Chapter 5 Transmission Lines

Transcription

1 hap 5 asmsso s 5- haacscs of asmsso s asmsso l: has o coucos cay cu o suppo a M av hch s M o quas-m mo. Fo h M mo a H M H M a a M. h cu a h M av hav ff chaacscs. A M av popaas o ff lcc ma h paal flco a h paal asmsso ll occu. A obys h follo uls. ll s la: s s p a θ =θ v v p

2 h flco coffc: Γ= a h asmsso coffc: τ= s s s s fo ppcula polaao s s a a fo paalll polaao M cas of omal cc h η = a η =. quval-ccu mol of asmsso l sco: m m H m m F asmsso l quaos: hh-fqucy a h asmsso l mol s ul o aaly M po flo. v v v v v v v v=[ ω ] =[ ω ] h γ=α+β=

3 haacsc mpac: = No:. aoal aa mpac of a asmsso s =5Ω.. asmsso-l quval-ccu mol.. h follo chaacscs hav b masu o a lossy asmsso l a MH: =5Ω α=.bm=.5-3 Npm β=.8πam. Dm a fo h l. ol π= pf m.3 m m 5. F m. A -c ao of vola a al ssac s coc o a lossy asmsso l chaac by a ssac p u lh a a coucac p u lh. a W h ov vola a cu asmsso-l quaos. b F h al soluos fo a. ol. a b osslss l ==: vp X X o-loss l <<ω <<ω: ] [ ] v Dsoolss l =: v p p

4 a-loss l ω<< ω<< : ] [ v p ] [. A ao h a op-ccu vola v =s8π a al mpac =4+3Ω s coc o a 5Ω soolss l. h l has a ssac of.5ωm a s lossy lcc mum has a loss a of.8%. h l s 5m lo a s ma a mach loa. F h saaous xpssos fo h vola a cu a a abay locao o h l. ol..8%=. = Dsoolss m H. =.Npm m a 5.58 γ=α+β= ] [

5 laoshp b asmsso-l paams: a =με =σε o- l: aj s s P a a s a f c c oaxal-cabl l: aj s bj so s P a s P o b s f c a b a b c. s s o cosuc ufom asmsso ls us polyhyl ε =.5 as h lcc mum. Assum lbl losss. a F h sac of spaao fo a 3Ω o- l h h aus of h couc s s.6mm; a b f h aus of h ou couco fo a 75Ω coaxal l h h aus of h c couco s.6mm. D ol. o- l: h a=.6mm ε=.5ε h D a a D h 7 a 4 3 D 5. 5mm oaxal l: a=.6mm b l l b a a 75 b l a b=3.9mm

6 Paalll pla asmsso l: x y xh x H y y A y= a y= x = y = H y = A y= y a sl sl y sl sl H J J H y D y A y= y a x su su y su su H J J H y D y H x y H x y y H y ] [ m H J J su su H y x H y x x x H ] [ m F y y v p ossy paalll pla asmsso l: ufac mpac: c c s s c x s s f X H J J J P s s su s su m f c c s

7 . os a asmsso l ma of o paalll bass sps σ c =.6 7 m of h mm a spaa by a lossy lcc slab μ=μ ε =3 σ= -3 m of hckss.5mm. h opa fqucy s 5MH. a alcula h a p u lh. b F γ a. f 3 ol. a. m 8 m c 7.57 H m. F m b γ= = ω=π 5 6 = =7..3. os losslss spl s fo a v chaacsc mpac. a Ho shoul h lcc hckss b cha fo a v pla h f h lcc cosa ε s oubl? b Ho shoul b cha fo a v f ε s oubl? c Ho shoul b cha fo a v ε f s oubl? ol. a c b Auao cosa of asmsso l: α= m-ava po loss a fsmal sac. P P h P s h [ ] uppos o flco * P [ ] P P P P P

8 Mcosp ls: a usually us h mm av a. c p ff p p f ff Assum h quas-m mo: as : h<.5 s lbl. v h W a ε oba as follos: Fo Wh : 6 ff h W l8.5 W h h ff Fo Wh : h W W.4 h ff W lw.444 h h h ff h W v h a ε oba W as follos: Fo Wh : W A 8h h A 6..3 h Fo Wh>: W B lb lb.6.39 h

9 377 as : h>.5. hs cas oba W ff fsly. W Fo Wh ff W h : l h h h W ff Fo Wh W 4W : l h h h A h subsu W ff o W h xpssos as. Assum o h quas-m mo: 377h Wff W f h W ff f W f p h cm W ff f ff f 8h f p 377h ff a W ff =.6+.9 ff f f H ff f f p h fqucy blo hch spso may b lc s v by f.3 h h h mus b xpss cm. Auao cosa: α=α +α c Fo a lcc h lo losss: Fo a lcc h hh losss: ff a B 7.3 cm ff ff B 4.34 ff cm Fo Wh : c 8.68 W s h s f Fo Wh : 8.68 sp c h h W ff h W ff 4W l W Fo s 8.68 <Wh : PQ c h h Wff P 4 h a Q h W ff h W ff h l h

10 Fo Wh : l 8.68 h W h W h W h W h W h Q ff ff ff ff ff s c. A hh-fqucy s ccu h mcosp ls.

11 5- Wav haacscs of F asmsso. ho ha h pu mpac s = ah ah. Poof =l l= l= ] [ ] [ h sh sh h ] [ ] [ ah ah = ah ah osslss cas α= γ=β = ahγl=aβl: = l l a a No: h hh-fqucy ccu h pu cu = : h valu h lo-fqucy cas. A h hh-fqucy s p o h lh l h chaacsc mpac h popaao cosa γ of h asmsso l a h loa mpac. Bu h lo-fqucy s oly p o a.

12 . A m losslss a-spac asmsso l hav a chaacsc mpac 5Ω s ma h a mpac 4+3Ω a a opa fqucy of MH. F h pu mpac. 4 ol m 3 v p a a 3. A asmsso l of chaacsc mpac 5Ω s o b mach o a loa =4+Ω houh a lh l of aoh asmsso l of chaacsc mpac. F h qu l a fo mach. ol. 4 a a.5. Pov ha a maxmum po s asf fom a vola souc h a al mpac o a loa mpac ov a losslss asmsso l h = * h s h mpac look o h loa l. Wha s h maxmum po asf ffccy? Poof Po ou [ *] [ X X ] Wh a X X Po ou Max * hs cas Po ou 4 P s [ *] Po P s ou

13 asmsso ls as ccu lms: ah os a al cas: = ah. Op-ccu mao : = o = cohγl. ho-ccu mao =: = s = ahγl = s γ= ah s 3. Qua-av sco a losslss cas l=λ4 βl=π: 4. Half-av sco a losslss cas l=λ βl=π:. h op-ccu a sho-ccu mpacs masu a h pu mals of a a-spac asmsso l 4m lo a 5-5 Ω a 36 Ω spcvly. a Dm α a β of h l. b Dm a. 5 ol. a ah b H m c pf m c. Masums o a.6m losslss coaxal cabl a kh sho a capacac of 54pF h h cabl s op-ccu a a ucac of.3μh h s sho-ccu. Dm a h lcc cosa of s sula mum ol. a 9 F m 5 H m.6.6 osslss =74.5Ω 4. 5

14 al xpssos fo a o h asmsso ls: Γ= =l- [ [ ] [ [ ] ] Fo a losslss l = [ ]. A MH ao h = a al ssac 5Ω s coc o a losslss 5Ω a l ha s 3.6m lo a ma a 5+5Ω loa. F a a a locao fom h ao b a h pu mals a a h loa c h vola sa-av ao o h l a h ava po lv o h loa. ] ol. 5 f 8 H m a m.4 a m 8 c a [ ] 5[.447 ].5 b c 3.6 5[.447 ] P av 5. W

15 . A susoal vola ao =sω a al mpac =5Ω s coc o a qua-av losslss l hav a chaacsc mpac =5Ω ha s ma a puly acv loa =5Ω. a Oba h vola a cu phaso xpssos a. b W h saaous vola a cu xpssos a. ol. a c 55. P 6.5 P av P b m[ ] 55[s ] m[ ].[s ]. A susoal vola ao h =. a al mpac = s coc o a losslss asmsso l hav a chaacsc mpac =5Ω. h l s l ms lo a s ma a loa ssac =5Ω. F a 錯誤! 尚未定義書籤 a ; b h sa-av ao o h l; a c h ava po lv o h loa. ol. a b c Pav [ *]. W

16 . os a losslss asmsso l of chaacsc mpac. A m-hamoc vola souc of a amplu a a al mpac = s coc o h pu mals of h l hch s ma h a loa mpac = +X. P c b h ava c po assoca h h av avl h + co. a F h xpsso fo P c ms of a. b F h xpsso fo h ava po P lv o h loa ms of a h flco coffc Γ. c xpss h ao P P c ms of h sa-av ao. ol. c c a 8 *] [ P c b } { ] [ ] * [ * * P } { 8 } { c 4 P P c

17 as Fo a pu ssv loa: = s s s s. Γ= = h = mach loa. Γ=- = h = sho-ccu 3. Γ= =- h = op-ccu & max m occus a max & m max occus a m f max 3... f f m max. h sa-av ao o a asmsso l s a asly masuabl qualy. ho ho h valu of a ma ssac o a losslss l of ko chaacsc mpac ca b m by masu. ol. f max occus a a m occus a. max m m max max m max o m. f m occus a a max occus a. m max max m. max max m m o

18 as Fo a losslss asmsso l a abay loa: m a m = m +l m =λ a F =?. m m. A θ Γ =β m -π s a mmum. 3. = +X =. os a losslss asmsso l. a Dm h l s chaacsc ssac so ha ll hav a mmum possbl sa-av ao fo a loa mpac 4+3Ω. b F hs mmum sa-av ao a h cospo vola flco coffc. c F h locao of h vola mmum as o h loa. ol [ 3 4 m ] m W o a losslss 5Ω ma l ma a uko loa mpac s 3. h sac b succssv mmum s cm. A h fs mmum s loca a 5cm fom h loa. Dm Γ l m a m. ol...4m m m m.5 5 m m.5 =.5m.5 m a a m m m

19 . A lossy asmsso l h chaacsc mpac s ma a abay loa mpac. a xpss h sa-av ao o h l ms of a. b F h mpac look oa h loa a h locao of a vola maxmum. c F h mpac look oa h loa a a locao of a vola mmum. ol. a b max max max max max max max c m m m m m m m 5-3 ouco o mh ha x x : -ccl x x : x-ccl

20 val sal pops of h -ccls:. h cs of all -ccls l o h Γ -axs.. h = ccl hav a uy aus a c a h o s h las. 3. h -ccls bcom possvly small as cass fom oa a h Γ = Γ = po fo op-ccu. 4. All -ccls pass houh h Γ = Γ = po. al pops of h x-ccls:. h cs of all x-ccls l o h Γ = l hos fo x> ucv acac l abov h Γ axs a hos fo x< capacv acac l blo h Γ axs.. h x= ccl bcoms h Γ axs. 3. h x-ccl bcoms possvly small as x cass fom oa a h Γ = Γ = po fo op-ccu. 4. All x-ccls pass houh h Γ = Γ = po. ummay. All Γ ccls a c a h o a h a vay ufomly fom o.. h al masu fom h posv al axs of h l a fom h o houh h po ps quals θ Γ. 3. h valu of h -ccl pass houh h sco of h Γ ccl a h posv-al axs quals h sa-av ao.

21 Applcao of mh ha losslss asmsso l: [ ] h kp Γ cosa a subac oa h clocks co a al 4 fom θ Γ. hs ll loca h po fo Γ φ hch m. cas avlh oa ao h clocks co A cha of half a avlh h l lh φ. A cha of. Us h mh cha o f h pu mpac of a sco of a 5Ω losslss asmsso l ha s. avlh lo a s ma a sho-ccu. ol. v 5.. h mh cha a h sc o of = a x= po o h xm lf of cha; s F.. Mov alo h pm of h cha by. avlhs oa ao a clocks co o P. A P a = a x. 75 o P sc. A losslss asmsso l of lh.434λ a chaacsc mpac Ω s ma a mpac 6+8Ω. F a h vola flco coffc b h sa-av ao c h pu mpac a h locao of a vola maxmum o h l. ol. a v l=.434λ =Ω =6+ 8. h mh cha a = =.6+.8 po P F.. Wh h c a h o a a ccl of aus OP.6. sc OP = 3. Da h sah l OP a x o P o h pphy. a. o avlhs oa ao scal. =.6. b h. 6 ccl scs h h posv-al axs OP oc a ==4.

22 c o f h pu mpac:. Mov P a. by a oal of.434 avlhs oa ao fs o.5 a h fuh o.54 o P 3.. Jo O a P 3 by a sah l hch scs h. 6 ccl a P a =.69 a x=. a P o fom P o P 3 h. 6 ccl scs h posv-al axs oc OP a P M h h vola s a maxmum. hus a vola maxmum appas a.5-. o.3 fom h loa.

23 Applcao of mh ha lossy asmsso l W ca o smply mov clos h Γ -ccl; auxlay calculao s cssay fo h -α faco.. h pu mpac of a sho-ccu lossy asmsso l of lh m a chaacsc mpac 75Ω appoxmaly al s 45+5Ω. a F α a β of h l. b Dm h pu mpac f h sho-ccu s plac by a loa mpac = Ω. ol. a h cha as P F. Da a sah l fom h o O houh P o P. Masu OP OP. 89 l l.4.9 Np m.89 4 co ha h ac P sc P s. avlhs oa ao a m. 4 b o f h pu mpac fo: o h mh cha as P.. Da a sah l fom O houh P o P h h avlhs oa ao a s Da a ccl c a O h aus OP. 4. Mov P alo h pm by. avlhs oa ao o P 3 a.364+.=.564 o Jo P 3 a O by a sah l sc h ccl a P Mak o l OP3 a po P such ha OP 3 OP A P a

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25 5-4 asmsso-l mpac Mach mpac mach by λ4-asfom: =. A sal ao s o f qual po houh a losslss a asmsso l of chaacsc mpac 5Ω o o spaa ssv loas 64Ω a 5Ω. Qua-av asfoms a us o mach h loas o h 5Ω l. a Dm h qu chaacsc mpacs of h qua-av ls. b F h sa-av aos o h mach l scos. ol. a b Mach sco No. : Mach sco No. :

26 Applcao of mh ha oba amac: Y h y Y Y Y Y y b Y y. F h pu amac of a op-ccu l of chaacsc mpac 3Ω a lh.4λ. ol.. Fo a op-ccu l sa fom h po P oc o h xm h of h mpac mh cha a.5 F.. Mov alo h pm of h cha by.4 avlhs oa ao o P 3 a Da a sah l fom P 3 houh O sc a P 3 o h oppos s. 4. a a P 3 : y. 6 Y.6. 87m. 3

27 Applcao of mh ha sl-sub mach: Y Y B Y Y y B y h y B = Y B y s = Y s +b s = y B y s =-b s a l B s qu o cacl h maay pa. Us h mh cha as a amac cha poc as y follos fo sl-sub mach:. h po ps h omal loa amac.. Da h Γ -ccl fo y hch ll sc h = ccl a o pos. A hs pos y B =+b B a y B =+b B. Boh a possbl soluos. 3. Dm loa-sco lhs a fom h als b h po ps y a h pos ps y B a y B. Dm sub lh l B a l B fom h als b h sho-ccu po o h xm h of h cha o h pos ps b B a b B spcvly.. l-ub Mach:

28 . A 5Ω asmsso l s coc o a loa mpac = Ω. F h poso a lh of a sho-ccu sub qu o mach h l. ol. v o h mh cha as P. Da a ccl c a O h aus OP.. Da a sah l fom houh O o P o h pm sc h P ccl a P hch pss y. No.9 a P o h avlhs oa ao scal. 3. o pos of sco of h ccl h h = ccl. P 3 : yb. bb A. A : 4. oluos fo h poso of h subs: Fo P f om P 3 o P 3 : Fo P 4 fom P o P 4 : Fo P 3 fom P sc o P 3 hch pss b B. : B Fo P4 fom Psc o P" 4 hch pss b B. : B P4 yb. bb ;

29 5-5 ouco o -paams -paams: fo aaly h hh-fqucy ccus. Df x x x x x x b a b l al a b l al al b l h a l b l a l b l a l al b l b l a l a a l. a l a l l l a l l b a N -paams oba by shf fc plas: b l b a l a b l b a l a b b a a h = a =

30 -paams: l b l a h l a l b a