RIGHT-ANGLED TRIANGULAR PATCH RESONATOR AND FILTER WITH FRACTAL HOLE

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1 Progress In Eectromgnetics Reserch B, Vo. 4, , 212 RIGHT-ANGED TRIANGUAR PATCH RESONATOR AND FITER WITH FRACTA HOE J.-K. Xio 1, 2, *, X.-P. Zu 3, X. i 3, nd. Tin 3 1 Schoo of Eectronic & mechnic Engineering, Xidin University, Xi n 7171, Chin 2 Stte Key bortory of Miimeter Wves, Nnjing 2196, Chin 3 Schoo of Computer nd Informtion, Hohi University, Chngzhou 21322, Chin Abstrct Frct-shped microwve pssive circuits offer gret de of promise for chieving good performnce in sm circuits. In this pper, isoscees right-nged tringur ptch resontor with frct hoe is nyzed, nd new singe-bnd nd du-bnd RF fiters by using isoscees right-nged tringur ptch resontors with frct pttern re proposed. It is shown tht the right-nged tringur resontor cn be miniturized with the ssistnce of frct, nd fiter performnce is grety improved. Simutneousy, the resontor s higher order mode resonnce is fortified, esing off the difficuty in du-bnd fiter design. Two proposed frct bndpss fiters re fbricted, nd their performnce is verified by mesurement. The proposed fiters demonstrte the ppictions of right-nged tringur ptch resontor nd exhibit dvntges of simpe structur topoogy nd compctness, which re essenti in RF circuit design. 1. INTRODUCTION Tringur ptch resontors [1 6], especiy the equiter tringur resontor nd isoscees right-nged tringur (IRT) resontor, hve importnt ppictions in microwve circuits with existing design methods. However, the IRT resontor received ess ttention. The good performnce of tringur ptch fiters hve been proven; however, few works hve been reported compred with the squre Received 6 Februry 212, Accepted 6 Apri 212, Schedued 16 Apri 212 * Corresponding uthor: Jin-Kng Xio (xiojk@zu.edu.cn).

2 142 Xio et. nd circur ptch fiters [4]. In [1, 3], bndpss nd bndstop fiters re deveoped by using equiter tringur resontors, nd in [2], new wide bnd bndpss fiter using muti-mode equiter tringur resontor is designed. [5] deveops new isoscees tringur resontor for wide-bnd bndpss fiter, nd [6] reports nove bndpss fiters with controbe opertion by using equiter tringur resontor. However, these works ony possess one singe opertion bnd, nd muti-bnd is not concerned. Compred with the trnsmission-ine bsed fiters, ptch fiters hve more compct size, ower oss, nd higher power hnding fetures. The bsic principe for designing ptch resontor fiter is the seectivity nd usge of sorts of resonnt modes. In the pst, ptch fiter design miny concentrtes on dumode (the dominnt mode nd its degenerte one) opertion, nd the higher order modes re not considered. Nowdys, frct technique [2, 7 1] ttrcts gret ttention of microwve reserchers in designing new microwve circuits nd improving circuit s performnce. However, their works focus on ntenns, not on fiters. Frct hs inherent properties, which re sef-simirity nd spce fiing. The typic frcts with their shpe nd dimensions decided by certin mthemtic method wys re stricty sef-simir, nd cn be ced we-reguted or regur frcts. Those not-crefuy-designed frct configurtions ppied in RF circuit, however, re irregur frcts with rough sef-simirity. In RF circuits design, frct cn be used in buiding ptch resontors, microstrip ines, nd the defected ground of microstrip. Frct hs the dvntges of minituriztion, wide bndwidth, nd muti-bnd opertion in the fiters design. Frct hoe in ptch provides the tter with fied perturbtion nd introduces higher order modes for muti-bnd opertion. It so reizes circuit minituriztion nd widebnd performnce. In this pper, frct-shped IRT resontor is proposed, nd nove RF fiters with singe- nd du-bnd using IRT resontor re designed with the usge of frct, which cts s fied perturbtion, resuting in desired higher order mode. The obtined higher order mode is utiized to impement the fiter s du-bnd response. The frct not ony miniturizes circuit size but so grety improves fiter performnce. 2. ISOSCEES RIGHT-ANGED TRIANGUAR PATCH RESONATOR Resonnt frequency of the isoscees right-nged tringur ptch resontor cn be expressed s [11]

3 Progress In Eectromgnetics Reserch B, Vo. 4, f r = c 2 ε r m 2 + mn + 2n 2 (1) where, is the ength of the tringe bse, c the veocity of ight in free spce, ε r the retive dieectric coefficient of substrte, nd integers m nd n determine the resonnt modes. When m = nd n = 1, the dominnt mode is obtined, nd its resonnt frequency cn be expressed s f 1 = 2c/(2 ε r ). Our reserch shows tht the simuted resuts got by Ansoft ensembe [12] EM simutor bsed on method of moments (MoM) re simir to the ccution from Eqution (1). Eqution (1) is importnt for determining the resonnt mode nd heping design the required fiter. Tbe 1. TM modes for IRT ptch resontor. Mode sequence m, n k m,n π 1, 1 2 f,1 = f r 2 2 c ε r 2 1, 1 2 f 1,1 = c 3 1, 2 7 f1, 2 = ε r 7 2 c ε r 4 2, f 2,1 = 2 c ε r Ccuted TM mode properties of the IRT resontor re shown in Tbe 1. Ccuted resonnt performnce vritions of the IRT resontor re shown in Fig. 1, which shows resonnt frequency decreses with tringe bse incresing. Fig. 2 shows the mgnetic fied ptterns nd current distributions of the IRT resontor with dumode opertion. In this pper, of the investigtions re on IRT resontors nd fiters, nd of the ccutions nd designs re got by using cermic substrte with dieectric constnt of 1.2 nd thickness of 1.27 mm. 3. RIGHT-ANGED TRIANGUAR PATCH RESONATOR AND BANDPASS FITER WITH REGUAR FRACTA-SHAPED HOE We know tht the bsic frct cn be cssified s Koch frct, Minkowski frct, Sierpinski frct, nd Hibert frct [13]. Cssic Sierpinski frct geometry is constructed by n isoscees tringe with reversed isoscees tringe cut itertivey, nd the cut prts hve strict simirity in the whoe structure, s shown in Fig. 3. In the reserch, we find tht the strict Sierpinski frct ptch resontor is

4 144 Xio et. Resonnt Frequency (GHz) f,1 f 1,1 f 1,-2 f 2, (mm) Figure 1. Simuted resonnt frequency of the first four resonnt modes for the IRT resontor. The dominnt mode The degenerte mode The dominnt mode (c) The degenerte mode (d) Figure 2. Mgnetic fied ptterns nd current distribution of the dominnt nd the degenerte modes for the IRT resontor, nd re mgnetic fied ptterns, (c) nd (d) re current distribution. hrdy ppied to RF fiter design becuse of the poor performnce. In this prt, of the ptch hoes re right-nged tringe shpe, i.e., frct cut prts hve strict simirity in the whoe structure. However, it is not the Sierpinski frct shpe but qusi one becuse the entire Sierpinski frct for the IRT resontor cnnot produce the desired fiter performnce. Ccuted resonnt performnce of the first two resonnt modes for the right-nged tringur resontor with the 1st frct is potted in Fig. 4, nd the ccutions show tht with the ction of frct, the resonnt frequencies of the first two resonnt modes re ower thn those of the right-nged tringur resontor without ptch hoe, nd rger ptch hoe size introduces ower resonnces. The ccuted curves of prmeters versus for the right-nged

5 Progress In Eectromgnetics Reserch B, Vo. 4, (c) (d) Figure 3. Sierpinski tringe itertion. -th order. 1st order. (c) 2nd order. (d) 3rd order. Frequency (GHz) f,1 f 1,1 13mm (mm) (mm) f = 3.68 GHz f = 4.7 GHz f = 4.35 GHz (mm) Figure 4. Resonnt chrcteristics of the right-nged tringur resontor with the 1st frct. Figure 5. Ccuted curves of prmeter versus for the frct right-nged tringur resontor t different resonnces. tringur resontor re potted in Fig. 5, which shows tht for certin resonnce, decreses with incresing, n dvntge for minituriztion. Certiny, resonnt frequency of the frct IRT resontor increses with prmeter decresing. Trnsmission chrcteristic comprisons of the frct right-nged tringur ptch resontors re shown in Fig. 6, nd of the resontors re designed to hve the sme resonnt frequency of 4.5 GHz. Figs. 6 nd 6 pot the trnsmission chrcteristics of right-nged tringur resontor with the 1st nd the 2nd order frcts, respectivey, nd both show tht frct resontor cn be miniturized when operting t the sme resonnt frequency. The two figures so show tht for the frct right-nged tringur ptch resontor, rger size of frct hoe introduces more miniture circuit dimension when operting t the sme frequency, whie resonnt frequency bnd between the two higher order modes is extended. Trnsmission chrcteristic comprison of the right-nged tringur resontor with the -th, 1st nd 2nd order frcts re shown in Fig. 6(c), which shows tht the circuit size reduces with incresing frct itertion order when operting t the sme frequency. A these figures show tht the dominnt mode hs the strongest resonnce.

6 146 Xio et. (db) = 16mm = 1mm = 14.5mm =15.5mm = 15mm = 6.36mm =4.5mm = 5.7mm Frequency(GHz) (db) = 16mm (db) =15.5mm =4.5mm g =16mm =1.5mm g=1mm =15mm =5.6mm g=2mm =14mm =6.8mm g=3mm Frequency(GHz) (c) g Frequency(GHz) =15mm =5.6mm g=2mm Figure 6. Trnsmission chrcteristics of the right-nged tringur resontor with the -th, the 1st nd the 2nd frct t 4.5 GHz. Trnsmission chrcteristics of right-nged tringur resontor with the 1st frct t 4.5 GHz. Trnsmission chrcteristics of the right-nged tringur resontor with the 2nd frct t 4.5 GHz. (c) Trnsmission chrcteristics of the right-nged tringur resontor with the -th, 1st nd 2nd order frct t 4.5 GHz. The extern quity fctor of singe ptch resontor my be expressed s Q ei = f i / f 3 db, where Q ei is the extern quity fctor of the i-th resonnt mode, nd f i nd f 3 db re the i-th resonnt frequency nd the corresponding 3-dB bndwidth of the singe ptch resontor, when the singe ptch resontor is externy excited one. Ccuted Q e versus feeding position t of the right-nged tringur resontor with the 1st frct is potted in Fig. 7, which shows tht the frct resontor hs dequte extern quity fctor of more thn 127 nd increses with incresing t. Bndpss fiters using singe right-nged tringur ptch resontor with the 1st nd 2nd frcts re so designed, s shown in Fig. 8, where I/O feed ines set t the tringe bottom re microstrip ines with chrcteristic impednce of 5 Ω, nd the frct ptterns re right-nged tringur shpes which hve strict simirity to

7 Progress In Eectromgnetics Reserch B, Vo. 4, Extern quity fctor (Q e ) t t (mm) Figure 7. Extern quity fctor Q e versus feeding position t, = 13 mm, = 5 mm. Port 1 h 1 h Po rt 2 Port1 s g h e g g h1 Port2 Figure 8. Topoogies of the bndpss fiter using singe IRT ptch resontor with frct hoe. With the 1st frct. With the 2nd frct. the IRT ptch resontor. Simuted frequency responses of the IRT resontor bndpss fiter with the 1st frct re shown in Fig. 9, which shows tht fiter performnce is grety improved with better frequency seectivity nd wider bndwidth for the upper stopbnd, nd fiter opertion frequency owered from 5. GHz to 3.2 GHz with the ssistnce of frct pttern. These chnges re due to frct hoe which brings perturbtion to the origin (the -th frct) IRT resontor. The fiter retive bndwidth nd pssbnd insertion oss re shown in Tbe 2. In order to verify the design, the proposed fiter s shown in Fig. 8 is fbricted, nd the hrdwre nd mesurement re shown in Fig. 1. The circuit occupies n re of bout 23 8 mm 2. The mesured resuts got by Agient E571C vector network nyser re cose to the simution, nd the mesured pssbnd insertion oss t centre frequency is bout 1.6 db. Simuted frequency responses of the IRT resontor bndpss fiter with the 2nd frct s shown in Fig. 8 re potted in Fig. 11, which shows tht smer frct hoes introduce incresed opertion frequency. The fiter performnce

8 148 Xio et. 1 s 11 =13mm, =5mm, h=6.5mm, h 1 =2.5mm =14.5mm, =6.36mm, h=7.25mm, h 1 =3.18mm =13mm,without frct Mgnitude (db) s Frequency (GHz) Figure 9. Simuted frequency responses of the IRT resontor bndpss fiter with the -th nd the 1st frct. Mgnitude (db) Simution Mesurement s 11 s Frequency (GHz) Figure 1. Fiter fbriction nd mesurement, = 13 mm, = 5 mm. Photogrph of the fbricted hrdwre. Comprison of the simution nd mesurement. is isted in Tbe 2. Fbricted hrdwre nd mesurement re shown in Fig. 12. It cn be seen the mesurement is simir to the simution, nd the mesured pssbnd insertion oss t the mesured centre frequency of 2.98 GHz is bout 1.2 db. The circuit occupies n re of bout mm 2. The fiters with the 1st nd 2nd frcts hve simir performnce, nd both operte t the TM 1 mode. For the two fbricted fiters, the min error of the simution nd experiment is opertion frequency shift, miny due to the mteri discrepncy nd fbriction uncertinty.

9 Progress In Eectromgnetics Reserch B, Vo. 4, Tbe 2. simuted fiter retive bndwidth nd pssbnd insertion oss (I). The 1st frct The 2nd frct Geometric prmeters (mm) Center Retive frequency bndwidth (GHz) (%) Pssbnd I (db) = 13, = = 14.5, = = 14, = = 14, = = 14mm, = 6.8mm, g = 3mm, s= 1.5mm = 14mm, = 6mm, g = 2mm, s= 1mm Mgnitude (db) g Frequency (GHz) Figure 11. Simuted frequency responses of the IRT resontor bndpss fiter with the 2nd frct. 4. RIGHT-ANGED TRIANGUAR PATCH RESONATOR WITH IRREGUAR FRACTA-SHAPED HOE For IRT ptch resontor with irregur frct hoe, ccuted curves of resonnt frequency versus prmeter b, prmeter h 1, nd prmeter d re shown in Fig. 13. It cn be seen from Fig. 13 tht the resonnt frequencies of the first nd second higher order modes decrese with prmeter b incresing, whie the dominnt mode hs nery no vrition. Fig. 13 shows tht the vrition of hoe height h 1 hs itte effect on resonnce of the higher order modes, but for the dominnt mode, resonnt frequency decreses with h 1 incresing, nd it owers much when the ptch deeted tringe top pproches the IRT top.

10 15 Xio et. Mgnitude (db) s 11 s 21 Simution Mesurement Frequency (GHz) Figure 12. Fiter fbriction nd mesurement, = 14 mm, = 6 mm, g = 2 mm, s = 1 mm, e = 3.5 mm, h = 7 mm, h 1 = 3 mm. Photogrph of the fbricted hrdwre. Comprison of the simution nd mesurement. Prmeter d hs different effects on resonnt modes, s shown in Fig. 13(c). It cn be seen for the dominnt mode, resonnt frequency increses with incresing d when d < 4 mm; however, the resonnt frequency decreses brupty when d > 4 mm. For the first higher order mode, resonnt frequency hs no obvious chnge with prmeter d, nd for the second higher order mode, resonnt frequency decreses with d incresing. It cn be concuded tht the higher order modes re miny reted with prmeters b nd d, nd the dominnt mode is miny reted with prmeters h 1 nd d. In the reserch, it is shown tht the resonnce of the first higher order mode my be suppressed when the tringe bse b of frct hoe is big enough to cut the isoscees tringe side, nd it is so shown tht the frct hoe in IRT resontor described bove is hrd to mke the dominnt mode spit to introduce du-mode fiter nd tht the higher order modes, such s TM 11, TM 1, 2, re so hrd to be spitted. Trnsmission chrcteristics of the IRT resontor with irregur frct hoe re shown in Fig. 14. Figs. 14 nd show the trnsmission chrcteristics of the IRT resontor with singe nd doube frct hoes which operte t 2.5 GHz nd 2.4 GHz, respectivey. Fig. 14(c) shows the trnsmission chrcteristics comprison of the IRT resontor without nd with frct hoes which operte t 3.8 GHz. A of the figures iustrte tht the resontor size reduction nd spurious response improvements go together with the hep of frct when the resontors operte t the sme frequency.

11 Progress In Eectromgnetics Reserch B, Vo. 4, Resonnt Frequency (GHz) f,1 f 1,1 f 1,-2 b b (mm) 8. h1 d Resonnt Frequency (GHz) f,1 f 1,1 f 1,-2 b h 1 (mm) h1 d 7.5 Resonnt Frequency (GHz) f,1 f 1,1 f 1,-2 b h1 d d (mm) (c) Figure 13. Ccuted curves of the first three resonnt frequencies versus geometric prmeters for the IRT resontor with frct hoe. Retionships of prmeter b nd resonnt frequency, = 17 mm, d = 1.5 mm, h 1 = 6 mm. Retionships of prmeter h 1 nd resonnt frequency, = 17 mm, b = 3.6 mm, d = 1.5 mm. (c) Retionships of prmeter d nd resonnt frequency, = 17 mm, b = 3.6 mm, h 1 = 5 mm. 5. RIGHT-ANGED TRIANGUAR PATCH RESONATOR DUA-BAND FITER Currenty, mny RF fiters re designed with du-bnd or muti-bnd opertion becuse the incresing demnd of wireess communiction ppictions necessittes RF trnsceivers operting t du-bnd or muti-bnd in order tht users cn ccess more services with singe hndset. In this pper, singe ptch right-nged tringur resontor du-bnd bndpss fiters with irregur frct ptterns

12 152 Xio et. -2 g w -2 g w (db) = 17.mm g = 6.8mm w = 3.4mm = 15.mm g = 6.5mm w = 3.8mm = 13.mm g = 6.1mm w = 4.mm (db) = 17.mm g = 3.6mm w = 3.mm = 15.mm g = 3.5mm w = 2.4mm = 13.mm g = 3.2mm w = 2.6mm Frequency(GHz) Frequency(GHz) -2 (db) = 17.mm = 15.mm g = 3.8mm w = 3.2mm g w g = 13.mm g = 2.3mm w = 2.mm w Frequency(GHz) Figure 14. Trnsmission chrcteristics comprison of the IRT resontor with different frct hoe. Trnsmission chrcteristics of the IRT resontor with singe frct hoe t bout 2.5 GHz. Trnsmission chrcteristics of the IRT resontor with pir of frct hoes t bout 2.4 GHz. (c) Trnsmission chrcteristics of the IRT resontor without nd with frct hoe t bout 3.8 GHz. re designed, s shown in Fig. 15, where the frct hoe which cts s perturbtion is used to strengthen the required resonnt modes, contro the opertion frequency, nd suppress the undesired spurious responses. The opertion du-bnd is due to the ppiction of the resonnt modes, nd the opertion modes cn be mde certin by formu (1). The couping structure nd equivent circuit potted in Figs. 15(c) nd (d) show tht the opertion of IRT resontor with frct hoe is equivent to the opertion of resontor 1 denoted by pre circuit of 1 nd C 1, nd resontor 2 denoted by pre circuit of 2 nd C 2 using two-pth couping. I/O feed ines denoted by cpcitor C 4 re microstrip ines with chrcteristic impednce of 5 Ω, (c)

13 Progress In Eectromgnetics Reserch B, Vo. 4, b h b c h Port 1 d Resontor Port 2 Po rt1 Por t2 C3 R1 C4 C4 Por t1 Port 2 1 C 1 2 C 2 R2 (c) (d) Figure 15. Du-bnd bndpss fiters using singe IRT ptch resontor with frct hoe, for topoogy 1, = 17 mm, b = 3.6 mm, d = 1.4 mm, h = 8.5 mm; for topoogy 2, = 17 mm, b = 3 mm, c = 3.6 mm, h = 8.5 mm. Fiter 1. Fiter 2. (c) Couping structure. (d) Equivent circuit. Quity Fctor Q e Q e1 Q e t (mm) t Quity Fctor Q e Q e1 Q e t (mm) t Figure 16. Extern quity fctor Q e versus feeding position t. With singe hoe. With du-hoe. nd their couping cn be denoted by cpcitor C 3. The ccuted extern quity fctor Q e versus the feeding position t is potted in Fig. 16, where Q e1 nd Q e2 re extern quity fctors corresponding to the dominnt mode nd the first higher order mode, respectivey. It

14 154 Xio et. is shown tht IRT resontor with singe nd doube frct hoes hs dequte extern quity fctor. Simuted frequency responses of fiters 1 nd 2 re shown in Fig. 17, nd the corresponding performnces re isted in Tbe 3. It is shown from ccution tht the du-bnd is got by resonnces f,1 nd f 1,1, respectivey, nd the fiters hve simir performnces. Both of the du-bnd fiters operte t bout 2.4 GHz nd 5.5 GHz, respectivey. It cn be seen tht if tringur ptch hoe hs the sme direction nd simir re, the fiters hve simir frequency responses, nd it so cn be seen tht with the ssistnce of frct ptterns, the resonnt frequency of the dominnt mode owers, nd the fiter performnce is grety improved. In the reserch, we notice tht the pssbnd insertion oss of the second bnd for the singe ptch frct Tbe 3. simuted fiter retive bndwidth nd pssbnd insertion oss (I). The 1st pssbnd The 2nd pssbnd Retive bndwidth Pssbnd I (db) Retive bndwidth Pssbnd I (db) Fiter 1 5.4%.27 2.% 2.7 Fiter 2 5.4%.3 1.8% 2.7 Fiter % % 1.3 Fiter 4 3.3%.4 3.9%.6 Fiter 5 5.8% %.4 Fiter 1 Fiter 2 without ptch defection S 11 Mgnitude (db) -2-4 f,1 f 1, Frequency (GHz) Figure 17. Simuted frequency responses of fiter 1 nd 2.

15 Progress In Eectromgnetics Reserch B, Vo. 4, IRT fiter is bout 2 db nd improved to 1.3 db when du-ptch (hve the sme size) frct IRT resontors re ppied, s shown in Fig. 18. Retive bndwidth nd pssbnd insertion oss of fiter 3 re isted in Tbe 3. In order to further enhnce the pssbnd insertion oss, du-bnd bndpss fiters with two-pth couping re deveoped, s shown in Fig. 19, nd the fiter couping structure is potted in Fig. 19(c), where R i (i = 1, 2) denotes the i-th resontor which introduces the i-th bnd. Here, for fiter 4, h 1 = 5.3 mm, h 2 = 2.5 mm, h 3 = 3.5 mm, h 4 = 8 mm, 1 = 5 mm, 2 = 1.6 mm, 3 = 16 mm, 4 = 7 mm, nd the ptch hoes re isoscees right-nged tringe. For fiter 5, h 1 = 6.5 mm, h 2 = 2.5 mm, h 3 = 3.6 mm, h 4 = 8.5 mm, 1 = 2 mm, 2 = 13 mm, 3 = 17 mm, 4 = 3 mm, nd the ptch hoes re isoscees tringes. Simuted fiter frequency responses re shown in Port 1 b e g c h Port 2 Port 1 Resontor R 1 R 2 R 1 Port 2 R 2 Mgnitude (db) S 11 with doube ptches With singe ptch Frequency (GHz) (c) Figure 18. Du-bnd bndpss fiter using du-ptch IRT resontor with frct hoes, = 17 mm, b = 3.2 mm, c = 5.1 mm, e = 2.8 mm, h = 8.5 mm. Fiter 3. Couping structure. (c) Simuted fiter frequency responses.

16 156 Xio et. h2 Resontor 1 h1 h1 Port1 2 3 h2 h 3 h4 Port2 Port Port2 Port1 R2 Port2 4 h4 R1 h3 (c) Figure 19. Du-bnd bndpss fiters using IRT ptch resontors with frct hoes nd two-pth couping. Topoogy of fiter 4. Topoogy of fiter 5. (c) Couping structure. S 11 S 11 Mgnitude(dB) -2-4 Mgnitude (db) Frequency(GHz) Frequency(GHz) Figure 2. Simuted frequency responses of fiter 4 nd 5. Frequency responses of fiter 4. Frequency responses of fiter 5. Fig. 2, nd the fiters performnces re isted in Tbe 3. It cn be seen tht both fiters 4 nd 5 operte t bout 2.4 GHz nd 3.5 GHz with pssbnd insertion oss of no more thn.6 db. Both fiters 4 nd 5 hve circuit size of no more thn mm 2. The right-nged tringur resontor with frct hoe cn so be used to design du-bnd bndstop fiter, s shown in Fig. 21, where h 1 = 5.5 mm, h 2 = 2 mm, h 3 = 3 mm, h 4 = 7.5 mm, 1 = 1.5 mm, 2 = 11 mm, 3 = 15 mm, 4 = 2 mm, nd the couping structure is the sme s in Fig. 19(c). Simuted frequency responses re potted in Fig. 21, nd it cn be seen tht the du-bnd bndstop fiter opertes t bout 3.6 GHz nd 4.53 GHz with retive bndwidths of 2.6% nd 2%, respectivey.

17 Progress In Eectromgnetics Reserch B, Vo. 4, h 2 1 h 1 Port Port 2 h 4 Mgnitude (db) -2-4 S 11 h Frequency (GHz) Figure 21. Du-bnd bndstop fiter using IRT ptch resontors with frct hoes nd two-pth couping. Fiter topoogy. Simuted frequency responses. 6. CONCUSION Frct-shped isoscees right-nged tringur ptch resontors re nyzed, nd new RF fiters hve been deveoped. The fiter design is demonstrted by experiment. It is shown tht the IRT resontor nd fiter cn be miniturized with the ssistnce of frct, nd the frct enbes the impementtion of du-bnd fiters. The nysis nd design method for the IRT resontor so cn be ppied to the equiter tringur resontor nd even the other ptch resontors. The proposed right-nged tringur ptch fiters hve good fiter performnces nd compct, simpe nd miniture structures which re esy for fbriction. The du-bnd bndpss fiters meet IEEE ppiction requirements. ACKNOWEDGMENT This work ws supported in prt by the Reserch Fund of Chin Stte Key bortory of Miimeter Wves (K2117) nd Fundment Reserch Funds for Chin Centr Universities. REFERENCES 1. Hong, J. S. nd S. i, Theory nd experiment of du-mode microstrip tringur-ptch resontors nd fiters, IEEE Trns. on Microwve Theory nd Techniques, Vo. 52, , 24.

18 158 Xio et. 2. Xio, J.-K., Q.-X. Chu, nd S. Zhng, Nove microstrip tringur resontor bndpss fiter with trnsmission zeros nd wide bnds using frct-shped defection, Progress In Eectromgnetics Reserch, Vo. 77, , Hong, J. S., Microstrip du-mode bnd reject fiter, IEEE MTT-S Interntion Microwve Symposium Digest, , Heszjn, J. nd D. S. Jmes, Pnr tringur resontors with mgnetic ws, IEEE Trns. on Microwve Theory nd Techniques, Vo. 26, 95 1, Ahwri, A. R. H. nd A. Ismi, Compct widebnd bndpss fiter using singe corners-cut isoscees tringur ptch resontor, Progress In Eectromgnetics Reserch C, Vo. 14, , Xio, J.-K., Tringur resontor bndpss fiter with tunbe opertion, Progress In Eectromgnetics Reserch etters, Vo. 2, , Kim, I. K., N. Kingsey, M. Morton, et., Frct-shped microstrip couped-ine bndpss fiters for suppression of second hrmonic, IEEE Trns. on Microwve Theory nd Techniques, Vo. 53, , Yousefzdeh, N., C. Ghobdi, nd M. Kmyb, Considertion of mutu couping in microstrip ptch rry using frct eements, Progress In Eectromgnetics Reserch, Vo. 66, 41 49, Asd, H., M. Zubir, nd M. J. Mugh, Refection nd trnsmission t dieectric-frct interfce, Progress In Eectromgnetics Reserch, Vo. 125, , i, T., G.-M. Wng, K. u, et., Nove bndpss fiter bsed on CSRR using koch frct curve, Progress In Eectromgnetics Reserch etters, Vo. 28, , Bh, I. nd P. Bhrti, Microwve Soid Stte Circuit Design, John Wiey & Sons Press, New York, Ansoft Ensembe 8., Ansoft Inc Jrry, P. nd J. Benet, Design nd Reiztion of Miniturized Frct RF nd Microwve Fiters, John Wiey & Sons Press, New York, 29.

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