Split Rings for Metamaterial and Microwave Circuit Design: A … · 2018. 10. 16. · Split Rings...

Split Rings for Metamaterial and Microwave CircuitDesign: A Review of Recent Developments (InvitedPaper)

Miguel Dur�an-Sindreu, Jordi Naqui, Jordi Bonache, Ferran Martı́n

GEMMA/CIMITEC, Departament d’Enginyeria Electr�onica, Universitat Aut�onoma de Barcelona, 08193BELLATERRA (Barcelona), Spain

Received 6 July 2011; accepted 5 January 2012

ABSTRACT: This article is a review of recent applications of split rings to the design of pla-

nar microwave circuits based on metamaterial concepts. The considered resonators, namely,

split-ring resonators (SRRs), complementary SRRs (CSRRs), and their open counterparts

(OSRRs and OCSRRs), are reviewed, and the equivalent circuit models of artificial lines based

on such resonators, including parasitics, are presented and discussed. The second part of the

article is devoted to highlight some recent applications of the considered resonators. This will

include the design of dual-band components and wideband bandpass filters based on the com-

bination of OSRRs and OCSRRs, the design of tunable components based on cantilever-type

SRRs, and the design of CSRR-based differential (balanced) lines with common-mode sup-

pression. VC 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:439–458, 2012.

Keywords: split-ring resonators; metamaterials; dual-band components; microwave filters; differ-

ential transmission lines

I. INTRODUCTION

Metamaterial transmission lines are artificial lines loaded

with reactive elements. Thanks to the presence of these

elements, there are more degrees of freedom, as compared

with conventional lines, and it is possible to tailor the dis-

persion and the characteristic impedance of these lines to

implement microwave devices with enhanced performance

or with novel functionalities [1–4]. Moreover, in metama-

terial transmission lines, the electrical length is no longer

related to the physical length of the lines; therefore, these

lines are also of interest for device miniaturization.

There are two main types of metamaterial transmission

lines: (i) those loaded with series capacitances and shunt

inductances (CL-loaded lines) [5–7], and (ii) those based on

resonant elements, like the split-ring resonator (SRR) [8, 9] or

the complementary SRR [10, 11] (CSRR), among others. The

latter approach has been called resonant-type approach. We

would like to mention that CL-loaded lines based on the lattice

network topology have also been recently reported [12, 13],

but such lines are complex and further effort is needed for

their implementation in monolayer PCB technology [14].

This work is focused on the applications of resonant-

type metamaterial transmission lines to the design of planar

microwave circuits. Specifically, we will review the recent

developments achieved by the authors. This will include the

design of dual-band components and wideband filters based

on the combination of open SRRs (OSRRs) [15] and open

complementary SRRs (OCSRRs) [16, 17], the design of

tunable stopband filters based on micro-electro-mechanic

systems (MEMS)-type movable SRRs [18], and the design

of CSRR-based balanced microstrip lines with common

mode noise rejection [19]. The article is organized as fol-

lows. In Section II, the fundamentals of metamaterial trans-

mission lines, including the propagation characteristics, and

the derivation of the dispersion relation and characteristic

impedance, are presented. The resonators considered in this

article and the circuit models of the artificial lines based on

them are reviewed in Section III. In Section IV, the previ-

ous cited applications are reported. Finally, the main con-

clusions of the work are highlighted in Section V.

II. FUNDAMENTALS OF METAMATERIALTRANSMISSION LINES

Metamaterial transmission lines are one-dimensional (1D)

homogeneous propagating structures consisting of a host

line periodically loaded with reactive elements and exhib-

iting controllable electromagnetic properties. Although

Correspondence to: F. Martı́n; e-mail: [email protected].

VC 2012 Wiley Periodicals, Inc.

DOI 10.1002/mmce.20635Published online 13 April 2012 in Wiley Online Library

(wileyonlinelibrary.com).

439

metamaterial transmission lines are 1D structures, effec-

tive constitutive parameters (the effective permittivity, eeff,and permeability, leff), can be defined according to the

following expressions:

Zs0ðxÞ ¼ jxleff (1)

Yp0ðxÞ ¼ jxeeff (2)

Zs0 and Yp

0 being the per unit length series impedance

and shunt admittance of the equivalent T- or p-circuitmodel of the unit cell of the structure. Expressions (1)

and (2) result from the mapping between the equations

describing TEM wave propagation in planar transmission

media and plane wave propagation in isotropic and homo-

geneous dielectrics (telegraphist’s equation) [1–4].

Depending on the signs of Zs0 and Yp

0, the constitutive pa-

rameters of such artificial lines can be both positive, both

negative, or of opposite sign, giving rise to forward (right

handed) wave propagation, backward (left handed) wave

propagation, or inhibiting wave propagation, respectively.

Rather than the effective permittivity and permeability,

the significant parameters in transmission lines are the

electrical length (or phase constant) and the characteristic

impedance. In fact, the nature of propagation (forward or

backward) in these artificial lines, and the regions where

wave propagation is allowed, can be derived without

invoking the effective constitutive parameters. They can

be simply inferred from the signs of the series and shunt

reactances (of the equivalent T- or p-circuit model) and

from the dispersion equation [20]:

cosh cl ¼ 1þ ZsðxÞZpðxÞ (3)

where c ¼ aþjb is the complex propagation constant, l isthe unit cell length, and Zs and Zp are the series and shunt

impedances, respectively, of the equivalent T- or p-circuit

model. In the regions where propagation is allowed, a ¼0 (losses are neglected), and (3) rewrites as

cos bl ¼ 1þ ZsðxÞZpðxÞ (4)

Thus, the key aspect in reactively loaded lines is the

controllability of the dispersion diagram and the character-

istic impedance. The latter is given by the following

expression

ZBðxÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZsðxÞ½ZsðxÞ þ 2ZpðxÞ�

q(5)

for a structure consisting of a cascade of unit cells

described by the T-circuit model, and, if the structure is

modeled by a p-circuit, by the following expression:

ZBðxÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZsðxÞZpðxÞ=2

1þ ZsðxÞ2ZpðxÞ

vuut (6)

This controllability is superior than that for conven-

tional lines, given the higher flexibility associated with the

presence of loading elements. Thus, in the context of this

article, metamaterial transmission lines (metalines from

now on) are artificial lines, consisting of a host line

loaded with reactive elements, which allow further control

on phase constant and characteristic impedance, as com-

pared with conventional lines. Homogeneity will not be

considered necessary, namely, in certain frequency

regions, the unit cell length might not be small enough as

compared to the guided wavelength. In 3D artificial

media, this loss of homogeneity may be critical, but this

aspect is not fundamental in transmission lines. Periodicity

is another aspect that we do not consider a due. Thus, in

many examples, we will consider a single cell (this is ben-

eficial for size reduction) or even a cascade of different

cells (in this latter case, the above equations are no longer

valid or do not make sense, but the resulting structures

can be useful to satisfy certain requirements or

specifications).

The first proposed metalines have been implemented

by means of the CL-loaded approach, where a host line

was loaded with series capacitances and shunt inductances

[21, 22]. Such lines can be implemented through lumped

circuit elements (smd inductances and capacitances) or by

means of semilumped components. Semilumped compo-

nents mean, in this context, electrically small planar com-

ponents. Through semilumped components, fully planar

configurations can be obtained, although the values of

capacitances and inductances that can be implemented are

limited. Typical topologies of fully planar CL-loaded lines

are depicted in Figure 1. In Figure 1a, a coplanar wave-

guide (CPW) transmission line is periodically loaded with

shunt connected strips (emulating the shunt inductances)

and gaps (accounting for the series capacitances). In Fig-

ure 1b, where a microstrip line is considered, the shunt

strips are replaced with vias. Finally, in Figure 1c, a

Figure 1 Typical topologies of CL-loaded metamaterial trans-

mission lines. (a) CPW structure loaded with shunt strips and se-

ries gaps; (b) microstrip structure loaded with vias and series

gaps; (c) microstrip structure loaded with grounded stubs and

interdigital capacitors.

440 Dur�an-Sindreu et al.

International Journal of RF and Microwave Computer-Aided Engineering/Vol. 22, No. 4, July 2012

microstrip line is loaded with series connected interdigital

capacitances and grounded stubs (acting as shunt induc-

tors). In all cases, the lumped element equivalent T-circuit

model of the unit cell is that depicted in Figure 2 (this

model is valid as long as the distance between the semi-

lumped elements is small). Losses are considered to be

negligible, and hence, they are not included in the circuit

model. The elements of the model are the line parameters

(capacitance, CR, and inductance, LR), the series capaci-

tance, CL and the shunt inductance, LL. As usual, the sub-

indexes denote the elements responsible for the left-

handed (L) and right-handed (R) bands of these artificial

lines. Namely, at low frequencies, the loading elements

are dominant and left-handed wave propagation arises in a

certain frequency band. At higher frequencies, the loading

elements are no longer dominant and wave propagation is

forward. Inspection of the dispersion diagram of the cir-

cuit of Figure 2, obtained from expression 4 (Fig. 3),

reveals that the group velocity is positive in the allowed

bands, whereas the phase velocity is negative (backward

waves) in the left-handed band, and positive (forward

waves) in the right-handed band. Thus, CL-loaded lines

do actually exhibit a composite right/left handed (CRLH)

behavior [23]. To obtain a purely left-handed line, we

would need a cascade of series capacitances alternating

with shunt inductances. This corresponds to the dual

model of a conventional transmission line, which is well

known to exhibit backward waves above a certain cutoff

frequency [24]. However, such line cannot be imple-

mented in practice, as a host line is required. The fre-

quency gap present between the left handed and the right

handed bands is delimited by the following frequencies

(Fig. 3):

xG1 ¼ minðxs;xpÞ (7)

xG2 ¼ maxðxs;xpÞ (8)

with

xs ¼ 1ffiffiffiffiffiffiffiffiffiffiffiLRCL

p (9)

xp ¼ 1ffiffiffiffiffiffiffiffiffiffiffiLLCR

p (10)

and the lower (x�) and upper (xþ) limits of the left-

handed and right-handed bands, respectively, are:

x6 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4þ LRCRðx2

s þ x2pÞ

2LRCR

61

2LRCR

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiL2RC

2Rðx2

s � x2pÞ2 þ 8LRCRðx2

s þ x2pÞ þ 16

qsð11Þ

By designing the structure with identical series and

shunt resonance frequencies, the gap disappears and there

is a continuous transition between the left-handed and

right-handed bands (balance condition). At the transition

frequency, the phase velocity is infinity, whereas the

group velocity is finite (Fig. 4). The implications of this

(out of the scope of this work) have been discussed in

detail in Refs. [3, 4]. The characteristic impedance (or

image impedance) of these lines, given by expression 5,

is:

ZB ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLRCR

1� x2s

x2

� �1� x2

p

x2

� �� L2Rx2

41� x2

s

x2

� �2

vuuut (12)

Figure 2 Lumped element equivalent T-circuit model of the

unit cell of CL-loaded metamaterial transmission lines.

Figure 3 Typical dispersion diagram (a) and characteristic im-

pedance (b) of a CL-loaded metamaterial transmission line. The

line exhibits a CRLH behavior.

Split Rings for Metamaterial and Microwave Circuits 441

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

for CRLH lines based on the model depicted in Figure 2

(see Fig. 3b for a typical representation of the dependence

of ZB with frequency), and this expression reduces to

ZB ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLRCR

� L2Rx2

41� x2

s

x2

� �2s

(13)

for balanced lines. In this latter case (balanced lines), the

impedance is maximum and roughly constant in the vicin-

ity of the transition frequency [3, 4] (see Fig. 4).

III. SPLIT RINGS: TOPOLOGIES AND CIRCUIT MODELS

The metalines considered in this work are based on pairs

of coupled split rings. The coupling between the rings

shifts the first resonance frequency downward and, hence,

the resulting resonator is electrically small. This small

electrical size is fundamental for the design of split-ring-

based metamaterials, where homogeneity is a key factor,

and for circuit miniaturization. The considered electrically

small resonators are the SRR, the CSRR, and their open

counterparts, the OSRR and the OCSRR. Let us review

the topologies of these resonators and the circuit models

of the main artificial lines based on them.

A. Split-Ring ResonatorsThe topology of the SRR [8] is depicted in Figure 5. It

consists of a pair of metallic rings, etched on a dielectric

slab, with apertures in opposite sides. The first resonance

of this particle is typically (although not exclusively)

excited by means of a time varying axial magnetic field.

The structure is, thus, a magnetically driven resonant tank,

where the inductance is given by the inductance of a sin-

gle loop with average radius and the same strip width, Ls,and the capacitance is given by the series connection of

the distributed (edge) capacitances of the upper and lower

halves of the SRR, as reported in Ref. [25] (i.e., Cs ¼ C0/

4, with C0 ¼ 2proCpul and Cpul is the per unit length ca-

pacitance between the rings).

These resonators can be inductively coupled with a

transmission line (typically, a CPW or a microstrip line)

to implement a 1D artificial medium exhibiting negative

effective permeability in a narrow band above the first

resonance frequency. This was demonstrated in Ref. [9],

where a CPW was loaded with pairs of SRRs, and the

resulting structure was found to exhibit a stopband behav-

ior in the vicinity of resonance that was interpreted as due

to the negative effective permeability. If narrow inductive

strips are introduced between the central strip and the

ground plane (above the positions of the SRRs), the

behavior of the structure switches to a bandpass that can

be attributed to the coexistence of negative effective per-

meability and permittivity (due to the inductive strips) in

a narrow band, where left-handed wave propagation

arises.

Nevertheless, these artificial lines can be easily ana-

lyzed from the lumped element equivalent circuit models,

valid up to frequencies beyond the first resonance fre-

quency of the SRR by virtue of its small electrical size.

The circuit model of the unit cell of a CPW structure

loaded with pairs of SRRs and inductive strips is depicted

in Figure 6a [26]. In this model, L and C account for the

line inductance and capacitance, respectively, Cs and Lsmodel the SRRs, M is the mutual inductive coupling

between the line and the SRRs, and Lp is the inductance

of the shunt strips. The circuit model of Figure 6a can be

transformed to the model of Figure 6b [26] with:

Ls0 ¼ 2M2Csx

2o

1þ L4Lp

� �21þ M2

2LpLs

(14)

C0s ¼

Ls2M2x2

o

1þ M2

2LpLs

1þ L4Lp

!2

(15)

Figure 4 Typical dispersion diagram (a) and characteristic im-

pedance (b) of a balanced CRLH CL-loaded metamaterial trans-

mission line.

Figure 5 Typical topology and circuit model of the SRR. The

relevant dimensions are indicated.



L0 ¼ 2þ L

2Lp

� �L

2� Ls

0 (16)

Lp0 ¼ 2Lp þ L

2(17)

Notice that the circuit model (unit cell) of SRR-loaded

lines without the presence of the inductive strips is

inferred from the circuit of Figure 6a by merely eliminat-

ing the inductance Lp.

In view of the circuit of Figure 6b, just above the reso-

nance frequency of the series connected parallel resonator,

where the series reactance is negative and the shunt im-

pedance is dominated by the inductance of the narrow

strips, left-handed wave propagation is expected. This has

been confirmed from the electromagnetic simulation of

the structure reported in Figure 7a (see Fig. 7c), where the

dispersion diagram shows that the phase and group veloc-

ities are antiparallel in this region and a bandpass arises.

Conversely, if the strips are removed (Fig. 7b), a stopband

behavior is obtained in the vicinity of resonance. Actually,

the structure of Figure 7a exhibits a right-handed behavior

at higher frequencies (beyond the depicted frequency

region), as the circuit of Figure 6b predicts. This right-

handed transmission band arises in that region where the

series and shunt impedances are dominated by the line in-

ductance and line capacitance, respectively. We would

like to mention to end this subsection that the model of

Figure 6a, formerly reported in Ref. [26], is an improved

version of the original model of SRR-loaded lines,

reported by some of the authors in Ref. [9}.

B. Complementary Split-Ring ResonatorsThe CSRR is obtained from the SRR by applying duality,

that is, by replacing the metallic regions with air and vice

versa [10] (Fig. 8). From duality arguments, it follows

that the first resonance frequency of the CSRR can be

(although not exclusively) excited by means of an axial

time varying electric field, and the resonator can be mod-

eled by means of a resonant tank, where the inductance Lsof the SRR model is substituted by the capacitance, Cc, of

a disk of radius ro-c/2 surrounded by a ground plane at a

distance c of its edge and the series connection of the two

capacitances C0/2 in the SRR model is substituted by the

parallel combination of the two inductances connecting

the inner disk to the ground [27]. Each inductance is

given by L0/2, where L0 ¼ 2proLpul and Lpul is the per

unit length inductance of the CPWs connecting the inner

disk to the ground. For infinitely thin perfect conducting

screens, and in the absence of any dielectric substrate, it

directly follows from duality that the parameters of the

circuit models for the SRRs and the CSRRs are related by

Cc ¼ 4(eo/lo)Ls and C0 ¼ 4(eo/lo)L0. From the above

relations, it is easily deduced that the frequency of reso-

nance of both structures is the same, as it is expected

from duality.

Figure 7 Layout of the considered CPW structures with SRRs

and shunt strips (a) and with SRRs only (b); simulated (through

the Agilent Momentum commercial software) and measured trans-

mission coefficient, S21, and simulated dispersion relation (c).

The considered substrate is the Rogers RO3010 with thickness h¼ 1.27 mm and dielectric constant er ¼ 10.2. Relevant dimen-

sions are: rings width c ¼ 0.6 mm, distance between the rings d¼ 0.2 mm, internal radius r ¼ 2.4 mm. For the CPW structure

the central strip width is W ¼ 7 mm and the width of the slots is

G ¼ 1.35 mm. Finally, the shunt strip width is 0.2 mm. The

results of the electrical simulation with extracted parameters are

depicted by using symbols. We have actually represented the

modulus of the phase since it is negative for the left-handed line.

Discrepancy between measurement and simulation for circuit (a)

is attributed to fabrication related tolerances.

Figure 6 Circuit model (unit cell) of a CPW loaded with

SRRs and shunt inductive strips (a) and transformed p–circuitmodel (b). Figure 8 Typical topology of the CSRR and circuit model.



CSRR-loaded microstrip lines with CSRRs etched in

the ground plane below the conductor strip have been

reported [10, 27]. The structure exhibits a stopband behav-

ior similar to that of SRR-loaded lines, but in this case

related to the negative effective permittivity. By adding

series capacitive gaps to the structure, the behavior

switches to a bandpass due to the simultaneous negative

permittivity and permeability (caused by the gaps) of the

structure in a narrow band [28, 29]. The circuit model of

the unit cell of the CSRR-loaded line with gaps included

is depicted in Figure 9a [30]. L and CL model the line in-

ductance and capacitance, respectively, Lc and Cc model

the CSRR and the gap is modeled by the series capaci-

tance, Cs, and the fringing capacitance, Cf, respectively.

This model can be easily transformed to that shown in

Figure 9b, with:

Cg ¼ 2Cs þ Cpar (18)

C ¼ Cparð2Cs þ CparÞCs

(19)

We have simulated a unit cell structure of a microstrip

line loaded with a CSRR and a series gap (Fig. 10a). The

result reveals that a left-handed transmission band appears

in the region where the series reactance is capacitive and

the shunt reactance is inductive. If the gap is removed

(Fig. 10b), a stopband behavior in the vicinity of the

transmission zero frequency appears. This transmission

zero is given by:

fz ¼ 1

2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiLcðCþ CcÞ

p (20)

The right-handed band expected for the structure with

gap is present at frequencies beyond the range shown in

the figure.

C. Open Split-Ring Resonators and Open ComplementarySplit-Ring ResonatorsOpen resonators are a different kind of electrically small

structures. Figure 11 shows the layouts and equivalent cir-

cuit models of the OSRR [15] and the open complemen-

tary SRR (OCSRR) [16]. The OSRR is based on the SRR

and is obtained by truncating the rings forming the reso-

nator and elongating them outward. The OCSRR is the

complementary particle of the OSRR. The resonators

shown in Figure 11 can be implemented either in micro-

strip or in CPW technology [17]. The equivalent circuit

model of the OSRR is a series LC resonator, where the in-

ductance is the same as the inductance of the SRR, Ls,and the capacitance is the distributed capacitance between

Figure 9 Circuit model (unit cell) of a microstrip line loaded with

CSRRs and series gaps (a) and transformed T–circuit model (b).

Figure 10 Simulated (through the Agilent Momentum commer-

cial software) frequency responses of the unit cell structures shown

in the insets. (a) Microstrip line loaded with CSRRs and series

gaps; (b) microstrip line only loaded with CSRRs. The response

that has been obtained from circuit simulation of the equivalent

model with extracted parameters is also included. Dimensions are:

the microstrip line width Wm ¼ 1.15 mm, the length D ¼ 8 mm

and the gap width wg ¼ 0.16 mm. The dimensions of the CSRRs

are: outer ring width cout ¼ 0.364 mm, inner ring width cinn ¼0.366 mm, distance between the rings d ¼ 0.24 mm, internal radius

r ¼ 2.691 mm. The considered substrate is the Rogers RO3010

with dielectric constant er ¼ 10.2 and thickness h ¼ 1.27 mm.



the concentric rings, C0. It means that for given dimen-

sions and substrate, the resonance frequency of the OSRR

is half the resonance frequency of the SRR, and hence,

the OSRR is electrically smaller than the SRR by a factor

of two [15]. Similarly, the equivalent circuit model of the

OCSRR is a parallel resonant tank in series configuration,

where the capacitance is identical to that of the CSRR,

and the inductance is L0, that is, four times larger than

that of the CSRR. Therefore, the OCSRR is electrically

smaller than the CSRR by a factor of two. Obviously,

under ideal conditions of duality, OSRRs, and OCSRRs of

identical dimensions etched onto the same substrate ex-

hibit the same resonance frequency.

Let us consider the open resonators loading a transmis-

sion line. Specifically, a CPW transmission line is consid-

ered because this is the host line used in the examples

reported later. The series connected OSRR and the pair of

shunt connected OCSRRs are depicted in Figures 12a and

12d, respectively, together with the equivalent circuit

models (Figs. 12b and 12e). To properly describe the

behavior of the structures, it is necessary to cascade phase

shifting lines, which are modeled as shown in the figure.

Notice that the circuits can then be transformed to those

depicted in Figures 12(c) and 12(f), where L and C must

be considered parasitic elements. The structures of Figure

12 are not the unit cells of metalines. However, we can

alternatively cascade these cells to implement artificial

transmission lines with CRLH characteristics, as will be

later demonstrated. Nevertheless, the response of the

Figure 11 Typical topology and circuit model of the OSRR

(a) and OCSRR (b).

Figure 12 Typical topology and circuit model of OSRR- (a)-

(c) and OCSRR-loaded (d)-(f) CPWs.

Figure 13 Topology (a), return loss (b) and frequency response

(c) of a typical OSRR loaded CPW structure. The considered sub-

strate is the Rogers RO3010 with thickness h ¼ 0.254 mm and

dielectric constant er ¼ 11.2. The dimensions are: W ¼ 5 mm, G¼ 0.55 mm, rext ¼1.6 mm, c ¼ d ¼ 0.2 mm. The values of the

equivalent circuit are: C ¼ 0.189 pF, L0s ¼ Lsþ2L ¼ 5.55 nH, Cs

¼ 0.58 pF. [Color figure can be viewed in the online issue, which

is available at wileyonlinelibrary.com.]



structures of Figure 12 is shown in Figures 13 and 14.

The agreement between the circuit simulation, with

extracted parameters according to the method reported in

Refs. [17, 31] (and reproduced in the Annex I for com-

pleteness), and the electromagnetic simulation is very

good. The reflection coefficient, S11, is also depicted in

this figure to demonstrate that the OSRR- or the OCSRR-

loaded CPWs cannot merely be modeled by series and

shunt resonators, respectively. This is apparent as the tra-

jectory of the reflection coefficient in the Smith chart is

not located in the unit resistance or conductance circles.

IV. APPLICATIONS OF SPLIT RING BASED LINES

The aim of this section is to highlight some recent appli-

cations of split ring based lines achieved by the authors.

Many other applications can be found in Ref. [4]. We will

divide this section in three subsections, devoted to show

some applications of OSRR/OCSRR, SRR- and CSRR-

loaded lines, respectively.

A. Applications of OSRR/OCSRR-Loaded Lines toDual-Band Components and Bandpass FiltersIf parasitics (L and C) in the models of Figure 12 are

neglected, it is apparent that by alternating series con-

nected OSRRs and shunt connected OCSRR, we obtain

the CRLH line model of Figure 2 (unit cell). In practice

parasitics cannot be neglected, but their effects are not

very significant, and hence, we have designed CRLH lines

based on the combination of OSRRs and OCSRRs. Here,

we report as a first example a CRLH line that has been

used for the implementation of a dual-band Y-junction

power divider [17]. The target has been to implement a

35-X impedance inverter functional at f1 ¼ 2.4 GHz and

f2 ¼ 3.75 GHz. The artificial line has been designed so

that it provides an electrical length of �90� at f1 and

þ90� at f2, which leads to Zs ¼ �Zp at both frequencies

f1 and f2, as inferred from the dispersion relation of the T-

circuit model, given by expression 4. These conditions

hence force that Zs(f1) ¼ �Zp(f1) ¼ �j35.35 X and Zs(f2)¼ �Zp(f2) ¼ þ j35.35 X, as reported in Ref. [17]. Thus,

we need to obtain the series and shunt impedance of the

whole structure formed by the cascaded OSRR-OCSRR-

OSRR stages. This has been done by calculating the

[ABCD] matrix of the equivalent circuit of Figure 15a.

From this analysis, the series and shunt branch impedan-

ces of the equivalent T-circuit model are found to be:

Zs ¼�j 1� x2L0sCs

� �þ Lx2 CL0sCsx2 � C� Cs

� �� x Cs þ Cx2 CL x2L0sCs � 1

� �� 2CsL� L0sCs þ 1x2

� �� (21)

Zp ¼�jxL0pC

2s

ð1� x2L0pC0pÞC2

1 þ Cx2C2 CLx2C2L2 � 2C1L1ð Þ(22)

with

Figure 14 Topology (a), return loss (b) and frequency response

(c) of a typical OCSRR loaded CPW structure. The considered

substrate is the Rogers RO3010 with thickness h ¼ 0.254 mm

and dielectric constant er ¼ 11.2. The dimensions are: W ¼ 5

mm, G ¼ 0.55 mm, rext ¼ 1.2 mm, c ¼ 0.2 mm, d ¼ 0.6 mm.

The values of the equivalent circuit are: L ¼ 0.32 nH, L0p ¼ Lp/2

¼ 0.983 nH, C0p ¼ 2(Cp þ C) ¼ 2.85 pF. [Color figure can be

viewed in the online issue, which is available at

wileyonlinelibrary.com.]

Figure 15 Circuit model (a) and layout (b) of the dual-band

impedance inverter based on a combination of series connected

OSRR in the external stages and a pair of shunt connected

OCSRRs in the central stage. The substrate is the Rogers

RO3010 with thickness h ¼ 0.635 mm and dielectric constant er¼ 10.2. Dimensions are: l ¼ 9 mm, W ¼ 4 mm, G ¼ 0.74 mm.

For the OCSRR: rext ¼ 0.9 mm, c ¼ 0.2 mm, d ¼ 0.2 mm. For

the OSRR: rext ¼ 1.5 mm, c ¼ 0.3 mm, d ¼ 0.2 mm. The wide

metallic strip in the back substrate side has been added in order

to enhance the shunt capacitance of the OCSRR stage, as required

to achieve the electrical characteristics of the device.



C1 ¼ Cs þ C 1� x2

x2s

� �(23)

L1 ¼ L0p þ L 1� x2

x2p

!(24)

C2 ¼ 2Cs þ C 1� x2

x2s

� �(25)

L2 ¼ 2L0p þ L 1� x2

x2p

!(26)

and

xs ¼ 1ffiffiffiffiffiffiffiffiffiL0sCs

p (27)

xp ¼ 1ffiffiffiffiffiffiffiffiffiffiL0pC0

p

p (28)

By forcing Eqs. (21) and (22) to take the above cited

values at the operating frequencies of the dual-band im-

pedance inverter, four conditions result. However, we

have six unknowns. The procedure to determine the ele-

ment values is as follows: in a first step, we consider that

L and C (the parasitics in the models of Fig. 12 or 15) are

null, and we obtain the other four element values (which

are perfectly determined). Then, we generate a layout for

the OSRR and OCSRR stages so that the extracted param-

eters for the resonators are identical to those inferred in

the first step. From this layout we infer also the element

values of the parasitics, which are introduced in Eqs. (21)

and (22). Then, we calculate the other element values to

satisfy the four cited conditions.

Through this procedure, we have obtained the follow-

ing parameters: C ¼ 0.2 pF, L ¼ 0.25 nH, Cs ¼ 0.66 pF,

L0s ¼ 3.74 nH, C0p ¼ 2.99 pF and L0p ¼ 0.83 nH. Finally,

by means of the parameter extraction technique, we have

inferred the layout topology of the dual-band impedance

inverter that provides these element values (see Fig. 15b).

The circuit simulation and electromagnetic simulation of

the dual-band impedance inverter are shown in Figure 16.

These results reveal that the required characteristics are

satisfied. By cascading a 50-X input (access) line and two

50-X output lines, the dual-band power splitter results.

The photograph of this device (fabricated on the RogersRO3010 substrate with thickness h ¼ 0.635 mm and

dielectric constant er ¼ 10.2) is shown in Figure 17, and

the simulated and measured power splitting and matching

are depicted in Figure 18. The required functionality at

the two operating frequencies is achieved.

The second example of application of OSRR/OCSRR

structures is a bandpass filter. In this case, periodicity is

sacrificed as our intention is to implement an order-5

bandpass filter subjected to specifications, that is, a Che-

byshev response with central frequency fo ¼ 2 GHz, 0.05-

dB ripple and 50% fractional bandwidth. The synthesized

filter layout is depicted in Figure 19 (together with the

photograph of the fabricated device). The device has been

fabricated on the Rogers RO3010 substrate with thickness

h ¼ 0.254 mm and dielectric constant er ¼ 10.2. The fre-

quency response of the structure obtained from electro-

magnetic simulation is compared with the response

inferred from the circuit simulation of the model of Figure

15a in Figure 20. The agreement is reasonably good, but

this agreement can be further improved if we include an

additional inductance, Lsh, in the model of the OCSRR, as

depicted in Figure 21. This inductance increases by

decreasing the width of the metallic strip connecting the

central strip of the CPW and the inner regions of the

OCSRR, is responsible for the presence of the transmis-

sion zero above the pass band and also improves the fre-

quency selectivity at the upper band edge. Many other fil-

ters with wideband response have been designed and

Figure 17 Photograph of the fabricated dual-band power splitter. (a) Top; (b) Bottom. [Color figure can be viewed in the online issue,

which is available at wileyonlinelibrary.com.]

Figure 16 Circuit simulation and electromagnetic simulation

of the dual-band impedance inverter.



fabricated using open resonators [32, 33]. We would also

like to mention that by combining the open resonators

reported here with other electrically small resonators, the

authors have designed quadband components [34] and

dual-band bandpass filters [34, 35].

B. Applications of SRR-Loaded Lines to the Design ofTunable ComponentsSRRs are of interest for the design of bandstop filters [36,

37] and bandpass filters [38]. By introducing tunability to

these resonators, the possibility of realizing reconfigurable

Figure 18 Frequency response of the dual-band power splitter.

Figure 19 Topology (a) and photograph (b) of the designed

fifth-order filter. Dimensions are: l ¼ 25 mm, W ¼ 9.23 mm, G¼ 0.71 mm, a ¼ 0.4 mm, b ¼ 10.64 mm, e ¼ 0.96 mm and f ¼3.2 mm. For the external OSRRs: rext ¼ 2.5 mm, c ¼ 0.3 mm

and d ¼ 0.35 mm. For the central OSRR: rext ¼ 3.4 mm, c ¼0.16 mm and d ¼ 1.24 mm. For the OCSRRs: rext ¼ 1.4 mm and

c ¼ d ¼ 0.3 mm. [Color figure can be viewed in the online issue,

which is available at wileyonlinelibrary.com.]

Figure 20 Frequency response without losses (a) and wideband

frequency response (b) of the designed fifth-order filter. The ele-

ment values for the circuit simulation without considering Lshare: for the external OSRRs: C ¼ 0.207 pF, Cs ¼ 0.763 pF and

L0s ¼ 8.501 nH. For the central OSRR: C ¼ 0.274 pF, Cs ¼0.436 pF and L0s ¼ 13.118 nH. For the OCSRRs: L ¼ 0.474 nH,

C0p ¼ 4.5 pF and L0p ¼ 1.224 nH. The modified values of the

OCSRR considering the wideband model with the additional par-

asitic element Lsh are (in reference to Figure 21): L ¼ 0.385 nH,

C’p ¼ 4.4 pF, L’p ¼ 1.259 nH and Lsh ¼ 0.35 nH. [Color figure

can be viewed in the online issue, which is available at


Figure 21 Wideband circuit of the pair of shunt connected

OCSRRs shown in Figure 12(d).



components has been demonstrated. Thus, varactor diodes

[39, 40] and MEMS switches [41] have been added to the

SRR (and also to the CSRR [42, 43]) to implement tuna-

ble notch filters and bandpass filters, and tunable compo-

nents based on barium strontium titanate (BST) thick-films

have also been demonstrated [44, 45]. In this article,

another type of tunable SRR is considered in more detail

and applied to the design of tunable stopband filters: the

MEMS-based deflectable cantilever-type SRR, which was

presented for the first time in Ref. [18].

The reported tunable resonators based on MEMS typi-

cally consist of the resonator plus a MEMS bridge on top of

it (or in the gap region) [41, 42, 46], which is electronically

actuated and modifies the equivalent capacitance of the

whole structure, and hence its resonance frequency. In Ref.

[18], a different principle was used, that is, the MEMS

structures are part of the resonator. Each ring constituting

the SRR has a fixed part (anchor) and a suspended part

(membrane), which is curled up in the absence of electro-

static actuation. By applying an external voltage to the

anchor with reference to the 500 lm-thick high resistivity

silicon substrate, (electrically isolated from the anchor

through a 1-lm-thick SiO2 layer), the rings are deflected

down, and the coupling capacitance between the pair of

rings is modified (Fig. 22). The movable rings behave, thus,

similarly to cantilever-type MEMS. This principle of elec-

trical actuation through the silicon substrate has already

been used in RF-MEMS switches [47–49] and extended to

reconfigurable antennas and filters [50].

The top view of a typical tunable cantilever type SRR

is depicted in Figure 22a. The movable portions of the

rings are indicated in grey. Figures 22b and 22c depict the

cross-sectional view of the anchor and the cantilever,

without (up state) and with (down state) electrostatic

actuation, respectively. The details of the fabrication pro-

cess are out of the scope of this article, but we recom-

mend the interested reader the original paper where these

resonators were proposed [18].

The movable SRR of Figure 22a was coupled to a

microstrip transmission line (Fig. 23), and the frequency

response was measured after applying different voltage

combinations to the internal and external rings of the SRR

(Fig. 24). The different transmission zeros in the frequency

response are indicative of the change in the capacitance of

the structure, caused by ring’s actuation. In a first-order

approximation, each ring in the up state can be modeled as

composed of two parts: (i) a portion accounting for the

anchor and thus in contact with the SiO2 layer and (ii) an

elevated portion, with an uniform and effective height (heff)from the SiO2 layer, corresponding to the movable part, in

contact with the anchor by means of a metallic via. In this

model, the effects of rings corrugation are neglected, and

the distributed capacitance between the rings in the up state

is approximated by the capacitance between noncoplanar

(i.e., in a different plane) parallel strips separated a vertical

distance heff. Electromagnetic simulations of the structure,

modeled as reported above, by considering heff as an

Figure 22 Typical topology of the tunable SRR based on can-

tilever-type MEMS. (a) Top view with relevant dimensions.

Black and grey parts correspond to anchors and suspended parts

(including corrugations), respectively; (b) cross section in the up

state; (c) cross section in the down state. [Color figure can be



Figure 23 Topology of the tunable SRR coupled to a micro-

strip line with microstrip to CPW transition. The separation

between the SRR and the microstrip line is 50 lm; the width of

the microstrip line is 400 lm. The photograph of the nonactuated

SRR is also shown. [Color figure can be viewed in the online

issue, which is available at wileyonlinelibrary.com.]



adjustable parameter, were carried out by means of the

commercial software Agilent Momentum. Good agreement

between measurement and simulation for the four states

was obtained by choosing heff ¼ 17 lm. This effective

height is substantially smaller than the actual (maximum)

elevation of the rings in the up state, which was estimated

to be roughly 100 lm. However, this is expected as the per-

unit length capacitance of the pair of rings decreases dra-

matically when their separation increases.

By cascading the cantilever type MEMS-based SRRs

in a microstrip transmission line, tunable stopband filters

can be implemented (the rejection level can be controlled

by the number of stages). A fabricated prototype device is

depicted in Figure 25a. It consists of a stopband filter

with two pairs of coupled SRR (the movable parts are

depicted in gray). The measured frequency responses cor-

responding to the four different switching states are

depicted in Figure 26. The tuning range is roughly 12%,

but it can be enhanced by merely extending the movable

portions of the rings (this decreases the capacitance in the

up state and hence increases the resonance frequency). To

demonstrate this, an identical filter to that of Figure 25a,

but with longer cantilevers was fabricated. The tuning

range dramatically increases (see Fig. 26, where the meas-

ured frequency responses corresponding to the extreme

switching states, i.e., all switches up or down, for this

new filter are also indicated). In this case, the tuning

range is �42%. We would also like to mention that it is

possible to control the position of the rejection band at

the intermediate states (1.0 and 0.1) through the geometry

of the rings (including the dimensions of the movable

parts). Finally, by applying different voltage combinations

to the different SRRs or by modifying their dimensions

bandwidth can also be controlled.

As compared to tunable stopband filters based on

SRRs and varactor diodes [39], the present filters exhibit

better insertion losses in the allowed bands. As compared

with other filters based on CSRRs and RF-MEMS bridges

on top of them [42], this approach can provide better

tunability.

C. Applications of CSRRs to the Design of DifferentialLines with Common Mode SuppressionCSRRs have been used in many applications, including

stopband filters [51], bandpass filters [52–54], and

diplexers [55], device miniaturization [56], enhanced

bandwidth components [57, 58], dual-band components

[59], and so forth. In this subsection, a different (and

recent) application is considered: the design of differential

transmission lines with common-mode noise suppression.

Differential (or balanced) lines are of interest for high-

speed digital circuits because of their high immunity to

noise, low crosstalk and low electromagnetic interference

(EMI). However, the presence of common-mode noise in

Figure 24 Measured (solid lines) and simulated (dashed lines)

frequency response of the structure of Figure 23 for the four dif-

ferent states. The applied voltage for each ring actuation is 30 V.

The state of the rings is indicated, where ‘‘1’’ (ring actuation)

stands for down state and ‘‘0’’ for up state, and the first bit corre-

sponds to the inner ring.

Figure 25 Tunable stopband filters based on square-shaped

short (a) and long (b) cantilever-type SRRs. SRR side length is

1200 lm, ring width 150 lm and ring separation 30 lm. The sep-

aration between the SRR and the microstrip line is 25 lm. The

actuation voltages are applied to the rings through the bias pads

and high resistive lines (HRLs). [Color figure can be viewed in

the online issue, which is available at wileyonlinelibrary.com.]

Figure 26 Wideband measured transmission coefficients of the

filters of Figure 25 for the extreme switching states. The fre-

quency responses in the region of interest of the filter of Figure

25(a) for the four states are depicted in the inset. For measure-

ment, device ports have been connected through wire-bonding to

commercial microstrip to CPW transitions. Solid lines correspond

to the filter of Figure 25(a); dash-dotted lines correspond to the

filter of Figure 25(b). As frequency decreases, rejection is

reduced due to the degradation of the quality factor of the resona-

tors (see [39] for more details). Actuation voltage is 30 V. [Color

figure can be viewed in the online issue, which is available at




differential lines is unavoidable in practical circuits. This

unwanted noise can be caused by amplitude unbalance or

time skew of the differential signals and must be reduced

as much as possible to avoid common-mode radiation or

EMI. Therefore, the design of differential lines able to

suppress the common-mode noise, while keeping the in-

tegrity of the differential signals is of paramount

importance.

For GHz differential signals, compact common mode

filters based on multilayer LTCC [60] or negative permit-

tivity [61] structures have been reported. These structures

are compact and provide efficient common-mode rejection

over wide frequency bands but are technologically com-

plex. There have also been several approaches for the

design of common-mode suppressed differential lines

based on defected ground structures. In Ref. [62], dumb-

bell shaped periodic patterns etched in the ground plane,

underneath the differential lines, were used to suppress

the even mode by opening the return current path through

the ground plane. This has small effect on the differential

signals (odd mode), as relatively small current density

returns through the ground plane for such signals. In Ref.

[63], the same authors achieved a wide stopband for the

common mode using U-shaped and H-shaped coupled res-

onators symmetrically etched in the ground plane.

The authors have developed another approach for the

design of differential lines with common-mode suppres-

sion using CSRRs [19]. The unit cell structure of the pro-

posed differential line is depicted in Figure 27. It consists

of a pair of coupled lines with a CSRR symmetrically

etched in the ground plane. The circuit model of this

structure is also depicted in Figure 27, where Cm and Lmmodel the mutual capacitance and inductance between the

coupled lines (the other parameters are those of Fig. 9b).

The circuit model of Figure 27 explains that the differ-

ential signals are insensitive to the presence of the

CSRRs, whereas these resonators prevent the transmission

of the common mode at certain frequencies. The equiva-

lent circuit model of the structure of Figure 27 under

common-mode excitation is depicted in Figure 28a,

whereas for the odd mode is depicted in Figure 28b. For

the odd mode, the resonator is short circuited to ground,

and the resulting model is that of a conventional transmis-

sion line. For the even mode, we obtain the same circuit

as that of a CSRR-loaded line (Fig. 9b without the pres-

ence of Cg), but with modified parameters. Thus, we do

expect a similar stopband behavior for the common mode.

In terms of field distribution, there is a strong density of

electric field lines in the same direction below both lines

for the common mode. This causes CSRR excitation and

hence a stopband. For the odd mode, the direction of the

electric field lines is opposite in both strips of the differ-

ential line. If the structure is symmetric, (i.e., the gaps of

the CSRRs are aligned with the symmetry plane of the

differential lines), the opposite electric field vectors in

both lines exactly cancel and the CSRR is not excited.

To achieve a wide stopband for the common mode,

the strategy is (i) to widen the stopband of the individual

unit cell, (ii) to couple the resonators, (iii) to etch resona-

tors with slightly modified dimensions to obtain different

transmission zero frequencies within the desired stopband,

or (iv) to combine some of these effects. Among the pre-

vious strategies, bandwidth enhancement by tightly cou-

pling three identical square-shaped CSRRs has been con-

sidered. This geometry provides better inter-resonator

coupling as compared with circular CSRRs. By this

means, we can improve the rejection bandwidth for the

Figure 27 Topology and circuit model (elemental cell) of a

differential line loaded with a CSRR.

Figure 28 Circuit models for the even mode (a) and odd mode

(b).

Figure 29 Circuit model for the even mode with inter-resona-

tor’s coupling through CR.



common mode, but bandwidth can be further improved if

wideband resonators are considered. To widen the rejec-

tion bandwidth of an individual unit cell, it is necessary

to increase the coupling capacitance C and to reduce the

inductance Lc and capacitance Cc of the CSRR as much

as possible. To enhance the coupling capacitance C,weakly coupled lines will be considered, as the width of

the lines necessary to achieve an odd mode impedance of

50 X is wider. However, this must be done carefully, as

the lines must lie inside the inner part of the CSRR to

obtain high electric coupling. According to it, we have

set a line width of W ¼ 1 mm and a separation between

lines of S ¼ 2.5 mm. The corresponding characteristic

impedances for the even and the odd mode are Zce ¼ 57

X and Zco ¼ 50 X, respectively. Notice that both impe-

dances are similar because the lines are weakly coupled,

and in consequence, there is a small impedance mis-

matching between the reference impedance Z0 and the

even mode impedance Zce. This is a convenient situation,

as it has been observed that a high mismatching can de-

grade the filtering properties of the structure. With respect

to the CSRR, square-shaped rings not only increase the

inter-CSRRs coupling (this can be modeled by adding a

capacitance CR, as depicted in Fig. 29) but also the cou-

pling with the line, C. To reduce the inductance and the

capacitance of the CSRR, it is necessary to increase the

rings width, c, and separation, d. This results in a physi-

cally and electrically larger CSRR. Therefore, there exists

a trade-off between optimizing either the size or the

rejection bandwidth. Thus, as mentioned, we have consid-

ered not only wideband (and electrically large) coupled

resonators but also coupled CSRRs with narrow inter-

rings distance to optimize the size (at the expense of

bandwidth).

Let us first consider the design of a stopband filter for

the common mode by optimizing the size. To reduce the

size of the structure as much as possible, a CSRR with

narrow and tiny spaced rings (c ¼ 0.2 mm and d ¼ 0.2

mm) has been considered. These values are close to the

limit of the available technology. From the even mode

model, the coupling capacitance C has been approximated

by the per-unit length capacitance of the coupled lines in

the even mode. Then, the external side length of the

CSRR has been estimated to obtain a transmission zero

frequency located at fz ¼ 1.4 GHz from the model of the

CSRR reported in Ref. [27], that relates the capacitance

Cc and the inductance Lc with the width c, distance d, andexternal radius rext. Obviously, optimization at layout

level has been required due to the previous approxima-

tions, being the optimized side length equal to 7.6 mm.

The layout of a single unit cell and the corresponding

electromagnetic simulation for the common mode inser-

tion loss are depicted in Figure 30. The circuit simulation

of the structure with the electric parameters extracted

according to the procedure reported in Ref. [64] is also

Figure 30 Unit cell layout (a) and simulated common mode

insertion loss (b) of the device designed to optimize the size.

Dimensions are W ¼ 1 mm, S ¼ 2.5 mm, c ¼ 0.2 mm, d ¼ 0.2

mm, and side length ¼ 7.6 mm. Substrate parameters are er¼10.2

and h¼1.27 mm. Extracted circuit parameters are Le¼4.93 nH,

C¼1.06 pF, Cc¼5.4 pF and Lc¼1.68 nH.

Figure 31 Layout (a) and simulated differential and common

mode insertion loss of the designed common mode filter with opti-

mized size (b). Dimensions are W¼1 mm, S¼2.5 mm, c¼0.2 mm,

d¼0.2 mm, side length¼7.6 mm, and inter-resonator distance¼0.15

mm. Substrate parameters are er¼10.2 and h¼1.27 mm. Extracted

circuit parameters are Le¼4.93 nH, C¼1.06 pF, Cc¼5.4 pF,

Lc¼1.68 nH, CR¼0.11 pF, Lo¼3.16 nH and Co¼1.26 pF.



depicted in that figure. There is good agreement between

the circuit and electromagnetic simulation.

To enhance the rejection bandwidth, we have imple-

mented an order-3 structure with tightly coupled CSRRs.

A separation of 0.15 mm between CSRRs, a value close

to the fabrication limits, has been considered to optimize

the rejection bandwidth. The layout of the resulting struc-

ture and the simulated responses are shown in Figure 31

(ohmic and dielectric losses have been neglected in the

electromagnetic simulation). The coupling capacitance

between resonators CR has been considered to be an ad-

justable parameter, and we have found that the capaci-

tance that provides a better fitting is CR ¼ 0.11 pF. The

capacitance Codd and the inductance Lodd of the odd

model have been found just as the capacitance and the in-

ductance of the considered differential line in the odd

mode. A photograph of the fabricated device is shown in

Figure 32. Access lines have been added to solder the

connectors. A comparison between the electromagnetic

simulation (with losses included) and the measurement is

depicted in the same figure. Simulations are in good

agreement with the measurements. As the two lowest

transmission zeros are too close, they degenerate in the

same transmission zero frequency when losses are consid-

ered. It is clear that differential signals are not altered by

the presence of the CSRRs, as the measured insertion loss

is lower than 0.1 dB. The active area (patterned CSRRs)

of the structure is 23 � 7.6 mm2, that is, 0.28 kg � 0.09

kg, where kg is the guided wavelength at the central fre-

quency. The device is thus very small, although band-

width has not been optimized in this structure. The meas-

ured fractional bandwidth at 20 dB is 14%.

Let us now consider the design of a common mode fil-

ter with optimized bandwidth. To enhance the bandwidth,

we have considered CSRRs with wider rings and inter-

ring’s space. The model of the CSRR is not so simple in

this case because the resonator cannot be considered to be

electrically small. Therefore, we have directly made the

optimization at the layout level. Three square-shaped

CSRRs separated 0.2 mm, with a side length of 10.8 mm,

with rings width c ¼ 1.2 mm and inter-rings separation d¼ 0.8 mm, suffice to achieve the target. The layout of a

single unit cell and the corresponding electromagnetic

simulation for the common-mode insertion loss are

depicted in Figure 33. The circuit simulation with the

extracted electrical parameters is also depicted to show

that there is good agreement between the circuit and elec-

tromagnetic simulation only near the transmission zero

frequency, as expected. The photograph of the third-order

filter and the differential and common-mode insertion loss

are depicted in Figure 34 (the response of the circuit

model with extracted parameters does not match the mea-

surement or electromagnetic simulation, and, for this rea-

son, it is not included). The dimensions of the active

region of the structure are 32.8 � 10.8 mm2, that is, 0.43

Figure 32 Photograph of the fabricated common mode filter

with optimized size (a) and simulated and measured differential

and common mode insertion loss (b). [Color figure can be viewed

in the online issue, which is available at wileyonlinelibrary.com.]

Figure 33 Unit cell layout (a) and simulated common mode

insertion loss of the designed common mode filter with optimized

bandwidth (b). Dimensions are W ¼ 1 mm, S ¼ 2.5 mm, c ¼ 1.2

mm, d ¼ 0.8 mm, and side length ¼ 10.8 mm. Substrate parame-

ters are er ¼ 10.2, h ¼ 1.27 mm. Extracted circuit parameters are

Le ¼ 33.25 nH, C ¼ 0.92 pF, Cc ¼ 9.13 pF and Lc ¼ 1 nH.



kg � 0.14 kg. In this design, the dimensions are larger but

the rejection bandwidth is also wider (as compared to the

previous design); the measured fractional rejection band-

width at 20 dB is 38%. It is also remarkable that the

measured insertion loss for the differential signal is

smaller than 0.5 dB.

To evaluate the degradation of differential signal integ-

rity produced by the CSRRs, the measured eye diagram of

the device of Figure 34 and that of the same differential

line but without CSRRs patterned in the ground plane, are

shown in Figure 35. The main eye diagram parameters are

summarized in Table I, from which it is clear that the

presence of CSRRs does not produce a significant degra-

dation in the differential signal integrity.

As compared to other approaches, the presented com-

mon-mode suppression strategy is technologically simple

(only two metal levels are used), the resulting common-

mode filters are electrically small, provide wide and high-

rejection stopbands, and their design is simple.

V. CONCLUSIONS

In conclusion, artificial transmission lines based on meta-

material concepts and implemented by means of split

rings have been reviewed. Specifically, we have consid-

ered transmission lines based on combinations of OSRRs

and OCSRRs, SRR-loaded lines and CSRR-loaded lines.

All these lines exhibit a CRLH behavior. Despite the pres-

ence of parasitics, OSRR/OCSRR-based lines exhibit a

behavior similar to that of a canonical CRLH line (i.e.,

similar to that achievable by means of the CL-loaded

approach). CRLH SRR- and CSRR-loaded lines exhibit a

transmission zero below the first (left handed) transmis-

sion band. SRR- and CSRR-loaded lines can also be use-

ful as stopband structures, as these resonators inhibit sig-

nal propagation in the vicinity of their resonance

frequency. In this article, we have reviewed some applica-

tions of these SRR- and CSRR- loaded lines as stop band

structures. Specifically, the possibility to implement tuna-

ble stopband filters on the basis of cantilever-type mova-

ble SRRs, as well as the potentiality of CSRRs to the

design of balanced lines with common mode suppression,

has been reviewed. Concerning the applications of OSRR/

OCSRR-loaded lines, it has been shown that these lines

are of interest for the design of wideband filters and dual-

band components. In summary, several applications of

split ring-based lines in the field of microwave circuit

Figure 34 Photograph of the fabricated common mode filter

with optimized bandwidth (a) and simulated and measured differ-

ential and common mode insertion loss (b). Dimensions are W ¼1 mm, S ¼ 2.5 mm, c ¼ 1.2 mm, d ¼ 0.8 mm, side length ¼10.8 mm and inter-resonator distance ¼ 0.2 mm. Substrate pa-

rameters are er ¼ 10.2 and h ¼ 1.27 mm. [Color figure can be


wileyonlinelibrary.com.] Figure 35 Measured eye diagram of the differential line of

Figure 34 without CSRRs (a) and with CSRRs (b). [Color figure

can be viewed in the online issue, which is available at


TABLE I Measured Eye Parameters

With CSRRs Without CSRRs

Eye height 237.8 mV 270.7 mV

Eye width 385 ps 387 ps

Jitter (PP) 15.1 ps 13.3 ps

Eye opening factor 0.67 0.75



design, recently achieved by the authors, have been pre-

sented. Much activity in this field has been already carried

out by the authors and other groups, but there is still

much space for continuing the research in this field and

generate innovative ideas and concepts.

ACKNOWLEDGMENTS

This work has been supported by MICIIN (Spain) through

the projects TEC2010-17512 METATRANSFER and

EMET CSD2008-00066 of the CONSOLIDER Ingenio 2010

Program. Special thanks are also given to Generalitat deCatalunya for funding CIMITEC and for supporting

GEMMA through the project 2009SGR-421.

ANNEX I

The parameters of the circuit model of a CPW loaded with

an OSRR (Fig. 12c) can be extracted from the electromag-

netic simulation of the structure following a straightforward

procedure. From the intercept of the return loss with the

unit conductance circle in the Smith chart, we can directly

infer the value of the shunt capacitance according to:

C ¼ B

2xjZs¼0

(29)

where B is the susceptance in the intercept point. The fre-

quency at this intercept point is the resonance frequency

of the series branch:

x2Zs¼0

¼ 1

CsL0s(30)

To determine the two element values of this branch,

another condition is needed. This condition comes from the

fact that at the reflection zero frequency xz (maximum

transmission) the characteristic impedance of the structure

is 50 X. In this p-circuit, the characteristic impedance is

given by expression 6. Thus, by forcing this impedance to

50 X, the second condition results. By inverting Eqs. (6)

and (30), we can determine the element values of the series

branch. The following results are obtained:

Cs ¼ x2z

x2jZs¼0

� 1

" #� 1

2Z20x

2zC

þ C

2

� �(31)

L0s ¼1

x2jZs¼0Cs

(32)

The parameters of the circuit model of a CPW loaded

with an OCSRR (Fig. 12f) can be extracted following a

similar procedure. In this case, the intercept of the return

loss with the unit resistance circle in the Smith chart gives

the value of the series inductance:

L ¼ v2xjZp!1

(33)

where v is the reactance in the intercept point. The shunt

branch resonates at this frequency, that is:

x2Zp!1¼ 1

L0pC0p

(34)

Finally, at the reflection zero frequency (xz), the char-

acteristic impedance, given by Eq. (5) must be forced to

be 50 X. From these two latter conditions, we finally

obtain:

L0p ¼x2

z

x2jZp!1� 1

" #� Z2

0

2x2zL

þ L

2

� �(35)

C0p ¼ 1

x2jZp!1L0p(36)

and the element values are determined.

The parameter extraction methods for CSRR- and SRR-

loaded lines are reported in Refs. [64, 65], respectively.

They are similar to the method reported in this annex but

are not reproduced to avoid further extension of the

article.

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BIOGRAPHIES

Miguel Dur�an-Sindreu was born in

Barcelona, Spain, in 1985. He

received the Telecommunications En-

gineering Diploma (specializing in

electronics), the Telecommunications

Engineering degree and the Ph.D.

from the Universitat Aut�onoma de

Barcelona, Barcelona, Spain, in

2007, 2008, and 2011, respectively. His research interests

are passive microwave devices based on metamaterials,

microwave filters and multiband components.

Jordi Naqui was born in Granollers,

Spain, in 1984. He received from the

Universitat Aut�onoma de Barcelona

(UAB) the Telecommunication Tech-

nical Engineering Diploma (specialty

in Electronics) in 2006, the Telecom-

munication Engineering Degree in

2010, and the Micro and Nanoelec-

tronics Engineering Master in 2011. He has prepared doc-

umentation of broadcasting equipment in Mier Comunica-

ciones, he has researched on automotive antennas in



Ficosa International, and he has been working as a tele-

communication engineering consultant in Say�os & Car-

rera. Currently, he is working toward his Ph.D. degree on

innovative passive microwave devices based on metamate-

rial concepts at CIMITEC (UAB).

Jordi Bonache was born in Cardona

(Barcelona), Spain, in 1976. He

received the Physics and Electronics

Engineering degrees and Ph.D.

degree in electronics engineering

from the Universitat Aut�onoma de

Barcelona, Bellaterra (Barcelona),

Spain, in 1999, 2001, and 2007,

respectively. In 2000, he joined the High Energy Physics

Institute of Barcelona (IFAE), where he was involved in

the design and implementation of the control and monitor-

ing system of the MAGIC telescope. In 2001, he joined

the Department d’Enginyeria Electr�onica, Universitat

Aut�onoma de Barcelona, where he is currently an Assist-

ant Professor. His research interests include active and

passive microwave devices and metamaterials.

Ferran Martı́n was born in Bara-

kaldo (Vizcaya), Spain, in 1965. He

received the B.S. degree in physics

and the Ph.D. degree from the Uni-

versitat Aut�onoma de Barcelona

(UAB), Barcelona, Spain, in 1988

and 1992, respectively. From 1994 to

2006, he was an Associate Professor

in Electronics in the Departament d’Enginyeria Electr�onica(Universitat Aut�onoma de Barcelona), and since 2007 he

has been a Full Professor of Electronics. In recent years, he

has been involved in different research activities including

modeling and simulation of electron devices for high-fre-

quency applications, millimeter-wave, and THz generation

systems, and the application of electromagnetic bandgaps

to microwave and millimeter-wave circuits. He is now very

active in the field of metamaterials and their application to

the miniaturization and optimization of microwave circuits

and antennas. He is the head of the Microwave and Milli-

meter Wave Engineering Group (GEMMA Group) at UAB,

and director of CIMITEC, a research Center on Metamate-

rials supported by TECNIO (Generalitat de Catalunya). He

has acted as Guest Editor for three Special Issues on meta-

materials in three international journals. He has authored

and coauthored more than 350 technical conference, letter,

and journal papers and he is coauthor of the monograph on

metamaterials entitled Metamaterials with Negative Param-

eters: Theory, Design, and Microwave Applications (Wiley,

2008). He has filed several patents on metamaterials and

has headed several development contracts. Prof. Martin has

organized several international events related to metamate-

rials, including Workshops at the IEEE International Micro-

wave Symposium (years 2005 and 2007) and European

Microwave Conference (2009). Among his distinctions, he

received the 2006 Duran Farell Prize for Technological

Research, he holds the Parc de Recerca UAB—Santander

Technology Transfer Chair, and he has been the recipient

of an ICREA ACADEMIA Award. Since 2012, he is Fel-

low of the IEEE.



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