Improved Computation of Electric Field in. Rectangular Waveguide. Based Microwave Components Using. Modal Expansion

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1 Journl of Innoviv Tchnolog n Eucion, Vol. 3, 6, no., 3 - HIKARI L, hp://.oi.org/.988/ji.6.59 Iprov Copuion of Elcric Fil in Rcngulr Wvgui Bs icrowv Coponns Ug ol Epnsion Rj Ro Dprn of lcronics n lcricl counicion nginring Inin Insiu of Tchnolog, Khrgpur, 73, Ini Coprigh 5 Rj Ro. This ricl is isribu unr h Criv Coons Aribuion Licns, which pris unrsric us, isribuion, n rproucion in n iu, provi h originl work is proprl ci. Absrc An iprov forulion of h ol pnsion ho o su isconinuiis in wvgui bs icrowv coponns is in coprison o wh ws rlir b h uhor n his collborors. W consir h cs of E-pln l insr filrs n onsr h h lcric fil cn b pric wih ccurc coprbl o hos of ohr hos. I. Inroucion Rcnl w hv us h ol pnsion chniqu o copu h lcric fil srnghs in icrowv filrs which is consruc ug l insrs or spus in rcngulr wvguis []. Is srucur is shown onc gin in figur blow. On of h rsons for no ging corrc vlus of h fil isribuion ws our inbili o l corrcl wih h unknown surfc currns on hs l insrs. W hv now corrc our concpul isunrsnings n hv obin rsuls h r coprbl wih h rsuls obin fro ohr hos lik hos of h ho of ons for pl. On of h iporn hings h w h ovrlook rlir whil wriing h s of lgbric quions for rining h ol pnsion cofficins is h h nubr of unknowns us sricl b qul o h nubr of linr siulnous quions. Th s of

2 4 Rj Ro linr quions ws obin in rf. [] b quing h ngnil coponns of h lcric n gnic fils on ihr sis of h plns of isconinui in h wv guiing ss which is cr b h l insrs (spus). As is plin blow in scion II in our rlir forulion w h qu boh h ngnil coponns of h lcric s wll s h gnic fil o ro on h fron fc of h spu which lis in h pln. This h cus h probl o bco unphsicl. In his prsn ppr w hv rcifi his probl b sing onl h ngnil coponn of h lcric fil o ro n hv obin uch br rsuls hn in h prvious cs n hs r prsn blow in scion IV. Th rsuls r copr wih hos obin fro h ho of ons whos forulion hs lso bn b us. Th ol pnsion chniqu ws propos n rs bck [], [3] bu hrfr i h no bn ppli o probls such s h of rining h fil srnghs wihin wvguis hving isconinuiis. I os hv so vngs such s csc of isconinuiis cn b nl b h ho b ring ch pir of isconinui cr b gl objc such s spu sprl fro h ohr isconinuiis n hn finll cobining h rspciv S prrs of ch pir of isconinui ino gl s of S prrs. II. Forulion of h ol Epnsion ho W h lr rgu h h srucur in fig. hs no vriions long h is n so i is sufficin o consir TE os onl. Th spu is loc bwn s shown in fig. (b) whr. Th lcric fil in h rgion of h in wvgui h is in h rgion whn n incin wv of pliu in h oinn o pprochs fro is givn b jk E B, () k, for n jk. whr ()

3 Iprov copuion of lcric fil 5 (b) Fig. Wvgui l-insr filr () Gor (b) Eplo viw of scion conining on l-insr (hicknss, n lngh, ) bifurcing h gui ino wo rgions I n II. Th spus r ll plc h cnr of h bro wll Hr h usul noions for ngulr frqunc n, for fr spc prbili n priivi rspcivl hv bn us. B r h plius of h scr (rflc) wv whos gniu n phs hs o b rin. Th rson for slcing o os onl ws s in rf. []. Th ngnil coponn of h gnic fil in rlion o h fc of h spu h pln (which is nohing bu surfc of insion b s sn in fig. (b)) is for prss s jk jh jk B. () On us no h in boh quions () n () h uppr lii of suion shoul b ill infini bu for prcicl clculions h suion us b suibl runc s ic b h n for ccurc. Th lcric n h gnic fils in h rgion of h bifurc wvgui h is in h rgion in fig. (b) r rspcivl prss s E A B (3)

4 6 Rj Ro B A H j (4) whr, is h uni sp funcion fin s for n for n A n B ulipli b r gin h unknown fil plius. In iion o hs h fils in h rgion r obin s A E (5) A H j (6) Now in orr o rin h unknowns B, A, A n B b his chniqu of ol pnsion on ns o qu h E coponn of h lcric fil on ihr si of boh h juncions n. Thus w s h pln B A B (7) n B A A (8) For h gnic fil coponn H howvr in iion o quing i on ihr sis of hs juncions on ns o k ino ccoun h surfc currn nsiis J (if h conucivi of ls r kn o b ill infini) on h

5 Iprov copuion of lcric fil 7 fron n bck fcs of h spu h is s lr plin surfcs of insions b in h plns n rspcivl. To k h poin clr w gin wri h quion hs wo plns (bu now for h H fil) s J j B A B jk (9) n J j B A A () A closr su of his s of quions (7) o () shows h i is no ncssr o know J in orr o solv for h 4 unknown cofficins B, A, A, B n his fc ws no rli b us whn w wro our rlir ppr h is rf. []. Th rson for his runnc of J s fr s his spcific probl is concrn cn b rgu s blow. Firs on hs o no h owing o h sr of h probl bou h cnr of h bro wll of h wvgui (s rf. []) i will suffic o sisf quions (7) o () onl in h inrvl in orr o rin ll h B, A, A n B s. N on us lso no h if w plc N uniforl spc poins in his inrvl o in ch of h plns n hn onl N of hs poins will b on fc of h spu h is on l surfc in hs rspciv plns. Hr is h spu hicknss fin rlir. W conn h hs N poins i is ncssr n sufficin o sisf onl quions (7) n (8) n in h rs

6 8 Rj Ro N N poins o sisf ll h four quions (7) o () in orr o rin h 4 unknowns B, A, A n B. Thus on hs o onl s N N n obsrv h J which pprs h N poins on ch of h fcs of h spu hrough quions (9) n () is no n for solving h probl b h ol pnsion chniqu. Th iprov rsul prsn in scion IV blow copr o hos of rf. [] suppors our connion. Thus whil king hs nw clculions of h fils w follow h s procur s w h op in h rfrnc cp now h w hv no nforc quions (9) n () in h inrvl ling o sligh oificion of h ingrion liis us hr. III. Forulion of h Probl b h ho of ons (o) Th ho of ons soluion o his probl cn b obin b sing h ngnil coponn of h ol lcric fil o b ro on ll h four fcs of h spu. Th ol lcric fil consiss of h incin fil of uni pliu in h oinn o n h scr fil which riss bcus of h currns inuc on h spu fcs. Sinc h srucur suppors onl h TE os whn ci b h oinn o h onl coponn of surfc currn nsi on n of h fcs is J. Th scr lcric fil u o his currn cn b obin b following for pl h ho of rkov [4] (s chpr 7 of his rfrnc) in rs of h wvgui Grn s funcion s sc E ^ j u J, J, () whr ^ u is h uni vcor poining in h ircion n h ohr noions inc E sn for h s quniis s i ws us bfor. Th incin fil lso poins in h ircion n hnc boh h scr s wll s h incin fils r ngnil o ll h spu fcs. W obin n ingrl quion for J b

7 Iprov copuion of lcric fil 9 inc sc sing E E on ll hs fcs n ppl h nuricl ho wil known in lirur s h ho of ons o solv for J. Th lcric fil n poin in spc cn hn b rin in rs of h known quion (). J b ug IV. Rsuls Obin fro Clculions s Pr h Forulions of Scions II n III W prsn in figs., 3 n 4 h rsuls for, n 3 rspcivl h bsolu vlus of h lcric fil plius s funcion of fro o 8.5 s i is clcul b h ol pnsion chniqu. Th vlus of, (pls rfr o fig. (b)) n h frqunc of oprion is. 6, n 8. 5 GH rspcivl. Th incin lcric fil pliu is norli o uni. In figur 5 h corrsponing clculion ug ho of ons is prsn. Th pc vlu of E on h fron fc of h spu is ro n his is os ccurl pric in figs. 4 & 5. Th o ss o b suprior in his rspc s wll s fr h copuion i is concrn. Fig. Fig.. Elcric fil s funcion of h pln for obin b h ho of ol pnsion s forul in scion

8 Rj Ro Fig. 3. Elcric fil s funcion of h pln for obin b h ho of ol pnsion s forul in scion Fig. 4. Elcric fil s funcion of h pln for 3 obin b h ho of ol pnsion s forul in scion

9 Iprov copuion of lcric fil Fig. 5. Elcric fil s funcion of h pln s copu b ho of ons Rfrncs [] A. V. G. Subrn,. Zishn n R. Ro, Liiions on h copuion of lcric fil in rcngulr wvgui bs icrowv coponns ug ol pnsion, Conporr Enginring Scincs, 7 (4), no. 8, hp://.oi.org/.988/cs [] R. Vlhlick, J. Born, F. Arn n D. Grurhol, Opii wvgui E-Pln l insr filrs for illir-wv pplicions, IEEE Trn. icrowv Thor Tch., 3 (983), no., hp://.oi.org/.9/ [3] Y. C. Shih, Dsign of Wvgui E-Pln Filrs wih All-l Insrs, IEEE Trn. icrowv Thor Tch., 3 (984), no. 7, hp://.oi.org/.9/

10 Rj Ro [4] G. rkov, Annns, Progrss Publishrs, oscow, 965. Rciv: Novbr 5, 5; Publish: Jnur 5, 6