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Home » Gate Sample Papers » Electronics & Communication Engineering Sample Papers » GATE EC 2001 Electronics Question Paper

GATE EC 2001 Electronics Question Paper

GATE EC 2001 Electronics Question Paper


1.  This question  consists of TWENTY-FIVE sub-questions  (1.1 - 1.25) of ONE mark each.  For  each of these sub-questions, four  possible alternatives  (A,B, C and D) are  given,  out  of  which  ONLY  ONE  is  correct.  Indicate  the  correct  answer  by darkening  the  appropriate bubble  against the question  number on the  left  hand side  of  the  Objective  Response  Sheet  (ORS).  You  may  use  the  answer  book provided for any rough work, if needed.

1.1  The voltage e  in figure 1.1 is

(a)  2V
(b)  4
(c)  4V
(d)  8V

1.2.  If  each  branch  of  a  Delta  circuit  has  impedance   then  each  branch  of  the equivalent Wye circuit has impedance.

1.3.  The  transfer  function  of  a  system  is  given  by         H s =          The  impulse response of the system is: (* denotes convolution, and U(t) is unit step function)

1.4.  The admittance parameter Y  in the 2-port network in Figure 1.4 is
(a)  -0.2 mho
(b)  0.1 mho
(c)  -0.05 mho
(d)  0.05 mho

1.5.  The region of convergence of the z-transform of a unit step function is
(a)  1     z        (b)  1
(c)  (Real part of z) > 0    (d)  (Real part of z) < 0

1.6.  The current gain of a BJT is

1.7.  MOSFET can be used as a
(a)  current controlled capacitor  (b)  voltage controlled capacitor
(c)  current controlled inductor  (d)  voltage controlled inductor

1.8.  The effective channel length of a MOSFET in saturation decreases with increase in
(a)  gate voltage      (b)  drain voltage
(c)  source voltage      (d)  body voltage

1.9.  The ideal OP-AMP has the following characteristics.

1.10.  The 2's complement representation of 17 is
(a)  01110  (b)  01111  (c)  11110  (d) 10001

1.11.  Consider the following two statements:
Statement 1: A stable multi-vibrator can be used for generating square wave.
Statement 2: B stable multi-vibrator can be used for storing binary information.
(a)  Only statement 1 is correct
(b)  Only statement 2 is correct
(c)  Both the statements 1 and 2 are correct
(d)  Both the statements 1 and 2 are incorrect

1.12.   For  the  ring  oscillator  shown  in  Figure  1.12,  the  propagation  delay  of  each inverter  is  100 pico second. What  is  the fundamental frequency of the  oscillator output?
(a)  10 MHz
(b)  100 MHz
(c)  1 GHz
(d)  2 GHz

1.13.  An  8085  microprocessor  based  system  uses  a  4K      8-bit  RAM  whose  starting address is AA00. The address of the last byte in this RAM is
(a)  0FFFH  (b)  1000 H  (c)  B9FF H  (d) BA00 H

1.14.  The equivalent of the block diagram in Figure 1.14 is given in

15.  If the  characteristic equation of a closed-loop  system  is  s s + + =  2 2 0     , then  the  system is
(a)  over damped      (b)  critically damped
(c)  underdamped      (d)  undamped

1.16.  The  root-locus  diagram  for  a  closed  loop  feedback  system  is  shown  in  Figure . The system is overdamped.

(a)  only if 0      = K  =  1
(b)  only if 1 < K < 5
(c)  only if K > 5
(d)  if 0       = K < 1 or K > 5

1.17.  The  Nyquist  plot  for  the  open-loop  transfer  function  G(s)  of  a  unity  negative feedback system is shown in figure 1.17 if G(s) has no pole in the right half of s-plane, the  number  of roots of the system characteristic equation in the  right half
of s-plane is
(a)  0
(b)  1
(c)  2
(d)  3

1.18.  Let  d (t) denote the delta function. The value of the integral  t dt cos 2     is
(a)  1  (b)  -1  (c)  0  (d)  2

1.19.  A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through
(a)  an RC filter      (b)  an envelope detector
(c)  a PLL
(d)  an ideal low-pass filter with appropriate bandwidth

1.20.  The  PDF of a  Gaussian random variable  X  is given  by  P x e =

1.21.  If a signal f(t) has energy E, the energy of the signal f(2t) is equal to
E   (c)  2E  (d) 4E
(a)  E  (b)  2

1.22.  A transmission line is distortion-less if

(a)  1    RL GC =    (b)  RL = GC  (c)  LG = RC  (d) RG = LC

1.23.  If a  plane  electromagnetic  wave satisfies the  equation  = c      ,  the wave  propagates in the
(a)  x-direction      (b)  z-direction
(c)  y-direction
(d)  xy plane at an angle of 45 between the x and z directions

1.24.  The phase velocity of waves propagating in a hollow metal waveguide is
(a)  greater than the velocity of light in free space.
(b)  less than the velocity of light in free space.
(c)  equal to the velocity of light in free space.
(d)  equal to the group velocity.

1.25.  The  dominant  mode  in  a  rectangular  waveguide is  TE ,  because  this  mode has
(a)  no attenuation      (b)  no cut-off
(c)  no magnetic field component  (d)  the highest cut-off wavelength

2.  This question consists of TWENTY-FIVE sub-questions (2.1 2.25) of TWO marks each.  For each of these sub-questions, four possible alternatives (A, B, C and D) are  given,  out  of  which  ONLY  ONE  is  correct.  Indicate  the  correct  answer  by darkening  the  appropriate bubble  against the question  number on the  left  hand side  of  the  Objective  Response  Sheet  (ORS).  You  may  use  the  answer  book provided for any rough work, if needed.      2

2.1  The voltage e  in figure 2.1 is                                      (a)  48 V  (b)  24
(c)  36 V  (d)  28 V

2.2.  In  figure  2.2,  the  value  of  the  load  resistor  R  which  maximizes  the  power delivered to it is
(a)  14.14
(b)  10
(c)  200
(d)  28.28

2.3.  When the angular frequency     in Figure 2.3 is varied from 0 to  8 , the locus of the current phasor I  is given by

2.4  The Z parameters Z  and Z  for the 2-port network in figure 2.4 are

2.5  An npn BJT has g  = 38m A/V, C =10  F, C =4 10 F, and DC current gain    =  - 14                 - 13

2.6  The  transistor  shunt  regulator shown  in  Figure  2.6  has  a regulated  output  voltage  of  10 V,  when  the  input  varies  from 20  V  to  30  V.  The  relevant V parameters  for  the Zener diode Z and  the  transistor  are:  V   =  V =20.  Neglect the  current  through  R .  Then the  maximum power dissipated in  the  Zener diode (P ) and the transistor (P  ) are

(a)  P     =75mW, P  =7.9W    (b)  P                  =85mW, P  =8.9W
(c)  P     =95mW, P  =9.9W    (d)  P                  =115mW, P  =11.9W

2.7  The oscillator circuit shown in Figure 2.7 is

(a)  Hartley oscillator with  f MHz =  79.6
(b)  Colpitts oscillator with  f MHz =  79.6
(c)  Hartley oscillator with  f MHz =  159.2
(d) Colpitts oscillator with  f MHz =  159.2

2.8  The  inverting  OP-AMP  shown  in  Figure 2.8  has  an  open-loop  gain  of  100.  The  closed loop gain

(a)  -8  (b)  -9  (c)  -10  (d) -11

2.9  In Figure 2.9, assume the OP-AMPs to be ideal. The output v  of the circuit is:

2.10  In Figure 2.10, the LED
(a)  emits light when both S  and S are closed.
(b)  emits light when both S  and S are open.
(c)  emits light when only S  or S  is closed.
(d)  does not emit light, irrespective of the switch positions.

2.11  In  the TTL circuit in Figure 2.11, S  to  S   are select lines and X  and X are input lines. S  and X  are LSBs. The output Y is
(a)  indeterminate      (b)  A                                 B
(c)  A B          (d)                               C A B C A B

2.12  The  digital  block  in  figure 2.12  is  realized  using  two  positive  edge  triggered  D-flip-flops.  Assume  that  for  t <  t , Q   =  Q  =0. The circuit  in the digital  block  is given by:

(a)  Figure 2.12 (a)      (b)  Figure 2.12 (b)
(c)  Figure 2.12 (c)      (d)  Figure 2.12 (d)

2.13  In  the DRAM cell  in Figure  2.13, the  V  of the NMOSFET is 1 V.  For the following three combinations of WL and BL voltages.
Word Line (WL)

(a)  5 V; 3V; 7V  (b)  4 V; 3V; 4V  (c)  5 V; 5V; 5V  (d) 4 V; 4V; 4V

2.14   The  impulse  response functions  of  four  linear  systems  S1,  S2,  S3, S4 are  given respectively by

where  U(t)  is  the  unit  step  function.  Which  of  these  systems  is  time  invariant, causal, and stable?
(a)  S1  (b)  S2  (c)  S3  (d) S4

2.15  An electrical system and its signal-flow graph representations are shown in Figure 2.15(a) and 2.15(b) respectively. The values of G  and H, respectively are

2.16  The  open-loop  DC  gain  of  a  unity  negative  feedback  system  with  closed-loop
(a)  4
13   (b)  4            9   (c)  4  (d) 13

2.17  The feedback control system in Figure 2.17 is stable
(a)  for all K  =  0
(b)  only if K     = 1
(c)  only if 0     =  K < 1
(d)  only if 0     =  K  =  1

2.18  A  video  transmission  system  transmits  625  picture  frames  per  second.  Each frame  consists  of  a  400      400  pixel  grid with  64  intensity  levels  per  pixel.  The data rate of the system is
(a)  16 Mbps  (b)  100 Mbps  (c)  600 Mbps  (d) 6.4 Gbps

2.19  The Nyquist sampling interval, for the signal Sinc (700t) + Sinc (500t) is
(a)  1 sec                                 (c)  1 sec
350   (b)  sec       350                700   (d)  sec     175

2.20  During  transmission  over  a  communication  channel,  bit  errors  occur independently with probability p. If a block of n bits is transmitted, the probability of at most one bit error is equal to
(a)  1  (1  p)           (b)  p + (n  1) ( 1  p)  n
(c)  np(1  p)                   (d)  (1  p)               + np(1  p) n-1

2.21  The  PSD  and  the power of  a signal g(t) are, respectively, S (   ) and  P .  The PSD and the power of the signal ag(t) are, respectively

2.22  A  material  has  conductivity  of  10   mho/m  and  a  relative permittivity  of  4.  The  - 2 frequency  at  which  the  conduction  current  in  the  medium  is  equal  to  the displacement current is
(a)  45 MHz  (b)  90 MHz  (c)  450 MHz  (d) 900 MHz

2.23  A uniform plane  electromagnetic wave  incident normally on a  plane surface of a dielectric  material  is  reflected  with  a  VSWR  of  3.  What  is  the  percentage  of incident power that is reflected?
(a)  10%  (b)  25%  (c)  50%  (d) 75%

2.24  A  medium  wave  radio  transmitter  operating  at  a  wavelength  of  492  m  has a tower antenna of height 124m. What is the radiation resistance of the antenna?
(a)  25        (b)  36.5               (c)  50             (d) 73

2.25  In  a  uniform  linear  array,  four  isotropic  radiating  elements  are  spaced  4  apart. The  progressive  phase  shift between the  elements  required  for  forming  the main beam at 60 off the end-fire is:
(a)  -      p  radians  (b)  2 -  radians  (c)  4 -  radians  (d)  8 -  radians

This  section  consists  of  TWENTY  questions  of  FIVE  marks  each.  Attempt  ANY  FIFTEEN questions. Answers must be given in the answer book provided.

3.  For the circuit shown in figure 3, determine the phasors E , E , I and I .

4.  The  circuit shown  in  Figure  4  is operating in steady-state with switch  S   closed.

The switch S  is opened at t = 0.
(a)  Find i      (0 ).

(c)  Using  nodal  equations  and  Laplace  transform  approach,  find  an  expression for the voltage across the capacitor for all t > 0.

5.  The  admittance  parameters  of  a  2-port  network  shown  in  figure  5  are  given  by Y   =  2  mho,  Y   = -0.5  mho,  Y   =  4.8  mho,  Y   =  1 mho.  The  output  port  is
terminated with a load admittance Y   = 0.2 mho. Find E  for each of the following conditions?
(a)  E     =10   0  V 

(b)  I     =10   0 A 

(c)  A  source  10  0  V  in  series  with  a  0.25     resistor  is  connected  to  the  input  port.

6.  For  the  circuit  shown  in  figure  6,  D1 and  D2 are  indentical diodes with  idealilty factor of unity. The thermal voltage V   = 25 mV.
(a)  Calculate V  and V .
(b)  If the reverse saturation current, I , for the diode is 1 pA, then compute the current I through the circuit.

7.  An  emitter-follower  amplifier  is  shown  in  Figure  7.  Z    is  the  impedance  looking into the base of the transistor and Z  is the impedance looking into the emitter of the transistor.
(a)  Draw the small signal equivalent circuit of the amplifier.
(b)  Obtain an expression for Z     .

(c)  Obtain an expression for Z    .

(d)  Determined Z      and Z  if a capacitor C  is connected across R  .

8.  Assume that the OP-AMP in Figure 8 is ideal.
(a)  obtain  an  expression  for  v        in  terms  of  v ,  R,  and  the  reverse  saturation current I   of the transistor.
(b)  If  R =  1        ,  I   = 1 pA and  the thermal voltage  V    = 25 mV,  then  what is  the value of the output voltage v   for an input voltage v   = 1V
(c)  Suppose that the transistor in the feedback path is replaced by a p-n junction diode  with  a  reverse  saturation  current  of  I .  The  p-side  of  the  diode  is
connected to  node A  and  the n-side to node B. Then what is  the expression
for v   in terms of v , R and I ?

9.  A monochrome video signal that ranges from  0 to  8V, is digitized using an 8-bit ADC.
(a)  Determine the resolution of the ADC in V/bit.
(b)  Calculate the mean squared quantization error.
(c)  Suppose  the ADC is counter controlled.  The counter is up count and positive edge  triggered  with  clock  frequency  1  MHz.  What  is  the  time  taken  in seconds to get a digital equivalent of 1.59 V?

10.  In figure 10, the output of the oscillator, V  has 10V peak amplitude with zero DC value. The  transfer  characteristic of  the Schmitt  inverter  is  also shown  in  figure
10. Assume that the JK flip-flop is resent at time t = 0.
(a)  What is the period and duty cycle of the waveform V ?

(b)  What is the period and duty cycle of the waveform V ?

(c)  Sketch V    , V   and  V  for the duration  0  =  t   =   6 s.  Clearly  indicate the exact timings  when  the  waveforms  V   and  V   make  high-to-low  and  low-to-high transitions.

11.  For the digital block shown in Figure  11(a), the output Y=f(S  ,S ,S ,S ) where S is  MSB  and  S      is  LSB.  Y  is  given  in  terms  of  minterms  as

(a)  Enter the logical values in the given Karnaugh map [Fig.11(b)] for the output Y.
(b)  Write  down  the  expression  for  Y  in  sum-of  products  from  using  minimum number of terms
(c)  Draw  the  circuit  for  the  digital  logic  boxes  using  four  2-input  NAND  gates only for each of the boxes.

12.  Consider the following sequence of instructions for an 8085 microprocessor based system.

Memory address  Instructions
FF00  MVI, A  FF H
FF03  JC  FF0C H
FF06  ORI  A8H
FF08  JM  FF15 H
FF15  MVI, A  FF H
FF17  ADI  02 H
FF1A  JZ  FF23 H
FF1D  JC  FF10 H
FF20  JNC  FF12 H

(a)  If  the  program  execution  begins  at  the  location  FF00  H,  write  down  the sequence  of  instructions  which  are  actually  executed  till  a  HLT  instruction.
(Assume all flags are initially RESET)
(b)  Which of the three ports (PORT1, PORT2 and PORT3) will be loaded with data and what is the bit pattern of the data?

13.  A feedback control system is shown in figure 13.
(a)  Draw the signal-flow graph that represents the system.
(b)  Find the  total  number of  loops in the graph  and determine  the loop-gains  of all the loops.
(c)  Find the number of all possible combination of non-touching loops taken two at a time.
(d)  Determine the transfer function of the system using the signal-flow graph.

14.  Consider the feedback control system shown in figure 14.
(a)  Find the transfer function of the system and its characteristic equation.
(b)  Use  the  Routh-Hurwitz  criterion  to  determine  the  range  of  K  for  which  the system is stable.

15.  For the feedback control system shown in figure 15, the process transfer function   and the  complification factor of the power amplifier is K  =  0.
The  design  specifications  required  for  the  system  are  a  time  constant  of  1  sec and a damping ratio of 0.707.
(a)  Find the desired locations of the closed loop poles.
(b)  Write  down  the  required  characteristic  equation  for  the  system.  Hence determine the PD controller transfer function  G s when K = 1.
(c)  Sketch the root-locus for the system.

16.  The  Fourier  transform  G(      )  of  the  signal  g(t)  in  Figure  16(a)  is  given  as Using  this  information  and  the  time-shifting  and

time-scaling  properties,  determine  the  Fourier  transform  of  signals  in  Figures 16(b), 16(c) and 16(d).

17.  The  periodic  modulating  signal  m(t)  is  shown  in  Fig.17.  Using  Carson's  rule estimate  B  (bandwidth  of  the FM signal)  and  B  (bandwidth  of  the PM signal)

18.  A baseband signal g(t) bandlimited to 100 Hz modulates a carrier of frequency f  Hz. The modulated singal g(t)cos 2 p f t is transmitted over a channel whose input x  and  output  y  are  related  by  y  =  2x  +  x .  The  spectrum  of  g(t)  is  shown  in  2
Figure 18. Sketch the spectrum of the transmitted signal and the spectrum of the received signal.

19.  A periodic signal g(t) is shown in Figure 19. Determine the PSD of g(t).

20.  A system of three electric charges lying in a straight line is in equilibrium. Two of the  charges  are  positive  with  magnitudes  Q  and  2Q,  and  are  50  cm  apart. Determine the sign, magnitude and position of the third charge.

21.  A medium has breakdown strength of 16 KV/m r.m.s. Its  relative permeability is 1.0  and  relative  permittivity  is  4.0  A plane  electromagnetic wave  is  transmitted through the medium. Calculate the maximum possible power flow density and the associated magnetic filed.

22.  A rectangular hollow metal  waveguide has dimensions a= 2.29 cm and b = 1.02 cm. Microwave power at 10 GHz is transmitted through the waveguide in the TE  mode.
(a)  Calculate the cut-off wavelength and the guide wavelength for this mode.
(b)  What  are  the  other  (TE  or  TM)  modes  that  can  propagate  through  the waveguide?
(c)  If  a  =  b  =  2.29cm,  What  are  the  modes  which  can  propagate  through  the waveguide?

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