-l

USN

Time: 3 hrs.

2a.b.c.

c. Determine the poles of and the residues at each pole.

O6MAT41

(07 Marks)

wherec:lzl=:.

(06 Marks)

the regions i) Z<lzl<Z

(07 Marks)

(07 Marks)

(06 Marks)

(07 lVlarks)

(07 Marks)

Fourth Semester B.E. Degree Examination, Decemb er 2Ol2Engineering Mathematics - lV

Max. Marks:100Note: Answer FIVEfull questions, selecting

at least TWO questions from each parl

value of y at x : 0.1 and

(06 Marks)

Z,

(.)ooIa(!

0):()!

E9

6V

oolg0a.= ai

x50oC

-g(l)

o>?.a

6=

oo)

tr\ooico .6

-o

'o(!

-a5)3

o-Atra.()j

uioa--,o4 t'cE.i

LO

O,=>'!oo"cb0o=qotr>o-

U<* C..l

oo'7

Po

PART _ A

I a. Given that +=x2 +y2 and y(0)=1, to find an approximatedx

x:0.2 by Taylor's series method.

b. Using Euler's modified method, solve foryat x:0.1 if {y - y-* , y(0): 1, carryoutthreedx y+x

modifications. (07 Marks)

c. Given 9=(r+yh'andy(1):1,y(l.1):1 .233,y(|.2):1548,y(l.3):1.979,determinedx\y(1.4) by Adams - Bash forth method. (07 Marks)

Show that an analytic function with constant modulus is constant. (06 Marks)Findthe analytic function f(2)= u+iv, if u= e-.{(x'-y')cos y +2xysiny} (07Marks)Find the bilinear transformation which maps the points z: l, i, -1 into the points w: i, 0, -iand hence find the image lrl.t.

3 a. Using the Cauchy's integral formula. to evaluate I "o,?T't - a,lQ-t)(z-2)

Obtain the Laurent's series for the function f 127 = ," = t

-inz- +52+6ii) lrl, z .

(z-l)'(z+ 2)

4 a. prove that e%Gx'= it'J,(x).b. Show that J, (.) = ;;.,

(x) + J,-, (r))

c. Explain the polynomial 2x3 - x' - 3x + 2 in terms o

PART - B5 a. Fitast ht line to the following data:te wx: 0 1 2 J 4

v: 1.0 1.8 -,.-, 4.5 6.3

1 of2

polynomials.

(06 Marks)

O6MAT41

b. prove that tan 6 = [' - t' ) G*ova=[ . )#,

where y, o*, G, have their usual meanings and

explain the significance of r = *1 and r : 0. (07 Marks)c. A certain problem is given to four students for solving. The probability of their solving the

problem are /r, /t , yo and /, respectively. Find the probability that the problem is solved.(07 Marks)

a. The probability density function P(x) of a continuous

P(x)=yoe-l*|, -6<x<oo, prove that yo=/2. Find

distribution.

random variables is given by,

the mean and variance of the

(06 Marks)(07 Marks)

ii) P(x>2) and(07 Marks)

b. Derive the mean and variance of the binomial distribution.c. If x is an exponential variate with mean 4, evaluate i) P(0<x<1)

iii) P(-co<x<l0).

a- Define the terms: i) Null hypothesis ii) Level of significance and iii) Confidence limits.(06 Marks)

b. A sugar factory is expected to sell sugar in 100 kg bags. A sample of 144 bags taken from aday's output shows the average and S.D. of weights of these bags as 99 and 4 kgrespectively. Can we conclude that the factory is working as per standards? (Table value ofz:1.96 at SYoLog) (07 Marks)

c. The following table gives the number of aircraft accidents that occurred during the variousdays of the week. Find whether the accident are uniformly distributed over the week.( X3o, =9.41 for 4 d.f.) (07 Marks)( Xio, =9.41 for 4 d.f.)

Day Sun Mon Tue Wed Thu Fri Sat TotalNo. of accident t4 16 8 t2 11 9 14 84

8a. n for the following table:

Determine the marginal distribution of x and y and verify that x and y are independentvariables. (06 Marks)

b. Find the fixed probability vector of the following regular stochastic matrix.- lY, Y^ y,1t,lo =l Y, 0 k l. (07 Marks)

[o I o]c. Define the following terms:

i) Regular state ii) Periodic state iii) Recunent state and iv) Transient state. Marks)

t'he bilitv distributicmt

xv 2 J 4

1 0.06 0. 15 0.092 0.t4 0.3s 0.21

USN 06ES42

Fourth Semester B.E. Degree Examination, Decemb er 2Ol2Micro Gontrollers

Time: 3 hrs. Max. Marks:100

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

PART _ A

I a. Give the comparison between microprocessor and microcontroller. (05 Marks)b. With diagram, explain the architecture of 8051. (10 Marks)c. Give the bit and bye addresses of special function registers available in 8051. (05 Marks)

d)oo

a

()

()!

3e(n=

Gle

-oo li

tro€.=N(o+:aots61otr

-.d 0)

*,^

a=

oc)(co

b0c6d

,6F='l,(!-2. ts

oi5

a6.oJ

o=AE!ox.YY.

ooocoo6)=*otr>o

(r<-Noo

Foa

2 a. With example, explain the following 8051 instructions:i) CJNE; ii) DAA; iii) XCHD; iv) PUSH; v) SUBB.

b. A byte is stored in internal RAM location 40h write an ALP to count thepresent in the byte and store the count in external memory location 5000h.

c. Explain bit level logical instructions of 805 1.

Explain jump instructions with reference to range. Give the diagram.

3 a. With example, explain the sequence of events that occur when a subroutine is executed.

high send

(10 Marks)number of 1's

(06 Marks)(04 Marks)

(05 Marks)(06 Marks)

(05 Marks)llh to P1

(05 Marks)(05 Marks)

b.

c.

4a.

Give the sequence of events that occur when a interrupt signal is generated. Also explain therole of bits in IE and IP SFR's in the process of interrupt. (09 Marks)

Write an 8051C program to toggle all bits of Port 0 and Port 2 such that Porl 0 displays thecomplement of Port 2 continuously with a delay of 250 m sec. (05 Marks)

b. Write a 'C' program to send out the value 44h serially one bit at,a time via Pl.0. The MSB

6a.b.

c.

should go out frst.c. Write an 8051 C program to monitor bit P 2.5

otherwise send FFh to P0.d. Give the different data types in 'C' with range.

PART _ B

Explain with diagram, different modes of operation of tiWrite an ALP to generate square wave with ON time of 10on Port P1.0. Assume XTAL of 22MHz. Use time 0 in mode

c. Assume that 60 Hz external clock is applied to To. Write amode 2 to display seconds and minutes on Pl andP2.

Explain RS 232 hand shaking signals.Explain the steps toi) Transfer character bytes seriallyiD Receive the data serially.Explain the methods to increase baud rate of datatransfer in 8051.

1 of2

n. (10 Marks)time of 3 m sec

(05 Marks)

counter 0 in(05 Marks)

(05 Marks)

(10 Marks)(05 Marks)

for

06ES42

Explain with diagram, how the sampling of low level triggred interrupt and edge triggeredinterrupt is done XTAL : 11.0592MH2. (06 Marks)Generate a square wave from all pins of Port 0 having half the frequency of signal applied to

7a.

b.

c.d.

8a.

b.

INTO pin of 8051. Use an ALP.What is the difference between interrupts and polling? Explain.Explain RI and TI interrupts.

(05 Marks)(05 Marks)(04 Marks)

With diagram, explain how to interface 4 x 4 matrix keyboard to 8051. Give the algorithm.(10 Marks)

Give a scheme to interface ADC with 8051. Also write a program to do the conversion.(10 Marks)

***d<r<

^ _f^

USN

Time: 3 hrs.

la.

b.

c.

the overall transformQ2(a)

06ES43

function of the system(10 Marks)

Fourth Semester B.E. Degree Examination, Decemb er 2012Gontrol Systems

b.

q)oo

(.)(!(.)

3e

-y, .6v

-.oo0 I

troo.= a-l

Eilo=so

a2

6=

oO

aoi

26

E6-?oor=

o.Eo.'(.) .i;o@=aLEGELO5.v>,hoo --Eil}

o=goF>Xov!o

L,)<

-61ooz

o

Max. Marks:100Note: 1. Answer FIVEfull questions atleast

TWO questionsfrom eoch part.2. Semi -log sheets may be providedfor Q7(b).

PART _ A

Define 'control system'. Draw the basic block diagram of a control loop giving all therelevant details. (04 Marks)Distinguish briefly between open loop and closed loop systems ; linear and non - linearsystems ; and time -variant and time - invariant systems. (06 Marks)For the mechanical translational system shown in Fig. Ql(c), draw the mechanical network ;

write the mechanical and electrical differential equation and obtain the force - voltageanalogy. (to Marks)

2 a. Using block diagram reduction technique, findrepresented by the block diagram shown in Fig.

Fig. Q2(a)Using Mason's gain formula, obtain 4/x1 for the signal flow graph shown in Fig.

lr,JoJ;.u.,

Fig. Q1(c)

.ss

2t4 4t n (t L7 fuFig. Q2(b)

3a.

b.

06ES43

Draw the typical time domain in response of an underdamped second order system to a unitstep input and define the various time domain performance parameters indicating the sameon the diagram. (10 Marks)Fig. Q3(b) shows a system employing proportional plus error-rate control. Determent thevalue of the error- rate factor k. so that the damping ratio is 0.5. Determine the values ofsettling time kr, maximum overshoot Mp, and steady state error e* for a unit ramp inputwith and without effor - rate control. Comment upon the effect of error - rate control onsystem dynamics. (10 Marks)

frr*tr. bjtA* ?la^*,

4 a. Explain BIBO andZerc - input stability.b. What are the benefits of feedback in a control system?c. Determine the range of values of k (k > 0) such that the characteristic equation

s3 + 31k + 1,1 s2 + (7k + 5) s +(4k + 7) :6has roots more negative than s : - l.

5a.

b.

(04 Marks)(04 Marks)

(12 Marks)

PART _ B

Define 'Root - locus'. Explain how a root - locus helps in stapling the time domainresponse of a control system. (08 Marks)Draw the root - locus fo the system having

G(s)H(s) =s(S+4)(s2 +8s+32)

As k is varied from 0 to co. Show all the steps involved in drawing the root - locus and alsomention all the details on the diagram. Comment on stability of the system. (12 Nlarks)

6 a. Explain the application of Cauchy's theorem (principle of arrangement) used in Nyquist(08 Marks)stability criterion.

b. Construct Nyquist plot for a feedback controlby

system whose loop transfer function is given

G(s)sH(s) =s(l - s)

Comment on the stability of open loop and closed loop system.

Fig. Q3(b)

) nf 2

(12 Marks)

06ES43

7 a. Derive the expression for resonance peak (Mr) for a second order system whose closed looptransfer function is

c(s)_=2

wn(08 Marks)

b.

i) Find the gain margin and phase margin for k : 1

ii) Determine the values of k so that the gain margin is +10 dBs and phase margin is +25'.(12 Marks)

8 a. Draw a comparison between the transfer function method of analysis and-state spacevariables approach. (06 Marks)

b. Write the advantages and disadvantages of state space representation of transfer function

R(s) s2 + 2sw,s + wiA system has the loop transfer function

G(s)H(s)s(l + s)(1 + 0. 1s)(1 + 0.0Is)

using phase variables.c. Obtain the Jordan canonical form of presentation for the transfer function

G(s) =s+3

s3 + 9x2 +24s +20Also draw the corresponding signal flow graph.

(06 Marks)

(08 Marks)

3 of3

USN 06E,C44

Fourth Semester B.E. Degree Examination, Decemb er 2O1.2

Signals and SystemsTime: 3 hrs. Max. Marks:100

Note: l. Answer FIVEfull questions, selectingat least TWO questions from each part.

2. Make vslid assumptions for any missing data.

PART _ AI a. Write the formal definition of a signal and a system. With suitable examples, state the

important differences between:i) Continuous and discrete sinusoid ii) Even and odd symmetry waveforms (10 Marks)

b. Illustrate how the stability of an LTI system can be computed in time domain. (02 Marks)c. The impulse response of an LTI system may be represented by("

hlnt=la n>0.

[u' n<oDetermine the range of values of a and b so that the given system is stable. (08 Marks)

2 a. State and prove the following properties of convolution sum:i) Commutative property ii) Associative property iii) Distributive property (10 Marks)

b. Find the convolution of two infinite duration sequences x[n]: crnu[n], h[n]: F"u[n] wheni) a > 0, ii) o: B, iii) a < B. (lo Marks)

3 a. Determine the total response y[n], n > 0 of a system described by the following differenceequation using time domain method:

ylnl - 3yln - 1l - ay[n - 2] = x[n] + 2x[n - 1]

Assume x[n] : 4'u[n] and zero initial conditions.b. Obtain direct Form - II representation for the following differential equation representation

dooIo-

(.):0)

oX

fn;irEOO

(o+:- OOY6l()trs(.)

a=

oO(00

ooc.8(g

-cd

E(!2aOE

o-Atrooj

o=6E!o

>' (Foootrouo=*otr>:oo-

\J<+C{ooZ

oaE

z$vf tl+ 4*y(t) + 6y(t) = 2x(t) + o$*ttlc. Obtain the difference equation representation for the following realized system

Fig.Q3(c)

(10 Marks)

(05 Marks)

shown in

(06 Marks)

Fig.Q3(c).

-l*

4 a. Evaluate the discrete time Fourier series (DTFS) representation of x[n]- (on n\

and phase spectrum when x[n] = cosl;n .; )

b. Determine the time domain signal x[n] when its discrete time Fourier coefficient specified as

xfKt=.",[ff*)-,-: r'*(ff*) (06 Marks)\

c. Determine the complex exponential Fourier series representation for the followingcontinuous time signal x(t) where x(t) : cos 4t + sin 6t. Plot its spectrum. (08 Marks)

5a.

b.

6a.

06r,c44

PART _ BFind the discrete time Fourier transformation of the time domain sequence x[n] : unu[n] andplot the magnitude and phase spectrum for the values of cr (i) crt : 0.5, (ii) cr : 0.9. 1os Marks)The DTFT of a time domain sequence is defined as

X(ejo,,=l' lol<wL0 W<lOl<n

c.

Find its IDTFT and plot x[n]. (06 Marks)

For a moving average spectrum is described by y[n] = ] ktrt + x[n - t1]. ninO its frequency

response H(d") and plot amplitude and spectrum. (06 Marks)

The input to a discrete time system is given by x[n]= *r(*, ).,r(*r).

,* the DTFT to

find the output of the system y[n], if the impulse response is given by

i) h[n] - snV*n)iln

' 'tn)ii) h[n] = (-l)"'(27[n

(10 Marks)

b. Consider the continuous time domain analog signal given by x(t) : 3 cos 100nt.i) Determine the minimum sampling rate required to avoid aliasing.ii) Suppose the signal is sampled at F, : 200 Hz, find the corresponding discrete time

sequence.iii) Suppose the signal is sampled at F, : 75 Hz, find the corresponding discrete time

sequence

iv) What is the frequency 0 < F. ! of a sinusoid that yields samples identical to those2

obtained in part (iii)? (10 Marks)

7 a. Define z-transformation and its inverse. State the important condition for the existence of thez transformation using ROC. (05 Marks)Explain how the ROC in the z domain can change if the corresponding time domainsequences can be left sided, right sided and two sided, while the length can be of finite orinfinite duration. (05 Marks)

Givethat *trl={u^ for o<n<N-1

tuotherwiseLeta:0'5'N:8'Findz{x[nl]using:i) Direct evaluation of finite sum of X [z], ii) Sample shifting property of X [z].Plot its poles and zeros, ROC, and comment on stability. (10 Marks)

8 a. A causal LTI system is characterized by having input sequence x[n] = (- +)'u [n] and

output sequence ylnl=3(-l)'rtr,.(+)'u[n]. Determine its transfer tunqtion impulse

response and difference equation representation. (10 Marks)b. Solve the following difference equation using unilateralz transforms and find time domain

solution:

i) y[n + 2]-3y[n + 1] + 2y[n] = 4'ulnl for y[0] : 0, y[1] : Lii) V[n]+ y[n - 2] = 6[n] zero initial conditions.

b.

*{<{<{.*

(10 Marks)

oo(J!s

(d

(),-a,)r

3e

696bo ll

coo.= a.l

o :i{oiFO

o;Es

6=

o(Jcoo

botr

>P6-

-4 .)

6 .!J

o5-o"oi?.Y6:'a lE

LO=+ .=:i ,.

b0oibo'nE6:.=*otr>=o5"o<-i 6i

0)

z

o

doo(d!a

Cd

()

C)!

Eg

6v

oo'-€.=N(i<f,NboEq)oi-E !l

USN 06EC45

Fourth Semester B.E. Degree Examination, January 2Ol3Fundamentals of HDL

Time: 3 hrs. Max. Marks:100

Note: Answer FIVEfull questions, selectingat least TWO questions from each part.

PART _ A

I a. Explain how data types are classified in HDL. Mention the advantages of VHDL data types

2 a. Explain signal declaration and signal assignment statements with relavant examples.(06 Marks)

b. Write a dataflow description (in both VHDL andenable.

verilog) for a full-adder with active high

over verilog.b. Explain composite and access data types with an example for each.c. Discuss the logical operators in VHDL.

c. Write HDL codes for 2 x 2 bit combinational array multiplier.

(06 Marks)(08 Marks)(06 Marks)

(08 Marks)

(06 Marks)

(08 Marks)

(06 Marks)number using

(08 Marks)(06 Marks)

4a.b.

a. Write behavioral description of a half-adder in VHDL and verilog with propagation delay of5 nsec. Discuss the important features of their description in VHDL and verilog. (0s Marks)

b. Explain the execution of process statement. (02 Marks)c. Write VHDL code for a D latch using variable assignment statement and signal assignment

statements. With simulation waveforms clearly distinguish between the two statements.(10 Marks)

What is binding? Discuss the binding between library and components.Write the HDL description of 2:l mutliplexer with active low enable in VHDl/verilog usingstructural style. (12 Marks)

PART _ B

5 a. Explain the following syntax with examples:i) Procedurei0 Taskiii) Function.

b. Write VHDl/verilog code to convert a fractional binary to realprocedures/tasks.

c. Describe all file processing tasks in verilog.

I of2

6a.b.

What is the necessity of mixed type description?Describe the development of HDL code for an ALU andALU shown below.

06EC45

(04 Marks)write VHDl/verilog code for an

C\ vr

O P ERAl lOII

Ogc'z

Fig.Q.6(b)

Assume the following operations: Addition, multiplication, division, no operation. (16 Marks)

a. How to invoke a verilog module from VHDL module? Explain with an example of a mixed

b

language description for a full adder using two half adders.b. Write a mixed language description of a 4-bit adder with zero flag.

a. What is synthesis? List the general steps involved in synthesis.b. Give synthesis infbrmation extracted, when the input and output are defined as:

i) bit; ii) std-logic-vector.

(10 Marks)(10 Marks)

(08 Marks)

(04 Marks)

c. Write a behaviroural code in VHDL and verilog for the signal assignment statement B : A.Explain the mapping to gate level logic diagram. (08 Marks)

Rta \-tt{ f ET\c LC cn( c

u rrr r.'r C a ur))

2 of2

USN

Fourth Semester B.E. DegreeLinear lG's and

Time: 3 hrs.

b.

c.

Examination, January 2Ol3Applications

068C46

Max. Marks:100

(08 Marks)

Show how it(08 lVlarks)(06 Marks)

d)oo

a

OJ

0)

8e

l>dU

-.oo0 I

t,6.= c-'I

o Y:J

osIeO-!

*,-

oO

o!50cc6(B

r'6

OE

q;

o.l;oa=aLE

!o

oo-coo0J=uotr>^-o5L

L.)<

-N(]o

(o

o.

Note: Answer FIVEfull questions, selectingat least TWO questions from each part.

PART _ Aa. Sketch an illustration to show the effect of op-amp slew rate and explain. State a typical op-

amp slew rate. (05 Marks)b. An op-amp inverting amplifier has a 0.5 volts input signal and its output is to be 9 volts. If

feed back resistor Rr: 12 Kf), calculate a suitable resistance value for Rt. (05 Marks)c. Explain why the resistances at the two input terminals of an op-amp should be

approximately equal in value. (04 Marks)d. A non-inverting amplifier is to amplify a 100 mV signal to a level of 3 volts, using a74l

op-amp, design a suitable circuit. Assume bias current as 500 nA (max). (06 Marks)

a. How to set the upper cut-off frequency in an inverting amplifier circuit? Explain. (06 Marks)b. Discuss the significance of using single polarity supply in an op-amp circuits. (06 Marks)c. A capacitor-coupled voltage follower is to be designed to have a lower cut-off fiequency of

120 Hz. The load resistance is 8.2 KO and the op-amp used has a maximum input biascurrent of 600 nA. Design a suitable circuit.

3 a. Sketch the circuit of a lead compensation network.affect s operatio nal amplifi er frequency re spo nse.Write a note onZinmod compensation.

c. Using 741 op-amp with a t 9V supplyfrequency of 10 kHz.

A74l op-amp with a slew rate of 0.5 V/p sec is used as

i) Calculate the slew rate limited cut-off frequency if is 5 volts.ii) If this circuit is to operate with a unity gain cut-off freq kHz, calculate the

maximum peak value of the sinusoidal output voltage.iii) If the upper cut-off frequency is 8 kHz, calculate the maximum value of the peak

output voltage. (06 Marks)

a. Draw the circuit of a precision voltage source using an op-amp and a zener diode. Explainthe circuit operation and derive the equation relating to Vo and V,. (08 Marks)

b. Show the realization of current to voltage converter using an op-amp. (04 Marks)c. Design an instrumentation amplifier to have an overall voltage gain of 900. The input signal

amplitude is 20 mV; 741 op-anrys are to be used and the supply is + 15V. (08 Marks)

PART _ Ba. Show the realization of logarithmic amplifier using an op-amp. Obtain the expression for the

output voltage. (08 Marks)b. Sketch the circuit of a voltage follower tlpe peak detector. Explain the circuit operation.

(06 Marks)design a phase shift oscillator to have an output

(06 Marks)

1 of2

,rY:r '

oeq;F:i$

c.

la.

06E,C46

6 a. Draw the circuits to show how diodes may be used to select the trigger points of an invertingSchmitt trigger circuit. Explain. (06 Marks)

b. Sketch the circuit of a capacitor coupled zero-crossing detector. Show the waveforms atvarious points in the circuit and explain its operation. (08 Marks)Design a second order low pass filter to have a cut-off frequency of 1.5 kHz, using741 op-amp. (06 Marks)

Define and explain the terms as applied to voltage regulator:i) Line regulationii) Load regulationiii) Ripple rejection.What is the principle of switch mode power supplies?disadvantages.

c. Explain the operation of switching regulatbr using op-amp.

With a neat block schematic, explain the operation of each component in PLL. (08 Marks)Write explanatory note on :

i) 555 timer as monostable multivibratorii) A./D converters.

c. A PLL has free running frequency of 500 kHz and bandwidth of the low pass filter is10 kHz. Will the loop acquire lock for an input signal of 600 kHz? Justifr your answer.Assume that the phase detector produces sum and difference ilequency components.

(02 Marks)

,6{<**{<

8a.b.

(06 Marks)Discuss the advantages and

(08 Marks)(06 Marks)

(10 Marks)

2 of2