Unit -1 (Feedback Amplifiers and Stability)

1. and abiLt1
beerytuot< concePt - gain 'uith ffeamcx
- e[[eet
9 ^r: ' ^,stabiLi+td , di,stor&n '-%
leedbvct<
' 0n ?^'
'
, 76,t imy>edanc€ r'bandaldth
, inf>u,'' and ott :
Topotoflio a4 pdmcrc.. arU>!"+
"".. .
ooo'At':
q 6exiu Seriq
-
$eedtucrc
6pli{'es - anr -
6Wt $eeetbacn
o*",!n::
,'*:::"X:t
,ft-,'"urn
^^'a^oa' Ireail€ncc/.,,U
g ' r''
tn anct Phrc maxgins J'Ttqutn'U'
rrlDenAoilt"
I 1
' t. l
i.
.'/'
llnil - 3''l" i :" r.' " '{Lf,t ll &
Ascittaws
bvrcLauson citeio
h.It a,s0 Ua.nr - W
Uv
rtleq obcittatov - CotPtc v o v'J -
u 2.frt efnl asd uabraU -,. a. a 1YO$tal
orciuinr - Ring oaeiuator's (
- v
- t?h,)a -Stabitixuattbn
Bcf uaror ahPAnae zalOtrsra
Unft -A
fineel Arnf,btert
lo,s.ses , unlwded
>vvta
and loadec{ I
q

2. .,-1 ,Unit: Lf
ad ,l,4ut|t ibrator' ci
U
nlaue .{ttitn8 % "MuLa
ci"cuits - Ane lytbr,s
'-- Bt ntega 'W '
"
fund
^.^ )I
circuii's r '." i'
" tf' +tjaqer -' Uf,T
byatOfd r_ ECh,mr . . L/u r !
I .,ri
Pouet nryfti|ters
t
and 'N onvefia.rs
t''''i
i
Bttct< ,
detign
U
i-
,_* {- ,,,
-lr '
t
fuot'ev
c lass
dass
DC to
boost
Ampl$eta '- ''i class 'A,,-' ctass B qlas$
c - Poas et MosFET - TernV?!*tcve
AB p@q am'Pl$ev
Dc conveTtor*
.o_t
nnat]StE &nA-U
ut ".''' -' '
I'

3. unit - r
XeedbcK ampli4iers and StaUtifrtr
YeedWK'a
U)hen a' Port s, $uacrten O'10 ouPu'a is
cnmbuvd fu the
10 ewist . rfius the
$racr[on el output
$eed tud< iz ctaz'si{el
into *wo +Ufr* namelctr :'
t' Posftfve $eedback
Jr Nrytiue gtedfuct<
?ositi,re pdaacK z-

4. ArnpAi$iet
ued tu arnPLt#4
, - ArnPtt{.ier
a 'stabte ou+Pub
'
0J€aK' nsf qnal-u-.
ka
*he
darfce
UJEAK
datice
unicn
Ull'ttCh
.stgnd,
ahich fli
ampli$tes
(
Asof Lnnr iA a ciicui'L tlthich Wtov
^b
OnU atrotrttr'Lt ' -O '
&herwis€ knocpn as fleTe wwtive civc'uit '
n 4 We aryrg$4'e=r :'
olp siqnai.U;
cto)
ilp
i ,'
olP sf gnar
(Vo)
flgtettotK :-
W,s og&ry','
cngEal ,B_t?g#F 9I E*%,
Mfqffi
Yo

5. in arryifier clvu-t'it
gain ancl clorcd looP
gpen tooP 7uin , Av
Av - oPea J-DoP
AVr ctosel IooP
Clwed looV voWe
, to trind open looP
gd,
Yo = olP voltEe
1@"
p = eedbacrc actor
'fteedncn voLfte , Vf = PVo
V1 =VIn-VP
V =Vin -PVo
Vo = Aili
Assume V1 = Vf
:" vi
Vin = Vi+ VP
Q
ga,tft
gain
Aut
Av+
qa:n ,
U
_ AvVi
Vf +Vt
= AVY| =
'Vl * Pvo
d
-
1ii1
6uU vo 7 Vin Yatues tn eqn iti)
Aw=V
Vin
I

6. Avr
,t+ p Av
tosp Bdr'
An+
L rSeAv
0*n uJm $eeArncx Vril is
Bdn uithout ineb*rc
( Av
)
w 4 @-'- feeo)
Aus a Av
Yatw
the
Jhe neqanve
Jhe 1an
TwAbacn
Artf
qoin lem
U
ol eircuit
uurcd ng
'nhtc,lq maKe
$rAbact<
(
zen,sltive to vattiatio
GrrLPOnenEl> ' JhIs VArr
crnnye et temPexatuw
lthe ornPli$er aiFh
mau
negatlue
o{
9'6,
dhe atabLifrJ e4 Zdn ia at's
tknoun oE Adn
aerusl$vtq
.__[J

7. enpl;Bcetton etith Pi b ia caneel
anJ
,sen,$+ivitt1 q
at{J eqn ti.l (,,r
"t "to Av
'
wdAv
dArlr z *,
dAu (t +Pav1^
dAvr = dAv
p+ pAiL
Diviotfng Av7 t
dAur = dAv
Auf 11+puf au t
AVr
t.+PAv
dAv
(t.+pADR x
-Y' (t'tBA-vZ
Servsi?'vitt
a)
uhere, WA
pVF
@
dnv
Av ( t-r pAv)
$actfonal ehange in amVli$'cauoD
ulm ffedbacr
$Wactrbna change fn am plilicaudn

8. &-
n0f
>the trannpv
contfunb '
depends
8,oi,
upn
q
tlg
tIv arnpl'f$ier ia
$aclort>tL
Voint And EnWYaF-we '
v nle reciVxocal e[
catted de' aenaivitT'
D
,d
= -,
1
n
L/
'l+BAv
D : t+pAv
B"w -- Su - fl
Jhe p'z.oduct
6b tl-P omPMSer
wW 4ladbaLt<
AvvB'W
'krtoa
*he zat'sinury i6
ag D'
%
betuteerr
clrt - olb
d$ned as the d
, Wlrer,cVuD
and
o{ voLra1e Bdn and bandt
citthout SeeZbaCI<
and '
6ffi9 r5AfTlA '
; Avp x E"wt
fub,
Qv
toe
Arla =

9. ,*he actuv
bq t+ pAy
B-wf x Av1
B.ulr
er/5
: B'W
T+pav
B.nl F = u+pAv)B"W
Jo 4ind wt - o[ Ye+unc7
utith
Ue ,Pnou that ' bezdtul<
pin, Avf = Av u'.r
ttpAv
bandui/th 7s lncneared| "'Andt+pAv
Bg us ut, rts , (Ae
)[wev cut' oft $t%uw]% r uDf>ex
and mid nar6e neM+endu
', t..' AVr |our)' =
' Avfjsu)
t+ PAvilow
r
(.1.,
l
Air (hi6h) - -Av &iAh)
L+ PAy (hrgn )
do
WbacK
v0LtaBe
can uiiLe-
Ar+ [ mid) = Av hid)
L+ PAv (nicl)
-[U
BuW
6ind lou), clf,t oft NeqPQnqj : -
Jhe nelailbn be1tteen )ou V.q,uen cg ndn
ab rnid VWuu'o4 it givw ctt'
cilh-
"$ V%Y*"U
-ilr)
-iriil

10. Avtmidl npqv tnia)
-- Yr)
Ay (.lou)
A v f rnid.)
9ub eqntv)
AVf Clot-rl)
Avr( lort) =
-
f"i)
Av tmid)
, r - jb*)+pAvtrnld)
D'ru eq,n Nr) Aq A+pAv'r;dD,
I' -de-) +pAv (rnid)
I,nB av rmld)
: Av@ia) / r+p Ayrrmid)
Lt PAv(rnict) dtsrt)
| +pAvftniil tt pAyl Mict )
-
6/ii
AurLlouf

11. | -'l'.
tvlll/
l +VAvfutd)
{r, : _lt
' L+ PAr(rnid')
flrqtrour) = @id) Cix)
,- jffH
Wlne're t'z
ta loetPr cut % WWy! otritn 8"y*
Jhe lotoex cut S $e+ueneV
ruith
Wbacx ( tr+) iA )e,st
-
fihan loue'r ru*'o$
tucx Crrl W tltu
Bg inr.roduur,g
nequenc7
%usPonrc,
i rnVnoved -
negadtre tgP-dfucK, thz- low
'v
{li iG,6
%
"'ttp ampli[ier it
Sirnitattg, to
Jhe fle-taHbn
Vqo',ud and
alvext als ,
o
Avrllnig =
hr (hifrh)
Av+ ( higb)
6'nd Wpes c-tLY @bb
Wq)to,%
Letutw:r A^, ak hlgh
gun aL rnid {.+*% 1,s
Av r( hinh)
r+pAv thiVn)
Av tm?d')
' -jrfi)
_u Avffiid/,_,t
[f/rr)
L+ Avlnid)

12. (n
O,
+>Z
+l
Fl
ri
c(it
i
. )l
I
I
JI
, ii
I
I
---,
j
I (;
r Ii
Irt,
I
Ta(FrrnrpAvr',)
t +P ftv
,r)ld)
Aur tmf"d)
k-+f vehigb
.+bV Ir+ PAuf"'id,
Avpthign) Z
Avp (kigh) =
Avl f mid)
r- dt#) + PAv Lnid)
*-0f
Av(m"td) / t + PaY trnid)
up*rmrd) -[ (r4r) I tr,P
| - j (r/F,l
I+PAugnid)
Avr tmid)Avs f ki1h) :
' Avp(h'Bnl = Al+frnid)
fnr = F; { [r +Bllvt"nidt '
Auq hinD
2
'Tt''e. UPPu{ crJt - sbf
fr,p is nr-eotdPedbacJl
tFtF 1g> d
M<,u"n"21 with
lhan " tl:te t

13. hnaw lhab ,
B"w= fn- L lwithout
B" hJs
f.dmcK"
6ain I
All imid
Aw (mid
Endbam
bedbacKJ
bartdusi{fh cPitn endbact<
It-te bandutidth ui*lout
B.hlg ) B.W
$eedrtact<J
04 @B
i* flYeevex
ir
[' r..-$
i* @nd a)> -the vaianbn
zlgnat '
a4ny>X$er uifh an ePqa
and to,ful ,havmarfic
'fhen tre intnducfrbn q
uttth lecdbacK 7 anb P '
nJ 'the
DeqMrve
U
the dFstovnbn
aer>w"Avin7

14. Distovfron
D
dertoved bUt6
aD
Noise :'
,Al',
vu
i
@ne mffia
l-
arn'S>),itriar
ecteTnat1a an
6aus@s q
uffich dePenda
L+ PAv
whefQ t
DF Distortt6n ulth
D - Dianvilbn uifts'tt
Av vLtune fr^nUvo
F leeaUarx nafia
I
T
r:-
fiti
h
rll
tt
t. a'
ril
:T
F'r
Jne omPl$iev cincwt rurlt
,1%"Y,
ard WdbaLK
ileAcucad bU
ilaIiD, hm the
ffie .9rne #L
w
cn
-l
-{N(.)
(i
-
1:-
Noise is dsoved bg N'
Nc2N
L+ f3 Av
u)heve ,
Nf - Noize uiil1 e"AbacK
N Naire u:1*'tot;Lt Sndbuct<
P 4eedbact< Yafrb
Au - vottage gain

15. ,
,/ lmpe&nce i,s the
iatarce and neactanez'
el An amPXi$er zhould
irnf>edance '.lo fr)eb ib
cnrndnalien e4
,hAVe ,Ltigh
uitt not
oJ tre inPut
@n be
aenir>z
v1ltaB
",npfr im@ane
negax"ve vowe
input irnPdancz
lul()rl srJ
zi tt I.F,!y>
input irnPedancs- u:it|-t
input :nrtPedctnu- ' cithoua
Yedbacx Ytatto
"
$eadb.LK
)he Pneceedf 'A
e ,'OUY@ -
") fligh
achieueA Ug ihe,
iedbacK'
bg zi
+ -TlP
given ,bA?,
Lit :
uhe"{e,
zif
7i
P
,*he
Awpuu impedan(t t-
An amPlt$ier
i's u'PabLe
_)
uitl't Jedbau
$eedbacK
t Jhe nPub irnpedanc" 'b
incrleased bZ
actuv
t t+ PAv)

16. co
olG
s'Y
-l
ri llf,
c.r ;i,
U 'I
!
___r,.i
, :l
bg
ll'te
JTB Jnu owtu imPeaarw in
.eiet 4eeabau<'
Oulpur impetan@- etith eeAfac
gTven bU,
7o
P
Av
uJheve,
7a+ 9utPuv
Zo
outPuL
'JPP615s1sK
t+pAy
impe.dancr-
ZoF
impedancz
pedbacr
ourP4U:E
I t + P,av). -iI
otr
%
"% Vottoge
l" Cu*<xent
h" OlWenb
.desdes
,shunb
aexia
.ShunY
Lseig- - sht^d
L@decK L zcttt'xttt ')'tv-.
tePd&cxL Eerfiu-8su1^J
'V
- n)n t'
C zhu*- &lurt
'eedw'cK t &'vnE-gtsg
'{
Jhexe
t" VoWary feua
badc
Trnpedanca i'5f,,
uith
wittlout
.rl ,0
dwnearseZ'
rfirfib'nafrJF
voLtuAe
nnnatue

17. blsr d+n et W
Vol+age *tiu ' eeAbaerc
amfliget :-
R5
+
Vr,
leedfucrc
nefufirtt
Drnptifi'er
Basic vdtuge
Ampt( [ier
leeamrr
Newort<
Sarnpt ing
Nefi-^DTf(
Volfage
tdn n, =un*
,{nenL [eeAaacx
arn p9ifi eY ' -,9TIgS
Rs
Basic
Tvarronducfurv
lmpti[iet

18. blg d+n €t W
,
erAbacrc
amfligor :-
eeAaacx
arn p9ifi eY ' -
Sannpt ing
NEIUDTK
VottaXe
3u, Ou =V
+
teedfucrc
NEKJfiTK
Bdsic vowe
Ampti [ier
leea&an
Newovr
Ornptifi'er
Tvarronducfrrtz
$mpti[iet

19. Basic Trans"reslstunu
Ampti$et
Li
R5
feecjbac r
nennNK
r>li"a
nefrnovt<
?rp
Tarwtprsixaner" z Rrn = OutX.t
"ot,fie{lg
tnpuL cLtt1fl?nL
(nwes.
*zT
<To
-LL
Rr-t[r
-b
Basic cuTrenb
, arnPt'"#u"
Yead baeK
C'Uttnent qaln , A', : To
uri

20. ewu4e{ "
Ade
/&'rll%
JI
ct
leedbct<
has
i,S dso
,9iU
ampli$iev',
eaLled dA
and zShunt
voLtage
cDnrec1on
The wtPut b
with
#te
the'neh))}rlk i"s
tte arnPLi$ev -
uol-tuBe to
viu uith
uzed
panaUel
-|he
$uacAon
c[ #te owub
it applied th
b
o
e/5
irnpdan(z'
Eouuvalent
Ric = )E r-
ri
cincuib v
aexiu $eadbacr
wnPLi[e'r Kxcuit
ulculattng *he inPut ond ourPuL
U
b
weA tot
'Wbo(K
oubPaI- ol
connedon aL inPut zide t's
*he inPut imPedoncz'
connec-abn of frie outPut
decne'ate the oWub
Rk and RocJ

21. Jo [ind input
Rir :
Apptgr"S
SiRf 7
I
Vs-Vi +
*ranqgv
llJ)
vf
FVa =a
-(iii)Jhe $uncuan
ot
gain,,&
; Au =Vo
vi
Av fru
t+ PA
RiEi+SpVo
-D
gdn
= Vg-
V6
AVr =
Av vf
Av riRf
Rirr" + p AvriRi
Rf
Rif.= b 2 Ri IIIPAUJ
.fi
Vs
V6
Vo
v5=
Va=
tvu
tpzi,sta,ne tJJtth enAbact<
-
li)
eV inPut slde
'
Y:-
Ti
KVL
Vs = Rfar +Vt
Vs- Rfi; -W =o

22. tf',u
$endmcrc
Lt+ PAv) /
Rit i's
input n*siatwc*
vatue rnuLttVtied
Ri uith
the $acmv
input nezLstanu
value.
utith
then *he
incnea'sed
$ind Auryut ,flr%f&onc-e usim $edbauc ( &Dt-
the oufluE $eeabacrc ,1.%i6tanQ- flae
VoLtaqe arnY>'$$ev i's detetmhed Ug
U
Equiualent ciYceitt " -
n . ,r A
c -- t1r^P tl tlt_r sg t
-7
rt
I'
.r I
fr-n Ytt)'v
Ror V tl"r)
T
APdU 'f<ircho$'S voltoge J^aIl ab ouQuE 'side'
Avvi
AvVi+ IRo -Vs =o
t. = Vo-AvVr" (,,)
Eo
KtL at "npua side,
1
$eedaacrc
ApPtA

23. Av i*
tat<inq Rr- '
U
To .(ind Rb ,,
U
Euu eqn ug) rh q,n Cn)
I = Vo t PVoAv
Ro,
T Z V6 [tNPAVJ
Rop =
t6 ft+p aul
@
IooP v1we Bain
f?oJt I Rl
RqR,
WR,
ffor
Bo + Br-
t+PAv
Rbt- = Ro Ru
Re+Rr-ft+P99
R'ot =
Rtaf '
L+
PAV

24. bU Qn r Rr-)
R 'oe
Av ia
Ahr nE
RoRu / no.t Rr-
Fo*Ru+ R;flf v fno+Ru.
RsRu
f Ro+nt
I + Rrp Au_
Ro+ Ru
RoRr- . Au --
no+n. 2
voL+age
Bdn,'tarcfng
RtAv
Rs*Ru
R1,
th e toPoto71 ' Pr Erarurqittanez
atnpt$ier irs cuea*L rni"tin voLtage aamNing
Lb i,s al'so ,knoern
'TFre
Werbn q -the
al>plid in PatatJel uitn
the nA-u.DrK'
+
zN-
P,
"- vo
I
IZ
es Ah etnt -
+evorofz
i^
lo
a'ransn&sfstarre
AmPti[i ev'
leecbocl{.=
netwoYK

25. frtansnajztanu-
OWQtt CL/t2Lent ntO
.Vi
gJ
[rs = pvo]
Rrn oW )oop hansxa'ustartu. qa-En
o
JiS = 59+ I;
Ig -- rEf + Fyo
oufrPu'Y voffie
b;3I'
Ra +Rl
cUxslenb lau Ab
uti*t-tock
@
I
I
I
I
I
I
V6 . Rr.rr" xi

26. Ts ; Xr' + pRfV rf
Ts =Ti(t+pRM) @
ilhe tnpuE .fleAigfrtn1e uift|1 [edboc.K
f s qiven ab ,
Rp= Yi
T;(tpRvr )
g" vofige anunb
hput ttai&artcz
the batur
(t+pRu)
gufput se*stana utlth ieeAmLK 6or') r-
-t Ti Ro o-t -7a-o +
$edba'cK arnP)tfiet '
uith $e&bacrc decxendes
@
*he
bcd
4
JO
p ptyinS
lufPuU 6ide ,
vohage anunb
-7
Ll
Rop= W
T
Jdrcno$[, voLfage Lutt ab
fiRr.1= -tRo lf6Ru
fiRm = Vo- fRo'

27. Jhe inptrt cuwEnb i,s
Is
-lleYe Ts-- o
ri = -!h
Ii = -pVo
Fvo = -I,l --
@
&b eryr@ in O,
= -% -{Srn
Ro
= lO I L1Pftn)
Ro
ri"r 6
Vo Ro
% f r+PRrt
Jhe outPub trwi9rance
elne [acro'r Ct+PRn)V
qiven o^ -
a
-@
c
.l
t
C
6uu O
I?or
@
br
I
'J
Ror demwa

28. .Suu
nbr
(t t2
Rr-
w
--t
(tO in
Cwwtent
nbr
Rs +
HPRm
_EqL + Ru
,+PRm
Re Rr-
Ro + Ry fi+psrn)
RoBr-
RetR;+ P RrnRu
Div Cte,) Ag (Ro t Rt) ot1
nbe __ RoWf ss+n,_
=
qn
@
rturrl A den ,
To
<-
@
Senfea $edmtrc amPligeY :'
pL
VJ
Jeedfuet<
netutovr
hsic trartsanducaoce
NnPil{et

29. Wivalent drcdt :-
-r r[
RiP --)q'
Il i
> Cowmu "6eY1%
T <- t -'7o
SnAbwrc
r
I
Rr-
arnPX{ot i'6
arnVli$er'
6P1121nNfgn
uLLd QA harusconducbance
. ), 6- taai?s) Jr hat" '6gfe
afi(fler$ - "pnets feedbacr
ampli$er,
deuercpd PrrcPOn:torwl to thea
l6
E t-te amPl[ier
el nnductonce '
Lrarvscondutfiorcz
emp)"Vo{
pt crlnuertrnB fie
-tttixtt voLrafle
*he wrut
.+la*%
18
LN
outPcfr
st%ittotnce
> dhe
Jne zenies mnnedgn aE t'ne inPuY
'side , ao rhe JnP& orf sfiPul
incvea^Ps "
f,raYv@dunn@ $erAfucr
flmtr
i'

30. $M
Ri-p = f
APVYing ltivcho44
= TiRi + Vf
Vs = Vi 1V!
e
Iau ab inPut aide,
f?tr : -
V5 = PTo+I/Ri
-@lJyw outPub atstspnb ro it Bi*n ba,
V,s = PGf"lVl"+ ljiRi
= PGrqVi + Vi
Vs = Vi ( t-+ pCt'r)
Vs =aiRf ( t+PGto)
Uheve, GM -_ q>en )oOp
usithout
Rv.
tmrb?nducn/te' gttn
JeeAbocrc
tat<ing Joad "rd'ftaoa
LogP bYonaattductance 7airt
[@dbaLK
Y:-
g

31. RoF.
t
l-1
ouPilt
t.t
Wsinvane
VE =o discon'necbtn
ApptyinX tcircnoA"s
GrnVf ;k:T i-T,o =^$
GrnVl"? -t**
I = -GmVi+Vg
RO
inpuu *ry" Vl" i's
tt
8 +Vf + VP --o
Vi ='VF
V' = -PTo
&u qYt O rh eo'n
Jo
Rr'
4
Vr--pro
Ror
'rE
bad na*anw
Bi* ar t
f'.'vs=oJ
@
vf
VJ
GmVi
@
@

32. (t
;a =}fr- - GmpT
T+BGrr[ = IRo
T ( t+ p6rn)
Rgi
Ro
Ro = RoF
r( r+pGrn)
t +P&m
Ror
Rwiatanr-z fncrea'ses
@
bV rhe
Jhe ouq>ub
f,octor
(t+Pcn)
Jo Jind '- dt
Rbr =
R'ol
Ro+ [l Ru
z- R6p X Rr-
R6p * Rl
= Ro Ct +P&n) x R r-
RoU+Pent -t Rt
RoRu + pRoRtGm

33. ,,((JN&
Div q
ruh:
Rot= RoRr-
(Wr Rr- r pctmpo) /po+R.
', qrq -- Ro&n
i"
)l t
t-tl
--lr':
.[rr
il;
ltll
'I11.!l
,-^l,
;8
,'H
if;-:-
R6+ Rr-
Fo +Rr_
P br
L +p?vj
uraenb thunt
@Uacx Amptil,ierv
*> Ti
Fqltvalent Clrcuit
RL
P'
-7 26
Rr
I
--:-Rir:w
7s
rt it aho utted
tsasfc Csrrent
0mptifr'ef
{tud,or'*
arnplrii<
r-P.r lt
I
I
rI
I
I
f Ro
Aio'

34. cuaJpnb .amfling
It ha,s
,afde and
.atde '
Bo if i^
amPLi$er'
ln 'thi's
rs ;6
cillnenb Xi '
-tepotogZ
.shunb
zevra
catted
@nne&tbn at
cPnnettion at
AA .shunb - 6evrA
tVte
#t e.
mPub
OutPut
$eedMrt<
onffguv-avbn, ttte oMut
dinedry PnoPortnonal
fr the
b
lnput
=Lqr
fcct aE "nput zide t
c
fo i*
/
Jhe
ft,:
outPut
fo=
cuxflenb
Ro Af Ei
given aa 2
f Cc,tWenf
@-
f,g = PAf Xt I fl'
ft z ri( L+pAr) .-@)

35. rn
o
<l
)<
Jhe inpub ,xeaiAtnncz
Jhe $arnv lrt,pas;
Jo {'nd
,-
Rpziabancz Ro r
Rs | , -th€
and Eouru-
T
dewqta
Ioad sai'sta
aJttler) F s-s
o
llt
0urput,
Yor
$inarn6
'^,r,7oo u,=uo
IRof =
a.o
APPryrnA Kcr . at ouypub aide
"
Ai ri z -rt-fo T=h-Airi
Apptging Kcr ab inPur -side ,
fJ = f;i+I;
Ytere I,S = o
Rr_
tr
nir
fi
ft
f
T
= -PTo f .To =
s( fi=pI.
= T0- AiTl
=Vo Ai Ii<
fb
=Vo AfPI
Ro

36. Ror-
Jh)e aurPut
p,tu, [tr P Ai)
Jo find : -
Rtor
bu
R'oP -- Rot tl R t
= Bsy xRr
,Rot +Rr
RoRt ( t+ pAf )
Ro[t+pAf)+Rr
R'oF
= RoRL [t + yzai)
Ro'tRy+ pRoAi
Ro + Rt-
R'or =
RoRt-
@
:bu0
fi+Bai) f Bonn,
O)h?-te,
Aa-
Rtop :
t.+pAr
TaTn
Ru.
q&4n
U
RL,
RoRr-
Ro+Ru
bg tarcin6 Joacl
Ai
without tuKiny lmd

37. e
tra
fr1at
L ar@) '
cl)^6ed
is
a]
-U
l6
uKA tu imPxotte the
.x'nqle Pote 48rcn '
U
uted fu contrel the
drl amPLitit' arn cizcta a
,*PUfrnB methd '
ubma
io tttd
Voaiave
it ured
fr avoid
beedbarK
-
fu ,xducz
uninreni,
the
uhich
un
"iy
'Pes VEpal @rnPenmfion:-
l. lntetnal WuPrtccd
at
it
elo
yP4lwtde6 iol
') {xeqlr*rrtr
$unctten ott>)
rnotte Pole's
)Jt
utdth
.l ,4t
e4
Vele.
.> Jt
o[
'> Jt
,tra$er $wcilen
ntue
Need
') 6n' clored , loeP *taraSer 4unchofr'
choosen Ft fr're cto@ twP
t, VequencZ
cnmPera0rnln i'
irs a techn
aru>l$'et cittcui$ and (%
neyaive $dmcx
') lt modi#'% the
arnphS'er.
6lD
.&
arnplifi'er
trep
uin
d MiLtet

38. c) Ieaa
d) fled
DomnanE
* the
Pote - zen
Zera
Pole
mut
wle
$oruard
comlvneL@n
Cnmryfionz'
uad @mPnsttorl teytniqPe iA
@rnpensatrbn uhich ia tt)e
rfn d[ t% cornPenlfre
* fumtna-nb Pole cornPen6a'Lion ia an
I urnPtuatron EchniqYe and it ia
'sed lgn lo, ctored JooP A^n '
', tn t-F'rirs rnettnd , &e a Inte is
flacz^el at .tout $?t@Luuc?l
in the oPen
t@P Jlt%fnrwe ,7teducz
ampli$'er *o o dbfin
the " )ouiul o1 nz'rt
'> the J.ounst fry% PeIe t'/s a'Ltd
V6
pefa- trat n6 - lad umPnatrbn '
and a
(t
fub n the oPqt laP nzPrvse
the pteo at orxn I@P Aetn ol
than I'
+ tt a&a Mh , & Iate (Jofl) ancl a'

39. ir
fleqYerr'td Resprue Ctvtactetifftcs / s
db:
8o
6o
r& loqt/B '+odl
- 20 dbldec
'-4o d
t{o
)o
/n2rf
I
T!)
I
?e+,, fp, fPa,
i + rte di,s- aduantane *4 MnqYa%
i
*-,orcahon rnenod ib rnLAb Fnque.neie's
bl dec
4
:
iaoes't ,)Pot> qain /har &n geduud
l"r- - , u - ..
oclne el $eedfucrc
t6
Potpwnar)@ el 'the
i.!
i @mPensted arnpti$er
'ta a|beuea'

40. Etabittitr1 PnMem:- ':(
'l 9tabiLttq Pnot>ten
o
ich the l@P,, g^'
thedetetr.lttl&5
a4 Wdtua< arnPri$et'
') tooP '6ain ( AP)
tte $eefucrc
arnPfi$ier
Sta*sfl $tncnc q $eedbacK
nrhpl$ier :'
i,s the mar)ner jn
' vdnies utin $nerytertcT
/gabiLit? or inatauitiktr
AtrSo demfntn(% ushetner
i6 AtaAle .
:
loep' Y66r>s[er $ncaul is
'..--- l-,*;;LJ.
lwP ffaryr $uncAon
us
' oenerallq
dPnstd bfl I;,
ttosed
.y low , the cLobed 'loo2 ttan'$ev
ncfuon q $eccttucr<
ampli$er b niven 04 ,
As-g -' !(2.,
, t + p(gAg
ptn AB) Pts) becomes @n6tenb '
., wy "=
jd.
ApQQ = A Qa)
Y Jhe
lunctrbn q'n
t+ pQut) Aqa)
Joq> 7oi, it garcrat tT

41. fficunu4
rnhtubiDv/
nxeatu
ffze,aaact<
Ng1uist
tuffia
with
e%tund
It+aP1
N66uwt flov i,s an aPPxmch
+fE, zfuailf
It Ls a ptar plt of .l@P
$tLeqenc7 ttoed aa a Pname|ov
Yo"r anel brnqu enc7 , lreP |ai'
1ffiide , tha cive te el un?f rdf
)r Then +h2- fiduarx fa neTa
I
4[a1
+ lhe JDsp gain vaYgtn7 uLrh
' Jhat ,dry+ermt
aA #E eabiufrl
q the 6ezdbad< arnPl$er
+ The ctozect )oop 3d, AY t['cD
tten opeD loop gain a Qil, frEn
t@p frar%rna"sbn fa give,rt
')6 .Stable .
LooP 1cun
AP tf ea ui
raditu *hen I :'+PAJ /t t
R8s po,sltive .
le
t,[
untt
?
lh$eedaa.x
lVoL€ ,.-

42. 6tain Ma :-
Gtvi 16
Lapl tr> db ab
Vhaze an7te ai
14 -ffie
de$ined al 'the
#e [ve4tencV
Ap f,s )80o ,
value Al
a.t ePhi ch
*he arnPt$eY
lf -the flain
t-te arnl>Li$eY iz
rnaqin i's
un6table -
N4argtn
It
nu lhe
trep rtn AP
(o db)
irs nenattve '
U
po$titr6' , I
aA 'the angte tsl
o{ the angle ei
ryfdulc.ts AP i's unft7.