Metamaterials 2 (2008) 186197

Available online at www.sciencedirect.com

Invited Paper

Metamaterial filters: AM. Gil , J. Bonache, F. Ma

GEMMA/CIMITEC, Departament dEnginyeria Electrnica, Univa, Spainuly 200t 2008

Abstract

In this pa ters bametamateria d showthe design o sults b 2008 Else

PACS: 84.30

Keywords: M sonato

1. Introdu

The main aim of this work is to review the workdeveloped in this research group during the last yearsin the implementation of metamaterial filters based onresonant-tycombine sother elemtances, loapropagatinThese linesand impedfilter, but,dividers, rsome exam

resonant-ty

Corresponfax: +34 93 5

E-mail adFerran.Martin

h evenment [4] or dual-band operation [5].

One of the first issues to be discussed may be, perhaps,the use of the term metamaterial to name these devicesbased on such kind of lines. The authors do not apply the

1873-1988/$doi:10.1016/jpe metamaterial transmission lines, whichub-wavelength resonators to, together withents like series capacitances or shunt induc-d a host transmission line and obtain a

g medium with controllable characteristics.offer the possibility of tailoring their phase

ance, what makes them suitable for, not onlyin general, microwave device design. Powerat-race hybrid couplers, phase shifters, areples of the application possibilities of thesepe metamaterial transmission lines [13],

ding author. Tel.: +34 93 581 3524;81 2600.dresses: Marta.Gil.Barba@uab.es (M. Gil),@uab.es (F. Martn).

label metamaterial intending to main that such structurescompose periodic, homogeneous and isotropic mediawith negative effective and parameters. Actually,most of our devices are based on only one unit cell andtalking about effective parameters has no sense. What theauthors try to point out calling these devices as metade-vices is the fact that they are based on sub-wavelengthresonators, like the SRRs [6], whose sub-wavelengthcharacteristics opened the door to the synthesis of thefirst left-handed medium [7], and the fact that, indeed,most of these transmission lines exhibit backward propa-gation. In fact, the nature of the propagation is irrelevantin most of the devices based on resonant-type transmis-sion lines. It is, on the contrary, the controllability oftheir electrical characteristics (beyond what is achiev-able in conventional lines) and the possibility thatthey offer to design compact devices what is exploited

see front matter 2008 Elsevier B.V. All rights reserved..metmat.2008.07.00608193 Bellaterra, BarcelonReceived 5 June 2008; received in revised form 17 J

Available online 15 Augus

per, a review on metamaterial filters is presented. Several fill transmission lines are revised. The different results presentef filters with different bandwidths and performances. Some revier B.V. All rights reserved.

.Vn; 84.32.-y; 84.40.Az

etamaterials; Filter; Split-ring resonator; Complementary split-ring re

ction whicreviewrtn

ersitat Autnoma de Barcelona,

8; accepted 21 July 2008

sed on resonant-type composite right/left-handedthe application possibilities of such structures in

ased on other approaches are also shown.

r

offer the possibility of bandwidth enhance-

M. Gil et al. / Metamaterials 2 (2008) 186197 187

from these metamaterial resonator-based transmissionlines.

As was mentioned above, in this article we will makea review on the different kinds of metamaterial filtersbased on resince theirresponse imsibilities asan importaimplementOne of theresonatorsments in cimprovemearea incremline sectiofilter and, wrious bandsuch filtersventional dbut they doate a contrsections, wrial resonatlines formistrategies abig varietyshown. Finare also shities that mdesign.

2. Resonalines

As has bmetamatersub-waveleresonatorsonators (Cand, in comagating mepropertiesistic impeddimensionssion lines cdesigned toin the desigin an impo

The resoicated to ttransmissio

lines with composite characteristics appeared in 2002[14,15] and consisted on a conventional transmission lineloaded with shunt inductances and series capacitances(which can be implemented, for instance, as capacitive

). Thesdanceency r

agatioents ot hightive ao a cooadedicrowonent

he firsmater[8]. ISRRssignalators,d by tt andft-han

ed wavshownhe equin Fig

citancroundsonat

s and Lgh thformee follo

2M2

Ls

2M2(2 +(

2L

he moon oficallyin Fighe shusonant-type metamaterial transmission linesappearance in 2003 [8]. Their frequencymediately suggested their application pos-filtering structures and, since that moment,

nt amount of works has been devoted to theation and improvement of this kind of filters.

first strategies applying such metamaterialconsisted in their inclusion as additional ele-onventional filters for out-of-band rejectionnt [9,10]. Without entailing a considerableent, SRRs can be printed close to the coupled-

ns in a conventional coupled-line bandpasshen properly tuned, they can eliminate spu-

s and thus improve out-of-band rejection. In, however, SRRs are merely added to a con-istributed filter as signal rejecting elements,

not contribute as basic elements to gener-ollable transmission band. In the followinge will focus on filters in which metamate-ors are essential elements in the transmissionng the different stages of the filter. Diversend kinds of unit cells applied to design aof filters with different performances are

ally, several filters based on other approachesown as examples of the application possibil-etamaterial transmission lines offer in filter

nt-type metamaterial transmission

een previously mentioned, the resonant-typeial transmission lines use different kinds ofngth resonators like, for example, split-ring(SRRs) [6] or complementary split-ring res-SRRs) [11] to load a host transmission linebination with other elements, obtain a prop-dia with controllable characteristics. These

are mainly the phase shift and the character-ance of the line [12,13]. Due to the smallof these resonators, the resulting transmis-

an be very compact and, once the line has beenexhibit certain characteristics to be applied

n of a specific device, its size can be reducedrtant factor [3,1].nant-type approach is not the only one ded-

he synthesis of composite right/left-handedn lines (CRLH TLs). The first transmission

gapsimpefrequpropelemtion ainducrise tCL-lof mcomp

Tmeta2003withandreson

erateshunthe lehand(not

Tseen

capaand gthe reby Cthroutransof th

Ls =

Cs =

L =

Lp =

Tversiphysseen

and te loading elements provide a series capacitiveand a shunt inductive impedance in a certainange, what is necessary to exhibit left-handedn [14]. Furthermore, the effect of the parasiticf the host line provides right-handed propaga-er frequencies, where the series impedance isnd the shunt impedance is capacitive, givingmposite right/left-handed behaviour. TheseCRLH TLs can also be applied in the design

ave devices giving rise to very competitives applying different design strategies [16,17].t resonant-type composite right/left-handedial transmission line was implemented int consisted on a coplanar waveguide loadedetched on the bottom layer of the substrate

-to-ground strips. The combination of thewhich were excited by the magnetic field gen-he line, and the metallic wires, provided theseries impedance values required to exhibitded propagation (see Fig. 1), whereas right-e propagation appeared at higher frequenciesin Fig. 1).

ivalent circuit model for this structure can be. 1(c). In the model, C represents the line

e, Lp, the metallic connections between line, L corresponds to the line inductance, and

ors are modelled by the resonant tanks formeds, which are magnetically coupled to the line

e mutual inductance M. This circuit can bed into the one depicted in Fig. 1(d) by meanswing transformations [18]:

Cs20

(1 + L/4Lp)21 + M2/2LpLs (1)

20

(1 + M2/2LpLs

1 + L/4Lp

)2(2)

L

2Lp

)L

2 Ls (3)

p + L2)

(4)

del shown in Fig. 1(c) is a recently improvedthe previous one and has been proved to bemore accurate than the existing one. As can be. 1(d), the loading elements, that is, the SRRsnt inductances contribute to obtain a capaci-

188 M. Gil et al. / Metamaterials 2 (2008) 186197

Fig. 1. (a) Layout of a SRR-based CPW left-handed transmission line.The CPW line is loaded with shunt inductances and SRRs lying on theopposite side of the substrate. Metallic parts are depicted in grey for thetop layer and in black for the bottom layer. The length of the unit cellis l = 5 mm while the centre conductor and slot widths are W = 4 mmand G = 0.3 mm, respectively. The rings have an internal radius ofr = 1.3 mm, widths of c = 0.2 mm and a separation of d = 0.2 mm. Arlon250-LX-0193-43-11 substrate with dielectric constant r = 2.43 andthickness h = 0.49 mm was used. (b) Measured frequency response ofthe device shown in (a). (c) Equivalent circuit model for the structureshown in (a). (d) Modified circuit (equivalent to that in c).

tive series impedance and an inductive shunt impedancein a certain frequency range, where left-handed propa-gation will be allowed.

SRR-based transmission lines were the first to appearand to be athe appearaterpart of thbased on tbecome thsimplest anCSRRs witThe resonacapacitivethe electricplane. Theas in the caimproved aobtained [2inductanceonant tankpresence othree differ(Cs, Cf) anthe CSRR-circuit iand Cf is thand the coutaken intobe transforof the follo

C = Cpar(

Cg = 2Cswith:

Cpar = CfThis tra

LC-loadedcapacitanca transmissband.

If a shuture, a neobtained: telement colower frequdom whenthe characquency innulls, the rpplied in the design of filters. However, sincence of the CSRR as the complementary coun-e SRR, several unit cells have been developedhese particles [19,11,20] and CSRRs havee most frequently applied resonators. Thed most commonly used unit cell combinesh capacitive gaps etched on a microstrip line.tors are etched on the ground plane, below thegaps (see Fig. 2(a)), and they are excited byfield going from the line towards the groundequivalent circuit model of these structures,se of the SRR-based lines, has been recentlynd a physically more accurate model has been1]. In the new circuit model (Fig. 2(c)) theof the line is represented by L and the res-formed by Lc and Cc takes into account the

f the CSRR. Additionally, the model includesent capacitances to model the capacitive gapd the electrical coupling between the line and(CL). By this means, the gap is modelled by an which Cs represents the series capacitancee fringing capacitance. The effect of the gappling between the line and the resonator are

account separately. This improved model canmed into the former one (Fig. 2(d)) by meanswing transformations:

2Cs + Cpar)Cs

(5)

+ Cpar (6)

+ CL (7)nsformed T-circuit model differs from thetransmission line one on the presence of the

e C, which is responsible for the existence ofion zero below the left-handed transmission

nt inductance is added to the previous struc-w unit cell with a different behaviour ishe hybrid cell (see Fig. 2(b)). The additionalntributes to obtain backward propagation atencies and represents an extra degree of free-designing the line. Furthermore, it modifies

teristics of the line. In this case, at the fre-which the shunt impedance (see Fig. 2(e))esponse presents a transmission zero which,

M. Gil et al. / Metamaterials 2 (2008) 186197 189

Fig. 2. (a) Laparts are depilayer. (b) Laydepicted in grhave been defor the purelythe purely rescell.

contrary tothe left-hanuseful to oband in filt

Providetransmissiosion line,yout of a purely resonant CSRR-based unit cell. Metalliccted in grey for the bottom layer and in black for the topout of a hybrid cell based on CSRRs. Metallic parts areey for the bottom layer and in black for the top layer. Viapicted in white. (c) Improved equivalent circuit modelresonant cell. (d) Modified equivalent circuit model foronant cell. (e) Equivalent circuit model for the hybrid

the purely resonant case, is located aboveded band. This transmission zero can be verybtain a good rejection level above the passer applications.d that both, the purely resonant and the hybridn line, just like the LC-loaded transmis-

have a composite behaviour [22], they can

Fig. 3. (a) Dianced transmleft-handed ain order to obteristics. (b) Lbalanced unittom layer andbeen used, wiDimensions anal radius of tseparation d =gers separateddifferent numnumber of sta[22]; 2007

be designeresponses.upper limilower limitthere is a cspersion diagram for a purely resonant CSRR-based bal-ission line. The frequency gap that usually separates thend the right-handed bands, has been forced to disappeartain a broad transmission band with composite charac-ayout of a high-pass filtering structure formed by threecells. Metallic parts are depicted in grey for the bot-in black for the top layer. Rogers RO3010 substrate has

th thickness h = 1.27 mm and dielectric constant r = 10.2.re: total length l = 55 mm, line width W = 0.8 mm, exter-he outer rings r = 7.3 mm, ring width c = 0.4 mm and ring0.2 mm; the interdigital capacitors are formed by 28 fin-0.16 mm. (c) Responses of several structures formed by

ber of stages. Frequency selectivity is enhanced as theges increases. Figure (a) reprinted with permission fromIEEE.

d to be balanced and exhibit broad-bandThe balance condition is satisfied when thet of the left-handed band coincides with theof the right-handed band. If that is the case,

ontinuous transition between both bands; the

190 M. Gil et al. / Metamaterials 2 (2008) 186197

frequency gap that normally separates the bands disap-pears and, as a result, a broad transmission band withright-handed and left-handed characteristics is obtained(see Fig. 3).

3. Metamaterial lters

The frequency selectivity of resonant-type metamate-rial transmission lines suggests their application in filterdesign. Furthermore, the possibility of obtaining suchbroad responses by means of balanced lines opens thedoor to the application of these structures in the designof broad-band filters. As has been previously mentioned,the characteristics of the lines can be tailored to someextent in order to obtain the desired response. Addition-ally, the position of the transmission zeros can be set toeliminate spurious bands and to control the out-of-band

rejection, which can also be improved increasing thenumber of stages. These properties have been exploitedand applied to the design of several kinds of filters sincethe first resonant metamaterial transmission lines arose.

3.1. Filters based on alternate right/left-handedcells

One of the first strategies applied in thedesign of filters based on these transmission lineswas the combination of different cells with right-handedand left-handed behaviour to obtain a bandpass response[2325]. These two kinds of lines present a transmissionzero above and below the first transmission band, whatallows to obtain a bandpass behaviour with a sharpcutoff at both sides of the band (see Fig. 4). The useof only one kind of cell provides a poor rejection level

Fig. 4. (a) Fre responfrequency res it cells.two left-hand d in gre250-LX-0193 ler SRRrings c = d = 0 .52 mmand the total l rmissioquency response of a SRR-based CPW left-handed line. (b) Frequencyponse of the filter combining one right-handed and two left-handed uned unit cells. Metallic parts are depicted in black for the top layer an-43-11 with r = 2.43 and thickness h = 0.49 mm was used. The smal.2 mm are the same in all SRRs. The radius of the bigger SRRs is r = 1ength of the filter is 1.5 cm [23]. Figures (c) and (d) reprinted with pese of a SRR-based CPW right-handed line. (c) Measured(d) Layout of the filter combining one right-handed andy for the bottom layer of the substrate. Substrate Arlonradius is r = 1.39 mm, width and distance between the

. Wire width is ww = 2.16 mm, gap length is lg = 1.6 mmn from [23]; 2004 IEEE.

M. Gil et al. / Metamaterials 2 (2008) 186197 191

at one of the edges of the band. This limitation can besolved alternating the two types of cells as explained.This strategy can be applied to design filters withdifferent bandwidths using either SRR-based coplanartransmissiostructures [

In coplaon the comof the linewaveguidemicrostriptances withthe desireddesigned fiof the activsymmetriccombinatiounit cells. Icoupled-lin3 Chebyshfilter is rouone.

3.2. Ultra-cells

As wasposite rightransmissiolines withapplied inpurely resoto be balantransmissioresponse otechnologyformed bythe variatiof stages.upper limitexhibit higpossibilityadding sombe rejectedtional resoincluded inpass filterstrategy.

The filteUWB commas shown ianced unit

. (a) Lag additiered suelectricRs: ex1 mm, couter = 0.22 mm and cinner = 0.16 mm for the external and

al ring, respectively. For the small SRRs: external ring radius0.89 mm, distance between rings d = 0.11 mm, couter = 0.17 mmner = 0.17 mm for the external and internal ring, respectively. Theof the host line is W = 0.80 mm and the capacitor is formed byce-to-face fingers separated a distance of 0.16 mm (finger lengthidth are 0.8 4 mm and 0.14 mm, respectively). (b) Simulatedncy response of the filter shown in (a).

Hz. Three additional CSRRs have been added anded in the centre of the big resonators formingnit cell. Their task is the rejection of the signald 10.6 GHz. As a result, the filter exhibits a passbehaviour covering the desired frequency range

in addition to this, its dimensions are very small.inclusion of the small CSRRs does not entail anyment in the total device area, which is aroundm 0.4 cm.hese additional resonators are useful, not only tool the upper limit of the transmission band, but alsolude attenuation poles, suitable for the rejection of

fering signals which may appear within the trans-ion band, as can be seen in the examples given belowThe resonators used to create the attenuation poles,ell as the ones controlling the upper limit of the, can be either metallic, being added close to then the top layer of the substrate, or complementary,etched on the ground plane under the transmissionor inside the bigger resonators like in the previ-n lines [23,26], or CSRR-based microstrip24,25,27].nar technology, the right-handed lines consistbination of SRRs etched on the bottom sideand capacitive gaps etched on the coplanar(see Fig. 4(b)). On the contrary, CSRR-basedright-handed structures combine shunt induc-CSRRs etched on the ground plane to obtainresponse. As can be seen in Fig. 4(c), the

lter, as well as being very compact (the lengthe part is 1.5 cm), exhibits a very selective andnarrow-band response obtained thanks to then of the two types of coplanar metamaterialf the device is compared with a conventionale filter with similar characteristics (an order-

ev filter), the total length of the metamaterialghly three times shorter than the conventional

wide bandpass lters based on balanced

mentioned in the previous section, the com-t/left-handed behaviour that CSRR-basedn lines exhibit, allows to design balanceda wide transmission band, which can bethe design of broad-band filters. Both, thenant and the hybrid cells can be designedced. Some examples including both kinds ofn lines are given below. Fig. 3(c) shows thef several devices implemented in microstrip

based on the purely resonant model and24 balanced unit cells. The graph shows

on of the rejection level with the numberAs far as no control is exerted on theof the band, purely resonant balanced linesh-pass behaviour. However, we have theof controlling the upper edge of the bande elements to our design. The signal canaround a certain frequency range if addi-

nators tuned at the frequency of interest arethe device. Fig. 5 shows an ultra-wide band-

(UWBPF) designed following the described

r was designed to cover the standard mask forunications going from 3.1 GHz to 10.6 GHz,

n Fig. 5(b). The filter is formed by three bal-cells whose high-pass response starts around

Fig. 5taininconsidand dibig SRd = 0.1internrext =

and cinwidthfive faand wfreque

3.1 Glocatthe uaroun

bandand,Theincre1.5 c

Tcontrto incintermiss[28].as w

bandline obeinglinesyout of a UWBPF filter based on balanced cells con-onal CSRRs to control the upper limit of the band. Thebstrate is the Rogers RO3010 with thickness h = 635mconstant r = 10.2. Dimensions are as followsfor the

ternal ring radius rext = 2.10 mm, distance between rings

192 M. Gil et al. / Metamaterials 2 (2008) 186197

Fig. 6. (a) Layout and photograph of a UWB filter including additionalcomplementary split-ring resonators (CSRRs) and complementaryspiral resonators (CSRs) to control the upper limit of the transmissionband and to add an attenuation pole at 4.8 GHz, respectively [28].Dimensions are those indicated in Fig. 5. CSR dimensions are:c = 0.17 mm, d = 0.11 mm and rext = 1.01 mm. The area of the dashedrectangle is A = 1.77 cm 0.41 cm = 0.73 cm2. (b) Frequency responseof the filter shown in (a). (c) Layout and photograph of a UWBfilter including additional split-ring resonators (SRRs) and spiralresonators (SRs) to control the upper limit of the transmission band and

ous example. This can be observed in the two followingexamples of UWBPF filters with attenuation poles cre-ated using spiral resonators (SRs) and complementaryspiral resonators (CSRs).

The first of the examples is based on complementaryresonators, as can be seen in Fig. 6(a). All the additionalresonators are complementary and have been etched onthe ground plane. The small CSRRs have been addedto reject the signal above 10.6 GHz like in the previousexample. The attenuation pole is due to the effect of theCSRs locain order tothus, elimiwere desig

In the sonators aresubstrate.square-shaFour SRRsand they aresponsibleThe attenuato the preseof the filteronators dothe total are1 cm2.

UWBPFresonant mbalanced hthis kind oisfy a set oinsertion lo3.5 GHz to

The finadesigned torange. Allby both thefrequencyout-of-banband; the cIn-band inbetter thantion to thisAll these c

to add an atteare: c = 0.14 marea of the daFrequency repermission ofJohn Wiley &ted under the access lines. They can be tunedplace the notch at the desired frequency and,nate undesired signals. In this case, the CSRsned to reject any signal around 4.8 GHz.econd filter (Fig. 6(c)) all the additional res-

metallic and lay on the top layer of theAs can be seen, this filter contains severalped metallic resonators close to the host line.can be found near the extremes of the filter

re, like the CSRRs in the previous example,for the control of the upper limit of the band.tion pole located at 5.6 GHz is in this case duence of the two SRs situated in the central part. As can be seen, the addition of the extra res-es not increase the size of the device. Indeed,a of both devices is significantly smaller than

s can be implemented not only with purelyetamaterial transmission lines, but also usingybrid cells [29]. Fig. 7 shows an example off UWB filters. The filter was designed to sat-f strong specifications: device area A < 1 cm2,sses IL < 80 dB at 2 GHz, bandwidth from9 GHz.l device was formed by four hybrid unit cellsbe balanced and cover the desired frequencythe mentioned specifications were satisfieddesigned and the fabricated prototype. The

response shown in Fig. 7(b) shows the strongd rejection achieved below the transmissionondition IL < 80 dB is satisfied at 2 GHz.

sertion losses are low and return losses are10 dB in the most part of the band. In addi-, no spurious bands are present up to 16 GHz.haracteristics are combined with very small

nuation pole at 5.6 GHz, respectively. CSR dimensionsm,d = 0.166 mm, lext = 2.03 mm andhext = 1.46 mm. Theshed rectangle is A = 1.57 cm 0.42 cm = 0.66 cm2. (d)

sponse of the filter shown in (c). Figures reprinted withJohn Wiley & Sons Inc. from the article: [35] 2004Sons Inc.

M. Gil et al. / Metamaterials 2 (2008) 186197 193

Fig. 7. (a) Laof the deviceness h = 127width W = 0.1rings width cwidth is 0.10gap is 0.4 mmthe simulatedresponse. Fig2007 IEEE.

dimensionsFig. 7(a) is

3.3. Desig

The desmits, not obased on bfilters basemethodolobased on CSuch filterwhich reprnormalizedresonatorsThese resoing rise tothe admittadesign of tof the mo

(a) Baresonatresonat

apprplied. Thes of 9iffereg. 2(d

s in thion anency,

he pos, to coyout of the hybrid cell-based UWB filter. The total areais

194 M. Gil et al. / Metamaterials 2 (2008) 186197

impedance reduces to zero, namely

fz = 12Lc(Cc + C)(9)

For a LCcapacitanc

= 2Z0

If we consiL and C vaby frequen

Ceq =[

FB

we get thewidths:

i = 2FBgi

The transmsome extenwhich mayfrequenciecentral freqthe approxconstant alshunt impepreviouslycan be exp

L

Lc21(C +

Lc22(C +

L

Lc20(C +

The previoand moderexpressionis not applifrequencieEqs. (13)(shunt react(assuming

Cg = 12Z0

All these specifications and impositions can be usedto univocally know all the elements of the circuit modelof the structure (see Fig. 2(e)), except for the line induc-tance, which can be neglected in the frequency range of

est. Tho veryns. Fignse of= 9%in Fi

, exclul wavperfo. SizeRRs.quiva

that thely haame dlines a-basedB ripdevicee timwith aducedugh thlossess they makl dim

andf inteand pcts.s wasme shrent tose 90

In [31ortedg CSR4 linee prevecessa

tions de modsicallycells oder ths the

the freparallel resonant tank, with inductance ande Leq and Ceq, respectively, we have

LeqCeq

(10)

der the filter structure of Fig. 8(b), where thelues come from the low-pass filter prototypecy and element transformation according to

1W0Z0

]gi, Leq = 1

20Ceq(11)

following expression for resonator band-

W (12)

ission zero frequency, fz, can be tailored tot and be used to eliminate spurious bandsappear close to the main band. The two 3 dB

s can be chosen to be equidistant from theuency, f0. These two frequencies are, under

imation that the series impedance is roughlyong the pass band, the frequencies at which thedance is Z0/2 and infinity, while, as has beenindicated, Zp = jZ0 at 0. These conditions

ressed as:

dLc31(C + Cc) Ld1

Cc) C21Ld(LcCc21 1) 1= Z0

2(13)

Cc) C22Ld(LcCc22 1) 1 = 0(14)

dLc30(C + Cc) Ld0

Cc) C20Ld(LcCc20 1) 1= Z0

(15)us approximation (which is valid for narrowate bandwidths) leads us to simple analyticals (Eqs. (13) and (14)). If this approximationed, then the conditions arising from the 3 dBs are not mathematically simple. Solution of15) and (9) leads us to the parameters of theance, while the series capacitance is given bythat L is negligible):

0(16)

interrise tcatiorespoFBWcatedfiltersignagoodsionsof CSare e

factimatthe ssionCSR0.3-dTheis fivfilterbe realthotion

Aologsmaltivitybe osizeaspe

Aschediffenot uers.

is repbininof /in ththe nequaof this baunitbroashowande application of this methodology has givencompetitive filters satisfying different specifi-. 9a and b shows the layout and the frequencyone filter with 0.3 dB ripple, f0 = 2.5 GHz and. Relevant dimensions of the layout are indi-g. 9(a), showing that the total length of theding access lines is around 0.4, being theelength at f0. The designed filter presents armance, combined with very compact dimen-can still be reduced if CSRs are used insteadTransmission lines based on these resonatorslent to the ones based on CSRRs, but thee resonance frequency of a CSR is approx-lf the resonance frequency of a CSRR withimensions, makes that CSR-based transmis-re considerably smaller. One example of these

filters is shown in Fig. 9c and d. It is aple filter with f0 = 1.1 GHz and FBW = 10%.

occupies an area A = 0.22 0.08, whiches smaller than the area that a CSRR-based

similar performance takes up [30]. Size canthanks to the small electrical size of CSRs,eir worse quality factor causes higher inser-

.results corroborate, this design method-es possible the synthesis of filters with

ensions, low-losses, high-frequency selec-good out-of-band performance, which canrest in such applications in which smalllanar technology compatibility are essential

mentioned above, filters modelled by theown in Fig. 8(b) can be synthesized usingpologies. In the previous example, we did transmission lines as admittance invert-], a variation of the previous methodology, in which the same kind of resonators com-

Rs and shunt stubs are coupled by meanss. The same conditions and specifications asious filters can be imposed, giving rise tory design equations. Although some of theseiffer from the former ones, as a consequenceification of the unit cell, the methodologythe same. The advantage that these new

ffer is their bandwidth, which can be muchan in the case of the hybrid cells. Fig. 10equivalent circuit, together with the layoutquency response of a periodic UWBPF fil-

M. Gil et al. / Metamaterials 2 (2008) 186197 195

Fig. 9. (a) Layout of the CSRR-based Chebyshev filter. (b) Frequencyresponse of the filter shown in (a). The dashed line is the simulatedresponse, whereas the solid line represents the measured response. (c)Layout of the CSR-based Chebyshev filter. (d) Frequency responseof the filter shown in (c). The dashed line is the simulated response,whereas the solid line represents the measured response. Substrate isRogers RO3010 with thickness h = 0.635 mm and dielectric constantr = 10.2 was used in both filters. Figures (c) and (d) reprinted withpermission from [30]; 2008 IEEE.

Fig. 10. (a) ECSRR-basedtop layer andresponse of ththickness h =ures reprinted2004 John W

ter implemThe fractiotral frequethe filter iimproved atuned to el17 GHz.

As canpossibilitycomplete dfilters withquivalent circuit model of the unit cell. (b) Layout of thebandpass filter. Metallic parts are depicted in grey for thein black for the bottom layer. (c) Simulated frequencye filter shown in (b). Substrate is Rogers RO3010 with

0.635 mm and dielectric constant r = 10.2 was used. Fig-with permission of John Wiley & Sons Inc. from [31]

iley & Sons Inc.

ented following the mentioned procedure.nal bandwidth is FBW = 90% and the cen-ncy is f0 = 6.8 GHz, whereas the order ofs N = 3. The out-of-band rejection can bedding at the filter output two CSRRs properlyiminate the spurious band appearing around

be seen, the use of these unit cells offers theof designing broad-band filters following aesign methodology and giving rise to compactan interesting performance.

196 M. Gil et al. / Metamaterials 2 (2008) 186197

3.4. Other approaches

Different approaches, not based on SRR-type res-onators, but applying different kinds of artificialtransmissioitive filterstransmissiolines haveimprovedCRLH TLssenting higimplementing a fractperformancare appliedquencies anthe band, i

Thanksdispersionpossible toarbitrary fand bandsthave beenloaded CRfrequency,to be an odchosen freegy can beand bandstperformanc

Metamato implemfilters [34]transmissioimpedanceline sectionare properreduced ancan be shiftbandpass fican be imp

These acation posin filter dedifferent Goptimize mtechnology

4. Conclu

A reviewin the field

transmission lines has been carried out. Part of the workcarried out by this research group has been exposed,showing different kinds of filters applying diverse struc-tures and design strategies. The presented work shows

ossibilines, diffes can bmissionsideed elea go

ementther apationossibin filt

owle

his wojectA andarta GeworkPHOeralita

rence

. Gil,urizatioeft hanropaga. Sis,

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at-racend righicrowa

007, pp. Sis,

ype meandwidnd Opti. Sis,ividersentaryicrowa

63666.B. Penetism fEEE Tr1999) 2n lines have also given rise to very compet-. Composite right/left-handed metamaterialn lines based on LC-loaded transmissionalso been applied in filter design. As an

structure, tapered coupled-resonators-basedcan be used to design broad-band filters pre-h frequency selectivity. In [32], such a filtered in MIM configuration is presented, show-ional bandwidth of 115% and a reasonablee. Such tapered coupled-resonator structuresto exhibit transmission zeros at different fre-d provide a sharp cutoff at the upper edge of

mproving frequency selectivity.to non-linearity and controllability of thediagram of CRLH transmission lines, it isdesign dual-band components operating at

requencies. In [33], for example, bandpassop filters based on quarter wave resonatorsimplemented by replacing the lines with LC-LH TLs. By doing this, the second operatingf2, where the phase is 3/2 does not haved multiple of the first one, f1, but it can be

ely. The results in [33] prove that this strat-applied to the design of dual-band bandpass

op filters with different bandwidths and goodes.terial transmission lines can also be usedent stepped-impedance resonator bandpass. In such devices, right- and left-handedn line sections with different characteristics alternate. If the length of the right-handeds and values of the characteristic impedancesly chosen, dimensions can be drasticallyd, at the same time, the first spurious banded to higher frequencies. As a result, compactlters with an improved out-of-band rejectionlemented.re some of the examples showing the appli-sibilities of metamaterial transmission linessign. Work is in progress in our Group androups worldwide to further miniaturize andicrowave filters on the basis of metamaterial.

sions

on the work developed during the last yearsof filters using resonant-type metamaterial

the psionshowalitietransbe columpfore,impl

Omentthe poffer

Ackn

Tby prNOVto MFramMOR(Gen

Refe

[1] MtlP

[2] GtE

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a

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I(lities that this kind of metamaterial transmis-offer in compact filter design. As the resultsrent bandwidths, performances and function-e obtained using resonant-type metamaterialn lines and, at the same time, dimensions canrably reduced without the need of includingments. Such metamaterial filters are, there-od alternative when size and fully planaration are key issues.proaches have also been applied to the imple-

of filters with excellent results, showing againilities that metamaterial transmission lineser design.

dgements

ork has been supported by MEC (Spain)contract TEC2007-68013-C02-02 METAIN-a FPU Grant (Ref. AP2005-4523) awardedil and by the European Commission (VIProgram) contract no. 500252-2 META-

SE. Special thanks are also given to CIDEMt de Catalunya) for funding CIMITEC.

s

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orth, T. Bonacarca-G. Soro

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romagn007), R. Gil,

te rightomplemery widicrowa. Gil,

mplemen: Proceosium D. Bonac. Soro

omplemechnolo.V. Ng

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arch 2. Tsengomposiroceediium Dig.B. Venryakova. Gil, A

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nd resonant type metamaterial transmission lines,

tW

[24] JGMtt5

[25] PbI5

[26] JLpa

[27] Js

L[28] F

r

m

Pt2

[29] Mic

v

M[30] M

iip

[31] JMc

T[32] H

tiM

[33] Cc

Ps

[34] IbMto

S[35] M

a

c

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Metamaterial filters: A reviewIntroductionResonant-type metamaterial transmission linesMetamaterial filtersFilters based on alternate right/left-handed cellsUltra-wide bandpass filters based on balanced cellsDesign methodology for bandpass filtersOther approaches

ConclusionsAcknowledgementsReferences