ISSN: 77-3754 ISO 9:8 tfd Itto Jou of Egg d Iovtv choogy (IJEI Vou 7 Iu 7 Juy 8 o dft wv gtzd duty cyd Ajy Ghot Dtt of Ad Sc Mhj Suj Ittut of choogy Dh-58 Id d ( x ( x Abtct- h ffct of dut chg fuctuto (DF o o- coug btw co dft wv d ow hybd u wv tudd gtzd cyd A d to & gowth t x fo th co dft wv dvd cootg both od otv d ohc htg ffct It foud tht th utb co dft od fqucy c d th gowth t dc hy wth th tv dty of otvy chgd dut g d ( x d th to go of th duty cou d f off dy th dg At qubu th cto cqu dgtc dft voty Idx : Dut g Dft wv gowth t & Low hybd wv I INRODUION Dft wv ow fqucy otouy xtd wv whch oducd du to dty o ttu gdt hy w ow uc of co tbt dvc h u of dft wv by th cto of ow hybd u wv hv b otd by y vtgto [-4] h tc xtto d u of dft wv by ctc fd th ow hybd fqucy w tudd by Sud d Kw [] Go t [] d Lu & th [3] dottd th u of dft wv by jcto of ow hybd wv Rcty th h b gt d of tt tudyg ctottc wv duty [5-9] B t [6] foud xty tht th c of gtvy chgd dut g hcd th gowth t of th tbty of cut dv ctottc o cycoto (EI wv duty Sh d Ajy [9] hv tudd th ffct of dut chg fuctuto o th xtto of u hybd wv gtzd cyd h dut h b otd to fuc th-wv tc oc ugtd [-] d gtzd [3] Pbu d J [4] hv tudd th hct of co dft wv cyd wthout dut vot I th w tudy th ffct of dut chg fuctuto o co dft wv gtzd cyd II DISPERSION RELAION W cod cydc duty cou of du d ufo x gtc fd B S th z dcto wth cto o d dut tc dt gv d d h chg d ttu of th th dotd by (- ( d (-Q d d d ctvy h dty of th v ˆ v wh vd v t t c voty d B c c th cto cycoto fqucy th cto th h qubu tubd by ow- fqucy ctottc tubto ( dft wv ( x[ ( t z] ( z h hgh tud ow hybd u wv ( x[ ( t z] cou wth dft z od d two ow hybd dbd z ( x[ ( t z] ( wh z z z z z z h tchg codto H w hv codd oy owt o coug h fou wv tc tcto oc h tubd dt of cto o d dut gv by (3 ( ( wh v v t d th v z t dbtc dft fqucy co fqucy d th cto o [( ( ] c c c c 37
ISSN: 77-3754 ISO 9:8 tfd Itto Jou of Egg d Iovtv choogy (IJEI Vou 7 Iu 7 Juy 8 I d (4 397 th vt wh d B th o cycoto fqucy c Q (5 d d d W obt dut chg fuctuto by foowg J t [5] Q (6 I d ( wh [ ( ( ] 79 D d th dut chgg t Subttutg tubd dt th Po quto 4 ( Q Q w obt d d d d ( [ ] L vt ( (7 wh z M L cto ttu ud th fuc of th u M [ ( ( ] v th qubu cto ttu d d t ( ( o L d d ( 4 4 Q 4 do d fqu ctvy d d th cto o d dut coug t I th bc of o- coug t Eq (7 h w ow uto AJ At ut vh hc x J [wh x th zo of th B fucto J (x = 3 ] I th c of ft RHS of Eq (7 w x t of cot othogo t of wv fucto: A J (8 Subttutg th vu of fo Eq (8 Eq (7 utyg both d of Eq (7 by J ( d tgtg ov fo to ( wh th du tg oy th dot od ( = w obt ( {[ ( ] ( ( A ( ( (9 wh d } ( ( J z J ( ( Ug wh th c of o o { [ Eq (9 c b wtt o o o o o o d ] } A o ( ( ( J ( o ( J ( ( ( 38
ISSN: 77-3754 ISO 9:8 tfd Itto Jou of Egg d Iovtv choogy (IJEI Vou 7 Iu 7 Juy 8 Sy foowg Pbu t [4] w obt ( ( ( c z A c J ( ( ( ( wh A th cott of wv fucto ( z A c J ( ( ( wh ( ( c ( A th cott of wv fucto Ug th vu of ug th u to b zuthy ytc ( = d codg th d od ub of th two dbd to b to Eq ( ( d ( gv d o o o ( o o ( o d o ( wh o ( ( z z z d (3 Equto (3 c b wtt (4 (5 wh o o ( o ( (6 o ( o d ( o ( o o o ( o ( o ( ( o ( o (7 Lt u wt d u tht th wv th wy dd o gowg h w y t (8 ( fo Eq(5 Equto (5 yd Gowth t: (9 ( ( / Now w cod two c of tt I: I th c of dut chg fuctuto dut chgg t η ft II: I th bc of dut chg fuctuto Q wh dut chgg t η d I th bc of dut g ( J c ( J = w cov th x fo th utb dft od fqucy d gowth t 39
ISSN: 77-3754 ISO 9:8 tfd Itto Jou of Egg d Iovtv choogy (IJEI Vou 7 Iu 7 Juy 8 of Rf[4] (cf g o 47 Dut g gtvy chgd fo d otvy chgd fo III RESULS AND DISUSSIONS o tt th uc vu of th fqucy d gowth t of th dft wv tbty w u tyc duty t: = 9 c -3 =V =V B =55x 3 G υ =3x 5 d/c =5x 5 d/c =c gth of cou L = 7 c 76 4 (Potu vg dut g z =µ od ub = th ft zo of th B fucto 385 c - z / L u wv tud 4 66 u W vy fo 4 to 95 fo otvy chgd dut g Ug Eq (8 w hv ottd Fg th ozd fqucy of th utb co dft wv fucto of / o o I Fg t tht th ozd wv fqucy c by fcto ~44 wh chg fo 4 to 8 f dut chg fuctuto t to ccout ud th t td bov B t [6] hv foud tht th wv fqucy w bout -% g th th o-cycoto fqucy th c of gtvy chgd dut g how d Robg [7] hv how th tc y o th ffct of gtvy chgd dut g o th co ctottc o cycoto tbty th wv fqucy c bout % wh chgd fo to 4 ud codto hu th c codby o c of co dft wv c of otvy chgd dut g cyd I Fg w hv ottd th ozd gowth t obtd fo Eq (9 fucto of fo th t tho ud Fg Fo Fg t c b tht th ozd gowth t dc wth both c Howv dc o dtc wh th dut chg fuctuto t to codto hu th dut chg fuctuto c y gfct o u of th co dft wv c of otvy chgd dut g IV ONLUSION h t wo vtgt th o of otvy chgd dut g u of co dft wv h otvy chgd dut c y jo o duty xt th th ooh ug c hutt xhut h dft wv tbty y cu o tto IER d oth fu cto REFERENES A K Sud d P K Kw Ptc xtto d u of dft wv by ow hybd fd Nuc Fu vo 3 9-9 993 R Go J Gu d H Lhy Stbzto of dft wv by ow hybd fd Phy Rv Ltt vo 4 4-44 978 3 S Lu d V K th Stbzto of dft wv by ow hybd wv of ft wv ub Phy Fud vo 3 345-347 98 4 G Pbu V K th d V K J Lowhybd u of dft wv cyd Phy Fud vo 3 345-347 988 5 M R J A S d P K Kw octv ffct du to chg-fuctuto dyc duty Phy Rv E Vo 48 393-3933 993 6 A B N D'Ago d R L Mo Lbotoy xt o ctottc o cycoto wv duty Pt Sc S Vo 43 95-98995 7 V W how d M Robg Ectottc o cycoto tbty duty Pt Sc S Vo 43 63-68 995 8 V W how d M Robg A ot o th ctottc o cycoto tbty duty o wth xt Pt Sc SVo 44 465-467 996 9 Sh d Ajy Ghot Extto of u- hybd wv by gytg tvtc cto b gtzd duty cyd Phy P Vo6 378-3785 9 P K Shu d SV Vdov Stutd cttg of ctogtc wv co duty Phy P Vo 379-383 995 JX M d P K Shu oct d to fo tc tbt of ctogtc wv duty Phy P Vo 56-59 995 SV Vdov Pogto of wv duty wth vb chg o dut tc Phy P Vo 76-767 994 3 RAou d VK th Stutd cttg of wht wv off o-cycoto d o-coutc od duty Phy P Vo 5 6-6 988 4 G Pbu d V K J Ehct of co dft wv cyd J Phy P vo 4 465-47 988 4
ISSN: 77-3754 ISO 9:8 tfd Itto Jou of Egg d Iovtv choogy (IJEI APPENDIX Vou 7 Iu 7 Juy 8 6 5 4 3 9 8 7 6 4 5 6 7 8 9 Fg: Nozd fqucy wthout dut chg fuctuto wth dut chg fuctuto of th co dft wv fucto / [wth d wthout dut chg fuctuto] / o o -5-5 9-6 wth dut chg fuctuto 8-6 7-6 6-6 5-6 4-6 wthout dut chg fuctuto 3-6 4 5 6 7 8 9 Fg: Nozd gowth t dft wv fucto / o o of th co [wth d wthout dut chg fuctuto] 4