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8/13/2019 Transmission Line Theory - Notes
1/91
8/13/2019 Transmission Line Theory - Notes
2/91
8/13/2019 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
8/13/2019 Transmission Line Theory - Notes
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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
8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
6/91
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
8/13/2019 Transmission Line Theory - Notes
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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
8/13/2019 Transmission Line Theory - Notes
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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'
8/13/2019 Transmission Line Theory - Notes
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'Dat.e: ' .
, \ i : . . l / , ;
I r :
' . . r l .
8/13/2019 Transmission Line Theory - Notes
10/91
,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
8/13/2019 Transmission Line Theory - Notes
11/91
8/13/2019 Transmission Line Theory - Notes
12/91
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 .
-)
8/13/2019 Transmission Line Theory - Notes
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C -oatJr",I;"n u Pokr;":t,,-
+
8/13/2019 Transmission Line Theory - Notes
14/91
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 , ,
8/13/2019 Transmission Line Theory - Notes
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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
8/13/2019 Transmission Line Theory - Notes
17/91
: ' r . j / '
8/13/2019 Transmission Line Theory - Notes
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i . r- ;' . . .
l t ) \
t l- ' - 1 1I
t . ' .
8/13/2019 Transmission Line Theory - Notes
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, ) t L l i :
.&-.:
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ra i . - /a)
8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
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i , ) iL l, . t t l , ' t ' i t : . " t ) ) t .a ' :
, . l i Ii I
r l l . l
8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
24/91
, , 1 . ) , r t / t , ;, ' . . 1 . 1 . / ) ' , .
1 , . l l i , t . yi . , i t i , /
' . , . , , 1 a. l '
i , ' :( ) : I t . i 1 ) 1 / - . I i',.,, :. t)a 1 i: I r,a
, , . t , , , : , , . 1 , ' , ,, , ' . ' , , 1 r . , 1 , r
t . t l / t t t . ,, ,1/:[ ' , l
' , t ) . (
I '. ./ t , ' .
l t li ; / ' , ,t . , ' 1 , , .' I
' i : .
8/13/2019 Transmission Line Theory - Notes
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1 1 . : . : : .
i : . , r . i.
t , / , , r . . , t , r
i il t . . i
: ,
I
' i . t : " .
i ' . , 1 :
8/13/2019 Transmission Line Theory - Notes
26/91
a^te: 03,aq 2po8-t t+ " -;-fLW =p,
8/13/2019 Transmission Line Theory - Notes
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. , . . t ) .
8/13/2019 Transmission Line Theory - Notes
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LJn t :
i l ) ' , :
l
8/13/2019 Transmission Line Theory - Notes
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l r
i ' . i I. : . , ,
. t ' r . ,i , t it , , ,a : ' r " , \
| . i . t '{ a
J
' i
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a,\/ a
f . i
/ \ , , . , i , t ' , i i f . i
- ;a , l i r ' , ' : . t . , r i \ ' ^ l l , i ' , / t : ^ ' i
{-'
8/13/2019 Transmission Line Theory - Notes
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i
lA r r / i
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i-\.
8/13/2019 Transmission Line Theory - Notes
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f i
" ' / - 1 " ", t . , , . 1 i / | j. L i \ , , I
y ' . ' .1 , ,. . . . / i
r . i
8/13/2019 Transmission Line Theory - Notes
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ltI K t,'' rtl.' ( | /,t.r- c: I ^i =_ _ r - _ : = ,I / l / r l r
i , . . , , i ' , . ,' , / , , , ,
/ . \ . ' . : i) , ' . ' ,
t , t / ' )
' . . i '
. . - t t ,1 ' / ' . , " | . 1
/ , '. , : t . . , , , , , i . ,' l l
t i , , ' . ' ,
i t , ,
i \
. -_,_:-/ rP3 AF / PanLs'4 ss 16\1 L,n, eS
8/13/2019 Transmission Line Theory - Notes
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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
8/13/2019 Transmission Line Theory - Notes
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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
8/13/2019 Transmission Line Theory - Notes
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q)afu: (9 "09 2obg2- I "a sT.l /ai t "
r ./1a.4'n
8/13/2019 Transmission Line Theory - Notes
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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
8/13/2019 Transmission Line Theory - Notes
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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
t1,? ( k) /S (.CZ A. 4,'4/.Lfc, At,rez aIeryLCle- .
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"
-\s / e . la'4
lt/ , H"
l'rLf ( fu-8e .a/4e 0
'J LJ AtJ o
g, i-*r-
1
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i
* i rtrt
8/13/2019 Transmission Line Theory - Notes
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-t/\sLl c-9
Aatu:
L
ILt * -t -
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
8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
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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
8/13/2019 Transmission Line Theory - Notes
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RC v(xi) ?v(x,tecl'v (F,t
K,+) = LC-DLI
8/13/2019 Transmission Line Theory - Notes
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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 . ,
, , . . ' i ]t ' ' ' \
t r . i
) ' i / ' ' "
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.i)itf(:
| / ,
Al . . 1
. I , l
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' : ' ) i t : . , , .
' l/ l
)
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.1 t '7'
d
vlz) _ (eL 4 UILL@ N
a\
e fal. e^act ilz,ivoluon u
'-K+i".r) I (*)'v(z) -(K+i'ui-
a
- (6+irn(ot
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t t
' . , i
a tar I
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.Jl,r/.c: '
C.l*,oi ,
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(Date: to" o'7 z.abgyrc'3(rDt-pZ+
V"-- V__ V^e' " e"'" e' '(..t
?1 : 41t 2".-e e'qn.
d^) kvL a'ropn/ L l /
+AV
-)
LRtz+i ooLr RLz.i 4rocrtT
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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"
Vc aVs) -t>LtrAVz) 4(B
--+O $ lsVs -OV,
.,,- '^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
(sR+' ,rrtL0^a7' ar ' Q4.Ll4rt4 /
t
8/13/2019 Transmission Line Theory - Notes
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. )r.tit::
8/13/2019 Transmission Line Theory - Notes
57/91
;.7 ', &r"r,1 ,,li //,.r'Jl,rL c z, ,;1u:,.t ;n- t,-'AL,,' t
2rq l - A / ) t,-A1' 1".',-
f irn hle, Jt , - tt
u-lun e y - L. 1/ LL
n qe,'n -la.L ^,lo.re A fva- e -.L-"nu ,l4z cu".a..l-tla-sed ar*r"Moe l/)-
V"(*) = vo--J
1+o 4 -tn / l , .ArorV&d o..--- ,= -.\ r l ^ ) ' a l / ^) = V"+ (, -1- v:
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,1, , ri . '
8/13/2019 Transmission Line Theory - Notes
59/91
&,.t ,-)YZL// /-s
8/13/2019 Transmission Line Theory - Notes
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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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8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
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n, / ) .f n&J' / /k 11 )4 L '4 tC OlN C,,:JZ
, . \
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, : '; i ,'"
I l* - Lnu.-"r,u,
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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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8/13/2019 Transmission Line Theory - Notes
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c,h av //z"A qaT -. YcAy t,'v-.v, (JE;
Gc- acAf 7 JZ-3x los ,,nfu-ae-
IL?-L(o')'L uo9alLo'lL o
9z,ai t e-r, A 7 a
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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,
" to t , /ap< a l l ( ,c , "L ^n t'', - , " ,t ttc{ tr"L e,r 6er" aAe,". o-r :,Eor.l //EC ^/r'1i-./ 7" a,zL \ '11 n-t -,4.L L t t ( L . .244 ae_v.na/, i,..--f n do.n ce, -
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=?,
u 1a.,, te,at',i 116,
u,'lL. ye
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( / t t )_ t lv) t Ce h.'n r tn Cl , l , 4 /".be .r'u I T4anotu ^r.
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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
vo .A0.'r'1 -
Lua, 4a,. C.ltl"1"airc"'t,"A(", h,T - 4 I l r '-LL L ( SLLdlT U) er"1
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t /" . /i.,2 a, tr- , ap-., lru d rJ 1" ezna,{ ctl
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t t I 'I .v - l t - , ' ) '" . t :
' t : ( 14414
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r(
rl A-drkvEk"t l-lt t t r .eC(a,.n Lr, Dl Ul'tfeni -
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I l , r i "
4/ - - tVa,tic'-.ti tn / I*,Ir.l.-r"" oknq fir, ,
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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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8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
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8/13/2019 Transmission Line Theory - Notes
91/91
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