1.
t+ 1t € LUSN
Time: 3 hrs.
Fourth Semester B.E. Degree Examination, June/July 2013
Engineering Mathematics  lV
1OMAT41
b.
c.
g
E
go
a !.)
5c!=
o;
AE
5 .:
r.) <
l 6i
z
ts
o
PARTA
I a. Use modified Euler's method to solre !I = x + y, y(0) = 1
2a.
b.
3a.
taking h  0.1.
solve !I
dx
=x+y,x=0, y = I at x:0.2 using RungeKutta method. Take h = 0.2.
Note: 1. Answer FIVE full questions, selecting
at 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 predictorcorrector method find y10.3) correct to three decimals given,
(07 Marks)
x 0.1 0 0.t 0.2
v 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)
dx
Using RungeKutta method solve y" : x(y')2 y2 at x: 0.2 with x0  0, yo = l, zo = 0 take
h: 0.2. (t0 Marks)
lf f(z) = u + iv is analyic prove that CauchyReimann 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 wplane.
State and prove Cauchy's integral formula.
Ifw:23 find dildz.
If the potential function is 0 = log . Find the stream function.
PARTB
Prove that J''' = [ .;r*.rr Ynx
State 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
2.
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 defective
items are 3, 4, 5 respectively. Ifthe item selected is defective what is the probability that it is
from 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 times
ii) At least once
ii) 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 that
shower 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's
tdistribution 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:
Roundr,ellow Wrinkled yellow Round green Wrinkled green Total
315 101 108 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 6
p(x) k 3k 5k 7k 9k 11k 13k
2 of2
3.
+
L E C.USN O6MAT41
Max. Marks:100
Note: 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  IV
Time: 3 hrs.
E
E
=d
.E.r
g;i
b!
a,i
cllo
5E
J<
z
E
PART _ A
I 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 and
dx
compare the numerical solution obtained atx 0.2 with the exact solution y : 31s2' e.).
(06 Marks)
b. Using Fourlh order RungeKutta method to solve (x+y)9=1, y(0.4) : 1 at x  0.5, dx
coffect 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)dx
corrected to 4 decimal places by using Milne's predictor and corrector formula (use
colaector formula twice).
2 a. Detine an andTtic function and obtain CauchyRdmann 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 function
and determine the conesponding analytic function. (0? Marks)
c. Find the bilinear transformation that maps the points 1, i, 1 respectively onto the points
i, 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 < z11< 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 (z1llz21
(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' dx
b. Obtain the series solution ofLegendre's differential equation.
(r x') 1 I 2x!r+n(n l)y =o' 'dx' dx
leading to Legendre's polynomial.
c. Prove the following:
[:[:*' .l ) fils 3x' I
J,,(x)=./i , Srlx  cosxf . J_.,(r)=,i  islnx , cosxl (07 Marks) lrxtx x I  /rxlx x ]
I of 2
(07 Marks)
(07 Marks)
(07 Marks)
4.
x 0 I 2 3 4
v 1 1.8 1.3 2.5 6.3
O6MAT41
PART  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 following
data: (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 with
mean: 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 and
toor(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 the
following 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.
v
x
1 3 6
,
1/
/9
t//6
1/
/t8
3 t//6
t//4
t/,/12
6 1/
/18 X, %u
5.
I]SN 10ES42
program should store accordingly OOH/FFH from
(10 Marks)
voltage connected to
(10 Marks)
+4 steps and
(10 Marks)
E
t9
*
3e
ao
!'
(,j
d.9
L)<
E
Fourth Semester B.E. Degree Examination, June/July 2013
Microcontrollers
Time: 3 hrs. Max. Marks:100
Note' Answer FIVE full questions, selecting
ol leqst Tl;ltO questions from each part.
PAR'I' A
I 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 07H
to OBH and the value ofregister SP, after executing the following code:
PUSH OAH
MOV 81H, #OBH
POP 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 following
program:
MOV R2. #04
MOV Rl. #06
WAIT: DJNZ R2, WAIT. (05 Marks)
c. Write 8051 ALP which checks whether the ten numbers stored from external RAM memory
address, 2000H are odd/even. The
internal location 30H onwards.
4 a. Interface ADC0809 to 8051 and write an ALP to convert the analog
second channel. Display the digital value on LEDs connected to port0.
b. Interface 8051 to a stepper motor and write an ALP to rotate the motor frst
then 6 steps.
b. Explain briefly the interrupts of8051, indicate their vector addresses.
PARTB
5 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, using
timerl. Assume XTAL frequency as 11.0592 MHz. What is the minimum frequency that
(10 Marks)can be generated?
1 of 2
6.
6a.
b.
10ES42
Explain the functions of the pirs of 9pin RS232 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 rrloded'bperur#
*o'uO
,:
(06 Marks)
is the content ofIf the'
register A
8a.
b.
r
2 of2
7.
USN 06ES42
Fourth Semester B.E. Degree Examination, June/July 2013
Micro Gontrollers
Time: 3 hrs. Max. Marks:100
Note: 1. Answer FIVE full questions, selecting
atleost TLI/O questions from eoch part
2. Missing dota, if ony, may be suitable assumecl.
PART_A
a. Explain with neat diagram, Harvard architecture and VonNeumann 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 22MHz
ii) 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 a
program to nealise rhe logic expression
E
o
E
E
39
^l
.EA
Y!.)
ts
!a
'E
^
o.;
(r;
:9
^:
E=
o. i:
e<
: 6i
a
z
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 internal
RAM location and store the result in external RAM location starting from 8000H. Assume
that fust sixteen bit number is present in intemal RAM starting from address 10H and
second 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 different
instructions.
(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 RAM
org 0000H
MOV A, 25H
ADD A,26H
DAA
xcHD A, @RO
Here : 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 using
8051C. 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. The
serial transmission should start liom LSB. (06 Marks)
1 of 2
Address Content
8.
068S42
PART  B
a. With a diagram, explain the start and stop of the timer 0 through pin P 3.2 when GATE bit
in 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 transmission
with 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 polling
disadvantages intemrpts.
b. Explain how extemal interrupts can be activated as level triggered and edge triggered in
8051 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 to
P 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 8051C
program 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
9.
USN 10ES43
Max. Marks:100
(06 Marks)
(05 Marks)
. (08 Marks)
Time: 3 hrs.
Fourth Semester B.E. Degree Examination, June/July 2013
Gontro! Systems
Note: Answer FIVE full questions, selecting
at least TWO questions from each part
o
EP
^t
.E c
ii 90
;i:
Jor
o. 6
iE
5.Y
o h'j
(, <
;
z
og
PART. A
I 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 mathematical
model and electrical analogue based on forcecurrent 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 _ T
LiEl
given in Fig.Q.2(c) obtain over all transfer function using Mason's
3a.
b.
10.
10ES43
The open loop transfer function ofa servo system with unity feedback is given by
Gtrl =
lo
s(0.ls + l)
Find out static error constanls and obtain steady state error when subjected to an i/p of
A.
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 equation
56 + 2S5 + 8S4 , l2sr  2oS'?+ 165  16 = 0.
PART  B
A 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 peak
iD Resonant frequency
iii) 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)
Io
l)
(05 Marks)
ll
"  (07 Marks)
rl
s(s2 +5s+9)'
11.
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
PARTA
tEl
.!
E
3q
.SN
E.9
;::
'€b
E!
ir
oi;
iE
X.:
E=
e<
...i t'i
z
E
q
E
Note: 1. Answer FIVE full questions, selecting
atleost 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 electrical
network. (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 under
damped 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 k
for stability. (10 Marks)
The open loop transfer function ofa UFB control system is given by
50
(i(c) =

s( I + 0.05s X I  0.2s )
Apply R H criteria. Show that the system is unstable confirm that the introduction oftho
two terminal pair network connected in cascade with G(s) makes the system stable.
Cr :0.5pF ; C:: 10 pF ;R1  I Mf)
(,t
rrl'1
r*{ry'= T€.t
IFig. Qa@)
I of2
(10 Marks)
12.
5a.
'b.
ta
6a.
b.
O6ES/EC/TE/E E/ML/8M43
PART_B
As applied to root locus, explain how to
i) Determine angle of departure or anival from a complex pole or zero
ii) Determine the break away or beak in points ifthey are present
iii) 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 by
F(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 damped
ii) Tow values of k for which the damping ratio is 0.95
iii) Write closed loop transfer functions for the values of k found in part(ii).  (12 Marks)
(08 Marks)
(12 Marks)
iii) Gain cross over frequency
iv) Phase crossover frequency
v) Corner frequency.
b.
v, rorlrcr [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 value of k for a gain margin of 20 dB and the value of k
margin 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
D
ii)
matrix
analvsis.
state model of the
of state variables.
Fie. Q8(b)
c. Construct a state model for a given system characterized by the differential equation :
drv 6d2v I ldv
ol
ff.?+6y +u =0
2 of2
Draw the state diagram. (06 Marks)
13.
t0EC44USN
Fourth Semester B.E. Degree Examination, June/July 2013
Signals and Systems
Time: 3 hrs. Max. Marks:100
..,,. N otel. Answer FIVE full questions, selecting
. ; at least TWO questions from each part
:^:_
'
PARTA
: 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 L
I r_a8=8= i,
/"', > ,/
=:
*; ' E
'.o I I t
I
:Ei i rL
E; Fig. Qr (b
E :* Fie.Q.l (bl
€ E c. Civen the signal x(n)  (6  n){u(n)  u(n6)} 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(ra)r a> 0 ii) y(t)rlu() u(ta)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(n4). The
$E system is excited by the input signal x(n) = u(n)  2uln21+ u(n4). 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(t2), 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(nl   4y(n2)  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(nl)y(n3)=3x(nl)+2x(n2)c orl
E g ... d'y(t) dv(t) dx(t)
3 E. rD #+5...:::.+4y(t) = i: (l0Nlarks)
:; dt' dt dr
a ? 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)
g
o
Z 4 a. Determine the DTFS coefficienls of.
i fl 3nl
E
x1n)= t +sin{;^".;} (06 Marks)
I of 2
14.
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.
..:.
PARTB
5 a. Find 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 spectrum
for 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 the
differential 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* 12
r) x(t)=l+coszuuuTlt+sul4uuurfti ,, "(t)=L] (06Marks)
c. Explain briefly, the reconstructionpf,continlous time signals with zero order hold.
7 a. Find the ztransform 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,2iiansform of the following:
. zo +z' 1
r) x(z) = .,:lzl >bv
) r l' 2",.24
 z+
,:..'. 4 8
. ryrtiat fraction expansion method.
azt 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 > 0
12' ' 12' '
With initial conditions y(1) = 2, y(2) = 4 and x(n) :
2 of2
(i) u(n). (10 Marks)
15.
FRNh] : FHX $1. : 18 HFn. iA1: 11:34PI'l Fl
USN
tl
Fourth Srmr:ster B,E. .Degree Exnmination, Junc/July 2013
Sigrtals aild Syst6m$
Time: 3 hrs.
Nute: ,4ri*wer F/YE fal! questlons, sdeuing
arl TWO qaesllotts lrohr each part.
PART _ A
I a, Distingulsh between :
i) Even afld odd signals
ii) Periodic and ronpcriodic signals
lli) Ilnerry :md power signals.
b. Siketch the foilowing signals
x(n) = 6(rD
x(u)=2u(n)
x(t)  (t  l) u(t)
x(t) = 2u(t l)  2u(t3)'
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
re
b
H
*s:l
.E .
EE
Ae
aE
EU
Eh
iag
6?
il d
'Ee
e&
FtsUJ
e,z
tso
HE
(J'l
'j r.i
a
3..
b.
c,
d.
4a.
b.
i) Linear ii) Tinre  invariant iii) Causal iv) Mernrrry 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( n2)
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 cach of fi9 impuls6 v65penss listed bslow, determine whcth€r the corresponding sysrcm
i.s I Causal ii) Mcmory L:sr iii) Stable. i) h(l)  er r'l ii) h(t)  e,ltb(t  l).
' (06 Morkl
Evalurte the forced response 0fthe systom
y'(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 series
i) 'l ime shift
ii) 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)
16.
PART  B
5 a. litflte and provc ths following propertics ofDTFl'
i) Irequency shift
ii) ltequcncy differentiarion,
b. Find the FT ofthe fr: llorving signals
i) x(t) = 6111
ii) r(t) : c'" u(t) ; a > 0.
c, Fidd the invers{, FT ol
iw+lXl 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) Linoority
ji) Differentiatio furzdomain,propertiesofz*transfurur. (06NIsrkF)
b, l)dtermiflc the z  tlansiirrmation ol
x(n) = it, 2,
t)
x(n)  (z) u(ru
x(n)6(n+2)
x(n)  (3)" u( n  l). (08 Morks)
c. Find out ihr invcrse z  beirstbrm of
1
x(z) =. RoC : lz l>  4 l,
l 4zt '
Using powcr scries expsnsion. {06 Nlarks)
8 a, Fhrd the rnilfltcrdl z  trsr1sfofm ol
x(tt={1,2.3,4
I
y(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'2
H(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{ output
iflthe input is x(n) : u(n) aud the initial coudition ou dre c,utput is y(l) = 2. tOB M6rks)
tolt
17.
c. With syntax, explain the sequential stdenents in HDL:
a.
b.
c.
€1
;i. ',
:: 3
3c
=.9
ai'i^
OJE
>'9 6
o. E
() <
;
o
7A
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, selecting
dt least TWO questions from each port
a.
b.
c.
a.
b.
a.
b.
PART_A
Describe 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 ELSEIF 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  B
a. 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 flipflop by invoking VHDL entity
liom 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, ifelse, case statement in HDL. Show the synthesized
logic symbol and gate level diagram. (08 Marks)
a.
b.
a.
b.
a.
b.
18.
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
)J.
iE
tson
e{
2
mTTill tr
Time; 3 hrs.
Fourth Sernester B.E, Dcgrcc Examinstion, June/.Iulv 2OlI
Fundamentals of llDL
Notcr .,lzsh,sr rifW full queslktns, selecting
least TWo questiotts froht eddt l,arl,
I a. flxprain the behavioral, struclurar ur#,r*.r".iprior1 tvpes irr Hr)L pmgrlrnming with
examP 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 simulalion
wavefornl' (oE Dlart(i)
b. wriLe HDL cotie for 2 x 2 unsigned combinstional array multiplier, Show its gate ievei
diagrarn antJ sinlulatiol wavefom. (I2 Mtrrks)
] a Write VHDI. oode fbr 3 hil binarv cotmter with active high synchronous clear il behirvioral
dcscription show excit tior rable and sirnulation wavcforri.
b, u'?it.; vHLrL onrl u.riJug ond* tirr caloulating ae taciorioluring behirvioral ,t.r".i;lir}*,'i
while  k:rp. {Io l{{r.fts}
4 a, Explain bindilrg bctwccfli
i) 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 tristate 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 rrrrks)
b. lVritc HDL oode for a Masrcr Slave D f)iprlop in rnixed tanguag" a"iscripri;; iffi,sir:rulation wtvefbrm. Go Msrkr)
I a. Write tlorv chad of F"vnth€sis srcpr flnd cxplain.
h Writc HOL;ode for signal assignment statetnenr ), =: *
synrbol and gote level ,.jj6gpfl11
x3.
(10 M*rkrj
19.
IJSN 10EC46
(08 Marks)
how it is done
(06 Marks)
(12 Marks)
(08 Marks)
Fourth Semester B.E. Degree Examination, June/July 2013
Linear lG's and Applications
Time: 3 hrs. Max. Marks:100
Note: 1. Answer FIVE full questions, selecting
at 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 for
741 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 the
design steps. (04 Marks)
Two signals each ranging from O.lV to lV are to be summed. Using 741 opamp design a
suitable inverting summing circuit. (04 Marks)
Draw a neat circuit diagram and give design steps for a
follower; ii) Capacitor coupled inverting amplifier.
i) capacitor couplsd voltage
la.
b.
E
*=
ooll
.E&
EY
.s.s
'C 
6E
3oo
6=
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 = lOKQ
and 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 the
working of a phase lag compensation network. (08 Marks)
Define: i) Slew rate effect; iD UGB. Determine the maximum distortion free output
amplitude for a voltage follower when 741 opamp is used with A:800 kHz and
S = 0.5 V/p.S. (06 Marks)
What are the advantages ofprecision rectifier over ordinary rectifier? Explain the working
of a precision halfuare rectifier. (06 Marks)
Draw the circuit of an instrumentation amplifier using opamp, explain the working and
derive the expression for output. (10 Marks)
Draw the circuit and explain the working of an opamp limiter to have voltage levels
V2 + 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? Explain
in an inverting opamp.
PARTB
Write a brief note on following opamp applications:
i) Negative clamper using opamp.
ii) Logamplifiers using opamp. r .
Explain the working of Weinbridge oscillator using opamp. l
1 of 2
20.
10EC46
a. Explain how opamp can be used as inverting and noninverting comparator. What are the
limitations? 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 the
working. (08 Marks)
b. Explain the working of D to A converter using R2R network. (06 Marks)
c. Explain the working of A to D converter using successive approximation method. (06 Marks)
2 of 2
21.
USN
068C46
Max. Marks:100
(08 Marks)
(06 Marks)
Fourth Semester B.E. Degree Examination, June/July 2013
Linear IG and Applications
Time: 3 hrs.
Note: 1. Answer FIVE full questions, selecting
al least TWO questions from each part.
2 Assume suilable values/data.
PART_A
Define the following terms with respect to operational amplifier:
i,) CMRR
ii) PSRR
iit) Slew rate
iv ) O/P impedance.
With a neat circuit diagram, expiain basic operational amplifier circuit.
o
E
09.
.EN
u
o' i':'
Fd
5.3
9JE
: !l
>':
E>
U<
;
o
E
E
1a.
b.
An opamp has R1 : R2 : 22KA wftI a resistor tolerance of x20o/o. Determine input offset
voltage due to i) the 741 specified, i/p offset voltage; ii) 741 ilp offset current; iii) the
resistor 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 load
resistor is 2.2.K, lower cutoff frequency 120H2. Make necessary modifications to give
heighest 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 opamp
if 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 fuIlwave
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
22.
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
AC '(07 Marks)
 lt. &.
S a. Effi$:qlhe functional diagram of 1C555 timer with neat sketch. ..
 (10 Marks)
U. exphqt{Cqarly PLL wittiblock diagram. also define: lock in rangrd&pture range, full in
time wiitr(Dpect to capture transient. n ' (10 Marks)'" "'"' F, r1'*''/&, ,' kr'ry
,Q'' .a 
vt *:*:+** 't
'rn rU*,t )
'r$. (]^.7), t" "
"d .,a.
n' ,
"{^l'Hr
C}L'/,V *
xv U
At
, rL,r
,< '#}
$t L'(.,
,^Y
r.f"' u
./
! ) ,rl)
..rh" t': ,("' ,/ !
A {,/
..o) ' f r
 (:' r ')'LVr )
/+' /'"
r+' ;
i,* &'.
t ' <,
^' Kn' ,
*f"' '/,
"
{h 1v.4
'tf
2 of2
Be the first to comment