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ACKNOWLEDGMENTS This work is partially supported by the Spanish Ministry of Sci- ence and Innovation (TEC2008-06881-C03-01 and TEC2011- 28724-C03-02), the Spanish Ministry of Industry, Tourism and Trade (TSI-020400-2010-55) and the ‘‘Programa de ayudas de Formaci�on del Personal investigador, de la Agencia Canaria de Investigaci�on, Innovaci�on y Sociedad de la Informaci�on del Gobierno de Canarias y la cofinanciaci�on y tasa de cofinanciaci�on del F.S.E.’’ REFERENCES 1. High rate ultra wideband PHY and MAC standard, ISO/IEC stand- ard 26907, March, 2007. 2. High rate ultra wideband PHY and MAC standard, Standard ECMA-368, 3rd ed., 2008. 3. Agilent Technologies, EM insights series, Agilent EEsoft EDA, Palo Alto, CA, September, 2008. 4. Yang Boon Quek, QFN layout guidelines, Texas Instruments, Dal- las, TX, July, 2006. 5. How-Siang Yap and Hee-Soo Lee, 3-D EM simulator is integrated with ADS to lower the cost of design, High Frequency Electronics, June, 2009. 6. Hee-Soo Lee, MMIC/RFIC packaging challenges, Agilent Technol- ogies, Palo Alto, CA, July, 2009. 7. Agilent Technologies, An integrated 3D EM design flow for EM/ circuit co-design, ADS user’s group meeting 2009, Rome. 8. H. Garcı´a-V�azquez, S.L. Khemchandani, R. Pulido, A. Go~ni-Iturri, and J. del Pino, A wideband active feedback LNA with a modified 3D inductor, Microwave Opt Technol Lett 52 (2010), 1561–1567. VC 2013 Wiley Periodicals, Inc. DUAL-BAND BANDPASS FILTERS BASED ON DUAL-MODE HILBERT FRACTAL RESONATOR Vesna Crnojevic-Bengin,1 Kirill Zemlyakov,2 Nikolina Jankovic,1 and Irina Vendik2 1 Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia; Corresponding author: bengin@uns.ac.rs 2 Faculty of Radio Engineering and Telecommunications, St. Petersburg Electrotechnical University, St. Petersburg, Russia Received 17 October 2012 ABSTRACT: We propose a compact planar dual-mode resonator based on a Hilbert fractal curve that operates at two arbitrary frequencies. The resonator is used to design two types of dual-band bandpass filters for WLAN applications, which exhibit a good trade-off between compact size and high performances, with the overall sizes ranging from 0.22 � 0.21 to 0.44 � 0.1 guided wavelengths and measured insertion losses from 0.38 to 2.5 dB. At the same time, the fabrication of filters is quite simple and requires no modifications in the ground plane or use of vias. In addition, the proposed resonator is used to design single-band filters as well. VC 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:1440–1443, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27667 Key words: bandpass filters; multiband filters; microstrip filters; fractals 1. INTRODUCTION As the number of various wireless communication systems is growing rapidly, each imposing its specific requirements, new challenges are posed to microwave passive devices, especially the filters. Besides small size, high performance, and low cost of production, modern communication systems need filters capable of dual-band operation at arbitrary (nonharmonically related) frequencies. Dual-band responses have been typically achieved by proper coupling of a number of single-band devices [1, 2], by using composite structure [3], by coupling of a pair of degenerate modes that propagate in a single structure [4, 5], or, recently, by using artificial electromagnetic materials [6, 7]. However, the first and second approach often result in resonators of relatively large size or complicated fabrication process, the third one exhibits perpendicularly positioned ports which limits the design flexibility and decreases the integration potential of the circuit, whereas the fourth approach lacks straightforward synthesis pro- cedures and inherently suffers from relatively large insertion losses. Another important aspect of dual-band filter performances is its operating frequencies. Although a considerable attention has been paid to the development of dual-band filters, many solu- tions operate at frequencies that are not closely positioned, which significantly eases the design procedure and reduces the overall size of the filter. On the other hand, only a small number of filters operate at 2.45/3.5 GHz, needed for various WLAN applications. In this article, we propose a compact dual-mode planar microstrip resonator based on Hilbert fractal curves. Fractal curves are used for their well-known size-reduction capability [8], whereas the Hilbert fractal in particular is selected for its specific geometry and the highest possible fractal dimension, that is, highest compactness of the final circuit. The proposed resonator, called dual-mode Hilbert resonator (DHR), consists of two Hilbert fractal curves of the second order connected in series and short-circuited at their upper part. In that way, two different paths of propagation through the structure are created, resulting in dual-band operation. Due to the specific design, the resonator exhibits small size and allows independent control of both resonant frequencies. Based on the novel DHR, two types of dual-band bandpass filters are proposed, both operating at 2.45/3.5 GHz, as well as a single-band filter designed by fine-tuning frequencies of two res- onant modes. The proposed resonator and the resulting filters are straight- forward to design and simple to fabricate-they are made using conventional PCB materials, on a single conductive layer, and require no vias or modifications to the ground plane. 2. RESONATOR DESIGN Novel DHR is shown in Figure 1(a), where the most relevant geometrical parameters of the resonator are indicated: w and g are the width and the spacing of the fractal line, respectively, whereas s denotes the distance between the two halves of the DHR. The resonator has been designed on 1.575-mm thick Rog- ers RT/Duroid 5880 substrate with er ¼ 2.2 and tand ¼ 0.0009. Because the proposed resonator is of a symmetrical structure, even/odd mode method can be applied to analyze its behavior. The current distributions of the two modes, Figure 2b, reveal that the first resonance is the fundamental odd mode resonance, whereas the second one is the fundamental even resonance. If mutual couplings between the segments of the DHR are considered negligible, using notation from Figures 1(b) and 1(c), even and odd input impedances can be expressed as: Zinodd ¼ jZ0 tan h1 tan h2 þ tan h3ðtan h1 þ tan h2Þ tan h1 þ tan h2 � tan h3 tan h1 tan h2 ; (1) 1440 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 7, July 2013 DOI 10.1002/mop Zineven ¼ jZ0 ðtan h1 þ tan h2Þ tan h3 � 1 tan h1 þ tan h2 þ tan h3 : (2) From the resonant condition 1/Zin ¼ 0, the odd and even res- onant mode equations are derived: tan h1 þ tan h2 � tan h3 tan h1 tan h2 ¼ 0; (3) tan h1 þ tan h2 þ tan h3 ¼ 0: (4) Although both h1 and h2 affect both resonant frequencies, it is possible to achieve almost independent control of the posi- tions of the passbands by separately changing lupper and llower. Namely, one can note that lupper � llower which implies that tanh1 � tanh2. From Eqs. (3) and (4), it can then be seen that the odd resonance is influenced only by changing lupper (i.e., h1), whereas the even mode is affected predominantly by changing of llower (i.e., h2). Figure 2 Current distributions at the first (a) and the second (b) reso- nant frequency of DHR. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] Figure 4 Layout of the Filter I Figure 1 (a) Configuration of the proposed DHR. (b) Even-mode equivalent circuit. (c) Odd-mode equivalent circuit Figure 3 Independent control of the first and the second resonant fre- quency of DHR. In the first case lS is varied while lL ¼ const, while in the second case lL is varied and lS ¼ const. Values on abscissa corre- spond to the length that is varied, respectively. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] Figure 5 Simulated and measured responses of the Filter I. Photo- graph of the filter is shown in the inset. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 7, July 2013 1441 To illustrate this, lL and lS are individually varied as indi- cated with dashed lines in Figure 1(a). Resonant frequencies of DHR are plotted in Figure 3 for both cases: when lL is fixed and lS is varied, and vice versa. In both cases, it can be seen that one resonant frequency changes significantly, whereas the other is virtually unaffected, thus illustrating independent control of resonant frequencies of DHR. In addition, the proposed configuration provides a transmis- sion zero that is positioned at the upper side of the second reso- nance. It occurs when the condition Zineven ¼ Zinodd is met, which causes S21 to become zero. DHR provides an additional degree of the design freedom: by varying line-to-spacing ratio w/g, different responses can be obtained for the same overall dimensions of the resonator. How- ever, it can be shown that DHR with line-to-spacing ratio w/g ¼ 1 offers the best trade-off between size and performance and thus DHR with w ¼ g ¼ 1.3 mm will be used as a basis for the design of filters proposed below. 3. DUAL-BAND BANDPASS FILTERS BASED ON DHR Using the proposed resonator, two dual-band filters for WLAN applications have been designed to operate at 2.45 and 3.5 GHz. Layout of the Filter I is shown in Figure 4, whereas its response is given in Figure 5. The position of the passbands has been determined by a proper choice of lupper and llower, whereas the fine tuning of the filter’s response has been performed by varying the parameter a. In the final design, a is not equal to w þ g but it has been optimized to equal 1.5 mm. The filter is characterized by low insertion loss, excellent return loss, and very good selectivity obtained by three carefully positioned transmission zeros. First two transmission zeros, closely positioned between the passbands, originate from split- ting of one transmission zero initially positioned at 3 GHz. The initial position of this transmission zero is controlled by the length of the extensions of the feed lines which act as quarter- wavelength resonators, whereas the exact positions of two resulting transmission zeros are controlled by the coupling between the resonators and the feed lines, that is, by varying the distance between them. The mechanism for positioning of the transmission zero at 4.01 GHz was explained in Section 2. To validate simulation results, the filter has been fabricated using a conventional PCB procedure. The measurement results agree very well with the simulated ones, Figure 5. The measured central frequencies are 2.44 and 3.49 GHz, while the corre- sponding insertion losses are 1 and 1.6 dB. To further improve selectivity of the filter, a dual-band filter with an additional transmission zero positioned at the lower side of the first passband is proposed. The layout and response of the Filter II are shown in Figures 6 and 7, respectively. The filter uses two DHRs coupled at the broadside that act as an antiparallel structure which provides an additional transmis- sion zero below the first passband. In the final design of the fil- ter, nonresonating nodes are added to improve the coupling between resonators. As in Filter I, fine tuning of the filter’s response has been achieved by varying parameter a, which equals 1.4 mm. Besides high-selectivity, Filter II exhibits low insertion losses and good return losses. Simulated and measured responses of the filter are in a very good agreement, Figure 7. The measured central frequencies are 2.43 and 3.47 GHz, whereas the corre- sponding insertion losses are 0.38 and 2.53 dB. The characteristics of the proposed filters and previously reported dual-band configurations operating at frequencies close TABLE 1 Comparison with Reported Dual-Band Bandpass Filters f1/f2 (GHz) IL (dB) RL (dB) Dim. (kg�kg) 3-dB FBW A B Filter I 2.45/3.5 1/1.6 25/21 0.44� 0.1 4.1/2.3 Y Planar Filter II 2.45/3.5 0.38/2.53 18.8/10 0.22� 0.21 8.7/3.18 Y Planar [2] 2.35/3.2 1.8/3 25/30 0.18� 0.19 3.9/2.8 Y DGS [3] 2.4/3.3 1.2/1.5 20/20 0.21� 0.18 8.1/4.2 N DGSþ vias [5] 2.5/3.5 1.8/2.4 20/15 0.24� 0.33 6.3/4.4 N Planar Figure 6 Layout of the Filter II Figure 7 Simulated and measured responses of the Filter II. Photo- graph of the filter is shown in the inset. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] 1442 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 7, July 2013 DOI 10.1002/mop to 2.45/3.5 GHz are compared in Table 1 where kg denotes guided wavelength at the first passband, A stands for independ- ent control of passband positions, whereas B stands for fabrica- tion technology. The proposed filters outperform other configu- rations: they exhibit high-selectivity, small size, and very good insertion- and return-loss characteristics, and, at the same time, allow independent control of both passbands. In addition, the fil- ters are straightforward to design and simple to fabricate-they are made using conventional PCB materials, on a single conduc- tive layer, and require no vias or modifications to the ground plane. 4. SINGLE-BAND BANDPASS FILTER BASED ON DHR In Section 2, the mechanism for independent control of two res- onant frequencies of the DHR has been shown. Here, we use that mechanism to design a dual-mode resonator with slight splitting between the resonant modes. In the structure proposed in Figure 8, llower is increased to lower the second resonant fre- quency of DHR to a value close to the first resonance. To save space, that segment is also meandered in a fractal manner. In that manner, a quasifractal single-band bandpass filter is obtained that exhibits one passband formed by merging of two resonant frequencies. Synthesis procedure of filters of this type is straightforward and relies on the independent control of the position of odd and even resonant frequencies by individual choice of lengths llower and lupper. The central frequency of the filter can be estimated as fc ¼ ffiffiffi f p 1f2 where f1 and f2 denote the first and the second reso- nant frequency of DHR, respectively. Simulated and measured responses of the filter are compared in Figure 9. The filter exhibits a transmission zero at the right side of the passband, which is inherent to DHR and its origin was explained in Section 2. This transmission zero provides an improved roll-off at the upper side of the passband. Slight dis- crepancies between measured and simulated results can be attributed to fabrication tolerances. The measured central fre- quency is equal to 2.37 GHz, whereas the simulated one was 2.4 GHz, measured insertion loss is equal to 0.78 dB, compared to 0.37 dB in simulations, and the measured fractional 3 dB bandwidth is equal to 13.56% as compared to 16.52% in simula- tions. The overall size of the filter is 20.6 � 16.9 mm2, that is, approximately 0.215 � 0.18 kg. 5. CONCLUSION Novel DHR is proposed, characterized by a specific geometry that allows dual-band operation at arbitrary nonharmonically related frequencies. DHR has been used to design two types of dual-band band- pass filters for 2.4/3.5 GHz WLAN applications, which outper- form other recently published configurations: Although relying on a simple single-layer PCB technology, the proposed filters simultaneously exhibit high selectivity, small size, and good transmission characteristics, and, at the same time, allow inde- pendent control of both passbands. To further illustrate applicability of the DHR, a very compact single-band bandpass filter with fractional bandwidth equal to 13.56% has also been proposed. ACKNOWLEDGMENT This work was supported in part by the European Commission under Marie Curie PIRSES-GA-2010-247532. REFERENCES 1. C.Y. Chen, et al. A simple and effective method for microstrip dual-band filters design, IEEE Microwave Wirel Compon Lett 16 (2006). 2. B. Wu, C.-H. Liang, Q. Li, and P.-Y. Qin, Novel dual-band filter incorporating defected SIR and microstrip SIR, IEEE Microwave Wirel Compon Lett 18 (2008), 392–394. 3. L. Ren and H. Huang, Dual-band bandpass filter based on dual- plane microstrip/interdigital DGS slot structure, IET Electron Lett 45 (2009), 1077–1079. 4. C. Yi-Chyun, W. Cho-Yu, and K. Jen-Tsai, New miniaturized dual-mode dual-band ring resonator bandpass filter with microwave c-sections, IEEE Microwave Wirel Compon Lett 20 (2010), 67–69. 5. C. Karpuz and A. Gorur, Dual-mode dual-band microstrip filters, Proceedings of the 39th European Microwave Conference; Rome, Italy, 2009, pp. 105–108. 6. P. Kapitanova, D. Kholodhyak, S. Humbla, R. Perrone, J. Mueller, M.A. Hein, and I.Vendik, Right- and left-handed transmission line resonators and filters for dual band application, Microwave Opt Technol Lett 51 (2009), 629–633. 7. K. Zemlyakov and I. Vendik, Tuneable microwave resonators and filters on combination of right/left handed transmission line sec- tions for multiband applications, In: Proceedings of the Metamate- rials’2010, Karlsruhe, Germany, 2010, pp. 423–425. 8. P. Jarry and J. Beneat, Design and realizations of miniaturized fractal microwave and rf filters, John Wiley & Sons, New York, 2009. VC 2013 Wiley Periodicals, Inc. Figure 9 Simulated and measured responses of the single-band band- pass filter. Inset shows the photograph of the filter. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] Figure 8 Single-band bandpass filter based on fine-tuning of two reso- nant frequencies of DHR DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 55, No. 7, July 2013 1443