ated
by an
anten
n
a
is inve
stiga
t
ed by u
s
in
g t
he m
odel
th
a
t
illustrated i
n
Figu
re
1. In t
h
is
ca
se,
wh
en
the most of radome
su
rface ar
e in
paral
lel positio
n wi
th antenna
surface then t
he effect on t
h
e
radiatio
n pate
r
n is
signifi
ca
nt in perp
end
icula
r
di
rectio
n. Theref
ore,
the model i
s
derived
only in
the point of view ante
nna i
nput impe
dan
ce. In
z
di
re
ction of the pla
nar a
n
tenn
a, rado
me effect
i
s
assume
d le
ss sig
n
ifica
n
t becau
se
E
field ra
diated
by the anten
na ha
s sm
all
value and t
he
rado
me area
whi
c
h is p
e
rp
endi
cula
r to its dire
ction h
a
s
sm
all dimen
s
ion.
If
the
E
field
that radiate
d
by the
plana
r anten
na
in t
he pl
ane
zy
plane
is ap
proximated
by the
E
field of half wave
length di
pole
antenn
a (1
) a
s
illu
strated i
n
Figu
re 1 th
at the field
E
of
the ante
nna i
s
p
a
rtly refle
c
ted ba
ck by t
he
surfa
c
e
of
the ra
dom
e to the a
n
tenn
a an
d affecte
d
t
o
the ante
nna
ch
aracte
rist
ics.
When
the radom
e
ha
s
ele
c
tri
c
al
prope
rtie
s
r
and
r
electroma
gne
tic wave tha
t
radiat
ed
by the a
n
t
enn
a will
be
pa
rtially refle
c
t
ed b
a
ck
by
the
reflectio
n
coe
fficient that can be
cal
c
ula
t
ed based o
n
(2)
with
a
Z
is the air intri
n
si
c
impeda
nce (
120
) and
r
Z
is the intrinsi
c imp
e
dan
ce that ca
n be determin
ed by (3).
sin
)
cos
5
.
0
cos(
)
(
E
(1)
a
r
a
r
Z
Z
Z
Z
0
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 4, Dece
mb
er 201
6 : 1356 – 136
1
1358
r
r
r
Z
0
0
(3)
The com
pari
s
on
b
e
twe
en
E
field that transmitted
by
the ante
nna
(
i
E
) an
d
E
field
that
reflecte
d ba
ck to the anten
na (
2
r
E
) is determined by (4
).
5
.
0
0
0
2
)
5
.
0
(
2
)
5
.
0
(
)
(
2
d
E
d
E
E
E
x
i
r
r
(4)
The refle
c
tion
coefficie
n
t of the antenna
is al
so influe
nce
d
by the electroma
gne
tic wave
that reflecte
d
back by the
rado
me surfa
c
e a
nd finally
, when
nr
is the refle
c
tion
coefficient of
the
ante
nna
without ra
do
me
a
nd
r
is th
e
refle
c
tion
co
efficient of
th
e ante
nna
wit
h
radom
e, th
en
the total reflection coefficie
n
t of the rado
me can b
e
ca
lculate
d
usi
n
g
(5-6
).
r
nr
i
r
r
i
r
r
i
r
nr
E
E
E
E
E
E
E
2
1
total
2
1
,
,
(5)
0
0
)
(
)
(
)
(
Z
f
Z
Z
f
Z
f
in
in
nr
(6)
Cal
c
ulation
of
the
antenn
a
input im
peda
nce
is
ap
proa
che
d
by
bico
nical
ante
nna
theo
ry
that is explai
ned first by Schel
ku
noff [12]. Acco
rding
to the image
theory, the g
r
oun
d plan
e
will
gene
rate the
image of the
uppe
r cone
a
nd the el
ectr
i
c
al dim
e
n
s
io
n of the ante
nna i
s
the
sa
me
with bi
coni
ca
l. Input impe
dan
ce of
sin
g
le c
one
ab
ove groun
d
plane i
s
half
of the bi
co
n
i
cal
antenn
a inpu
t impedan
ce.
Furthe
rmo
r
e
the input im
peda
nce of monop
ole cal
c
ulate
d
as (7
-10
)
that also men
t
ioned in [10].
inB
in
Z
f
Z
5
.
0
)
(
(7)
L
f
f
jZ
Z
L
f
jZ
f
Z
Z
f
Z
L
k
k
L
k
inB
)
(
tan
)
(
)
(
tan
)
(
)
(
(8)
L
f
f
jZ
Z
L
f
jZ
f
Z
Z
f
Z
m
k
k
m
k
L
)
(
tan
)
(
)
(
tan
)
(
)
(
(9)
L
f
f
jZ
Z
L
f
jZ
f
Z
Z
f
Z
m
k
k
m
k
L
)
(
tan
)
(
)
(
tan
)
(
)
(
(
1
0
)
With
is
/
2
is,
L
i
s
the
le
ngth
of the
co
nical
and
Z
k
i
s
the
ch
aracte
risti
c
im
ped
an
ce
of the
transmissio
n line model
s of
biconi
cal a
n
tenna that can
be determi
ne
d by (11).
)
2
ln(cot
c
k
Z
(11
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Lea
st Mean
Erro
r Algorith
m
for Determ
ining the Rad
o
m
e
Dim
ensi
on of… (Ad
y
a
Pram
udita)
1359
Effect of the
environ
ment
arou
nd th
e a
n
tenna,
a
s
p
e
c
ially at n
ear
field ra
diu
s
n
eed to
be
con
s
id
ere
d
in
the in
stallati
on o
r
anten
n
a
me
asur
em
e
n
t [12]. The
radome
effe
ct
will b
e
in
crea
sed
whe
n
the rad
o
me po
sition
is clo
s
e
r
to
the antenn
a
and vice ve
rsa. In de
sign
ing the ante
n
na
rado
me, mini
mun di
stan
ce of the rad
o
me to
the
antenn
a su
rf
ace
(d) i
s
al
so an i
m
po
rtant
con
s
id
eratio
n
in addition to
its effect on the anten
na chara
c
te
risti
c
s.
The ra
dome
effect can
be
obseved by calcul
ati
ng the total of reflection c
oeffic
i
ent in (5).
In this paper,
Least Mean
Erro
r (LME
) algorith
m
is
a
pplied to find
the minimum distance of the
rado
me. The
minimum average difference (
∆
r
) b
e
twee
n
nr
and
total
becom
es stoppin
g
crete
r
ial of the algorithm
calcul
ation. LME fl
ow chart is sh
own in Figure 3. The value of
∆
r
descri
b
e
s
the
satisfi
c
ation
level that sh
ould b
e
re
ached by the
al
gorithm th
at related
with t
h
e
minimum
dist
ance bet
wee
n
ra
dome
an
d
anten
na. Calcul
ation wa
s
do
ne over
N
sa
m
p
le
s
in th
e
freque
ncy
ran
ge of o
b
serva
t
ion.
∆
n
i
s
th
e average
differen
c
e
(
∆
r
) b
e
twee
n
nr
and
total
at
n
-th
iteration. Wh
en
the
∆
n
still
larger than
∆
r
, then
d
for
n
e
xt iteration i
s
ad
ded
by
∆
s
.
∆
s
is st
ep s
i
ze
for upd
ating the value of d
in each ite
r
a
t
ion that
is de
termine
d
ba
se on the mini
mum re
soluti
on
of radom
e fabrication. In this
re
se
arch
we u
s
ed 0.5
mm for
∆
s.
N
nf
d
nf
n
n
total
nr
n
)
,
(
)
(
(12
)
Figure 2. Flow ch
art of LM
E algoritm wh
ich is u
s
e
d
to find the minimum value of
d
3. Results a
nd Analy
s
is
Re
sin fibe
rgl
a
ss is
ch
oose as
rad
o
me
material
with a rel
a
tive permittivity of 4.1 [11].
Figure 4
sh
ows the infl
uen
ce of th
e rad
o
me to
the refle
c
tio
n
co
efficient
of the ante
nna.
Significant inf
l
uen
ce o
c
curs at a
r
oun
d 5
00-8
00
M
H
z
whi
c
h i
s
the f
r
equ
en
cy op
eration
ra
nge
of
the ante
nna.
The
refle
c
tion
co
efficient i
s
deter
mine
d
by the in
put i
m
peda
nce of
the a
n
tenn
a
(6)
so that cha
n
ges in reflect
i
on coeffici
en
t, indi
cates a
chang
e in the input imp
edan
ce of the
antenn
a. The
rad
o
me
influ
ence to th
e a
n
tenna
inp
u
t i
m
peda
nce i
s
not si
gnifican
t
enou
gh
at the
greate
r
di
sta
n
ce
(
d
) a
nd v
i
ce ve
rsa. Fo
r the
sam
e
ra
dom
e
dimen
s
ion, sm
aller radome
di
stan
ce
gene
rate
s la
rger
refle
c
tion
wave to th
e
antenn
a surf
ace
rath
er th
an lon
ger di
stance.
Ho
we
ver,
the greate
r
di
stan
ce (
d
) will
lead to a larg
er final dime
n
s
ion for the a
n
tenna.
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 4, Dece
mb
er 201
6 : 1356 – 136
1
1360
Figure 3. The
effect of
d
to
the antenn
a
reflec
tion c
oeffic
i
ent
Figure 4. Averag
e differe
nce (
∆
n
) b
e
tween
nr
and
to
t
a
l
in correspondi
ng with
rado
me
distan
ce
d
Contras
t
dielec
tric
between radome ma
terial and air betwe
en radome and antenna
surfa
c
e
al
so
affects to th
e
amount
refl
ection
wave.
Base
d on th
e inform
ation
about a
n
ten
na
radiatio
n
p
a
tern, refle
c
tio
n
coefficie
n
t model of
pla
nar anten
na due
to
the existen
c
e of
ra
dom
e
can b
e
deriv
ed. The mai
n
purp
o
se of studyi
ng the influence of radom
e on antenna in
pu
t
impeda
nce is determini
ng the minimum
dimensi
on of
the radom
e on anten
na d
e
sig
n
. Rad
o
m
e
minimum
di
stance i
s
the
v
a
lue
of
d
whi
c
h
ca
uses th
e ave
r
ag
e dif
f
eren
ce
bet
ween
nr
and
to
t
a
l
is 0.1
dB or
other val
ue t
hat rel
a
ted t
o
the
satisfa
c
tion level
in
desi
gnin
g
th
e anten
na. T
he
radome mini
mum distance can
be det
ermined by
running the LSE algorithm
that illustrated as
flow ch
art in
Figure
3 wit
h
step
size
0.5 mm.
The
result sh
ows that the ra
dome mini
m
u
m
distan
ce i
s
1
3
.
5 mm and
re
flection
coeffi
cient
comp
ari
s
on between antenn
a
with
out
rad
o
me a
nd
antenn
a with
rado
me at a
distan
ce
of 13.5 mm
i
s
shown in Fig
u
r
e 5. At a di
stance
13.5 m
m
,
rado
me effe
ct to the ante
nna in
put im
peda
nce
ha
s been
sm
all
enou
gh. Figu
re 5
sh
ows t
hat
reflectio
n
coe
fficient of the antenn
a ha
s
very sm
all di
scre
pan
cy co
mpari
ng with
without rado
me.
Re
sults i
n
Fi
gure
5 in
dicated that the
propo
sed
meth
od can
be u
s
ed to d
e
termi
n
e the mi
nim
u
m
dimen
s
ion
s
o
f
the rado
me
for plan
ar
ant
enna. the
pro
posed meth
o
d
is h
e
lpful to
accele
rate th
e
pro
c
e
ss of pa
rametri
c
studi
es that are oft
en co
ndu
cted
on the anten
na de
sign p
r
o
c
e
ss.
Figure 5. Refl
ection
coefi
c
i
ent comp
ari
s
on bet
ween a
n
tenna
witho
u
t radom
e an
d antenn
a
wit
h
rado
me at a distan
ce of 1
3
.5 mm
4. Conclusio
n
Lea
st Mean
Erro
r algo
rith
m has
pro
p
o
s
ed fo
r a m
e
thod in d
e
si
gning a
rad
o
m
e for
plana
r anten
n
a
. The analitical study of L
M
E algorit
hm
to determine
the optimum dimen
s
ion
s
o
f
a
plana
r
a
n
ten
na rado
me h
a
s bee
n con
d
u
cted. The
re
flection co
efficient mod
e
l
o
f
plana
r ante
n
na
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TELKOM
NIKA
ISSN:
1693-6
930
Lea
st Mean
Erro
r Algorith
m
for Determ
ining the Rad
o
m
e
Dim
ensi
on of… (Ad
y
a
Pram
udita)
1361
due to the
existen
c
e of
ra
dome h
a
s
de
rived ba
se
o
n
the ante
n
n
a
radi
ation p
a
tern. Th
e re
sults
sho
w
e
d
that the metho
d
is very helpful to acce
le
rate t
he process of
par
a
m
etri
c studies th
at are
gene
rally n
e
cessary fo
r
de
terminin
g the
optimum
di
mensi
o
n
s
of
the ante
nna.
The
study
wa
s
con
d
u
c
ted ref
e
rs to a
singl
e para
m
eter,
namely
anten
na input impe
dan
ce. Furth
e
r stu
d
ie
s al
so
need to be d
o
ne with refe
re
nce to the oth
e
r anten
na p
a
ram
e
ters.
Referen
ces
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g
fu Me
ng,
W
enbi
n D
ou. A
nal
ysis
a
n
d
De
sign
of
Ra
dome
i
n
Mi
llim
eter
Wave Ba
nd. In
: Igor Mi
nin
.
Editors
. Micro
w
a
v
e
and M
ill
i
m
eter W
a
ve T
e
chn
o
lo
gi
es: from Photo
n
ic B
and
ga
p Dev
i
ce
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plic
atio
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In
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e
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Gustafsson, G Kristensso
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c
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on
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i
su
aliz
ati
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ival
e
n
t currents
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a
radome
us
in
g an i
n
tegr
al r
epres
entati
on f
o
rmulati
on.
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ogress i
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ectromag
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tena
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m
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Che
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Z
h
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l
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arat
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a
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Cearm
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R
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agnetics Research
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HF
Meng, W
B
Dou. A H
y
b
r
id
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ys
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me
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gneti
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e
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a
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enn
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und
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u
rte. A Comp
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p
le Ba
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hed Pl
an
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a
w
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w
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Lump
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e
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E
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e
l
w
a
r
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n
, M Az
ad H
o
ssai
n
, M
uhamm
ad As
a
d
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al Orthog
on
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i
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ar
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a
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nna
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e
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e
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b
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m
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mensi
o
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nop
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r
i
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.
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