Int. J. Electron. Commun. (AEÜ) 64 (2010) 177–185

www.elsevier.de/aeue

LETTER

A slow wave structure and its application in bandpass filter design

Kumud Ranjan Jhaa,∗, Manish Raib

aSchool of Electronics and Communication Engineering, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, IndiabDepartment of Electronics and Communication Engineering, M.J.P. University, Bareilly, Uttar Pradesh, India

Received 2 October 2008; accepted 12 December 2008

Abstract

This paper presents a new slow wave open-loop resonator filters with reduced size and improved stopband characteristics.A comprehensive treatment of different kind of coupling in this structure is demonstrated. Two and four resonator band passfilters at center frequency 2.15 and 2.30GHz with different bandwidth are designed. The simulated results are verified withthe help of two different software packages (IE3D and Sonnet Lite).� 2009 Elsevier GmbH. All rights reserved.

Keywords: Open-loop resonator; Bandpass filter and slow wave resonator

1. Introduction

Planar band pass filters are required in a number of mod-ern wireless communication systems [1]. Due to volumeconstraint in these systems the compactness of bandpassfilters has become paramount requirement. The half wave-length open-loop resonator inherently has a spurious passband at 2 f0 where f0 is the resonant frequency of the struc-ture. The quarter wavelength resonator filter has first spu-rious frequency at 3 f0, but this kind filter needs the shortcircuit connection via hole. Previously most of the studiesdemonstrated various techniques for the suppression of spu-rious passband of filters using microstrip parallel coupledlines. Parallel coupled microstrip filters with over coupledend stages have been proposed to extend the electric lengthof odd mode to compensate the difference in the phase ve-locities [2]. The wiggly line microstrip filter using a continu-ous perturbation of the width of the coupled lines followinga sinusoidal law has been studied in [3]. Parallel-coupled

∗ Corresponding author.E-mail address: jhakr@rediffmail.com (K.R. Jha).

1434-8411/$ - see front matter � 2009 Elsevier GmbH. All rights reserved.doi:10.1016/j.aeue.2008.12.005

microstrip filters with the width of slots in the ground planehave been proposed [4,5] to control the spurious signal instopband. The substrate suspension structure has been de-signed to speed up the even-mode phase velocity to makethe modal phase velocities equal for the suppression of spu-rious band [6]. Step impedance resonators (SIR) requires alarge impedance ratio to shift the spurious band to higherfrequencies [7–9].

Cross coupled filters are traditionally realized usingwaveguide or dielectric resonators which are bulkier thanplanar structures. Planar filters using open-loop resonators[10–12] normally require �g/2 resonators. Recently, bandpass filters have been proposed in [13], which uses heavilycapacitive asymmetric slow wave structure.

In the present paper, a new microstrip slow wave structureand its various applications in the filter design has beenproposed.

In Section 2, a brief comparison of proposed structure andclassical open loop resonator has been made in the view ofsize. In Section 3, optimization of filter has been presented.In Section 4, two and four resonator filters are designed andsimulated results have been compared using two differentsoftware packages.

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Fig. 1. Conventional open-loop resonator.

Fig. 2. Proposed structure.

2. Comparison of conventional open-loopresonator with proposed microstrip slow waveresonator

Fig. 1 shows the conventional open-loop resonator andFig. 2 shows proposed structure of same size with arbitrarilychosen feed point on the structure. Their return losses havebeen shown in Fig. 3. It is seen from Fig. 3 that the proposedresonator when excited at the same feed point as conven-tional open-loop resonator, resonates at multiple frequenciesin which one frequency is quite lower than the resonatingfrequency of open-loop resonator. This is due to the exten-sion of line inside the enclosed open loop, as this extensionbehaves as a capacitive load to the structure.

Both structures have been simulated on the same sub-strate of dielectric constant 3.2 and thickness 0.762mm. It is

Fig. 3. Performance of resonators.

Fig. 4. Symmetrically electric coupling.

noticed that conventional open loop resonates at 6 and8.9GHz whereas proposed structure has multiple resonancesat 2.1, 6.7 and 8.9GHz, respectively. In other word, it isconcluded that increasing the length of open-loop resonator,creates a slow wave structure, if feed line is placed appro-priately. Since the first resonance frequency of proposedstructure is 2.1GHz, lower than the fundamental resonancefrequency of open-loop resonator which is 6GHz, indicatesthat the proposed structure is smaller than the open loop forthe same resonance frequency.

Different types of possible weakly coupled configurationsof the proposed structures are shown in Figs. 4 and 5. Com-parison of coupling coefficients (K ) are shown in Fig. 6.

From Fig. 6 it is seen that proposed structure has less valueof K in comparison to conventional open-loop structure.Among the group of possible coupling, the symmetrically

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Fig. 5. Asymmetric electric coupling.

Fig. 6. Coupling co-efficient (K) vs. separation ‘s’.

electric coupled structure has the smallest coupling coef-ficient. For the narrow band filter design smaller couplingcoefficients between two resonators are preferred [14]. Inview of the published research articles, it is understood thatelectric coupled structures are more suitable for the narrowbandpass filter design. In the subsequent parts of the presentpaper, structures shown in Figs. 4 and 5 have been used inthe filter design.

3. Optimization of slow wave structure

The size of the proposed slow wave resonator has beenoptimized from the standpoint of the unloaded Q-factor ofresonator with Sonnet Lite simulator [17]. We assume thatthe conductivity of metal is �=5.8×107 S/m, the dielectricconstant of substrate is 3.2, and thickness is 0.762mm. To

Fig. 7. Q vs. gap g in mm.

Fig. 8. Q vs. distance of feedline p in mm.

optimize the structure, open-loop gap ‘g’ and feed positionfrom left arm ‘p’ in Fig. 2 are varied. At the resonancefrequency unloaded quality factor (Q) can be calculated bythe following equation [15]:

Q = QL

1 − 10−L A/20 (1)

where QL is loaded Q-factor and L A is insertion loss indecibels at the resonance frequency which is obtained fromthe simulated response of resonator.

Fig. 7 shows that unloaded quality factor Q which in-creases with increase in the gap width for a particular feedposition and finally it will get saturated at the higher valueof gap ‘g’. As the Q increases, selectivity of the filter in-creases and bandwidth is reduced. Variation in the feed

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position from a fixed arm at a constant gap width ‘g’ alsodescribes the selectivity of the filter. The selectivity is highin the range of ‘p’ from 1 to 2.5mm which is due to theinteraction of feed line with the extended line as shown inFig. 2. Depending upon these two parameters, filter can bedesigned. With the help of Figs. 7 and 8, value of ‘g’ and‘p’ can be selected to meet the specific requirement of thefilter.

Fig. 9. Layout of two resonator band pass filter.

Fig. 10. Response of the filter up to 3GHz.

4. Filter design and verification of results

4.1. Coupling structures

The Sonnet Lite software [17] was used to simulate thefrequency response of structures. The coupling in any struc-ture is characterized by two dominant resonance frequen-cies, which split off from the resonance condition due tothe electromagnetic coupling. The coupling coefficient Mi j

for resonator i and j is then extracted from the simulatedfrequency response using [11]:

Mi j = ±( f 21 − f 2

2 )/( f 21 + f 2

2 ) (2)

where f1 and f2 corresponds to either even or odd moderesonance frequencies. The external quality factor Qe maybe characterized by equation

Qe = ( f0)/( f3 dB) (3)

where f0 shows resonance frequency and f3 dB is 3dB band-width of resonator (when excited alone).

4.2. Two resonator filters

4.2.1. Two resonator bandpass filter with symmetricloading

The filter is designed with a substrate of dielectric constant3.2 and thickness 0.762mm. In order to have the maximally

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Fig. 11. Response of filter up to 6GHz.

flat response in the present design, the pass band of the filteris 133MHz (fractional bandwidth FBW = 6%) at f0 equalsto 2.15GHz. The external quality factor Qe and coefficientM21 are calculated as

Qe = c0c1/FBW = 22.8 (4)

M21 = −FBW/√

c1c2 = −0.0424 (5)

where c0, c1, and c2 are elements values of low pass pro-totype filter [16]. Values of ‘s’, ‘p’ and ‘g’ are adjustedto achieve the approximate quality factor. The proposed fil-ter is shown in Fig. 9. The filter parameters are l1 = 9mm,l2 = 9mm, l3 = 7.4 mm, l4 = 3.11mm, l5 = 4.08mm, p =4.54 mm, g = 0.21mm, s = 0.26mm and width of resonatorand feed line =0.05mm. The size of two resonator filter isabout 0.209�g0 × 0.103�g0 where �g0 is the guided wave-length of a 50� line on the substrate at the center frequencywhich shows reduction in size compared to open-loop res-onator filters [11]. Simulated results are shown in Figs. 10and 11. To verify the analysis, the structure has been simu-lated with software, (a) Sonnet Lite [17] and (b) IE3D [18].The passband response of the filter is shown Fig. 10. Fur-ther to see the stop band characteristics the structure hasbeen simulated up to 6GHz with the help of IE3D which isshown in Fig. 11.

Fig. 10 shows the convergence of two simulated resultsand predicts the accuracy of the filter. A wide stop band re-sponse has been obtained using IE3D simulator as shown inFig. 11. Further, the spurious pass band is suppressed below−20 dB at 4.30GHz which is inherited draw back of con-ventional open-loop resonator. The proposed filter is highly

Fig. 12. Asymmetric loaded bandpass filter.

selective towards the upper stopband side which is the de-sired feature in the modern communication filter. Transmis-sion zero at the right side of passband is created due totapping position of feed line at the resonator. The positionof transmission zero can be varied to right or left side ofpassband with selection of suitable tapping position of feedline of the resonator.

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Fig. 13. Response of asymmetric loaded bandpass filter.

Fig. 14. Four resonator filter.

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4.2.2. Two resonator filter with asymmetric loadingTo investigate the effect of asymmetric loading and effect

of variation in the length of extended line, a filter is de-signed using the asymmetric electric coupling of resonators.The resonant frequency of the filter can be controlled byvarying the length of the line. When this length is shortenedthe resonance frequency is shifted towards the higher value.However the pass bandwidth is determined by the couplingcoefficient of the structure, gap ‘g’ and feed position ‘p’.In the present design, a filter of bandwidth 100MHz at cen-ter frequency 2.3GHz is designed using formula (4) and(5). The calculated values of Qe and M21 are 32.49 and−0.030, respectively. To achieve the desired value of cou-pling, separation between two resonators and feed positionare varied. The proposed structure is shown in Fig. 12. Theobtained simulated response is presented in Fig. 13. Thefilter parameters are l1 = 9mm, l2 = 9mm, l3 = 7.4 mm,l4 = 3.11mm, p = 2.54 mm, g = 0.21mm, s = 0.47mm,respectively.

Fig. 15. Layout of resonators.

Fig. 16. Response of four resonator filter.

The pass bandwidth of the proposed filter is extendedfrom 2.24 to 2.34GHz and insertion loss in the pass bandis −1.2 dB. The filter is highly selective in the upper stopsideband and it is better than −30 dB from 2.4 to 4.8GHz.Also, the proposed filter is free from spurious signals inthe wide stopband and is not appearing at 2 f0. In Fig. 13,slight variation in results is seen. This variation is due tothe simulation technique involved in two software packages,Sonnet Lite is finite ground simulator whereas IE3D workson infinite ground.

4.3. Four resonator bandpass filter

The third filter is an example of four resonator cross-coupled microstrip bandpass filter, designed on the samesubstrate. The configuration of the filter is shown in Fig. 14.Fig. 15 shows the typical coupling structure of the pro-posed filter. In Fig. 15, solid and dotted lines indicate themagnetic coupling and electric coupling respectively. Thefilter could be synthesized using the method described in[16], from which lumped-element values of low pass proto-type are determined as c0 = 1, c1 = 0.95947, c2 = 1.42292,J1 = −0.21083, J2 = 1.11769. Design parameters of thefilter at 2.3GHz center frequency and 300MHz bandwidth(FBW = 11.7%) are calculated as

M12 = M34 = FBW/√

c0c1 = 0.100 (6)

M23 = FBW × J2/c2 = 0.091 (7)

M14 = FBW × J1/c1 = −0.025 (8)

Qe = c0 × c1/FBW = 8.2 (9)

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Fig. 17. Response of filter up to 6GHz.

In the above equations positive coupling coefficients indi-cate magnetic coupling and negative coupling coefficientindicates electric coupling of resonators. Basic parametersof a resonator are same as of resonator shown in Fig. 12.The distance between resonators and feed position ‘p’ areadjusted to achieve the desired coupling coefficient. In thepresent design, s12 the distance between resonators 1 and 2 is0.10mm, s23 the distance between resonators 2 and 3 is equalto 0.47mm, s34 the distance between resonators 3 and 4 isequal to 0.12mm, s14 distance between resonators 1 and 4 isadjusted to 0.41mm and value of ‘p’ is adjusted to 5.81mm.Effective area of this filter is about 0.22 × 0.21mm2. Theinsertion loss of this filter is −0.4 dB in passband. Stopbandrejection is better than −20 dB in lower side and betterthan −17dB in the upper side of the pass band. This filteralso exhibits the wide stop band characteristics as shown inFig. 17 and spurious signal is suppressed at 2 f0 frequency.The simulated response by (a) Sonnet Lite [17] and (b) IE3D[18] shown in Fig. 16, shows similar results. To see the stop-band characteristics the filter has been simulated up 6GHzas shown in Fig. 17 which shows the suppression of spuri-ous pass band at 2 f0. The physical reason of the suppressionof spurious sideband at upper stopband side is the shiftingin the transmission zero at the right side of the passband.

5. Conclusion

In the present paper, a new kind of slow wave structure hasbeen proposed and analyzed. With the help of the proposed

structure, three filters have been designed and their responseshave been validated. The proposed resonator is quite flexiblefrom the resonance frequency point of view and a widerange of resonance frequency can be adjusted by simplychanging the length of the extended line without affectingthe total effective area on substrate. The proposed filter isquite compact in comparison to open-loop resonator. Theproposed work can be further extended at other frequenciesand different topologies.

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Kumud Ranjan Jha born in 1973passed AMIE(I) examination in 1999and Maser of Engineering from BirlaInstitute of Technology, Mesra, Ranchi,Jharkhand, (India) in 2006. Presentlyhe is Assistant Professor in the Schoolof Electronics and CommunicationEngineering, Shri Mata Vaishno DeviUniversity, Katra, Jammu and Kash-mir, India. His area of research ismicrowave/RF component design.

Manish Rai born in 1968 passedB.Tech. and M.Tech. examinationsfrom Allahabad University, India, andcompleted Ph.D. in 2006 from MNIT,Allahabad. Presently he is AssistantProfessor in the Department of Elec-tronics and Communication Engineer-ing, M.J.P. Rohilkhand University,Bareilly (U.P).