;? \ J

GN-5594

[Total Marks: 100

( . ;... /~ 01 - ~ I-.I.

L, h- Ic.-t

Con. 3789-12.

(3 Hours)

N.B.: 1.2.3.4.

Attempt question 1 which is compulsory and any 4 questions from the remaining 6 questions.Draw neat diagrams wherever necessary. Related waveforms should be drawn one below the other.Answer should be brief and to the point.All sub-questions of ~e same question should be answered at one place only in $eir serial order, andnot scattered.

5. Write everything in ink only. Do not use Pencil

1. (a) Design a circuit with Op Amp, resistors and a capacitor that simulates an inductor of 1 H.

(b) Design an Op Amp circuit that simulates the relation Vo =2Vl + 5V2 with the minimumnumber of resistors and Op Amps. .

(c) Draw a sampleandhold circuitwith two buffers;Bi at the input side and Bo at the outputside.

Write down the requirements (very high or very low) regarding ~:herise time, oias current,input impedance and the output impedance for the twobuffers and justify. .

(d) Differentiate between the static and dynamic RAMs.

2. (a) Draw the circuit of a voltage to current converter (VCC) for a grounded load and derive thecondition for it to act as a VCC. .'

Design a VCC that has a trans-conductance of 1mAN.

How VCC can be used to generate a triangular wave from a square wave.

(ii)

Obtain its voltage transfer function (in terms of various admittances).

From the transfer function, identify the elements (resistors and capacitors)"for aband pass filter.

Design a band pass filter for a central frequency of 1 kHz and Band width of 200Hz.

(ill) How can the gain at the centr~ frequency be reduced by 50% using only one extrare~stance? .

Modify the above band pass filter to obtain a band reject filter.

[5]

[5]

[1]

[4]

[5]

[5]

[2J

[3]

[2]

[2]

[4]

[2]

[2]

[4]

[2]

[4J

[4]

(4]

- -.. ' "'..

[TURNOVER. "," "

._. '- -..----

(b) (i) What are the functions of the 'control pin' and the 'discharge transistor' in theastable mode of operation of timer 555?

(ii) Draw the circuit for IC 8038 operating as an astable multi-vibrator with 50% dutycycle.

Derive a relation for the :frequencyof the square wave.

Design the circuit for a frequency of20 .

3. (a) (i) Draw a general circuit tor a multiple feedback filter.

. 7.

Con. 3789-(;N-5594-12. 2

4, (a) Give a circuit for simulating a resistor using a switched capacitor,

Derive the relation for the simulated resistance.

What are the requirements for the ideal switch, the capacitor and the clock frequency?'

(b) An inverting type Schmitt trigger has the following transfer characteristic: Threshold levelsare 5 V and -6 V, output voltage ::I:10 V. Plot the output voltages when the input voltagesare

(i)

(ii)

8 sin lOt,

positive half-wave rectified 8 sin lOt.

5. (i) Compare the R-2R ladder (voltage mode) and weighted resistor DACs under thefollowing heads.

Number of resistors, Spread, Number of single-pole single-throw switches and theSpeed of operation .

(a)

(ii) Draw the CUITentmode R-2R digital to analog .converter. .

Why is it suitableforhigh speedoperation?

(b) 'A multi-meterdoesnotm~urethe 'tru~RMSvalue' of a voltagesignal.' Justify.

How can the true RMS value of a voltage signal be measured using analog multipliers?

6 (a) Design a moduo-lO counter with the counting sequence 5,6, , 14,5;,6, ..." 14 usingMSI74X163.

[4] -

[2]

[6]

[4]

[4]

[4]

~

[2]

[4]

[4]

[6]

[10]

(hi Draw the block diagramof internalarchitectureof XC,9500family CPLD and explainthe [10]workingof eachblock.

(a) Write VHDL code for a four bit up counter.

(b) Design a Moore machine for overlap sequence detector for the string 1110. The output mustbe I when the input matches this string.. (i) Drawthe state diagram.(ii) Write the transisiton and output tables.

.(iii) Drawthe logicdiagram.

[6]

~

[4][6][4]

( )

/31:1sthalf-12-(i)JP5..;;;/ If '0' c/ S--e.rn -r!- C~H () 2--€>, '2- .Con. 3576-12. g ~ :-~'P<f~ VU alid -1 V

L,t~- Ls~~.. (3 Hours) ~

1:>t~ r ~f O~,-/ } '2-.

GN-5600

[Total Marks: 100

N.B. (1) Question No.1 is compulsory.(2) Attempt any four questions out of the remaining six questions.(3) Figures to the right indicate full marks.

1. (a) Show that

(48 8

) (24

)J4 (x) = x3 - -; J1(x) + 1- x2 Jo(x)

(b) Show that the matrix

5,.

5

[

7 4 -1

]A = 4 7 -1 is derogatory

-4 -4 4

J(-)

- x y z(c) Evaluate VxF. ds , where s is the surface of the plane - + b

+- =1 in the firstsac

octant and F =y2i + zx2j + x2k

. e3z

(d) Evaluate fz - i dz , where C is the curve Iz- 21 + Iz + 21 = 6c

5

5

2. (a) Prove that for positive integer 'n' J-n(x)= (-1)n In(x).

[

8 -8 -2

]

(b) Show that the matrix A = 4 -3 -2 is diagonalizable. Alsofindthe transforming3 -4 1

matrix and diagonal matrix.(c) (i) Show that the area bounded by a simple closed curve 'c' is given by

.! txdy-ydx2 c

7

7

6

x2 y2(ii) Find the area of the ellipse a! + 'i)2 = 1.

3. (a) VerifyCauchy's theorem for function f(z) =3Z2 + iz - 4 if 'c' is the perimeter of 7square with vertices at 1 :t i ; -1 :t i.

(b) Prove that J" (x) ~ J 2 . sin x/2 nX

(c) Show that F =(2xy + 23) i + x2j + 3xz2 k(i) is a conservative force field

(ii) find the scalar potential(iii) findthe work done in moving an object in this fieldfrom (1, -2, 1) to (3, 1, 4).

[ TURN OVER

7

6

32: 1st half-12-(i)JP

Con. 3576-GN-5600-12.

4. (a) Define Analytic function. State and prove Cauchy-Riemann equations in Polar 7Co-ordinates.

(b) Verify Gauss divergence theorem for F= xi + xj - 3y2zk, taken over the surface 7of the cylinder x2 + y2 = 16 between the planes z = 0 and z = 5.

(c) If A = [0 1

], find eAt-1 0

2

6

5. (a) Define conformal mapping. Find bilinear transformation which maps the points 7z = 2, i, -2 onto the points w = 1, i, -1.

00 dx

.(b) Evaluate using contour integration [x4 + 1

(c) Show that Cos(xsin8) = Jo(x)+ 2 Cos28J2(x) + 2 Cos48 J4(x)+ . . . . . . .

7

6

"7z-2

6. (a) Find all possible Laurent's series expansion of the function f(z) = Z (z - 2)(z +1) 7

about z = "7"1 indicating the region of convergence.(b) Prove that there does not exist an analytic function whose real part is 3x3_2x2y+ y2 7(c) State Cayley-Hamilton theorem. Use it to express 2A5- 3A4+ A2- 41as a linear 6

polynomial in A, when A =[

3 1

].

-1 2

7. (a) Explain removable singularity with example. Evaluate Jtanz dz, where 'c' is the 7c

circle Izi = 2, using residue theorem.(b) Find the analytic function whose real part is e-X{(X2_y2)Cosy+2xy siny}.(c) Reduce the following quadratic form to canonical form and find its rank and

signature.x2+ 4y2+ 9Z2+ F - 12yz + 6zx - 4xy - 2xt - 6zt.

7

6 ----.

mk.H.1stHlf12.55

Con. 4025-12.

, ,

yS E/~~;JY-( E?nLIf2-w~:~6J)c -If-

(3 Hours) [Total Marks: 100

25105 I~ r.2..GN-5603

~

N.B. (1) Question No.1 is compulsory.(2) Solve any four 'questions from remaining six questions.

,'(3) Assume suitable data with proper justification.(4) Figures to the right indicate full marks.

1. Give reasons for the following :-(a) When JFET is biased in constant current "region the gate source junction

capacitor has a higher value compared to gate drain junction capacitor.(b) In case of transistorised oscillator circuit the transistor used is generally

connected in common emitter mode only.(c) In transistorised Monostable and Bistable Multivibrator negative edge triggering

is preferred over positive edge triggering.(d) Small signal voltage amplifiers does not face problem of harnomic distortion,

whereas power amplifiers suffer from the problem of harmonic distortion.

5

5

5

5

2. (a) Design a two stage RC coupled CS amplifier using JFET BFW-11 to meet the 15following specifications :-,

Av~ 100 Vo/P= 2.5 V IDsa = 1.38 mA FL ~ 25 HzNeglect rd for your design.Find maximum peak to peak value of undistorted output that the designed circuitcan provide. ,

(b) For the above designed circuit if Cgd= 0.1 pf, Cgs= 1 pf. What will be the higher 5cut-off frequency?, , .

3. (a) For the given circuit find DC.operating point of Q1 and Q2, Find mid frequency 10voltage gain, current gain input and output impedance. Explain importance of

. Cascode amplifier.

1 \<6V..

b°'K\Q.u~

1. \(a

'-\'<-1\~ ~- ~ ~~~.:= \f{C)

\\\e, ~h)~= ~ ¥:-SL

-

(b) Draw a neat circuit diagram of a transistorised Schmitt trigger circuit. Explain 10its working with proper waveforms. Explain the need of speed up capacitor.

[TURN OVER

mk.H.1stHlf12.56

Con. 4025-GN-5603-12. 2mk.H.1!Coli. 4

4. (a) For the following circuit identify the type of negative feedback (with proper 15reasoning). Find circuit input impedance, output impedance and voltage gainwith feedback.

6. (a

~~\\'1" (j,\-\\~

~

V-s

(b

Rc.~o)c.-SL "",~,="~e2..::' \00

,,\~\ =Y\\e.:z..= ':l ')c...sL

C'~~-U~

1S-'

7. (a

- 1~~\ (b:

~~

\co k.

-\<..'

-=

(b) Draw a current amplifier. State its characteristics. Introduce a negative feedbackto it and name the topology. Draw a transistorised circuitto implement the topology.What will be the important characteristids of the circuit?

5

5. (a) Determine values of Ico, VCEO'differential mode voltage gain, common mode 10gain, com,monmode rejectibn ratio and differential input impedance for the followingcircuit :-

~ \15"V

i

'

:t- ~~..2.-

'lot"/ -0~,

..

~,~~.sL ~ \ -=. f> 2..'=' \ CJ'\)

\00 ..sL.

t~~

-\ ::;:...

'5' S'~SL-

-,~V

(b) Draw a neat circuit diagram of Darlington amplifier. Derive expression for its 10current gain, input impedance and output impedance. Draw mid frequency modelfor derivation neglect hre and hoe' '

I

mk.H.1stHlf12.57

COrio 4025-GN-5603-12. 3

15 6. (a) Draw a neat circuit diagram of a transistorised Wein bridge oscillator. Explain 10its working. Derive expression for frequency of oscillation and find conditionfor sustained oscillation.

(b) Design a RC phase shift oscillator using JFET BFW 11 for frequency of oscillation 10of 1 kHz.

7. (a) Design a class A transformer coupled power amplifier for the following 10requirements :- .

o/p ac power = 8 W Vcc.= 15 VLoad resistor = 10 n S ~ 8

Assume transformer efficiency "r = 90%. Calculate collector efficiency of thedesigned circuit. ,,'

(b) Draw a neat circuit diagram of clasS B push-pull power amplifier. Draw suitable 10waveforms and graphs showing ac and dc dc load line, input and output waveforms.Derive expression for maximum collector efficiency.Why this amplifier face problem of crossover distortion? Suggest a suitablemethod to overcome this problem. '

5

[TURN OVERI

10

\

~

'<

DBEC DATA SHEET

.'

Transisror type

1J{ 3055ECN 055ECN 149ECN 100BC147A2N 525(PNP }BC147B

BFW II-JFET MrnUAL CHARACIERISTICS

03Or?;E.j:>.Q;'oI\)C11,I\),,0,ZOO,

Derare C11m

VSE °fe above 0eN

max. °C/W 25°C '

W/oC I\)

1.8 }.5 0.71.5 3.5 0.41-2 4.0 0.30.9 35 0.050.9-

0.9

Pdnun lcmax V (oaI) Vao VCEO Vea Vea V.EO D.C. current gain Small Signal hfeCE

@ 25°C @ 2j°C volrs volrs (Sus) (Sus) volts volls T. maxJ

Wails Amps d.c. d.c. vollS d.c.volls d.c. d.c. d.c. °C min Iyp. max. min. ryp. max.

70 90 7 200 20 50 70 15 Sp 120

55 - 60 5 200 25 50 100 25 75c.. 125- - 8 " 150 30 50 110 33 60' 115

65 - 6 200 50 90 280 50 90 28050 - 6 125 115 180 220 125 220 260- - - 100 , 35 - 65 - 45 -

50 - 6. 125 200 290 450 240 330 500

115.5 15.0 1-1 100 6050.0 5.0 1.0 60 5030-0 4.0 1.0 50 40

5-0 0.7 0.6 70 600.25 0.1 0-25 50 45

0.225 0.5 0.25 85 30 '

0.25 (}'1 0.25 50 45

hoe hre Oja

18J1U 1.5 x 1()-"4 04°C/mw2511U 3.2 x 1()-"4 -

30J1 U 2 x 1()-4 04°C/mw

Transislor type ,hie

BC 147A 2.7 K a1J{ 525 (PNP) l-4KaBC 147B 4.5KaECN 100 500.aECN 149 25Q.aECN 055 ,100.a1J{ 3055 25 a

N-Channel JFEr

Type-

2N3822

BFW11 (typical)

-Vas volts ().O ().2 0.4 Q>6 0.8 1.0 1.2 1.6 2.0 2.4 2-5 3.0 3.5 4.0

IDs Diax. mA 10 9.0 8.3 7.6 6.8 6.1 5.4 4.2 3.1 2-2 2.0 1.1 0.5 0.0

IDs typ- mA 7.0 6.0 54 4-6 4-0 3.3 2.7 1-7 0.8 0.2 0.0 0.0 0.0 0.0

IDsmin. mA 4.0 3.0 2.2 ].6 1.0 0.5 0.0 0.0 0.0 0.0 0-0 0.0 0.0 0.0

VDSmax. VDGmax VGSmaL P" maz. T. max. loss K- -V,. Volts 'd Derale 9.I JII

Volls Volls VollS @25°C (Iypical) . above 25°C

50 50 50 300 mW 175°<: 2mA 3000 J1U ' 6 50 Kil 2 mwrC O.59°C/mW

30 30 30 300 mW 200°C 7 mA 5600 J1U 2.5 50 Iffi - Q.59° C/mW

06( exTc /60>1-3 (;:'(o"b:-EIAJT 1m :Z-OJl--

85-',\""'-12m;",(I) Lib, C Df,! ' @ J)1:-c> ff/() ( /J 1-Con.4817-12. . GN-9614

(3 Hours) [Total Marks: 100.~

N. B.: (1) Question No.1 is compulsory.(2) Attempt any four questions out of remaining six questions.(3) Assume any suitable data ifnecessary.(4) Figures to the right indicate full marks.

1. Explain the following (any four) :-(a) Continuity equation(b) Boundary conditions for electrostatics(c) Polarization of electromagnetic waves(d) "Ampere's circuital law(e) Magnetic vector potential.

20

2. (a) Two conducting cones at e = 111:0and e = ~ of infinite extent are separated 10

by an infinitesimal gap at r = O. If V ( e = to ) = OV and V Ce = ~ ) =' 50V:

Find potential V and eleCtic field intensityEbetween the cones. Neglect Fringingeffect. .

(b) Find electric field intensity Edue to an infinite line charge. 10

3. (a) A circuit carrying a current of I amp form a regular polygon of "n' side inscribed 10

in circumscribing circle of radius R. Calculate the Magnetic Flux density B at

the centre of the polygon and show that B approaches that for a circular loopif "n' tends to infinity...

(b) Give the pot~ntial V = 1~ sin e cos $ :-r10

(i) Find the electric flux density 5 at ( 2,~, 0 ).(ii) Calcuate the work done in moving a 5 J.!C

A (1, 30°, 120°) to B (3, 90°,60°).charge from point

4. (a) A vector field is given by :

A(r,$,z) = 30e-r ar - 2zaz.

Verfiy Divergence theorem for the volume enclosed by r = 2 m, z = 0 mand z = 5 m.

(b) Define Poynting Vector. Obtain the integral form of Poynting theorem and explain 10each term.

10

[TURN OVER

B6-1st Half-12 mina (f)

Con. 4817-GN-9614-12. 2

5. (al Verify Stoke's theorem for portion of a sphere r = 4 m, 0 s e s 0.1 n, 0 S ~s 0.4 n. 10

Given :,- H = 6 r sin ~ar + 18 r sin e cos ~ap'

(b) Derive Maxwell's equation in point forRl and integral form for free space. 10

6. (a) Derive the expression for the potential for the potential energy stored in a static 10electric field.

(b) A charge distribution with spherical symmetry has density: 10

Po rPv = a

O~r~a

= 0 r > a

Determine E everywhere.

. 7. (a) Prove that static electric field is irrotational and the static magnetic field is 10solenoidal.

(b) Derive general wave equations for E and H fields. Give solution to the wave 10equation in perfect dielectric for a wave travelling in z-direction which has only

. x-component of E field.

>.

6£ / EX7G /cS-f'A'J~.JJC/ fZ/uuA".,fc»J F/-(ZOJL

Lib. COfY-@ JJf:j8o/~J~

{

Con. 4490-12 GN-8441[TotalMarks100

r

(3I-burs)N.8.: (I) QuestionNos.I iscolnpadsory.

(2} Out ofremoining questions iittcmpt an)' four questions.(3) In "II five questions (0 be attempted.(4) Assume suiroble data whcrever n~ssnry.

I a. List frequency band and oommunh:.atiob aPI»tfcaOoh of u.able frfqu.a.cyspecCrum shown beto,"'.

i. Vol~"frtquenc)'iI.. VerylowrrequthQ"

. m. Mc4hlmfrequtnt)'i\'. High rr~quel1~Yv. (JUra hieh frtqueDcy

b. A Chrte stageilmplititr bas tbe foUowine power calns and noise figurt (as~tios. not in dB) foreneb ~tae:c.(;*,I('uh.(~Chi'pnw~r ga~n.tu"~$OO~u.~ Qndnoiseteml)erutUtefor th~clUcad«lampUf.er,mumio(l.matched(ondition.

F=-:~~P;' .-+~--E-L-"~=:--J:"-. . -:-.

t.

e. Coml~re lIlgh 1C\'c1and Low It\'cl modulation 10Ctrmsorpower 'e\.tl~ ')'PC$of ompllneruscd. efficloncy, IimiCidonand appUcndon.

d. Explain dr~t of thanae bl moduJadne frtqucnty ror AmplJ(udt,FrcqutA~'and "hase modulation.

1 a. Explain AntpUtud~ Modulation (AM) for moK' Ih~u'One modul.tine signllin followlnt: terms:

i. Mllthcmuticaal«&ulI8ion.ii~ AMW..vefQrm .

m. AMamplitudeand powerspectum.iv. Mooulatli'ineocffic:icnt

v. Transmission power

b. Draw blo.:k diagram of superheterodyne r~eiver. Writo fre-quencycompone.ntp~ent at the output of eachbloc~If.modulatingfrequencyis 2kHz, carrier frequency SSOkAt andlnttrmcdia.e frequent)' (IF) of 4SS kHtalso sketch w1\\'eforms at thc output of IF ~nd detcttorsCage.. .

3 a. With help of a neat block diagram eXI)lalnthe principleand generation orindirect method ofFM geneNtion.

b.Explain ?I'j,h block diagram hQwAFC wilt counteract a downward drift inrrequency oscillator being ~(abUizoo.

(TURN OVER

(OS)

(05)

[05)

(OS)

1101

[101

1101

[06)

(;.iri"'- Noi" FIurt'10 2-_. --_ ..10 430--:-: 5w' ----"

Coo.4400-GH-8447-12 2

c. A 10 Mllz carrier I$modulatc:d by iii400 H2 audio sine wave. If the carrier"olraae i$ S volts and mAximumdc\'iatiop.is 10 kHz, write an equation (orFM wave nnd calculate>the:power'dissipaced across 100{} resistor.

4 a. State and prove-sampling theorem for low pIUSband Umltedsignal.b. Witb cb~help of neat circuit diagram CXl)lalnlI.e geaeration and dct«(foD of

Pulse Position Modulation (PPM.)signal.

...

~- 8. Dra\y'blockdiag.rR'uof AdaluiveDeltaModulatorand explBlnItsworking.b. flow is Adaptive Delca Modulation (ADM) an improvement o"er Linear

Delta Modulation (DM) In followingterms:i. slope-o,'crlo8d

-ii. distonloDiii. SNRI". BW

, .

c. -Compare- OM, ADM. PCM and DPCM in following terms;.t. Number of bits per sampleii. St~p SiuIIi.Dtstortion

Iv.Compluity,', Application

6 8. Draw block dill2ram of PCl\'. ,y:stemand explain aha fuaction of each block-

b. nna\V tbe block diagram or phsue canc.:cllutlon5SB eCaCt1lforand cXI)lalnhow (arrler aDd unwanted $idebnnds arc suppr~S5(d~

7 Wrhc:shorCDoleson (allYCour)i. Ind~pondent shJcbulu}sYStcmU. Trac10ne in AM r-e«iy~rIii. Phasc Modulationiv. Noise In communication sY$temv. Quantizationtrror,'i. RfttioOt(c:dor

(04)

(10)110)

(10)

(051

(051

(1°)

(10)

.; 15x4J