A New Narrow Band Dual-Mode Miniaturized Bandpass Filter Design for Wireless Communication Systems

A new narrowband, compact, and low profile microstrip filter design is presented i n this paper a s a c andidate for use in modern wireless systems. Th e proposed design is based on t he u se of fractal multiple ring resonator. Multiple ring resonators have a dvantages to possess much narrower and shaper performance responses than those of the single ring resonator. The proposed filter design is fractally generated using M inkowski-Like Pre-Fractal c urve geometry applied to the conventional square microstrip square ring filter. F ilter structures resulting from the successive iterations in the fractal generation process show a cons iderable siz e reduction compared with the conventional microstrip square ring filter designed at the same frequency using the same substrate material. The performance of the generated bandpass filter structures have been analyzed using method o f moments (MoM) b ased software package Microwave Office 2007. Performance Simulation re sults show that filter st ructures employing 2 nd a nd 3 rd iterations offer size reduction percentages of about 61.5% and 77.7% respectively as compared with the conventional square ring filter.

Fractal geometries are different from Euclidean geometries in that they have two common properties, space-filling and self-similarity.It has been shown that the selfsimilarity property of fractal shapes can be successfully applied to the design of multi-band fractal antennas, such as the Sierpinski gasket antenna, while the spacefilling property of fractals can be utilized to reduce filter size.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.
In this paper, a new four pole microstrip bandpass filter, based on double fractal dual-mode ring resonator, has been presented.filter structures are fractally generated based on Minkowskilike pre-fractal (MLPF) geometry, and using the conventional dualmode square ring resonator as a starting step in the fractal generation process.The resulting filter structures are supposed to have miniaturized sizes with adequate reflection and transmission responses.

Minkowski-Like Pre-Fractal Geomet-ry for Miniaturized Filter Design
The starting pattern for the presented bandpass filter as a fractal is a square ring with a side length L o , Figure (1.b) fractal, the generator is composed of five segments with equal length of one third.However in the present work, generator is composed of five unequal length segments.According to this, the term Minkowski-like pre-fractal has been used to describe the resulting pre-fractal geometry.The middle segment w 1 is chosen such that it is less than the two end segments.The other two vertical segments are tuned to adjust the overall perimeter of the fractal length.This tuning length is called the indentation width, w 2 [6].
The basic idea, to propose this fractal technique to generate a miniaturized microstrip bandpass filter structures, has been borrowed from the successful application of such a technique in the microstrip antenna design, where compact size and multi-band behavior have been produced due to the space filling and self-similarity properties of the resulting microstrip fractal antenna design [7][8][9][10][11].
Practically, shape modification of the resulting structures in Fig( 1.c, d, and e) is a way to increase the surface current path length compared with that of the conventional square ring resonator; resulting in a reduced resonant frequency or a reduced resonator size, if the design frequency is to be maintained.Theoretically the size reduction process goes on further as the iteration steps increase.It is expected then, that the 2 nd iteration, shown in Fig( 1.d) will exhibit further miniaturization ability owing to its extra space filling property.
The presented fractal scheme has an additional property that is the symmetry of the whole structure in each of the iteration levels, about its diagonal.This property is of special importance in the design of dual-mode loop resonators [9,10].The resulting pre-fractal structure has the characteristic that the perimeter increases to infinity while maintaining the volume occupied.This increase in length decreases the required volume occupied for the pre-fractal bandpass filter at resonance.It has been found that [7-10] while the enclosing area, A n , has been found to be [7][8][9][10] where A o is the area occupied by the conventional square ring resonator.

Two Pole Single Ring Filter Design
Up to 3 rd iteration microstrip dualmode single ring bandpass filter structures have been designed for the (ISM) band applications at a design 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 thickness of 1.27mm.At first, the side length of the square ring resonator, L o , has to be calculated as [12-15] where is the guided wavelength and Then the side length n L for the successive iterations can be calculated, based on the value of o L , using Equ.(2).Small perturbations have to be applied to each dual-mode resonator, at locations that are assumed at an angle o 45 offset from its two orthogonal modes.These perturbations are in the form of a small patch added to the square ring, and the other subsequent iterations resonators.It should be mentioned that, for coupling of the orthogonal modes, the perturbations could also take forms other than this shape.But since the proposed resonating structures are characterized by their diagonal symmetry, this shape of perturbation is the most convenient to satisfy the required coupling [10,16].The dimensions of the perturbations of each filter must be tuned for the required filter performance, since the nature and the strength of the coupling between the two degenerate modes of the dual-mode resonator are mainly determined by the perturbation's size and shape.However, extensive details about this subject can be found in [17,18].
It is worth to mention that, the filter structures based on the 1 st 2 nd and 3 rd iterations depicted in Figs.(3)(4)(5) have similar structures with those reported in [10].These filter structures have been found to possess size reductions of about 40%, 64% and 78% respectively, as compared with those of the conventional dual-mode microstrip square ring resonator, Fig (2), with accepted filter performances [10].Table ( Favoring the coupling between the modes 2 and 3 and reducing all the others, the coupling between the rings can be controlled either by the length D of the microstrip which connects the two stubs or by the capacitive gap g between the resonators and stubs.By using this layout, a four pole filter, with a center frequency of 2.4 GHz, has been designed on the same substrate that has been used for single resonator filter previously reported.The dimensions of the basic fractal dual-mode rings are unchanged as in the case of the corresponding single stage filters.The coupling between the degenerate modes of the rings is achieved by suitable perturbations.Table (2) summarizes the resulting dimensions and the satisfied size reduction percentages of the simulated four pole double ring filters against the conventional double square ring resonator filter.The values of D and the spacing g have to be tuned to achieve the required performance

Performance Evaluation
A Two pole dual-mode filter structure based on the conventional square ring resonator, and three filter structures corresponding to the first three fractal iterations, depicted in Figs( 2-5) respectively, 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 AWR Software Inc.This simulator performs electromagnetic analysis using the method of moments (MoM).
The corresponding simulation results of return loss and transmission responses of these filters are shown in Figs.(10 -13) respectively.
Results show that the resulting bandpass filters possess good performance curves.As can be seen, all of the filter responses show two transmission zeros symmetrically located around the deign frequency.The previous filter designs can easily be scaled to other frequencies required for other wireless communication systems.In this case, the resulting new filter will be of larger or smaller in size according to the frequency requirements of the specified applications.
Similarly, A four pole dual-mode filter structure based on the conventional square ring resonator, and three filter structures corresponding to the first three fractal iterations, depicted in Figs( 6-9) respectively, have been modeled and analyzed at the same operating frequency.

Conclusions
In this paper, a new miniaturized narrowband fractal four poles bandpass filter structures have been presented as a new technique for dual-mode narrow band BPF design.In this technique, the four poles dual-mode bandpass filter structures have been generated based on the 2 nd and 3 rd iterations Minkowski-like pre-fractal geometry and using the conventional dual-mode square ring resonator as an initiator.Up to the 3 rd iteration, double ring microstrip bandpass filters structures have been designed, according to this technique, and analyzed using the method of moments (MoM), at the ISM frequency band.Results showed that, these filters possess a progressive size reduction with reasonable return loss and transmission responses.The 2 nd and 3 rd iterations filters have been found to offer size reductions of about 61.5% and 77.7% respectively as compared with the conventional dual-mode microstrip square ring resonator under the same design specifications.Consequently, the proposed technique can be generalized as a flexible design tool for compact microstrip bandpass filters for a wide variety of wireless communication systems.
where P n is the perimeter of the nth iteration pre-fractal and a 2 is equal to the ratio w 2 /L o .Theoretically as n goes to infinity the perimeter goes to infinity.The ability of the resulting structure to increase its perimeter, at each iteration, was found very triggering for examining its size reduction capability as a microstrip bandpass filter.The length, L o, of the conventional micro-strip dual-mode square ring resonator has been determined using the classical design equations reported in the literatures [12-15].As shown in Figure (1), applying geometric transformation of the generating structure Fig.(1.a) on the square ring resonator Fig.(1.b), results in the 1 st iteration filter structure depicted in Fig.(1.c).Similarly successive bandpass filter shapes, corresponding to the subsequent iterations can be produced as successive transformations have been applied.Fig.(1.e) shows an enlarged copy of the 3 rd iteration fractal structure, on which the proposed bandpass filter design is based.At the n th iteration, the PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal ,Vol.27,No.
The correspond-ding simulation results of return loss and transmission responses of these filters are shown in Figs.(14-17) respectively.For demonstration, the surface current distribution of the 3 rd PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal ,Vol.27,No.ring resonator filter has been shown in Fig.(18).

Figure( 18 )
Figure(18) Surface current distribution of the four pole microstrip bandpass filter based on the 3rd iteration fractal dual-mode ring resonator at the design frequency

27, No.10,2009 A New Narrow Band Dual-Mode Miniaturized Bandpass Filter Design for Wireless Communication Systems 1939
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& Tech. Journal ,Vol.27, No.10,2009 A New Narrow Band Dual-Mode Miniaturized Bandpass Filter Design for Wireless Communication Systems
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