Microwave Engineering

Transcription

1 Miwv giig Chg-sig su Dptmt f ltil giig Ntil Uit Uivsit

2 Outli. Tsmissi Li Th. Tsmissi Lis Wvguis Gl Slutis f TM T TM wvs ; Plll Plt wvgui ; Rtgul Wvgui ; Cil Li ; Stipli ; Mistip 3. Miwv Ntw Alsis Imp quivlt Vltgs Cuts ; Imp Amitt Mtis ; Th Sttig Mti ; ABCD Mti ; Sigl Flw Gphs ; Distiutis Ml Alsis 4. Imp Mthig Tuig Mthig with Lump lmts ; Sigl-Stub Tuig ; Dubl-Stub Tuig ; Th Qut-Wv Tsfm ; Th Th f Smll Rfltis 5. Miwv Rsts Sis Plll Rst Ciuits ; Tsmissi Li Rsts ; Rtgul Wvgui Cvitis Dilti Rsts 6. Pw Divis Ditil Cupls Bsi Pptis f Divis Cupls ; Th T-Juti Pw Divi ; Th Wilis Pw Divi ; Cupl Li Ditil Cupls ; 80 hbi 7. Miwv Filts Pii Stutu ; Filt Dsig b th Isti Lss Mth ; Filt Tsfmtis ; Filt Implmtti ; lti Mtils Dvis Applitis Lb

3 . Tsmissi Lis Wvguis Gl Slutis f TM T TM wvs Plll Plt wvgui Rtgul Wvgui Cil Li Stipli Mistip lti Mtils Dvis Applitis Lb

4 Gl Slutis f TM T TM wvs I this sti w will isuss th gl sluti t Mwll s qutis f th spifi s f TM T TM wv ppgti i liil tsmissi lis wvguis. W ssum tim - hmi fils with With ˆ h h ˆ wh h pst th tsvs whil t Th lti mgti fils th b witt s h if ut ilti lss is pst th ppgti stt will b mpl ; p th th mpts f ; ; ; th lgituil lti mgti fil mpts Assum tht th tsmissi li wvgui gi is su f Mwll's qutis b witt s ; p wv ppgti lg th - is. h f ˆˆlti mgti fil mpts βshul th b pl with th bv vt qutis b u t th fllwig : lti Mtils Dvis Applitis Lb

5 lti Mtils Dvis Applitis Lb t b m mpl b usig pst th ilti lss is If fillig th tsmissi li wvgui gi th mtil f th wvumb is / wvumb th utff b fi s hs wh Th si qutis b slv f th fu tsvs fil mpts i tms f Th lss tgt f th mtil

6 TM Wvs Tsvs ltmgti (TM) wvs hti b = = 0. If = =0 th th tsvs fils ls ll => = 0 ( = ) W limit t bti = => = () / = Th utff wv-umb = ( - ) / is thus f TM wvs => th lmhlt wv quti f but f h -ωω ˆ 0 A simil sult ls pplis t t I th ltistti s wh This ult shws tht th tsvs lti fils t t 0 0 p 0 t 0 wh ˆ ˆ I f th lti i bv quti t b vli th ul f is t s usig th fm f ssum w wit It is s t shw i th sm w tht th tsvs mgti fil ls stisf Lpl's quti Th tsvs fils f TM wv thus th sm s th stti fils tht ist btw th uts. is th Lpli pt i th tw tsvs imsis. f TM wv stisf Lpl's quti. t must vish lti Mtils Dvis Applitis Lb

7 Usig th ft tht D ε 0 Th Th ut Z th Z h I Φ t TM TM C (th wv imp f TM m) pi flw Z 0 f ut wh C tsvs ˆ TM t V is th fil Cmbiig th bv sults givs Th vltg btw tw uts b fu s b ss fu tu mpts fm f Amp' s TM wvs ist wh tw m uts pst th Lw ut Pl wvs ls mpls f TM wvs si th fil mpts i th iti f (i this s th tsmissi li uts m b si t b tw ifiitl lg plts spt t ifiit Th bv sults shw tht ls ut (suh s tgul wvgui) t si th spig stti pttil i suh gi wul b ( pssibl stt) lig t gl pssi f th tsvs fils s s ppgti suppt TM wvs 0. lti Mtils Dvis Applitis Lb

8 Th pu f lig TM li b summi s fllws:.slv Lpl's quti. Fi ths stts 3. Cmp fm h Z 0 f. Φ ˆ ˆ h h ˆ 4. Cmp V TM fmv b pplig th bu itis f th w vltgs th uts. Φ Φ t 5. Th ppgti stt is giv b th t I fm I Th sluti will ti svl uw stts... C. Cmp h fm htisti imp is giv b Z V / I. lti Mtils Dvis Applitis Lb

9 lti Mtils Dvis Applitis Lb T wvs Tsvs lti (T) wvs (ls f t s -wvs) hti b = 0 0 gui. th li th gmt f fqu futi f gll is 0 th ppgti stt I this s ; ; th u t t b m mpl b usig pst th ilti lss is If fillig th tsmissi li wvgui gi th mtil f th wvumb is / wvumb th utff b fi s hs wh f b slv f th fu tsvs fil mpts i tms Th si qutis

10 lti Mtils Dvis Applitis Lb m uts. btw tw s wll s T wvs b suppt isi ls uts whih is s t b fqu pt Th T wv imp b fu s gui gmt. th spifi b slv sut t th bu itis f quti must This. si 0 : wv quti f tw - imsil b u t si whih 0 Th lmhlt wv quti f Z h h T

11 lti Mtils Dvis Applitis Lb TM wvs Tsvs mgti (TM) wvs (ls f t s -wvs) hti b 0 = 0 gui. th li th gmt f fqu futi f gll is 0 th ppgti stt I this s ; ; th u t t b m mpl b usig pst th ilti lss is If fillig th tsmissi li wvgui gi th mtil f th wvumb is / wvumb th utff b fi s hs wh f b slv f th fu tsvs fil mpts i tms Th si qutis

12 lti Mtils Dvis Applitis Lb m uts. btw tw s wll s TM wvs b suppt isi ls uts whih is s t b fqu pt Th TM wv imp b fu s gui gmt. th spifi b slv sut t th bu itis f quti must This. si 0 : wv quti f tw - imsil b u t si whih 0 Th lmhlt wv quti f Z T

13 Th pu f lig T TM li b summi s fllws: h h.slv th u lmhlt quti 0 0 f Th sluti will ti svl uw stts th uw utff wvumb.. Us vt Mwll's quti t fi th tsvs fils fm h 3. Appl th bu itis t th pppit fil mpts t fi th uw stts. 4. Th ppgti stt is giv b Z Z T TM th wv imp b is.. lti Mtils Dvis Applitis Lb

14 Attuti Du t Dilti Lss Attuti i tsmissi li wvgui b us b ith ilti lss ut lss. => If is th ttuti stt u t ilti lss is th ttuti stt u t ut lss => ttl ttuti stt is = + Attuti us b ut lss b lult usig th ptubti mth => ps th fil istibuti i th gui s must b vlut sptl f h tp f tsmissi li wvgui If th li gui is mpltl fill with hmgus ilti th ttuti u t lss ilti b lult fm th ppgti stt. lti Mtils Dvis Applitis Lb

15 Th mpl ilti stt llws th mpl ppgti stt t b witt s I pti mst Th si I ths sults t t f t t Np/m (TM wvs) wh ilti mtils hv v smll lss (t ) s this pssi b simplifi b usig th fist tw tms f th Tl pssi t t is th (l) wvumb i th bs f lss. Th bv quti shws tht wh th lss is smll th phs stt is uhg whil th ttuti stt u t ilti lss is giv b (mpltl fill with th ilti) Np/m (T TM wvs) 0 b lttig lti Mtils Dvis Applitis Lb

16 Plll Plt Wvgui Th plll plt wvgui is pbbl th simpl tp f gui tht suppt TM T TM ms si it is fm fm tw flt plts stips. its pti is quit simil t tht f vit f th wvguis mls th ppgti f high ms i stipli. TM Ms TM m sluti b bti b slvig Lpl's quti f th ltstti pttl btw th tw plts. t Φ Assum th bttm plt is th is viti i Th mgti fil is wh Φ Th tsvs lti fil is th ttl ltil fil is f 0 W 0 gu () th tp plt t V A B fm bu iti wh is th ppgti stt f TM wv ˆ V ˆ is th istisi imp f t V ˆ V ˆ pttil f V V / th mium btw th plll plts 0 tht th fils simil i fm t pl wv i hmgus gi. lti Mtils Dvis Applitis Lb

17 Th vltg f V Th ttl ut th tp plt b fu fm Amp's lw suf ut sit I w 0 0 J ˆ ˆ Th htisti imp th tp plt with spt t th th bttm plt b lult ˆ 0 0 V Z ( stt; pt th gmt mtil pmts f th gui) I w Th phs vlit ls stt v V p w w wv tδ Attuti u t ilti lss is giv bα.th fmul f ut tttuti will b iv fm spil s f TM m ttuti. lti Mtils Dvis Applitis Lb

18 TM Ms TM wvs hti b =0 fil tht stisfis th us wv quti => / =0 wh Th gl sluti is A si 0 β is th utff B s th bu itis ω A B 0 0 t 0 ( is A si s - π...is sti t ist vlus) 0 ; wvumb th sluti f Th tsvs fil mpts b fu -β A s - ; 0 A si 3... lti Mtils Dvis Applitis Lb

19 Obsv tht f =0 = () / tht =0. Th fils th stt i s tht th TM 0 m is tull itil t th TM m F th situti is ifft h vlu f sps t ifft TM m t TM m ; h m hs its w ppgti stt fil pssi giv b bv quti O th th h is l l wh >. Si = () / is pptil t fqu th TM ms (f > 0) hibit utff phm whb ppgti will u util th fqu is suh tht >. Th utff fqu f th TM m th b u s f TM m tht ppgts t th lwst fqu is th TM m : f = / [() / ] TM m hs utff fqu qul t twi this vlu s. Th wv imp f th TM ms ZTM wh w s is pu l f > f but pu imgi f f < f Th phs vlit is ls futi f fqu v p = / is s t b gt th / () / = / => th sp f light i th mium si < Th gui wvlgth is fi s g = / (Nt tht g > = / th wvlgth f pl wv i th mtil. Th phs vlit gui wvlgth fi l f ppgtig m f whih is l. O m ls fi utff wvlgth f th TM m s = /. lti Mtils Dvis Applitis Lb

20 Cmput th Ptig vt t s hw pw ppgts i th TM w w * * P R ˆ R w R A f 0 wr 4 A s 0 wr A f 0 P is psitiv wh is l whih us f f f. Wh th m is blw utffβ is imgi s P Th TM ( T) wvgui m ppgti hs itstig itptti wh viw s pi f si th mit TM / si ; whih b witt s A si A s buig pl wvs m whih hs / / This sult is i th fm f tw pl wvs tvlig bliqul i th - itis. s tht ( /) ppgti stt si s ˆs ˆsi i i i i i B mpis with th phs ft f sii si ˆ i th gltht h pl wv ms wih th - is stisfis th ltis m 0. lti Mtils Dvis Applitis Lb

21 F f f is l lss th s is sm gl btw 0 90 th m b thught f s tw pl wvs lttl buig ff f th tp bttm plts. Buig pl wv itptti f th TM plll plt wvgui m. Th suppsiti f th tw pl wv fils is suh tht mplt llti us t = 0 = t stisf th bu iti tht = 0 t ths pls. As f ss t f pph s tht pph 90. Th tw pl wvs th buig up w with mti i th + iti l pw flw us i th iti. t Attuti u t ilti lss b fu fm. Cut lss b tt usig th ptubti mth. P P wh P ωεr s Rs α β βη As isuss pviusl th TM m is itil t th TM s th bv ttuti sults f th TM 0. F this s th is th pw flw w th gui i th bs f is th pw issipt p R w s Rsw P J A s 0 th ttuti u t ut lss P Np/m f 0 wh R Rs 0 α Np/m η s th ut lss uit lgth i th tw lss uts is th suf sistivit f th uts. m f th plll plt wvgui m b us t bti th TM m ttuti b lttig lti Mtils Dvis Applitis Lb

22 T ms T ms hti b With 0 h th sluti is h A 0 wh β is th utff wvumb h s Th bu itis tht B si Th ppgti stt f A si Th utff fqu f th T Th wv imp f th T 0 must stisf th u wv quti B si ; th T 0 t 0 ; whih is th sm s th ppgti stt f b ppgt th plll wvgui. B s β B si m is thus β m is m is f Z th TM (is με 0 f T ms Fm bu iti A 0 π 3... s f th TM s Th fil sluti f is th B s Th tsvs fils b mput s - T - π m ls itil t tht f th TM m) Th phs vlitgui wvlgth utff wvlgth simil t th sults f thtm ms. ; ωμ η β β 0 lti Mtils Dvis Applitis Lb

23 Th pw flw w th gui f T P IF R 0 th lss is giv b 0 thus P Rs Rs Np/m ˆ R w w * m b lult s 0 implig tht th is T m. f 0 Attuti b lult i th sm w s f th TM ms. Th ttuti u t ilti * w B 4 t. th ttuti u t ut lss f T ms is giv b R Obsv tht s utff is pph f th T TM ms Attuti u t ut lss f th TM TM T ms f plll plt wvgui. lti Mtils Dvis Applitis Lb

24 lti Mtils Dvis Applitis Lb

25 Fil lis f th () TM (b) TM () T ms f plll plt wvgui. Th is viti ss th with f th wvgui. lti Mtils Dvis Applitis Lb

26 Rtgul Wvgui Rtgul wvguis w f th list tps f tsmissi lis us t tspt miwv sigls still us t f m pplitis. (suh s upls tts islt ttuts sltt lis fm G t v 0G Th isvtg is th si t lg. But still f wvguis i m pplitis suh s high-pw sstms millimt wv sstms i sm pisi tst pplitis. O th th h th hllw tgul wvgui ppgt TM T ms but t TM wvs si l ut is pst. Phtgph f K-b (WR-8) tgul wvgui mpts. Clwis fm tp: vibl ttut - (mgi) t uti itil upl pt t ig wvgui -pl swpt b ustbl sht sliig mth l. lti Mtils Dvis Applitis Lb

27 T ms Th T ms hti b fils with = 0 whil must stisf th u wv quti h Slv b th mth f X X h X Y Y X 0 0 with h Y Th gl sluti f h Y A s B si C s D si 0 0 b witt s spti f vibls b lttig h X is utff Y h f th tms must b qul t stt s w fi spti stts wvumb suh tht Gmt f tgul wvgui. lti Mtils Dvis Applitis Lb

28 h Th gl sluti f h h fi 0 with h A s B si C s D si s D 0 th sluti f 0 t 0 b 0 t 0. wh A m fm h A b m A A s B si C si D s Asi B s C s D si m m b witt s / b f 0... ; B 0 m m s si b m si s b ppl th bu itis th lti fil mpt is Am s s b is bit mplitu stt mps f Th tsvs fil mpsts f th T ; ; m b fu m A A m / f m 0... m th miig stts A C m is utff tgtil t th wvgui wlls m si s b m s si b wvumb lti Mtils Dvis Applitis Lb

29 Th ppgti stt is m b whih is s t b l spig t ppgti m wh m b h m (mbiti f m ) thus hs utff fqu f m giv b f m Th m with th lws utff fqu is ll th mit m; si w hv ssum b Th T πμε πμε 0 th lwst f us f th T m is th mit T ms th vll mit m f Obsv tht th fil pssis f i th tsvs fil mpts f th T if bth m 0; thus th is T f 0 mπ π b 0 ( m 0) m : 00 m. th tgul wvgui m m ll With ptig fqu f l ths ms hvig f <f will ppgt ; ms with f >f will l t imgi ( l ) mig tht ll fil mpts will ptill w fm th su f itti. Suh ms f t s utff vst ms. If m th m is ppgtig th wvgui is si t b vm. lti Mtils Dvis Applitis Lb

30 Wv imp tht lts th tsvs ltil mgti fils is Z Z T T π π λg λ β v p is l wh is Th gui wvlgth Th phs vlit is ω ω β Spiliig t th m 0 s givs th fllwig sults f tht π A 0 s A π 0 si π I iti f tht m 0 l ( ppgtig m) but με π wh β A π is th itisi imp f π 0 0 is imgi whβis imgi ( vst m) si π 0 th mtil fillig th wvgui m fils : lti Mtils Dvis Applitis Lb

31 Th pw flw w th gui f th T P 0 R 3 ωμ b π ωμ A0 b R β A0 si R β π 0 0 4π tht this sults givs l pw l wh is l sp ig t ppgti g m. F ttuti : Dilti lss b tt b mig mpl usig Tl sis ppimt i Cut Rs utivi t is P Th suf uts s th uts th lft ight si wlls. Cmput th pw lst i th wlls t 0 0 ubl thi sum t bti th ttl pw lss. Th suf ut th 0 (lft) wll is J s ˆ π π J ˆ ˆ ˆ ˆ s 0 ( 0 ˆ 0 ) ˆ A0 si A 0 s π 3 b β P Rs J s Rs J s J s Rs A0 b 0 0 π Th ttuti u t ut lss f th T m is th P α P 0 0 lss is bst tt 0 0 b ˆ ˆ πr s * b ˆ 0 usig th ptubti mth. Th pw lst p uit lgth u t fiit wll J C ll fu wlls but fm smmt t h ˆ R / β 3 ωμbβ ˆ A / π m is lult b 0 0 w h R 0 0 s * Rs 3 b is wll suf whil th ut th 0 (bttm) wll is s bπ sist uts th tp bttm wlls itil 3 Np/m lti Mtils Dvis Applitis Lb

32 TM ms Th TM ms hti b fils with Th gl sluti is th A 0 mπ f m Th sluti 0 with Th bu itis b ppli itl t 0 t 0 0 t 0 b. th us t A s B si C s D si 0 whil 3... ; C 0 πb m Bm si si b wh B is bit mplitu stt m must stif th u wv quti β f 3... lti Mtils Dvis Applitis Lb

33 Th tsvs fil mpts f th TM m B B b m m m s si b m si s b As f th T ms th ppgti stt is m ; ; m b mput B b ω mπ B m m si s b m m s si b m β b is l f ppgti ms imgi f vst ms Th utff fqu gui wvlgth phs vlit f th TM is ls th sm s tht f th T Obsv tht th fil pssis f Th TM 00 TM 0 TM 0 m ms itill if ith m is. ms th lwst TM m ms m t ppgt (lwst f ) is TM f b whih is s t b lg th f 0 f th utff fqu f th T 0 m. lti Mtils Dvis Applitis Lb

34 Th wv imp ltig th tsvs lti mgti fils is Z TM = / = - / = / Th ttuti u t ilti lss is mput i th sm w s f th T ms with th sm sults. Th lulti f ttuti u t ut lss is lft s pblm Attuti f vius ms i tgul bss wvgui with =.0 m. lti Mtils Dvis Applitis Lb

35 Fil lis f sm f th lw ms f tgul wvgui lti Mtils Dvis Applitis Lb

36 X. Csi lgth f Tfl-fill p K-b tgul wvgui hvig imsis =.07 m b = 0.43 m. Fi th utff fqu f th fist fiv ppgtig ms. If th ptig fqu is 5 G fi th ttuti u t ilti ut lsss. <Sl> Tfl =.08 t= Cmput f f th fist fw vlus f m givs: M m f (G) Thus th T 0 T 0 T 0 T TM ms will b th fist T fiv ms t ppgt. T T T TM 6.07 T TM 3.03 At5 G β α Rs α 3 bββ 345. m f m f tδ 09. p/m 03. B/m β Th suf sistivit f m b R s th ttuti u t ut lss is - th ppgti stt f th T th pp wll is 345. m 3 bπ p/m B/m - (σ S / m) 0 m is lti Mtils Dvis Applitis Lb

37 Cil Li TM Ms Th fils b iv fm sl pttil futi () whih is sluti t Lpl s quti; i liil its Lpl s quti ts th fm 0 This quti must b slv f subt t th bu itis tht fm s b R P R P 0 R B th usul spti f ρ R ρ ρ R ρ ρ Th gl sluti t is 0 Usig th mth f spti f vibls w lt b pss i put P V A s Bsi wh si isigb multipl f shul t hg th sult. vibl gumt th tw tms must P P must b itg b qul t stts ρ 0 lti Mtils Dvis Applitis Lb

38 Bus f th ft tht th bu itis t v with th pttil () shul t v with. Thus must b this implis tht must b s tht th quti f R() us t R 0 Th sluti f R is th s R C l C Applig th bu iti givs tw qutis f th stts C D : b V D l D. C l D 0 C l b D Aft slvig f C D th fil luti f b witt s V l b l b lti Mtils Dvis Applitis Lb

39 igh O Ms Th il li li th plll plt wvgui ls suppt T TM wvgui ms i iti t iti t TM m. Aviig th ppgti f high ms sts upp limit th si f il bl; this ultimtl limit th pw hlig pit f il li. T m is th mit wvgui m f th il li s is f pim impt. F T ms Th gl sluti h Th bu itis Fm t fi 0 wh ρφ h ρ A si B s CJ DY I this s b s w hv ss t is th Y CJ ' ' ' A si B s CJ DY ' ' ' DY 0 ; CJ b DY b Si this is hmgus st f qutis th l tivil ( C 0 D 0) sluti us wh th tmit is. ' th fi th T J 0 ' Y b ms f stisfis th wv quti 0 ' by Th is htisti ( igvlu) quti f m J μ ' h il li. f ρ b. tm 0.Th vlus f lti Mtils Dvis Applitis Lb tht stisf bv quti β

40 Figu shws th sult f suh sluti f = f vius b/ tis. A ppimt sluti tht is ft us i pti is = / ( + b) => is w th ppgti stt utff fqu b tmi. => sluti f th TM ms b fu i simil m Fil lis f th () TM (b) T ms f il li. Nmli utff fqu f th mit T wvgui m f il li. lti Mtils Dvis Applitis Lb

41 Mst il bls ts i mm us hv 50 htisti imp with pti big i 75 us i TV sstms. Tp-N: vlp i 94 m ft its ivt P. Nil. Th ut imt f th fml is but 0.65 i. Th mm upp fqu limit gs fm t 8 G pig bl si. This ugg ut lg t is ft fu l quipmt. TNC: This is th vsi f th mm BNC t. Its usg is limit t fquis blw G. Fm th tp lft: Tp-N TNC SMA APC-7.4 mm SMA: Th f smll light t l t th vlpmt f this t i th 960s. Th ut imt f th fml is but 0.50 i. It b us up t fquis i th g f 8-5 G is pbbl th mst mml us miwv t t. APC-7: This is pisi t tht ptl hiv SWR lss th.04 t fquis up t 8 G. This t is us mst mml f msumt istumtti pplitis..4 mm: Th f ts t millimt wv fquis l t th vlpmt f tw vitis f th SMA t: th K t is usful t but 40 G whil th.4 mm t is usful t but 50 G. Th si f ths ts is simil t th SMA t. lti Mtils Dvis Applitis Lb

42 Suf wvs gu ilti slb I gl s suf wvs ist i vit f gmtis ivlvig ilti itfs si th T TM suf wvs b it lg gu ilti slb. Suf wvs s ptill w fm th ilti suf with mst f th fil ti i th ilti th fil gll tightl bu t th ilti wh isig th fqu (high fqu).=> mig suh wvguis ptil O th th h th phs vlit f suf wv is lss th th vlit f th light i vuum u t th ilti. Sm tps f pl tsmissi lis suh s mistip sltli m ls b it suf wv. T ms Assum ppgti i th + iti with - ppgti ft viti i th - iti (/ = 0). W must sptl si th fil i tw gi (i ilti) th mth tgtil fils ss th suf. must stisf th wv quti i h gi. wh th sig h th utff wvumbs f th tw gis s 0 f wh ; 0 f 0 hs b slt i tiipti f ig sult f. Ths sm ppgti stt hs b us f bth gi u t phs mthig f th tgtil fils t h ptill. lti Mtils Dvis Applitis Lb

43 Th gl slutis Nt tht ths slutis vli f it will tu ut tht bth Th bu itis tht must b stisfi 0 t 0 ; s ; tiuus t ; B 0 C 0 Th tiuit f A si 0 Appl tiuit t F tivil sluti th tmit f lig t limitig givs Asi A s C D h h D h B s D ls t tp pbti h t h h l. f. h Fm bv quti stitut st f simultus h h f 0 ith l tw qutis f tht must b slv f th ppgti stts imgi bv quti must vish tstl qutis h giv. tiuus t lti Mtils Dvis Applitis Lb

44 Multiplig bth sis f ( ) Th ius f. Obsv tht 3. A is stt t f ( h) t h - - t TM m is TM h ) lst ppgtig TM m ( TM whih is th quti f il i th h pl. ε is t lg - th il m itst m th bh f th tgt futi. Th itsti f th il is ( Cutff fqu f th TM 0... b ths uvs implis sluti m b psitiv gtiv - m th TM m ppgt m th b givs whih is pptil t th ltil thiss f th ilti slb. 0 m) f thiss slb with pmittivit gt th uit m willt tu util th ius f th il bms gt th Gphil sluti f th tstl quti f th utff fqu f TM suf wv m f th gu ilti slb. lti Mtils Dvis Applitis Lb

45 lti Mtils Dvis Applitis Lb f A h f A f A h f A f A f A h h h h si 0 s si 0 s si 0 si b fu s th fil pssis ptiul suf wv m hv b fu f O

46 T ms T ms ls b suppt b th gu ilti slb. Th th quti Ctiuit f h h h As f TM ms th gl slutis 0 f with h Asi B s ; h T stisf th iti iti : C 0 ; t h ; Abv quti must b slv simultusl f th vibls f h B D si h t givs B s D 4 h A pst ils i th h pl f 0 A 0 f f tiuit f t h pltt s fmil f th uvs i th h pl. Si th gtiv vlus f h must b lu th fist T m s t stt t ppgt util th ius f th il Th utff fqu f th T 0 bms gt thπ/. h h ms th b fu s f 3... C D 0 t 0 h t. fil stisfis th wv quti h h. lti Mtils Dvis Applitis Lb

47 Cmpig with h th TM T Aft fiig th stts f B s ms is TM B s B si B h s h B si B h s h shws tht th f ppgti f h th fil pssis b iv s f 0 f f 0 0 T TM T TM f f 0 f... Gphil sluti f th tstl quti f th utff fqu f T suf wv m. Figu pits m blw utff. lti Mtils Dvis Applitis Lb

48 Stipli A pl-tp f th tsmissi li tht ls itslf wll t miwv itgt iuit phtlithgphi fbiti. It suppt TM wv ls suppt high T TM ms but ths usull vi i pti (suh ms b suppss with shtig sws btw th gu pls b stitig th gu pl spig t lss th /4). Fmuls f ppgti stt htisti imp ttuti Th phs vlit f TM v Z L C LC C If w w C - fi Z Z v C wh L C 30 b whw is th fftiv with f W 0.44 b p t fi th pit p lgth f th stipli uv fittig t th t sluti. th t ut giv b m is giv b p Th htisti imp f tsmissi li is giv b W W W 0 f b b b W W/b f b htisti imp ss s th stip with W iss wv th sultig sluti ivlvs mplit spil futis s f ptil mputtis simpl fmuls hv b vlp b v p thus usig Lpl's quti b slv b fml mppig th ppgti stt f th iut pit p uit lgth f th li th stipli is Stipli tsmissi li. () Gmt. (b) lti mgti fil lis lti Mtils Dvis Applitis Lb

49 Wh sigig stipli iuit giv th htisti imp ( hight b pmittivitε) W f εz 0 30 wh 0.44 b f εz 0 Z Si stipli is TM tp f li th ttuti u t ilti lss f th sm f s tht f th TM lis Th ttuti u t ut lss b fu b th ptubti mth W's imtil iut ul. A ppimt sult is usull t fi th tip with Rs Z A f εz 0 30 b t Np / m 0.6R s B f εz 0 Zb W b t b t with A l b t b t t b 0.44t 4W B 0.5 l wh t is th thiss f 0.5 W 0.7 t W t th stip lti Mtils Dvis Applitis Lb

50 . Fi th with f 50pp stipli ut with b = 0.3 m =.0. If th ilti lss tgtil is 0.00 th ptig fqu is 0 G lult th ttuti i B/. Assum ut thiss f t = 0.0 mm. <Sl> Si Z Z givs th with sw Th ttl ttuti stt is I B B πfε - At0 G th wvumb is m tδ Dilti Attuti isα 055. Np/m Th suf sist f pp t0 G is R 0. 06Ω RεZ s Cut Attuti isα 30πb t At0 G th wvlgth th stipli is s i tms f 0lg b.4b/m wvlgth th ttuti is m αα α Np/m s A 0. Np/m si A f.0 m B B / lti Mtils Dvis Applitis Lb

51 A ppimt ltstti sluti M ptil pblms i miwv giig v mplit t l thmslvs t stightfw lti slutis but qui sm st f umil pph. => bgiig with umil sluti f th htisti imp f stipli. Th fils f TM m stipli must stisf Lpl s quti i th gi btw th tw plll plts. -> th tul stipli ts t ms th lsis m iffiult. => th fil lis t t v f w fm th t ut => simplif > / plig mtl wlls th sis. wh >>b s tht th fils u th t ut t ptub b th siwlls. Fiit gi i whih th pttil stisfis Lpl's quti t 0 f / 0 b with th bu itis tht 0 t / ; 0 t 0 b. Usig th mth f spti f vibls th t Du t D is istiuus t b/ th pttil A B Spti sluti f t A s sih f 0 b / B s si b f b / b l th tms u t th sluti is v futi f. Th pttil must b tiuus t b/ ut t b/ must b fu f 0 b/ b/ b. will ti suf hg sit will hv slp istiuit Gmt f ls stipli. lti Mtils Dvis Applitis Lb

52 Th miig st f stts A b fu b slvig f th hg sit th t stip Si A s sh A s sh b Th suf hg sit th stip t b/ is D s b / D b / b / b / th s fi uw stts A th pit s 0 whih is s t b Fui sis i f W / f W / Th ttl hg p uit lgth th t ut is Th htisti imp is th fu s Z f 0 b / f b / b f th uf hg sit Usig th thglit pptis f th s( / ) futis givs th stts Th vltg f th t stip ltiv t th bttm ut is L C Q LC C W / Q S tht th pit p uit lgth f th stipli is C V V W / si W W / sih b / sh b / v C C p s b / 0 s A 0 C / m W s A b A s sh si W / π sh b / b A sih F / m lti Mtils Dvis Applitis Lb

53 Mistip Mistip li is f th mst ppul f pl tsmissi lis u t it b fbit b phtlithgphi psss is sil itgt with th pssiv tiv miwv vis. If th ilti w t pst ( =) w ul thi f th li s tw-wi li sistig f tw flt uts f with W spt b ist. => I this s : hv simpl TM tsmissi li with v p = =. O th th h th ps f th ilti ptiull th ft tht th ilti s t fill th i gi bv th stip (>) mplits th bhvi th lsis f mistip li => Mistip hs sm f its fil lis i th ilti gi tt btw th stip ut th gu pl sm fti i th i gi bv th substt. Mistip li ls t suppt pu TM wv si th phs vlit f TM fils i th i gi wul b. => A phs mth t th ilti-i itf wul b impssibl t tti f TM tp wv. =>th t fils f mistip li stitut hbi TM-T wv. I iti th ilti substt is ltill v thi ( <<) s th fils qusi-tm v p = / ( ) / = ( ) / is fftiv ilti stt f th mistip li ; < < pt th substt thiss ut with W. Mistip li() Gmt. (b) lti mgti fil lis. lti Mtils Dvis Applitis Lb

54 Fmuls f ppgti stt htisti imp ttuti Th fftiv ilti stt f mistip li is giv / W Giv th imsis f th mistip li th htisti imp b lult s Z F W 60 8 W l f W/ ε W 4 0π f W/ εw lW/ 444. giv htisti imp Z ilti sttε W/ ti b fu s A 8 A B l π Z wh A 60 Csi mistip s qusi - t ptl i th ilti B lb ε 0 ε. 377π 0 3. ; B ε ε Z ε TM li th ttuti u t ilti lss b tmi s Np/m ε ε This sult is iv b multiplig b "fillig ft" f W/ ε wh tis th lss tgt f th ilti whih uts f th ft tht th fils u th mistip li ptl i i (lsslss) : f W/ quivlt gmt f qusi-tm mistip li wh th ilti slb f thiss ltiv pmittivit ε hs b pl with hmgus mium f fftiv ltiv pmittivit ε. lti Mtils Dvis Applitis Lb

55 Th ttuti u t ut lss is giv ppimtl b Rs Z W Np / m wh R s / is th suf sistivit f th ut. F th mistip substt ut lss is muh m sigifit th ilti lss. Clult th with lgth f mistip li f 50 htisti imp 90 phs shift t.5 G. Th substt thiss is =0.7 m with =.0. <Sl> Fist fi W/ f Z B W/ S W/ ; thwis w wul us th pssi f W/ Th W m Th fftiv ilti stt isε87. 90β 50Ω iitill guss tht W/ ε ; Th li lgth f 90phs shift is fu s πf m - ;. 90π/ 80 ε 9. m lti Mtils Dvis Applitis Lb

56 A ppimt ltstti sluti Cvit t pl utig siwlls th mistip li th siwlls pl t = / wh >> s tht th wlls shul t ptub th fil lis lli u th stip ut t s 0 with bu itis 0 Si th tw gis fi b th i/ilti itf with hg istiuit th stip w will hv spt pssis f Th gl sluti s A s sih f 0 / B s f Nw th pttil must b tiuus t A sih B b witt s f / 0 / A s sih 0 A s sih t / t 0 i ths gis. / f 0 f Gmt f mistip li with utig siwlls. lti Mtils Dvis Applitis Lb

57 lti Mtils Dvis Applitis Lb ) th mistip li with ilti substt ( lgth f uit pit p ) th mistip li with ilti substt ( lgth f uit pit p ; / sh sih / sih / si 4 th mistip li is lgth f uit Stti pit p C/m stip is th t lgth uit p hg Th ttl sih 0 th stip ltiv t th gu l is Th vltg f / sh / sih / si 4 s th stts futi fivs / th s Usig th thglit f / f 0 / f uifm istibuti w ppimtl th hg sit th mistip li b As f th stipli s f th suf hg sit sis i Fui whih is s t b sh sih s is Th th suf hg sit th stip t f sih s 0 f sh s b fu b siig th suf hg sit th stip Th miig stts / / 0 s s / C C C C v Z C C W W V Q C W Q A V W A A W W A D D A A Φ - A p W W s s

58 Summ f tsmissi lis wvguis Summi sm f th bsi pptis f ths tsmissi mi thi ltiv vtgs i b tt. -> W bsv tht TM wvs ispsiv with utff fqu whs T TM wvs hibit ispsi gll hv utff fquis. A th ltil sitis ilu bwith ttuti pw hlig pit. Chtisti Ms: Pf Dispsi Bwith Lss Oth Pw pit Phsil si s f fbiti Itgti with th mpts C TM TMT N igh Mium Mium Lg Mium Wvgui T 0 TM T Mium Lw Lw igh Lg Mium Stipli TM TM T N igh igh Lw Mium s Fi Mistip Qusi TM bi TM T Lw igh igh Lw Smll s s lti Mtils Dvis Applitis Lb

59 Rig wvgui => th bwith f tgul wvgui is lss th tv ( : fqu g). This is bus th T 0 m bgis t ppgt t fqu qul t twi th utff fqu f th T 0 m. sist f tgul wvgui l with utig igs th tp / bttm wlls. This lig ts t lw th utff fqu f th mit m -> isig bwith impvig imp htistis. Suh gui is ft us f imp mthig pupss but us th pw-hlig pit. lti Mtils Dvis Applitis Lb

60 Dilti wvgui => Du t th mtlli uts t ss t fi suppt ppgtig ltmgti fil. Fm th gmt th fils thus mstl fi t th u th ilti ig suppt T TM ms is vit f itgti with tiv vis. Its smll si ms it usful f millimt wv t ptil fquis lthugh it b v lss t bs utis i th ig li. lti Mtils Dvis Applitis Lb

61 Sltli => Of th m tps f pl lis tht hv b pps sltli pbbl s t bhi mistip stipli i tms f ppulit. Li mistip tw uts f sltli l t qusi-tm tp f m. Chgig th with f th slt hgs th htisti imp f li. lti Mtils Dvis Applitis Lb

62 Cpl wvgui => A stutu simil t sltli is pl wvgui. Bus f th ps f this itil ut this tp f li suppt v qusi-tm ms pig whth th -fils i th tw slts i th ppsit iti th sm iti. Cpl wvgui is ptiull usful f fbitig tiv iuit u t th ps f th t ut th ls pimit f th gu pls. lti Mtils Dvis Applitis Lb

63 Cv mistip => Th mtlli v plt is ft us f ltil shilig phsil ptti f th mistip iuit is usull situt svl substt thiss w fm th iuit. ptub th pti f th iuit ugh s tht its fft must b t it ut uig sig. lti Mtils Dvis Applitis Lb