Lecture 27. Rectangular Metal Waveguides

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Silas Little
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1 Lctu 7 Rctgul Mtl Wvguids I this lctu u will l: Rctgul tl wvguids T d TM guidd ds i ctgul tl wvguids C 303 Fll 006 Fh R Cll Uivsit Plll Plt Mtl Wvguids d 1 T Mds: Dispsi lti: ( ) si { 1,, d d d 1 TM Mds: Dispsi lti: d ( ) cs { 0,1,, d C 303 Fll 006 Fh R Cll Uivsit 1

Plll Plt Mtl Wvguids d 1 T Mds: Dispsi lti: ( ) si { 1,, d d d 1

2 C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids Swht li plll plt tl wvguid tht is clsd tl wlls th iig tw sids C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids: T Guidd Mds - I Th lctic fild f th guidd wv will stisf th cpl wv qutis: W l f slutis f th quti: ( ) [ ] D C B A T spti f vils (with -fild pitig i dictis tsvs t th dicti f ppgti) Wh: C A cs si, D B cs si,

lctic fild f th guidd wv will stisf th cpl wv qutis: W l f slutis f th quti: ( ) [ ] D C B

3 Rctgul Mtl Wvguids: T Guidd Mds - II ( ) [ A( ) B( ) C( ) D( )] Bud cditi: Cpts f -fild plll t th tl wlls ust g t t th tl wlls: 0 0, 0 0, This iplis: A D ( ) si( ) ( ) si( ) S w hv: wh : 0,1, wh : 0,1, ( ) [ si( ) B( ) C( ) si( )],, C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids: T Guidd Mds - III ( ) [ si( ) B( ) C( ) si( )] Ath Bud Cditi: Cpts f -fild l t th tl wlls ust g t t th tl wlls: 0 0 0, 0, Tus ut tht th v sluti f ld stisfis th -fild ud cditis Wht d w d w? W us sthig tht w v hd t us f i th ctt f guidd wvs: Guss Lw:. ( ) 0 Pluggig i th v sluti f i Guss Lw givs: B si ( ) B Guss Lw c l stisfid if: ( ) cs( ) ( ) C( ) si( ) C( ) cs ( ) C 303 Fll 006 Fh R Cll Uivsit 3

Cditi: Cpts f -fild l t th tl wlls ust g t t th tl wlls: 0 0 0, 0, Tus ut tht th v sluti f ld stisfis th -fild ud cditis Wht d w d w?

4 4 C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids: T Guidd Mds - IV ( ) si cs cs si Fill, th sluti is:, 0,1 : wh,, 0,1 : wh, Wh: Ths ds clld T ds B cvti, th fist suscipt i T is ltd t th cpt f -vct tht is lg th lg tsvs disi f th ctgul wvguid NOT: Th T 00 d ds t ist (i.. it cspds t fild ig tivill vwh) C 303 Fll 006 Fh R Cll Uivsit T Guidd Mds Cut-ff Fquc ( ) si cs cs si {,,1 0, {,,1 0, Th cut-ff fquc f th T d is: If th fquc is lss th th cut-ff fquc th cs til igi d th d ds t ppgt (ut dcs ptill with distc)

5 T Guidd Mds Dispsi Rlti ( ) si( ) cs( ) cs( ) si( ) { 0,1,, { 0,1,, pl wv dispsi lti: T 10 d dispsi lti T 01 d dispsi lti C 303 Fll 006 Fh R Cll Uivsit T Guidd Mds Fild Pfil f T 10 Md ( ) si( ) / / C 303 Fll 006 Fh R Cll Uivsit 5

dispsi lti 10 01 C 303 Fll 006 Fh R Cll Uivsit T Guidd Mds

6 Rctgul Mtl Wvguids: TM Guidd Mds - I Th lctic fild f th guidd wv will stisf th cpl wv qutis: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) W l f slutis f th quti: ( ) ( ) ( ) ( ) T spti f vils (with -fild pitig i dictis tsvs t th dicti f ppgti) ( ) [ A( ) B( ) C( ) D( )] Wh: A B ( ), C( ) si( ) cs( ) ( ), D( ) si( ) cs( ) C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids: TM Guidd Mds - II ( ) [ A( ) B( ) C( ) D( )] Bud cditi: Cpts f -fild l t th tl wlls ust g t t th tl wlls: 0 0 0, 0, This iplis: C( ) si( ) wh : 0,1,, B( ) si( ) wh : 0,1,, S w hv: A si si D ( ) [ ] C 303 Fll 006 Fh R Cll Uivsit 6

), D( ) si( ) cs( ) C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids: TM Guidd Mds - II ( ) [ A( ) B( ) C( ) D( )] Bud cditi: Cpts f -fild l t th

7 Rctgul Mtl Wvguids: TM Guidd Mds - III ( ) [ A( ) si( ) si( ) D( ) ] Ath Bud Cditi: Cpts f -fild plll t th tl wlls ust g t t th tl wlls: 0 0, 0 0, Tus ut tht th v sluti f ld stisfis th -fild ud cditis Wht d w d w? Guss Lw f -filds:. ( ) 0 Pluggig i th v sluti f i Guss Lw f -filds givs: A ( ) cs( ) D( ) cs( ) Guss Lw f -filds c l stisfid if: A( ) cs( ) D cs ( ) ( ) C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids: TM Guidd Mds - IV Fill, th sluti is: ( ) cs( ) si( ) si( ) cs( ) Wh: wh : 0,1, wh : 0,1,, Ths ds clld TM ds, B cvti, th fist suscipt i TM is ltd t th cpt f -vct tht is lg th lg tsvs disi f th ctgul wvguid NOT: Th TM 00, TM 0 TM 0 ds d t ist (i.. th cspd t fild ig tivill vwh) C 303 Fll 006 Fh R Cll Uivsit 7

( ) 0 Pluggig i th v sluti f i Guss Lw f -filds givs: A ( ) cs( ) D( ) cs( ) Guss Lw f -filds c l stisfid if: A( ) cs( ) D cs ( ) ( ) C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl

8 8 C 303 Fll 006 Fh R Cll Uivsit TM Guidd Mds Cut-ff Fquc {, 1, {, 1, Th cut-ff fquc f th TM d is: If th fquc is lss th th cut-ff fquc th cs til igi d th d ds t ppgt (ut dcs ptill with distc) ( ) cs si si cs C 303 Fll 006 Fh R Cll Uivsit TM Guidd Mds Dispsi Rlti {,,1 0, {,,1 0, pl wv dispsi lti: 11 1 TM 11 d dispsi lti TM 1 d dispsi lti ( ) cs si si cs

ptill with distc) ( ) cs si si cs C 303 Fll 006 Fh R Cll Uivsit TM Guidd Mds Dispsi Rlti

9 9 C 303 Fll 006 Fh R Cll Uivsit TM Guidd Mds Fild Pfil f TM 11 Md / ( ) cs si si cs / C 303 Fll 006 Fh R Cll Uivsit Rctgul Mtl Wvguids Rctgul tl wvguids cl usd t guid lctgtic pw wh dlig with high pw lvls (ds, stllit d spc cuictis, wilss/il s sttis, tc) Th usull d f cpp d th st gld pltd Itgtd vsis usd i su-illit wvlgth ulthigh spd lctics (.g. Gu scillts, supcductig T lctics, li Schtt did is) ptig t fqucis tw 300 G t 1000 G

stllit d spc cuictis, wilss/il s sttis, tc) Th usull d f cpp d th st gld pltd Itgtd vsis usd i su-illit

10 Wvguids t C Adpts Stis it is css t tsf pw tw wvguid d c cl Lp Dsig Th lp is plcd d itd s tht iu gtic flu gs thugh it d iducs cut i it (Fd s lw) pw ut Pi Dsig Th pi is plcd t th iu -fild lcti, d itd i its dicti, s tht th -fild pducs cut i th pi pw ut pw i pw i Wvguid t C Adpt C 303 Fll 006 Fh R Cll Uivsit Wvguid t C Adpts 10

pi is plcd t th iu -fild lcti, d itd i its dicti, s tht th -fild pducs cut i th

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