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GATE EC – 1993 Electronics and Communication Engineering Question Paper

SECTION – A
1.  This questions 1.1 to 1.7 below one or more the alternatives are correct.
W rite  the  code  letter(s),  (A,B,  C  and  D)  corresponding  to  the  correct
alternatives in the answer book. Marks will be given only if all the correct
alternatives have been selected and no incorrect alternative is picked up.

1.2  The differential equation,   + + =  sin 0,  is:
(a)  linear  (b)  non-linear  (c)  homogeneous  (d) of degree two

1.3  Simpson‘s  rule  for  integration  gives  exact  result  when  f x is  a  polynomial  of degree
(a)  1  (b)  2  (c)  3  (d) 4

1.4  Which of the following is (are) valid FORTRAN 77 statement(s)?
(a)  DO 131 = 1  (b)  A = DIM***7  (c)  READ = 15.0  (d) GOTO 3 = 10

1.5  Fourier series of the periodic function (period 2 ) defined by   p

1.6  Which of the following improper integrals is (are) convergent?

1.7  The function  f x y x y xy y x , 3 2 , = – + +  has   2

(a)  no local extremum
(b)  one local minimum but no local maximum
(c)  one local maximum but no local minimum
(d)  one local minimum but one local maximum

2.  In questions 2.1 to 2.10 below, each blank (_________) is to be suitably
filled  in. in the answer  book  write  the  question  number  and  the  answer
only. Do not copy the question. Also no explanations for the answers are
to be given.

2.2  The radius of convergence of the power series   is _________

2.3  If the linear velocity   is given by  V x yi xyzj yzk = + -               the  angular velocity  at V  the point (1, 1, -1) is _________.

2.4  Given  the  differential  equation,  y x y = -  with  the  initial  condtion  y 0 0.  =    the value  of  y calculated  numerically  up  to  the  third  place  of  decimal  by  the  0.1 second order Runge-Kutta method with step size h = 0.1 is _________

2.5  For X = 4.0, the value of I in the FORTRAN 77 statement
3       I X X = – + + 2 **2 5.0 * *3 4         is _________

2.6  The value of the double integral is _________

and  S the surface of a unit cube with  one
2.8  Given,    ä V x y i x e j z y k = + + cos sin 2 2 2          x
corner  at  the  origin  and edges  parallel to  the  coordinate  axes, the value of  the  —— integral     V ndS .  is _________

2.9  The  differential  equation  0 y y + =    is  subjected  to  the  boundary  conditions
( ) ( )       y y 0 0 0 + =         .  In  order  that  the  equation  has  non-trivial  solution  (s),  the  general value of  is _________

2.10  The  Laplace  transform of the periodic function  f t described by the curve below i.e.

SECTION B: PHYSICS
3.  In  the  following  questions  3.1  to  3.17  there  ar e  some  multiple  choice questions  and  some  questions  where  blanks are  to  be  filled  in.  Answer ALL  the  questions.  All  multiple  choice  questions  have  ONE  or  MORE correct  answers  those  suggested.  Credit  will  be  given  only  if  every correct  alternative(s),  and  no  incorrect  alternative,  is  selected.  Write only  the  letters  corresponding  to  the  select  alternatives  in  the  answer book. In the fill in the blank type questions, write the answer only in the answer book.

Useful data:  h J m s = × = × 6.63 10 3 10

3.1.  Two  particles  of  masses  M M  and  M M >  attract  each  other  with  a  force inversely proportional  to the square  of  the distance between them. The  particles are  initially at rest and then released. The centre of mass relative to a stationary observer
(a)  moves towards  M     (b)  moves towards

(c)  remains at rest

(d)  moves with a speed proportional to

3.2.  The  temperature  of  an  ideal  gas is  held  constant  while  its  volume  is increased.
The pressure exerted by the gas on the walls of the container decreases because its molecules
(a)  strike the walls with smaller force
(b)  strike the walls with lower velocities
(c)  strike the walls less frequently
(d)  collide with each other more frequently

3.3.  Although  a  laser  beam  is  highly  directional,  its  beam  width  increase  with propagation. This increase is due to
(a)  coherence  (b)  diffraction   (c)  polarization   (d) interference

3.4.  A plane electromagnetic wave of the form

Where  E   is a  constant  and y  is  the unit  vector  along  y-direction)  represents  a wave propagating along
(a)  + x direction  (b)  + y direction   (c)  – x direction   (d) – y direction

3.5.  While  you  are listening  to a  programme  from  a  radio,  if a  near by  electric  light bulb is  switched on or  switched  off, you hear  a momentary  noise  in  your  radio.
This is due to electromagnetic radiation emitted by _____.

3.6.  Nuclear fusion reactions required very high temperatures so as to overcome
(a)  nuclear forces      (b)  van der waals forces
(c)  coulomb forces      (d)  gravitational forces

3.7.  In radioactive decay, the disintegration rate of the nuclei is:
(a)  constant at all times
(b)  inversely proportional to half-life of the nuclei
(c)  inversely proportional to the number of nuclei at any time
(d)  directly proportional to the number of nuclei at any time

3.8.  In  an hydrogen atom  10.2 eV  is  given  out  as  radiation  when an electron  is de-excited to the ground state. The principal quantum number of the excited state is
___________.

3.9  Typical current voltage characteristic of a solar cell is given in the following figure by
(a)  curve A  (b)  curve B  (c)  curve C  (d) curve D

3.10.  Consider  a  solid  sphere  and  a  hollow  sphere,  both  of  mass  M,  radius  R  and initially at rest, which start rolling down the same inclined plane without slipping.
At the bottom of the inclined plane, the ratio of speeds  / V V is:
(a)  1  (b)  12
7   (c)  10              7   (d)  25         21
[Note: The moment of inertia about any diameter for a solid sphere is (2/5) MR ,  2/2 and for a hollow sphere (2/3) MR ].

3.11.  An  optical  fibre  consists  of  a  cylindrical  dielectric  rod  of  refractive  index  n ,  1 surrounded  by  another  dielectric  of  refractive  index  n ,  where  n n <  ,  as  shown in the following figure. If a  ray is incident from air at an angle i to the axis,  then it undergoes total internal reflection at the interface AB if

3.12.  For  a  uniformly  charged  sphere  of  radius  R  and  charge  density  p,  the  ratio  of R  and 2R from the centre, i.e.,  magnitude of electric fields at distance

3.13.  A  long  solenoid  of  radius  R,  and  having  N  turns  per  unit  length  carries  a  time dependent current  I t I t =  cos .   The magnitude of  induced electric field at a R readily from the axis of the solenoid is distance

3.14.  In  an  electron  diffraction  experiment,  planes  of  a  crystal  with  spacing  1A° between  them  yield  the  first  maximum  at  a  Bragg  angle  of     =30°.  The momentum of the electrons is _____ J-s/m.

3.15.  A conventional unit cell of close packed face centered cubic (FCC) structure made up of hard  spheres has  a cube edge of  a A°.  The  radius of the  sphere  is _____ A°.

3.16.  A  light  beam  of  frequency  1.2 10 ×  Hz  is  incident  on  a  metal  in  a photoelectric effect  experiment.  The  corresponding  maximum  kinetic  energy  of  the  ejected photoelectrons  from  the  metal  is  6.63 10 . × J    The  characteristic  cut-off  frequency of the metal is _______ Hz.

3.17.  Consider the semiconductors A and B. the figure shows variation of In p with I/T, where p is resistivity and T the temperature, for the two semiconductors. Choose the correct statements(s).
(a)  the bandgap energy of A is larger than that of B.
(b)  the bandgap energy of A is smaller than that of B.
(c)  the  maximum  wavelength  of light needed  to  create  an  electron  hole  pair  is larger in A than in B
(d)  the  maximum  wavelength  of light needed  to  create  an  electron  hole  pair  is smaller in A than in B

SECTION F

4.  The questions 4.1 to 4.9  below  are  multiple choice  questions  carrying  1 mark  each.  There  could  one  or  two  or  more  choices  for  the  answer.
Indicate  your  choice  by  writing  the  appropriate  capital  letter/letters
against  each  question  number.  No  credit  will  be  given  for  writing  only
one choice  in  cases  where more  than  one correct  answers are possible.
Answer the questions 4.1 to 4.9 on one page, in the same order  in which
they appear.

4.1.  A dc circuit shown in figure has a voltage source V, a current source I and several resistors.  A  particular  resistor  R  dissipates  a power  of 4  Watts  when  V  alone  is active. The same resistor R dissipates a power of 9 Watts when I alone is active.
The power dissipated by R when both sources are active will be
(a)  1 W
(c)  13 W
(d)  25 W

4.2.  In  the  series  circuit  shown  in  figure  for  series  resonance,  the  value  of  the coupling coefficient K will be

(a)  0.25
(b)  0.5
(c)  0.999
(d)  1.0

4.3.  If  the  secondary  winding  of  the  ideal  transformer  shown  in  the  circuit  of  the figure  has  40  turns,  the  number  of  turns  in  the  primary  winding  for  maximum power transfer to the 2° resistor will be
(a)  20  (b)  40  (c)  80    (d) 160

4.4.  While starting a dc shunt motor:
(a)  reduced armature  voltage  V  and  reduced  field voltage  V  should  be applied  and full regulator resistance  R  should be included in the field circuit.

(b)  reduced  V but full  V  should be applied and  R  should be zero.

(c)  rated  V but rated  V  should be applied and  R  should be zero.

(d)  rated  V and rated  V  should be applied and  R  should be maximum.

4.5.  A 6 pole 3 phase wound rotor induction machine is driven by another machine at 180  rpm.  The  rotor  of t he induction  machine is  connected to  a 50 Hz system. If the mechanical rotation of the rotor is in the same direction as the rotor winding flux rotation, then the frequency of the stator voltage will be
(a)  50 Hz  (b)  140 Hz  (c)  150 Hz    (d) 200 Hz

4.6.  For the amplifier circuit of figure, the transistor a B of 800. The mid-band voltage gain  V V of the circuit will be

(a)  0  (b)  < 1  (c)  = 1  (d) 800

4.7.   The wave shape of  V in figure will be

4.8.  For the logic circuit shown in figure, the output Y is equal to

4.9.  In figure, the ideal moving iron voltmeter M will read
(a)  7.07 V
(b)  12.24 V
(d)  20.0 V                     ~  10sin314t

5.  The question 5.1 to 5.8 below  carry 2 marks each. Give the complete calculation necessary for arriving at the results.

5.1.  In the circuit of figure, when switch  S  is closed, the ideal ammeter  M reads 5A.

What will be ideal voltmeter  M  read when  S is kept open? (The value of E is not M specified).

5.2.  For  the  circuit  shown  in  figure,  determine  the  readings  of  the  two  wattmeters. Phase sequence is RYB.

5.3.  Figure  shows  the  core  and  armature  of a  relay. Flux  of 50  mWb  is  produced  in this circuit. Find the force in Newtons acting on the armature. Neglect fringing.

5.4.  In a 110 volts compound generator, the armature, shunt and series windings are 0.06   , 27.5    and 0.04    respectively.  The load consists of 200 lamps each  rated at  55W,  110V.  Find  the  total  e.m.f  an  armature  current  when  the  machine  is connected for long shunt operation.

5.5.  Two 500 kVA alternators operate in parallel to supply the following loads:
(i)  250 KW at 0.95 p.f. lagging
(ii)  100 KW at 0.85 p.f. leading
One  machine  is  supplying  200  KW  at  0.9  p.f.  laying.  Calculate  the  p.f.  of  the other machine.

5.6.  For  the ideal  op-amp circuit of figure  shown, determine  the  outpour  voltage  .

5.7.  The  truth table for the output Y in terms of three inputs A, B and  C are given in table. Draw a logic circuit realization using only NOR gates.

A  0  1  0  1  0  1  0  1
B  0  0  1  1  0  0  1  1
C  0  0  0  0  1  1  1  1
Y  1  1  1  0  1  0  0  0

5.8.  M in figure, is a rectifier type 200 V full scale voltmeter having a sensitivity of 10 k   /Volt.  What will be  the reading in M  if the source voltage  V   is a symmetrical  square wave of 800 volts peal to peak?

PART II

1.  This part contains 16 questions: 6 to 21. Answer all the questions. Question 6 consists of 25 sub-questions each carrying 2 marks. All the sub-questions must be answered in the sequence in which they appear.
2.  In the multiple choice questions, four alternatives A, B, C and D are given, of which more than one may be correct. Indicate the correct alternative(s) by writing the corresponding letter (s) in CAPITALS. Marks will be given only if all the correct alternatives are written. For the —Fill in the blanks“ type of questions and for questions asking for illustrations, sketches etc. only the answers must be written against the relevant question number in the answer book.
3.  Questions 7.21 carry 5 marks each. Answer to each question should appear at one place only. Answers must be neatly and legibly written and well separated from any rough work.
4.  Make reasonable assumptions wherever necessary. There is no negative marking.

6.1.  A network contains linear resistors  and ideal voltage  sources.  If  values of all the resistors are doubled, then the voltage across each resistor is
(a)  halved      (b)  doubled
(c)  increased by four times  (d)  not changed

6.2.  The  two  electrical  sub  network  N N are  connected  through  three  resistors   and  as  shown  in  figure.  The  voltage  across  5  ohm  resistor  and  1  ohm  resistor  are given to be 10 V and 5V, respectively. Then voltage across 15 ohm resistor is
(a)  – 105 V  (b)  + 105 V   (c)  – 15 V  (d) + 15 V

6.3.  In  figure,  A A A   are  ideal  ammeters?  If  ,  and                                A reads  5A,  A reads  12A,  then A should read.
(c)  13 A
(d)  17 A

6.5.  If  s s s A + + + = 3 4 0,            then all the roots of this equation are in the left half plane  provided that
(a)  A > 12  (b)  -3 < A < 4  (c)  0 < A < 12  (d) 5  <  A  <  12

6.6.  The built-in potential (Diffusion Potential) in a p-n junction
(a)  is  equal  to  the  difference  in  the  Fermi  level  of  the  two  sides,  expressed  in volts.
(b)  increases with the increase in the doping levels of the two sides
(c)  increases with the increase in temperature
(d)  is equal to the average of the Fermi levels of the two sides

6.7.   a  – cut off frequency of a bipolar junction transistor
(a)  increase with the increase in base width
(b)  increases with the increase in emitter width
(c)  increase with increase in the collector width
(d)  increase with decrease in the base width

6.8.  Negative feedback in amplifiers
(a)  improves the signal to noise ratio at the input
(b)  improves the signal to noise ratio at the output
(c)  does not affect the signal to noise ratio at the output
(d)  reduces distortion

6.9.  In a multi-stage R-C coupled amplifier the coupling capacitor
(a)  limits the low frequency response
(b)  limits the high frequency response
(c)  does not affect the frequency response
(d)  blocks the d.c. component without affecting the frequency response

6.10.  The  bandwidth  of  an  n-stage  tuned  amplifier,  with  each  stage  having  a  band width of B, is given by

6.11.  In a transistor push-pull amplifier
(a)  there is no d.c. present in the output
(b)  there is no distortion in the output
(c)  there are no even harmonics in the output
(d)  there are no odd harmonics in the output

6.12.  2‘s  complement  representation  of  a  16-bit  number  (one  sign  bit  and  15 magnitude bits) is FFFI. Its magnitude in decimal representation is
(a)  0  (b)  1  (c)  32, 767  (d) 65, 535

6.13.  Boolean expression  for the  output  of  XNOR (Equivalent) logic  gate with inputs A and B is:

6.14. Consider the circuit shown in  figure  (a).  If  the  diode  used  here  has  the  V-I characteristic as in figure (b), then the output wave form is:

6.15.  A  pulse  train  with  a  frequency  of  1  MHz  is counted using  a  modulo  1024  ripple counter  built  with  J-K  flip  flops.  For  proper  operation  of  the  counter,  the maximum permissible propagation delay per flip flop stage is ______ n sec.

6.16.  In  a microprocessor, the register  which  holds  the address of the next instruction to be fetched is:
(a)  accumulator       (b)  program counter
(c)  stack pointer      (d)  instruction register

6.17.  In a microcomputer, wait states are used ot
(a)  make the processor wait during a DMA operation
(b)  make the processor wait during an interrupt processing
(c)  make the processor wait during a power shutdown
(d)  interface slow peripherals to the processor

6.18.  The  function  shown  in  figure,  can  represent  a  probability  density  function for  A _____

6.19.  Which  of  the  following demodulator(s)  can  be  used  for  demodulating  the  signal
(a)  Envelope demodulator   (b)  square law demodulator
(c)  synchronous demodulator   (d)  None of the above

6.20.  A  superheterdyne  radio  receiver  with  an  intermediate  frequency  of  455  KHz  is tuned  to  a  station  operating  at  1200  KHz.  The  associated  image  frequency  is ______ KHz.

6.21  Sketch  the  waveform  (with  properly  marked  axes)  at  the  output  of  a  matched filter matched for a signal  s t of duration T, given by   ,

6.22  Six independent low pass signals of bandwidth 3W, W, W, 2W, 3W and 2W Hz are to be time division multiplexer on a common channel using PAM. To achieve this, the minimum transmission bandwidth of the channel should be _______.

6.23  A  material  is  described by the following  electrical  parameters  as  a  frequency  of

(a)  a good conductor
(b)  a good dielectric
(c)  neither a good conductor, nor a good dielectric
(d)  a good magnetic material

6.24.  Consider  a  transmission  line  of  characteristic  impedance  of  50  ohm.  Let  it  be terminated  at  one  end  by  +j50  ohm.  The  VSWR  produced  by  it  in  the transmission line will be
(a)  +1  (b)  0  (c)                                           8   (d) +j

6.25.  A plane wave is incident normally on a perfect conductor as shown in figure. Here

7.  An  infinite  grid  is  built  up  by  connecting  resistors  in  the  manner  indicated  in figure,  where  each  branch  represents  one  ohm  resistor.  Calculate  the  effective resistance between the nodes A and B.

8.  Find  the  Y-parameters  (short  circuit  admittance  parameters)  for  the  network shown in figure.

9.  Consider  the  following  interconnection  of  the  three  LTI  systems  (figure),   are the  impulse responses of these three LTI systems with  ,  and —-   as their respective Fourier transforms. Given that .. Find the output  y t   .

10.  The  reverse  saturation  current  of  the  collector  base  junction  I of  a  BJT  is found to be 10n A at low collector voltages. The low voltage current amplification factor  ( a )  is  0.98.  Find  out  the  change  in  collector  current  with  its  base  open I when the collector voltage is increased such that  a  increases by the 1.0%.

11.  A  JFET  with  the  following  parameters  is  used  in  a  single  stage  common  source amplifier  with  a  load  resistance  of  100k   .  Calculate  the  high  frequency cut off (upper 3 dB cut off frequency) of the amplifier.

12.  In  the following  circuit the  capacitance varies  as C = KW,  where K is  a constant equal  to  0.5  Farads/Coulomb  and  Q,  the  charge  on  the  capacitor  in  Coulombs.
Determine  the  current  through  the  circuit  and  sketch  the  voltage  waveform across the capacitor  V for a step input  V  as shown in figure.

13.  Find the output voltage,  V  in the following circuit (figure), assuming that the op-amps are ideal.

14.  Signals A, B,  C, D and  D  are available.  Using  a single 8  to  1 multiplexer and  no other gate, implement the Boolean function  f A B C D B C A B D A CD , , , . . . . . = + +

15.  A clocked sequential circuit has three states, A, B and C and one input X. As long as the input X is 0, the circuit alternates between the states A and B. If the input X  becomes  1  (either  in  state  A  or  in  state  B),  the  circuit  goes  to  state  C  and remains in state C as long as X continues to be 1. The circuit returns to state A if the input becomes 0 once again and from then on repeats its behaviour. Assume that the state assignments are A = 00, B = 01 and C = 10.
(a)  Draw the state diagram of the circuit
(b)  Give the state table for the circuit
(c)  Draw the circuit using D flip flops

16.  A  microprocessor  has  five  address  lines  A A -  and  eight  data lines  D D -  An input device A, an output device B, A ROM and a RAM are memory mapped to the  microprocessor  at t he  addresses  as  shown  in figure.  Devices  A  and  B  have four addressable registers each; RAM has 8 bytes and ROM has 16 bytes.

(a)  Indicate the address lines t o be connected t o each device and memory.
(b)  Obtain  the  minimum  sum  of  product  expression  for  the  chip  select  (CS) function of each device/memory.

17.  It  is  desired  to  generate  a  random  signal  x(t),  with  autocorrelation  function,   R T e = 5 ,  by  passing  white  noise  n(t),  with  power  spectral  density   -  S f watts Hz =        / ,   through a LTI system. Obtain an expression for the transfer function H(f) of the LTI system.

18.  Obtain  an  expression  for  the  signal    t  in  figure,  for and  that the BPF is an ideal unity gain filter with pass band from 800 Hz to 1200 Hz.

19.  A low pass signal m(t) band limited to B Hz is sampled by a periodic rectangular pulse train,  P t  of period  T B =     sec. assuming natural sampling and that the pulse amplitude  and pulse  width  are  A volts  30 B sec,  respectively,  obtain expression for the frequency spectrum of the sampled signal  m t    .

20.  Consider  an  array  of  two  non-directional  radiators  with  spacing  0.5 . d =      Determine the directions of maximum radiation when the radiators are excited as shown in figure. Calculate the phase shift required for turning the direction of the maximum radiators by 90°, keeping the separation, d, unchanged.

21.  Match the following descriptions with each of  the diagrams given in figure. Fields are near the interface, but  on opposite sides of the boundary. Vectors  are drawn to scale.

(a)  Medium 1 and medium 2 are dielectrics with  >
(b)  Medium 1 and medium 2 are dielectrics with  <
(c)  Medium 2 is a perfect conductor
(d)  Medium 1 is a perfect conductor.