Transmission Line Theory - Notes

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    Q)4f,9; 2D " t->A 2oos,

    ( t t t tJ- ; c ) t , 11 .r O( | Llla: .'r

    A:l- --Jf[r: t(/ '+ 2t

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    q&- Lar )/e.Z A/te,- -a-.U ,/"#"qJt(P." L" xr-t

    'oo- r-1/tZ)o * a.q.neJ.'c-

    I atn e- t4 a^/t, m-t er^,A,ten koq nTzt t, ^ JDc.-.2ez " /4 aLl.mLne

    i, LJa-c-' *noTc,- l-n $ e-a ?fa.;ez/ec 6l.elz&ic-, 1 f LA,/r1e- ^-)a^,/ (, aLe,[p-c-tt / c- .

    0 f n,b'n, Theoy e*n ve,-"4t )1'2'L 4 /l =-r.{4C b 'r t

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    9a. ag " Zaog

    , /p,= PAot- Veloc.= Z\ tb ' , - /sect " , - vc-l"a:L .{ It

    vr ' ve'ID o ' -t laLlz y - |,4, ,l-Q,t4CJ-X t C- :

    ,btt. eo aa/.o-,t :v'E. = - k'L

    o,rA,zr ,'

    ?oA-t c,na-t,t-t 4,nc>eu?,bllrL ,-0.

    -6uz eau o,L"- "b4 (-a4e *W L.e

    ^/-r,t

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    = (e,Likl =

    = -n \ 1K 2 \t/ \FlJnn e-

    A , - - l it, - L.b t T o,.n I e,4,Le,'f\t V -a-I'h a,4e, UQ,U) A /9 r

    l ^ - L4 | ce: a/ae:a Le'ot -uJ",'n)itr) 4os3j ol,e-lealrfc z 'ndt y'4eote-n

    a't ,(ogSz A{',eQtl,rfa, .

    t t J A /1 , t /J 4_ 7- .{'-ro""t V6/tt'*t'u AExH).J< (^'^A

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    . Q- .Fs_ cf_ = kr x Ll-a

    Qt p,-0

    Ttr(./YT

    Nafra/n-L

    = I 2(^)t-QA-_0

    = -L Ru

    b, -Qahti,tz'

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    'Dat.e: ' .

    , \ i : . . l / , ;

    I r :

    ' . . r l .

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    ,ra/n Ly

    Qr1 btlL 4ti6ve, +tui L> 9lzt u.a, qT"to u'iy e 0L'0.t- 4L t- L> Qq,"-aite, L, Grd*nJ 'I urt 3l,Ld. PcLLf L2e; Yc"lo'/ Dq Ly $Pzrc

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    Aatu:

    Ib l rd^r t ioD ol x s, ; rvc: l ) J j : rcrr .h) circ l I r , rLnd c) cI ip l ic i , t .

    -)

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    C -oatJr",I;"n u Pokr;":t,,-

    +

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    tbilD'P,P,p,n.F,F,til{t.tt{tililil#4)oDfi(>d>bi)i,bbbDf>Db

    ^/ l \l;,r Fj\ - //-->(1;:)

    :i: -t:,.iifl,\ i t . /

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    t , ,

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    ' 1 . : , . , . . l ', ' ia t t / i , . , , .

    1 , t l ' " , ' . t ii l: i , . . , . i : ' - t t . t i

    'i"l' ' -"" "/ . . : , L , ' , :

    _ - :i _i llr

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    : ' r . j / '

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    i . r- ;' . . .

    l t ) \

    t l- ' - 1 1I

    t . ' .

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    , ) t L l i :

    .&-.:

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    ra i . - /a)

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    i , ) iL l, . t t l , ' t ' i t : . " t ) ) t .a ' :

    , . l i Ii I

    r l l . l

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    , , 1 . ) , r t / t , ;, ' . . 1 . 1 . / ) ' , .

    1 , . l l i , t . yi . , i t i , /

    ' . , . , , 1 a. l '

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    ' , t ) . (

    I '. ./ t , ' .

    l t li ; / ' , ,t . , ' 1 , , .' I

    ' i : .

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    1 1 . : . : : .

    i : . , r . i.

    t , / , , r . . , t , r

    i il t . . i

    : ,

    I

    ' i . t : " .

    i ' . , 1 :

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    a^te: 03,aq 2po8-t t+ " -;-fLW =p,

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    . , . . t ) .

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    LJn t :

    i l ) ' , :

    l

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    l r

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    | . i . t '{ a

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    - ;a , l i r ' , ' : . t . , r i \ ' ^ l l , i ' , / t : ^ ' i

    {-'

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    i

    lA r r / i

    . i l . 2 . ) ' i : (

    i-\.

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    f i

    " ' / - 1 " ", t . , , . 1 i / | j. L i \ , , I

    y ' . ' .1 , ,. . . . / i

    r . i

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    ltI K t,'' rtl.' ( | /,t.r- c: I ^i =_ _ r - _ : = ,I / l / r l r

    i , . . , , i ' , . ,' , / , , , ,

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    i t , ,

    i \

    . -_,_:-/ rP3 AF / PanLs'4 ss 16\1 L,n, eS

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    1oma,zag4,64t - P"n^.11 /- - L^'np-9t,;rl./e,)

    4'ro1* l,'n.lied neo,uunLy, i." 7-'

    ^tt,T : s . .ae c,nLeS _ tJe u-n'Al

    eJ .y4o-/e- /LororoL,b //-&,/- /X - Lrx tS lTao- 115;ru2, Line t

    '*r/l o - u,t)re /ine-t,\l' ie y'6al ne ntt,( aXr.

    J z l . *ce 'htg"la(J SAecers 1Ax -trh. ur,LO .v'LDJ L

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    ParaUeL Tao - irtve L,re Aate: oq.pq " qobgS*r4 Lnz,a " cr-/ /zl eq-va*'h Lnzd i./44"/ u.led o'J tL

    4/u;a- trt M@Am A'n'rLA- 01' /17' Jn aJ,ta..f.e o/ l,z.e )'n or'A c.L c od^rtar-( o/ #iirt;,moi.ce/ k) 'sca 4 4 ,>/ la r&sh?14; 'ao/' ,r-il,on ' ku e,a a, e'oldt rnp)fuol 6, cLanqn167 -/u:o- u:y'?- i h l tM, .b4be Ane-:*

    /V a/,1,(Ln,4q-ovlAe cl a7 eere t/t'rl -1, rn 4. -i V

    Se,L. -l 't /tT1e ,t4 e ll ?nL,ca-(ty J a/','r 'C A?a - c't)z e 'n4, e7L "P,oi7 unifn",t9Aaa'ns aaure,cl Av L-^A"Ui

    o ^, e-aA, {nota-, ;n1a tareJ atr o e.--4e 4.6Jf \ J nLa) 1'1 "4' t)

    'ol,ve hle."tz- -f ie-bJ^,,7l v tul /rtn

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    q)afu: (9 "09 2obg2- I "a sT.l /ai t "

    r ./1a.4'n

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    (DAte: M.o1- lpaLV- bn'nd z{ oclvp,,.troo../ tilAZJ bd, toil"X c.-iJ," a4'rt ,/*o / A-/o-i/]/ uq,ournd i - -'nu 1-,/*citam c,e- .er" utiz.e,.t\' /^ u".,',/o'rm /4 nrtl or1 fr-rU "l U-- lal",balon/t;t cl"- /Lo ' .1- aT- ,-t .o '{6-zn '/ha c- .zg o/q,0,.- J. -,1 th elJ 1Pa7 // 2"r-ro*-dl nI;(/aA,tq /42,, e^V'y- r , - r2' ; -^ / -^lt r Q L.{1 //'7Q, 62 a) al

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    t +t,ne// Lb't t{uaIa.y ,t4 L "1c&"/ Jza.'n L,A7'4uqduc6r ; . ,tu,l txlr.t ( or'tr m ,Aur.dt-)n &fr'a,Lz . Jf A CC.'/>/ CL.r -o/ / t ,ex b, l-t t r?nu/ o-, (pn,4-Aal qooJ *,a,y'ati

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    cl,; o/ z,eid .L'n"i [""'.t o. in, lln iz 1/_ a-al, af-04)u br7';e ,,elJ )n cr

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    r/1e- (, "(za /Aatn t 'Dul ,"-ilu.4e, .,1/^l-'.n,' z,atc'e.?li e di :t"t a tA e.Ll.x /r .:/44e- /-.4af, l '7v1A/J(A.r-'r,2,,114 '":t

    u-&betr ,raul-f"rt ^ h J I 'T O L Y E I H ' T L N I'4, hmz laz Tc- ern re# la ce,e- &,t,t ert /na,/alrh,,"LrC, /" a- to/i/ / t l P l ^ h - - al/p,%'8&, /274- 7tyh9e a, /e4' a ) LL,t L.t) et A'71 ecLLat b UAXL AL"

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    g, i-*r-

    1

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    i

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    -t/\sLl c-9

    Aatu:

    L

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    l *I

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    ljAfie:-lq'EJaQs ' "

    /-yk\ Pe- u.4 e-eo^"-Xb"rt,U Iq,rr-t "/ a- )"{Ze-n u.a,i,/mo'aln-L,'nu/ i"z Z-,-/.k-n or'.n /) , u- : _t P i. t-tz e^E I r c?14?'t )

    So,'.tee-E-dL

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    Aafu: to-o3-apPAti(r,1-) - -Gv(: )? v+ ({ooJ"- )

    J, + 2:.4/a.oh- o{ e, @ ;,n Du,4-t su /42 I a,(t o / atav1 .>z Di ral/age ,, 4 .Lsto.-.e a/,-,4 /,'nn/ oll*t'/ ko,nt D').1 l|nu zs / 3,'*- "/1 0"e o (/4ptn / ra co..l--V 67- V6"-.l a",*u, l J o,z'nq y'/",oueA &|t;iXtrW-.: 9e-,r,cz I zoats1fa.-re /o/ &'n, ,b b,oy'*I,-ol- fi r"trt"ni*neo"z raU"e, "l /1n.' ai.-;l= ".t z4ot l-a'rTr*{"r tt;rl/ ZA" a42,?'.: ao-*lrnun/' o*-cc-( 1, 'A n e Lazt )a9i /)-,le ct^zto,-zl /h,u,r? /fu"oLp4 J,4-/,,YJrJr. ?eft'e4 ),/"cla.Ace /",/ l.'^nc / N h"hnZ,r.J- '1," Vi"rle ,ok "l Ua.,"qe "/ il'{*nto-- ,ol",e o,/ /r,',el st r(,,-/,/dl /,AAI U"t""/a" h.'-rt I- / , .- g t:4^1-""7;ott ol en(q) ^ ^arr/os,o?" "/ "/r,,- "z o au-rerttr 6,)/[ 6111^-ru nla,re / -U / clu /L7- a.ot4 hotnt o'4 ,Lirld- ).., 3",-z o/ laa- U uJrl"-J,oll* ,'1,,,[1)[)27 fire- - 2nn{t U

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    , , _e M Ca(p

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    RC v(xi) ?v(x,tecl'v (F,t

    K,+) = LC-DLI

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    Q46s; lo - o9 - 2tb&.1 -/rLJ. eq z7 a24C, 2 -'" D, a&/"c+2..,t7- c'+t.knzzrrn ltLe1'AJA)r R. , G c;-J crt aam9

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    '/' :- I ' " I r . ,

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    e fal. e^act ilz,ivoluon u

    '-K+i".r) I (*)'v(z) -(K+i'ui-

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    t t

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    a tar I

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    .Jl,r/.c: '

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    (Date: to" o'7 z.abgyrc'3(rDt-pZ+

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    ar^z r---t- o ---+ oZ>z

    the, 'e a crclJ - / J7a,L ,4t*u4/ v -la,/re'n V. + n -,.lceZn 2-a{,^) 'n9 KCL a.tot-o/ in n uolr- -T"

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    .,,- '^714a\s e l e c I

    vs = -(K+inL

    J(, ,d7 + l ,P26

    AIs = _( C, t,ac

    ., AJ. _ JL

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    --n-+'tuC, v\ _0) I 'A Lt o).15 -

    2"4 Or/e", Knzb-"sil;,tt : \7- (v / at , ^u/e ,'u//e4 on h 6LtL ,.+ of- *nT /4

    {s

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    t

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    . )r.tit::

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    ;.7 ', &r"r,1 ,,li //,.r'Jl,rL c z, ,;1u:,.t ;n- t,-'AL,,' t

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    V"(*) = vo--J

    1+o 4 -tn / l , .ArorV&d o..--- ,= -.\ r l ^ ) ' a l / ^) = V"+ (, -1- v:

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    ,1, , ri . '

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    &,.t ,-)YZL// /-s

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    ( ,nrn LeL": 'RrL E o 'R

    Lz

    K, = {u t,t ta,- r,e- o/ .[- h pire.K- -- ' '4 lolf' -n ^ " eL. . I- /u"t"- "2. o/ t; b usi e, -) L^ -, o "' Ao z.o,n ; , noc, I tzm ,:y l,/"u at: re-

    Lo- t/L

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    n, / ) .f n&J' / /k 11 )4 L '4 tC OlN C,,:JZ

    , . \

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    , : '; i ,'"

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    ..i.),: t .-\"l ./ I -tl "fo Po';411'6'1 ,/ nc1Ir.^,u

    (-,, t t1 . 't -. ' h r l : , tL Ct1: , rg t tcrz l- ( - /ekuh ftat'o7,ifro,t__/ /.-_X

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    c,h av //z"A qaT -. YcAy t,'v-.v, (JE;

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    , ' .)r i r' l

    : , , ' \

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    Vi -t \,r - V; _ Vy

    z

    L+

    3,,-,'/^.i,R +o = I,

    I iK"- -1 o < |RHrl-

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    ,Dit t :

    i f i i ' i ' ' ,1, : t , 'l

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    atry t -

    Lta+e 9nR (veuR) ,s tz',tzvc I.n .n'u n -- l \1

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    , -ra'"#_4 ldK: (M/,,o/ue

    +l < \JswK ( .t-,

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    AAfu: le.aq ?cogf) - ?.^'

    As =-l;-(- ( ;

    Lne./ /4\ ,4 TeJa,na'a,l- U- '" &f "J a-r a l, t.,z ,.ee4 4-/k n ALNZT{ .t | .16, ) "nf o.fancu ).e. ,n;t eI oZ.,no". ),,- *lr^^-Le,

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    =?,

    u 1a.,, te,at',i 116,

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    :

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    ( / t t )_ t lv) t Ce h.'n r tn Cl , l , 4 /".be .r'u I T4anotu ^r.

    "r , " lr nr /(-Q-L LA A "7"a( In -14 a?,"tt";l-z.l /Y ;c*l /r,.

    L"l;fca.L Ln-,of/. = lUtal:EtLDatto L"- +lt-,[ o;t;., - J-"J t^x - - j #aal.in*'ot nnH

    a"r- e

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    IL ) = V7 .o+ \ las 7" 641 z+ t"l8, -"t.i.J L-" l A d

    7, e4vsL'J< = /-{-I , F)9e et -vcDK = 7L_ 2oo^L:7 6b

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    n?.- /e-c/1a;grualn lrt- l,r,.z y'6n" o.,. ,X*o '%/.l o,Q"o, t'- -o-n L- q/+ 7-,r,- r ula--, ",,t

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    OLt

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    t t I 'I .v - l t - , ' ) '" . t :

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    I l , r i "

    4/ - - tVa,tic'-.ti tn / I*,Ir.l.-r"" oknq fir, ,

    i ..:

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    . : : . . i / : :

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    u - L z DAe," ' {, " it aben or ar;t ..1A K;n ^ V" zL

    D ,-- X = L t'L +J Ft Lo'.j c 'f. Line,la .+ l a , tc - .pL

    - V- = K . {' . "/Zi +I ?t"-g2. It+ J *t^-0

    "t K' -- .' '7',

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    . NAo'n '2,' it Stort- a;"c,rlt".(,= D *nJ a.-" 'r4u" at--e

    ) {- = 7" 7,rJ /^to--G - y'. ^ o+.fu "."9o , 7' ta*' &

    % t-t Av CL4 L 7;.

    {)- = i {.-tca-',O, \ JA"ot-J,i---vJ-

    3: ltAw 2,' ;t 7^ L;nu /-,"-AA -'t.L" t ah tZ lt+ i z"t*"lt z.

    L-,;t4 ^ ,L= ^/: Ar cj - 1St- 4 2i'n = F^+i3"+^-f (7) -, {;,= 7.* r7'z

    Vo.u i, ,^ oU^.ol '>J,et )t t nnoTzLa/;-nAl/"^cu ,\ e.,-Abn et 6), (-

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    -Q z t"sXan '2,' k l;ne, 1"-t-L^/t,- |

    0. eF - - ti/^\ "> s--?

    = ''',t l* .nu qr^l[r;",

    e4 o4.Ltr )onbeJa,- ct";n

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    Diiit:f /I I l l r rt 1 P t t t t / / - - 1 "X - - l t11P Tr f f U U)- t l 6n l 1 - ' i l

    ,i, BatunL

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    ' :. t.i .t::( i i ) / /)"t ?L- .u.r) ?,, a.t a, J,lle* t

    ( i;; Sl"tl,,l o{-.:,nou

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    r. iu) (..70R)

    , . / . \

    -; t)/ (me - L/1ma/'r7

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    . , ' i i J i ' :

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    j i i i f t : :T t - L lI .r. hal La.n I._:_ / -/u ' ' 'n ,1.. ;