hw3_solution - 2-8. Cascaded transmission lines. The...

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Unformatted text preview: 2-8. Cascaded transmission lines. The reflection coefficients are 1" = 0{sinoe Ra = 50(1), Zoz—Zm =75—502w‘2 r” = 4‘“ = 303 +201 75+so and 11 = +1 (since R; = on} respectively. The bounce diagram and the sketches- of‘voltages $26) and $1.6} are as shown. {1:0 1'21=—l"l1=-0.1 ["La-H “FLU! MW 1030 “FEESV Ins l'lS fir,=o.5v “ 1 2n: Van] .III3\Ir 1003 311.9 TEEN“? 0.0] 92V 4115 Fig. 2.14. Figlme [or Problem 2-8. (a) Bounce diagram for me cascaded lines. (WV, and “FL versus t. 3-1. Rab-lath: load. {a} The lead reflection coeffieiem is given by _zL—3.:._ l5fl—5EI_ 1' _ _—---_ " gag“ 1so+5u I15 SineeV+=1ME we have 1"1mm 2 +13) = l = V Fm =fot1—p}=1—n.5 =05 v fin—fl- Im— 3” m cm A. _ _vmin_u.5v_ 1m- 2” _m_nm A [by The sketch ut‘ Wtle and [Infill 1versus z are as slime. hflflum Zn-fim %Z._—flL—J sun Ill-“I'M”le Will “(all . |.5"-"{|:|.'53A} new [n.nu; "mm 1:: Hi LEI 5 Fig. 3.1. FigumfiJerhlan 3—2. Shawn of |1.-"'{z}| and |flzJ| nusus z. 34 Capacitive termination. in]: The luau] reflection cocfficient is given by 40' 50 — IL'HJ' -- 5U 50 Ill-3.1 _-iMD'P - :- ZL ZU- _'{ 3 J _ .7 I: N 0,525611195 n = ENE _ {40—3'50]+1|]U _ 140—ij} 2143.?6‘i'9-‘55‘ _ 'l‘huel'nre. the standing wave min 5' can be calminth as l+p l+E|L525 3=—"_-' -—-—-n-- 23.2] l—p 1—0.525 {b} Using 1f: + flaunt-m = —1r where y; : —11I.'?I_.‘i° 2 —2_lfl rad, th: voltage minimum position can be; fund as. 2.32mi" I: —1'r + 1.11] "_v —l.[!|3fl —I 2m : —|.'].EIESIIJI._ The first voltage maximmn position is then given by arm; = t"... — 0.15); 2 —[}.33~3i. (c3111: sketch of |'|."'I:r)| man: 23'}. with V" = I V is as shown. zn=mun 2540453: ‘5'“- I I: am 0.5 Fig. 3.1 Figure for thlm 3-11. 3-5. Input impedance. For an air Iim flu: wavdmgfll at 1.5 GHQ. i5 ---—- — 2o: (LSXIIJ‘jl-Iflz m Sinai: flit: longlh oi‘ lite lint: Irt‘itu Uh: capatiimlu the: load is if: = 5 cm = lla'l'i, II'H: lint: impcdancn: 55511 from tho capacitor is gim by , _ t_§&_loo1_ fib—at-a-oo'm The inmadanoo of the 2. I2 pF oapanitor at 1.5 GE: is 1_ -i 3 = :- - 'fiflfl '3 jwt‘: arc-moi:1o=':-:2.122»c1t1""i 5' {a} Combining tho impodonos of tho capacitor 1Iii-"iii: the- line impodanco at that position. we have _ {mi—550} _ {—jSDH1+_:'} i . 3°“3*"5“'3“‘ su—isn ‘m'fl'fim Simon mo othar half oftho iino is also M4 in leagm. the input importance of the line is tomato": Sivan 11:.r 3% 1001 40ou+jj 43m = — _ fit. 3 3 .‘i [In] Combining do»: impedancu to! "It: capacitor with ill: lint: impodm at that Position. wt: lulu: i 3.1] = Zfi-EH 3r} =S‘U-j50fl Thumlom. the input impedance: oflho line is E'.‘2 MINI]z z- =—°=—=Iou1--'t‘t .u Zn mflfl t Ii} 3-1“. Initiative termination {a} The load tofloctbun conflicitmt is n m” = 31. at. = {1oo+3'soo'§}—_so a glowing? - zL+zn {Jut:+j5tfly'fi}+50 l50+jfiflofi _1+iv’§ _t1+ixr"§}t3 main _ Maw? _3+jv’3_ (331+twfil - u '111: mmponding sanding wow: ratio can: lac found [ts w oswam’ _ l-t-p W I+D.STT S_l—p_I-C|.5TT : 3.13 {b} Using it + Him = [I whom. a:- = it)“ = «#6 rad and A = lfll om. we find the. closest voltogc maximum position as w." Hi ——i :—D--1]Tom 311m: = — Eli .. -1{2?Trr}'} 24 {a} Not: that the current mimum position ammsptmds to the. voltage minimum position. 5o, using all + 253m = —7r, we find llu: closmt Ming: minimum position as Not: that 3m." could also have bee-n found from Emu as Lenin = 3m M4 '2 BAIT — 2.5 = —2.E|2 cm. 3-3. Mint-wave filter. Since Hag coaxial] Jim: is air-fillmfl1 .1 = CH = :3 x In“ m-s" MES GI-lzJ=12 cm. {5] Th: input impcdnncl: mi :9 shm-clrcuined lransmissjnn lime is given by 3'“ = 3535 tanth = 313m 2. —- mm=(fjamzt.2smd —. Ewan“: (h) Th: input impudm'c, of an DPEn-uircuitcd Jim: 1': givcn by 3n: = —_'JZ[| entailing? =523-lfl 21! —r .51.“: I}. Em22.33rfld —: E¢¢=5.4r.:|:n Nola U131! :11: diffcrcnm tact-mom the two lengths is in — If“: = 541 — 2.4 = 3cm = M4. as mpucled. ...
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This note was uploaded on 11/16/2010 for the course ECE 305 taught by Professor Staff during the Summer '08 term at Michigan State University.

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hw3_solution - 2-8. Cascaded transmission lines. The...

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