7/28/2019 D12SE4-EXTC

1/10

5G ) EXTL' J ~ (p-eJI)A . M .r - \ v - . - > -

KR- 7043

[Total Marks: 100

N.D. : (1) Question No.1 is compulsory.(2) Attempt any four questions from Q.2 to Q.7.

x- y1. (a) Find the analytic u + iv given u + v =eX(cos y + siny) + x+y'

(b) The matrix A is given by A ~ [~

ofB where B =I~6 A-I.

(c) Evaluate ic

fdf along the arc of the curve from the point (1,0) to (e21t,0) 5

~ -~]. Find the eigen values and eigen vectors 5

o -2

- xi+yj -where f = - - - ~ and' curve C is i' = et cos t i + et sin t j.

~2+y2)%

7/28/2019 D12SE4-EXTC

2/10

. . , 2 (A ~ -4 )3. (a) Show that f{x) = x2, 0 < x < 2, f(x) = L J ( ) Jo(A.jx) where

i=1 A i J I A .j

A i ' i =0, 1, 2, are roots of JO {A ) =0

(b) Show that 2 x 2 + 2 t a n - J ( r ) is imaginary part of an analytic function. Find its 6x +y x

real part and hence find the analytic function.

r Z2(c) Evaluate J , ~1 dz,

c z -

cis (i) IZ -11 = ~ (ii) Iz-l/=1 (Hi) IZ+il=l.

4. - .(a) Evaluate using stokes theorem Icy dx+zdy + xdz, where C is the curve of 6

intersection of surfaces x2 + y2 + z2 = a2 and x + z = = a.

(b) Evauate J ; X/+l~'(c) Find an orthogonal transformation which reduces the quadratic form 8

2x2 + y2 - 3z2 - 8yz - 4xz + 12xy to a diagonal form. Find the rank, index, signature

and class value of the given form.

7/28/2019 D12SE4-EXTC

3/10

(b) Evaluate r21t cos3e deJo S-4cose

(c) Verify Gauss divergence theorem for F = xi + yj + z2

k, s in the surface bounded by 8the cone x2 + y2 = z2 and plane z = I.

7. (a) Show that under the transformation'w = z2, the circle Iz-11 = 1 is mapped onto 6cardiode p = 2(1 + cos e jl) where w = p ei+ in w plane.

I' (b) Find the matrix represented byA8_S A7 + 7A6- 3A5 + A4 - SA3 + 8A2 - 2A + I 6

where A =

l~~~ j112(c) (i) State and prove the Cauchy residue theorem.(ii) Evalu~te I e z6 e-!~dz;c: I z l= I -

7/28/2019 D12SE4-EXTC

4/10

t~'K'f c~

A IAC~ \"~T ~ D; l~t-J

~I ((~ 111-

iJ~;; f'" 9 (\ 19KR- 7160

[Total Marks: 100(3 Hours)

N.D. : (1) Question No.1 is compulsory.

(2) Solve any four questions from the remaining six questions i.e. Q. No.2 to Q. 7,

(J) Figures to the right indicate full marks.

1. (a) State and explain the important advantages of three op-amp instrumentation amplifier. S

(b) Compare static RAM and dynamic RAM. S(c) Give the comparison between Melay machine and Moore machine. S(d) Draw and explain voltage and current converter. S

2. (a) With neat diagram explain 'two techniques of A to D conversion. 10

~. (b) Draw and explain the block diagram of IC 810 audio power amplifier in detail. 10

3 . (a) Design a Melay state machine for overall sequence detector for the string' 1110' .The output must be I, when the input matches this string :-

(i) praw the state diagram - 4(ii) WrIte its transition and output table 4

(Hi) praw logic diagram. 4(b) Draw and explain the diagram of IC 566 vca and explain its features. 8

7/28/2019 D12SE4-EXTC

5/10

~.(, 41< 6j(JTt

$-\-1:'&', . / ~j) c--rr:.

4.~J.d-upqSH Kl12 8

Con. 7822-12.

(3 Hours)

N.B. :(1) Question Nos. 1 and 2 are compulsory.

(2) Answer any three from remaining questions.

(3) Figures to the right indicates full marks.(4) Assume suitable data if required.

I. (a) Design two stage R-C coupled CE amplifier for the following specifications: 15

Av?: 1600, Vo = 32V. Use transistor BC 147A from data sheet (Assume for

BJT hre = hoe = 0).

(b) For the above designed amplifier determine voltage gain input impedance, DIP 5

impedance and tota! .curren~ supplied by source Vcc.

2. (a) Design class A .transformer coupled power amplifier for the following 10. .

specifications.: -peak output voltage 6V, load resistance RL =6Q and Supply

voltage of 20V. .

(b) For dual input oalanced output differential amplifier analyze and derive the expression 10

f (i) Diff i l d i (Ad) (ii) C d i (A ) (Hi) CMRR ( )

7/28/2019 D12SE4-EXTC

6/10

(b) Explain the principle of working of Weinbridge oscillator circuit. Explain why 8

negative feedback in addition to the usual positive feedback is employed in

Weinbridge oscillator.

5. (a) An amplifier with negative feedback has an overall gain of 100. Variation of this 10

gain of only 1 percent can be tolerated for some specific use. If the open loop

gain variations of + 10% are expected owing to production spreads in device

characteristics, determine the minimum value of the feedback fraction Band

also open loop gain to satisfy the above condition.

(b) Explain the practical cascode amplifier and derive the expression for Av, Ri and 10 -.....

. Ro. List the applications of cascode amplifier.

6. (a) Explain why a voltage amplifier cannot be used as a good power ampli_fier. 8(b) With neat sketch, explain the working of an astable ~ultivibrator. On what factors 12

does the-frequen"cy of the output waves depend?

7.' Write short notes on the following (any two) :- 20

(a) Crystal oscillator andits applications

(b) Explain Low frequency response of Recoupled CE amplifier

( ) i di i i lifi d h 2

7/28/2019 D12SE4-EXTC

7/10

of09-:s~.t. . . . ;;(X)~

" ' ; ; :NI

D u t ": x J. . . . ~

D .c. turrtlll I4iIl s..r. SlpII '10"

Q ' .~ N\ " '? I W . . . . f ; 1 I a lIIU.~

~d~. ~C . - tIP I'lIU. , . " . "cr. ~I

o . i rN

7 '200 2 0 S O 70 l' S O 1 .2 0 l a IS$ ' 2 0 0 2 S 50 10 0 2 S 7 S 12 5 1 -S ~S ~II 1 5 0 3 0 S O no"

60 11 5 .1 . .2 4 . 0I S 20 0 5 0 90 280 90 ~ 0 0 9 " s ( ) ~ I~ us u s 180 120 1 2 S Z 20 260 0 0 9

100 35 65 4j() 125 2 0 0 290 4 s o . % t 3 3 0 5 0 0 09

V4: U Vt :: Il lI Va ll " '__ 'IOlft (S laJ (Su) 'f,)lu~~. t114.c.NbtU. U.

7Q 9055 60

6S50,

s o

Pdw=z It:IUZ Vat1t4

@ 25'C @ 1.rC 1 1 1 1 1 1 3Watrs A!q: Jot.

YI JO S S US-S 150 lot l D O - 6 0-

E C N a s s . S f ) . O s.l) 1.0 '0 s oE C H 1 4 9 3 0 .0 4 - t Ht S~ 40eC H lO ll S - o 0 . 1 ( ) . 6 70 60BCI4'JA ( ) ' 2 S o .t 0 . 2 5 50 45'2 N S '2 5 (P , '1 r> ) o ,m 0 . 5 o . , s , IS 3DBCH', 0 -2 5 0 0 1 0 0 15 , S 4) 4 'TI'fWi:tor rypt Me l ID . Itrt lJjll

Be 147). 27 KO l~ (7 1 5 x 1 0 '" O~lIIW1}l 52' (PIIP, 10 4 K n 2 3 1 0 1 " 3- 2 x 10 '+B e 1 4 1 t 4S r1l 3 : l J . I 0 2 x l~ 0 0 4 -etm 1 l'"E C N 1 0 0 SOOQf C N 1 4 9 1 5 0 i lUN o s s 100 n2N " 3 O S S zn.

NChannel JFEr

-Va \'Oks ().O 0 . 2 04 ().4 0-8 1.0 lt t-4 2 . 0 t 0 4 2 . . 5 ~.o 3 -S o C . ( )

bs IlW.. CIlA Ut M .3 1 - ' 6- 8 61 H 4 -1 .3-1 2Z' W \.1 0 0 5 4 ) . 0I l l S C W o m A 7- & ~ S '" 4 - ' '--0 3- 3 H11 ~

0 . 1 0- 0 0 . 0 Q .O 0.0

b/Din. 1II'A '4-0 3 -0 1. 2 1-6 1-0 o - s 1 J .O 04 0 -0 0- 0 ~ 0 -0 1)0 c ) G

Type vn~'Y

C I GI\ilX. 'or- P 4 ftC, 1i~. f. I. -VrVoltl' " O .::rO le 8 .; -vo l ts

v .v.Ita

@2SC fOPiUl>. 2 S " C

11J1821 S O

"~ 300 mW I1S"C l/DA llO O I L O . 6 so m 1mWrc O S 9"C 1m W

ltr~'11( ty p icaO 3 t 30 30 3Q( ) mW 2 O O ~ C 7m A S 6 OOI 1U Z s so x n 'o-ff' C/raW

{)(

7/28/2019 D12SE4-EXTC

8/10

{)(c~~lei'iL-ru: (~)

feE

(3 Hours)

N.H. : (1) Question No. 1 is compulsory.(2) Attempt any four questions out of remaining six questions.

(3) Assume suitable data if required.

KR-7391

[Total Marl

7/28/2019 D12SE4-EXTC

9/10

N.D.: (1) Question No.1 is compulsory.

(2) Attempt any four from remaining six questions.(3) Assume suitable data if necessary.

1. Attempt any four questions :-

(a) State ap.dexplain Coulomb's law

(b) Method of Images

(c) Gauss's Law

(d) Poynting Vector(e) Polarization of electromagnetic waves.

2. (a} Find electric field intensity due to a volume charge.

(b) Calculate the total charge within the volume

o :s P :s 0'1, O:s ~ :s 1t, 2:S z :s 4 given P I) =p 2Z2 sin 06~.

7/28/2019 D12SE4-EXTC

10/10

6. (a) Derive Poisson's and Laplace's equation. 10

(b) Use Laplace's equation to find capacitance of a coaxial cable of inn~r radius 'a' 10

and outer radius 'b' m, given V=Vo at r = a and V = 0 at r=b.

7. (a) Derive general wave equations for E and 11fields. 10

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

P rP

v= _0_ for 0 :$ r :$ a

a

Pv = 0 for r > a