Lecture 25. Guided Waves in Parallel Plate Metal Waveguides

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Whitney Arlene Bryan
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1 Lctu 5 Gu Wavs n Paalll Plat Mtal Wavgus In ths lctu u wll lan: Paalll plat tal wavgus T an TM gu s n wavgus C 33 Fall 7 Fahan Rana Cnll Unvst Paalll Plat Mtal Wavgus W Cns a paalll plat wavgu (shwn abv) W hav stu such stuctus n th cntt f tansssn lns W nw that th can gu TM wavs (Tansvs lctc an Magntc) n whch bth th lctc an agntc fls pnt n ctn ppncula t th ppagatn ctn But ths stuctus can gu than ust th TM wavs that w hav cns s fa. C 33 Fall 7 Fahan Rana Cnll Unvst 1

2 C 33 Fall 7 Fahan Rana Cnll Unvst Basc Wav quatns Cns a paalll plat wavgu: Th lctc fl f an gu wav wll satsf th cpl wav quatns: W l f slutns f th quatn, wh th -pnnc s that f a wav gng n th -ctn, an wh th -fl s pntng n th -ctn: F S unnwn functn f C 33 Fall 7 Fahan Rana Cnll Unvst T Gu Ms - I Th assu slutn f: F psnts a T gu wav (Tansvs lctc) snc th ctn f -fl s tansvs t th ctn f wav ppagatn Pluggng th assu slutn nt th quatn gvs: ( ) F F Pfct tal buna cntns F F

3 N t slv: F T Gu Ms - II ( ) ( ) F( ) Wth buna cntns Slutn s: F( ) ( ) sn F F But th valu f cannt b abta buna cntn at ctats that: wh : 1,, 3, KK Slutn bcs: F( ) sn An: ( ) sn { 1,,3, KK Autatcall satsfs th F buna cntn: ( ) 1 C 33 Fall 7 Fahan Rana Cnll Unvst T Gu Ms - III ( ) sn { 1,,3, KK -fl: 1 -fl: C 33 Fall 7 Fahan Rana Cnll Unvst 3

4 T Gu Ms Dspsn Rlatn 1 ( ) sn { 1,,3, KK Dffnt valus cspn t ffnt T s labl as T s Th quatn: F ( ) ( ) F( ) pls: Dspsn latn f T gu C 33 Fall 7 Fahan Rana Cnll Unvst T Gu Ms Cut-ff Fqunc 1 Dspsn latn f T gu plan wav spsn F th T, f th fqunc s latn: lss than: 1 Thn bcs ntl agna an th s nt ppagat (but cas pnntall wth stanc) T 1 spsn latn T spsn latn Cut-ff fqunc f T : 1 1 C 33 Fall 7 Fahan Rana Cnll Unvst 4

5 5 C 33 Fall 7 Fahan Rana Cnll Unvst T Gu Ms Magntc Fl 1 ( ) { K K,3, 1, sn Magntc fl s gvn b th quatn: ( ) sn cs Nt that th pfct tal buna cntn f th agntc fl s autatcall satsf.: C 33 Fall 7 Fahan Rana Cnll Unvst T Gu Ms Fl Pfls Th -fl an -fl lns f th T 1 a shwn blw: ( ) { K K,3, 1, sn ( ) sn cs

6 6 C 33 Fall 7 Fahan Rana Cnll Unvst T Gu Ms Anth Pspctv - I Cns T-wav flctn ff a pfct tal: ( ) Γ 1 Γ ( ) [ ] sn Ntc th sn vaatn f th -cpnnt f th -fl C 33 Fall 7 Fahan Rana Cnll Unvst T Gu Ms Anth Pspctv - II sn If anth tp tal plat s plac at n f th ns f th sn functn thn ths atnal tal plat wll nt stub th fl Ths s actl what gu T s a T-wavs buncng bac an futh btwn tw tal plats an ppagatng n th -ctn!

7 7 C 33 Fall 7 Fahan Rana Cnll Unvst TM Gu Ms - I Cns TM-wav flctn ff a pfct tal: ( ) TM Γ 1 Γ TM ( ) [ ] cs Ntc th csn vaatn f th -cpnnt f th -fl C 33 Fall 7 Fahan Rana Cnll Unvst TM Gu Ms - II If anth tp tal plat s plac at th au pnts f th csn functn thn ths atnal tal plat wll nt stub th fl cs Ths s actl what gu TM s a TM-wavs buncng bac an futh btwn tw tal plats an ppagatng n th -ctn!

8 TM Gu Ms Basc quatns - I N t slv th quatn: ( ) ( ) Assu th slutn f: G It psnts a TM gu wav (Tansvs Magntc) snc th ctn f -fl s tansvs t th ctn f wav ppagatn Pluggng th assu slutn nt th quatn gvs: ( ) ( ) ( ) ( ) G( ) ( ) G( ) C 33 Fall 7 Fahan Rana Cnll Unvst TM Gu Ms Basc quatns - II 1 N t slv: G ( ) ( ) G( ) Slutn s: G( ) ( ) cs wh :,1,, 3, KK Slutn bcs: ( ) G cs An: ( ) cs {,1,,3, KK Mtvatn f ths s btan f th TM-wav flctn analss scuss al C 33 Fall 7 Fahan Rana Cnll Unvst 8

9 9 C 33 Fall 7 Fahan Rana Cnll Unvst TM Gu Ms lctc Fl lctc fl s gvn b th quatn: ( ) cs sn ( ) { K K,3,,1, cs Nt that th pfct tal buna cntn f th lctc fl s autatcall satsf,..: 1 C 33 Fall 7 Fahan Rana Cnll Unvst 1 TM Gu Ms Dspsn Rlatn ( ) { K K,3,,1, cs ( ) G G Th quatn: pls: Dspsn latn f TM wavgu Dffnt valus cspn t ffnt TM s labl as TM s

10 TM Gu Ms Cut-ff Fqunc 1 Dspsn latn f TM gu TM spsn latn F th TM, f th fqunc s lss than: 1 Thn bcs ntl agna an th s nt ppagat (but cas pnntall wth stanc) TM 1 spsn latn TM spsn latn Cut-ff fqunc f TM : 1 1 C 33 Fall 7 Fahan Rana Cnll Unvst TM Gu Ms Fl Pfls Th -fl an -fl lns f th TM 1 a shwn blw: ( ) cs {,1,,3, KK ( ) sn cs C 33 Fall 7 Fahan Rana Cnll Unvst 1

11 ( ) ( ) TM Gu M Fl Pfls Th -fl an -fl f th TM a: Nt that fls a nt a functn f Th -fl an -fl lns f th TM a shwn blw: Th TM s ust th TM that w w wth whn alng wth tansssn lns! C 33 Fall 7 Fahan Rana Cnll Unvst 11

Lecture 26. Dielectric Slab Waveguides

Lecture 26. Dielectric Slab Waveguides Lectue 6 Delectc Slab Wavegudes In ths lectue yu wll lean: Delectc slab wavegudes T and TM guded mdes n delectc slab wavegudes C 303 Fall 005 Fahan Rana Cnell Unvesty T Guded Mdes n Paallel-Plate Metal