Substrate Integrated Evanescent Filters Employing Coaxial Stubs

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1 Downloded from orbit.dtu.dk on: Jul 21, 2018 Substrte Integrted Evnescent Filters Employing Coxil Stubs Zhurbenko, Vitliy Published in: Progress in Electromgnetics Reserch C Publiction dte: 2015 Document Version Publisher's PDF, lso known s Version of record Link bck to DTU Orbit Cittion (APA): Zhurbenko, V. (2015). Substrte Integrted Evnescent Filters Employing Coxil Stubs. Progress in Electromgnetics Reserch C, 59, Generl rights Copyright nd morl rights for the publictions mde ccessible in the public portl re retined by the uthors nd/or other copyright owners nd it is condition of ccessing publictions tht users recognise nd bide by the legl requirements ssocited with these rights. Users my downlod nd print one copy of ny publiction from the public portl for the purpose of privte study or reserch. You my not further distribute the mteril or use it for ny profit-mking ctivity or commercil gin You my freely distribute the URL identifying the publiction in the public portl If you believe tht this document breches copyright plese contct us providing detils, nd we will remove ccess to the work immeditely nd investigte your clim.

2 Progress In Electromgnetics Reserch C, Vol. 59, 21 30, 2015 Substrte Integrted Evnescent Filters Employing Coxil Stubs Vitliy Zhurbenko * Abstrct Evnescent mode substrte integrted wveguide (SIW) is one of the promising technologies for design of light-weight low-cost microwve components. Trditionl reliztion methods used in the stndrd evnescent wveguide technology re often not directly pplicble to SIW due to dielectric filling nd smll height of the wveguide. In this work, one of the reliztion methods of evnescent mode wveguides using single lyer substrte is considered. The method is bsed on the use of coxil stubs s cpcitive susceptnces externlly connected to SIW. A microwve filter bsed on these principles is designed, fbricted, nd tested. The filter exhibits trnsmission zero due to the implemented stubs. The problem of evnescent mode filter nlysis is formulted in terms of conventionl network concepts. This formultion is then used for modelling of the filters. Strtegies to further minituriztion of the microwve filter re discussed. The pproch is useful in pplictions where shrp roll-off t the upper stop-bnd is required. 1. INTRODUCTION Evnescent mode wveguide technology llows for more compct component design in comprison to the trditionl dominnt mode wveguide technology [1, 2]. Evnescent microwve components cn be integrted into substrte in order to further reduce the mss nd volume. Severl successful ttempts hve been mde in this direction. They re bsed on introducing vrious ridge wveguides into multilyer substrte [3, 4] nd etching split ring resontors in the metl lyer of single lyer substrte integrted wveguide (SIW) [5 7]. This work investigtes n lterntive reliztion method, which is bsed on introducing cpcitive susceptnce into SIW in form of either lumped cpcitors or coxil stubs, s it is shown in Fig. 1. The technology relies on single lyer PCB reliztion nd llows for reltively simple nlysis. Using well described lumped cpcitors or coxil stubs s susceptnces llows to void rigorous full-wve simultions. Implementtion of coxil stubs provides more preferble response, since they introduce trnsmission zeros, s it will be shown lter. On the other hnd, lumped cpcitors llow for more compct volume of the filter, though the filter footprint remins the sme. The filters re excited using direct coxil-to-evnescent mode SIW trnsition rther thn the conventionlly used series connection of two trnsitions: coxil-to-plnr trnsmission line followed by plnr-to-siw trnsition. According to uthor s knowledge, the method to integrte n evnescent mode wveguide into single lyer PCB voiding the use of plnr resontors is described here for the first time. Hving n nlyticl model would be beneficil for nlysis of such structures. A lumped element equivlent circuit representtion is trditionlly used for design of evnescent filters. A correction fctor Δ ws used in the originl pper by Crven describing the design theory [8]. This fctor compenstes stisfctory in moderte- to nrrow-bnd designs [9]. A more refined method of correction involving the use of frequency trnsformtion hs been proposed lter in [9]. An pproch bsed on impednce mtrix representtion is used in this work for the design of evnescent wveguide filters, nd is described Received 24 June 2015, Accepted 9 August 2015, Scheduled 13 August 2015 * Corresponding uthor: Vitliy Zhurbenko (vz@elektro.dtu.dk). The uthor is with the Technicl University of Denmrk, Oersteds Plds 348, 2800 Kgs. Lyngby, Denmrk.

3 22 Zhurbenko COAX COAX SIW 3 SIW 2 SIW 1 IN Cox. connectors () OUT b (b) Figure 1. Evnescent mode substrte integrted wveguide filter with coxil stubs. () Sketch of the filter cross-section, (b) Top view. On this sketch, is the wide side of the wveguide, b isthe nrrow side. in Section 3 of this pper. The developed models llow to predict the filter response in wide frequency rnge. In order to vlidte the developed filter models s well s the reliztion method, microwve filter, s the one shown in Fig. 1, is designed, fbricted nd tested. The mesured results re presented in Section 4. Implementtion of inductive posts for stop-bnd improvement is discussed in Section EVANESCENT MODE WAVEGUIDE INTEGRATED INTO A SUBSTRATE 2.1. Integrtion into SIW nd Susceptnce Reliztion A section of n evnescent mode wveguide is trditionlly represented by π-network consisting of two prllel inductors nd one series [8]. The vlues of the inductors depend on the cross-sectionl dimensions of the wveguide nd the length of the section. Introducing cpcitors in prllel to the prllel inductors will form two prllel LC resontors with inductive coupling between them. This will then form conventionl coupled resontor filter. The trditionl wy to relize cpcitive susceptnce is to plce cpcitive posts, cpcitive strips, or cpcitive resontors into wveguide [10, 11]. These solutions hve proven their vibility in stndrd wveguide technology, however, it is technologiclly chllenging to implement in SIW. For exmple, cpcitive posts in SIW would require two lyer PCB process. The cpcitnce will depend on the gp between the post nd the wll of the wveguide mking filter sensitive to the process vritions. One of the solutions to this is to use lumped surfce mounted device (SMD) cpcitors s cpcitive susceptnce in SIW. The cpcitors cn be mounted on surfce of the PCB bringing the lower metl lyer to the top lyer with metlized vi hole. This, however, might introduce rdition loss due to the opening in the wveguide wll. If this opening is kept nrrow nd rrnged long the wveguide such tht it does not cross the surfce current lines, the rdition loss cn be minimized. Further on, the rdition loss cn be completely voided if the cpcitor is inserted directly into hole in the wide wll of SIW, s it is shown in Fig. 2(). The cpcitive susceptnce stores the energy in the electric field, nd the Q-fctor of the overll structure is sensitive to the loss in the susceptnce. The Q-fctor provided by SMD components is insufficient in mny cses resulting in high insertion loss of evnescent mode wveguide filters. Distributed components cn be used to mitigte this drwbck nd reduce insertion loss. One of

4 Progress In Electromgnetics Reserch C, Vol. 58, Cox. stub b SIW Lumped cpcitor b SIW Top view Top view () (b) Figure 2. Cpcitive susceptnce in the evnescent mode SIW. Cross-section nd top view. () Lumped cpcitor; (b) Coxil stub. the wys to relize cpcitive susceptnce is to use stub bsed on, for exmple, section of coxil trnsmission line. The centre conductor of the coxil line should be connected to one of the wide wlls of the wveguide nd the outer conductor should be connected to the opposite wll, s it is shown in Fig. 2(b). Stndrd off-the-shelf coxil trnsmission lines cn be used for susceptnce reliztion. The dvntge over lumped cpcitors is tht the open-circuit stub cn be used to relize cpcitive susceptnces rnging from zero to virtul infinity. In ddition, the vlue of the stub susceptnce is not limited by discrete vlues s it is the cse of the lumped SMD cpcitors, which increses flexibility of the filter design. The obvious drwbck of course is the increse in the filter volume in comprison to the lumped cpcitor implementtion. Another concern is the rdition loss due to open end of the coxil line. As the wvelength pproches the dimeter of the coxil line, the rdition loss will become more pronounced. There re two pproches to overcome this problem. The first is to use short-circuit coxil line incresing its length to over qurter of guided wvelength. The second pproch is to terminte the coxil line by cpcitive gp s it is described in [11]. In this cse the cpcitnce of the gp should be tken into ccount in ddition to the fringing cpcitnce of n open-circuit coxil line Excittion The centre conductor of the feeding coxil connector is directly connected to one of the wide wlls of the wveguide nd the outer conductor is connected to the opposite wll, s it is shown in Fig. 1. In some cses this excittion structure is more preferble thn the trditionlly used coxil-to-plnr trnsmission line trnsition followed by plnr line-to-siw trnsition. Employing two series connected trnsitions insted of single one is not lwys optiml if coxil interfce to SIW filter is required. Moreover, plnr trnsmission line-to-siw trnsition usully requires creful full-wve nlysis nd optimiztion, which is time consuming tsk. Due to electriclly smll dimensions of the trnsition (refer to Fig. 1), the influence of the discontinuities ssocited with it on the overll response of the filter cn be neglected in the network nlysis. This will be used during the filter modelling in the following Section. 3. MODEL OF THE EVANESCENT MODE SIW FILTER Currents nd voltges re employed s mesures of the fields within the evnescent mode SIW structure in the following filter nlysis. Informtion bout the behviour of the structure is then derived using

5 24 Zhurbenko network nlysis voiding the necessity of solving field equtions. As n exmple, the filter in Fig. 1 is considered here, however, the nlysis of more complex structures contining severl wveguide sections cn lso be done using this pproch. The structure of the filter is symmetric with regrd to its centre. The core of the filter is section of n evnescent mode SIW (denoted s SIW 1 in Fig. 1) with cpcitive susceptnces connected t both ends of it. The cpcitive susceptnces re relized in form of open-circuited coxil stubs COAX. An equivlent network representing the filter in Fig. 1 is illustrted in Fig. 3. [Z CL ] [Z CL ] [Z 3 ] [Z 3 ] IN [Z 2 ] [Z 1 ] [Z 2 ] OUT Figure 3. Filter model bsed on impednce mtrix representtion. It consists of seven two-port networks. Ech two-port network is described by n impednce mtrix. SIW 1 is described by n impednce mtrix [Z 1 ]. Coxil line stubs COAX re described by impednce mtrices [Z CL ]. Two short sections of evnescent mode wveguide SIW 2 re introduced between the coxil stubs COAX nd feeding point for convenience of fbriction. Technologiclly, it is difficult to connect the coxil stub nd feeding line t the sme point, nd moving them slightly prt simplifies the fbriction process. Those short sections (SIW 2) re represented by [Z 2 ]networksinfig.3. The filter is extended with the evnescent mode wveguide sections SIW 3onbothsides([Z 3 ] networks in Fig. 3). Since these wveguide sections operte below cut-off frequency, the mplitude of the field rpidly decys over the wveguide length. The length of sections SIW 3 is therefore usully chosen minimizing their effect on the filter response. The outermost side of the SIW 3cnbeleft open-circuited or short-circuited. It ws chosen to short-circuit the wveguide in this design to void ny possible rdition loss. In cse of open-circuit, the length of SIW 3 should be chosen such tht the rdition from the perture of the wveguide is negligible. The impednce mtrices for the section of evnescent mode wveguide, [Z i ], nd coxil line, [Z CL ], re given by [ ] Z0(W) coth (γ W l i ) Z 0(W) csch (γ W l i ) [Z i ]=, (1) Z 0(W) csch (γ W l i ) Z 0(W) coth (γ W l i ) [ ] Z0(CL) coth (γ CL l CL ) Z 0(CL) csch (γ CL l CL ) [Z CL ]=. (2) Z 0(CL) csch (γ CL l CL ) Z 0(CL) coth (γ CL l CL ) Here Z 0(w) is the chrcteristic impednce, γ w is the propgtion constnt, nd l i is the length of the corresponding evnescent mode wveguide section i, withi = 1, 2, 3 (refer to Fig. 3). Similrly, Z 0(CL) is the chrcteristic impednce, γ CL is the propgtion constnt, nd l CL is the length of the coxil line sections. In order to pply trnsmission line theory to wveguides, propgtion constnt nd chrcteristic impednce of prticulr guide configurtion should be defined, s it is required by Eqution (1). The considertions in Section 2 indicted tht the coxil lines re the min source of loss in the filter due to high electric field density in them. Therefore, the ttenution due to conductor nd dielectric losses in the wveguide cn be neglected. The propgtion constnt cn be expressed using the reltionship for the TE 10 mode [12] ssuming tht there re no mgnetic mterils in the wveguide γ w = (π ) 2 kc 2 k2 = 4π 2 f 2 ε r ε 0 μ 0 (3) Here is the width of the wveguide, f is frequency vrible, ε r is the dielectric constnt of the mteril filling the wveguide, ε 0 = F/m, μ 0 =4π 10 7 H/m.

6 Progress In Electromgnetics Reserch C, Vol. 58, Chrcteristic impednce in rectngulr wveguide is expressed using power-voltge definition [13]: Z 0(W) =2 120π b λ g λ ε r = 2 120πb, (4) 1 ε r 1 2 4f 2 ε r ε 0 μ 0 where b is the nrrow side of the wveguide which corresponds to the height of the substrte in the cse of SIW reliztion. It should be noted tht [Z i ] in Eqution (1) completely describes the behviour of the TE 10 mode in the dielectric-filled lossless wveguide below s well s bove the cut-off. This llows to use this expression for nlysis of wveguide filters in wide frequency rnge (t lest t frequencies below the cut-off of the second propgting mode). The chrcteristic impednce of coxil cble filled with dielectric in Eqution (2) [12]: Z 0(CL) = 1 2π μ0 ε r ε 0 ln ( do d i ), (5) Here ε r is the dielectric constnt of mteril filling the coxil cble; d o nd d i re the dimeters of the outer nd inner conductors. The propgtion constnt ( 1 1 γ CL = α c + α d + jβ = + 1 ) fμ0 2Z 0(CL) d o d i πσ + πf ε r ε 0 μ 0 tgδ + j2πf ε r ε 0 μ 0, (6) where σ is the conductivity of metl nd tgδ is the loss tngent of dielectric mteril [12]. Substituting Equtions (3) (5) into Equtions (1) (2) llows to clculte the response of the filter pplying network nlysis to the network in Fig. 3. Since this clcultion is efficient in terms of computtionl time, the design of the filters cn be done using n itertive pproch [14]. 4. DESIGN EXAMPLE An exmple of microwve filter, s the one shown in Fig. 1, hs been designed. The filter suppose to hve mximlly flt response with bndwidth of 2.5% nd operting frequency round 1.4 GHz. The implemented substrte is RO 4003 [15] with 1.52 mm thickness. Reltive permittivity of the substrte mteril is The implemented coxil cble for stubs COAX is EZ 141 [16], hving copper conductor (σ S/m). The centre conductor dimeter is 0.92 mm, nd the outer conductor dimeter is 3 mm. The cble is filled with PTFE dielectric (ε r 2.1, tgδ 0.002). These design requirements nd implemented mterils result in the following prmeters of the model: f 0 =1.4GHz;δf =2.5%; =25mm;b =1.52 mm; d i =0.92 mm; d o =3mm;σ = S/m; tgδ =0.002; (7) ε r =3.55 (for wveguide, Equtions (3) nd (4)); ε r =2.1 (for cox. line, Equtions (5) nd (6)). The width of the SIW, = 25 mm, results in cut-off frequency of pproximtely 3.2 GHz. Synthesis of evnescent filters, nmely, nlyticl determintion of filter prmeters from low-pss prototype is not trivil nd requires itertive procedure [17]. Therefore the itertive design pproch is directly pplied here to the network in Fig. 3 to find the prmeters of the filter, s described below. The prmeters (7) re substituted in Equtions (3) (6), which provide bsis for trnsmission line impednce mtrices (1) (2). These mtrices describe corresponding components of the network in Fig. 3. This network is then used to synthesize the filter by optimiztion [14]. During optimiztion, the lengths of the SIW sections SIW 1, SIW 2, SIW 3(describedby[Z 1 ], [Z 2 ], nd [Z 3 ]) nd coxil line COAX (described by mtrix [Z CL ]) re itertively selected. The optimiztion concerns the following prmeters of the model (refer to Equtions (1) (2)): l 1,l 2,l 3,l CL. (8) The obtined lengths of the wveguides nd coxil lines re listed in Tble 1.

7 26 Zhurbenko Tble 1. Lengths of the filter components. Prmeter l 1 l 2 l 3 l CL Vlue, mm The totl length of the filter is l 1 +2l 2 +2l 3 =64.3mm. Coxil stub SIW l 3 l 2 l1 l CL SMA connector Figure 4. Photogrph of the evnescent mode SIW filter with coxil stubs. The designed filter is then fbricted nd tested. A photogrph of the relized filter is shown in Fig. 4. If smller volume is required, coxil stubs cn be bent. In tht cse, eventul chnge in the input impednce of the stub should be tken into ccount. The mesured mgnitudes of the scttering prmeters re shown in Fig. 5. The mesured minimum insertion loss of the filter is under 2.1 db. The considertions bove indicted tht the loss minly stems from the coxil stubs due to finite conductivity of the copper. These losses cn be decresed by choosing coxil cble with lrger dimeter, or incresing the width of the wveguide which will result in lower current density in the coxil lines. This will of course led to n increse in the filter dimensions. Mgnitude of S21 (db) S S Frequency (GHz) Mgnitude of S11 (db) Figure 5. Mesured response of the filter in Fig. 4. The 3 db bndwidth is pproximtely 35.5 MHz, which corresponds to 2.6% of frctionl bndwidth t centre frequency of pproximtely 1.38 GHz. Even though the fbricted structure exhibits filtering behviour, one cn note tht there is room for reflection loss improvement. The mesured nd predicted scttering prmeters of the filter in wide frequency rnge re shown in Fig. 6. As one cn note, the filter exhibits trnsmission zero on the upper side of the pss-bnd, which results in shrp roll-off. The frequency of the trnsmission zero corresponds to the frequency where the electricl length of the coxil stub is pproximtely qurter of guided wvelength. The frequency of this trnsmission zero is reltively difficult to control since the length of the stub lso defines the

8 Progress In Electromgnetics Reserch C, Vol. 58, Mgnitude of S21 (db) Mesurements Model Frequency (GHz) Figure 6. Brodbnd response of the filter. cpcitnce required for the evnescent mode propgtion. It would be lso preferble to generte trnsmission zero t the lower pss-bnd side in order to generte qusi-elliptic behviour. There is, however, no simple wy to relize tht in the present structure. The filter model hs resonble ccurcy in wide frequency rnge. There is, however, still visible discrepncy between the clculted nd mesured response of the filter in Fig. 6. The clculted minimum insertion loss is 2.4 db, which is 0.3 db more pessimistic thn the mesurements. The clculted response is shifted up in frequency by pproximtely 66.7 MHz, which corresponds to 4.86% error. It ws observed tht the filter is sensitive to the length of the coxil stubs, which cn be used for fine tuning of the centre frequency. The discrepncy between the clculted nd mesured response prtilly results from the fct tht effects of the open end of the coxil stubs s well s the short-circuited wveguide termintions were not included in the model for simplicity resons. A higher ccurcy cn be chieved, if necessry, by using full-wve electromgnetic nlysis. This is of course will be more computtionlly expensive. It cn be noted tht the upper stop-bnd degrdes bove the trnsmission zero, exhibiting low rejection pproximtely t the cut-off frequency of the implemented wveguide. The frequency of this spurious response is defined by the cut-off frequency of the dominnt mode in the implemented wveguide, SIW 1 (3.2 GHz in this cse) nd depends on its width. Above this frequency the wve esily propgtes s TE 10 mode. This suggests severl pproches to improving the upper stop-bnd response. The strightforwrd wy to control the cut-off frequency of the wveguide is to chnge its width,. The lterntive wy is to introduce discontinuity into the wveguide. In this wy the filter cn lso be further miniturized s lso indicted in [9]. The pproch of using inductive posts for these purposes is discussed in the following Section. 5. STOP-BAND IMPROVEMENT USING INDUCTIVE POSTS Introducing n inductive post into n evnescent mode wveguide, s it is shown in Fig. 7, increses the equivlent inductnce of the wveguide nd potentilly llows reducing the length of the wveguide section required in the filter. Increse in the inductnce decreses coupling between the resontors formed by coxil stubs nd evnescent mode SIW sections. The length of the wveguide section should be decresed in order to compenste for tht. The inductive post increses the cut-off frequency of the propgting mode which should improve the upper frequency stop-bnd chrcteristics. In order to test these specultions, the model developed in Section 3 hs been extended including network describing the inductive post. The resulting model for the structure in Fig. 7 is shown in Fig. 8. Here, the evnescent mode SIW section is split into two equivlent prts, which re described by [Z 1 ]. The inductive post is described by mtrix [Z p ]. Since it is one port component, the impednce mtrix contins only one impednce coefficient [Z p ]=[1/j B], (9)

9 28 Zhurbenko COAX COAX SIW 3 SIW 2 SIW 1 IN post OUT b Figure 7. Sketch of the filter cross-section (not to scle). where B is the susceptnce of single post centred in the guide [8] given by Here λ g = 2π β = 2λ g B = ( )]. (10) Z 0(w) [ln r λ 2 2π k 2 ( π ) = 2π 4π 2 f 2 ε r ε 0 μ 0 ( π ) 2, λ = 2π k = 1 f ε r ε 0 μ 0, (11) r is the rdius of the post nd Z 0(w) is found from Eqution (4). The post in SIW is relized in form of metlized vi hole. [Z CL ] [Z p ] [Z CL ] [Z 3 ] [Z 3 ] IN [Z 2 ] [Z 1 ] [Z 1 ] [Z 2 ] OUT Figure 8. Filter model bsed on impednce mtrix representtion. The length of SIW 1ndCOAX is djusted using the model in Fig. 8 such tht the centre frequency of the filter corresponds to the frequency of the originl filter. The corresponding prmeters of the filter re listed in Tble 2. Tble 2. Prmeters of the components for the filter in Fig. 7. Prmeter l 1 l 2 l 3 l CL r Vlue, mm 12.5 / The totl length of the filter is 2l 1 +2l 2 +2l 3 =58.5mm. The length of the filter is reduced by 5.8 mm shortening the evnescent SIW section between stubs by 31%. The clculted responses of the filters with nd without the post re given in Fig. 9. It is seen, tht the rejection performnce of the filter is slightly improved by dding post. However, the price to py is n increse in the insertion loss. In order to vlidte presented clcultions, filter in Fig. 7 hs been fbricted nd tested. The mesured performnces for both filters (with nd without the post) re shown in Fig. 10. As predicted, the upper stop bnd response improves. In some pplictions, however, even better stop-bnd performnce still might be required. Further stop-bnd improvement cn be chieved by open-circuiting the wveguides SIW 3 exploiting nturl rdition from the open ended wveguide t frequencies bove the cut-off. This pproch, however, hs been left out of the scope of this pper.

10 Progress In Electromgnetics Reserch C, Vol. 58, Mgnitude of S21 (db) Frequency (GHz) with post without post Figure 9. Response of the filter with nd without post. Clculted using models developed in Sections 3 nd 4. The filter exhibits trnsmission zero s for the cse of the originl filter. The mesured minimum insertion loss, however, degrded by 0.8 db nd corresponds to 2.9 db for the filter with the post. Mgnitude of S21 (db) with post without post Mgnitude of S11, S21 (db) Frequency (GHz) Figure 10. Mesured response of the bnd-pss filters in Fig. 1 nd Fig. 7. The bndwidth hs reduced to 25 MHz, which corresponds to frctionl bndwidth of pproximtely 1.8%. Another impct of the post is the reduction of the coupling between two resontors formed by coxil stubs COAX nd wveguide sections SIW 1. The mesured mgnitude of S 11 t the centre frequency is below 9 db, which could still be improved. This cn be chieved by either djusting the distnce between the feed point nd coxil stub, or choosing n lterntive excittion method. In conclusion, the implementtion of the post llows for up to 10 db better stop-bnd rejection nd more compct design, however, leds to degrdtion of in-bnd performnce in comprison to the structure without the post. 6. CONCLUSION It is shown tht the evnescent mode wveguide cn be integrted into single lyer substrte using cpcitive susceptnces in the form of externlly connected coxil stubs. A microwve filter bsed on these principles ws developed nd tested in order to investigte this experimentlly. The presence of the coxil stubs results in trnsmission zero improving overll selectivity of the filter. The filter hs spurious response bove the cut-off frequency of the implemented SIW. It is possible to improve the upper stop-bnd of the filter up to 10 db by introducing n inductive post t the expense of insertion loss, which degrded by 0.8 db. The modified filter is shorter in comprison to the originl filter due to reducing the length the evnescent mode SIW section between the stubs by 31%.

11 30 Zhurbenko A model for the filters is developed. It is efficient in terms of computtionl time, which llows filter synthesis by optimiztion. It ws observed tht the filters re sensitive to the length of coxil stubs. Using this property, fine tuning of the filter cn be chieved. This feture could lso be used for constructing tuneble filters. REFERENCES 1. Shen, T. nd K. A. Zki, Length reduction of evnescent-mode ridge wveguide bndpss filters, Progress in Electromgnetics Reserch, Vol. 40, 71 90, Kirilenko, A., L. Rud, V. Tkchenko, nd D. Kulik, Evnescent-mode ridged wveguide bndpss filters with improved performnce, IEEE Trnsctions on Microwve Theory nd Techniques, Vol. 50, No. 5, , My Wu, L.-S., X.-L. Zhou, nd W.-Y. Yin, Evnescent-mode bndpss filters using folded nd ridge substrte integrted wveguides (SIWs), IEEE Microwve nd Wireless Components Letters, Vol. 19, No. 3, , Mrch Wu, L.-S., X.-L. Zhou, W.-Y. Yin, L. Zhou, nd J.-F. Mo, A substrte-integrted evnescentmode wveguide filter with nonresonting node in low-temperture Co-fired cermic, IEEE Trnsctions on MTT, Vol. 58, No. 10, , October Hung, L., I. D. Robertson, W. Wu, nd N. Yun, Substrte integrted wveguide filters with brodside-coupled complementry split ring resontors, IET Microw. Antenns Propg., Vol.7, No. 10, , Dong Y., C.-T. M. Wu, nd T. Itoh, Miniturised multi-bnd substrte integrted wveguide filters using complementry split-ring resontors, IET Microw. Antenns Propg., Vol. 6, No. 6, , Zhng, Q.-L., W.-Y. Yin, nd S. He, Evnescent-mode substrte integrted wveguide (SIW) filters implemented with complementry split ring resontors, Progress In Electromgnetics Reserch, Vol. 111, , Crven, G. F. nd C. K. Mok, The design of evnescent mode wveguide bndpss filters for prescribed insertion loss chrcteristic, IEEE Trnsctions on MTT, Vol. 19, No. 3, , Mrch Crven, G. nd R. Skedd, Evnescent Mode Microwve Components, 180, Artech House, Snyder, R. V., Inverted-resontor evnescent mode filters, IEEE MTT-S Microwve Symposium Digest, Vol. 2, , Mrcuvitz, N., Wveguide Hndbook, IEEE Electromgnetic Wves Series, 446, Rmo, S. nd J. R. Whinnery, Fields nd Wves in Modern Rdio, 2nd Edition, John Wiley nd Sons, New York, Rizzi, P. A., Microwve Engineering: Pssive Circuits, Prentice-Hll, Englewood Cliffs, NJ, Hong, J.-S., nd M. J. Lncster, Microstrip Filters for RF/Microwve Applictions, 457, John Wiley & Sons, Inc., RO4000 Series High Frequency Circuit Mterils, 8, Dtsheet, Rogers Corp Coxil Cble: EZ 141, Dt Sheet, 2, Huber+Suhner. 17. Jrry, P., J. Benet, E. Kerherve, nd H. Bher, New clss of rectngulr nd circulr evnescentmode wveguide filter, Interntionl Journl of RF nd Microwve Computer-Aided Engineering, Vol. 8, No. 2, , Mrch 1998.