Biomedical Circuits & Networks - Network synthesis and filter design (It includes cauer form, poles and zeros, Impedance function, Hurwitz polynominal, Positive real function, Types of filters, Initial value theorem, Butterworth filter, Chebyshev filter, Chebyshev approximation, Low pass filter, T and pie network, m -derived low pass filter, transfer function, selectivity parameter & discrimination parameter)

1. o
SyZvwteSS *frF,E . besya-a*
XrcS) ' C*4s, s : --_'
e2+4e + e
Bs+ gt+ es s cs1 6s+B )
Cs+a1 Cs+r)
A C s++)Cs+ z)
I
Xe,raq oL'
'.
folos +
,,51!|.;Sf{
rg#ffi,.**re
/asr - 4
,l ' @eltn*,be #o Vr{"s^*a,,,/, zoas$ 1,n7edrn6.,.$,a"Ab"- .,cg= 9r4c+ .3
ss+6,f +ss
e' f/*l- /a d;lkn* t*-'f finl Cot'*1 tY* -"/ &*ra Cdr,rl
do-* "t L. o"hor& '

2. lluru;/2.
9ol"lyq,1:
A[,
3- Cl".k ,kC"* #o y"to*inut s?r €€*as4-zss+4.s-ts rs
G;n /rb. ?eas6r)
iL is
^ol
lloruilx ' 88. sa, ag, s' /.r*,
*s.g,ai^/s a,re l44o '7k C*!CI";'^L
{iven 1*lVnoni.l
is - ,ol Hurri/* '
w nisiV t
,f ss * -ve.L.e #eir
llen" s //*
4 . Di-#ere"L;ot" Ftt" e^J Core' {*- -
fosler forrn Cou* Foro,
par4 J {r^.A^ an//o/
f6/* {-- -t ttsl & trnV/*r*
lurokon arn hs/"- in--E oe/ {q
a/mi4*,oce tar&t- .
foshr {:^ ,.givcs * m./,st co,,h;oin7
8er1s5 1"""J.
yosE* A: ! 6)ves * neArwk crc,+fry
{ paw/hl itor./*s
Gnlrnanl {roJr'^ lw{Al
F- ft* ,frr."A*s lcsl * l.Csl sn
lc rs/;s"J fu ["/t canet J
a.n/ caup6 Z ae/lJ
B"'A fus.ev {*. Z a.,,f -E Synl$esis
hlo lolJe, ne/n at:,,s /*trry ,biq
oal prrilel L*onl*s ,
s. c/n.u /t, psi/ir,- ,"J o! /{" {"rr4* /vg) - 8f',
's2f za+l
€r&-'
fourt lnobbn, "[, /d /ort^ oJ /b Jrr-
F* 7s;/irc q"o/o"", o, b. c Z o or, !r2o
Hq" o*t , L,a oo e = 6-
$", Jt -t{^. eo.,.$S.ierrt tat..r,t G, t, c @tc
AJt-r t=? ornl q., t,"t f,>o. 8s
so."o-&J '
E+^
s'2+6s7 c
psikw $.-, a,f.c.2o
L.rr^ G,lri tio* "r*
J!r"n*J <rre h* S.,"*ton is o' q*'.H"*

3. Nn , ll (/*, ot F;0b,.
Jf'e'. .oaq - J.* hr*I
r.-o*-
F*s J.f{_,
p."" Jtt"- ( ,r, )
E[,,,,;,,*L* J+tL* [gA-E:i 6]- Bo-r sQ &tr", (srg)
,- ZCs) : 8+(
s cs+a)
L;/af v^1,*
,!" [t't'y ' us,5-+oo
[ {u'J
ry,{w+a2
{C t +*l
-trrhl vatt,rs = [[
S-;.o
t.
2.
g.
4.
LhAL
b.r,l
B.rtt
fqss Ji[+e-
( r-r rl
I upr)
1' hltJ ?s .ltu i^ikJ vJn. od A. hJ,^
=LLS->xr
rct+$)
l+o ,
[ "l-o
E. G^y*n" e*tt.'*orl[, -J d"fuu{*," aprod'*h" '
&o.ls.;li on
spae g-tls
grll*,,",r.rtt, .
un ltlk,
S'tvo Bulktuoili d.lrsk,
'1
L,
E
+
lYanatf tlJ filkr
Ta tSe give n orole,
nn'
tf" l"*;l;*,
[nnJ is cniLer, i,.c, fr" r/rtl nbAs
o/oo,
fo;"y l;r,rn- pb" aeslow.
Tr* W {^lts og o
"-k
2ra /1,/t*" 1".
E'J r;ple t;//vr
for -t/* Same clw'n: ,L &-,r,i
l*/ ,s tbmoure", . 7k- 1$fu9
vpa$
l,r& l;,* Anp"*/ 6, S$le
4 t*[t ^l t-.b,rre nk 2,,,
lp-ciL"Is
+ €@- t)

4. -il
lE* Jv.1-.nX CJ.). *L;J *lf,"J* fh- p*, t^J "J
*tLn.*t;* L"*,J ia *tl"d cJ o.f.$ Srawff'
i ! 'j': :.-
lo . N",1" /k /"s,7n .7,-h*, o I LpF .
, , Prp
-=
Tr J"
, I ..
,.-

5. {V."***"*e Syursests
*
1- F,'n/
qo(, F*adfu, &'sfiAfu'
ro/r#.* #. fiten ptryrrrinJ ls Hcrruilx sr nol .
#Pcsr. 34FEL+,e+l
fL is r*L'' !q+,*uffi"&
. ': ".,:''' , .
!Cg
rS fnrSSr ns
0
-1
. Sin"" ..$3 L"*.
Pcs) '
g4+ g3*.''ss^+,qq+
ECsr e-* E4 +'s*Fi 4
g cs) ' C.* .**
*
4
pcs) €
" -IE* e.,thn-l.d
Ecs)
o cs)
r5
gs+ gs ,
+S's {4
)tP, cc-) 1'+ aa
zs"++J, 1s* ( sh
?s
*'l G4
E cr)
' frs: :
o ts)
a:
J.a-
...
SI
-+-L, ata J- I
S
o
;S' X.*.L*rL
*G,
"$$;riernL, .,,n.-
afe.
v4 ,,
l, t(n, t
Att ,*U*L L floii.,e

6. Fcul = 64+ s"+ r$'+ gs+ 2-
E esr . 64r r$; a
Ocs) = s8+ .3S
Fcs: = E c|)
ocS)
Fnu, . Ecsl
:
ors)
s+J-
-s+ |
-S , I
:T-5
+s
Tr*L; u,L Qped.si.iel,to - tlt 15-
'o7*[+,,". L{on"q ;t ,o ,*L fio.r*i}* .
-1F'
t*-" o,Ta
o/rc I -l 5/n ., t{*. L.. y,-k*L
**
/ ct) : s3a +,f+ss+ r
Ecs) = 4*+z : .
OcS ) ' EB+'€S -' : r' :.
l cs) '
gcs)
Ers}
-It- c.nlia*J {'*l** g}a?qnta{'n i s
4s"+1 ) ss* ss (
+
e"{ *s
*') ff-"(fs
e.) fiso
-fs
(+*
t- E.rr-f + I
9"+-J-'l 5s+
-T-
7,*h*rL ooe;Ei;sierr.t a,re + , +, +:
ve g.'eivu, . tlenc- '.! is ' .lr*oi,x.
A ft Jl* 7,,.h"r,t*

7. lVefnoon SyarH€src oc ;rurep, DE alhN
fenr- a
@ tl'*{l'et +'* giw', /un.h* is p"*; five t.o.[ o] *L .
ff^J
Z CA)x#. = gsa+ 5
s csl+r, ;
Qs.h*&ffir,
Zcsl -- =i'+ t
s cs? r)
af+s
=A+s
B8+ c
*+t
( gs+c) sA cf+r) +
p^6)
>:Htg"1+ s !:
Co*k r[
A cr1+t) +6g*o) s
t*rr.* A = s
E Xu^* "l
eteT /"^rrt
EL*#.,"l A.-r"
S
a
a
(A+ats + cs+ A
ai+A+aS+ es
eso
A-[B = e
d'. A-fr = g-5 = -e-
S ino tr*
'"sr&rr*
ikve **l J*"k.ri .
Zds) = G*rn) Cs+a)
(s+t) ts+a)
ssffiii'*:
:((s) - Cs+l) cs++)
qs+r) cst c)
p* t* -S.rr.c.ko', q+ tr*
Contitio" J.r g.si[..,e *^
llere-. a, =6, A.*B
b, 14. ba, o g
s2+6s+ a
sn+ 4s+ g
Ba{ ots $ qo
g,'+L.s { bo
*98 arLrZ C.r^,
.: Grbr = 614 :
./{o- {; : 2.BaB
fE "-|$ . l.Taq
,.-@1)
(@t
L
: s+ as+4s +E
sfrar+a{ g
=sE
*+es+s
r t. eolq
&-
-{trf
94
?r2aL
( ( {au -G.) =
(e'Brr - fie)
J
B
A" L GaJJ..* erL.:, cr^,-eel is s,ke&"a , Bo tn^ gir,e,, d.*hq)

8. ,ffi Hrcl ' ,f+.ss
6*+ *2+ r
t*t B> = s3+ qsv'-4
-- .s(s?ql
s tr:f +r
Ntsl -- srls+ 6
f+s+t
*+ t,s+ t o
****
"i'' Ntsl "
ga+s+G
-
s'+g+ I' 'i
-1F*
J.r.*b* ^ e r- r. f+*,stqo,Jl ls --ls,rln
= O. lo+9
lb +r* &a$k-.-' 611 t,' I t,la -4b"f lo *L oh=&"l . -II*
fliuo,
,r z cJ?;-{E)o
h.-" erct c1o=6
ti __' tr=,
T&.a, arbr : [x.[ s I
{t . tl-6 a' Q.4s
1E..rT = L
J*.h- u,r qot .* tro,-t$am' .,,r L j*,.."L;,* =

9. "t'lefUog16 ,9yrTil€€tl'. & fttfee, OE5,,11N
@ p;o/ +t, /"*& {,*"h*, HG) uh..l 6iues allwc,,,rlA >"s?w
ffr&r -'8
{ ne!1,,
ffie
6to" e
s;" ;
. / tp*z_,
J tE/Tr'
;(3fllt"
a
J
trt s Q,
a
,l
se
et
4
o
raS
to[*, k. o
ru
PA ! a a,Ao,*,e ,qA')" dnu*
Ld,
ru
0l.n o=g
ko lg,
crh* k, t
= ees S +j .i"
= c.os s
lA> + ; Err1
gr s _o., __,. ,. .-,'uJ-qJ +i eJpf
i laezl+ I r
92 : e '[--7-)r
;gI=e+
= cos *+jsin€L 4
s C-oc 1rrrro + j S" 22_5; "
ga : -o.-fefrf _io.To-r
t.,e
e-'.: @Eo tisinA

10. TL /r**/"- l,,J'* Hcst ;
$cst :
(
G-sL) fs-sJ
I
l-lcsl = . i ,, , , ,,,, l
(" +o"to4i o'rc+ ) ('a o'zaft'ti'7q)
[.rm.la (aXl) C*tg.) = .d+J"*'
Co+o.ro+ )a + C.'ToT )-
I
-,,
16r1b)!o J+&ot+f
ffis -'
2'
6Da aao'-tTo?xl + ovd':[ *o'IoT
l
-: ,'
s*+- t-4t+s * o's#o'5
t -r.
T
Hca) s ''

11. pe ;, ,By Fgiggg gq,
A*/^aI
ftt*{,*&t.&fisfi6 @
@ fnl n'*,/b' !,o a
", ff*lr*rr/= o6*fil*
ffi
ffi
f.". |*,,rl
sQ Lo,,J
fcrrs Lo,rnJ
s+"p L- J
cA$s1", rtU" e-il| fess l*,/ rVy'e=o.sJt
. ;/** /;t l,ss , -8r/l J 4/Yt*.
ripple oc? =
r,fqle di.r=.*,
r
ll) 12
I
o"sJL
,6o..lL
n :+:
lir::1- '-
e l1 l+a
+ l-Yt*r ,
I.s-nJ' 'n, .,-:
:
s", $*l k ;,^r ko Gs kJ U.[*ae
( tq.) :
lle
f,""'r(6o)-,JL
E " y, !
EI
't I
ka
to-
ltt- |
l
1r
-l'
,o6-,
l-.la:z - ,
st
loooooo - t
o'(re?r
c""[*'( ,
k-I
allrel

12. r
a
T; $"f 'n'.
lltkir,
,
f
; = 3t6.9g b -+qa.lrro*+
c,*r-' (q )
&b{ ,'
C*t)
o1I" forr"j
..ea[-t f e I
l/TL
I
_l-
dre
n>
8.ds
-
-_-
. I-al7
]f,- or&rr
[* qJ th*
oJ,,*+,.-$t+ar ,**J
$'$; isffi'
fl.at!"t =1**'f,;s6t .tr1Le
&^ = b ,14 tn e")I 1 {/ l!,...,...,-.., 1..,.-,,u-.,,. : r, .,:r; ,..,''.;,:
", i. .
o"€ al [o &0,.C*4

13. TVaro"roera
faer - B
rt/* J,4u 9 Cs+r) k*a)
(s**) (s+e )
'),s
,i, '-
bta )ffirt : Itn+ss4 C
eu+ss tlz
ps,-t rs{ f,
d s'- .
2
6 165 fg,s
lz+Fsfs g
es7*rt"t;a,
,E}
Z$) =
eL
fs (-)t
-t/ 5
" L j7€p-
sn
:frfr
-
rS)rnlzyesr" .x frzTERl
"DE.vont
gl/;, /r" Cor, /o,n -V reo/,hol"* P/- ru/*vb J,-
bca) =
a
fu V;r"+, -$r.fu
Zu),
€r+&+ r.s+ tz g2+ 6s+ ,s * tz ' s'+s$'l /*
Arrry;V /- aoier^L ..d /ena,iooL 7,/Vn*,;J in 4*
as""rt/;y orlrr" ,{ /oo,"/}
d/ /?- A,r#",r*l rt*Ga
12{ Bsr
"') /tf,:a*" ( * + P'
t-Li'o* +* sn
I
+L
r_s + ,") l"*+ i( * + *"_ _,!,
l*l.f*,
"+*(#+t
+ &f+,,6s+ 9.s + (
S

14. .r,,.. .f-{_g}.- =..,'::
:ai
Fcsr
,'$ *J f
: _. -.- :'l:
,t '-
t t-'s ; {,.. Sevier orn
.q,ra I H,-[t{.1.. . =6.-- 4e
'Vn*
I 'r:
Yt+e
t*h,l*ho^ is
|,lt
lo
A?
.i:
' ::: ' :: :i::: a

15. '."4& fr"*
'lDestaa
.:'
@
F***
@ A Lprie A*y e*l *t, {,:t*,0 t b k* ",/ tel *f4 6o,ru.
Desi;7n +r* J, [-, ^" 4 T ",,J Tr nol.ork,
cJ.os* {""Xi*.d .tA) ?-
Cbr- bl
Ita ux = e.oo5 llrs
= 6oo r-
g[r*L.*a ,o{,,,: g",r
t,
L':r* F,tt " J- t'*1,aa:r+ ,^,..l/i
^,'.-,z-
Lo.,
for^" Fll- Tt-s=.{.r*,.,..,A,,,- *
^.-/.-
F'ril* Tr - s-.tion )
tlrr)r ."1.:,... i
k--.-<, --:f
LT
3^ L*
slr,^.to.'.'
,e-frr*ar/irf
r. -, a' l, .]::
o
,t
j =
--
-
Jq
-. K/.-
o
Stl. c.L,^-e.
;-r-a..-
t.r)

16. *t 1.,* O
,hL =.-
rr d.
6oo
3.1+ X ooOG
-$
= $s.ztq X to Fl
T3 $roJ 'g ".-
-
u"T.
a*h* @. e :
t
-
-
r- II te irc
Ig
-:-
ts-r6tooo' 3't+ nGrroYatro@
: o. z6s xtc-6 p
qs.4q
tu
o, s.6s
4
a*t
L
--
-
9t
o L
Ir
L". F"" Fff.. -a illel""-&,
)
- T 61qf.o.rk'
1s.+gn tl
o.tsasrF

17. @
.ft/er4oO* SynruEsu
''D(
FII.JEP, Oesrtrz^, '
fnm-@'
: '1,. .'
4. iDe"silo
k, of*Je
a l*," Fss -r- $e.k* $ill"r *itb .r C*t o$[ d"tX*J { 2'F,!{E
t
,^ril* o ooA resisoryrcls og
''
4gog. .
C,^t.u &Wf [d.). zt+Hrr :
,
L-t resi{rt..mes Lpar* h) : 4oo .ur-
"$ Ls^o po.ss $,t"*: (n- s."[i*)
-- *
zooo tfi
sL*"L.r,
av^rz^v-
J.s
T6.t+^I u :-
LL
t
-----
'Nt<i e
tt'l,
';
J*E
tc
:':-
*Tr^ti* O LT
I
L= -te
{' T
4oo
9Oooy 1ry
4ooo
roefg'tt
Usi"6
([.'*, = A't4)

18. L: .4oo
Lz
6eaa.tstt
o . e6."t Fl 6a"7 *,iu
'i
6s.l nll:.
ar)
;:l
lo J"d e :-
u"rt +[.* o J.:
.C o,l
-IFBce'
t. '
f,"'t, *
''r
t
?spl(4pqx]I
I
'zooo-X-44xa.rf
t tL* 't:, B. t4)
I
!.
)a.tgs Y tol
_6
o'?ft8 )t to F
-r'.*,:. -=
% ?= o'eq8
L: 6s.rrrfi
:

19. fl/efxo*re I yttrtlEsts .. o( FtLTi€pl DEa/q^)
PaRr - @
' Dayn a. 'm'
antJ
{* = a6ooHr
4
_)a G.
F"t !n LPF,
'""'''/
" = &e.T&
lo* f* $lLo J' fuo' 6ooo-, 3f, = tsooHt
ko Prp = doo*o
{. = Irsol-li
,Ix = ebo l'l:o
t*j,:r 5x{Ex m - J.eri.,el L,.- p"s" Jttl"r^-z-4.- ..,Az1a l1z-l'a
i*r st.-4..-e
(G9,
. . -If r-Ll
t
o
'@,-J, 1rb
LPF,,m-J*riv"J
fn= ,.-(*)" --+ @
-''-
T - t6ge, str.-t.oe,

20. *,t e1"*L"n 6,
L = rrg.16,',$
k
t"
L=
ItL
k
T.f
"
=
6oo
8't+ xt8oo s(sr
to6. t6 mH'L E o.to6b tJ
-g
o, to6,16 )r lo H er
F {,*{.,-c**;
'rtt(l,c
I
r--
=
T l,uJ
"
t
____ri
3Bq t a-oo
I - ( -J:-)'
l- / lh r'L 36ooJ
1ffi,6
.fnL
od.J
tnc
F
tu
o.E66 ,fO
T
o'g'r5l+7.xrs-6
= o.la-I7 dri6 = o,(s-"rFF
fn : o.E
o. € lct35
-
so-o/5596
g,
9r
O- OglqBS =
r a9.a-ss47p1id
mL
rne
-6.lqs )tro
o'866 + 0.fo616 =.
o ,t66 * o.aqs-^,;€
= i t'?.3sm H
d-r#
)r: t
| ^ Co.E66)2 "l
l* o.10616 * f ,-o.7col) L E464 J+o'(oct(
o "9,.s
s .4C+,
o;olat-r r+ o"lo6t(
u"t?
7,*[* @
- nn :
o-s66 + o.to6r6
--
2-
6o
s
TI I ltoo
ql ".tgS iroJ
" O.g,sS s FF
Tt x(oo x ttoo A- t+x 6o X I Boo
= -o" gq,f r ,i( r s, o.n6pF
I
0sio3 *X#- @, f. :
C=
4r o"sg6

21. 0
r- rno
-l
e-
4ff' I ],'
5[
* x o.a66
:- : -'
-,:-!
I : o,.r,IS
: i: 'L
r- cs.rg6l
o, 919
l
4s.q6mH 4,s - 16,nH
1" 68*n H

22. a t. tgsfrH
:
o. ra ",If:f
i:-,1 ..:,i .:_:'_:j:lrr:
. I ..:.: .:': t
1 i - ja.=',i
:i'- ir --a-, I 1- *i'
;:-r:'"o':;:-,:r : ". '::i:
J -;1;:"; ii r-*,,- . .-
-' --r' --- -: ir
,::
r I o.ozrarF
tj:di"ie{ i : F

23. TNef*o&k
fua*.,Su
@ Pe,nb"" .lt- nJ-* r. in L"+J,- Cnnol S; , Grirnn X,ul :
€csa+ a1
8 y*rtl 6:s1g, -. 04 P*rte-t': M* q^)..
ti(+* (' c'
tet-,11s'+r)
to Ee. [,7["t +lear {a
"
4+ro.1
t
s"+ +u
<.L
/," r . (*a+r) (sa+q )
r.-
=
' **+ q*"+s^+l
.,.,..:-----
*o4 {rs
s co?+41,-
t IrrtrT l-.hrr...a F I ^
-srln.sl{a ea.lvrior,
*"+,o.tfflt$+rts (c
,
I
Yu': s :, a-r-" -1
+
t!3 r.a
s-
I
E;s
-ir
Yu, E>

24. ;
lk Catq l*- I ,T*,o *l i- k*
ll,* 7L /" o* /.++ #*r,' /1"/ rl /tryaia*q "
#,^t A k{ #:r"1,
' 4s.+ss
cral:oi*d !r,-har
go 4r;tlen * {'a*L'*z
+L
?s onts,ibr"l '
-,. /est
: S 4g ps,'t ?
ett 4e
lUr'r'tr *- Jua.A?w irt a'cer6a7F-.ry*_:a
o{ pooa o{ s ,I
qlfasl+,g4
'or/er
ftfaJla*
/ c"l s
er'/,1 o.&/ ,
4s+ sa
fc"t '
+.L,1rrfo*+s
alL
ts
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