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A novel PBG structure for filter application

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A novel PBG structure for filter application
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   A NOVEL PBG STRUCTURE FORFILTER APPLICATION S. C. Bera, 1 R. V. Singh, 1  V. K. Garg, 1 N. S. Arora, 2 andS. S. Nair 2 1 Space Applications Center (ISRO) Ahmedabad, India 2 Department of Physics & ElectronicsUniversity School of Sciences Ahmedabad, India  Received 13 July 2005 ABSTRACT:  This paper presents the design, simulation and test re-sults of a novel photonic band-gap (PBG) structure for filter applica-tion. The proposed PBG structure is a 50  meander microstrip linewith a single rectangular ground-etched pattern instead of conventional periodic ground-etched pattern. The simulated results, verified by thetest results, demonstrate that this proposed structure provides less ripplein the lower pass-band with an increased rejection bandwidth of about 20%, as compared to a conventional PBG filter with same fill-factor.This single etched ground pattern enables easier fabrication and pack-aging, as compared to conventional multiple ground-etched patterns. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48:188–190, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21302 Key words:  photonic band gap (PBG); defected ground structure(DGS); wideband reject filter; compact PBG filter  INTRODUCTION A photonic band-gap (PBG) structure (or, more properly, an elec-tromagnetic crystal) for the microwave and millimeter-wave re-gion is a periodic structure where the propagation of electromag-netic waves is not allowed for some frequency bands or directions(antennas). These periodic structures exhibit wide band-pass andband-rejection properties at certain microwave frequencies. Intro-ducing periodic perturbations such as dielectric rods, holes, andpatterns in the waveguides or in the PCB substrates forms PBGmaterials. Electromagnetic waves in the PBG material are impededdue to periodic discontinuities, thus creating a slow-wave structure[1]. In microstrip technology, a PBG structure is obtained byintroducing an adequate periodic pattern drilled in the substrate oretched in the ground plane [2]. The planar etched PBG configu-rations have attracted much interest due to their ease of fabricationwith photolithographic MIC, MMIC, and MEMS processes [3].A simple conventional PBG filter structure with a microstripconfiguration is a 50  transmission line with the periodic ground-etched pattern. To achieve a sharper band-rejection property withsmaller substrate dimensions, a bended 50   transmission line isused with a 1D or 2D periodic ground-etched pattern, called acompact PBG structure [4]. Such a structure allows us to increasethe number of cells in less space with almost the same character-istics of a straight PBG structures.In this paper, we propose a novel PBG structure for filterapplication where a bended 50   transmission line is used withsingle rectangular ground-etched pattern instead of a conventionalperiodic ground-etched pattern. The proposed structure and a con-ventional one are designed and the simulated results are comparedusing a Sonnet 9.53 EM simulator. The simulated results show thatthe proposed structure provides less ripple in the lower pass-bandwith an increased rejection bandwidth of about 20%, as comparedto a conventional PBG filter with same fill-factor. The proposedstructure is realized on alumina substrate and the test results arepresented. DESIGN OF A PBG FILTER A conventional simple PBG structure for filter applications inmicrostrip configuration is a 50  transmission line with a period-ically etched ground plane, as shown in Figure 1. The centerfrequency of the band-reject filter is governed by the periodicity  a of the etched cells in the ground plane. The center frequency of thestop-band can be calculated by Bragg’s condition and is givenapproximately by  a    , (1)where  a  is the period of the PBG pattern, and  is the wave numberin the dielectric slab, defined as follows:   2    f  0 c     e . (2)From Eqs. (1) and (2), the center frequency can be written as:  f  0  0.5  ca      e , (3)where  c  is the velocity of light in vacuum and  e  is the effectivedielectric constant of the substrate material, approximately definedas  e  r   12   r   12   1  12 h  /  w , (4)where  r   is the dielectric constant,  h  is the height of the dielectricsubstrate, and  w  is the width of the microstrip line.The depth (in dB) and width (in terms of frequency) of theband-reject filter directly depends on the number of cells and widthof the etched pattern. Figure 2 shows a bended 50  microstrip lineused to accommodate a larger number of cells in the ground plane.This structure contains six cells of size 8  3 mm with periodicityof 21 mm, that is, a fill-factor of 0.381. This structure is designedin 25.4    25.4 mm alumina (  r     9.9) substrate of thickness0.635 mm.The simulated results, shown in Figure 3, indicate that thecenter frequency is 2.72 GHz with 20-dB rejection bandwidth of 1.18 GHz. It is also observed that the lower pass band containsripple on the order of 1.2 dB p-p. Figure 1  Layout of the 50  microstrip line with periodic ground-etchedslots: (a) top view; (b) bottom view 188  MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 1, January 2006 DOI 10.1002/mop  MODIFIED PBG FILTER WITH SINGLE SLOT: A NEWPROPOSED STRUCTURE The conventional ground-etched PBG structures in microstrip con-figuration contain a periodically ground-etched pattern, whichleads to a complex fabrication process and packaging difficulties.Here we have proposed a novel PBG structure with a microstripconfiguration that has a single rectangular ground-etched patternand bended 50   transmission line. This proposed structure isshown in Figure 4. The basic requirement for the PBG effect is toproduce periodic discontinuity in the transmission path so as toimpede EM wave propagation periodically. In this structure, al-though the single ground-etched slot is used, periodic discontinuityoccurs due to periodically passing the upper 50   microstrip lineon the ground-etched pattern. This proposed structure simplifiesthe packaging and fabrication process. This proposed structure issimulated for 0.635-mm-thick alumina (  r   9.9) substrate of size25.4  25.4 mm. The simulated result is shown in Figure 5. Thisresult shows that the center frequency is 2.48 GHz with 20-dBrejection bandwidth of 1.72 GHz and no low-frequency pass-bandripples. This filter seems to be useful as a low-pass filter with 3-dBcutoff frequency at 1.42 GHz and band rejection up to 3.4 GHz.This structure also minimizes the spurious effect due to resonancethat appears in the meander line, which was a problem in [4]. COMPARISON OF THE STRUCTURES AND THEIRSIMULATED RESULTS The proposed structure shown in Figure 4 and conventional struc-ture shown in Figure 2 have identical 50   bended transmissionlines on the top layer of alumina substrate (  r     9.9); the onlydifference is in the ground-etched pattern. The conventional struc-ture contains six of 8    3 mm ground-etched slots, whereas theproposed structure contains a single ground-etched slot of size24    8 mm. Both structures have same periodicity  a    21 mm.Thus proposed structure is simpler than the conventional structureand enables simpler packaging and fabrication processes.The simulated results ( S  21  in dB) of both the structures areshown in Figure 6. From this figure, it is clear that: Figure 2  Layout of the bended 50   microstrip line with rectangularperiodic ground-etched slots: (a) top view; (b) bottom view Figure 3  Simulated  S  -parameter result of the structure in Fig. 2 Figure 4  Layout of the bended 50   microstrip line with the proposedsingle rectangular ground-etched slot: (a) top view; (b) bottom view DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 1, January 2006  189  1. the center frequency decreases from 2.72 to 2.48 GHz(nearly 10%), implying that the slow-wave characteristics of the proposed structure are enhanced to some extent, result-ing in size reduction;2. the single-slot etched PBG structure provides negligibleripples in the lower pass-band frequency and the 20-dBrejection bandwidth increases from 1.18 to 1.72 GHz; thus,the proposed structure becomes more suitable as a low-passfilter. TEST RESULT The proposed structure has been fabricated in alumina substrateand tested using a network analyzer E8363B. The test results,shown in Figure 7, indicate nearly the same performance as thesimulated results, except for lesser band rejection. CONCLUSION A novel way of designing a 1D PBG structure has been studiedand compared with the conventional bended compact PBGstructure. The proposed structure provides a wider band-rejectproperty with less ripples in the low-pass region for the samefill-factor as that of a conventional PBG structure. This newstructure is suitable for designing low-pass filters, and it enableseasier packaging and fabrication. This novel structure adds onemore design in the list of the various PBG structures emergingfor microwave devices. REFERENCES 1. N.C. Karmakar and M.N. Mollah, Potential applications of PBG engi-neered structures in microwave engineering: Part I, Microwave J 47(2004), 22–24.2. V. Radisic, Y. Qian, R. Coccioli, and T. Itoh, Novel 2D photonicbandgap structure for microstrip lines, IEEE Microwave Guided WaveLett 8 (1998), 69–71.3. N.C. Karmakar and M.N. Mollah, Microstrip lines on annular ringphotonic bandgap structures, Microwave Opt Technol Lett 32 (2002),431–433.4. F. Falcone, T. Lopetegi, M. Irissarri, M.A.G. Laso, M.J. Erro, and M.Sorolla, Compact photonic bandgap microstrip structures, MicrowaveOpt Technol Lett 23 (1999), 233–236.© 2005 Wiley Periodicals, Inc.  ANALYZING CHAOTIC PHENOMENONIN A COLPITTS OSCILLATOR BASEDON LUR’S SYSTEM FORM AND THEHOPF BIFURCATION THEOREM Hsi-Chiang Chou Department of Electrical Engineering Tung Nan Institute of TechnologyShen-Keng, 22202 Taipei, Taiwan  Received 11 July 2005 ABSTRACT:  In this paper, we analyze the chaotic phenomenon in aColpitts oscillator. Theoretical analysis identifies the dominant compo-nent that affects the accuracy and stability of the Colpitts oscillator, and also derives the bifurcation of the chaotic region of those components. In addition, the period-doubling bifurcation routes to chaos are ob-served from the simulation and experimental results. This approach issuitable for any other 3 rd  -order autonomous nonlinear system. It is be-lieved that future designs of the Colpitts oscillator can benefit from our  Figure 5  Simulated  S  -parameter results of the proposed structure with asingle ground slot Figure 6  Simulated  S  -parameter ( S  21 ) results of the proposed and con-ventional bended structures Figure 7  Measured result of the proposed structure in Fig. 4 190  MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 1, January 2006 DOI 10.1002/mop
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