T ansmission Line Theory Smith Chart
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1 Tranmiion Thory Smih har
2 Tranmiion Thory Wir conncion Anao / Diia circui: No voa rop on wir conncion Tranmiion Microwav circui: wav on ranmiion Fi anayi: E H EM wav
3 Tranmiion Thory Fiur. p. 5 oa an currn fiion an quivan circui for an crmna nh of ranmiion. a oa an currn fiion. b ump-mn quivan circui. ri rianc pr uni nh for boh conucor /m. ri ucanc pr uni nh for boh conucor H/m. G hun conucanc pr uni nh S/m hun capacianc pr uni nh F/m 3
4 Tranmiion Thory a o o y a voa aw : From Kirchhoff' v i i v From Kirchhoff' currn aw :.a v i v :.b. i v v G i.a : i i v.b v G v i / raphr quaion im - oma ranmiion quaion 4
5 Tranmiion Thory a o o y h phaor form : ay a coniion For h uoia.6a Trav wav ouion :.3a o.6a : Appy.3a.6b..3b. G : an quaion for Wav pp y.4a : an Wav quaion for 7 characriic impanc.4b..7 G h compx propaaion conan i.5 whr G 5
6 Tranmiion Thory Th v voa wavform h im oma : co co wavnh on h :. h pha vociy: v p f f..9 Th o : G.a.b Th characriic impanc :.3 Th nra ouion : v p.4a..4b. 6
7 Fi Anayi ayof Tranmiion o Fiur. p. 53 Fi on an arbirary TEM ranmiion. Th im - avra or manic nry : Wm H H 4 S an circui hory iv : W m 4 S H H H/m.7 Simiary for or cric nry : 4 W E E S an circui i ihory iv i : W S 4 E E F/m.8 7
8 Fi Anayi ayof Tranmiion o owr o of h conucor : c H H aum H i annia o S an circui hory iv : c H H /m.9 whr owr o of h oy icric: E E S an circui hory iv : G G S E E S/m. 8
9 Fi Anayi of Tranmiion ayo a o Tab. Tranmiion aramr for Som ommon OAX TWO-WE AAE ATE a a D w b a D D b w w a D a b coh n a D a b coh n w a D a b G w a b a coh n 9 a D a b coh n
10 Trma o Tranmiion a o a o Fiur.4 p. 58 A ranmiion rma a oa impanc. moifi f.34a voa/currn on h : oa Th.34b.. w mu hav A
11 Trma o Tranmiion a o a o.35 : oa rfcion coffic.35 : oa rfcion coffic voa/currn on h : oa Th.35 im - avra powr fow aon h : Th.35.36b..36a m av A A A f i N an wav mach No rfcion :.
12 Trma o Tranmiion ncin owr : maniu of h voa on h : fc owr : r Tranmi owr : r Whn h oa i mimach no a of avaiab powr i ivr o h oa f h rurn o B a : B o B. B max m voa SW / SW can b f a SW an wav raio max m
13 Trma o Tranmiion Th pu impanc n owar h oa a : nrai rfcion coffic : h pu impanc n owar h oa a :.43 ranmii on co co an.44 an impanc quaion 3
14 Trma o Tranmiion Spcia ca: hor rma Fiur.5 p. 6 A ranmiion rma a hor circui. Th oa voa/currn on h : Th pu impanc :.45a co..45b an. Fiur.6 p. 6 a oa b currn an c impanc = or variaion aon a hor-circui ranmiion. 4
15 Trma o Tranmiion Spcia ca: opn rma Fiur.7 p. 6 A ranmiion rma an opn circui. Th oa voa/currn on h : Th pu impanc : co.46a..45b co. Fiur.8 p. 6 a oa b currn an c impanc = or variaion aon an opn-circui ranmiion. 5
16 Trma o Tranmiion f n / n. 3 :..47 f / 4 n / n 3 : quarr wav.48 ranformr Th oa fiy on : T irion o :..49.5a T ot B...5.5b Fiur.9 p. 63 fcion an ranmiion a h uncion of wo ranmiion wih iffrn characriic impanc. 6
17 Smih har Fiur. p. 65 Th Smih char. 7
18 Smih har Th Smih char : Th o wih a oa a poar po of maniu : raiu whr. o o an : 8 8 rfcion coffic Expr an imaary par : normai impanc amianc normai impanc : r r r i x x rm of r r i i. ra an : 8
19 Smih har r i r r i i x r i rarran.55 : r r r r.55a.55b i i x r x. onan rianc r circ x 3 r ONSTANT ESSTANE NES N THE =r +x ANE +x i 3 x onan racanc x circ x 3 - r -3 ONSTANT EATANE NES N THE =rr +x ANE +x x x ANE i - ANE 3-3 r r 9
20 Smih har Th conan r an h conan x oci form wo famii of orhoona circ h char. Th conan r an conan x circ a pa hrouh h po r = i =. Th uppr haf of h iaram rprn +x. Th owr haf of h iaram rprn x. For amianc h conan r circ bcom conan circ an h conan x circ bcom conan ucpanc b circ. ThianconcarounhSmih aroun h char i on-haf wavnh /
21 Smih har -Examp oca Smih har wih foow normai impanc. =+. = = = = 6. 6 = 7. 7 =
22 Smih har -Examp oa impanc: f? ouion : SW B WTG:.6.3 : Fiur. p. 67 Smih char for Examp..
23 Smih har v Y /4 on ranmiion i : / normai amianc Smih char Y Smih char Y Smih char 3
24 Y Smih char 4
25 Smih har -Examp /4 on ranmiion : / normai amianc oa impanc: f Y? ouion : y.4. y Y y Y S WTG:.4.5 :.364 y.6.66 y Y yy..3 S 5
26 So.cm.cm cm 4.cm.7cm.7cm 4.7cm Fiur.3 An X-ban wavui o. mima ii rpa vry / 4 cm m cm.37 SW -.5. SW o o 6
27 Th Quarr-Wav Tranformr Fiur.6 p. 73 Th quarr-wav mach ranformr. an an f a / Fiur.8 p. 75 Muip rfcion anayi of h quarr-wav ranformr. 7
28 Th Quarr-Wav Tranformr Examp.5 onir a oa rianc = o b mach o a 5 wih a quarr-wav ranformr. F h characriic impanc of h mach cion an po h maniu of h rfcion coffic vru normai frquncy f / f whr f i h frquncy a which h i / 4 on. Souion: f f vp 4 v p 4 f f an an Fiur.7 p. 74 fcion coffic vru normai frquncy for h quarr-wav ranformr of Examp.5. 8
29 Gnraor an oa Mimach Fiur.9 p. 77 Tranmiion circui for mimach oa an nraor. Th powr ivr o h oa : X X oa Mach o : X Gnraor Mach o oa : 4 X 9
30 Gnraor an oa Mimach onua Mach : fix o maximi X X X X X X X or max X 4 maxmum avaiab powr from h nraor 3
31 oy Tranmiion oy a o G G : Diorion Th G Th ow - o : conan G v p / conan G G 3
32 oy Tranmiion oy a o Fiur p 8 A oy ranmiion Fiur. p. 8 A oy ranmiion rma h impanc. Trma oy : Th o Th rurbaion Mho for anh anh 3
33 oy Tranmiion oy a o W/m ucanc u Th Whr ncrmna H W/m H H 4 c α α c urfac: conucor rouhn of v p c.4 an conucor urfac: rouhn of α c α c α c p c c 33
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Tranmiion in Thory Dr. M.A.Moawa nroducion: n an cronic ym h divry of powr rquir h conncion of wo wir bwn h ourc and h oad. A ow frqunci powr i conidrd o b divrd o h oad hrough h wir. n h microwav frquncy
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