TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 15, No. 3, September
2015, pp. 49
7
~ 503
DOI: 10.115
9
1
/telkomni
ka.
v
15i3.840
4
497
Re
cei
v
ed
Jun
e
21, 2015; Revi
sed
Jul
y
1
9
, 2015; Acce
pted Augu
st 2, 2015
Resonance Characteristics an
d Effective Parameters of
New Left Hand Metamaterial
Rajni
*1
, Anupma Mar
w
ah
a
2
*1
Dept. of Electronics a
nd Co
mmunicati
on E
ng., Shah
eed
Bhag
at Sing
h Coll
eg
e State T
e
chnical Cam
pus,
F
e
rozep
u
r, Punja
b
, India. Ph
.
/
F
a
x: 91-9
7
7
9
1
900
66/1
632-
24
213
8
2
Dept. of Electronics a
nd Co
mmunicati
on E
ng., Sant
Lon
g
o
w
a
l Institute
o
f
Eng. and T
e
chno
log
y
,
Lon
go
w
a
l, San
g
rur, Punj
ab, Indi
a
Ph./F
ax: 9
1
-98
722
24
05
5/167
2-25
31
17
*Corres
p
o
ndi
n
g
author, em
ail
:
rajni_c
123
@
y
aho
o.co.in
1
, mar
w
a
ha_
an
up
ma@
y
ah
oo.co.
i
n
2
A
b
st
r
a
ct
It is essenti
a
l t
o
alter
effectiv
e el
ectro
m
a
g
n
e
tic
par
a
m
eter
s of a
mater
i
al
to enh
anc
e its
respo
n
se.
In the pres
ent
w
o
rk, w
e
propose a
nove
l
L
e
ft Hand Meta
materia
l
(LHM) s
t
ructure co
mpr
i
sing
dou
bl
e tur
n
spiral
reso
nato
r
(DT
S
R) an
d
capac
itanc
e lo
ade
d strips
(
C
LS). T
h
is struc
t
ure is n
u
m
er
i
c
ally
expl
ore
d
to
exa
m
i
ne the re
sona
nce a
nd e
ffective mater
i
al par
a
m
eters i
.
e. permeab
ilit
y and per
mittivity. The negati
v
e
refraction
in
th
e u
n
it c
e
ll
is c
onfir
me
d w
i
th i
dentif
ic
atio
n of
do
ubl
e
ne
gati
v
e re
gio
n
(
neg
ative
per
mittivit
y
,
ε
and n
egativ
e per
me
abi
lity,
µ
)
on placi
ng th
e unit cell i
n
a
w
a
veguid
e
w
i
th w
e
ll define
d
Perfect Electric
Con
ductio
n
/Pe
r
fect Magnetic
Con
ductio
n
bo
und
ary con
d
itio
ns.
Ke
y
w
ords
:
left han
d me
tamat
e
ria
l
(L
HM), spiral r
e
son
a
tor (SR)
, negativ
e p
e
rmittivity, ne
gative
per
me
abi
lity, hi
gh frequ
ency s
t
ructure simul
a
tor (HF
SS)
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
There ha
s b
e
en a g
r
eat
d
eal of attra
c
ti
on an
d
attent
ion in d
e
si
gn
of stru
ctures based
material
s in last de
cad
e
, whi
c
h exhibit
new unn
at
ural qualitative respon
se
fun
c
tion
s. A recent
example
of these a
r
tificial
materi
als i
s
‘Metamat
eri
a
l
s
’
which h
a
ve led to
pa
ra
digm
shifting
by
openi
ng p
r
o
s
pect
s
for imp
r
oved
anten
n
a
de
sign
to
overpo
we
r th
e limitation
s
of co
nvention
a
l
antenn
as. T
hese mate
ria
l
s dem
on
stra
te negativ
e
permittivity and/or n
egativ
e permea
b
ility.
Metamateri
al
s
a
r
e unn
atural materi
al
s
that co
uld
be engi
nee
red by
em
b
eddin
g
spe
c
i
f
ic
inclu
s
io
ns
of metal in
so
me ho
st m
e
dia. Thi
s
e
n
s
ua
nt mate
ri
al can
be ta
ilored
to a
c
h
i
eve
electroma
gne
tic characte
ri
stics
(su
c
h
a
s
pe
rme
abilit
y and p
e
rmit
tivity) acco
rdi
ng to
syste
m
requi
rem
ents [1]. Due to their exoti
c
feature
s
, t
hese
material
s ha
ve applicatio
ns in the fiel
d of
antenn
a to d
e
sig
n
small
a
n
tenna
s [2]
with e
nhan
ce
d directivity [3] and
bea
m-width
co
ntrol
[4].
Another ap
plication
of met
a
materi
als is
to
enh
an
ce t
he ma
gneti
c
perm
eability
of nonm
agn
e
t
ic
material
s by metallic inclusions [5].
The ma
n beh
ind the rema
rkabl
e discov
ery of these
material
s
wa
s Victo
r
Vese
lago [6]
who, in
196
8, made a t
heoretical
assumptio
n
of
artificial m
a
terial
s which
exhibit neg
ative
permittivity and p
e
rm
eabili
ty. His
wo
rk
wa
s a
c
kno
w
l
edge
d after
more
than
three d
e
cade
s
whe
n
Pendry et
al. pro
p
o
s
ed
p
e
riodi
cal t
h
in-wire
(T
W)
st
ructure that e
x
hibits
the
n
egative effect
ive
permittivity [7]. It was also
demon
strate
d in
[8] that negative ma
gnetic p
e
rm
e
ability could
be
achi
eved u
s
i
ng an
array
of split-ring
re
sonato
r
s
(SRR). In 2
001, Smith realized the f
i
rst
prototype Lef
t Hand Meta
material (LHM) stru
ctu
r
e by combini
n
g
split ring re
sonators an
d thin
wire
s [9]
.
LHMs have n
u
m
ero
u
s ex
ce
ptional prope
rtie
s p
a
rticul
arly the ba
ckward wave a
nd
negative refraction.
Ca
rbo
nnel et al ve
rified the
ba
ckward
wave
prop
agatio
n i
n
[10]. Neg
a
tive
refra
c
tion wa
s
confirm
ed experim
entall
y
by
Pendry
and Smith i
n
[11-1
2
]. A numbe
r of n
e
w
stru
ctures
su
ch as spiral multi-split,
o
m
ega
shape
and S
-
shap
e
have
bee
n
prop
osed
in [
13]
whi
c
h show
LHM cha
r
a
c
teristi
cs. In [14-16], aut
ho
rs analy
z
ed th
e SRR st
ru
cture
s
to con
c
l
ude
depe
nden
ce
of effective material p
a
r
amete
r
s
on
geometri
cal
dimen
s
ion
s
of metamaterial
stru
cture to upgra
de the p
r
operti
e
s
of the microwave device
s
.
It is well
kn
o
w
n fa
ct that
antenn
a give
s lo
w
efficie
n
cy wh
en it
s size i
s
redu
ce
d belo
w
Chu limit [1
7-20]. Becau
s
e of this re
aso
n
, antenn
a desi
gn ha
s bee
n a bi
g chall
eng
e for
resea
r
chers. Many
miniatu
r
izatio
n techn
i
que
s are ava
ilable in liter
a
t
ure like in
sertion of slots
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 15, No. 3, September 20
15 : 497 – 503
498
the ra
diating
patch
[21] an
d de
si
gn
of fractal
ba
sed
a
n
tenna
[22] e
t
c., but this
p
r
oble
m
can
b
e
solved th
rou
g
h
magn
etic p
e
rme
ability enhan
ce
d met
a
materi
als
which a
r
e u
s
e
d
to desi
gn
small
antenn
as b
e
l
o
w Chu limit with co
nsi
derable si
ze red
u
ction [5], [23-24].
In this p
ape
r, a ne
w left h
and m
e
tamat
e
rial
stru
ctu
r
e co
nsi
s
ting
of doubl
e turn spi
r
al
resonato
r
(DTSR) an
d two
capa
citively loade
d st
rip
s
(CLS) of copp
er, is mod
e
lle
d, optimized
and
simulate
d u
s
i
ng Finite
Element Met
h
o
d
(FEM
) b
a
sed An
soft HFSS softwa
r
e to p
r
ove t
he
negative
refraction
p
r
ope
rty. The p
r
op
ose
d
stru
ct
ure ha
s
a
singl
e spiral reso
nator alon
g
with
C
L
S
w
h
ic
h is d
i
ffe
r
e
n
t
fr
om wo
rk
d
o
ne in
[25
]
wh
ere
d
o
u
b
l
e
c
u
t
SR
Rs
a
r
e be
in
g
us
ed
. T
he u
s
e
of spiral reso
nator (S
R) is
prop
osed in this pa
per b
e
cause the spi
r
al
resonato
r
s
use the unit cell
area
effective
l
y and have
signifi
cant po
tential to re
d
u
ce the
ele
c
trical
si
ze of the metamate
rial
unit cell than
the conventi
onal squa
re
SRR
stru
ctures [5, 23]. We prefe
rre
d a
spiral lo
op a
s
it
use
s
le
ss a
r
ea to p
r
ovid
e equival
ent
cap
a
cita
nce
while
sim
u
ltaneo
usly p
r
o
v
ide additio
n
a
l
indu
ctan
ce a
nd hen
ce a
d
d
i
tional perme
ability [16, 23].
This p
ape
r i
s
organi
se
d in four
sectio
ns.
After discu
ssi
on of previous
wo
rk
done i
n
Introdu
ction, Section 2
di
scus
se
s
pro
posed d
e
si
g
n
of L
H
M
st
ructu
r
e. Se
ct
ion 3
prese
n
ts
simulatio
n
m
e
thodol
ogy of
LHM u
n
it cel
l
insi
d
e
a wa
veguide with suitabl
e
bo
un
dary
conditio
n
s
and excitatio
n
s. Section
4 pre
s
ent
s numeri
c
ally
an
alyzed results and di
scussion
s. Sectio
n 5
gives con
c
lu
sion of pape
r.
2. Proposed
Design o
f
L
H
M Stru
ctur
e
The propo
se
d LHM u
n
it cell stru
cture consi
s
ti
ng a
d
ouble tu
rn sp
iral re
so
nato
r
(DTS
R)
and t
w
o
cap
a
c
itively loade
d stri
ps (CLS
) on
both
si
d
e
s
(left an
d
ri
ght si
de) of S
p
iral
Re
so
nat
or
(SR) i
s
sh
own in Figure 1
.
The geomet
rical p
a
ra
met
e
rs of SR an
d CLS are gi
ven in Table 1.
The propo
se
d stru
cture is patterne
d
on
FR-4
su
bs
trate with pe
rmittivity 4.7, thickne
s
s 1.6 mm,
and lo
ss tan
g
ent of 0.019.
Figure 1. LHM unit cell structure geo
me
try
Table 1. Geo
m
etrical Para
meters of the Propo
se
d LHM Unit Cell
S.N.
Dimension of LH
M Structure
Units (mm)
1
Height of t
w
o ca
pacitance strips (L1)
17.52
2
Length of full CL
S (L2)
15.2
3
Length of half stri
p (L3)
7.6
4
Gap bet
ween SR
and CLS (
G
1
)
3.5
5
Gap bet
ween t
w
o CLS strips (G2
)
1.16
6
Width of CLS (W
1)
1.16
7
Width or
metallic
thickness of a tur
n
of SR (
W
2)
0.45
8
Gap o
r
split of SR (G3)
0.45
9
Spacing between
two turns of SR
(G4
)
0.45
10
Length of out
er a
r
m of SR (
L5 and
L4)
8.19
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TELKOM
NIKA
ISSN:
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046
Re
son
a
n
c
e Chara
c
te
risti
c
s and Effective
Param
e
ters
of New L
e
ft Hand Metam
a
terial (Raj
ni)
499
Metallic len
g
th of DTSR a
n
d
CLS is e
qui
valent to indu
ctive coil. The
gap in SR a
n
d
CLS
gene
rate
s pa
rallel pl
ate capa
citor. An
electri
c
circul
ar current is induced in t
he metalli
c ri
ng
whe
n
pla
c
ed
in a time varying ma
gn
etic field. Th
us, SR i
s
a
resonato
r
wh
ich
coupl
es t
o
a
perp
endi
cul
a
r magneti
c
field and can be
cha
r
a
c
teri
ze
d by the effective ca
p
a
cit
ance of the g
ap
and effective
indu
ctan
ce of
the loop defi
ned by t
he m
e
tallic ri
ng. T
he CLS int
r
o
duces a
n
extra
cap
a
cita
nce [
25]. We
can t
une
seve
ral
para
m
eters
o
f
SR like
size
of SR,
spa
c
i
ng b
e
twe
en t
h
e
ring
s, si
ze of
the split [15
], thickne
s
s of su
b
s
trate,
length, width
and hei
ght
of CLS an
d gap
betwe
en two
CLS to cont
ro
l magnetic a
n
d
electri
c
resonan
ce.
3. Simulation Method
olo
g
y
of LHM in Wav
e
guide
We
put the
p
r
opo
se
d L
H
M
unit
cell i
n
a
wave
guid
e
a
s
sho
w
n
in
Fi
gure
2
and
simulate
the metamat
e
rial st
ru
cture. Perfect ele
c
tri
c
co
ndu
ct
or (PEC) bo
u
ndary conditi
ons a
r
e a
s
sig
ned
on the
z-fa
ce
s of the
unit
cell. Th
e pe
rfect ma
gneti
c
con
d
u
c
tor (P
MC) bou
nda
ry
conditio
n
s are
applie
d o
n
th
e y-fa
ce
s of
the u
n
it
cell. T
he two
wave
ports 1
an
d 2
are a
s
sign
ed
alon
g e
a
ch
of
the sub
s
trate
line on the x-face
s form –x
to x direction.
Figure 2. Boundari
e
s a
nd e
x
citations in L
H
M unit cell
The m
e
tama
terial u
n
it ce
ll is mo
delle
d in
HFSS
and all
o
cate
d suitable
b
ound
ary
con
d
ition
s
for far-field
calculation to g
e
t
con
s
i
s
tent re
sults. After m
ode
lin
g, the a
daptive me
sh
ing
is appli
ed to probl
em dom
ain. The ada
ptive meshin
g algorith
m
lo
oks for the la
rge
s
t gra
d
ien
t
s in
the E field or
error a
nd the
n
su
bdivide
s
the mesh
in t
hese area
s o
r
re
gion
s. Fo
r the simul
a
tio
n
,
25 pa
sse
s
ha
ve been ta
ke
n with a
n
e
r
ror tole
ran
c
e
of 2%. HFSS
com
pares th
e S-Paramet
e
rs
from the
cu
rrent me
sh to t
he results of t
he p
r
e
c
edin
g
mesh. With
e
a
ch ada
ptive pass,
maxim
u
m
30% refine
m
ent per
pa
ss is achieved
in soluti
o
n
s.
Once the u
s
er defin
ed e
r
ror tol
e
ra
nce
is
attained, then
the solution
get conve
r
ge
d and the cu
rrent or p
r
e
c
e
d
ing me
sh is
use
d
to execute
a freque
ncy swee
p.
The effective perme
abili
ty (
)
and e
ffective permittivity (
) of an equivalent
metamateri
al
ca
n be det
ermin
ed usi
n
g Nicol
s
o
n
-R
oss-Wei
r
ap
proa
ch [20].
This metho
d
is
applie
d to ret
r
ieve effectiv
e materi
al pa
ramete
rs
and
MATLAB co
de is
written t
o
impleme
n
t the
followin
g
equ
ations:
(1)
(2)
The com
p
le
x
t
e
rms,
and
symbolize the summ
ation and di
fference of S-
para
m
eters a
nd are e
s
tim
a
ted usin
g Equation
s
(1
) and (2
) by exporting valu
e
s
of transmi
ssion
coeffici
ent (
) and refle
c
tion
coefficie
n
t (
).
∗
√
√
(3)
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02-4
046
TELKOM
NI
KA
Vol. 15, No. 3, September 20
15 : 497 – 503
500
Whe
r
e
is
complex wave number
,
is
angul
ar fre
q
u
ency,
is wave numb
e
r in f
r
ee
spa
c
e
(
=
/
,
is effective permeability,
is effective
permittivity of equivalent m
e
tamateri
al a
n
d
is spe
ed of light.
(4)
(5)
is
thic
knes
s
of s
u
bs
trate.
By putting the Equatio
n
s
(1
) a
nd (2
) in eq
ns. (4) an
d (5
),
we
can g
e
t effective
perm
eability (
)
and effe
ctive permittivity
(
).
4. Results a
nd discussio
n
A Full wave
simulation
of the p
r
op
osed
LHM
unit
cell
in a
wave
gui
de i
s
pe
rform
ed
with
electroma
gne
tic solver. Af
ter ap
plying
approp
ri
ate
boun
dary
co
ndition
s an
d
excitation
s,
as
mentione
d in
Section
3, the mo
del i
s
then exe
c
ut
e
d
to verify its meta
materi
al features.
Th
e
transmissio
n
and
reflectio
n
cha
r
a
c
teri
sti
cs i
n
term
s
of S-pa
ramete
rs a
r
e pl
otted for the
pro
p
o
s
ed
LHM st
ru
cture for validatin
g the perfo
rm
ance.
4.1. Reflec
ti
on Coe
fficie
n
t (
) and Tra
n
smission c
o
efficient (
)
Figure 3
shows reflect
i
on coefficie
n
t (
) a
nd
transmissio
n
coeffici
ent
(
)
characteri
stics of
LHM
w.
r.t. frequency. It can be
not
iced from the si
mulated
resul
t
s that there
i
s
stron
g
refle
c
tion of
-2
3.7
d
B
at 1.84
GHz. Thi
s
sig
n
ifies th
at p
r
op
o
s
ed
L
H
M
re
sonate
s
at
1.8
4
GHz. Re
so
na
nce
occu
rs at
the freq
uen
cy close to
the
frequ
en
cy lo
cation
wh
ere
the loga
rithmi
c
transmissio
n has a mi
nimu
m value. The
first tran
smi
s
sion mi
nimu
m for the pro
posed st
ru
ctu
r
e is
-37.8 dB at 2.12G
Hz.
Figure 3. Tra
n
smi
ssi
on co
efficient (
) an
d reflectio
n
coefficient
(
)
Figure 4. Rea
l
and imagin
a
r
y part of refl
ection
coeffici
ent (
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
son
a
n
c
e Chara
c
te
risti
c
s and Effective
Param
e
ters
of New L
e
ft Hand Metam
a
terial (Raj
ni)
501
The dip in the phase of
is observed for the desi
gne
d
LHM structu
r
e and the neg
ative
refra
c
tion re
g
i
on is identified. Real and
imaginary parts of
are depi
cted in Figure 4 and
Figure 5 re
spectively. Th
ese valu
es
are u
s
e
d
to evaluate th
e negative
chara
c
te
risti
c
s of
perm
eability and pe
rmittivity for the proposed L
H
M structu
r
e.
Figure 5. Rea
l
and imagin
a
r
y part of tran
smissio
n
co
efficient
The mag
n
itu
de and p
h
a
s
e of
and
a
r
e shown in
Figure 6 a
nd Figu
re 7
respe
c
tively. The reversal of phase
of
and
at particula
r frequen
cy validates the
metamateri
al behavio
ur of SR.
Figure 6. Magnitude a
nd p
hase of reflection coeffici
en
t
)
Figure 7. Magnitude a
nd p
hase
of transmissi
on coefficient (
)
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02-4
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TELKOM
NI
KA
Vol. 15, No. 3, September 20
15 : 497 – 503
502
4.2. Effectiv
e
Permeability
and Effecti
v
e
Permitti
v
i
t
y
Figure 8
dep
icts th
e extracted
re
al p
a
rt
of p
e
rm
e
ability and
p
e
rmittivity. Red
curve
sho
w
s real p
a
rt of perm
e
a
b
ility. Green line pre
s
e
n
ts
t
he real p
a
rt o
f
permittivity.
To evaluate t
he
effective permeability and effective permittivity
, fir
s
t MATLAB code is generated. T
hen by
exporting
the
values of
and
obtaine
d from Fi
gu
re 4 a
nd Fig
u
re
5 in MA
TLAB and
impleme
n
tation
of
Equati
ons (4) and (5),
we evalu
a
te effective perm
eability,
and effe
ctive
permittivity,
to verify the metamateri
al propertie
s
.
1.
3
1.
5
1.
7
1.
9
2.
1
2.
3
2.
5
2.
7
2.
9
3.
1
3.
3
3.
5
3.
7
3.
9
4.
1
4.
2
4.
2
-
300
-
250
-
200
-
150
-
100
-5
0
0
50
100
150
200
FREQUENCY
(GHz
)
P
e
rm
e
a
b
i
li
t
y
(m
u
)
/
P
e
r
m
i
t
ti
v
i
ty
(
e
p
s
)
Ne
g
a
ti
v
e
re
fr
a
c
ti
o
n
r
e
g
i
o
n
Re
(
m
u
)
R
e
(
eps
)
Figure 8. Permittivity, Permeability and
Negative ref
r
action regio
n
of LHM Unit
cell
Acco
rdi
ng to
the theory of
metamateri
al
s, the real part of
and
must be negative for
the propo
se
d
LHM
struct
ure. It can b
e
ob
se
rved
f
r
om the
plot
that the ne
gative value
s
of
permittivity and pe
rme
abil
i
ty are a
c
hie
v
ed for th
e
prop
osed structure.
Th
e real part of
the
permittivity is app
are
n
tly negative from 1.95-
3.2
8
GHz. The
s
e are the
electri
c
pla
s
ma
freque
nci
e
s for
pro
p
o
s
ed
LHM
structu
r
e. The
ne
gati
v
e real
pa
rt o
f
the pe
rme
a
b
ility lies
bet
wee
n
2.88-3.9
8
G
H
z. Th
ese a
r
e
mag
netic pl
asma
fre
que
ncie
s fo
r th
e
propo
sed
L
H
M. Th
e n
e
g
a
tive
band of refra
c
tive index for the pro
p
o
s
e
d
LHM exi
s
ts at overlapp
e
d
regio
n
of m
agneti
c
pla
s
ma
freque
nci
e
s a
nd elect
r
ical plasm
a
frequ
ency sh
own
in Figure 8. F
o
r the pro
p
o
s
ed stru
ctu
r
e, the
perm
eability and p
e
rmittivity simultane
ously b
e
com
e
neg
ative for a fre
que
ncy range
of 2
.
88
GHz to 3.28
GHz. He
nce it is
marked th
at the pro
p
o
s
ed L
H
M exhi
bits ne
gative refra
c
tion in
2
.
88
GHz to 3.28 GHz freq
uen
cy rang
e.
5. Conclusio
n
This
wo
rk
su
ccessfully de
monst
r
ate
s
th
e me
tamate
ri
al pro
pertie
s
of prop
osed
LHM u
n
it
cell. Thi
s
ne
w st
ru
cture
e
x
hibits do
ubl
e neg
ativ
e propertie
s
from
2.88 G
H
z to
3.28 G
H
z.
Hence
negative ref
r
action i
s
ob
serve
d
with
this LHM
in
this freque
n
c
y rang
e. This work ca
n be
extended to
get pe
riodi
c
structu
r
e of thi
s
unit
cell
an
d ca
n b
e
u
s
e
d
as supe
rst
r
ate for mi
cro
s
trip
antenn
a to
enha
nce its
perfo
rman
ce
ch
ara
c
te
rist
i
cs. T
h
is stru
cture
can
al
so
be u
s
e
d
to
con
s
tru
c
t ne
w functio
nal d
e
vice
s su
ch a
s
ele
c
trom
ag
netic filters, a
n
tenna
s an
d waveg
u
ide
s
.
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Param
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