A New Microstrip Bandpass Filter Design Based on Hilbert Fractal Geometry for Modern Wireless Communication Applications
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1 A New Microstrip Bandpass Filter Design Based on Hilbert Fractal Geometry for Modern Wireless Communication Applications Department of Electrical and Electronic Engineering, University of Technology, Baghdad, Iraq P.O. Box (35239), Baghdad, Iraq doi: /ijact.vol1.issue2.4 Abstract This paper introduces a new microwave narrowband bandpass filter with a miniaturized size as well as adequate transmission and return loss characteristics for use in modern wireless communication systems. The proposed filter design topology is based on a single-mode microstrip resonators constructed in the form of Hilbert fractal geometries of the 2 nd and 3 rd iteration levels. Filter structures have been designed for the ISM band applications at a resonant frequency of 2.4GHz using a substrate with a relative dielectric constant of 10.8 and thickness of 1.27mm.The most effective parameters on filter performance such as edge spacing and stub length variations have been introduced and evaluated. The performance of each of the resulting bandpass filter structures has been analyzed using a method of moments (MoM) based software package, Microwave Office 2007, from Advanced Wave Research Inc. In addition, it has been found that, the bandpass filters based on 3 rd iteration Hilbert geometry show a high degree of 2 nd harmonic suppression which accompanies the performance of most bandpass filter topologies. Keywords Microstrip bandpass filter (BPF), Hilbert fractal curve, microwave filter miniaturization, narrow-band bandpass filter, electronic design automation (EDA). 1. Introduction Bandpass filter (BPF) is one of the most important components in microwave circuits. To meet the size requirement of modern microwave communications systems, compact microwave BPFs with narrowband is in high demand. Recently, there has been an increasing interest in planar BPFs due to their ease of fabrication. Filters using various planar resonators such as the open loop, miniaturized hairpin, stepped-impedance, quarter-wave, and quasi-quarter-wave resonators have been proposed for either performance improvement or size reduction. Recent developments in wireless communication systems have imposed new challenges to design and produce high selectivity miniaturized components. These challenges stimulate microwave circuit designers and antenna designers to seek out for solutions by investigating different fractal geometries [1]. Different from Euclidean geometries, fractal geometries have two common properties, space-filling and self-similarity. The dimension of a fractal provides a description of how much a space it fills. It is a measure of the prominence of the irregularities when viewed at very small scales. A dimension contains much information about the geometrical properties of a fractal [2, 3]. It has been shown that the self-similarity property of fractal shapes can be successfully applied to the design of multi-band fractal antennas, such as the Sierpinski gasket antenna, while the space-filling property of fractals can be utilized to reduce antenna and filter sizes. Research results showed that, due to the increase of the overall length of the microstrip line on a given substrate area as well as to the specific line geometry, using fractal curves reduces resonant frequency of microstrip resonators, and gives narrow resonant peaks[1]. Among the earliest predictions of the use of fractals in the design and fabrication of filters is that of Yordanov, et al. Their predictions are based on their investigation of Cantor fractal geometry [4]. Hilbert fractal curve has been used as a defected ground structure in the design of a microstrip lowpass filter operating at the L-band microwave frequency [5]. Sierpinski fractal geometry has been used in the implementation of a complementary split ring resonator [6]. Split ring geometry using square Sierpinski fractal curves has been proposed to reduce resonant frequency of the structure and achieve improved frequency selectivity in the resonator 35
2 A New Microstrip Bandpass Filter Design Based on Hilbert Fractal Geometry for Modern Wireless Communication Applications performance. Koch fractal shape is applied to mmwave microstrip bandpass filters integrated on a highresistivity Si substrate. Results showed that the 2 nd harmonic of fractal shape filters can be suppressed as the fractal factor increases, while maintaining the physical size of the resulting filter design [7]. Minkowski-like prefractal and Koch fractal curves has been used successfully in producing high performance miniaturized dual-mode square ring microstrip bandpass filters [8]. In this paper, a new narrow-band microstrip bandpass filter with miniaturized size has been presented as a candidate for use in modern compact wireless communication systems. The filter is composed of dual-resonators based on 2 nd and 3 rd iteration Hilbert curve geometries. The resulting single-mode bandpass filters are supposed to have noticeably miniaturized sizes with adequate performance responses. 2. The Hilbert Fractal Curve The Hilbert fractal curve, as outlined in Figure1, consists of a continuous line which connects the centers of a uniform background grid. The fractal curve is fit in a square section of S as external side. By increasing the iteration level k of the curve, one reduces the elemental grid size as S (2 k 1) ; the space between lines diminishes in the same proportion. Figure 1. Hilbert iteration (a) 1 st iteration (b) 2 nd iteration (c) 3 rd iteration (d) 4 th iteration For a Hilbert resonator, made of a thin conducting strip in the form of the Hilbert curve with side dimension S and order k, the sum of all the line segments L(k) are given by [9]: L(k) = (2 k + 1)S (1) resonator in the smallest area. However, it has been found that, when dealing with space-filling fractal shaped microstrip resonators, there is a tradeoff between miniaturization (curves with high k) and quality factor of the resonator. For a microstrip resonator, the width of the strip w and the spacing between the strips g are the parameters which actually define this tradeoff [9]. Both dimensions (w and g) are connected with the external side S and iteration level k (k 2) by: S = 2 k (w + g) g (2) From this equation, it is clear that trying to obtain higher levels of fractal iterations; this will lead to lower values of the microstrip width, thus increasing the dissipative losses with a corresponding degradation of the resonator quality factor. Hence, for these structures, the compromise between miniaturization and quality factor is simply defined by an adequate fractal iteration level. However, it has been concluded, in practice, that the number of generating iterations required to reap the benefits of miniaturization is only few before the additional complexities become indistinguishable [10]. 3. Filter Design At first, a single resonator based on the 2 nd iteration Hilbert fractal geometry, has been designed at a frequency of 2.4 GHz. It has been supposed that these filter structures have been etched using a substrate with a relative dielectric constant of 10.8 and a substrate thickness of 1.27 mm. The resulting resonator dimensions have been found to be 6.25x5.05 mm 2 and a trace width of about 0.4mm. The performance offered by this resonator is too poor to be presented here. The same resonator with depicted dimensions and substrate specifications has been used to build a tworesonator microstrip bandpass filter. The topology of this filter is shown in Figure 2. The overall dimensions of this filter are of 11.56x5.05mm 2. The corresponding performance curves are shown in Figure 3. The previous steps have been repeated, but now with a microstrip resonator based on the 3 rd iteration Hilbert fractal geometry, designed at the same frequency and using a substrate with the same specifications. Figure 4 shows the topology of the dual-resonator microstrip bandpass filter. This filter has overall dimensions of 8.84x3.82mm 2 with a trace width of 0.22 mm, to resonate at the design frequency. The main idea here is to increase the iteration of the Hilbert curve as much as possible in order to fit the 36
3 Hilbert resonator as compared to 2 nd iteration filter structure. Also, these filters possess a considerable miniaturization over the conventional half-wavelength resonator filter. Figure 2. The modeled microstrip bandpass filter with two resonators based on 2 nd iteration Hilbert curve geometry Figure 5. The return loss and transmission responses of the resulting 3 rd iteration fractal two-resonator microstrip bandpass filter 4. Filter Performance Evaluation Figure 3. The return loss and transmission responses of the resulting 2 nd iteration fractal tworesonator microstrip bandpass filter Figure 4. The modeled microstrip bandpass filter with two resonators based on 3 rd iteration Hilbert curve geometry Figure 5 shows the related performance curves. The guided wavelength at the design frequency is calculated by ( λ g ) [1, 11, 12]: λ g = c f εeff (3) and ε eff = ( ε r + 1) 2 (4) Where ε eff is effective dielectric coefficient. Size reduction percentages for 2.4GHz (ISM band) of about 42% have been obtained from 3 rd iteration stubbed Filter structures, depicted in Figure 2 and 4, have been modeled and analyzed at an operating frequency, in the ISM band, of 2.4 GHz using the Microwave Office 2007 electromagnetic simulator from Advanced Wave Research (AWR) Inc. This simulator performs electromagnetic analysis using the method of moments (MoM). The corresponding simulation results of return loss, S 11, and transmission, S 21, responses of these filters are shown in Figure 3 and 5 respectively, where the return losses are of about 15.2 and 10.4 db and insertion losses of about and 0.45 db for 2 nd and 3 rd iteration Hilbert designs respectively while the fractional bandwidths are of about 3.7% and 4.1 % for the same Hilbert designs respectively. It is clear, from Figure 3, that the resulting bandpass filter based on the 2 nd iteration Hilbert fractal geometry offers a quasi-elliptic transmission response with transmission zeros that are not symmetrically located around the deign frequency. However, this response and its consequent zeros could be, to a certain extent, controlled through the variation of spacing between coupled resonators. Performance curves shown in Figure 5 for bandpass filter based on the 3 rd iteration Hilbert fractal geometry depicted in Figure 4, implies that this filter possesses better transmission response with transmission zeros more symmetrical around the design frequency. Besides the resonator dimensions, two other important parameters play an important role in the resulting multi-resonator filter performance [13]. These are the spacing between the adjacent resonators and the additional stub. Additional stub is used to enhance the 37
4 A New Microstrip Bandpass Filter Design Based on Hilbert Fractal Geometry for Modern Wireless Communication Applications coupling between two resonators. Figure 6 and 7 show the resulting filter responses corresponding to different values of the spacing between the two resonators, for the 2 nd and 3 rd Hilbert fractal based bandpass filters respectively. length is not only varying the resonant frequency, but also shifting the locations of the transmission zeros. Figure 6. The transmission responses of the resulting 2 nd iteration fractal microstrip bandpass filter of different spacing edges values, s, (in mm) Figure 8. The transmission responses of the resulting 2 nd iteration fractal microstrip bandpass filter of different stub length values, t, (in mm) Figure 7. The transmission responses of the resulting 3 rd iteration fractal microstrip bandpass filter of different spacing edges values, s, (in mm) It is clear, in both figures; the variation in the spacing slightly affects the resonant frequency, while its effect is more noticeable on the transmission zeros. In addition, the transmission response, corresponding to the 3 rd iteration based bandpass filter, shows a high degree of 2 nd harmonic suppression which accompanies the operation of a wide variety of bandpass filters [11,12].It is clear, from Figure 7, that this harmonic, located at about 5.3 GHz, has been diminished to a level of about from 5 db to 8 db. Figure 8 and 9 demonstrate the effects of changing the stub length of these filters. The variation of the stub Figure 9. The transmission responses of the resulting 3 rd iteration fractal microstrip bandpass filter of different stub length values, t, (in mm) Figure 10 and 11 demonstrate the surface current distribution on the conducting surface of both resonators at the design frequency, where red color indicates higher coupling effect while blue color indicates the opposite effect. The previous filter designs can be applied for many other wireless communication systems; the filter dimensions can easily be scaled up or down depending on the required operating frequencies. In this case, the resulting filters might be of larger or smaller in sizes according to the frequency requirements of the specified applications. 5. Conclusions A new narrowband microstrip bandpass filter design for use in modern wireless communication systems has 38
5 been introduced in this paper. The proposed filter structures have been composed of dual microstrip resonators based on 2 nd and 3 rd iteration Hilbert fractal geometries. The space-filling property the proposed filter structure possesses, results in a high degree of miniaturization with reasonable passband performance, making it suitable for a wide variety of wireless communication applications. The new filters have small sizes, compact and low insertion loss as well as high performances, which are very important for microwave/rf circuit applications. In addition, it has been found that, the bandpass filter based on 3 rd iteration Hilbert geometry shows a high degree of 2 nd harmonic suppression in output response. Additional research work has to be carried out to evaluate a compact size dual band filter based on Hilbert fractal geometry. Figure 10. Current density distribution at the surface of the 2 nd iteration microstrip bandpass filter simulated at a frequency of 2.4 GHz [3] B.B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, [4] O.I. Yordanov, et al, Prospects of Fractal Filters and Reflectors, IEE 7th Inter. Conf. on Antenna and Propagation, ISCAP91, pp ,1999. [5] J. Chen, Z.B. Weng, Y.C. Jiao and F. S. Zhang, Lowpass Filter Design of Hilbert Curve Ring Defected Ground Structure, Prog. In Electromag. Res., PIER 70, pp , [6] Crnojevic-Bengin, V. Radonic, and B. Jokanovic, Complementary Split Ring Resonators Using Square Sierpinski Fractal Curves, Proceedings of the 36th European Microwave Conference, Manchester, UK, pp ,2006. [7]I.K. Kim, N. Kingsley, M.A. Morton, S. Pinel, J. Papapolymerou, M.M. Tentzeris, J. Laskar and J.G. Yook, Koch Fractal Shape Microstrip Bandpass Filters on High Resistivity Silicon for the Suppression of the 2nd Harmonic, Jour. Kor. Electromag. Engin. Soc., JKEES, 6(4), pp. 1-10, [8] J. K. Ali and N.N. Hussain, A New Fractal Microstrip Bandpass Filter Design Based on Dual-Mode Square Ring Resonator for Wireless Communication Systems, Iraqi Journal of Applied Physics, 6(1), pp.7-12,2009. [9] M. Barra, Miniaturized Superconducting Planar Filters for Telecommunication Applications, PhD Thesis, University of Napoli, Italy, [10] P. Gianvittorio, Fractals, MEMS, and FSS Electromagnetic Devices: Miniaturization and Multiple Resonances, PhD thesis, University of California, U.S.A, [11] J. S. Hong and M.J. Lancaster, Microstrip Filters for RF/Microwave Applications, John Wiley and Sons Inc., New York, [12] K. Chang and L.H. Hsieh, Microwave Ring Circuits and Related Structures, John Wiley and Sons Ltd., New Jersey, [13] D. G. Swanson, Narrow-band Microwave Filter Design, IEEE Microwave Mag., Vol.8, No. 5, pp , Figure 11. Current density distribution at the surface of the 3 rd iteration microstrip bandpass filter simulated at a frequency of 2.4 GHz 6. References [1] J.K Ali, A New Miniaturized Fractal Bandpass Filter Based on Dual-Mode Microstrip Square Ring Resonator, Proceedings of the 5 th International Multi-Conference on Signals, Systems and Devices, IEEE SSD 08, Amman, Jordan, July 20-23, [2] K. Falconer, Fractal Geometry; Mathematical Foundations and Applications, John Wiley and Sons Ltd.,
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