Stepped-impedance lowpass filters withspurious passband suppression

J. Garcıa-Garcıa, J. Bonache, F. Falcone, J.D. Baena,F. Martın, I. Gil, T. Lopetegi, M.A.G. Laso,A. Marcotegui, R. Marques and M. Sorolla

It is demonstrated that spurious passband suppression in stepped

impedance lowpass filters can be achieved by simply patterning

appropriate geometries in the low impedance sections. These patterns

consist of concentric rings with splits etched in opposite sides, that

behave as sub-wavelength resonators electrically coupled to the line.

By tuning ring dimensions, signal propagation is inhibited at the

frequencies of interest, and spurious passbands are rejected. The main

advantages of the technique are: (i) no additional cascaded stages are

needed, (ii) no extra area is added, (iii) the passband is virtually

unaltered and (iv) the conventional design methodology of the filter

holds. A prototype device fabricated in CPW technology exhibits

spurious suppression levels above 30 dBs.

Introduction: The elimination of spurious frequency bands in distrib-

uted filters has attracted a growing interest in recent years. One of the

reasons is the great impact of electromagnetic bandgaps (EBGs) [1]

on microwave and millimetre-wave technology. EBGs are periodic

structures, able to inhibit signal propagation in certain frequency

bands and=or directions, that provide a natural way to reject undesired

bands or frequency parasitcs. Compared to traditional techniques

(where half wavelength short circuit stubs, chip capacitors or

cascaded rejection band filters are used), EBGs neither add extra

layout area to the devices, nor introduce significant insertion losses in

the frequency region of interest [2]. However, since the frequency

selective properties of EBGs are based on the well-known Bragg

effect, their period scales with signal wavelength, and hence the

dimensions of the structure might be too high (in certain applications)

to achieve the desired rejection levels. In this Letter, an alternative

approach, based on the use of complementary split ring resonators

(CSRRs) [3], is proposed. These particles provide an elegant solution

for the suppression of undesired frequencies in microwave circuits

since their dimensions are electrically very small and they can be

integrated within the device active region.

Frequency selective properties of CSRRs: The basic topology of a

CSRR is depicted in Fig. 1. This consists on a pair of concentric rings

etched on a metallic surface with splits in opposite sides. CSRRs are

the dual counterparts of split ring resonators (SRRs) (topology also

depicted in Fig. 1), well-known particles (originally proposed by

Pendry [4]) with very interesting properties for the design of micro-

wave and millimetre-wave circuits. The frequency selective properties

of SRRs are explained by the quasi-static resonance that takes place in

the structure at the appropriate frequency. This is due to the capaci-

tance between concentric rings and overall inductance of the ring pair,

that can be calculated according to the model reported in [5]. When

SRRs are excited by a time-varying magnetic field with a non-

vanishing component applied parallel to the ring axis, current loops

are generated that are closed through the distributed capacitance

between concentric rings (under resonance). Therefore, if SRRs are

magnetically coupled to a transmission line, the effect is the inhibition

of signal propagation in the vicinity of resonance. This frequency

selectivity of SRRs has been successfully applied to the rejection of

undesired bands in coupled line bandpass filters [6]. By virtue of

duality, a similar behaviour is expected for CSRRs. However, in this

case, a time-varying electric field in the axial direction is necessary. In

planar transmission lines, this condition is guaranteed by etching

CSRRs in the ground plane, as has been pointed out by the authors

[3]. An alternative procedure is to etch these particles directly on the

conductor strip, provided there is space enough for this purpose. In

this regard, CSRRs (as SRRs) are sub-wavelength structures (i.e. they

can interact with the host line at their quasi-static resonance) that can

be designed to be very small, depending on the limits of tolerance of

the technology in use. According to these comments, it follows that

CSRRs can find a practical application in the rejection of undesired

bands in stepped impedance lowpass filters, where the low impedance

sections can be designed wide enough to accommodate the rings. In

this way, the stopband of the filters is expected to increase, while the

design methodology holds and no etching in the ground plane is

applied (something desirable from a practical point of view).

CSRR

SRR

d

rext

c

Fig. 1 Topologies of CSRRs and SRRs and relevant dimensions

Design of CSRRs lowpass filters: Based on the reflection properties

of CSRRs, we have designed a stepped impedance lowpass filter in

CPW technology. The specifications are given by the cutoff frequency

( fc¼ 2 GHz), filter order (ninth-order) and frequency response (maxi-

mally flat Butterworth). The design of the structure is a two-step

process.

First, the conventional layout of the filter is obtained according to the

standard procedure. To this end, the characteristic impedance of the

high and low impedance sections has been set to Zo¼ 150 O and

Zo¼ 30 O, respectively. From these values, the electrical length of each

transmission line section has been obtained (following the design

formulas [7]), and by using a commercial transmission line calculator

(Agilent LineCalc) the geometry of the filter has been determined

(the parameters of the Rogers RO3010 substrate have been considered,

i.e thickness h¼ 1.27 mm, dielectric constant er¼ 10.2). To provide

space for the connectors, 50 O access lines have been cascaded at the

input=output ports.

Fig. 2 Simulated and measured frequency response for conventionalstepped impedance lowpass filter

---- simulated —– measured

The second step consists on etching the appropriate CSRRs in the

low impedance sections (where the conductor strip width is substantial)

to suppress the first spurious band of the filter. To succeed in this aim,

the position and broadness of such undesired band should be known.

The simulated (using Agilent Momentum) and measured (using the

Agilent 8720ET vector network analyser) frequency responses of the

filter without CSRRs (depicted in Fig. 2) show that this band extends

from roughly 4 up to 5 GHz. To efficiently reject this relatively wide

band, a set of CSRRs, tuned at different frequencies within the band, is

necessary. Since the resonant frequency of CSRRs and SRRs of

identical dimensions roughly coincide, we have used the model

described in [5] to have a first approach on CSRR dimensions.

Specifically, by setting c¼ 0.2 mm, d¼ 0.2 mm and r¼ 1.92 mm

(Fig. 1), the resonant frequency of the rings is found to be at

fo¼ 4.5 GHz, i.e. in the centre of the spurious band. From this

geometry, we have slightly scaled up and down CSRRs dimensions

in order to obtain multiple closed notches and hence achieve whole

band rejection. An optimisation tool, included in Agilent Momentum,

has been finally used to determine the optimum CSRRs dimensions.

The final layout of the structure, including CSRRs, is depicted in Fig. 3.

As can be seen, CSRRs have been distributed in pairs along the

ELECTRONICS LETTERS 8th July 2004 Vol. 40 No. 14

structure with the aim to enhance the electric coupling between line and

rings at their resonant frequency.

Results: The simulated and measured frequency responses for the

CSRR lowpass filter are depicted in Fig. 4. Significant rejection of the

spurious band (>30 dBs) is achieved, while the allowed band is

virtually unaltered. The slight discrepancies between simulation and

measurement are due to tolerances, that are inherent to the fabrication

process (a standard photo=mask etching technique) and are specially

critical as a consequence of the small CSRRs dimensions and narrow

strips for the high impedance sections. Nevertheless, these results

reveal that the proposed technique is very promising for the design of

stepped impedance lowpass filters with improved stopband. These

ideas can be also applied to other technologies (microstrip, stripline,

m) and frequency responses (bandpass). In this regard, the possibility

to etch CSRRs in the ground plane introduces a new degree of

flexibility in the designs (work is in progress in this direction).

Fig. 3 Layout of fabricated CSRR-based stepped impedance lowpass filterdrawn to scale (total device length including 50 O access lines 94 mm)

Fig. 4 Simulated and measured frequency response for CSRR steppedimpedance lowpass filter

---- simulated —– measured

Conclusion: It has been demonstrated that the frequency response of

stepped impedance lowpass filters can be improved by merely etching

complementary split ring resonators (CSRRs), a new particle intro-

duced by the authors, in the low impedance sections of the structure.

By properly tuning the dimensions of an array of CSRRs, it has been

experimentally found that the first spurious band of the filter can

be rejected, with no effect on the allowed band. Since CSRRs are

electrically small particles, they can be integrated within the active

device region and no extra area is added to the final layout. We would

like to highlight the fact that the topology of the proposed structure

only differs from that of the conventional design on the presence of

CSRRs, and these are etched in the central strip. In our opinion, this is

the most simple approach for the suppression of frequency parasitics

reported so far.

Acknowledgments: This work has been supported MCyT by project

contracts BFM2001-2001, TIC2002-04528-C02-01, TIC2001-3163

and PROFIT 070000-2003-933. We also thank the European Commu-

nity (Eureka Program) for supporting this work (project TELEMAC-

2895). The authors are also indebted to R. Pineda from Omicron

Circuits, s.l. for fabrication of the prototypes.

# IEE 2004 16 April 2004

Electronics Letters online no: 20040560

doi: 10.1049/el:20040560

J. Garcıa-Garcıa, J. Bonache, F. Martın and I. Gil (Departament

d’Enginyeria Electronica, Universitat Autonoma de Barcelona,

08193 Bellaterra, Barcelona, Spain)

F. Falcone, T. Lopetegi, M.A.G. Laso and M. Sorolla (Departamento

de Ingenierıa Electrica y Electronica, Universidad Publica de

Navarra, 31006 Pamplona, Spain)

J.D. Baena and R. Marques (Departamento de Electronica y Electro-

magnetismo, Universidad de Sevilla, 41012 Sevilla, Spain)

A. Marcotegui (Conatel, s.l. Sancho Ramırez, 1-3, 31008 Pamplona,

Navarra, Spain)

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2 Lopetegi, T., et al.: ‘New microstrip ‘‘Wiggly-Line’’ filters with spuriouspassband suppression’, IEEE Trans. Microw. Theory Tech., 2001, 49, (9),pp. 1593–1598

3 Falcone, F., et al.: ‘Effective negative-e stop-band microstrip lines basedon complementary split ring resonators’, IEEE Microw. Wirel. Compon.Lett. (accepted for publication)

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