A Band-Pass/S op Fil e Made o SRRs and C-SRRs
Juli´
an D. O iz
and Juan D. Baena∗
Depa men o Physics
Uni e sidad Nacional de Colombia
Bogo ´
a, Colombia
Email: [email p o ec ed]
R. Ma qu´
es
and F. Medina
Depa men o Elec onics and Elec omagne ism
Uni e sidad de Se illa
Se illa, Spain
Email: [email p o ec ed]
Abs ac —F equency Selec i e Su aces (FSS) a e usually clas-
sified in o wo big g oups depending on we he hey a e made
o unconnec ed elemen s o connec ed elemen s. Close o hei
esonance equency, he fi s ype beha es like a band-s op
fil e while he second ype like a band-pass fil e . In his
pape we p opose a new ype o su ace made o Spli Ring
Resona o s (SRRs) and, a he same ime, Complemen a y Spli
Ring Resona o s (CSRRs), placed in such a way ha he su ace
is sel -complemen a y. The main esul is ha his FSS shows
band-s op ea u es o one linea pola iza ion s a e and band-
pass ea u es o he o hogonal pola iza ion. The e o e, i is in
he middle be ween he wo usual g oups o FSS, wha could
d i e us o new designs o band-pass/s op fil e s which a e a e
easily swi chable om band-pass o band-s op, and ice e sa, by
simply o a ing he su ace h ough 90 deg ees.
I. INTRODUCTION
F equency Selec i e Su aces (FSS) ha e been de eloped
since many yea s ago (50’s). Classical books on his opic
we e w i en by T. K. Wu [1] and B. A. Munk [2]. Bo h books
ag ee in classi ying FSSs in o wo big g oups: hose made o
unconnec ed elemen s (unconnec ed pieces o me al), which
show band-s op fil e ea u es, and hose o med by connec ed
elemen s (o unconnec ed slo s), which show band-pass fil e
ea u es. In he las decade his opic has ecei ed new b ea hs
comming om he new concep s o me ama e ials. In 1999
John Pend y p oposed he Spli Ring Resona o (SRR)[3] o
ge esonan magne ic p ope ies a high equencies wi hou
using magne ic ma e ials. Soon a e , he SRR was used o
design he fi s bulk le -handed medium by Da id Smi h’s
g oup [4]. Ins ead o bulk me ama e ials, he e we will ocuse
ou a en ion in o he possible use o he SRR and simila
pa icles in he design o me asu aces. One o he fi s a emp s
was de eloped by Falcone e al. in Re . [5] whe e also he
Complemen a y Spli Ring Resona o (CSRR) was p oposed.
They demons a ed ha a pe iodic sc een o med by SRRs
ac s like a band-s op fil e o ce ain linea ly pola ized plane
wa e, while he sc een o CSRRs ac s like a band pass fil e o
he o hogonal pola iza ion. One o he ad an eges is ha he
elec ical size o he uni cell is conside ably small (wi hou he
need o a subs a e o high dielec ic cons an ) so ha g a ing
lobes a e a oided. A e , su ace admi ance models o hese
wo sc eens we e p oposed in [6] and he o -no mal incidence
was s udied in [7]. Recen ly, an in e es ing sel -complemen a y
sub-wa elengh hole a ays has been p oposed by Be ue e e
(a)
(b)
(c)
Fig. 1. The s udied sel -complemen a y me asu ace (a), he unloaded uni
cell (b), and he loaded uni cell (c). The geome ical pa ame e s a e: a=8
mm, ex =3.5 mm, 0=2.9 mm, and c=d=g=l=0.4 mm. Ll
and C
lo (c) a e lump ci cui elemen s used o push down he esonance
equency o he o iginal pa icles (b).
al. [8] in o de o design a pola ize . Howe e , in ha wo k
he uni cell size was simila o he pe iodici y so ha g a ing
lobes could make he su ace no sui able o many ypical
applica ions o FSS.
In his pape we p opose a new kind o FSS, based on a
sel -complemen a y me asu ace made o SRRs and CSRRs
(see Fig. 1(a)), which beha es like a band-pass fil e o
ce ain linea pola iza ion and band-s op fil e o he o ogonal
pola iza ion.
II. THEORY
Fig. 1 shows he sel -complemen a y me asu ace unde
s udy, made o SRRs and CSRRs. In wha ollows we will
always conside pe ec conduc o s o infini esimal hickness
and no dielec ic subs a es (sc een a e hold in ai ), so ha
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he duali y p inciple and he Babine ’s p inciple a e s ic ly
alid. Fo he lowes esonan equency, and when he SRR
size is much smalle han he esonan wa elengh , i can be
modeled like an LC ci cui [3]. S ong cu en s can be exci ed
i a ime a ying magne ic field is applied o hogonally o he
SRR. In some a e age sense, he cu en s o e he wo ings
o m a closed loop o cu en s which ha e an associa ed sel -
induc ance L. The spli s o ce some accumula ion o cha ge,
so ha a capaci ance Cmus be included in o he ci cui
model. The small loop o cu en could be eplaced by a
magne ic dipole. A mo e accu a e model was p esen ed in
[9], whe e analy ical o mulas o Land Cwe e ob ained
and he magne oelec ic coupling e ec was poin ed ou . This
las e ec means ha he SRR is no pu ely a magne ic
esona o s, bu ha i has also an associa ed elec ic dipole and,
ecip ocally, can be exci ed by angen ial elec ic field di ec ed
along he x-axis. This is a key poin because i allows he
esonan esponse o a su ace o SRRs unde no mal incidence
al hough he magne ic flux is ze o. The baha io o he CSRR
can be in e ed by duali y om he SRR (see he pape s [5],
[6], [7]).
Howe e , Fig. 1(c) is showing a modifica ion o he o iginal
esona o s, which now appea s sime ically loaded wi h lump
induc o s (Ll) o SRR and lump capaci o s (C
l) o CSRR.
They a e jus in oduced in o de o push down he esonan
equency o he o iginal pa icles, which will be a key poin
o his pape as explained below. These lump elemen s a e
ounded by ci cles o s ess he ac ha hey a e blinded o
any ex e nal field so ha hey do no a ec he mechanism
o exci a ion o he esona o . In oducing he lump elemen s
implyies ha he sel -complemen a yness is no pe ec , bu i
will be clea below ha his pe u ba ion is no ele an , excep
o ce ain sligh shi in equency. The equi alen ci cui
models o single esona o s a e shown in Fig. 2. Since he
magne ic esona o is he complemen a y coun e pa o he
elec ic esona o , hei ci cui models mus be dual one each
o he . The ules o passing om Fig. 2(le ) o Fig. 2( igh ) a e
e y simple: change se ies connec ions o pa allel connec ions,
and in e change induc ances and capaci ances. In passing om
an induc ance o i s dual capaci ance we ha e o include a
ac o 40/μ0[10], being he ac o 0/μ0 o co ec he uni s
and he ac o 4 o ake in o accoun he di e en symme y
p ope ies o he sca e ed fields (sca e ed elec ic field is e en
espec o he su ace while sca e ed magne ic field is odd).
Al hough he duali y is only applied o he ci cui elemen s
co esponding o he p in ed s ips, we a bi a ily o ce he
lump elemen s Lland C
l o ollow he same ules. Then,
by duali y, bo h ypes o esona o s will esona e a he same
equency.
Le us now imagine a linea ly pola ized plane wa e no -
mally impinging on he su ace o Fig. 1(a). I i s equency is
a om he esonan equency o a single esona o , hen he
wa e will mainly see a pa allel s ip g a ing wi hou he e ec s
o he esona o s. Fo low equencies, i should ejec he wa e
when i is pola ized wi h he Efield pa allel o he s ips ( he
baseline o band-pass fil e s) while i allows he wa e o go
Fig. 2. Ci cui models o a single SRR (le side) and a single CSRR ( igh
side). The SRR ci cui pa ame e s a e: L=13.0 nH, C=6.31 ×10−2
pF, and Ll=35.5 nH. Duali y ela ions gi es he ollowing CSRR ci cui
pa ame e s: C=0.365 pF, L=2.24 nH, and C
l=1pF.
h ough when Eis o hogonal o he s ips ( he baseline o
band-s op fil e s). Resona o s play an impo an ole jus when
he equency app oach hei esonan equency. Then, o E
along he y-axis (o y-pola ized wa e) he SRR is no exci ed,
while he CSRR is exci ed by Bx. Based in ou p e ious
expe ience o Re s. [5], [6], [7], we expec ha close o he
esonan equency he ansmission coe ficien should be 1.
Fo he case o an x-pola ized inciden wa e, he elec ic
esona o s will be exci ed by Exwhile he magne ic esona o s
will no be exci ed, so ha he sca e ed field will be impo an
and he wa e will be comple elly ejec ed a some equency
close o he same esonan equency. The e o e, he s uc u e
would beha e as a band-pass fil e o y-pola ized wa es and
band-s op fil e o x-pola ized wa es. Thus, i makes sense
o use a new e minology band-pass/s op fil e , because i can
fil e he wa e in a double way: as band-pass o band-s op
depending on he pola iza ion s a e.
III. NUMERICAL SIMULATIONS
A. The me asu ace wi h unloaded esona o s
In o de o demos a e he p ope ies o he sel -
complemen a y me asu ace shown in Fig. 1(a), we ha e
nume ically simula ed he no mal incidence o plane wa es.
The co esponding esul s a e shown in Fig. 3( op). The e exis
a dip o o al ejec ion o x-pola ized wa es a 6 GHz (solid
line), while a he same equency a peak o o al ansmission
appea s o he y-pola ized wa es (dashed line). Howe e , he
bands a e e y unsymme ic due o he apid a ia ion o he
baselines because he wa eleng h is no much smalle han he
pe iodici y.
I is wo h o no e ha bo h sub-a ays – he s uc u e wi h
only SRRs o CSRRs – a e independen . In Fig. 3(middle)
only he SRRs a e p esen s and hus only he s opband o
x-pola iza ion can be obse ed (solid line), while o y-
pola iza ion he esonance dissapea s (dashed line). On he
o he hand, i is shown in Fig. 3(bo om) ha he CSRRs sub-
a ay losses he s opband o x-pola iza ion (solid line) while
keeps he passband o y-pola iza ion (dashed line). In ac ,
his independency is also demons a ed by Fig. 4, whe e i
is shown ha o he case o x-pola iza ion ele an cu en s
a e only exci ed o e he SRR, while o y-pola iza ion only
he CSRR a e s ongly exci ed. I is also wo h o no e ha
he diag am o cu en s co esponds o he LC ci cui model
o [9]. Following he o mulas he ein we ob ained he alues
o L=13.0 nH and C=6.31 ×10−2pF which ca y o a
esonan equency o 5.57 GHz. This equency, which is o
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Fig. 3. T ansmission coe ficien s o he case o unloaded esona o s o
di e en configu a ions: he ull sel -complemen a y me asu ace ( op), he
sub-a ay o SRRs including he long me al s ips wi hou CSRRs (middle),
and he sub-a ay o CSRRs (bo om). Solid lines ep esen s he ansmission
o x-pola ized wa es and dashed lines o y-pola ized wa es.
a single SRR, is no a om he simula ed alue o 6 GHz
ob ained o he whole coupled sys em o SRRs and CSRRs.
B. The me asu ace wi h loaded esona o s
Wi h he aim o imp o ing he shape o he s opband and
passband we ha e loaded he esona o s wi h lump ci cui
elemen s as shown in Fig. 1(c). In ha way we expec o push
down he esonan equency o e y low alues whe e he
baselines a e mo e fla . Using he pa ame e s o he cap ion
o Fig. 2 i is easy o ge a heo e ical esonan equency
o 2.19 GHz. O cou se, i can be much lowe i we use
highe alues o Lland C
l. The nume ical simula ions o
no mal incidence d i ed us o he esul s shown in Fig.
5( op). Now, a double esonance appea s being he lowes
esonan equency a 2.15 GHz. Ac ually, Fig. 3 o unloaded
esona o s should also show a second esonence i we would
(a)
(b)
Fig. 4. Elec ic su ace cu en s o e he unloaded esona o s o x-pola ized
wa es a 6.00 GHz (a) and y-pola ized a 6.06 GHz(b).
inc ease he equency ange o he simula ion a ew GHz
mo e. This double esonance can be in e p e ed as he fi s
an isymme ic (A1) and symme ic (S1) esonan modes o
he SRR demons a ed in [11] (simila ly o he CSRR). The
bands ela ed wi h he S1 mode a e wide han he band o A1
because he e ec i e dis ance be ween posi i e and nega i e
cha ges o he S1 mode is highe han o he A1 mode,
which makes he esonance o be s onge . Apa om his
double esonance, i is clea ha he bands o Fig. 5( op)
look mo e symme ic han hose o Fig. 3( op), which means
an impo an imp o emen om a p ac ical poin o iew
when somebody wan s o design a fil e . Ac ually, he double
esonance allows he design o a dual band fil e s. Apa om
he double esonance, i is wo h o s ess he ac ha we
ha e go again he same fil e ing beha io : a s opband o x-
pola iza ion and a passband o y-pola iza ion. And ollowing
he same easoning a he end o Sec. III.A, he independency
be ween he sub-a ays o loaded SRRs and loaded CSRRs is
again demons a ed by esul s o Fig. 5(middle and bo om)
and Fig. 6.
IV. CONCLUSION
In his pape we ha e demons a ed ha a sel -
complemen a y me asu ace made o SRRs and CSRRs can
beha es like a band-pass fil e o a ce ain linea pola iza-
ion and band-s op fil e o he o hogonal pola iza ion. The
idea was de eloped o SRR and i s complemen a y e sion
named CSRR, bu i can be easily ex ended o o he ypes
o esona o s. I is jus impo an o sa is y wo condi ions.
Fi s he esona o should esona es unde an applied elec ic
o magne ic angen ial field, in o de o assu e he esponse o
no mal incidence. Second, he pa icle mus esona e a e y
low equency in such a way ha he esonan wa elengh is
much bigge han he pe iodici y. This las condi ion assu es
ha he baseline o he fil e is fla enough. Since i is a
new concep in he ame o FSS we ha e deal wi h he
ideal case o pe ec conduc o o infini esimal hickness hold
in ai . Subseequen wo k abou he e ec s o me al losses,
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Fig. 5. T ansmission coe ficien s o he case o loaded esona o s o
di e en configu a ions: he ull sel -complemen a y me asu ace ( op), he
sub-a ay o SRRs including he long me al s ips wi hou CSRRs (middle),
and he sub-a ay o CSRRs(bo om). Solid lines ep esen s he ansmission
o x-pola ized wa es and dashed lines o y-pola ized wa es.
hickness and dielec ic subs a e is cu en ly being done. We
hope his idea could open he way o a new kind o FSS ha
can be swi ched om band-s op fil e o band-pass fil e by
only o a ing i h ough 90 deg ees.
ACKNOWLEDGMENT
This wo k has been suppo ed by Uni e sidad Nacional de
Colombia (p ojec no. DIB-8003310), Colciencias (schola -
ships p og am), and Spanish Minis e io de Ciencia e Inno-
aci´
on (p ojec Consolide EMET CSD2008-00066).
REFERENCES
[1] T. K. Wu, F equency Selec i e Su aces and G id A ays. New Yo k:
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(a)
(b)
(c)
(d)
Fig. 6. Elec ic su ace cu en s o e he loaded esona o s o x-pola iza ion
a 2.15 GHz (a), y-pola iza ion a 2.13 GHz(b), x-pola iza ion a 3.27 GHz (c),
and y-pola iza ion a 3.01 GHz(d). (a) and (b) co espond o he an isymme ic
mode A1 a he lowes esonan equency, while (c) and (d) co espond wi h
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(A1 and S1) was in oduced in [11].
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