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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)
References
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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)
4 Pendry, J.B., et al.: ‘Magnetism from conductors and enhanced nonlinearphenomena’, IEEE Trans Microw. Theory Tech., 1999, 47, pp. 2075–2084
5 Marques, R., et al.: ‘Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory andexperiments’, IEEE Trans. Antennas Propag., 2003, 51, (10), pp. 2572–2581
6 Garcıa-Garcıa, J., et al.: ‘Spurious passband suppression in microstripcoupled line band pass filters by means of split ring resonators’, IEEEMicrow. Wirel. Compon. Lett. (accepted for publication)
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ELECTRONICS LETTERS 8th July 2004 Vol. 40 No. 14