CS (MA.N) EXAM, 2010

ELECTRICAL ENGINEERING
Paper-I
Time Allowed Three Hours Maximum Marks 300

INSTRUCTIONS
Each question is printed both in Hindi and in English. Answers must be written in the medium specified in the Admission Certificate issued to which must be stated clearly on the cover of the answer-book in the space provided for the purpose. No marks lllill be given for the answers written in a medium other than that specified in the Admission Certificate. Candidates should attempt Question Nos. and 5 which are and any three of the remaining questions selecting at least one question from each Section. The number of marks carried by each question is indicated at the end of the
question.
Assume suitable dati:z ifconsidered necessary
and indicate the same clearly.
Syrnbols/notations carry their usual
unless othen»ise indicated.



Section-A

1. Determine the time constant for the network shown in the fig.1:


For a 3-phase, 400 50 Hz,
acb system, write the voltages v ac
and vbn in instantaneous fonn,
assuming V be as a phasor. 5
The discrete time system. is
c:Iescribed by nx(n 1).
Check whether this systetn is
causal/tUne variant. 5
For the circuit shown In Fig_ 2­
1. determine the operating point;
2. find the stability factor.
Given: VSE 0·6 J3 50. 6+4=10
vee 15 V

39 K 4·7 K 4·7 K 50 1 K

Fig. 2
C-DTN-K-FFA/43 2
. 'tSII0 g-C6
1. 1 if 42qcfl Cfil

f€a 1
"QifiCftI, 400 50 acb
ell 13ft v ac v bn
if V bc q:il 5
3ifldd nx(n
i=t qfOffi f€fi<rr 'ifl(fT t I <Bi
5
2 it Tro.:. -mn

1. Sloql<:1 ....
2. !10[4l1
VSE =O·6V, 13=50. 6+4=10
Vee 15V


4-7 K
39 K
f3 50
K
1K

C-DTN-K-FFA/43 P.T.D.
....

Draw the circuit of tTL NAND gate and explain its operation. 5
. Draw a circuit diagratn for a single-phase, full-'Wave, Illidpoint diode rectifier. Sketch waveforms for source voltage, load voltage, voltage across one diode and source current. Take turns ratio frolD each secondary to primary as unity. Derive expressions for average and T.rn.s. output voltages. 10
Why is the air-gap length in a 3-phase induction motor kept as small as is m.echanically possible? 5
Determine the priItlary constants of a 50-ohITl lossless line at 100 MHz, if it has a phase constant of 3-14 rad/In. Sketch its n-type equivalent circuit. Is this a distortionless line? 5
DeteITIline the power spectrum of the noise across the terminals cireuit shown in Fig. 3 density voltage of the 10


Fig. 3

C-DTN-K-FFA/43 4

'TTL NAND liR Cf)l (fWT 5
QOifi<?1-Cfiffi, :.s14ts F:l!Cf)lfI Cfi1 I ma 241(""201, sl41g cfil om mo 'EITU d(J I<t§:ql <til ifo:t ICfi( it 31j)qld c6t 3fi:ad om q1f-l{T2J (3lR0 t;Ilo c6t 10
fii) "QCfii:"1f Fiid"'il 01C!1 CflI1 Gt"'iI..... 1 '51101 5
ll.Cfl 50-.Q t?f1$01 Cf)J 100 MHz "tR Cfit?11 3'14 rad/rn. 611 CIlT gf"4i:6ltl (Cq Oi(tml €1 5
l
3 it R€lftJ> ..q llUT et1 t""2"dl q)l 1fTfu; E1 ""i fCt tf?ll 10

IQ

20
1F
1F
1H
C-DTN-K-FFA/43

2. fa) Use Thevenin's theorem to find the current in 4 Q branch of the network given in Fig. 4
lOh




Fig. 4 Obtain the convolution SUITI yen) hen) for n using the property O{n x(n ­no). AssuITle hen) 10
. DraW" the circuit of a Cascade anlplifier. Indicate the tv.ro configu­rations of transistors used. Why is this circuit preferred in high­frequency applications? For the voltage series feedback amplifier shovvn in Fig. 5,. calculate V f feedback ratio f3,. v.oltage gain Mthout feedback A v and voltage gain 'With feedback A Vf 6 6

1
Fig. 5
C-DTN-K-FFA/43 6


2. 4 it ZGqcfi c#it 4.Q. Cflt?ft "it, >ritll Cfil Sl41il mu Cfi1 10

1011

12 A


S(n no) x(n no) qi1
$141 11 n 2 Bq{",Ff citrI
yen)
hen) 10
(Cascode atnplifier)
Cf)T -qftqw 51!!ffi cit
c6T
it 1te cit eft 6
5 -if
Vf 3'W1d f3.,
A v 3fR
A Vf CfiT -mo 6

skv A v


L



19K
It. Il

C-DTN-K-FFA/43 7 P.T.O.
Design a decade counter using JK FF's (MOD-lO counter) and draW" the tilDing diagrmns. 8
A d.c. battery having a constant e.In.f. E is charged through a I-phase full converter. A resistor R limits the battery charging current. Single-phase source voltage is VTn sin oot. Sketch wavefonns for source voltage, output voltage and charging current. Derive an expression for the average charging current on the assuTIlption that each pair of thyristors is fired continuously In each half-cycle. Take Vr as the voltage drop in each conducting pair. 16
In part Ii) above, find the value of R in case battery charging current is 5 supply voltage is 40 50 Hz; E 12V and V,. 1V. 4
3 .. Draw the circuit of Darlington
..
emitter follower. Obtain the expressions for overall current gain and input i:rnpedance. You can use suitable approximations. Find the above two quantities if R B 2 M.Q, R E 1 k.Q.. The device parameters are identical.
h fe1 h fe'2 50 h· =h· =lK
rei le2
hoe] h Oe2 20 J.LA V 6+4=10
C-DTN-K-FFA/43 8
JK FF's (MOD-IO JIUI<fI) Cfi1 s:I?41JI flUICfi om "Ch1 I 8
lito io E 1(R1 1ffittlt:Jifl R 3'11 mu"cit «901 -«rn V m sin rot I am .qm C!i(.... CflT 51 Cf) 51RI if en 3TIl:ia 3'lICl=lI"'1 t:rRJ 69)iG'A llR "SIflICfi oqlelCf) if "Ql(f t I 16
r
if, R CIi1 llR 'ETTU 5 SI<:14 40V, 50Hz; E 12 V V r 1V tl 4
3.. (CiJi) q)T 3lit€r
I OWl
cfiT 31111
CfiT 5I;q1fl 4;1Cfia I
R B 2 MQ R E 1 k.Q
<iRl ufWil cn=t Wffi 5I1:qa
QO<ti<f?l l::fl9i I

hr. hfi SO
Jet, e2
h· =lK
let le2
hoe! h oe2 20 J,JA IV 6+4=10
C-DTN-K-FFA/43 9 .. P.T.O.
Design a binary to Gray code converter. 10
Drav.r the exact equivalent circuit of a three-phase induction motor. Write clearly what the various parmneters represent. 10
A three-phase, 400 20 kW. 1440 r.p.tTl., SO Hz, star-connected induction Il1otor has rotor leakage iITlpedance of . 4 j 1 . .Q. per phase. Stator leakage ilTIpedance and rotational losses are assumed negligible. If this lTIotor is energized from 120 Hz, 400 three-phase sourceJ then calculate­
1. the lTIotor speed at rated load torque;
• 2. the slip at which rnaxi:murn. torque occurs. 10
A plane ""ave has
E Eo cos(rot
and Eo cos(rot -fjx)z 11
In free space, satisfying MaxW"eiPs equations. Find the general expressions for .phase constant J3 and intrinsic irrlpedance in terms of :medium paralTleters. Hence, calculate their values at 10 MHz. Identify the direction of propagation and type of polarization. 10
C-DTN-K-FFA/43 10
ctiTs q cfit 10
mur CFiT (Oft Gt .... Ii'$QOI it 51 Cfm Cfi1it I 10
400V, 20kWJ 1440 r.p.rn., 50 Hz, m:ur
(0.4 1. Cf1{'11 iI a.n:ul om 4<11 0 Ll cit 120 Hz, 400 it 'lui....
1.


2.
(slip) "CR 31RIihdLt I 10


ti) e41Cfi{ort cfit cn@ elOldifl qrr 31qQ;Pfl if
Eo cas{rot
am H Eo cos(rot -f3x}z
11
tI 13 om lffUP:{ 51 l"q -qcif it a:i'i1cnl WO 10 MHz l:R 3 ....it "11R e:qtOI mrr Cf)J YCfiI( "4t 10
C-DTN-K-FFA/43 11 I P.T.G.

A message signal containing the frequency components 100 Hz, 200 Hz and 400 Hz is applied to an 8SB modulator together 'Vith a carrier at 100 kHz with only USB retained. The coherent detector elTIployed at the receiver uses a local oscillator that gives a sine W'ave of frequency 100'02 kHz.
1 . Determine the frequency components ofdetector output.
2. Determine the frequency cOIllponents of detector output if only LSB is transm.itted. 10
4. Determine the resonant frequency
of the following circuit (Fig. 6 4HIF
Fig. 6 The applied a.c. voltage and the resulting CUITent in the following circuit (Fig. are in phase. Determine the coefficient of coupling and the dot polarity of coil PQ


P Q
Fig. 7 C-DTN-K-FFA/43 12


fiChd Plflih EfcCfi
100 Hz, 200 Hz 400 cit
8SB USB
100 kHz ClIf(:Cfi Tf1U i I
31Bi!J 1R: S1"!iffi r{Of 104 4 fi fl'i4 Cfi
51411 1 ChUtf
100·02 kHz 'ffi:Tf I
1 . q o:nl <it

2. ChCfcl LSB cit 'iitldl
(Fif fgZC"R( €f2Chl ct?t
10
4. Cfil
6


31' a.c . crh...·c:<11 (fWl q ttoI p:ft mu, 1ft if I (IWT PQ -mo RI QO 4


P Q

C-DTN-K-FFA/43 13 P.T.O.
The input (x)-output relationship for the system is given by yen 3 yen
yeO) 1 and yen) 0 for n 0 DeterlTIine for unit step sequence input. 10
Discuss how volts/hertz control for a three-phase induction motor is sitnilar to arITIature-voltage control of a d.c. motor. 8
A 10 kW, 50 Hz, 6-pole polyphase induction Il1.otor has a full-load slip of 0·04. If its friction and windage losses are of the output, then
compute-­
1.
rotor ohm.ic loss at full load;

2.
full-load electrofilagnetic torque;

3.
rotor efficiency. 12


Find the reflection coefficient and VSWRof a 75Qrl line terminated in each case with a load of short circuit, open circuit, 75 Q and 75 and corn.pare the results with those of matched load.
What is the shortest length of such a line to produce an input reactance of j75 if its propa­gation constant is jl .25) 7
C-DTN-K-FFA/43 14
N4!t1 t y(n 3y{n n 0
Q}*liCh 3"IiSfi4 mo
10
Ffi f5tCf)(?l1 m:rrr F4:=40 1 "{fto 3Hq.q{-cft<:""co(11 "R45t0 1 tIT<n t I 8
v:cti 10 kW, 50 Hz, q:a 0·04 tl wfuT qld>a1 CPS{
11 0 1;r1
1.
2.
3. Uv:"G&.1ffi I 12
75 Q rf !J:01i6fi om
I ." ,II l"
VSWR j75 Q -j75 Q om -qf{o11141 g)cl....1
eta 81:.sil{ "u.;:qi 5IRtEIld +j75.Q. .g:q{UI j1· 25) 7
C-DTN-K-FFA/43 15 P.T.O.
A lossIess coaxial cable has the two­conductor dianleter ratio of 2-0. Find its inductance, capacitance and Z 0 assuITling a filling of dielectric "With E r 2 . 25. 3
For the probability density function ae-4l x l of a randoITl variable X with x ranging between -00 to find the distributioD function value of a and the probability that X lies between 0 and 1. 6
For the angle-lllodulated signal given by 5cos{1t x 107 t 2 sin500nt}
find the ITIaxiInum phase deviation and frequency deviation, and band"Width. Is this an FM signal or a PM signal? 4
Sect:ion-B
5.. fa) ti) Sketch the following function find its Laplace trallsfonns ret) is unit ratnp function. and 5
Sketch the following function and .determine the energy or contained in a signal 5
5u(t 6u(t
C-DTN-K-FFA/43 16

m Cfil OlIIB 2·0 mftm (rm Zo mo fEtl E r tl 3
m.: X ... ae--41 xl, x CfiT qftm: -eo +00
a 3=lIG:lZPJ Cfii?1PJ 1=JR (fWl 0 1 11Uf urnT 6
ci'tur 5cos{n x lO? t+2sinSOOnt}
3fR om m-a q;lff FM fi 41 d t 31'4q I PM :eiChct? 4

5.. CflT (f2JT (ftICfctlfl l!:if)iCh $lqUJ lfiC'i01 I 5
CfiT CJ> om :fiCfJd
1lTfffi·ma Su(t
C-DTN-K-FFA/43 17 P.T.O.
In the circuit shown below (Fig. the switch S is in position long enough to establish steady-state conditions and at t 0 is switched to position Draw 's-dolUain' network 5
50 V 1 1 2 100 V 25 Q
Fig. 8 Draw the circuit of an Opanlp integrator. Sketch the output "WaveforITI" ",hen the input IS a syrrunetrical square wave of amplitude V and the repetition frequency is 1 kHz. Deter:mine the reading of the ideal voltllleter connected across a silicon diode shown in Fig. 9 4


Fig. 9 Assume the forward voltage ofdiode to be 0·7 V. Find also the current through the diode.
C-DTN-K-FFA/43 18
R€iJIJ> qft1:m S -ij q4hl il dlfCfi "SITH m om t 1R ffC4:q .... it t I
• : 5

25 Q
sov

2H

OpaDl.p ftJ4ICfii:?tCh Cf)l qft1:m I
d:(JfJiq CIiT ±3 V
3'"11;QIIl cpf otrT
lkHztl 4
9 jf TIt; fufH<tiTWi sl:Jls "it
Cfi1 Qlauii:f1


l:fR :$141s 3l!l 0-7 V t 1
:SJ41:S it 1:lTG I 4
C-DTN-K-FFA/43 19 P.T.c.

I I
Realize an Astable Multivibrator using 555 tinIer to produce a square wave of frequency 1 kHz with duty cycle of 500/0. Mention three applications of tiITler. 7
In three-phase discuss the use windings. of tertiary 10
A three-phase star-delta trans­former has its secondary delta open-circuited. A voltmeter IS placed across open-circuited tertninals4 Will the voltmeter read zero? Discuss. 5
A 50-ohIn lossless line IS . terminated with a dipole of input impedance (73 j42) Q. Find the reflection coefficient, and estitnate the reflected and transInitted powers, if the input power to the line is lOW. Also calculate the znaxirnUID and IDln1TIlUIl1. iInpedances on the line, and suggest two rn.ethods of D1atching such a load to the line appropriately. 10
Detennine the noise bandwidth of the first-order RC integrator with cut-off frequency Define the terITl noise bandwidth. 5
C-DTN-K-FFA/43 20

500/0 (duty cycle) atR 1 kHz qq 555 q)f Sjlj)'1 Cfl(Cf; Astable Multivibrator I 3'i:!Sfti"1 atd 1
It *ascl=i 5JlI)"
<fiT 10
"QCfi&11 cfit 'QdhFfi
CfiT TT<rr t I
cfif;rffi
it
Wrr? OQI&:U 5
50 .Q c#it dliFI q?r -.zen
ll, PiecE1 (73 j42) Q
TIm 1 q(ICiJ";J
VSWR om ma
if 10 W
(tWT t1q cIiT
:ft cit
Mlij" if ct?t CJi"{
10
fii) RC
Ie
c€r 5

C-DTN-K-FFA/43 21


6. fa) Using Fourier transfortn obtain expression for in the following nenvork (Fig. 10)

1F
0-5 .Q
Fig. 10
The z-paraITIeters of a syITunetrical two-port network (consisting of passive elenlents only) are by ztl Q and z21 Q. Obtain equivalent T-network. If this network IS excited by a 2-volt source having internal resistance of 1 ohm, detennine the load resistance to be connected across port-2 -which will receive rnaxiIIlurn power. 10
State the differentiation property of Fourier tranSfOTITlS. Hence;p obtain the Fourier transforID of a Signunl function. Sketch its rnagn.itude spectrum. 4
Design an Opantp second-order Butterworth low-pass filter for a cut-off frequency of 2 kHz. Cotnpare the response curve with that of first-order LPF. 10
With the aid of circuit, draw R /2R ladder DAC and discuss its operation. 6
With V for the find
VREF the resolution and full-scale output of this converter. 4
C-DTN-K-FFA/43 22
6. (Cfi) TW, (ftrn 10) {bOqJ41(Oj Cfil Cfl JITR 6

1F
10
(hqa fZlftii1fi4 3iCl=tlQ z zll z21 1.0· T-42:Qcfi '5rnf chlf.3i(( I "W ?l2Cf$ cfit 2 q")172 Titer il filftChI I,Q 3lfuChd"'l >rrn Cfi{Jlll 10
CfJ'tlt ildli?Qll tri"t"'lIUI .q;y f4
oparn.p QRCh i:fto 2 kHz
J. •.
qSf} fi<.9";u.?JWf ctitf2 0 -eft0 10
fli5l:£1dl' 1J R /2R mq I"i "QIo «to C4IMI t€lFitv.:' .
6
Bt0 ,.5V
CfiT -'E"42dJ .... om
4
C-DTN-K-FFA/43 23 P.T.D.
Write voltage equations governing the perfonnance of type-A chopper during on-period Ton and off-period Torr for the RLE type load. Hence, obtain therefroITl)' using Laplace transforrn Jl the expressions for the tnaxiIl'lurn and tninirnuIll. currents taken by the load. Assume continuous conduction. 20
7. ra) Using an Oparrlp and RC network)' explain the working of a Wien bridge oscillator. For a frequency of 1 kHz, design a Wien bridge oscillator. 6+4=10
Convert a clocked SR Flip-Flop to a clocked JK FF.
Speed control of a three-phase induction motor v.rith constant supply voltage and reduced supply frequency is rarely used in practice. Justify this statement. 6
Describe stator frequency control for the speed control of a three­phase induction motor. Derive expressions for lTIotor torque, maximum torque and the slip at which it occurs. State the various assumptions made. 14
te) A lossy non-magnetic medium has Er 4·0 and a phase constant of 0'10 rad/ITl at MHz. Detennine its loss conductivity, propagation constant)" intrinsic inlpedance and skin depth. 10
C-DTN-K-FFA/43 24
3lRo SJ,&q cit Ton WIT TofT
r.::'114."11f1 1 'ilR IDU TT{ J:I mu oti'iiii.fi >rm "6ffif 20
7. lJ:CFl o paInP RC =l2q
etA cit
1

CJiT 6+4=10
ChI(1G SR fCR;:tq -4{"1Tq CfiT ihl€1C: JK FF it
"f.tlmr etl<."'2:dl om lIm fiCfl€11 q?r Cfi1=r 5I41 J I 'illal t I 6
fStCficlf m:ur c#iT f;i4:;i4UI q)f EtOH <Sfa-3iIE{?f om equl, >rm -mm cnl TTTJ: 14
'lfTUfIl c€t £r 4·0 0·10 2·0 MHz 1R 1 "'6I1{1CfidJ, fCI*41 10
C-DTN-K-FFA/43 25 P.T.C.
An FM system uses pre-elTIphasis
and de-emphasis filters having the
following transfer functions
Hplf) j
H d
1 . Find the scaling factor k so
that the average power of the
etnphasized signal is satne as
that of original signal m.{t).
2. Find the corresponding value
of improvement factor I
produced by using this pair of
pre-eInphasis and de-eIDphasis
filters. 10
8. A linear network has a driving-point
adITlittance yes) given by
12(s
. s(s
Determine current in the network
supplied by unit impulse voltage.
What W'ould be the current in the
circuit when a unit step voltage is
applied? 10

C-DTN-K-FFA/43 26

FM it Flt)5l!it<?Ft Cf)T 3l<1(0I
k[l jJ


1. IQ'"1 k Pu:n3 'EiCbd 3ftfld BCho mI
2. Pi6SC iii ("Fe ;q111 ac:q I em Wrn
'il"R 10
8..
am "'i1ldt t .

12 . S(S
.q l(ChiCfi a:rrW1 1ITU cRt
mu mc:r t(ChjCb «jql9i e.nC""2dl
cfit <it if tlm "Phd 10
C-DTN-K-FFA/43 27 P.T.D.
Write the node equations for the network sho'Wn in Fig. 1 1. Assume node as a reference node 10

Fig. 11
The priIllary winding of a single-phase transfonner is energized frolTl a tlXed sinusoidal voltage with secondary open­circuited. If a small portion of iron core is retnoved, discuss what would happen to the magnitudes of its exciting current, core flux and the no-load povver factor. 7
Explain why transformer rating is expressed in VA or kVA. Describe the significance of all the items ITlentioned on the nmneplate of a single-phase transfOTITIer. 6
Derive an expression for the per unit voltage regulation of a single-phase transformer. Show that Illagnitude of per unit voltage regulation is. equal to per unit value of equivalent leakage iITIpedance of the tranSfOTtTler. 7
C-DTN-K-FFAJ43 28

11)
cit ma qit
llH 10


11
Q;Cflct cit, CfiT cil(""cctl it GiI(11 tI 3Tfl em "Plihl(?t 'iffifT (pSf OQI&U 3ti4; sf?ts am qf{lOIlol qi1 tOTfT I 7
Cfit VA o3l!l:l ell kVA -if CFit <Xfffi 'iffifl t I 1R 1lG
"'Sffif QOChiCfi aj'5li:fi ogN;;iI -srra QA'iiif' etI C"Gill AllJ:f ctil qftq "5ffif QChiCh W""4ti H aRUl l:fftqfol iit{I<St( I7
C-DTN-K-FFA/43 29 P.T.O.
A plane w-ave having
E 110cos(wt -41tx)z VIm
is nonnally incident on a medium of
£r J.-lr 4 and Cf fron1 a
perfect dielectric medium of
€ r 4 . O. Find the reflection and
transITlission coefficients, phase
constants and list out the
tirrle-dornain expressions for
incident, reflected and transmitted
electric fields. 10
Establish the tirne-dolTla1n
expression for the AM signal at 600/0
modulation level with !nodulating
signal as 5 cos(2001tt) and carrier
as and list out its
Fourier transform. Find out the
amplitude sensitivity constant,
side-band powers and efficiency. 10

C-DTN-K-FFA/43 30


(it {i1H1C1 am CfiT, fatflCh'
E 11 Ocos(wt 4nx)z VIm
i:i1eChI J.l. r 4 OWl
cr 0 QUa"ija J41U4J4, "f-iieCflI
E r 4· 0 it .a<l14rl.... m-r I
4(161tR 1dT:4(OI
lffiCffifo
if; c4"i1Cfil
10
AM ...T§t'1.... «R: 60%
om qT§<"Ff 5 cos (2OOn alR: ct IeC'h
5 acos(I 0 4 1t Oli:it Cfl mlf
(iiq 1r(1(oJ ttt
I I
om G8:Till lffif 10




e-DTN-K-FFA/43 31 . B8-700
C-DTN-K-FFA



3lr441 JfR am-31Y4} cit;ff if f§W t J
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JlH :#1..-041 J 5 :sIP/en4 I "WFif if tr it Cfi11-N-<:fiTf t?ifi" Wcreff rfR" JPR1 41MQ,1
3lr4i#J JlR ff;ro: A'4d aiGfi J1R 3Rf if g I
erfit 3"114:14Cf) fit ffi 3jiChi! W 'Tif7;Ff cIiJPI v. QP.fT ARf2 4fJFafQ,'
3UfJr:ti/84-Jrl 31'ilr&d 31Wf if Jl1m g" 3F<l2lr Ptfife gJ
Note: English version of the Instructions is
printed on the front cover of this
question paper.