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Biomedical Circuits & Networks - Transient Analysis and Two Port Networks

Biomedical Circuits & Networks - Transient Analysis and Two Port Networks (It includes AC and DC Response, R-L-C Circuits, time constant, Symmetrical networks, Z-Parameter, Y-Parameter ABCD Parameter and h-Parameter)

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@ ttl. Jrc,,r* +4,J, V *- V*+ V. VE a P, ittr) =/d;;(t-.-tt) vE = v(r-e t') VL - v-vR/ E : v ' v(r-d+t) 'PR = Vo* [Ls) = v(r-*-&t) ,4 ,/ ,/ -86 = )4 -X+vu L - ''uF '. :.(v^u*+')^ (+- I ,' * (,-rqo ) +r+e) L v B., -fk, k."". -.
.. .: -Ee.-Ll l-e ) f v -tet-.ar-t I, r.2 _ e.G tYb -al- R* ' '.'- " 3.- :L:.' , .:: ,. v(* E- *G- i.:; E5 L ,,:..] 2 Fr= vL+ic9r"v - 9,8 =Vev Qr -+L b :Ve !D I .': fRI
ffi ffi,ffiffiffiw@ @ @ + q tVr J, - 5.. = Y,, u, 5.r- . )ro-. V, t* L'.".L;= *.*,*1" in s6e. *l*l$ o.ct-e . -IE - .&d$;* * t . _** Tb fina yu: -. - ;t o^ L :u.-{$"4 t0 J*t *hI+Y vr =fr zq b " ur- il. tq.- I hT{*,o ,q rie,nnn (r-, cr -a / - vr ='$t /a+Y s VVtrt Wa" :{ F = Yn+Yn //* rry* L!- T' v^ t + Y,-!. +-|**v* o5, h^ $.,"- L 1[ *L"o, .b /o"
/u," " t L .I VT6 = J"l : .;/v,=o sL)l eiroi,{. t &.^&' Y,. :- y*: t"; b ^l ,ro$t 7u,-/ a^*t "{*/ Gn;Ll , '{ ,*a/ 7,*Ar* L ro ef v, tt ko -U Iu bt -VYs tg lo [^* y^ Y,, k;/4 f*/ Ls, J A^sd.s. ,L Fl.o, , /^ ^,t/ y4*, -= rryb ,v ?, I 'WYo /z_t =-l -- -_> v1 l%"o fr -]i. I =j, I -l- - I Yz-lI V,r: o -VYo --- .4 - _vtts t o 2 d'ues ) ,YU yo lg lle=o
@ T i", trL,'- /o* t l*, f*/ I r-l= -l Vn- I r lY/t =o ,^-,' o Jrt 6nit'd ' v':o vr= L'Y1 '5 Yr*Y' bo: ,q, ra : lo*/' 7L 4*;dt"7 /;,^, I I */*://*" I parra**Jero a''<- I ecoq# IL ad* tn ,{ [y*y- ru) v, ''t1 Y"vn
@/ffiffiq*pffiffirffi Y- f*L ;r/,*, r z-7,,-,,*/*n f ^A^ @' ft-/ */r-'/o - I eJe Cotrt Wr'k fi" :e-' .''t f I,l.fl"lLJIvJ I X, fCua+*t+r - I tN e J..,r,* /r I u, =" r,= Ar A A f,5 t. t vt xl, --'-47, =[ 7Z a V,-,r*/a */* d(, -/'d/- ,V, ; Zn7, J zr* E^ VA = zor Zz .{ *r-- i L, F* / f**4 t, : Y,, Y, I* t lot)l ) J" (tA* {-.. [: i) egr**,* d4t4 + li -v, + Y*v' '3t Vr ud *l :"rarrr^bt' to{o, kq X,r- I *'; ;:f=-* D- x'-7,- = 8z I'' rtzl . I e xa- I ' -f ut Ba:r- -t
F.*= '" -rla fr'n* /,, a'tb.l ' I vr39 V;:l I t* !.? I L x vr -4ia ! :. , ::t i: r_ i- E- S tI , 'T I Y r ->1 | tr tl- -l- v, =o '. r !,., ...t'.,t......'",.t,.-. 1....'1.,t,t.. {' tI r t,ro t 'l "r-:. . =.€'a' t' ,4 +-
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Mrn q fi/ LJI Lw T, :. 6 -L. r,- a.! r-.*. ^ ,:. }r. l' .Lr . .!- - *t-:* ' . __f '::i1.. f.- .:. rl a - r!*. t: , "it i,- !L , '-' p:l *'*: $ z -o.r l.t --6 ;. . "luo-r',= : *erf vt *', ''' -' - '::'':1i''q3 t- , .':.. ,j . l! : " }i';:'., +!,.+- j Lr. '' l. :,. :- :', f'p,L g ', :,3"... .1 f,
trf ?L.^*Lh, $r' :1. [. ' a:: '@ 'l;- ;j t',. Iso.rq -.t "ll & .r' -: il i. : F TA va +j$ ? 1.,1,.:,,.,$';-$'tf , :...' l.;,
r u- mt,"+1 pr$s,7 .t I * tl, l'-t,'. b. e- '6 err't r :tf 'l l
ffiffiM,ffi{kffiffiffi @ O V- C;"'-*;/ G^;rl ,J a &ti*t p,L 4*-*1. uill ,o=s6cru on/ /=o.stl l*'-, Tf/;"1 ^try" is v= loou-*twt*.d b *"iA it ckJ nl *h' A,,r- f=o 'o"Ar-r)* ft,tgel,Dn er,-ol wrrl inih-/ wk oJ Jr*r,. ,J an*r/U Sott*:- o ArrtF'? kvt, _,1"r lno J"-r = _s s Gr) + o. 5 diLE) LL;"I-JF.-.^ -*? ["ft"* l;"",Js]na {t Lsq [o.s -=5b a+ $D fso -=-- B+Ss Lso -_+ 'ts +S 1;r.e) t _= B5 X$ -L s.S> Sr!) i-. .a : Ir") [6'ss +s"] Ic.$+ o.=G-Icrr-t*l f.f rrD Ass.'*tT i.r.',H* GnJ,rIi",q Lt-"1 = e ep* o.s Ll [srr*) G'ss+,ss)
*d eFit t-.1t" ;,-.-[-*^ , Ita= c-qs aeg .B aoo : t"+p ts{-t".1 to Eo 2-so (s+.s) G+toe) -T.tsr = o -s [s+sr1 (s+tos) r B +O a+ttls A c8+sb1 + B ts +st ?+ ts+ggdaL*) 2$o : Acs+r*1' 4ets+ss)t". : A>e* * Bt--w+s.J S : -L(R, -a$ * g-so P-L S: 5o : A (-so+LsJ ssA eso -A =. o -?- + B t#i*)/ - €ro g-sb ?-aa A sd*tiLh. d Alo Ll RJ= -J d*6 A q.-.e,t = & ts 16.*r 'm .1*l * O Ic"r. * + ^f I rls +so slr+r L S+"" - a*^J -**t In,,",aq. t* 1p-or.r{"**r qn !.tt riJr Lut : " [e-*l=-e-r€or] # : 4 F*e*L+ ts*- *'] e t$ es"rrwA, = * l, =. = 4[-soeo+to.eP] = 4 [i- su,{. too] i,r. * r* o+. *s
ffi@e%@rcffirea zn l. G"-;/ ,4*n in JV*re LL* Jut /. @'**r/ J/"o fr-;s awikl rls e/"r"/ ul I ,o, @ a o=7re-sisn d, b"g*[ assc.,n)V t@-7o 1n i h-l " LI---..ffi , Vo = ?, itr) = Vr- = Lf C) = s ."1ru 'V = e-s g. iu) Jiu) du f,cs) + s f "..., - t*r] iai Lts.l Gn/., f,i*" itol = c, s : LEqB).+Esl'ca) ao 1. = (z+s-=) tcs') 1 LO -Iest : I cs) Ic>> B ( t+rs) Ao rs Cs+f ) 4 I ts+o'4) z" /s < scs+f) ,A ,+ ts >o a .g+o'4 Aepr?,n..l**t &.[**', nU amu ? txvLt h"-. -Fh7 V = Vp-+ vi 2-e = si(6l+s Jiat lr Lyl*.* Tt.r'J*^ , o4, [-*[ bs ossrsralr 6 2s I-ts) tts+o'+)
F' 4 A G4o'4{ 8s sr6+7 - - '- saffi) 4 = A(s+o,4)*Bs 7J 8=o ' 4i = A. (o+o_4) t B$) ts = -_t_ =_ro IEFIg-.+ r- . eJs*L*V A ,* c vJ""t i,t 7r,*1"*, g -Zcst = e* C-rO s, ..:*-,r,, r,Y A *O-4 r- csl = -Jg / o- a s+o'+ 'i(E) s t;- beto'48-- drc): lu C'/*e,-.o,,a|) @r
+,& (az o /a 4 6, { 'v* 0 ,Lt rt Iv. .1, I'tV -! El t f.* t) vr - l+ b*z ** .L( eq : q2-. U lr "t { -qoVt - - arl^ x @. ZtJl- @ & - f*qo^e/??s /- h On.*it eA-n in {,0,*, fwv^r -1 , 0,- ffi :i: Vr : 1.,,7 t -t 7.r- 7 * Ur- : ,4;r"Z t" *'Y4"Za r' Tb *find rlq , ' -,. - '--: xr --v' / ^E- r /5r-= o l-L nto = o., !, cqm L" i^b*I e2rPte$ed t h* d4tt* 7;"-h,41 )T"/-^!: g u^V /*;,*l a --/ [4 t,s: 9r.s <zr__ V, = r., x 7, % q 6^4. i,,- h : a':r.n-
T, $"r r/ ^tz e/ A, o- 0,*.t ', t^ : ? sb-J- l. t q-csro:s tsr* O-.fr .L.n- iS^1eJ^ onlrr t t I vf J- cr- i" t* o- 16 =&Iu- / -71 j = L .-ff_:-__ V* Ie*
@ Z=LI , ..Jr -! L"L- h* G,.* I in ft,. 4s- , a, : J. r( ? A - i-Lr n B vr. 3 Vo- 3 v*u: T-. x+ = d T I v' I TI-Lr =;=.' { ',Y^ T"Al1*,ag <-t*=o I. ,re- inlAonc-e -t" =Lt + J-. , vxl td, I vt- {vr- r v
r JJ ,t* { F- I^lt* G*-[* Yrn : p*[ e 3r:trI ( rt i" Ve Iz* F -q- e-fr*8"*e f* t ",^r t *, el..^.t..[A h. rrse, I ytl U-Lt j"-. -,4 L 1.i""*[ +Fo* t-tt .sJ"""" "l5 b Cr.;f uiu,5pt t.n- z-dt'- f,,4Ll' vL l,d{sL ,L 7, tVr t !"+ a+t 4 = q, ;i 4en l/ : -I-1a *"r,: i &* V, vo /J** Kn- e 4u , k an-lr,rt . 7tu A*;/;V r Val **t 3 -f t-L> | T. = o r fl*- :Lvu -d-/ ),a;/-, lL /;lL/ ru* 6 e7,'h"d i *r' hft */,-,u ), A Vrr""r*/* a,?o L,r- V, = L.,rZ, + 2, Vt = Jt +z2z- /** 7 i*fr.A^e
k+rffi*rkrc*'#F*# @ @-77* Se,"Sg.l *L Cr**/ ,''o/o.n o;/6 a tv$v L-n , /"; n i a /r>* go*i,A ,l p,, L @J e contJ*r/ *r-rce -A^ L s*-kL t C**/ i**i*{ . n , ku( s i,, ItlUrl OfftEt [cvu, tss j z_o qro, = ?-s Ltul t,cgr f o. os * s.os & JE *rF iJl L &9' t llJt ' aoroJ .: o & o.o- f iJ,f, {.O t +*: Jttl a.. ,. - .3O t +**J i eL o A l.rk, It"^ r- cn"J*1t,r, r.--':'- ; = I = o,o=-'[ i,dt_.a fso s % i,(}) ,F o,os l.ir"e> Jl= =t? tTt"",- tTr.^h so g h**X
F V L, t: i : !oo --* : 2slsfg tso G SF * $. oss .s eg; + foso ? I(s.) fts) tco [s+ t-"uf+ (:ni e soo <Ktlo 1go f-=. s s. sss L' t cf0 t--I__=a4:l ,{L J a 0r -g d -u| o a c{ Io) [o o +o ; h11 11 Er t) ts({ ,d l-. SEOoo- + -Jrts) ,€a +-'O. OS f f Iss 2-ss -$ s.os-3 A-5oooo t tst> * g'o=r.3+ ei +s +5ooo.9= "] {i$oo o I c>r 5 cs) fl;" i'' I lL a L.:+ S*t I ts+dz+ea 4 4d3+ t x to s. or f i+ 4dost I,f t$ /o.o,- s"+ 40!s + l,,rJ Zs.co f++o* *t*,J A6e o 4" 2 =g+ gtq eo" +&+i- f++-t* 'o$6L t+ oa I i.1 fJr I -0 'a { ,o) fl J leir$' A I Kto I qs) f c-s) = J c;) Lo-O a. = 4to z Ceoo - onlo 1r_ F *Y*'^) c'wt*'l *+t = L:= tQ- l,e ra b . $= t *rJ -&, r ;( - s.o"s lTq'aol98 Cs+r^.i + Ctnf =. ero$oB I= 1* -l L(st*')'+(?Bo!l
@ :t, 5*:' - 5--:. .: F.j . !. :'. : Ti L't, - *,* AL ;i*t L=8 ,:'..," ' *.,..-' i- ':1t'-t .'' 8t, *- C*J t tsd.? .I - -r*t 'l I I t^t{tt'+h'ljr ' , ,5. {5 L =.,.-. .tQ11+ - '& a+t'rt L e (*r,.} _ Bi^ 11q.*t _1 ob t J At t r r__ _ t^ +lg" A ?o rr)- tb! -o-a{+c,r!r,{E + AA'l=*s t -t:q'.F-B t.t: -brA f -, e IEBi"a+r-rE ILJ
B: Z.ss 0 *r e--o1 0**l _ y"^^k i. A^,1", .( ,- o+$nl+r-yt )
,*e. ffii6, @ A '&ties P,tc O;r*a/ sln,, in 4J* (u= 6{*t*ttu, pz9*t L = Lu n"rl C, ..zsF), fL s*,"1.l T, etoseJ .t [.To,.t =o " gLk;n ;cE) . Ass$nns ?7a,qo e,"r*errt 4A".V/, zntrr/r t "a/ lcgrto q" arlaoq c t"Jr-" C/r"e /I_ sc,, ikt, . v=d;"t tl:- A?iltit Lovu , V = h*V,_* V o , -aL6 e' : sice) + -J'p., 'ftr dA- '; J-' tr E cs) .1 .St$ = *i* snJ*.lt*. $* .,^ih:J or*.o^ itol-u SfcE)+ a5sg)+ | Ics) o_zsS [-s+.s* I IL- "";J =cs) r I S+ ss{+l & r- s J S*z- &s -J s+z sass+4 hJ. &."*I t"tro = VL: u:, V= 5 iLtl r diG) - E I -(;et o.2s ) 0 6e -'L -T*h? t",. T.^.J,.-., I g+z AI g 8{r- 1,, a+L s rcs) * [u I-s) - iorJ + o.ass at") S+ s+ J- o.2sS sls + 4 's E"rS++ =a 3ro+ r*-s __
nletr? ?*l$,] -e"*e:m. i f-r$ = 6" 'r- e,sa &+t Cs&a) ts++) ;'gD ,,,.'. . e - 6+r) Cs+C) LnrD = I G,) 6 &{ z- 6s Cs+t) cs+z) cs++) =ArBtQ.g+t a+ g s+4 --+ @ z ,l| 9+4 s+q) + B ts{O cs+{) * e ts4j csr z) as+olryds++l ,: 6" =6 ?+ 8=-r- 6t-o tr 6 Lr +r) cr*>*rryrf1-r+a+1* .*2nft*rg c s+1) cs-{q) + s t5+0 rs++) + ccs {r) Cs+ z] A C0 Cg) 8A _-u-/g =) -6= '=( = A -) -a+ = e C^s) c-O =-4 B a+ ,.L 8+2- g 8{z . c-+)&l- s++ + "; UEI: -2e= -r#+i.$-4*-4L :>*Tx = B (-r)(z) B r:*=6 ffi _z+ = EC *e=-aq, 6, B ofr g y...*s '1", *1**h.^ 0 :v 3.cg1 = =$+- f.t$ = -z PJ s=-$, s*tehl-l-n1 T*brn f-.,n=-o- *f*s€. Ty. rJ"*,, .

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  • 1.
    o 4 " .be.Jioe!r^."i..L re.sfonse -|fi'. re,fynse , "f.-iA:."., dS {{r:, A.k E^t,:{{"{.,,^Jb $nr. krrrg, anJ ts rr&r-"d &o .s +L -I+-nsie,[ ,..g^.n- ' z ' A A*ro grrt ne-t.,r"rk [r." +tt J"tt"*,"il xr frt<m"k, Xnr = ts* )Lr. =n"] Et, =. h^, :SdL. Finl ttl. V*t..q eJ IU : A. B.; e Ear B' g I*r *rl )C*t , Irt' l( o-t ' t Xr_t ) Xu - a Xrr Jtr,",ufo, L.s Ie.r tSrT):t-') 5 8oo -1F,_ {t-L ?':' I E E !O: SrE$ "'3 o r,{$ . ,-.,. ;. s ga D:. t $sn- e' D I F Xa1 = Xle tz &aeasia { }r.pdm"e Jiilr.rlm d &lrqi.rr gffn'{t*."e. less. 2. Li*; 4* , /r, *L.ol Ct,rre*-il-tA ?*!"t-qele - Tofu, ="
  • 2.
    ' @ A/c Wrff: o{ 29o wlle is ,,qpl./ la. . ,Wria Qst, &rcuc{ (/ :{ o/ lo,,it UifA g=w*. k1*{ wi( k tL C,q.o.trl in /A 4r.* L #'*, Cons/*/ I rc A" ++- rrotLos e- , oiuT.,.,{[n*L ,, t = rt tlse- tn tJr.r* is 5Nt* r,1 , bri= rtr_"-+l t:. . E + Ct-";^] = 4 [r-..[geal : |Co-e$rll': rc t{l..' r 1g;,,-{.3.--6..3 3 .?*- e'$-AFFs O tr"fi*l o'r* e6 .-otd* ,n!F..srrh+ ? " A iu"frso'fir is s.rJ,''Lo..t o strtn*.ri* ,$,.r*to i.$ tb* *o,[ot.* pr.ge,r$es aX |t.- L.-drr, o.rq *rt *S*-.. *Lon }t* qL -nI . it f*, *{*t"'t.J rs-vrl",
  • 3.
    o @ S k*t"t .: +LGrr"n/ ----- fyen !6 c (4 .-- 5 - s-roA b (u es** .[ l+-t t".tq. Borrre. fr..[q [tr- L=o,o<tr o.rro.ls, o"z oo o.es; - . -2o(e) 5-e * 5-e =gl1=4. IL B 1 6 s 4 o-L 0.u- o.r D.zs -+t ',p'"
  • 4.
    ffi:- r o.lmH s s-tXtoisg .: .:ri:tr ,r,: _3 o.txto GE = t -z- -':..::l:- -= {g:..aec-,. 'to := -* [mF ses. I I
  • 5.
    o O Onn orY* 0c *l* ,*d P-L 0;r.*-l *,c/ Jonit" h 7r*r* 7,r*Ao, * rzes;srLi ur( ialncLr. -/g***n*rfuryaru8"+ffiFffi Fffi t=o P ts*it u2 G*i&^ q' c;..*ll e5 J,s** it Jig.r"e . s ' Indr.t-, (., ftr ,.*r"rL 1.esi,sL.s . H^ Awrnx V= trle' h* s.J.$^ 'S' tb oourf -L +t,o. hrcs ti"rl."rl) tso , "ept h- e.6s v t s.Ser RL e-q,iL C^"*iekntr grrr$tL is nU* .r..L*-6.d e.J, "s irt &le! lsvu f t* at-*;t, +Aok ve +-vL V* = B ice) vL: L l{,TK .t o$ o. 6'isfsrr.e "ra.d lrr Jrct*rr-e- V -- E 'G) +, L i!9) dL : pIc.e) + L*s Ics) 14 ,LO : E Ers: f . LgTs) - #.1 l/ a5 Jts uI t,to = o [., i*ti. g^"1.
  • 6.
    "Y.g E l.tq1[ .Fr"+'Uel V f. cB) = s Ie+us] u ]f,,ts) : , ,v,, ' sfl*+ uJ. s ts+l A I ---f s i t hub1 F-rJ S,p, vlt .Tu) z ets+gl :- v L P"L a- $., -, . uL' s/T' o f***) Rrs+gl+ ts s A 6*+) +Bs sfiy v T , t.::. - ,,,.,.i ,A P& "= -+, vk-- -L. v ' T R./ _v e. d ra : *Ylv -+7h K, ot'A B yo.[..or in "1,*&* B: s"{++"*? A T-5 Oi.' V tu nv.rse, t.iLr..: TL
  • 7.
    @ ttl. Jrc,,r* +4,J, V*- V*+ V. VE a P, ittr) =/d;;(t-.-tt) vE = v(r-e t') VL - v-vR/ E : v ' v(r-d+t) 'PR = Vo* [Ls) = v(r-*-&t) ,4 ,/ ,/ -86 = )4 -X+vu L - ''uF '. :.(v^u*+')^ (+- I ,' * (,-rqo ) +r+e) L v B., -fk, k."". -.
  • 8.
    .. .: -Ee.-Ll l-e ) f v-tet-.ar-t I, r.2 _ e.G tYb -al- R* ' '.'- " 3.- :L:.' , .:: ,. v(* E- *G- i.:; E5 L ,,:..] 2 Fr= vL+ic9r"v - 9,8 =Vev Qr -+L b :Ve !D I .': fRI
  • 9.
    ffi ffi,ffiffiffiw@ @ @ + q tVr J, -5.. = Y,, u, 5.r- . )ro-. V, t* L'.".L;= *.*,*1" in s6e. *l*l$ o.ct-e . -IE - .&d$;* * t . _** Tb fina yu: -. - ;t o^ L :u.-{$"4 t0 J*t *hI+Y vr =fr zq b " ur- il. tq.- I hT{*,o ,q rie,nnn (r-, cr -a / - vr ='$t /a+Y s VVtrt Wa" :{ F = Yn+Yn //* rry* L!- T' v^ t + Y,-!. +-|**v* o5, h^ $.,"- L 1[ *L"o, .b /o"
  • 10.
    /u," " t L .I VT6 = J"l: .;/v,=o sL)l eiroi,{. t &.^&' Y,. :- y*: t"; b ^l ,ro$t 7u,-/ a^*t "{*/ Gn;Ll , '{ ,*a/ 7,*Ar* L ro ef v, tt ko -U Iu bt -VYs tg lo [^* y^ Y,, k;/4 f*/ Ls, J A^sd.s. ,L Fl.o, , /^ ^,t/ y4*, -= rryb ,v ?, I 'WYo /z_t =-l -- -_> v1 l%"o fr -]i. I =j, I -l- - I Yz-lI V,r: o -VYo --- .4 - _vtts t o 2 d'ues ) ,YU yo lg lle=o
  • 11.
    @ T i", trL,'- /o* tl*, f*/ I r-l= -l Vn- I r lY/t =o ,^-,' o Jrt 6nit'd ' v':o vr= L'Y1 '5 Yr*Y' bo: ,q, ra : lo*/' 7L 4*;dt"7 /;,^, I I */*://*" I parra**Jero a''<- I ecoq# IL ad* tn ,{ [y*y- ru) v, ''t1 Y"vn
  • 12.
    @/ffiffiq*pffiffirffi Y- f*L ;r/,*,r z-7,,-,,*/*n f ^A^ @' ft-/ */r-'/o - I eJe Cotrt Wr'k fi" :e-' .''t f I,l.fl"lLJIvJ I X, fCua+*t+r - I tN e J..,r,* /r I u, =" r,= Ar A A f,5 t. t vt xl, --'-47, =[ 7Z a V,-,r*/a */* d(, -/'d/- ,V, ; Zn7, J zr* E^ VA = zor Zz .{ *r-- i L, F* / f**4 t, : Y,, Y, I* t lot)l ) J" (tA* {-.. [: i) egr**,* d4t4 + li -v, + Y*v' '3t Vr ud *l :"rarrr^bt' to{o, kq X,r- I *'; ;:f=-* D- x'-7,- = 8z I'' rtzl . I e xa- I ' -f ut Ba:r- -t
  • 13.
    F.*= '" -rla fr'n*/,, a'tb.l ' I vr39 V;:l I t* !.? I L x vr -4ia ! :. , ::t i: r_ i- E- S tI , 'T I Y r ->1 | tr tl- -l- v, =o '. r !,., ...t'.,t......'",.t,.-. 1....'1.,t,t.. {' tI r t,ro t 'l "r-:. . =.€'a' t' ,4 +-
  • 14.
    o -T; -(; I y,,'- - -^- / ltt" 't,: ,. _ Jo. I -t -l oV, Iu*= o q {o- Vl . Ax - Yro V /o* Y /tt a t.^ 9b fl I r o- [= I vr-ro AI(LI Ivr".-r- *A& -x,* U, -a'; ur 'd -' I ,;.., , lgu I x,o- -' i' :,. t*V, -Ctol. Y4 s O +tt I " J-"' {' y* s,-l __ Vt=o ',[ V-f-,-II!; /tz- -i Vz_ rr.ro /Jal -l I y1=O A,l =I I V1 =o I A:& I l*, ol I o- r,*l : 7f,,,b**o 3 e.,B-
  • 15.
    Effi;l', " : :: EHv* -*::# A* l_-, --Io_ : -:{.i- Ji ',,.'l : ,/ r.,fr4* I ., .' -1 --..i.- :*-
  • 16.
    ffiwffi,*TY"tr @ ,l' vr t, ,fu /- 7*,^,,,.L A- u,l*,^ ur 3 4,,r1 1{,*v. iu= l*, i, llr*-v* !- 'o, ,* Cir*t L.; t4,, I Yc^ U -j !t [Oo.,r- n^/*V Vu: o f U1 v +t Loqu-- do -."i"L* e,r)Er t* sl.,rtr BJt, iL LT t*L q'^{ , = [oss'. *tsq,**-) Vt = zosi,. +(us -lX -o : tsNtI+J +t"oT, & :- t,s i'. + z"su1, + b i*,-q
  • 17.
    Mrn q fi/LJI Lw T, :. 6 -L. r,- a.! r-.*. ^ ,:. }r. l' .Lr . .!- - *t-:* ' . __f '::i1.. f.- .:. rl a - r!*. t: , "it i,- !L , '-' p:l *'*: $ z -o.r l.t --6 ;. . "luo-r',= : *erf vt *', ''' -' - '::'':1i''q3 t- , .':.. ,j . l! : " }i';:'., +!,.+- j Lr. '' l. :,. :- :', f'p,L g ', :,3"... .1 f,
  • 18.
    trf ?L.^*Lh, $r' :1. [. ' a:: '@ 'l;- ;jt',. Iso.rq -.t "ll & .r' -: il i. : F TA va +j$ ? 1.,1,.:,,.,$';-$'tf , :...' l.;,
  • 19.
  • 20.
    ffiffiM,ffi{kffiffiffi @ O V-C;"'-*;/ G^;rl ,J a &ti*t p,L 4*-*1. uill ,o=s6cru on/ /=o.stl l*'-, Tf/;"1 ^try" is v= loou-*twt*.d b *"iA it ckJ nl *h' A,,r- f=o 'o"Ar-r)* ft,tgel,Dn er,-ol wrrl inih-/ wk oJ Jr*r,. ,J an*r/U Sott*:- o ArrtF'? kvt, _,1"r lno J"-r = _s s Gr) + o. 5 diLE) LL;"I-JF.-.^ -*? ["ft"* l;"",Js]na {t Lsq [o.s -=5b a+ $D fso -=-- B+Ss Lso -_+ 'ts +S 1;r.e) t _= B5 X$ -L s.S> Sr!) i-. .a : Ir") [6'ss +s"] Ic.$+ o.=G-Icrr-t*l f.f rrD Ass.'*tT i.r.',H* GnJ,rIi",q Lt-"1 = e ep* o.s Ll [srr*) G'ss+,ss)
  • 21.
    *d eFit t-.1t";,-.-[-*^ , Ita= c-qs aeg .B aoo : t"+p ts{-t".1 to Eo 2-so (s+.s) G+toe) -T.tsr = o -s [s+sr1 (s+tos) r B +O a+ttls A c8+sb1 + B ts +st ?+ ts+ggdaL*) 2$o : Acs+r*1' 4ets+ss)t". : A>e* * Bt--w+s.J S : -L(R, -a$ * g-so P-L S: 5o : A (-so+LsJ ssA eso -A =. o -?- + B t#i*)/ - €ro g-sb ?-aa A sd*tiLh. d Alo Ll RJ= -J d*6 A q.-.e,t = & ts 16.*r 'm .1*l * O Ic"r. * + ^f I rls +so slr+r L S+"" - a*^J -**t In,,",aq. t* 1p-or.r{"**r qn !.tt riJr Lut : " [e-*l=-e-r€or] # : 4 F*e*L+ ts*- *'] e t$ es"rrwA, = * l, =. = 4[-soeo+to.eP] = 4 [i- su,{. too] i,r. * r* o+. *s
  • 22.
    ffi@e%@rcffirea zn l. G"-;/,4*n in JV*re LL* Jut /. @'**r/ J/"o fr-;s awikl rls e/"r"/ ul I ,o, @ a o=7re-sisn d, b"g*[ assc.,n)V t@-7o 1n i h-l " LI---..ffi , Vo = ?, itr) = Vr- = Lf C) = s ."1ru 'V = e-s g. iu) Jiu) du f,cs) + s f "..., - t*r] iai Lts.l Gn/., f,i*" itol = c, s : LEqB).+Esl'ca) ao 1. = (z+s-=) tcs') 1 LO -Iest : I cs) Ic>> B ( t+rs) Ao rs Cs+f ) 4 I ts+o'4) z" /s < scs+f) ,A ,+ ts >o a .g+o'4 Aepr?,n..l**t &.[**', nU amu ? txvLt h"-. -Fh7 V = Vp-+ vi 2-e = si(6l+s Jiat lr Lyl*.* Tt.r'J*^ , o4, [-*[ bs ossrsralr 6 2s I-ts) tts+o'+)
  • 23.
    F' 4 A G4o'4{8s sr6+7 - - '- saffi) 4 = A(s+o,4)*Bs 7J 8=o ' 4i = A. (o+o_4) t B$) ts = -_t_ =_ro IEFIg-.+ r- . eJs*L*V A ,* c vJ""t i,t 7r,*1"*, g -Zcst = e* C-rO s, ..:*-,r,, r,Y A *O-4 r- csl = -Jg / o- a s+o'+ 'i(E) s t;- beto'48-- drc): lu C'/*e,-.o,,a|) @r
  • 24.
    +,& (az o /a 4 6, { 'v* 0 ,Lt rt Iv. .1, I'tV -! El t f.* t) vr -l+ b*z ** .L( eq : q2-. U lr "t { -qoVt - - arl^ x @. ZtJl- @ & - f*qo^e/??s /- h On.*it eA-n in {,0,*, fwv^r -1 , 0,- ffi :i: Vr : 1.,,7 t -t 7.r- 7 * Ur- : ,4;r"Z t" *'Y4"Za r' Tb *find rlq , ' -,. - '--: xr --v' / ^E- r /5r-= o l-L nto = o., !, cqm L" i^b*I e2rPte$ed t h* d4tt* 7;"-h,41 )T"/-^!: g u^V /*;,*l a --/ [4 t,s: 9r.s <zr__ V, = r., x 7, % q 6^4. i,,- h : a':r.n-
  • 25.
    T, $"r r/ ^tz e/ A, o- 0,*.t', t^ : ? sb-J- l. t q-csro:s tsr* O-.fr .L.n- iS^1eJ^ onlrr t t I vf J- cr- i" t* o- 16 =&Iu- / -71 j = L .-ff_:-__ V* Ie*
  • 26.
    @ Z=LI , ..Jr -! L"L- h* G,.*I in ft,. 4s- , a, : J. r( ? A - i-Lr n B vr. 3 Vo- 3 v*u: T-. x+ = d T I v' I TI-Lr =;=.' { ',Y^ T"Al1*,ag <-t*=o I. ,re- inlAonc-e -t" =Lt + J-. , vxl td, I vt- {vr- r v
  • 27.
    r JJ ,t*{ F- I^lt* G*-[* Yrn : p*[ e 3r:trI ( rt i" Ve Iz* F -q- e-fr*8"*e f* t ",^r t *, el..^.t..[A h. rrse, I ytl U-Lt j"-. -,4 L 1.i""*[ +Fo* t-tt .sJ"""" "l5 b Cr.;f uiu,5pt t.n- z-dt'- f,,4Ll' vL l,d{sL ,L 7, tVr t !"+ a+t 4 = q, ;i 4en l/ : -I-1a *"r,: i &* V, vo /J** Kn- e 4u , k an-lr,rt . 7tu A*;/;V r Val **t 3 -f t-L> | T. = o r fl*- :Lvu -d-/ ),a;/-, lL /;lL/ ru* 6 e7,'h"d i *r' hft */,-,u ), A Vrr""r*/* a,?o L,r- V, = L.,rZ, + 2, Vt = Jt +z2z- /** 7 i*fr.A^e
  • 28.
    k+rffi*rkrc*'#F*# @ @-77* Se,"Sg.l *L Cr**/ ,''o/o.n o;/6a tv$v L-n , /"; n i a /r>* go*i,A ,l p,, L @J e contJ*r/ *r-rce -A^ L s*-kL t C**/ i**i*{ . n , ku( s i,, ItlUrl OfftEt [cvu, tss j z_o qro, = ?-s Ltul t,cgr f o. os * s.os & JE *rF iJl L &9' t llJt ' aoroJ .: o & o.o- f iJ,f, {.O t +*: Jttl a.. ,. - .3O t +**J i eL o A l.rk, It"^ r- cn"J*1t,r, r.--':'- ; = I = o,o=-'[ i,dt_.a fso s % i,(}) ,F o,os l.ir"e> Jl= =t? tTt"",- tTr.^h so g h**X
  • 29.
    F V L, t: i : !oo --* : 2slsfg tso G SF * $.oss .s eg; + foso ? I(s.) fts) tco [s+ t-"uf+ (:ni e soo <Ktlo 1go f-=. s s. sss L' t cf0 t--I__=a4:l ,{L J a 0r -g d -u| o a c{ Io) [o o +o ; h11 11 Er t) ts({ ,d l-. SEOoo- + -Jrts) ,€a +-'O. OS f f Iss 2-ss -$ s.os-3 A-5oooo t tst> * g'o=r.3+ ei +s +5ooo.9= "] {i$oo o I c>r 5 cs) fl;" i'' I lL a L.:+ S*t I ts+dz+ea 4 4d3+ t x to s. or f i+ 4dost I,f t$ /o.o,- s"+ 40!s + l,,rJ Zs.co f++o* *t*,J A6e o 4" 2 =g+ gtq eo" +&+i- f++-t* 'o$6L t+ oa I i.1 fJr I -0 'a { ,o) fl J leir$' A I Kto I qs) f c-s) = J c;) Lo-O a. = 4to z Ceoo - onlo 1r_ F *Y*'^) c'wt*'l *+t = L:= tQ- l,e ra b . $= t *rJ -&, r ;( - s.o"s lTq'aol98 Cs+r^.i + Ctnf =. ero$oB I= 1* -l L(st*')'+(?Bo!l
  • 30.
    @ :t, 5*:' - 5--:. .: F.j . !. :'.: Ti L't, - *,* AL ;i*t L=8 ,:'..," ' *.,..-' i- ':1t'-t .'' 8t, *- C*J t tsd.? .I - -r*t 'l I I t^t{tt'+h'ljr ' , ,5. {5 L =.,.-. .tQ11+ - '& a+t'rt L e (*r,.} _ Bi^ 11q.*t _1 ob t J At t r r__ _ t^ +lg" A ?o rr)- tb! -o-a{+c,r!r,{E + AA'l=*s t -t:q'.F-B t.t: -brA f -, e IEBi"a+r-rE ILJ
  • 31.
    B: Z.ss 0 *r e--o1 0**l_ y"^^k i. A^,1", .( ,- o+$nl+r-yt )
  • 32.
    ,*e. ffii6, @ A'&ties P,tc O;r*a/ sln,, in 4J* (u= 6{*t*ttu, pz9*t L = Lu n"rl C, ..zsF), fL s*,"1.l T, etoseJ .t [.To,.t =o " gLk;n ;cE) . Ass$nns ?7a,qo e,"r*errt 4A".V/, zntrr/r t "a/ lcgrto q" arlaoq c t"Jr-" C/r"e /I_ sc,, ikt, . v=d;"t tl:- A?iltit Lovu , V = h*V,_* V o , -aL6 e' : sice) + -J'p., 'ftr dA- '; J-' tr E cs) .1 .St$ = *i* snJ*.lt*. $* .,^ih:J or*.o^ itol-u SfcE)+ a5sg)+ | Ics) o_zsS [-s+.s* I IL- "";J =cs) r I S+ ss{+l & r- s J S*z- &s -J s+z sass+4 hJ. &."*I t"tro = VL: u:, V= 5 iLtl r diG) - E I -(;et o.2s ) 0 6e -'L -T*h? t",. T.^.J,.-., I g+z AI g 8{r- 1,, a+L s rcs) * [u I-s) - iorJ + o.ass at") S+ s+ J- o.2sS sls + 4 's E"rS++ =a 3ro+ r*-s __
  • 33.
    nletr? ?*l$,] -e"*e:m. i f-r$= 6" 'r- e,sa &+t Cs&a) ts++) ;'gD ,,,.'. . e - 6+r) Cs+C) LnrD = I G,) 6 &{ z- 6s Cs+t) cs+z) cs++) =ArBtQ.g+t a+ g s+4 --+ @ z ,l| 9+4 s+q) + B ts{O cs+{) * e ts4j csr z) as+olryds++l ,: 6" =6 ?+ 8=-r- 6t-o tr 6 Lr +r) cr*>*rryrf1-r+a+1* .*2nft*rg c s+1) cs-{q) + s t5+0 rs++) + ccs {r) Cs+ z] A C0 Cg) 8A _-u-/g =) -6= '=( = A -) -a+ = e C^s) c-O =-4 B a+ ,.L 8+2- g 8{z . c-+)&l- s++ + "; UEI: -2e= -r#+i.$-4*-4L :>*Tx = B (-r)(z) B r:*=6 ffi _z+ = EC *e=-aq, 6, B ofr g y...*s '1", *1**h.^ 0 :v 3.cg1 = =$+- f.t$ = -z PJ s=-$, s*tehl-l-n1 T*brn f-.,n=-o- *f*s€. Ty. rJ"*,, .