Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
5, No. 6, Decem
ber
2015, pp. 1363~
1
371
I
S
SN
: 208
8-8
7
0
8
1
363
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
Modeling of Split Ring Resonators
Loaded Micros
trip Line with
Different Orientations
Rajni*,
Gurw
inder Sin
g
h
*
*, Anupm
a
Marwaha***
*
,
**
Departmen
t
of Electronics
& Comm
unication Engin
eering
,
Shaheed Bh
ag
at
Singh State Technical Campus,
Ferozepur, Punjab, Ind
i
a
***
Departm
e
nt
of El
ectron
i
cs
&
Com
m
unication
Engin
eerin
g
,
Sant Longowal Ins
titut
e
of
Engg
.
&
Technolog
y
,
Longowal (Sang
r
ur), Punjab
, Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 2, 2015
Rev
i
sed
Au
g
20
, 20
15
Accepte
d
Se
p 4, 2015
This
paper
pres
ents
the d
i
ffer
e
nt cir
c
uit
appro
aches
of
the
el
ectr
i
c
and
m
a
gnetic in
ter
a
c
tion of Single Split Ring Resona
tor (SRR) loade
d
m
i
crostrip
line
.
W
e
lo
aded
the m
i
crostr
ip li
ne with
p
l
an
ar s
quare split ring
r
e
sonator in
differen
t
configurations and
orient
ations. The
modeling behavior
of
m
e
tam
a
teri
als-b
a
sed m
i
crostrip
lines lo
aded wit
h
single and
two-m
i
rrored
split ring resonat
o
rs is anal
y
z
ed num
erica
l
l
y
in t
w
o orientations
(with gap of
S
RR paral
l
el
an
d perpend
i
cul
a
r
to th
e
line)
.
The full wave simulations
ar
e
perform
ed for t
h
e single
and
t
w
o-m
i
rrored split ring
resonato
rs loade
d
microstrip inside a waveguide
with
‘High Frequency
Stru
ctur
e Simulator’
software.
The equivalent
circu
i
t
param
e
t
e
rs
ar
e
obtain
e
d for
the single split
ring resonator
l
o
aded with m
i
cr
ostrip lin
e wi
th
the gap p
a
ral
l
el
and near
to
the lin
e from
transm
ission line theor
y
tha
t
m
a
ke use of just the resonanc
e
frequency
and minimum
of
th
e refl
ect
ion co
e
ffici
ent.
The simulation of
differen
t
orient
at
ions of split ring resona
tor gives bett
er refle
c
t
i
on coeffi
cien
t
and wider
frequ
ency
.
Keyword:
Meta
m
a
terials (MTM)
Micro
s
trip lin
e
Sp
lit ring
reson
a
tor (SRR)
Copyright ©
201
5 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
:
Raj
n
i,
Depa
rt
em
ent
of El
ect
r
oni
cs
a
n
d
C
o
m
m
uni
cat
i
on E
n
gi
nee
r
i
n
g
,
Sha
h
eed Bha
g
at Singh
St
ate Technical
Campus
,
Mo
g
a
Ro
ad
, Fer
o
zepu
r
(1
5200
4)
,
Punj
ab
, I
n
d
i
a.
Em
a
il: raj
n
i_
c1
23@yaho
o.co.in
1.
INTRODUCTION
Th
e
d
e
v
e
lop
m
en
t
o
f
m
e
ta
m
a
t
e
rials op
en
ed a n
e
w
po
ssib
ility for
d
e
sign
ers to
create a
nov
el stru
cture
wi
t
h
u
nus
ual
p
r
o
p
ert
i
e
s o
r
en
hance
d
pe
rf
o
r
m
a
nce [1]
,
[2
]. Meta
m
a
terial
s are artificiall
y in
v
e
n
t
ed
m
a
terials
t
h
at
sh
ow
pr
o
p
e
rt
i
e
s not
det
e
c
t
ed i
n
n
a
t
u
ral
l
y
occu
rri
ng m
a
t
e
ri
al
s and
ha
ve
negat
i
v
e re
fra
ct
i
on i
n
de
x.
O
n
e o
f
t
h
e m
o
st
im
port
a
nt
co
nt
ri
b
u
t
i
ons t
o
t
h
i
s
t
o
p
i
c was m
a
de in 1
9
68
by
V
G
Vesel
a
g
o
wh
o sai
d
t
h
at
m
a
t
e
ri
al
s
with
bo
th
n
e
g
a
tiv
e p
e
rm
itt
iv
it
y an
d
p
e
rm
eab
ilit
y is th
eo
re
tically p
o
ssib
l
e [3
]. In
199
9, Joh
n
Pend
ry i
d
entified
a practical way
to m
a
ke left-hande
d m
e
ta
m
a
terials (L
HM
) wh
ich
d
i
d
no
t fo
llow
t
h
e right
h
a
nd
ru
le
[4
].
Later
th
en
,
Sm
i
t
h
and
h
i
s co
lleag
ues d
e
m
o
n
s
trated
m
e
ta
material
s to
sho
w
n
e
gativ
e p
e
rm
itt
iv
ity an
d
p
e
rm
eab
ilit
y
sim
u
l
t
a
neousl
y
and ca
rri
ed
o
u
t
m
i
crowave e
xpe
ri
m
e
nt
s t
o
test
i
t
s
unus
ual
pr
o
p
ert
i
e
s i
n
2
0
0
0
.
In
20
0
1
,
Sm
i
t
h
et al sh
o
w
ed
neg
a
tiv
e refractio
n
ex
p
e
rim
e
n
t
ally, u
s
in
g
a meta
m
a
terials w
ith
rep
eated
u
n
it cel
ls o
f
sp
lit-ri
ng
reso
nat
o
rs
(SR
R
) an
d c
o
ppe
r
st
ri
ps
[
5
]
-
[
7
]
.
In
2
0
0
2
,
M
a
r
q
ues et
al
i
n
ves
t
i
g
at
ed
a m
odi
fi
ed
versi
o
n o
f
SR
R
i
.
e. b
r
oadsi
d
e c
o
u
p
l
e
d
(B
C
-
S
R
R
)
t
o
a
v
oi
d
b
i
ani
s
ot
r
opy
a
n
d s
h
owe
d
c
o
m
p
arat
i
v
e
anal
y
s
i
s
of
t
h
e c
o
n
v
e
n
t
i
onal
(o
r ed
ge-c
o
upl
ed) SR
R
a
nd
B
C
-
SR
R
wi
t
h
pri
n
t
e
d m
e
t
a
ll
i
c
ri
ngs o
f
t
h
e B
C
-
SR
R
on
bot
h si
des
of
t
h
e
di
el
ect
ri
c subs
t
r
at
e [8]
.
In
2
0
0
5
, J
u
an
Do
m
i
ngo B
aena
et
al
prop
ose
d
new ap
pr
oac
h
for
desi
g
n
i
n
g
pl
anar
meta
m
a
terial s
t
ru
ctures
with SRR and
com
p
le
men
t
ary sp
lit-ring
reson
a
tors (CSRR
s
) coup
led
t
o
p
l
an
ar
transm
ission lines and a
n
alyzed the stop band/p
ass
ban
d
ch
aracteri
s
tics o
f
th
e
SRR/CSRR l
o
ad
ed
tran
sm
issio
n
lin
es [9
]. Bilo
tti et al, in
200
7 d
i
scusse
d
m
u
ltip
le sp
lit ring reson
a
t
o
rs
(M
SRR) with
m
u
ltip
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1363 –
1371
1
364
rings a
n
d spi
r
a
l
ring (SR) to increas
e
t
h
e m
i
ni
at
uri
z
e
d
rat
e
and
co
ncl
u
de
d
that increase
in nu
m
b
er
of
turn
s and
r
i
ng
s of
SRs an
d
MSRRs
r
e
sp
ectiv
ely,
i
n
cr
eases t
h
e sat
u
r
a
t
i
on o
f
t
h
e re
s
ona
nt
f
r
eq
ue
nc
y
[10]
. B
o
ja
ni
c
et
al,
in
20
11
,
p
r
op
osed
m
u
ltib
an
d
d
e
lay lin
e with b
r
o
a
dsid
e coup
led
an
d
th
e si
n
g
l
e SRRs and
exh
i
b
its two left-
h
a
nd
ed
b
a
nd
s th
at can
b
e
sh
ift
e
d
b
y
twisting
th
e sp
lit rin
g
s fo
r certain
ang
l
e o
r
b
y
ch
ang
i
n
g
t
h
eir leng
ths [11
]
.
I
n
201
2, Si
n
d
reu
et al
sugg
ested
th
e use
of
SRR i
n
co
upled
tran
sm
issi
o
n
lin
e as
c
o
m
p
ared to m
i
crowa
v
e
com
pone
nt
s, t
o
achi
e
ve
bet
t
e
r per
f
o
rm
ance param
e
t
e
rs [12
]
. Naq
u
i
et
al
in 2
0
1
3
propo
sed
a
m
o
d
e
l with
the
electro
m
a
g
n
e
tic p
r
op
erties of transm
issio
n
lin
es lo
ad
ed
wi
t
h
SR
R
s
a
n
d C
S
R
R
s
ra
n
dom
l
y
ori
e
nt
ed a
n
d
reso
nat
o
rs
are
al
i
gne
d i
n
a
no
n
o
r
t
h
og
o
n
a
l
di
rect
i
o
n t
o
t
h
e l
i
n
e
axi
s
, c
r
oss
-
pol
a
r
i
zat
i
o
n
ef
fect
s a
r
i
s
es[1
3]
.
Youn
esiraad
et al in
2
014
an
alysed
reson
a
t
o
r an
tenn
a fo
r m
u
lti-b
a
n
d
app
licatio
n
with
Finite Ele
m
en
t M
e
th
od
and
Fi
ni
t
e
I
n
t
e
gral
Tec
h
ni
q
u
e
[1
4]
. I
n
20
1
4
,
Kul
d
eep
K
u
m
a
r Para
sha
r
p
r
op
ose
d
a
new
pat
c
h a
n
t
e
n
n
a
wi
t
h
co
m
p
act size a
n
d
larg
e b
a
ndwid
th
b
y
u
s
ing si
m
p
le in
set f
eed technique [15]. In 2014
,
Boja
nic et al presente
d
an en
hance
d
e
qui
val
e
nt
ci
rcu
i
t
appr
oach f
o
r
t
h
e
m
a
gnet
i
c
/el
ect
ri
c i
n
t
e
ract
i
on o
f
SR
R
s
wi
t
h
pri
n
t
e
d l
i
n
es an
d
ex
tract th
e d
i
fferen
t
p
a
ram
e
ters
o
f
m
i
cro
s
tri
p
lin
e wi
t
h
pa
r
a
l
l
e
l
and per
p
e
ndi
c
u
l
a
r ga
p
t
o
l
i
n
e
[
1
6]
.
Th
e aim o
f
p
r
esen
t work
is to
d
e
sign
a
micro
s
tri
p
lin
e lo
ad
ed
with
meta
m
a
terials a
n
d
ex
am
in
e
shi
f
t
i
n
g
of
res
ona
nt
fre
qu
enc
y
wi
t
h
di
ff
ere
n
t
o
r
i
e
nt
at
i
o
ns
o
f
si
n
g
l
e
a
n
d
t
w
o m
i
rro
red
SR
R
s
. T
h
e
out
l
i
n
e o
f
p
a
p
e
r is as
follo
ws: Section 1
g
i
v
e
s t
h
e brief literatu
re
rev
i
ew of th
e
work don
e in
th
e area. Section
2
descri
bes t
h
e
pr
o
pose
d
SR
R
s
l
o
ade
d
m
i
cr
ost
r
i
p
l
i
n
e m
odel
wi
t
h
di
ffe
r
e
nt
ori
e
nt
at
i
o
n
s
. Sect
i
o
n 3
p
r
esent
s
resul
t
s
a
n
d
di
scussi
o
n
.
Sect
i
o
n
4
gi
ves
t
h
e c
oncl
u
si
o
n
of
t
h
e pa
per
.
2.
PROP
OSE
D
SR
R
LO
ADE
D MIC
R
O
-
ST
RIP
LI
NE M
O
DEL
In t
h
e
pr
o
pose
d
m
odel
,
a conve
nt
i
o
nal
m
i
crost
r
i
p
l
i
n
e i
s
l
o
ade
d
wi
t
h
pl
a
n
ar s
qua
re SR
R
s
wi
t
h
t
h
e
g
a
p p
a
rallel to
th
e lin
e.
Th
e sq
u
a
re sh
ap
e SRRs is cou
p
l
ed
t
o
m
i
crost
r
i
p
l
i
ne by
pl
aci
ng
it at distance‘s
’
, in t
h
e
sam
e
pl
ane. Fi
gu
re
1 sh
o
w
s l
a
y
out
o
f
SR
R
cou
p
l
e
d t
o
m
i
crost
r
/
i
p
l
i
n
e i
n
t
h
e sam
e
pl
ane wi
t
h
ga
p
paral
l
el
t
o
t
h
e l
i
n
e. Thi
s
cou
p
l
e
d l
i
n
e i
s
m
odel
e
d
on
R
oge
rs R
O
30
1
0
su
bst
r
at
e
of
t
h
i
c
kne
ss (
h
)
1.
27 m
m
, di
elect
ri
c
p
e
rm
itt
iv
ity
ε
r
=10
.
2 a
nd l
o
s
s
t
a
nge
nt
0.
03
5. T
h
e di
m
e
nsi
ons
of SR
R
c
o
upl
e
d
t
o
rect
a
n
gul
a
r
m
i
crost
r
i
p
l
i
n
e
are
gi
ve
n i
n
Ta
bl
e 1
.
Fi
gu
re
1.
Lay
o
u
t
o
f
SR
R
l
o
a
d
ed m
i
crost
r
i
p
l
i
ne
Fi
gu
re
2.
Eq
ui
val
e
nt
ci
rc
ui
t
o
f
SR
R
l
o
ade
d
micro
s
trip
lin
e
Tabl
e 1. Di
m
e
nsi
o
ns of
SR
R
l
o
ade
d
m
i
crost
r
i
p
l
i
n
e
S
. No
Para
m
e
ters
Nam
e
of param
eter
Representation
Dim
e
nsions(mm
)
1
W
i
dth of
m
i
cr
ostr
ip line
W
l
1.
2
2
L
e
ngth of SRR
L
r
3.
0
3
W
i
dth of SRR
W
r
0.
2
4
Gap of split
Lg
0.5
5
Gap between
m
i
crostr
ip line &
SRR
S
0.
1
Micro
s
trip lin
es lo
ad
ed
with
SRRs
fo
r
di
f
f
e
r
ent
c
o
n
f
i
g
ur
at
i
ons a
r
e e
x
am
ined
. It
has
bee
n
f
o
un
d t
h
at
di
ffe
re
nt
con
f
i
g
u
r
at
i
o
ns o
f
S
R
R
l
o
aded m
i
crost
r
i
p
l
i
n
e can
be
m
odel
e
d
b
y
t
h
e sam
e
ci
rcui
t
t
opol
ogy
,
b
u
t
wi
t
h
diffe
re
nt values of the circ
uit
param
e
ters. For each topol
ogy,
resonance fre
que
n
c
y
and the m
i
nim
u
m
refl
ect
i
o
n f
r
e
q
uency
ca
n
be
o
b
t
a
i
n
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Mod
e
lin
g o
f
Split Rin
g
Resona
to
rs Lo
ad
ed
Micro
s
tr
ip
Line with
Different Orien
t
a
tio
n
s
(Ra
j
n
i
)
1
365
1)
Sin
g
l
e SRR load
ed
m
i
cro
s
trip
lin
e with
th
e g
a
p
p
a
rallel t
o
th
e lin
e (i) gap
n
e
ar o
r
ien
t
atio
n
(ii)
gap
fa
r ori
e
nt
at
i
on
2)
Sin
g
l
e
SRR load
ed m
i
cro
s
trip
lin
e
with
t
h
e
g
a
p p
e
rp
end
i
cular to
t
h
e lin
e
3)
Two
mirro
red
SRRs with
th
e g
a
p
p
a
rallel to
th
e lin
e (i
)
B
o
t
h
ga
ps ne
ar ori
e
nt
at
i
on
(i
i
)
B
o
t
h
gap
s
fa
r ori
e
nt
at
i
on
4)
Two
m
i
rro
red
SRRs with th
e
g
a
p p
e
rp
end
i
cular to
t
h
e lin
e
5)
Two
SRRs
with
th
e g
a
p
p
a
rallel to
th
e lin
e (i
)
o
n
e
g
a
p
n
ear
an
d on
e
far ori
e
n
t
atio
n
6)
Tw
o casca
ded
SR
R
s
wi
t
h
t
h
e ga
p
paral
l
el
t
o
th
e
lin
e(i)
g
a
p
n
ear orien
t
atio
n
(ii) g
a
p
far
ori
e
nt
at
i
on
7)
Tw
o casca
ded
SR
R
s
wi
t
h
t
h
e
ga
p
per
p
e
ndi
c
u
l
a
r t
o
t
h
e
l
i
n
e
8)
Doub
le SRR load
ed m
i
cro
s
trip
lin
e
with
t
h
e
g
a
p p
a
rallel to
th
e lin
e
2.
1. SR
R
L
o
aded
Micros
t
rip Line with
the Gap P
a
r
a
llel to the Line
Micro
s
trip lin
e lo
ad
ed
with SRRs
with
g
a
p
s
p
a
rallel to
th
e
lin
e is shown i
n
Fi
g
u
re
3
and 4
.
Figure
3
depicts the m
i
crost
r
ip line l
o
ade
d
with
sin
g
l
e SRR
with
g
a
p
p
a
rallel to
th
e lin
e an
d
g
a
p
is n
e
ar to
th
e
micro
s
trip
lin
e. In
Fi
g
u
re
4
the g
a
p
o
f
SRR l
o
ad
ed
m
i
cro
s
trip
lin
e is
p
a
rallel an
d far
fro
m
th
e lin
e.
(a)
(b
)
Fig
u
re
3
.
Micro
s
trip lin
e l
o
aded
with
SRRs
with
g
a
p
p
a
rallel to
th
e li
n
e
.
(a)
On
e SRR
with
g
a
p
n
e
ar th
e lin
e
(b)
On
e SRR
with
th
e g
a
p
far fro
m
th
e lin
e
To extract the
pa
ram
e
ters L and C
of the
transm
ission l
i
ne in Figure
2, ta
king i
n
to
account t
h
e
coupling
between t
h
e line
and
the
nearest
S
RR arm
,
induc
tance is m
odel
e
d as
if t
h
ere
were
two inductances..
On
e is coup
led
with
th
e tran
sm
issio
n
lin
e o
r
seco
nd
is
i
s
o
l
ated
tran
sm
issio
n
lin
e wit
h
leng
th equ
a
l
to
th
e
rem
a
in
in
g
un
co
up
led p
a
rt of
th
e SRR leng
th
. Fi
g
u
re
3
sh
ows th
e equ
i
v
a
l
e
n
t
circu
it
o
f
micro
s
trip
lin
e co
up
led
t
o
SR
R
whe
r
e
Ls an
d C
s
i
s
ind
u
ct
ance a
n
d capaci
t
a
nce o
f
SR
R
respect
i
v
el
y
and L an
d
C
i
s
i
nduct
a
nc
e an
d
capacitance of
m
i
crostrip
line respectively. The G
1
and G
2
are t
w
o
po
r
t
s and M
i
is
mutual inducta
n
ce. The
capacitance C
s
is ob
tain
ed from
th
e
SRR res
ona
nce
fre
quency
as fo
llows:
√
(1)
Whe
r
e
res
ona
nce fre
quency is
also calc
u
lated as:
(2)
The c
o
upli
n
g c
o
efficient
is then
ob
tain
ed as
a fu
n
c
tion of
.
,
the re
sona
nce
freque
ncy
, and
th
e lin
e
p
a
ram
e
ters L and
C as fo
llo
ws:
1
1
(3)
Th
e term
m
u
tu
al ind
u
c
tan
c
e
is also affecte
d
by va
riation
of the
distance ‘S’
betwee
n the
micro
s
trip lin
e an
d sp
lit ri
n
g
reson
a
tor
(SRR). Where
co
rrespon
d t
o
t
h
e
circu
it
with one cell an
d
. T
h
ese c
o
effic
i
ents are
given
by:
2
(4)
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I
S
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:
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088
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08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1363 –
1371
1
366
Whe
r
e
is the c
h
aracteristic a
d
mittance
of th
e micro
s
trip lin
e and
:
;
(5)
2.2.
Two Mirrored SRRs
L
o
aded
Micr
ostr
ip Line w
i
th
t
h
e G
a
p
Par
a
llel to
the
Line
Th
e m
i
cro
s
trip lin
e lo
ad
ed
with
two
m
i
rro
red
SRRs with
th
e g
a
p
p
a
rall
el to
th
e lin
e i
s
sh
own
in
Fi
gu
re 4
.
T
h
e
gap
of t
w
o m
i
rro
red
SR
R
s
i
s
near a
n
d fa
r fr
om
t
h
e
m
i
cros
t
r
i
p
l
i
n
e as i
n
Fi
gu
re 4
(
a
)
an
d 4
(
b
)
respectively.
(a)
(b
)
Fig
u
re
4
.
Micro
s
trip lin
e l
o
aded
with
SRRs
with
g
a
p p
a
rallel to
th
e li
n
e
.
(a) Two SRRs
with
g
a
p n
e
ar t
h
e lin
e
(b) Two
SRRs
with
th
e g
a
p
far fro
m
th
e lin
e.
2.3.
SRRs L
oaded
Micros
t
rip Line with
the Gap Per
p
endicular
to the
Line
Th
e m
i
cro
s
trip lin
e lo
ad
ed
w
i
t
h
si
n
g
l
e
SR
R
an
d t
w
o m
i
rrore
d SR
R
s
wi
t
h
t
h
e
ga
p
pe
rp
endi
c
u
l
a
r t
o
th
e m
i
cro
s
trip
l
i
n
e
sh
own
in the Figu
re 5.
(a)
(b
)
(c)
Fig
u
re
5
.
Micro
s
trip lin
e l
o
aded
with
SRRs (a) Si
n
g
l
e SRR with
g
a
p
p
e
rp
en
d
i
cu
lar
t
o
th
e lin
e
(b
) Two
SRRs
m
i
rrore
d
wi
t
h
gap
pe
r
p
en
di
cu
l
a
r t
o
t
h
e l
i
n
e
(
c
) SR
R
s
wi
t
h
o
n
e
gap
pa
ral
l
e
l
and
an
ot
he
r
pe
rpe
n
di
cul
a
r t
o
t
h
e
lin
e
2.4. SRRs
L
oaded Micros
t
rip
Line
with
the Gap Pa
ra
llel to
the Line
Th
e m
i
cro
s
trip lin
e
lo
ad
ed
wi
th
two
SRRs with
th
e g
a
p
parallel to
th
e lin
e b
u
t
o
n
e
SRR g
a
p
h
a
s
n
e
ar
to
th
e line an
d
o
t
h
e
r
h
a
s
far
fro
m
th
e lin
e as
d
e
p
i
cted in th
e
Fig
u
re
5
(
c).
2.
5. T
w
o
C
a
sc
aded
S
RRs
L
o
aded
Mi
cr
ostr
i
p
L
i
ne w
i
th
t
h
e G
a
p
Par
a
l
l
e
l
to
the
L
i
ne
Th
e m
i
cro
s
trip lin
e is lo
ad
ed with
two
cascad
ed S
RRs
with
th
e
g
a
p
p
a
rallel to
th
e line as seen in
Figure 4. The
distance‘d’ bet
w
een t
h
e two
cascade
d
SRRs
i
s
0.5m
m
.
The gap
of t
w
o c
a
scade
d
SR
R
s
near
t
o
th
e micro
s
trip lin
e as an
d
far fro
m
th
e
micro
s
trip
lin
e is sh
own
in th
e Figu
r
e
6(
a)
an
d
Figu
re 6
(
b)
respectively.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Mod
e
lin
g o
f
Split Rin
g
Resona
to
rs Lo
ad
ed
Micro
s
tr
ip
Line with
Different Orien
t
a
tio
n
s
(Ra
j
n
i
)
1
367
(a)
(b
)
(c)
Fig
.
6
Micro
s
trip
lin
e load
ed
with
two
cascad
ed SRRs
with. (a) Two
SRR
s
with g
a
p
p
a
rallel an
d
n
ear the lin
e
(b) Two
SRRs
with
th
e g
a
p
p
a
rallel an
d far
fro
m
th
e lin
e (c)
g
a
p p
e
rp
end
i
cular to
t
h
e lin
e
2.
6. T
w
o
C
a
sc
aded
S
RRs
L
o
aded
Mi
cr
ostr
i
p
L
i
ne with
the Gap
Perpe
ndicular
to the Line
Th
e m
i
cro
s
trip
lin
e is lo
ad
ed
with
two
cascad
e
d
SRRs
with th
e g
a
p
p
e
rp
en
d
i
cu
lar to
th
e
lin
e as seen
in
Figur
e
6
(
c)
.
2.7.
Double
SRR Loaded Microstrip Line
w
i
th the
G
a
p
Par
a
llel to
the
Line
Micro
s
trip lin
e lo
ad
ed
with
d
oub
le
SRR
with
th
e g
a
p
p
a
rallel to
the lin
e is seen in
Fi
g
u
re
7
.
It
d
e
p
i
cts th
e m
i
cro
s
t
r
ip
lin
e lo
ad
ed
with
do
ub
l
e
SRR with
g
a
p
p
a
rallel to
the lin
e and
bo
th sp
lits are opp
osite to
each othe
r.
Fig
u
re
7
.
Micro
s
trip lin
e l
o
aded
Doub
le SR
R with
g
a
p
p
a
rallel to
th
e lin
e
3.
RESULTS
A
N
D
DI
SC
US
S
I
ON
Th
e SRR l
o
aded
m
i
cro
s
trip
l
i
n
e
is sim
u
late
d
in
si
de a
wa
v
e
gui
de t
o
at
t
a
i
n
t
h
e
res
o
nat
i
n
g f
r
e
que
ncy
regi
on. The Pe
rfect Electric Conductor
(PEC) boundary c
o
nditions are e
m
ployed on the z-faces
of the unit
cell. The Pe
rfe
ct Magnetic C
o
nductor
(PMC) boundary c
o
nd
itions are
used
on top a
nd bottom
y-faces of the
u
n
it cell so th
at th
e n
e
g
a
tiv
e
p
e
rm
eab
ility b
e
h
a
v
i
o
r
of SR
R wou
l
d b
e
excited
.
Th
e two
wav
e
po
rts
1
an
d 2
are
assigne
d t
o
the
bot
h side
s of
microstrip line
on t
h
e
x-faces
of wa
veguide
.
The propos
e
d
s
t
ructure is simulated
with
Ans
o
ft s
o
ftware
‘
H
ig
h
F
r
eq
ue
ncy
Str
u
c
t
ure
Sim
u
lator (HF
S
S
)
’.
Fi
gu
re
8.
R
e
fl
e
c
t
i
on c
o
ef
fi
ci
ent
and Tra
n
sm
ission c
o
e
fficie
n
t
o
f
SRR lo
ad
ed m
i
cro
s
trip
lin
e with
t
h
e
g
a
p p
a
rallel and
n
ear to
t
h
e lin
e an
d far
from
th
e lin
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1363 –
1371
1
368
Fi
gu
re 8 s
h
o
w
s t
h
e refl
ect
i
o
n an
d t
r
ansm
i
ssi
on c
o
ef
fi
cient o
f
SRR lo
aded
micro
s
trip
l
i
n
e
with
th
e
gap
paral
l
e
l
t
o
t
h
e l
i
n
e.
It
sh
o
w
s t
h
at
res
o
na
nt
f
r
e
que
ncy
i
s
shi
f
t
e
d t
o
t
h
e
ri
g
h
t
as t
h
e
ga
p
of
SR
R
i
s
ch
ange
s
fro
m
n
ear to the micro
s
trip line and
far
fro
m
lin
e.
Fi
gu
re
9.
R
e
fl
e
c
t
i
on c
o
ef
fi
ci
ent
a
n
d T
r
an
s
m
is
s
i
o
n
co
ef
f
i
c
i
en
t
of
t
w
o m
i
rrore
d
SR
R
s
l
o
a
d
ed
micro
s
trip
lin
e
with
th
e g
a
p
p
a
rallel an
d
n
e
ar
to
th
e line an
d
far
fro
m
th
e line
Fi
gu
re 9 sh
o
w
s t
h
e refl
ect
i
o
n
and t
r
ansm
i
ssi
on c
o
ef
fi
ci
ent
of t
w
o m
i
rror
e
d SR
R
s
l
o
ade
d
m
i
crost
r
i
p
lin
e with
t
h
e
gap
p
a
rallel to
t
h
e lin
e. It shows th
at
res
ona
nt
f
r
eq
ue
ncy
a
n
d
ret
u
r
n
l
o
s
s
get
i
n
c
r
eased
a
s
t
h
e
gap
of
SR
R
i
s
vari
e
d
fr
om
near t
o
far
fr
om
t
h
e m
i
crost
r
i
p
l
i
n
e
.
Figure
10. Re
flection c
o
efficient
and Tra
n
s
m
ission coe
ffic
i
ent
of
si
n
g
l
e
and
t
w
o m
i
rror
e
d SR
R
s
lo
ad
ed
m
i
cro
s
trip
lin
e with the g
a
p
p
e
rp
en
d
i
cu
lar t
o
th
e line
Fi
gu
re 1
0
s
h
o
w
s t
h
e re
fl
ect
i
on a
n
d t
r
ansm
i
ssi
on c
o
ef
fi
ci
ent
of si
ngl
e a
n
d t
w
o m
i
rro
red
SR
R
s
l
o
ade
d
micro
s
trip
lin
e
with
th
e
g
a
p
perp
end
i
cu
lar t
o
th
e lin
e. It
s
h
o
w
s t
h
at
t
h
e
ba
n
d
wi
dt
h a
nd
ret
u
r
n
l
o
ss i
s
i
n
cr
eased
as t
h
e
ga
p
of
SR
R
cha
nge
s
fr
om
near t
o
t
h
e m
i
crost
r
ip l
i
ne and
fa
r from
line. The
re
sonant
fre
quency is
sh
if
ted r
i
g
h
t
as th
e
g
a
p ch
anges fr
o
m
near t
o
the
far
from
the line.
Figure
11. Re
flection c
o
efficient
and Tra
n
s
m
ission coe
ffic
i
ent
o
f
dou
b
l
e SRRs lo
ad
ed
micro
s
trip
lin
e
with
th
e g
a
p
p
a
rallel an
d on
e
SRR is n
e
ar and
o
t
h
e
r is
far
fro
m
th
e lin
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Mod
e
lin
g o
f
Split Rin
g
Resona
to
rs Lo
ad
ed
Micro
s
tr
ip
Line with
Different Orien
t
a
tio
n
s
(Ra
j
n
i
)
1
369
Fi
gu
re
11 s
h
o
w
s t
h
e
refl
ect
i
on a
n
d t
r
a
n
sm
issi
on c
o
e
ffi
ci
ent
o
f
d
o
ubl
e S
R
R
s
l
o
ade
d
m
i
crost
r
i
p
l
i
n
e
with
th
e g
a
p
parallel to
th
e li
n
e
bu
t th
e g
a
p
o
f
o
n
e
SRR is n
ear to
the lin
e an
d
o
t
h
e
r
h
a
s
far fro
m
th
e li
n
e
. It
sho
w
s t
h
at
t
h
e
ba
nd
wi
dt
h i
s
i
n
crease
d
a
n
d
res
ona
nt
f
r
eq
uency
i
s
s
h
i
f
t
e
d f
r
o
m
l
o
wer
t
o
hi
ghe
r f
r
e
q
uency
regi
on
.
.
Figure
12. Re
flection c
o
efficient
and Tra
n
s
m
ission coe
ffic
i
ent
of two ca
scade
d
SRRs l
o
ade
d
micro
s
trip
lin
e
with
th
e g
a
p
p
a
rallel an
d n
e
ar
to
th
e line
Figure
12 s
h
ows t
h
e re
flection and t
r
ansm
ission co
e
fficie
n
t of t
w
o casca
ded SRRs l
o
aded m
i
crostrip
lin
e with
th
e gap
p
a
rallel an
d n
ear to
th
e li
n
e
. It sh
ow
s t
h
at th
e return
lo
ss is i
m
p
r
oved
with
a sh
ift
in
th
e
reso
na
nt
f
r
eq
u
e
ncy
i
s
f
r
o
m
l
o
wer
t
o
hi
g
h
er
r
e
gi
o
n
Figure
13. Re
flection c
o
efficient
and Tra
n
s
m
ission coe
ffic
i
ent
of two ca
scade
d
SRRs l
o
ade
d
micro
s
trip
lin
e
with
th
e g
a
p
p
a
rallel an
d far
fro
m
th
e lin
e
Figure
13 s
h
ows t
h
e re
flection and t
r
ansm
ission co
e
fficie
n
t of t
w
o casca
ded SRRs l
o
aded m
i
crostrip
lin
e with
t
h
e
gap
p
a
rallel and far fro
m
th
e lin
e.
It sh
ow
s t
h
at
t
h
e ret
u
r
n
l
o
ss an
d
ba
nd
wi
dt
h i
s
i
n
crea
se
d a
nd
reso
na
nt
f
r
eq
u
e
ncy
s
h
i
f
t
t
o
hi
ghe
r si
de.
Figure
14. Re
flection c
o
efficient
and Tra
n
s
m
ission coe
ffic
i
ent
of two ca
scade
d
SRRs l
o
ade
d
micro
s
trip
lin
e
with
th
e g
a
p
p
e
rp
end
i
cu
lar t
o
t
h
e lin
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1363 –
1371
1
370
Figure
14 s
h
ows t
h
e re
flection and t
r
ansm
ission co
e
fficie
n
t of t
w
o casca
ded SRRs l
o
aded m
i
crostrip
l
i
n
e wi
t
h
t
h
e
g
a
p
per
p
e
ndi
c
u
l
a
r t
o
t
h
e l
i
n
e
.
It
can
be
seen
t
h
at
reso
na
nt
f
r
e
que
ncy
i
s
s
h
i
f
t
e
d t
o
hi
ghe
r si
de.
Figure
15. Re
flection c
o
efficient
and Tra
n
s
m
ission coe
ffic
i
ent
of
do
ub
le
SRR lo
ad
ed
m
i
cro
s
t
r
ip
lin
e
with
th
e g
a
p
p
a
rallel to
th
e line
Fi
gu
re
15 s
h
o
w
s t
h
e
refl
ect
i
on a
n
d t
r
a
n
sm
i
ssi
on c
o
ef
fi
ci
ent
o
f
d
o
ubl
e
SR
R
l
o
ade
d
m
i
crost
r
i
p
l
i
n
e
with
th
e
g
a
p
parallel to
th
e lin
e. It sho
w
s t
h
at th
e tr
ansm
is
sion line
resonates at lower freque
ncy as com
p
ared
to
all o
t
her com
p
ared
to
all
oth
e
r
o
r
ien
t
atio
ns.
4.
CO
NCL
USI
O
N
In th
is
p
a
p
e
r, micro
s
trip lin
es l
o
ad
ed
wi
th
sing
le an
d
d
oub
le sp
lit-rin
g
reson
a
tors
in
d
i
fferent
ori
e
nt
at
i
ons ha
ve
bee
n
pr
o
pos
ed.
T
h
ese ori
e
nt
at
i
ons of
t
h
e
SRR with
respect to
th
e
line are
analy
zed
with
th
e
paral
l
e
l
ga
p ne
ar
an
d far fr
om
t
h
e
l
i
n
e, wi
t
h
t
h
e
ga
p per
p
end
i
cu
lar t
o
th
e lin
e. Th
e
p
r
in
ted
lin
e is lo
ad
ed
wit
h
a si
ngl
e SR
R
a
t
one si
de,
or
wi
t
h
t
w
o m
i
rro
red
SR
R
s
pl
ac
ed
with resp
ect to
th
e lin
e. Th
is typ
e
of structu
r
es
dem
onst
r
at
es
st
op
ba
nd
res
p
o
n
se
, b
u
t
t
h
e
pr
o
p
o
s
ed
eq
u
i
val
e
nt
ci
rc
ui
t
m
odel
can e
a
si
l
y
be ext
e
n
d
ed
t
o
st
ruct
u
r
es
wi
t
h
pass
ba
nd
res
p
o
n
se
. T
h
e i
m
pr
o
v
ed e
q
ui
va
l
e
nt
ci
rcui
t
o
f
pr
o
p
o
s
ed
SR
R
m
odel
m
oves t
h
e
reso
na
nce t
o
h
i
ghe
r f
r
eq
ue
nci
e
s. T
h
e ca
use
of
fre
q
u
ency
s
h
i
f
t
i
n
g i
s
vari
a
t
i
on i
n
capaci
t
a
nce
of
st
ri
p l
i
ne
due
t
o
SR
R
s
c
o
upl
ed i
n
va
ri
o
u
s c
o
n
f
i
g
urat
i
o
ns
.
There
f
ore,
th
e
b
a
ndw
id
th is i
n
cr
eased
al
o
ng w
ith
go
od
m
a
t
c
h
i
ng
.
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ip
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BIOGRAP
HI
ES OF
AUTH
ORS
Rajni
is
curr
entl
y As
s
o
ci
ate
P
r
of
es
s
o
r at S
B
S
S
t
ateT
echni
cal
Ca
m
pus
F
e
rozepur,
India.
S
h
e
has
completed h
e
r
M.E. from NITTTR, Ch
andig
a
r
h
, I
ndia and B
.
Tech from NIT,
Kurukshetra Ind
i
a.
S
h
e is
purs
u
ing her P
h
.D. in
m
e
tam
a
teri
al an
tennas
.
S
h
e has
approx. 17
ye
ars
of acad
em
ic
experi
enc
e
. S
h
e has
authored a num
ber of res
earch
papers in Internation
a
l journals, National and
Interna
tiona
l co
nferenc
e
s
.
Her
areas
of int
e
re
st inc
l
ude
Wireless c
o
mmunication and Antenna
design.
G
u
rw
inde
r
Sin
g
h
is currently
pursuing M.Tech from SB
S
State Technical C
a
mpus, Ferozepur,
India. He h
a
s completed B.Te
ch from PTU Ja
landhar in 2012. Hi
s areas of interest in
clud
e
Antenna d
e
sign.
Dr
Anupma M
a
rw
aha
is
currently
Associate P
r
ofessor at
Sant
Longowal Institute of
Engg.
&
Tech
, Logowal (
S
angrur). She has done her Ph.D
from G
NDU, A
m
ritsar, M. Tech. from R
E
C
Kurukshetra (Now NIT, Kurukshetra)
, B.E from Punjab University
,Ch
a
ndig
a
rh.Sh
e
has 22
y
e
ars
of acad
em
ic ex
periem
ce
. S
h
e has
authored 25
res
earch pap
e
r
s
in Internation
a
l and Nation
a
l
Journals and 50research p
a
pers in National
and
I
n
ternational con
f
erences.She has
supervised 02
Ph.D Thesis an
d 10 M.Tech
thesis and 04 ar
e under progres
s.Her areas of interst in
clud
e
Electromagnetics,Microwave
Comm,
Wi
re
l
e
ss c
o
mmuni
c
a
t
i
on an
d Antenna Desig
n
Evaluation Warning : The document was created with Spire.PDF for Python.