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Time: 3 hrs.

Fourth Semester B.E. Degree Examination, June/July 2013Engineering Mathematics - lV

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PART-A

I a. Use modified Euler's method to solre !I = x + y, y(0) = 1

2a.

b.

3a.

taking h - 0.1.

solve !Idx

=x+y,x=0, y = I at x:0.2 using Runge-Kutta method. Take h = 0.2.

Note: 1. Answer FIVE full questions, selectingat least TWO questions from each part.

2. Use of Statisticdl tables permitted

Max. Marks:100

at x = 0.1 for three iterations

(06 Marks)

(06 Marks)(07 Marks)

(07 Marks)

, (07 Marks)c. Using Milne's predictor-corrector method find y10.3) correct to three decimals given,

(07 Marks)x -0.1 0 0.t 0.2v 0.908783' 1.0000 1.1 1 145 1.25253

Approximate y and z at x : 0.2 using Picard's method for the solution "f * = r,

Y=*'ly *r) with y(0.) : l, z(O): l/2. Perform two steps (yr, yz,zt,za). (t0Marks)dxUsing Runge-Kutta method solve y" : x(y')2 y2 at x:- 0.2 with x0 - 0, yo = l, zo = 0 takeh: 0.2. (t0 Marks)

lf f(z) = u + iv is analyic prove that Cauchy-Reimann equations ux : vy, uy : -vx are true.

4a.

b.

5a.b.

c-

Find the bilinear transformation which maps the points z: 1, i, -1 onto the points w = j, o, -i.(06 Marks)

will map what portion of w-plane.State and prove Cauchy's integral formula.

Ifw:23 find dildz.If the potential function is 0 = log . Find the stream function.

PART-B

Prove that J''' = -[ .;r*.rr YnxState and prove Rodrigues

^formula for Legendre's polynomials. Y"}i| rt %7 Marks)

Express f1x): x' + 3x'- x' | 5x - 2 in terms olLegendre polynomial. (07 Marks)

l +y

1of2

6a.

b.

1OMAT41

The probabilities offour persons A, B, C, D hitting targets are respectively 112, 113,114,115.What is the probability that target is hit by atleast one person if all hit simultaneously?

(06 Marks)i) State addition law ofprobability for any two events A and B.ii) Two different digits from 1 to 9 are selected. What is the probability that the sum of

the two selected digits is odd il'2' one ofthe digits selected. (07 Marks)

Tluee machine A, B, C produce 50%,30%,20Yo of the items. The percentage of defectiveitems are 3, 4, 5 respectively. Ifthe item selected is defective what is the probability that it isfrom machine A? Also find the total probability that an item is defective. (07 Marks)

(06 Marks)

(07 Marks)

7 a. The p.d.f of x is

Find k. Also find p(x > 5), p(3 < x < 6).

A die is thrown 8 times. Find the probability that '3' falls,i.1 Exactly 2 timesii) At least onceii) At the most 7 times.

What is null hypothesis, altemative hypothesis significance level?8a.b.

c. In a certain town the duration of shower has mean 5 minutes. What is the probability thatshower will last for i) 10 minutes or more; ii) less than l0minutes; iii) between 10 and 12

minutes. (07 Marks)

(06 Marks)

The nine items of a sample have the following values: 45, 47,50,52,48,47,49.53,51.Does the mean ofthese differ significantly from the assumed mean of47.5. Apply student'st-distribution al 5olo level ofsignificance. (to us for 8df= 2.31 ). (07 Marks)

c. In experiments on a pea breading. the following frequencies of seeds were obtained:

Round-r,ellow Wrinkled yellow Round green Wrinkled green Total315 101 108 -tz 556

Is the is in the agreement of theory which predicts proportion of frequencies

,10,, 3df = z.sts). (07 Marks)

I

x 0 1 2 3 4 5 6p(x) k 3k 5k 7k 9k 11k 13k

2 of2

+L E C.USN O6MAT41

Max. Marks:100Note: 1. lzsxrer FIVE full questions, selecting

ot least TWO questions from eoch part.2. Any missing dato moy be suitably assumed.

Fourth Semester B.E. Degree Examination, June/July 2013

Engineering Mathematics - IVTime: 3 hrs.

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PART _ AI a. Employ Taylor's series method to obtain approximate value ofy at x:0.1 and x: 0.2 for

the diff'erential equation 4 = 2y * 3.' , y(0) : 0 considering upto fourth degree term anddx

compare the numerical solution obtained atx- 0.2 with the exact solution y : 31s2' e.).(06 Marks)

b. Using Fourlh order Runge-Kutta method to solve (x+y)9=1, y(0.4) : 1 at x - 0.5,-- dxcoffect to 4 decimal place. (07 Marks)

c. If !I=2e'-y, y(0) : 2, y(0.1) :2.0t0, y(0.2) : 2.oao, y(0.3) :2.090 lind y(0.4)-dxcorrected to 4 decimal places by using Milne's predictor and corrector formula (usecolaector formula twice).

2 a. Detine an andTtic function and obtain Cauchy-Rdmann equations in the Cartesian form.(06 Marks)

b. Show that the function u = sin x cosh y + 2 cos x sin hy + x' - yt + 4xy is a harmonic functionand determine the conesponding analytic function. (0? Marks)

c. Find the bilinear transformation that maps the points 1, i, -1 respectively onto the pointsi, 0, -i under the transformation find the image oflz < 1. (07 Marks)

(07 Marks;

inaregion, (i) zl < 1, (ii) 1< z < 2, (iii) zl> 2, 1iv)0 < z-11< l,

3 a. If (z) : u + iv is an analyic function and f(z) is continuous at each point with in and on a

closed curve c, then show that [fpSar=0. (06 Marks)C

h. Exoand- (z-1llz-21(iv) lz ll, t.

c. Evaluate 1-(l a, wherec: zl:2 wingCauchy's residue theorem.! tz' -tt

4 a. Obtain a series solution for the difI'erential equation t1 +x',;!*r, ly-,=r. (06 Marks)'dx' dxb. Obtain the series solution ofLegendre's differential equation.

(r -x') 1 I -2x!r+n(n -l)y =o' 'dx' dxleading to Legendre's polynomial.

c. Prove the following:

[:[:-*' .l ) fils 3-x' IJ,,(x)=./-i , Srlx - -cosxf . J_.,(r)=,i - i-slnx- , cosxl (07 Marks)- lrxtx x I - \/rxlx x ]

I of 2

(07 Marks)

(07 Marks)

(07 Marks)

x 0 I 2 3 4

v 1 1.8 1.3 2.5 6.3

O6MAT41PART - B

5 a. Fit a curve ofthe form y=a111 1cx' to the data by the method of least squares. (06 Marks)

b. Find the lines of regression and hence find the coefficient of correlation for the followingdata: (07 Marks)

c. Let a and B are any two events, then prove that P(A u B) = P(A) + P(B) - P(A n B) and

hence prove,P(AuBuC) = P(A) + P(B) + P(C) - P(A.B) P(B^C) P(A/1C) + P(A.\B^C). (07 Marks)

6 a. Find the value of K, such that the following represents a finite probability distribution and

find P(X < 1), (ii) P(x > 1), (iii) P(-1 < x < 2)and standard deviation also finc I

x ., _) -1 0 i 2 3

P(x) K 2K 3K 4K 3K 2K K

fixed probability vector.c. Explain: i) Regular and irreducible Markov chain

ii) Periodic state

iii) State distdbution and higher transition probabilities.

2 of2

[o 1 o.l

b. Show that p I g 9 t I i, un r.gulu, stochastic marrix and find the corresponding unique

lY, Y, o)

(06 Marks)

(07 Marks)

(07 Marks)

(07 Marks).

If 10% ofthe rivets produced by a machine are defective, find the probability that out of 12

randomly choosen rivets: i) Exactly 2 will be defective; ii) At least 2 will be defective;iii) None will be defective. (07 Marks)

c. 200 students appeared in an examination, distribution of marks is assumed to be normal withmean: p : 30 and S.D. : o: 6.25, how many students are expected to get marks.i) Between 20 and 40 ii) Less than 35. (07 Marks)

7 a. A coin was tossed 400 times and the head turned up 216 times. Test the hypothesis at 5%level ofsignificance that coin is unbiased. (06 Marks)

b. A sample of l2 measurement of the diameter of metal ball gave the mean 7.38 mm with S.D.1.24 mm. Find 95% and 99% confidence limits for actual diameter given t0 s5(1 1) : 2.2 andtoor(11):3.11.

c. A set of similar coins are tossed 320 times and the observations are

No. ofheads 0 1 2 3 4 5

Frequency 6 27 72 112 71

Test the hypothesis that the data follows a binomial distributions. For 5df we have

xios = 11.07 (07 Marks)

8 a. The joint probability distribution of two discrete random variable x and y is given by thefollowing table. Determine the marginal distribution of x and y. Also find whether x and y

(06 Marks)

x I 3 4 2 5 8 9 10 13 15

v 8 6 10 8 t2 16 16 10 )z )Z

ent.

vx

1 3 6

,| 1//9 t//61//t8

3 t//6 t//4 t/,/12

6 1//18 X, %u

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program should store accordingly OOH/FFH from(10 Marks)

voltage connected to(10 Marks)

+4 steps and(10 Marks)

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Fourth Semester B.E. Degree Examination, June/July 2013Microcontrollers

Time: 3 hrs. Max. Marks:100Note' Answer FIVE full questions, selecting

ol leqst Tl;ltO questions from each part.

PAR'I'- AI a. Compare the CPU architectures: i) CISC and RISC; ii) Von - Neumann and Harvard and

iii) Microprocessor with microcontroller. (12 Marks)

b. Interface 8051 to external ROM and RAM and explain how 8051 access them. (08 Marks)

2 a. Explain briefly the five addressing modes of8051 with an example for each. (l0Marks)b. After reset, the contents of internal memory of 8051 with address OAH and OBH contains

data 22H and 33H, respectively. Sketch the contents of internal memory from address 07Hto OBH and the value ofregister SP, after executing the following code:PUSH OAH

MOV 81H, #OBHPOP 09H. (0s Marks)

c. Write a subroutine which checks the contont of location 20H. If it is a positive number, the

subroutine finds its TWO's complement and stores it in same location and returns. (05 Marks)

3 a. What are assembler directives? Explain any four of them. (05 Marks)

b. If the XTAL frequency of 8051 is 8 MHz, find the time taken to execute the followingprogram:MOV R2. #04MOV Rl. #06WAIT: DJNZ R2, WAIT. (05 Marks)

c. Write 8051 ALP which checks whether the ten numbers stored from external RAM memoryaddress, 2000H are odd/even. Theinternal location 30H onwards.

4 a. Interface ADC0809 to 8051 and write an ALP to convert the analogsecond channel. Display the digital value on LEDs connected to port-0.

b. Interface 8051 to a stepper motor and write an ALP to rotate the motor frstthen -6 steps.

b. Explain briefly the interrupts of8051, indicate their vector addresses.

PART-B5 a. What is the diff'erence between timer and counter operation of 8051? How to start/stop the

timer/counter of 8051 when i) GATE control is nol used and ii) GATE control is used.(05 Marks)(05 Marks)

c. Write an ALP in 8051 which generates a square wave of frequency 10kHz on pin 1.2, usingtimer-l. Assume XTAL frequency as 11.0592 MHz. What is the minimum frequency that

(10 Marks)can be generated?

1 of 2

6a.b.

10ES42

Explain the functions of the pirs of 9-pin RS-232 cormector. (04 Marks)Explain how 8051 transmits the character and receives a character serially using its UART.

(06 Mar(r)Write 8051 C program to transmit serially the message 'SWITCH ON' or 'SWITCH QFf'.".depending on the status of the simple switch connected to pin 1.2. Use 2400 baud pte" I

stop bit, 8 data bits format and assume XTAL frequency as 11.0592 MHz. . (fi&M;rks).'/1,*Pr

b.

c.

Z a.(hterface an LCD display to 8051 aad write an ALP to display the message '@.Y,fg?|*block schematic explain the features 8255 PPI chip and its rrlode-d'bperur#

*o'uO,:-

(06 Marks)is the content ofIf the'

register A

8a.b.

--r

2 of2

USN 06ES42

Fourth Semester B.E. Degree Examination, June/July 2013Micro Gontrollers

Time: 3 hrs. Max. Marks:100Note: 1. Answer FIVE full questions, selecting

atleost TLI/O questions from eoch part2. Missing dota, if ony, may be suitable assumecl.

PART_A

a. Explain with neat diagram, Harvard architecture and Von-Neumann architecture. (06 Marks)b. Write the block diagram of 805 1 micro controller and explain each b1ock. (t 0 Marks)c. Calculate the time required for one machine cycle :

i) At89C51 with crystal 22MHzii) DS5000 with crystal 1 1.59MH2. (04 Marks)

2 a. Name the bit addressable SFR's presenr in 8051 microcontroller with its address and lrrite aprogram to nealise rhe logic expression

EoE

E

39

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.EA

Y!.)

-ts

!a'E ^

o.;

(r;

:9^:E=o. i:

e<-: 6i

az

Y=ABC+AB C. (06 Marks)b. Explain the working of following instructions, with an example.

i)RLA ii) DAA iiDMOVC. bit iv)MOVC A v)Atdptrv)XCHDOA, @RO.(toMarks)c. Write an assembly level program t' subtract two sixteen bit numbers present in internalRAM location and store the result in external RAM location starting from 8000H. Assumethat fust sixteen bit number is present in intemal RAM starting from address 10H andsecond sixteen bit number is present in internal RAM starting lrom memory location 12H.

3 a. What is the difference between jurnp and call instruction.diflerent types ofjump instructions.

b. With a diagram, explain the differentinstructions.

(04 Marks)

Explain the ranges associated with. (08 Marks)

steps that take place on execution ol CALL and RET(08 Marks)

c. Find the content ofaccumulator after execution ofeach instruction :

$ include <reg51 h> Internal RAMorg 0000HMOV A, 25HADD A,26HDAAxcHD A, @ROHere : sjmp here

end

Content

4a.b.

c.

(04 Marks)

Explain the different tJpes bit logical operators present in 805lC. (06 Marks)Write a program to toggle all the bits of P2 with a delay of 250 m seconds delay using8051C. Use the exclusive OR operator. (08 Marks)Write a 8051C program to send out the data AA H serially one bit at a time via P2.3. Theserial transmission should start liom LSB. (06 Marks)

1 of 2

Address Content

068S42

PART - B

a. With a diagram, explain the start and stop of the timer 0 through pin P 3.2 when GATE bitin TMOD register is set to high. (06 Marks)

b. Explain the steps to program timer 1 in mode 2 with a diagram. (06 Marks)

c. Find the number to be stored in THI and TLI register to generate the waveform shown in- . Fig. Q5(c). Also write the assembles level program to generate the waveform shown in Fig.

b-

-a *-

Fig. Qs(c)

What is the need lor serial communication? Explain half duplex and full duplex transmissionwith the help of figure. (06 Marks)

What is the need of SBUF register and explain dll the bits of SCON register. (08 Marks)

Write the programming steps to transfer data serially in 8051. (06 Marks)

What is the differenqe between pollingdisadvantages intemrpts.

b. Explain how extemal interrupts can be activated as level triggered and edge triggered in8051 with the help of diagram. (06 Marks)

c. Write a 8051 C program that continuously gets a single bit of data liom P1.7 and send it toP 1.0, u{iile simultaneously creating a square wave of 200 ps period on pin P2.5. Use timer 0

a creite ihe square wave. Assume that crystal frequency used is 11.0592 NHz. Also send

letter A to the serial port. Use baud rate 9600. (08 Marks)

8 a. Explain with a diagram, how the DAC 0808 can be interfaced to 8051 chip. Write a 8051Cprogram to generate a square wave offrequency 10 KHz using OAC interface. (08 Marks)

Q5(c) on P3.1, using timerl. Assume the crystal frequency as 22 MHz. (08 Marks)

bn6

6a.

b.

7a. and interrupts? Write the advantages and(06 Marks)

(06 Marks)(06 Marks)

b. Explain the use of register select, read/write and enable pins of LCD.' c. Explain how a stepper motor can be connected to 805 I micro controller.

2 of2

USN 10ES43

Max. Marks:100

(06 Marks)

(05 Marks)

. (08 Marks)

Time: 3 hrs.

Fourth Semester B.E. Degree Examination, June/July 2013Gontro! Systems

Note: Answer FIVE full questions, selectingat least TWO questions from each part

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PART. AI a. Compare open loop and closed loop control systems and give one practical example ofeach.

(06 Marks)

b. For the system shown in Fig.Q.1(b) write mechanical network afld. obtain its mathematical

c. For the system shown in Fig.Q.l(c) write its mechanical network and obtain mathematicalmodel and electrical analogue based on force-current analogy. (08 Marks)

Fie.Q.l (c)

model.

Fig.Q.l(b)

Define transfer function and what are its properties.2a.b. Obtain the transfer function foi the block diagram ghown in Fig.Q.2(b) using block diagram

reduction method.

Rr,)

(07 Marks)

Fie.Q.2(b)

c (.)

c. For the block diagram,gain formula.

f

Fig.Q.2(c)

I _- TLiEl--given in Fig.Q.2(c) obtain over all transfer function using Mason's

3a.

b.

10ES43The open loop transfer function ofa servo system with unity feedback is given by

Gtrl = los(0.ls + l)

Find out static error constanls and obtain steady state error when subjected to an i/p ofA.

r(1) = Ao + AJ + ---!t' . (08 Marks)

Explain RH stability criterion used for finding of stability ofcontrol systems.

Find the range ofK for the system to be stable using RH criterion.

G(s)H(s)=

(06 Marks)

(06 Marks)

(08 Marks)

(20 Marks)

(04 Marks)

(13 Marks)

(03 Marks)

(06 Marks)

(02 Marks)

(12 Marks)

Take er(t), ez(t) as i/p(08 Marks)

Inv,estigate the stability ofthe system give by characteristic equation56 + 2S5 + 8S4 , l2sr - 2oS'?+ 165 - 16 = 0.

PART - BA feedback cirrcirffirol system has an open loop transfer function

V

Draw the root locus as K varies from 0 - to - "o.

6 a. Define the following terms:i) Resonant peakiD Resonant frequencyiii) Band width

7a.b.c.

8

iv) Cut offfrequency.b. Sketch the bode plot lor the transfer function

3001s: +2s+41

s(s+10)(s+20)s(s 1- | u/\s -i zu,,

c. Write a note about gain margin in brief.

Fig.Q.8(a) i.cr)\r.ci):r c

List out the properties olSTM.

Obtain the state transition matrix for a system matrix given by

2 of2

?.

b.

c.

G(s)H(s) = 5

s(l - s)

Obtain the state model for the electrical system given in Fig.Q.8(a).variables and voltage across R as o/p variables.

L, Lo

+

)+,

er(r) ( gr(F)

Iol)

(05 Marks)

ll" | (07 Marks)

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s(s2 +5s+9)'

TISN 06ES/EC/TE/EE/]\/l L/BM43

Max. Marks:100

(06 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013

Time: 3 hrs.

Gontrol System

PART-A

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Note: 1. Answer FIVE full questions, selectingatleost TV4O questions lfrom each part

I a. Define control system. Explain the differences between open loop control system and closed

loop control system, with examples. (10 Marks)

b. Draw the signal flow graph and obtain the closed loop transfer function ofa system whose

block diagram is given Fig. Q1(b). (10 Marks)

Fig. Q1(b) Fig Q2(a)

For the mechanical system shown in Fig. Q2(a), obtain the F - V analogous electricalnetwork. (12 Marks)

Obtain the transfer function of field controlled servo motors. (08 Marks)

Starting {iom fundarnentals derive an expression to- i: ihe step response of tJpical underdamped second order closed loop control system. Show the typical variation ofthe response

and mark the settling time on 570 tolerance basis. (14 Marks)

Explain the following time domain specifications of a second order system

2a.

b.

3a.

b.

4a.

b.

i) Delay time ii) Rise time iii) Settling time iv) Peak time.

For the system with characteristic equation sa + ks3 + s'+ s + 1= 0 , determine the range of kfor stability. (10 Marks)

The open loop transfer function ofa UFB control system is given by50(i(c) =

-

s( I + 0.05s X I - 0.2s )

Apply R H criteria. Show that the system is unstable confirm that the introduction ofthotwo terminal pair network connected in cascade with G(s) makes the system stable.

Cr :0.5pF ; C:: 10 pF ;R1 - I Mf)(-,t

rrl'--1r-*{ry-'=- T€.tI

Fig. Qa@)

I of2

(10 Marks)

5a.

'b.

ta-

6a.b.

O6ES/EC/TE/E E/ML/8M43

PART_B

As applied to root locus, explain how toi) Determine angle of departure or anival from a complex pole or zeroii) Determine the break away or beak in points ifthey are presentiii) Calculate k on a given point on the root locus (08 Marks)The characteristic equation ol a single loop unity feedback control system is given byF(S.1 = rj + 8sr + 20s + k : 0. Sketch the complete root locus diagram and liom that find :

i) Two values of k that make the system critically dampedii) Tow values of k for which the damping ratio is 0.95iii) Write closed loop transfer functions for the values of k found in part(ii). - (12 Marks)

(08 Marks)

(12 Marks)

iii) Gain cross over frequencyiv) Phase crossover frequencyv) Corner frequency.

b.v, r-orlrcr [cqucrr.:y.The open loop transfer function of a unity feedback control system in given by

(06 Marks)

G(s) =k(s + 1)

s(s + 0.1s)':(1 + 0.02 s)

i) Draw the bode plo! dnd hence find phase margiir and gain margin for k = 1

ii) Determine the v-alue of k for a gain margin of 20 dB and the value of kmargin of 30i'. ,

(06 Marks)electric network shown in Fig. Q8(b) by choosing minimal

. (08 Marks)

for a phase(14 Marks)

I a. Write sho

Dii)

matrixanalvsis.

state model of theof state variables.

Fie. Q8(b)c. Construct a state model for a given system characterized by the differential equation :

drv 6d2v I ldvol -ff.?+6y +u =0

2 of2

Draw the state diagram. (06 Marks)

t0EC44USN

Fourth Semester B.E. Degree Examination, June/July 2013Signals and Systems

Time: 3 hrs. Max. Marks:100..,,. N otel. Answer FIVE full questions, selecting. ; at least TWO questions from each part

:^:_ '

PART-A\

: I a. Determine whether the discrete time signal x(n.1 = 965[ I ]rir[] I is period;c. tf periodic.e \)/ \r/o.

E find the fundamental period. (04 Marks)

H b. Detemlirlp whether the signal shown in Fig. Ql (b) is a power signal or energy signal.

! Justift yow answer and further determine its energy/power (06 Marks)

t4dg LI r_a8=8= i, /"'-, > -,/=:*; ' E'.o I I \t

I:Ei -i r---LE; Fig. Qr (bE :* Fie.Q.l (bl

€ E c. Civen the signal x(n) - (6 - n){u(n) - u(n-6)} make a sketch ofx(n). yltn} - x(4 n) and

5 E yz(n) - x(2n - 3). (04 vtarks)

9 e d. Find and sketch the lollowing signali and their derivatives:;: i) x(r): u(r) - u(r-a)r a> 0 ii) y(t)-rlu()- u(t-a)l :a>0. (06 Marks)c5

'EE -5 2 a. The impulse response ol a discrete LTI system is give by. h(n) : u(n+l) - u(n-4). The

$E system is excited by the input signal x(n) = u(n) - 2uln-21+ u(n-4). Obtain the response of: ; the system y( n) : x(n)*h( n ) and plot the same. (07 Marks)

S* b. Civen xfl)=r 0<tsl and 0 elsewhere

5 B and h(t) = u(0 i(t-2), evaluate and sketch y1t) = x(t)*h(t), x(t) and h(t). (07 Marks)

! : c. Showthat : i) x(t)*h(t): h(t)*x(r)=:\ ..

* * .iii{x(n)*h1(n)} *hz(n) : x(n)* {h1(n)*hdn)}. i .-', (06 Marks)d(!<);g E 3 a. Solve the difference equation. y(n) - 3y(n-l | - 4y(n-2) - x(n) with x(n) :4\(n). Assume

a € that the system is initially relaxed. (06 Marks)

i E b. Driw the dhect form I and direct form implementations for.1

a? i) y(n)-^y(n-l)-y(n-3)=3x(n-l)+2x(n-2)c orl

E g ... d'y(t) -dv(t) dx(t)3 E. rD --#+5...:-:--:.+4y(t) = ------i---: (l0Nlarks):; dt' dt dra ? c. Define causality. Derive the necessary and sufficient conditions for a discrete LTI system to-j ''i be causal in terms of the impulse response. (04 Marks)go

Z 4 a. Determine the DTFS coefficienls of.i fl 3nlE x1n)= t +sin{;^".;} (06 Marks)

I of 2

4 b. Find the exponential Fourier series ofthe waveform shown in Fig. Qa @).

toEC44

(08 Marks)ztltl

Fie. Qa (b)Explain the Direchlet conditions for the existence ofFourier serres.

..:.PART-B5 a. Fi-nd the DTFT of the signal *tn) FJil(n)= u(n)-u(n -N): where N is any +ve

integer. Determine the magnitude and phase components and draw the magnitude spectrumfor N=.5. (10 Marks)

b' D.t...ih" .the fourier transform of the following signals : i.1 x(t) = e''u(t - 1)

ii) x(t) = "'"1'l

. ' (lo Marks)

6 a. Determine the freqlency response and the impulse response for the system described by thedifferential equation.

d2vt t) - dv(l) - d

;-*ti-+6y(t)=-x(1) (loMarks)

b. Determine the Nyquist sampling rate and Nyquist sampling interval for,

. '1..'r'. , ',.-.i f sin/400nr*\ 12r) x(t)=l+coszuuuTlt+sul4uuurfti ,, "(t)=L--] (06Marks)

c. Explain briefly, the reconstructionpf,continlous time signals with zero order hold.

7 a. Find the z-transform ofthe following and indicate tlie region ofconvergence:

it x(t)=l+cos2000nt+sin4000nr ii) -(r)=[!gt9004)]'

(06 Marks)

(10 Marks)

-,, r.. (10 Marks)

Stable ii) Causal.(10 Marks)

i) x(n) = 6' cosOo (n -.'2)u(n - 2)

ii) x(n) = 1(111;sr11r)b. Find the inverse,2-iiansform of the following:

. zo +z' 1-r) x(z) = .,:lzl >-bv) r l' 2",.24 - z+,-:..'. 4 8

. -ryrtiat fraction expansion method.

|-az-t 1

7. -a a

E a. A discrete LTI system is characterized by the difference equation,y(n) = y(n -1)+ y(n - 2) + x(n - 1)

Find the system function H(z) and indicate the ROC if the system, i)Also determine the unit sample response of the stable system.

b. Solve the following difference equation using the unilateral ztransform.

ytn) -]y(n - I.1 +]y1n -2) = x(n) lor n > 012' ' 12' '

With initial conditions y(1) = 2, y(-2) = 4 and x(n) :

2 of2

(i) u(n). (10 Marks)

FRNh] : FHX $1. : 18 HFn. iA1: 11:34PI'l Fl

USN tlFourth Srmr:ster B,E. .Degree -Exnmination, Junc/July 2013

Sigrtals aild Syst6m$Time: 3 hrs.

Nute: ,4ri*wer F/YE fal! questlons, sdeuingarl TWO q|aesllotts lrohr each part.

PART _ A

I a, Distingulsh between :

i) Even afld odd signalsii) Periodic and ron-pcriodic signalslli) Ilnerry :md power signals.

b. Siketch the foilowing signalsx(n) = 6(rDx(u)=-2u(-n)x(t) -- (t - l) u(t)x(t) = 2u(t- l) - 2u(t-3)'

c. For tho sigfisl x(n)={1,2,3,a}, skerch thc sigD€l x(- 2n + l).

d. Determjne whether lhe systenl y(n) = x(n) + 3u(n + t) is

2a.b.

c.

d.

E?E

rebH

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.E .\

EE

AeaEEU

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e&FtsUJe,z

ts-o

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a

3..

b.

c,

d.

4a.

b.

i) Linear ii) Tinre - invariant iii) Causal iv) Mernr-rry less v) Slahta. (06 t48rksi

Dcrivc thc cxprcssion ttrr oonvolut.ioll sum.Convolve the signals xr(n) = l8(n) + 28(n -l) + 3E (n - 2)v*(n) = 6(n) + zE(n - l) r 36( n-2)-State and prove associative property ofconvoluriern integral.Find the rer;ponse y(t) - x(t) * h(t) thr thc signal x(t) = c'i u(r)i a >h(r) * uC),

!01 c-ach of fi9 impuls6 v65penss listed bslow, determine whcth€r the corresponding sysrcmi.s I Causal ii) Mcmory L:sr iii) Stable. i) h(l) - er r'l ii) h(t) - e,ltb(t - l). ' (0-6 MorklEvalurte the forced response 0fthe systomy'(t) + 2y(t) - c.2' u(t).Solve tlre homogeneous diffcrcnce equation (tind natural response)y(n)+y0r- t; + |y(I -Z) = 0 \rith y(- l)=- landy(-2)=1.Dr8ly difeet tbr m - I and direot forfit - II impl€mentalions lor the ,system

.l!I{Q * 511,1 = 3*i,1 .(ll

Statc and provs thc followitlg prope ies off'ourier seriesi) 'l ime -shiftii) I'requcncy -shili. '

Eyahra(c rhc I)TFs reprcicentation for thc sigflal

-(,) =,il,(*,) - *,[TI,) -,Sketoh the rnagnitude and phase spectra.

u. For the signalx(t): sin w6t, find the fourier $eries and dfaw irs

068C44

Max. Merks: IOQ

{06 M$rks)

(0{ i}rsrIE}(04lllrrks)

(04 MurLs)-f +3( n -t1) alld

(05 Msrk{)(05 M*rksi

0 and inrpulse response

{0,1Matks}

(04 Mrrkr)

(06 Msrks,

i04 Mn*s)

(l)6 Mrrks)

PART - B

5 a. litflte and provc ths following propertics ofDTFl'i) Irequency shiftii) ltequcncy differentiarion,

b. Find the FT ofthe fr: llorving signalsi) x(t) = 6111

ii) r(t) : c'" u(t) ; a > 0.

c, Fidd the invers{, FT oliw+l

Xl llv | = -----_-:-- ,(.hir)r + 5jw +6

068C44

(06 i!ti*s)

(06 M&rkc)

(0* MEr*s)

6 a. Find the impulse responsc of

4iG) * l*yft) o ?y(r) = 21x(t) + x(t)dr'" ' dr" dt "b. By app lying Fourier trsnsfornr and IFT. (08 iHrrkE)

State and provc sempling theorenr lot low pass signol. (08 Marks)c. Consider the analog signal x(t) - 3 cos 5}nt + l0 sin 300*t - cos l 00m. What is the Nyquist

rlto lor this signal? {04 Marhs)

7 a. Statc and provo :

i) Linoorityji) Differentiatio furz-domain,propertiesofz*transfurur. (06NIsrkF)

b, l)dtermiflc the z - tlansiirrmation olx(n) = it, 2, t)x(n) - (z) u(rux(n)-6(n+2)x(n) - -(3)" u(- n - l). (08 Morks)

c. Find out ihr invcrse z - beirstbrm of1

x(z) =-. RoC : lz l> | 4 l,l- 4z-t 'Using powcr scries expsnsion. {06 Nlarks)

8 a, Fhrd the rnilfltcrdl z - trsr1sfofm olx(tt\={1,2.3,4\

Iy(n)=a" u(n + l); a { l. 106 Mrrtrs)

b. Fiud the dift'ercncc - cquation dcscription for a systcn: rvilh lranstbrm function :

v(z\ 5t't'2H(zt =: = ):; ;. (0ti yrrk!)

x(7) z, l Jz). 1

c. Consider the systern rleseribed the ditTerence quostion y{r) - 0.9y(n - l) = x(tr), Fin{ outputiflthe input is x(n) : u(n) aud the initial coudition ou dre c,utput is y(-l) = 2. tOB M6rks)

tolt

c. With syntax, explain the sequential stdenents in HDL:

a.

b.c.

€1

;i. ',

:: 3

3c=.9

ai'i^

OJE

>'9 6

-o. E

(-) <

;o7A

USN

,r'fime: 3 hrs.

10EC4s

Max. Mark* 100

(08 Marks)(08 Marks)(04 Marks)

(05 Marks)

(06 Marks)(09 Marks)

(06 Marks)

(06 Marks)

(08 Marks)

(08 Marks)(04 Marks)(08 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013

Fundamentals of HDL

Note: Answer FIVE full questions, selectingdt least TWO questions from each port

a.

b.

c.

a.

b.

a.

b.

PART_ADescribe VHDL scalar data types with an example.Explain shift and rotate operators in HDL with an example.Write a note on simulation and synthesis.

Explain the execution of signal assignment statements in HDL.

i) Constant declaration and assignment slatement.ii) Signal declaralion and assignment slatement.Write VHDL/Verilog code for 2 x 2 bit combinational array multiplier.

Write VHDL code for 3 bit binary counter using CASE statement.Explain verilog casex. Write verilog description of priority encoder using casex statement.

i) IF statement ii) IF as ELSE-IF iii) For loop

Write structural description of an VHDL SR latch using NOR gates.Write the facts of structural description.Write verilog code for.N bit magnitude comparator using generate statement.

PART - Ba. Write VHDL code to convert unsigned binary vector to integef conversion using procedure.(08 Marks)

b. Explain the syntax of function in verilog with an example. (04 Marks)c. Write. VHDL code lor reading a string of characters from file and store in an array

E&-COLLEGE. (08 Marks)

Write VHDL code for 16 x 8 SRAM using mixed type description. (t2 Marks)Write verilog code for ALU using mixed tlpe description. (08 Marks)

Write mixed language description of Master Slave D flip-flop by invoking VHDL entityliom verilog module. (10 Marks)Explain the process of invoking a verilog module from VHDL module. (10 Marks)

With an example, explain mapping the function statement in HDL. (06 Marks)Discuss some important facts related to synthesis basics. (06 Marks)With an example, explain mapping if, if-else, case statement in HDL. Show the synthesizedlogic symbol and gate level diagram. (08 Marks)

a.

b.

a.

b.

a.

b.

1f, fipr. ;-[11I 11:21Fll FfFRIII.i : Fr.i llrl. :

06EC45

Max, Ivi ark s: 1Q0

(08 lhrks)(01 Mnrks.t(0S Mirk!)

(I0 Mar.k$)

ized lcgic

E

B

&

fr)

,EA

es

va

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tson

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2

mTTill trTime; 3 hrs.

Fourth Sernester B.E, Dcgrcc Examinstion, June/.Iulv 2OlIFundamentals of llDL

Notcr .,lzsh,sr rifW full queslktns, selectingleast TWo questiotts froht eddt l,arl,

I a. flxprain the behavioral, struclurar ur#,r*.r".iprior1 tvpes irr Hr)L pmgrlrnming withexamP les. (u lrfirks)b. Erplirin thc foliowing tlata rvperi;i) Physical, srd_logic in VHDL ii) Nets, reglsters in vcrilog (0E lu:r!.ks)

! a. write HDl. code rirr ? x I n*rltiplcxer wirh rotir,e low enable. show its simulalionwavefornl' (oE Dlart(i)b. wriLe HDL cotie for 2 x 2 unsigned combinstional array multiplier, Show its gate ieveidiagrarn antJ sinlulatiol wavefom. (I2 Mtrrks)

] a Write VHDI. oode fbr 3 hil binarv cotmter with active high synchronous clear il behirvioraldcscription show excit tior rable and sirnulation wavcforri.

b, u'?it.; vHLrL onrl u.riJug ond* tirr caloulating ae taciorioluring behirvioral ,t.r".i;lir}*,'iwhile - k:rp. {Io l{{r.fts}

4 a, Explain bindilrg bctwccflii) Enlily and afchitdotur?

. ii) Ehli(y dEd componeut ir: VHDL. (oE llflrks)b write vr IDL codE ot- a 2. x 4 r.rccorrer with tri-state oulpur in structurfli acscrrptiat- iiowlogic diaglarn and sirnulation wavclirrm. (!2 Mrrks)

5 a. what are procedures in VHDL I r*r#*E#,,rro fbr procerJures. (05 Marks)b. writc Vr'lrL code for a fillr adder using procedure arrd task, (r0 llirrks)c. Write VHI)I, codc to fitrj rhe grenter o{tw.o sign+tl mrn:trers usjt}g fxnction. il;;;;.;;6 a. [xplan hoiv to attach pLrokage to rh€ VHDL morluie. Give an exurple.[:. Why mixed trle descr\:lion is nccdcrJ? Explain.

c. 'llrrite HDL descriptior.: oode of l6 r 8 SRiU.

7 a' Explain horv to invoke s ,HDL cntity f'rom a. verilog modure, Givc an extrmplc. (r0 r\rrrks)b. lVritc HDL oode for a Masrcr Slave D f)ip-rlop in rnixed tanguag" a"iscripri;; iffi,sir:rulation wtvefbrm. Go Msrkr)

I a. Write tlorv chad of F"v-nth€sis srcpr flnd cxplain.h- Writc HOL;ode for signal assignment statetnenr ), =: *

synrbol and gote level ,.jj6gpfl11x-3.

(10 M*rkrj

IJSN 10EC46

(08 Marks)how it is done

(06 Marks)

(12 Marks)(08 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013Linear lG's and Applications

Time: 3 hrs. Max. Marks:100

Note: 1. Answer FIVE full questions, selectingat least TWO questions from each port.

2. ase Is^,o: 500nAfor 741 opamp.

PART _ A

With a neat circuit diagram, explain the basic opamp circuit. (06 Marks)Give definitions of the following opamp parameters and give their typical values for741 opamp: i) CMRR; ii) Input ofiset voltage; iii) PSRR. (06 Marks)Draw a neat circuit diagram for a direct coupled noninverting opamp circuit and explain thedesign steps. (04 Marks)Two signals each ranging from O.lV to lV are to be summed. Using 741 opamp design asuitable inverting summing circuit. (04 Marks)

Draw a neat circuit diagram and give design steps for afollower; ii) Capacitor coupled inverting amplifier.

i) capacitor couplsd voltage

la.b.

E

*=

ooll

.E&

EY

.s.s

'C -

6E

3oo6=E>OY

rJ<-i c.i

z

E

d.

b.

c.

3a.

b.

c.

4a.

b.

c.

5a.

b.

A capacitor coupled noninverting opamp is to have Ap = 100 and Vo = 5V with RL = lOKQand fi : 100 Hz. Design suitable circuit. (06 Marks)

Define gain margin and phase margin and explain how they help for stability check.(06 Marks)

What is meant by frequency response compensation? Why it is required? Explain theworking of a phase lag compensation network. (08 Marks)Define: i) Slew rate effect; iD UGB. Determine the maximum distortion free outputamplitude for a voltage follower when 741 opamp is used with A:800 kHz andS = 0.5 V/p.S. (06 Marks)

What are the advantages ofprecision rectifier over ordinary rectifier? Explain the workingof a precision halfuare rectifier. (06 Marks)Draw the circuit of an instrumentation amplifier using opamp, explain the working andderive the expression for output. (10 Marks)Draw the circuit and explain the working of an opamp limiter to have voltage levelsV2 + Vp for negative cycle of input and -V,"1 for positive cycle ofinput. (04 Marks)

What is meant by setting upper cutoffin a capacitor coupled opamp? Explainin an inverting opamp.

PART-B

Write a brief note on following opamp applications:i) Negative clamper using opamp.ii) Log-amplifiers using opamp. r .

Explain the working of Weinbridge oscillator using opamp. l

1 of 2

10EC46

a. Explain how opamp can be used as inverting and noninverting comparator. What are thelimitations? Explain howthe limitations can be overcome using a Schmitt trigger. (10 Marks)

b. An inverting Schmitt trigger circuit is to have UTP = 0V, LTP: -1V. Design a suitable

cicuit using bipolar opamp with +l 5V supply.c. Design a second order active Iowpass filter for a cutofffrequency of7 kHz.

(05 Marks)(05 Marks)

a. Mention the advantages of IC voltage regulators. Draw the intemal schematic for 1C723

regulator and briefly explain the working. (10 Marks)

b. Explain briefly about 78XX and 79XX series voltage regulators. (10 Marks)

a. Draw the intemal schematic of 555 IC, configuring it for astable operation, explain theworking. (08 Marks)

b. Explain the working of D to A converter using R-2R network. (06 Marks)

c. Explain the working of A to D converter using successive approximation method. (06 Marks)

2 of 2

USN 068C46

Max. Marks:100

(08 Marks)(06 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013Linear IG and Applications

Time: 3 hrs.

Note: 1. Answer FIVE full questions, selectingal least TWO questions from each part.

2- Assume suilable values/data.

PART_A

Define the following terms with respect to operational amplifier:i,) CMRRii) PSRRiit) Slew rateiv ) O/P impedance.With a neat circuit diagram, expiain basic operational amplifier circuit.

oE

09.

.EN

-u

o' i':'Fd5.3

9JE

: -!l>':

E>

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;o

E

E

1a.

b.

An opamp has R1 : R2 : 22KA wftI a resistor tolerance of x20o/o. Determine input offsetvoltage due to i) the 741 specified, i/p offset voltage; ii) 741 ilp offset current; iii) theresistor tolerance. (06 Marks)

2 a. Explain capacitor coupled non inverting amplifier with circuit diagram. (06 Marks)

b. Design an noninverting amplifier to be capacitor coupled at input and output. The loadresistor is 2.2.K, lower cutoff frequency 120H2. Make necessary modifications to giveheighest i/p impedance 4nd determine capacitor values for Vi - 15mV, Av: 66. (10 Marks)

c. Briefly explain how will you set the upper cutoff frequency in inverting amplifier. (04 Marks)

3 a. Explain opamp circuit stability with feed back in inverting ampiifier. (08 Marks)b. Draw the circuit of head compensation network. Explain its operation and show how it

affects the frequency response ofan opam. (06 Marks)

c. i) Calculate the slew rate cutoff frequency for voltage follower circuit using 741 opampif the peak of sine wave o/p is to be 5V.

ii) Also determine maximum peak value of the sinusoidal o/p voltage that will allow 741

voltage follower circuit to operate 800 kHz, unity gain cutoff frequency. (06 Marks)

4 a. Explain with neat circuit of differential i/p and differential output amplifier. (08 Marks)b. Explain neatly with circuit and WF's at various points of high input impedance fuIl-wave

precision rectifier. (12 Marks)

PART - B

5 a. With neat circuit diagram and wavelbrms, explain precision clamping circuit. (10 Marks)b. Explain with neat circuit diagram and waveform of triangularirectangular waveform

generator with frequency and duty cycle control. (t0 Marks)

1of 2

6a.b.c.

06EC46

Explain an inverting Schmitt trigger circuit with waveform. (07 Marks)Draw the circuit of opamp astable multivibrator and explain its operation. (07 Marks)Using opamp, design a first order low pass filter to have cutoff frequency lkHz. (06 Marks)

)", I a. Explain with neat circuit of regulated power supply with different parts. (06 [y{q$\'-t-)z b. List and briefly explain the characteristics of three terminal IC regulators with st&dald'""n tu representation ofthe same. lQfluarks)

I.49. Wtrat is principle of switched mode power supply? Discuss their ad;antdgis and

A\C '(07 Marks)- lt. &.

S a. Effi$:qlhe functional diagram of 1C555 timer with neat sketch. .. - \ (10 Marks)

U. exphqt{Cqarly PLL wittiblock diagram. also define: lock in rangrd&pture range, full intime wiitr(Dpect to capture transient. n ' (10 Marks)'-"- "'"' -F, r1'*''/&, ,'-\ kr'ry

,\Q'' .a\ -vt\- *:*:+** '\t

'rn rU*,t- )'r$. (]^.-7), t" "

"d .,a.n'- \,"{^l'Hr\C}L'

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At

,\ rL,r,<\ '#}-$t L'(.,,^Y-\

r.f\"' u- -./! \) ,rl)

..rh"\ t': ,(\"' \ ,/ !A\ {,/-..o)- '- f r

- (\:' r ')'L\Vr )/+' /'"r+' ;-i,* &'.t ' <-,

^\'\ Kn' ,*f"' '/,\"

-{--h 1v.4't-f

2 of2