Small Size Defected Ground Structure (DGS) Coupled Resonator Band Pass Filters with Capacitor Loaded Slot Using FDTD Method

Transcription

1 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah Small Se Defeced Groud Srucure (DGS) Coupled Resoaor Bad Pass Flers wh Capacor Loaded Slo Usg FDTD Mehod ADL ABD LRAMAN ADL ZIN LDIN AMD ABD LMONM ad SAM FATI Facul of geerg gh Isue of erg The hgher sue for geerg ad Techolog Facul of geerg Souh Valle Uvers-Qea Souh Valle Uvers Aswa l-ma l-ma adel_b5@ahoo.com aem00@homal.com ahmed00677@ahoo.com hfah66@ahoo.com Absrac: - Ths paper preses a desg of a small se secod ad hrd order bad pass coupled resoaor flers b usg fe dfferece me doma mehod (FDTD). Two of he proposed flers coss of compac folded DGS resoaors he oher cosss of compac recagular DGS resoaors ad a lumped capacor s combed wh he slo of each fler. The sero of lumped capacor wh resoaors creases he effecve capacace ad reduces he resoa frequec so he dmesos of he fler wll reduce ad he performace of he fler wll be mproved b ehacg he eerg sored he resoaor. The resoace badwdh s decreased leadg o creasg he resoaor qual facor. A secod order bad pass fler wh cere frequec of.4 G has bee desged fabrcaed ad measured. The fler has a wde sop bad wh a reeco hgher ha 0 db up o more ha 0 G. Isero loss of less ha 0.7 db s acheved wh he pass bad. Aoher secod order bad pass fler wh cere frequec of 3. G has bee desged fabrcaed ad measured. The fler has a wde sop bad wh a reeco hgher ha 0 db up o more ha 0 G. Isero loss of less ha 0.8 db has bee acheved wh he pass bad. I s foud ha he epermeal resuls agree well wh he M-smulao ad FDTD smulao resuls. Fall a hrd order bad pass fler wh ceer frequec of.4gz wh sgle rasmsso ero a.6 G s desged ad smulaed. The fler has pass bad from.3 o.5 G ad wde sop bad wh reeco hgher ha 0 db up o more ha 8GZ ad sero loss lower ha db s acheved wh pass bad..ke-words: - Bad Pass Fler Coupled resoaor fler Defeced groud srucure Lumped capacor FDTD Iroduco Moder mcrowave commucao ssems requre maured hgh-performace bad pass flers wh hgh selecv ad wde sop bad respose. These flers ca be desged ad fabrcaed o varous maerals. Plaar flers are parcularl aracve because of her smaller se easer maufacure ad lower fabrcao cos []. Wh he developme of wreless commucao he more crowded he specrum s he more srge specfcaos for desgg flers are. These specfcaos have become harder o be me b coveoal Buerworh ad Chebshev flers. Now s cross coupled flers wh fe rasmsso eros ha he bes choces are whch are carred ou b he geeral Chebshev fuco. Compared wh coveoal flers ca o ol mee specfcaos bu also reduce he umber of resoag elemes ad hs ur reduces he sero loss se ad maufacurg cos of he desg. Bu s more complcaed o shess ad desg ha coveoal flers. Researchers have proposed varous cofguraos for reducg he se of flers ad mprovg fler performace. Several compac ad hgh performace compoes have bee repored b usg DGS for he mcrosrp le [-8]. DGS has bee aracve o oba he fuco of uwaed frequec reeco ad crcu se reduco. Varable capacors are used fler applcao for mmg he se of resoaors ad ug her resoa frequeces [9-0]. The me-depede Mawell's equaos paral dffereal form are dscreed usg ceral dfferece appromaos o he space ad me paral dervaves. The resulg fe-dfferece equaos are solved sofware a leapfrog maer he elecrc feld vecor compoes a volume of space are solved a a gve sa me; he he magec feld vecor compoes he same spaal volume are solved a he e sa me; ad he process s repeaed over ad over aga ul he desred rase or sead-sae ISSN: Issue 3 Volume 0 March 0

2 elecromagec feld behavor s full evolved. The fe dfferece me doma mehod (FDTD) was all used o solve he M scaerg problem b Taflove [] 975 whch s he frs brea hrough FDTD hsor. I hs paper we propose a mproveme o he performace of bad pass coupled resoaor fler b combg lumped capacor he slo of resoaor a place whch has mamum elecrc feld. Also hs paper a sud of he effec of capacace o he resoa frequec s vesgaed ad good agreeme s acheved bewee he smulao resuls ad he resuls from FDTD mehod program. Fall compac bad pass secod ad hrd order s desged usg M smulaor program. I s foud ha he smulao resuls obaed from he 3-D M smulaor program are good agreeme wh FDTD code ad measureme resuls. The Fe Dfferece Tme Doma Mehod.The Fe Dfferece Tme Doma Mehod Basc quaos The FDTD algorhm dvdes he problem geomer o a spaal grd where elecrc ad magec feld compoes are placed a cera dscree posos space ad solves Mawell s equaos me a dscree me saces. Ths ca be mplemeed b frs appromag he me ad space dervaves appearg Mawell s equaos b fe dffereces ad e b cosrucg a se of equaos ha calculae he values of felds a a fuure me sa from he values of felds a a pas me sa. The sarg po for he cosruco of a FDTD algorhm s Mawell s me-doma equaos. The dffereal me-doma Mawell s equaos eeded o specf he feld behavour over me are []: Subsug for he me ad space dervaves a me sep ad a space lace po () we have all I a smlar maer we ca derve fe-dfferece epressos based o Yee's algorhm for he ad feld compoes gve b Mawell's equaos []. We ca derve fe-dfferece epressos based o Yee's algorhm for he ad feld compoes gve b Mawell's equaos where / σ represes he loss erm o he rgh-had sde of each equao whch s esmaed usg appromao procedure aalogous o ha of equao (4) ha resuls a se of hree equaos havg a form smlar o ha of he equaos above ad ca be wre as []:. Numercal Sabl The umercal algorhms for Mawell's curl equaos defed b he fe dfferece ssems requre ha he me creme have a specfc boud relave o he lace space cremes ad. Ths boud s ecessar o avod umercal sabl a udesrable possbl wh eplc dffereal equao solvers ha ca cause he compued resuls o spurousl crease whou lm as me marchg coues. lecromagec wave propagao free space cao go faser ha he speed of he lgh. The choce of cell se s crcal applg FDTD. I mus be small eough o perm accurae resuls a he hghes frequec of eres. Cell se s drecl affeced b he ρ () ε σ ε () ρ (3) (4) ρ ρ ρ (5) / ε σ ε ε σ ε σ (6) WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah ISSN: Issue 3 Volume 0 March 0

3 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah maerals prese. The greaer he permv he shorer he wavelegh a a gve frequec ad smaller he cell se requred. The fudameal cosra s he cell se mus be much less ha he smalles wavelegh for whch accurae resuls are desred. The sde of each cell se should be /0 λ or less a he hghes frequec (shorer wave legh) of eres. The Coura codo 3- dmesos s [3]: v Where; v s he speed of he lgh eperece has dcaed ha for acual compuaos he value gve b above equaos wll provde accurae resuls..3 Gaussa Waveform A Gaussa waveform s he bes choce for a source waveform sce ca be cosruced o coa all frequeces up o a hghes frequec ha s ed o a cell se b a facor. Ths facor whch s he proporo of he hghes frequec wavelegh o he u cell se s referred as umber of cells per wavelegh. A Gaussa waveform ca be wre as a fuco of me as [4]: (7) descrbes he capacor's behavour a semmplc maer s [5]: Sar Se problem space ad defe parameers Se al values for elecrc ad magec felds Compue feld coeffces Defe Gaussa pulse as a Calculao magec felds Updae magec feld compoes Calculao elecrc felds Updae elecrc feld compoes g ( ) e ( 0 ) τ (8) Appl boudar codos where τ s a parameer ha deermes he wdh of he Gaussa pulse ad 0 s he amou of me shf. We ca fd 0 ad τ as [4]: Compug volage ad curre aroud feed po τ.3 π f (9) ma 0τ 4. 5τ (0) 0 Icreme me sep No Las eraos Yes.4 Modellg of Lumped Capacor Cosder he sero of a umercal lumped capacor o he FDTD grd. Assumg a - dreced lumped eleme locaed free space a he volage-curre characersc ha Oupu daa Sop Curre ad volage Fg. Flow char of FDTD program ISSN: Issue 3 Volume 0 March 0

4 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah / I C J / I () Where С s he value of he capacace. The correspodg me-seppg relao s [5]: L 3.. ffecs of he DGS Capacors o he Resoaor Performace Fg.4 ad Fg.5 show he elecrc ad magec feld dsrbuos wh he slo. The am of hs par s o ow he effec of serg he lumped capacor o he performace of he resoaor bu he queso s where ca we pu? ε 0 C ε 0 / / / / / / / / () 3 DGS Resoaors 3. Folded Slo A DGS resoaor wh capacor groud plae eced b 50Ω le as show Fg. ca be modeled b LC crcu as show Fg.3 Fg.4 lecrc feld dsrbuo Folded slo srucure. Fg. 5 Magec feld dsrbuo Folded slo srucure Fg. Three-dmesoal vew of DGS resoaor wh capacor loaded Fg. 3 quvale crcu of he resoaor The values of L P ad C P are foud from [6] as: 5f 50 Cp (3) π c PF Lp ( f f ) C ( πf ) p c Where f c s 3dB cu off frequec G ad f p s he pole frequec p p As show Fg. 4 he elecrc feld s coceraed wh he ceer of he folded slo oppose o he ope gap ad he magec feld s coceraed aroud he gap as show Fg.5. A vesgao o he bes poso of he lumped capacor has bee doe o he srucure usg he M smulaor program. We oced ha he capacor whch s placed he ceer of he folded slo oppose o he ope gap has a srog effec o he resoace frequec. If we loo a Fg.4 we fd ha he elecrc feld s a mamum a he ceer of he slo. So he capacor has o pu wh he ceer of he slo as show Fg.6. The resoace frequec ca be decreased b serg a lumped capacor he ceer of he resoaor where he elecrc feld s of s mamum value as show Fg. 4 ad Fg.6. The sero of he lumped capacor creases he effecve capacace of he slo so he resoa frequec of he slo wll be reduced he fler performace wll be mproved ad fler se wll be reduced ha leads o more compac. Fg.7 shows he comparso ISSN: Issue 3 Volume 0 March 0

5 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah bewee he desg of folded resoaor wh FDTD mehod ad M smulaor program where a good agreeme s acheved bewee her resuls. a wdh of mm as show Fg. 8. The slo resoa frequec s foud o be 4 G. D Fg.8.DGS recagular slo Fg.9 ad Fg.0 show he elecrc ad magec feld dsrbuos wh he slo. Fg.6 DGS resoaor wh lumped capacor Fg.9 lecrc feld dsrbuo Folded slo srucure. Fg.7 M ad FDTD Smulao resuls of folded slo resoaor wh ad whou lumped capacor The used folded resoaor has he followg parameers: D6mm gmm ad wmm. The resoa frequec of he slo s proporoal o he value of he capacace C. The resoa frequec s 6.5 G for DGS resoaor whou capacor as show Fg.7 f a lumped capacor C s sered as show Fg.6 he resoa frequec decreases. From Fg.7 s see ha he resoa frequeces have he values 3.9 G 3.3 G.9G ad.46 G or drop b 40% 49% 55%ad 6% respecvel whe serg a lumped capacor of 0.3pF 0.5pF 0.7PF ad pf respecvel. Ths meas ha he resoa frequec drops b 6% b creasg he lumped capacor from 0 o pf so serg lumped capacor leads o more compac se. 3. recagular Slo We are usg a recagular slo wh D 8.6 mm ad Fg. 0 Magec feld dsrbuo Folded slo srucure As show Fg. 9 he elecrc feld s coceraed wh he ceer of he slo. A vesgao o he bes poso of he lumped capacor has bee doe o he srucure usg he M smulaor program. We oced ha he capacor whch s placed he ceer of he slo has a srog effec o he resoace frequec. If we loo a Fg.9 we fd ha he elecrc feld s a mamum a he ceer of he slo. So he capacor has o pu a he ceer of he slo. B addg a lumped capacor of pf he ceer of he slo as show Fg. he resoace frequec decreased from 4GZ o 3.38 GZ. Fg. shows a comparso bewee rasfer characerscs of he slo wh ad whou capacor usg FDTD smulao malab code. I s see ha he resuls obaed b FDTD smulao program agree well wh he resuls obaed from M smulaor program. ISSN: Issue 3 Volume 0 March 0

6 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah D Fg. DGS recagular slo wh lumped capacor Fg.4 Comparso of sero Loss S of log slo whou capacor ad shor slo wh capacor 4 Desg of Secod Order coupled Resoaor Flers Fg. Comparso of sero Loss Sof shor slo wh ad whou capacor 3.. ffec of Capacor o Compacess To verf he compacess of he srucure we have smulaed he rasfer characerscs for he proposed slo wh lumped capacor ad a log recagular slo as show Fg.3 wh D36mm ad has he same wdh of 0.883mm of ha gave he same resoa frequec. The lumped capacor bascall corols he resoaor capacace. The proposed srucure gave se reduco where he legh of he slo s reduced b more ha 75% as show from Fg. 8.ad Fg Secod Order Coupled Resoaor Fler Deped o Folded Slo 4.. Couplg Coeffce Fg.5 llusraes couplg srucure ad he curve of he couplg coeffce ha resuls from he oreao of par of decal DGS resoaors whch are separaed b spacg S. The couplg coeffce show Fg.5 s eraced usg M smulaor b couplg he srucure ver weal o a 50 Ω mcrosrp feed. The couplg coeffces ca be also eraced from he separao frequeces [7]. D S Fg.3 DGS Log recagular slo. Fg. 4 compares rasfer characerscs of he proposed compac resoag slo ad recagular log slo. I see ha he proposed srucure ehb free wde pass bad compared o he log slo. Fg.5 Couplg coeffces for DGS resoaors (Med couplg). ISSN: Issue 3 Volume 0 March 0

7 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah 4.. eral Qual Facor As show Fg.6 he eeral couplg s realed b a 50 Ω mcrosrp le o he oher sde of he subsrae eeded b a sub d. The value of he eeral qual facor s eraced from he fullwave M smulaor. The resoa frequec of hese resoaors affeced slghl whe he feed le s slghl eeded b a sub wh legh d. The 50 Ω mcrosrp le s perpedcular (wh sub) o he resoaor m Q Q.6 (6) we selec a capacor wh 0.7 pf based o he vesgao meoed seco ad 4... Some opmao ca be doe o ae o accou he effec of he machg sub o he resoa frequec. Fg.7 compares he heorecal resuls wh hose of he M smulao program ad FDTD smulao code. I s oced ha a reasoable agreeme s acheved. d Fg.6 eral couplg (qual facor) 4..3 Fler shess Realao ad Desg Realao couplg mar whch coforms for chose opolog s eraced whe frs we defe he fler specfcao usg a opmao-based scheme [8 9]. The couplg coeffce ad qual facor curves are he used o reale he obaed couplg coeffces [7]. A secod order fler has he followg parameers: badwdh BW 70 M reur loss RL 8 db ad cere frequec f 0.4 G. The obaed couplg mar from he opmao scheme s [8] Fg.7 Comparso bewee he resuls of M smulao program FDTD smulao code ad Theorecal. A comparso bewee he smulaed s-parameers of fler wh ad whou lumped capacor s show Fg.8. The lumped capacor bascall corols he resoaor capacace. The fler ceer frequec s reduced from 5. o.4 G. The proposed srucure shows sgfca se reduco. The se of he fler s reduced b more ha 53%. M (4) ad he eeral qual facors are q q.3. To reale he ormaled couplg mar ad qual facors we use he requred fracoal badwdh FBW BW f o (5) he acual (deormaled) couplg mar becomes Fg.8 ffec of lumped capacor o fler respose ISSN: Issue 3 Volume 0 March 0

8 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah 4..4 permeal Resuls The desged fler has bee fabrcaed o a hgh frequec pred crcu board RO4003 wh a relave delecrc cosa of 3.38 ad a hcess of 0.83 mm. The 50 Ω mcrosrp feed le has wdh of.9 mm. Fg. 9 shows he fler ha cosss of wo coupled resoaors. ach resoaor cosss of folded slo loaded b capacor a s ceer. A sub s used o mach he 50 Ω mcrosrp le o he resoaor b movg he feed le o a dsace equals o d. Whle Fg. 0 shows a phoograph of he fabrcaed compac badpass coupled resoaor fler usg he capacor loaded DGS resoaors. The lumped capacors are soldered a he cere of he slos. Fg. shows a epermeall cofrmao for he desged fler. Also s see ha a good agreeme bewee M smulao FDTD mehod ad measured resuls has bee acheved. Fg.0a Phoograph of he fabrcaed fler (op vew ) Fg.0b Phoograph of he fabrcaed fler (boom vew ) Fg.9a 3-D vew of he DGS coupled resoaors fler slo Fg.Comparso bewee M smulao measureme ad FDTD smulao of a secod order fler 6mm 6mm mm 0.4 mm mm d Fg.9b Coupled resoaor fler cofgurao 4. Secod Order Coupled Resoaor Fler Deped o Recagular Slo The am of hs par s o desg secod order coupled resoaor fler wh ceer frequec f o 3.GZ bad wdh BW640MZ ad reur loss RL8dB usg he compac resoag recagular slo as a buldg bloc for a coupled resoaor fler. The proposed fler s show Fg.. I cosss of wo decal compac coupled resoaors. ach resoaor cosss of a recagular slo loaded b lumped capacor a s ceer. The feed srp wdh of.9 mm s chose for a characersc mpedace of 50 Ω. A sub s used o mach he 50 Ω mcrosrp feed le o he resoaor. ISSN: Issue 3 Volume 0 March 0

9 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah lo W Machg sub d Feed Fg.a Coupled resoaor fler cofgurao Fg.3 ffec of separao dsace bewee resoaors ceres DGS recagular slos wh Lumped capacors. Fg.b Three-dmesoal vew of coupled resoaor fler wh capacor loaded 4.. permeal Resuls The desged fler has bee fabrcaed o a hgh frequec pred crcu board RO4003 wh a relave delecrc cosa of 3.38 ad a hcess of 0.83 mm. Fg. 4 shows phoographs of he fabrcaed badpass coupled resoaor fler usg he proposed compac groud plae slo resoaors. The lumped capacors are soldered a he ceer of he slos. Fg. 5 shows a epermeall cofrmao for he desged fler. I s see ha a good agreeme bewee M smulao program FDTD smulao code ad measureme resuls s acheved. Fg. 3. shows he rasfer characerscs of he proposed coupled resoaor fler. Fg. 3 dcaes he presece of rasmsso eros. Ths s due o he fac ha he resoaors eed ver close o feedg les ad couple o hem weal. The poso of he rasmsso ero s corolled b he separao bewee resoaors d. The poso of he rasmsso ero s decreased b shfg he resoaors close o he feed les as show Fg. 3. Fg.4 Phoograph of he fabrcaed fler ISSN: Issue 3 Volume 0 March 0

10 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah rasmsso ero a.6gz. The obaed couplg mar from he opmao scheme s [8] M (7) Fg.5 Comparso bewee he resuls of M smulao measureme ad FDTD smulao of a secod order fler 5 Desg of Thrd Order Coupled Resoaor Fler 5. Fler Shess Realao ad Desg The equvale crcu of he rseco cross-coupled fler s gve Fg.6 he equvale crcu of he resoaor s equal o a LC resoa a. The couplg bewee adace resoaors are dcaed b he couplg coeffces M ad M 3 ad he cross couplg s deoed b M 3. Q e ad Q eo are he pu ad oupu eeral qual facors respecvel. Sce he cofgurao of he rseco fler s smmerc we ca le M M 3 ad Q e Q eo [7]. ad he eeral qual facors are q q.059 To reale he ormaled couplg mar ad qual facors we use he fracoal badwdh. The acual (deormaled) couplg mar becomes m (8) Q Q. 55 where m FBW M ad q Q. FBW The fler s desged o a hgh frequec pred crcu board RO3003 wh a relave delecrc cosa of 3ad a hcess of 0.75 mm. Fg.7 preses fler ha cosss of hree coupled resoaors. ach resoaor cosss of folded slo loaded b capacor a s ceer. The feed srp wdh of.9mm s chose for characerscs mpedace of 50 Ω. A sub s used o mach he 50 Ω mcrosrp le o he resoaor b movg he feed le o dsace equals d. 0.6 mm 0.8 mm Fg. 6 quvale crcu of he rseco crosscoupled fler 7. mm d mm mm 7. mm.9 mm Realao couplg mar whch coforms o chose opolog s eraced whe frs we defe he fler specfcao usg a opmao-based scheme [8 9]. The couplg coeffce ad qual facor curves are he used o reale he obaed couplg coeffces [7]. The am of hs par s o desg hrd order fler wh a badwdh BW 0 M reur loss RL 8 db cere frequec f 0.4 G ad sgle Fg.7 Coupled resoaor fler cofgurao To reale he fler usg lumped capacor some opmao ca be doe o ae o accou he effec of he machg sub o he resoa frequec so lumped capacor wh ISSN: Issue 3 Volume 0 March 0

11 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah 0.6pF s chose o gve he desred specfcaos. Fg. 8 compares he heorecal resul wh resuls obaed b he M smulao program ad FDTD smulao code. I s oced ha a reasoable agreeme s acheved bewee hem. Fg.8 Comparso bewee resuls of M smulao program FDTD smulao ad Theorecal A comparso bewee he smulaed s-parameers of he wo flers s show Fg. 9. The lumped capacor bascall corols he resoaor capacace. The fler ceer frequec s reduced from 4.34 o.4 G. The proposed srucure shows sgfca se reduco. The se of he fler s reduced b more ha 44.7%. Fg.9 ffec of lumped capacor o fler respose 6 Coclusos I hs paper we have roduced a compac coupled resoaors badpass fler usg DGS folded slo resoaors ad recagular slo loaded b lumped capacors. The frequec reduco of he resoaor has bee acheved owg o he crease he effecve capacace of he resoaors. The resoa frequec drops b 6% b creasg he lumped capacor from 0 o pf.the fler usg recagular slo has a compac se whch s 75% smaller ha he coveoal fler usg slos whou lumped capacors. A good agreeme bewee resuls of M- smulao program ad FDTD smulao code was acheved. The fler has a compac se whch s 53 % smaller ha he coveoal fler usg uloaded DGS slos. Secod order fler wh Chebshev respose was preseed. The fler was desged fabrcaed ad measured. Aga a good agreeme bewee resuls of M- smulao program FDTD smulao code wre Malab heorecal ad measureme was acheved. Fall a desg of a hrd order coupled resoaors bad pass fler usg DGS folded slo wh capacor loaded s roduced. A compac bad pass fler has bee preseed ad s foud ha he fler compac se s 44.7% smaller ha of he coveoal fler usg slo whou lumped capacor. Aga a good agreeme bewee resuls of M- smulao program FDTD smulao code ad heorecal resuls was acheved. Refereces: [] D. M. Poar Mcrowave geerg d ed. NewYor:Wle 998 ch. 8. [] C.S. Km J.I. Par ad A. Dal e al A ovel - D perodc defeced groud srucure for plaar crcus I Mcrowave Guded Wave Le 4 pp [3] P. Ga-Balma ad F. Mar lecromagec resoaces dvdual ad coupled spl-rg resoaors J Appl Phs 5 pp [4] Weg L.. Y. C. Guo X. W. Sh ad X. Q. Che A overvew o defeced groud srucure ProgressI lecromagecs Research B Vol. 7 pp [5] Bouedar A. A. lsherb A. Balalem J. Machac ad A. Omar Desg of ew DGS harp mcrosrp badpass fler usg couplg mar mehod PIRS Proceedgs Prague Cech Republc Augus 007 [6] B. Wu B. L C.. Lag Desg of lowpass fler usg a ovel spl-rg resoaor defeced groud srucure Mcrowave Op Techol Le 49 pp [7] A. Abdel-Rahma A. R. Al S. Amar ad A. S. Omar Compac Badpass Flers Usg Defeced Groud Srucure (DGS) Coupled Resoaors Proc. I MTT-S Ieraoal Mcrowave Smposum (Log Beach) Jue 005. ISSN: Issue 3 Volume 0 March 0

12 WSAS TRANSACTIONS o COMMUNICATIONS Adel Abd lrahma Adel Ze lde Ahmed Abd lmoem esham Fah [8] Adel B. Abdel-Rahma Adel Z. l De esham F. A. amed Ahmed A. Ibrahm Small Se Thrd Order Coupled Resoaor Bad-Pass Fler Usg Capacor Loaded Slos I APS Mddle as Coferece o Aeas ad Propagao (MCAP)Caro gp 00 [9] M. Mamoo ad M Sagawa Varacor ued badpass fler usg mcrosrp-le rg resoaors I MTT-S Dgs I. Mcrow Spo. pp.4-44 Jue 986. [0] X.. Wag B. Z. Wag. Zhag ad K. J. Che A uable badsop resoaor based o a compac sloed groud srucure I Trasaco o Mcrowave Theor ad Techques Vol. 55 No. 9 pp [] Taflove A. ad Brodw M.. Numercal soluo of sead sae elecromagec scaerg problems usg he me depede Maewell s equaos I Tras. Mcrowave Theor Tech. vol.3 o.8 pp Aug [] Alle Taflove Compuaoal lecrodamcs: The Fe- Dfferece Tme-Doma Mehod. Arech ouse Publshers.995. [3] Karls.KuRamod J.Lubbers The fe dfferece me doma mehod for elecromagecs CRC press 993 [4] Aef lsherbe Vesel Demr The fe dfferece me doma mehod for elecromagecs wh matlab smulaos Ocober 008 [5] Pe Ma M. J. A. Taflove ad J. Baro FD-TD modelg of dgal sgal propagao 3-D crcus wh passve ad acve loads I Tras. Mcrowave Theor ad Techques vol. 4 pp [6] A. Abdel-Rahma A. K. Verma A. Bouedar ad A. S. Omar Corol of Bad Sop Respose of - Low Mcrosrp Low pass Fler Usg Slo Groud Plae I Tras. Mcrowave Theor Tech. vol. 5 No. 3 pp Mar [7] og J. S. ad M. J. Lacaser Mcrosrp Flers for RF/Mcrowave Applcaos Wle New Yor 00. [8] S. Amar Shess of Cross-Coupled Resoaor Flers Usg a Aalcal Grada- Based Opm-ao Techque I Tras. Mcrowave Theor Tech. vol. 48 No. 9 pp Sep. 000 [9] A. B. Jaous ad M. J. Lacaser A grade-based Opmao Techque mplog Deerm-as for he Shess of Mcrowave Coupled Flers I MTT-S PP ISSN: Issue 3 Volume 0 March 0