Effective Size Reduction Technique for Microstrip Filters

Transcription

1 Joural of Electromagetic Aalysis ad Applicatios, 13, 5, Published Olie April 13 ( Effective Size Reductio Techique for Microstrip Filters Dhiredra Kumar 1, Asok De 1 ECE Departmet, Maharaja Agrase Istititute of Techology, Delhi, Idia; NIT, Pata, Idia. dhiredra_7@rediffmail.com, asok.de@gmail.com Received Jauary 1 st, 13; revised February th, 13; accepted March 6 th, 13 Copyright 13 Dhiredra Kumar, Asok De. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. ABSTRACT I this paper a effective size reductio techique usig fractal structure is suggested. The proposed techique has bee applied o a bad stop ad a low pass filter separately. This techique provides 4% reductio of size for the bad stop filter ad about 6% for the low pass couterpart. Both the desiged structures are fabricated ad the measured results are compared with the simulated results. The proposed techique does ot require ay recalculatio or optimizatio of dimesios of the filter, ad is straightforward to implemet. The bad stop filter is desiged for the ceter frequecy of 3 GHz where as the cut-off frequecy for low pass filter is.5 GHz. A good agreemet betwee the simulated ad measured results is observed. A comprehesible explaatio of the proposed techique is also provided. Keywords: Bad Stop Filter; Fractal Structures; Kotch Curve; Low Pass Filters; Ope Stub; Step Impedace Network 1. Itroductio Filters are a very importat compoet i the microwave ad RF commuicatio systems. I the advaced commuicatio systems, a compact filter circuit with better performace is a basic requiremet these days. I this paper the bad stop ad low pass filters are cosidered to demostrate the proposed techique. To remove the uwated frequecy bads from the microwave ad radio frequecy sigals a bad stop filter (BSF) plays a very importat role i wireless commuicatio systems. Thus the BSF have bee widely used i several wireless circuits ad systems. The low pass filters are the idispesable compoets i ay microwave commuicatio system especially at the receivig ed. There are various BSF structures developed usig plaar substrates to achieve a compact circuit size. A wide bad stop filter is proposed by usig sigle quarter wave legth resoator with oe sectio of ati-coupled lies with shorted at other ed [1]. Few structures of bad stop filter have also bee preseted usig the defective groud with the aim of a compact size of the filter. Defected groud plae with mushroom structures is proposed i [], where a multilayer structure has bee used to achieve a compact structure. Aother compact mictrostrip bad stop filter based o defective groud structure (DGS) is desiged; these DGS uits are cosidered buildig blocks of the BSF to achieve the bad rejectio [3]. A small-size Electromagetic Bad Gap (EBG) microstrip structure with triple EBG structures is desiged, this EBG structure is based o the mai EBG microstrip lie with rectagular patches periodically iserted i the lie [4]. The spiral resoators also are used to desig a bad stop filter. This microstrip bad stop filter based o spiral resoators ca be implemeted with small size because of the subwavelegth effect of the resoators [5]. I [6], a parallel coupled bad stop filter usig a double egative coupled trasmissio lie is desiged. It requires a shorter couplig to achieve a compact size. A compact bad stop filter is also preseted usig a meader spur lie ad a pair of capacitive loaded stubs [7]. Usig the microstrip lie with ope ed stubs separated with quarter wavelegth lies at the ceter frequecy of stop bad is oe of the most widely used method to desig a wide bad stop filter [8-1]. This techique is oe of the covetioal ad more widely used methods. These quarter wave legth coectig lies are used as uit elemets. Sice the uit elemets of this type of bad stop filter are redudat, ad their filterig properties are ot well utilized, the resultat bad stop filter is ot a optimum oe. For bad stop filters the uit elemets ca be made early as effective as the ope-circuited stubs. Therefore, by icorporatig the uit elemets i the desig, sigificatly steeper atteuatio characteristics ca be obtaied for the same umber of stubs as is possible for filters desiged with redudat uit elemets. Also, a specified filter characteristic ca Copyright 13 SciRes.

2 Effective Size Reductio Techique for Microstrip Filters 167 be met with a more compact cofiguratio usig fewer stubs if the filter is desiged by a optimum method [11,1]. This optimum method is used i this paper to desig the bad stop filter ad the the fractal structure [13] is applied o the coectig lies of the ope eded stubs. Similar techique of size reductio is applied o the low pass microstrip filter. The fractal curve has bee applied o the high impedace lie of the stepped impedace microstrip low pass filter. Usig microstrip structure the low pass filter is desiged by usig either ope stub or stepped impedace techique [8,9]. The stepped impedace techique is more commo because of its simpler desig methodology. The low pass filter desig usig this techique occupies larger area. To achieve the compact structure several efforts have bee made. A compact low pass filter has bee desiged usig slow wave resoators [14], whereas a compact semi lumped low pass filter is proposed i [15]. However the lumped elemets raised fabricatio difficulties ad lumped elemets have stray capacitive ad iductive effects which affects the desired results. I [16], a low pass filter usig a sigle microstrip stepped impedace hairpi resoator with direct-coected feed lies is proposed, which has the advatage of extedig the stop bad betwee the first ad secod resoat frequecy because of the effect of loadig capacitace. I [17], a low pass filter usig coupled lies is proposed, which has two atteuatio poles i the stop bad. However, the use of coupled lies reduces the varieties of filter cofiguratios, ad the reduces applicatios of the type of filter. The utilizatio of microstrip ope-loop resoators allows various filter cofiguratios icludig those of elliptic or quasi-elliptic fuctio respose to be realized [18]. I this paper a Chebyshev low pass prototype of order five ad pass bad ripple is.1 db are cosidered to desig a low pass filter usig stepped impedace techique. For the desigs, bad stop as well as low pass filter, the dielectric costat ad height of the substrate cosidered i this paper is take as 3. ad.76 mm respectively.. Desig of Fractal Structure Usig Kotch Curve The basic structure of 1-D, 9 agles Kotch curve [13] is take ito cosideratio for the proposed desigs. This fractal curve is show i Figure 1 up to two iteratios. The first iteratio is show i Figure 1(b) ad the secod iteratio is show i Figure 1(c). The legth of the lie that is the distace betwee the two ed poits p ad q is cosidered as d which is show i Figure 1(a). For first iteratio the legth of the uit sectio lie becomes d/8 which makes the distace betwee p ad q shorter by half that is d/ i order to make p p p d/64 d/8 d (a) (b) (c) Figure 1. Basic structure of the Kotch curve: (a) Zero iteratio; (b) First iteratio; (c) Secod iteratio. the physical legth of the lie uchaged as show i Figure 1(b). I similar fashio the distace betwee p ad q becomes d/4 for the secod iteratio as the legth of the uit sectio lie becomes d/64 as show i Figure 1(c). The structures show i Figure 1 may be utilized to reduce the legths of the microstrip filters where log thi microstrip lies are used. It has bee applied o two differet structures i the preseted work where a cosiderable reductio i legths has bee observed. I both the desigs, oly first iteratio is utilized to avoid the complexity i fabricatio. 3. BSF Desig Usig Fractal Curve The basic structure of the proposed bad stop filter is based o the ope circuited trasmissio lie stub etwork as depicted i Figure. Filterig characteristics of this filter etirely deped o the desig of characteristic impedaces Z i for the ope-circuited stubs, ad characteristic impedaces Z i,i+1 for the uit elemets, as well as two termiatig impedaces Z A ad Z B [8,9]. The sythesis of the above show ladder etwork q q q Copyright 13 SciRes.

3 168 Effective Size Reductio Techique for Microstrip Filters Z A Z 1 Z 1, Z,3 Uit Elemet Z Z 3 Uit Elemet Figure. Trasmissio lie etwork represetatio of ope stub bad stop filter. show i Figure is based o followig trasfer fuctio give i Equatio (1). 1 S1 f (1) A f 1 where ε is the pass bad ripple costat ad A is the filterig fuctio represeted by the followig fuctio t t 1 t c A f B B 1 tc tc 1 t () t t 1 t c C C 1 t c tc 1 t where t is the Richards trasform variable which is give by π f t jta (3) f π tc j ta FBW 4 (4) FBW f f Z B 1 1% (5) f where f is the mid-bad frequecy of the bad-stop filter ad FBW is the fractioal badwidth. B x ad C x are the Chebysheve fuctios of the first ad secod kids of order : 1 cos cos B x x 1 si cos (6) C x x (7) The elemetal values are ormalized admittaces, ad for a referece Impedace Z = 5 ohm, the impedaces are determied by the set of Equatio (8). ZA ZB Z Zi Z gi (8) Z Z J ii, 1 ii, 1 A optimum microstrip bad-stop filter with three ope-circuited stubs ad a fractioal badwidth FBW = 1% at a mid-bad frequecy f 3 GHz is desiged. By cosiderig a pass bad retur loss of db, which correspods to a ripple costat ε =.15. For optimized filter the ormalized elemet values are take from [9] which are g1 g3.9486, g , ad the impedace iverters as J 1, J, The filter is desiged to match 5 ohm termiatios. Therefore Z = 5 ohm, ad from Equatio (8) we determie the electrical desig parameters for the desired filter etwork as give below: ZA ZB 5 ohm Z1 Z ohm Z 9.88 ohm Z Z 88.6 ohm 1,,3 The legths ad widths of the correspodig microstrip lie ope stub filter are determied. The microstrip BSF of such desig with their dimesios is show i Figure 3. The microstrip filter depicted i Figure 3 takes ito accout the ope ed ad T-juctio effects. The width of the microstrip lies coected with two ope ed stubs are.45 mm ad width of the 5 ohm microstrip lie is 1.8 mm. The fractal structure show i Figure 1(b) is ow applied i the structure show i Figure 3. The thi microstrip lie is modified usig the fractal curve. The proposed filter is depicted i Figure 4. I the modified filter a L b Figure 3. Microstrip BSF with optimum desig with a =.3 mm, b =.3 mm, W = mm, L = 15.5 mm. L L/ L/ Figure 4. Bad stop filter with fractal lies. w a Copyright 13 SciRes.

4 Effective Size Reductio Techique for Microstrip Filters 169 there are o chage i the dimesios, oly the structure of coectig lies are chaged. With the applicatio of Kotch fractal the distace betwee the two ope ed stubs becomes half. The total legth reductio of L = 15.5 mm is achieved. The simulated results of the modified BSF with fractal structure are compared with the filter without modificatio. Figure 5 gives the compariso of the S 11 parameters of the filter structures show i Figure 3 ad 4. I this result it ca be clearly observed that the retur loss is very much similar i both the cases. The S 1 parameters are also compared for the filters with ad without the fractal implemetatio which is show i Figure 6. The isertio loss is also similar for both the structures. The proposed desig is fabricated usig photolithographic techique. The fabricated structure is show i Figure 7. The S 11 ad S 1 parameters of the fabricated structure are measured usig vector etwork aalyzer. Figures 8 ad 9 compare the measured values of S 11 ad S 1 respectively of the fabricated structure with the simulated parameters of the structure show i Figure 4. A very good agreemet has bee observed betwee the simulated ad tested results as evidet from the S-parameters. Thus the bad stop filter usig ope stubs ca be desiged i a compact size with o chage i the desig equatios give i [9], oly a structural chage of fractal curve o the coectig lies are required. From the Figures 5 ad 6, it is clear that with a cosiderable size reductio same respose of the bad stop filter ca be obtaied. 4. Low Pass Filter with Fractal Curve I this sectio a compact microstrip low pass filter is desiged usig the fractal structure discussed i Sectio. To desig a microstrip low pass filter stepped impedace techique is used i which higher ad lower impedaces are used to get the effects of iductive ad capacitive impedaces respectively from the distributive structures. I a microstrip as the impedace of the lie icreases the width of the lie become thier ad vice-versa. So to get the appropriate values of the iductaces ad capacitaces i microstrip Notch filter without fractal Notch filter with Fractal Structure S11 i db Figure 5. Compariso of S 11 parameters of otch filter with ad without fractal structure. Notch filter without fracctal Notch filter with Fractal structure S1 i db Figure 6. Compariso of S 1 parameters of otch filter with ad without fractal structure. Copyright 13 SciRes.

5 17 Effective Size Reductio Techique for Microstrip Filters the ratio of higher to lower impedace value of lies Zhigh Zlow should be as high as possible (where Z high ad Z low are the higher ad lower impedaces of the microstrip lies), but limited by the practical values that ca be fabricated o a prited circuit board because very thi lie is impractical to fabricate. The typical values are Z high = 1 to 15 ad Z low = 15 to 5. Sice a typical low-pass filter cosists of alteratig series iductors ad shut capacitors i a ladder cofiguratio, we ca implemet the filter o a prited circuit board by usig alteratig high ad low characteristic impedace sectio trasmissio lies. I this desig we have selected Z low = 4 Ω ad Z high = 1 Ω. For the filter specificatio give above followig calculatios are made. For these low ad high impedaces the width of the microstrip lie is determied as 6.35 mm ad.48 mm re- spectively. Also for Z = 5 Ω, the width of the trasmissio lie obtaied is w = 1.8 mm. The relatioship of iductace ad capacitace to the trasmissio lie legth at the cut-off frequecy c are: Figure 7. Fabricated structure of proposed bad stop filter. Measured S11 parameters Simulated S11 parameters S11 parameters i db Figure 8. Compariso of measured ad simulated values of S 11 parameters. Measured S1 parameters Simulated S1 parameters -1 S1 parameters i db Figure 9. Compariso of measured ad simulated values of S 1 parameters. Copyright 13 SciRes.

6 Effective Size Reductio Techique for Microstrip Filters 171 CZ c L λ (9) L L c 1 λ 1 (1) HZH where λ ad λ 1 are the physical legths. Usig the desig Equatios (9) ad (1) ad the lumped parameter values obtaied above, the legths of the iductive ad capacitive lies are determied as below which have bee depicted i Figure mm, 9.33 mm, mm, 9.33 mm, 3.95 mm, 4 5 There are stray capacitive ad iductive effects produced by high impedace ad low impedace lies respectively. By miimizig these effects the circuit size ca be made compact [9]. From the Figures 11 ad 1 this pheomeo of stray capacitace ad iductace ca be uderstad. These effects are miimized by solvig the Equatios (11) ad (1). l 1 l l 3 l4 l 5 Figure 1. Layout of Chebyshev LPF usig stepped impedace techique. Cp L Figure 11. Stray capacitace (Cp) i high impedace lie. LS Figure 1. Stray iductace (Ls) i low impedace lie. C LS Cp 1 g Cp ta cz (11) high Ls Z g ta low c (1) where Cp ad Ls are the stray capacitaces ad iductaces, β is the phase costat, ad λ g is the wave legth of the respective lies. Miimizig the stray capacitace ad iductace effects requires a legthy calculatio sice it requires umber of mathematical iteratios ad the the legths of the resoators are eeded to be optimized by usig the simulatio software. I the proposed method, to reduce the complexity of the desig process fractal structure has bee applied to the iductive lies of the stepped impedace structure. It has bee ivestigated that by usig first iteratio ad 1/8th order of Kotch curve, the size of filter reduces by more tha 6%. By usig the fractal shape there is o eed to recalculate the dimesios of high ad low impedace lies. Usig this method there is o eed to go for ay cosideratio of ed effect or T-juctio effects. The desiged low pass filter usig fractal lies reduces the legth of the overall structure by l = l 4. The proposed structure is show i Figure 15. The simulated values of S 11 ad S 1 of the low pass filter with ad without fractal structure are show i Figures 13 ad 14. From these S 11 ad S 1 parameters it ca be clearly observed that there is o cosiderable deviatio betwee the values with ad without fractal structures. Moreover the pass bad characteristics usig the fractal structure are slightly improved. The fabricated structure of the proposed desig is show i Figure 16. To provide the close compariso betwee the tested ad simulated results the S 11 ad S 1 parameters are show i Figures 17 ad 18 respectively. From these results it has bee observed that there is a good match betwee simulated ad measured values ad a slight mismatch is due to the imperfectio i fabricatio. 5. Coclusio The proposed method is a effective ad efficiet size reductio techique with simplicity. This techique of size reductio may be applied o most of the lie based microstrip circuits. I the preseted work more tha 46.5% reductio of the size has bee observed without chage i the respose over the covetioal optimized bad stop filter. I the case of low pass filter the proposed techique is effective to achieve the compact size with the same respose as the covetioal low pass filter. The size reductio i the case of low pass filter is more tha 6%. This method does ot require legthy calculatios or optimizatio. The proposed techique is Copyright 13 SciRes.

7 17 Effective Size Reductio Techique for Microstrip Filters Without fractal structure With fractal structure -1 - S11 i db Figure 13. S 11 parameters of low pass filter with ad without fractal structure. Without fractal structure With fractal structure -5 S1 i db Figure 14. S 1 parameters of low pass filter with ad without fractal structure. L L4 Figure 15. low pass filter with ad without fractal structure. Copyright 13 SciRes.

8 Effective Size Reductio Techique for Microstrip Filters 173 Figure 16. Top view of fabricated structure. Simulated S11 Measured S11 S11 i db Figure 17. S 11 parameters of simulated ad measured values of the proposed filter. Simulated S1 Measured S S1 i db Figure 18. S 1 parameters of simulated ad measured values of the proposed filter. Copyright 13 SciRes.

9 174 Effective Size Reductio Techique for Microstrip Filters verified by comparig the measured results with the simulated results givig good agreemet betwee the two. REFERENCES [1] M.-Y. Hsieh ad S.-M. Wag, Compact ad Widebad Microstrip Badstop Filter, IEEE Microwave ad Wireless Compoets Letters, Vol. 15, No. 7, 5. [] Y.-H. Hsu, C.-H. Tsai ad T.-L. Wu, A New Badstop Filter Usig Artificial Defected Groud Structures with Compact Size ad Low Radiatio 1 IEEE 19th Coferece o Electrical Performace of Electroic Packagig ad Systems (EPEPS), 5-7 October 1, pp [3] S. U. Rehma, A. F. Sheta ad M. Alkahal, Compact Badstop Filter Usig Defected Groud Structure (DGS), 11 Saudi Iteratioal Electroics, Commuicatios ad Photoics Coferece (SIECPC), 4-6 April 11, pp [4] S. Y. Huag ad Y. H. Lee, A Tapered Small-Size EBG Microstrip Badstop Filter Desig with Triple EBG Structures, Microwave ad Optical Techology Letters, Vol. 46, No., 5, pp [5] H. Lim, J.-H. Lee, S.-H. Lim, D.-H. Shi ad N.-H. Myug, A Novel Compact Microstrip Badstop Filter Based o Spiral Resoators, Proceedigs of Asia-Pacific Microwave Coferece 7, pp [6] J.-G. Lee ad J.-H. Lee, Parallel Coupled Badstop Filter Usig Double Negative Coupled Trasmissio Lie, IEEE Microwave ad Wireless Compoets Letters, Vol. 17, No. 4, 7, pp doi:1.119/lmwc [7] H. W. Liu, R. H. Koechel ad K. F. Schueema, Miiaturized Badstop Filter Usig Meader Spur Lie ad Capacititively Loaded Stubs, ETRI Joural, Vol. 9, No. 5, 7. [8] D. M. Pozar, Microwave Egieerig, 3rd Editio, Wiley, New York. [9] J.-S. Hog ad M. J. Lacaster, Microstrip Filters for RF/Microwave Applicatios, Joh Wiley & Sos, Ic, Lacaster RF/Microwave Filter Desig, Lacaster, 1 [1] B. M. Schiffma ad G. L. Matthaei, Exact Desig of Bad-Stop Microwave Filters, IEEE Trasactios o MTT-1, 1964, pp [11] M. C. Horto ad R. J. Mezel, Geeral Theory ad Desig of Optimum Quarter Wave TEM Filters, IEEE Trasactios o MTT-13, 1965, pp [1] M. C. Horto ad R. J. Mezel, The Effectiveess of Compoet Elemets i Commesurate Lie Legth Filters, IEEE Trasactios o MTT-16, 1968, pp [13] [14] C. Jiaxi, Y. Megxia, X. Ju ad X. Qua, Compact Microstrip low pass Filter, Electroics Letters, Vol. 4, No. 11, 4, pp doi:1.149/el:4481 [15] J.-W. Shee, A Compact Semi-Lumped Low-Pass Filter for Harmoics ad Spurious Suppressio, IEEE Microwave ad Guided Wave Letter, Vol. 1, No. 3,, pp doi:1.119/ [16] L.-H. Hsieh ad K. Chag, Compact Low Pass Filter Usig Stepped Impedace Hairpi Resoator, Electroics Letters, Vol. 37, No. 14, 1, pp doi:1.149/el:16 [17] D. H. Lee, Y. W. Lee, J. S. Park, D. Ah, H. S. Kim ad K. Y. Kag, A Desig of the Novel Coupled Lie Low- Pass Filter with Atteuatio Poles, IEEE MTT-S Iteratioal Microwave Symposium Digest, Aaheim, Jue 1999, pp [18] J.-S. Hog ad M. J. Lacaster, Theory ad Experimet of Novel Microstrip Slow-Wave Ope-Loop Resoator Filters, IEEE Trasactios o Microwave Theory ad Techiques, Vol. 45, 1997, pp Copyright 13 SciRes.