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GATE EC – 2002 Electronics and Communication Engineering Question Paper

SECTION A    (75 m arks)
1.  This question  consists of TWENTY-FIVE sub-questions  (1.1 œ 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 dependent current source shown in Figure 1.1
(a)  delivers 80 W
(b)  absorbs 80 W
V
(c)  delivers 40 W                                        -                               5
(d)  absorbs 40 W

1.2  In  figure 1.2, the switch was  closed for a long time before opening at t =  0. the voltage Vx at t = 0 +  i s
(a)  25 V
(b)  50 V
(c)  -50 V
(d)  0 V

1.3  Convolution of x(t + 5) with impulse function  d (t œ 7) is equal to
(a)  x(t – 12)  (b)  x(t + 12)  (c)  x(t – 2)  (d) x(t + 2)

1.4  Which  of  the  following  cannot  be  the  Fourier  series  expansion  of  a  periodic signal?
(a)  x(t) = 2cos t + 3 cos 3t  (b)  x(t) = 2cos                            p t + 7 cos t
(c)  x(t) = cos t + 0.5     (d)  x(t) = 2cos 1.5                                 p t + sin 3.5  p t

1.5  In  Figure  1.5,  a  silicon  is  carrying  a  constant  current  of  1  mA.  When  the temperature  of  the diode is 20°C,  V    is found to  be 700  mV. If the  temperature rises to 40°C, V   becomes approximately equal to
(a)  740 mV
(b)  660 mV
(c)  680 mV
(d)  700 mV
-
1.6  In  a  negative  feedback  amplifier  using  voltage-series  (i.e.  voltage-sampling series  mixing)  feedback.  (R   and  R    denote  the  input  and  output  resistance respectively)
(a)  R       decreases and R   decreases  (b)  R        decreases and R   increases
(c)  R       increases and R   decreases  (d)  R         increases and R   increases

1.7  A  741-type  op-amp  has  a  gain-bandwidth  product  of  1  MHz.  A  non-inverting amplifier using this op-amp and having a voltage gain of 20 dB will exhibit a 3-dB bandwidth of

(a)  50 KHz  (b)  100 KHz  (c)  1000
17  KHz  (d)  1000 7.07

1.8  Three  identical  RC-coupled  transistor  amplifiers  are  cascaded.  If  each  of  the amplifiers has a frequency response as shown in Figure 1.8, the overall frequency response is as given in  A  dB

1.9  4-bit 2‘s complement representation of a decimal number is 1000. The number is
(a)  +8  (b)  0  (c)  -7  (d) -8

1.10  If the input to the digital circuit (Figure 1.10) consisting of a cascade of 20 XOR-gates is X, then the output Y is equal to

(a)  0  (b)  1  (c)  X   (d) X

1.11  The number of comparators required in a 3-bit comparator type ADC is
(a)  2  (b)  3  (c)  7  (d) 8

1.12  If the transistor in Figure 1.12 is in saturation, then

1.14  Which of the  following points is NOT on the root locus of a system with the  open loop transfer function  G s H s s s s = +

(a)  s =  3    – j    (b)  s= – 1.5  (c)  s= -3  (d) s = -

1.15  The  phase  margin  of  a  system  with  the  open-loop  transfer  function
(a)  0°  (b)  63.4°  (c)  90°  (d)

1.16  The  transfer  function  Y s U s of  a  system  described  by  the  state  equations
x(t) = -2x(t) + 2u(t) and y(t) = 0.5x(t) is

1.18  A linear phase channel with phase delay T   and group delay T  must have

1.19.  A 1 MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave of  period  100 sec. Which of the following  frequencies will NOT be present in the modulated signal?
(a)  990 KHz  (b)  1010 KHz  (c)  1020 KHz  (d) 1030 KHz

cos(8 p× 10 )t  and  T   =100 sec.  When  y(t)  is  passed  through  an  ideal  low-pass filter with a cutoff frequency of 5KHz, the output of the filter is

1.21.  For  a bit-rate of 8 Kbps,  the  best  possible  values of the  transmitted  frequencies in a coherent binary FSK system are
(a)  16 KHz and 20 KHz    (b)  20 KHz and 32 KHz
(c)  20 KHz and 40 KHz    (d)  32 KHz and 40 KHz

1.22.  The  line-of-sight  communication  requires  the  transmit  and  receive  antenna  to face each other. If the transmit antenna is  vertically polarized, for best reception the receive antenna should be
(a)  horizontally polarized   (b)  vertically polarized

(c)  at 45° with respect to horizontal polarization
(d)  at 45° with respect to vertical polarization

1.23.  The VSWR can have any value between
(a)  0 and 1  (b)  -1 and +1  (c)  0 and                       8   (d) 1 and      8

1.24.  In  an impedance Smith chart, a clockwise movement along a constant resistance circle gives rise to
(a)  a decrease in the value of reactance
(b)  an increase in the value of reactance
(c)  no change in the reactance value
(d)  no change in the impedance value

1.25  The  phase  velocity  for the  TE -mode in  an air-filled  rectangular waveguide is (c is the velocity of plane waves in free space)
(a)  less than c      (b)  equal to c
(c)  greater than c      (d)  none of the above

This question consists of TWENTY-FIVE sub-questions (2.1 œ 2.25) of TWO marks  2 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.
2.1  In the network of Figure 2.1, the maximum power is delivered to R   if its value is
(a)  16        (b)  40                  (c)  60               (d) 20

2.2.  If the 3-phase balanced source in Figure 2.2 delivers 1500 W at a leading  power factor of 0.844, then the value of Z   (in ohm) is approximately

2.3.  The  Laplace transform of a  continuous-time signal x(t) is  X s =           If the Fourier transform of this signal exists, then x(t) is

2.4.  If  the  impulse  response  of  a  discrete-time  system  is
the system function H(z) is equal to
(a)             and the system is stable

(b)             and the system is stable
(c)              and the system is unstable

(d)   and the system is unstable

2.5.  An amplifier using an opamp with a slew-rate SR = 1V/ sec has a gain of 40 dB. If  this  amplifier  has  to  faithfully  amplify  sinusoidal  signals  from  dc  to  20  KHz without introducing  any  slew-rate  induced  distortion,  then  the  input signal  level must not exceed.
(a)  795 mV  (b)  395 mV  (c)  79.5 mV  (d) 39.5 mV

2.6.  The  circuit  in  Figure  2.6  employs  positive feedback  and is  intended  to  generate sinusoidal  oscillation.  If  at  a  frequency  f B f V f =   =   °             then  to  sustain oscillation at this frequency

2.7.  A zener diode regulator in Figure 2.7 is to be designed to meet the specifications:
I   = 10 mA, V   = 10 V and V  varies from 30 V to 50 V. The zener diode has
V V I = 10  and   (knee current) = 1 mA. For satisfactory opertion

2.8.  The voltage gain  A V   =  of the   I  =1mA  JFET  amplifier  shown  in  Figure  R  (3K   )     D
2.8 is
(a)  +18
(b)  -18
(c)  +6
(d)  -6

2.9.  The  gates  G   and  G   in  Figure  2.9  have  propagation  delays  of  10  nsec  and  20 nsec  respectively.  If  the  input  V  makes  an  abrupt  change  from  logic  0  to  1  at time t = t  then the output waveform V  is

2.10.  The circuit in Figure 2.10 has two CMOS NOR gates. This circuit functions as a:

(a)  flip flop      (b)  Schmitt trigger
(c)  Monostable multivibrator  (d)  Astable multivibrator

2.11.  Consider the following statements in connection with the CMOS inverter in Figure 2.11 where both the  MOSFETs are of  enhancement type  and both have  a thresh old voltage of 2V.
Statement 1: T     conducts when Vi  =  2V.
Statement 2: T    is always in saturation when V  = 0V.

Which of the following is correct?
(a)  Only Statement 1 is TRUE   (b)  Only Statement 2 is TRUE
(c)  Both the statements are TRUE  (d)  Both the statements are FALSE
2.12.  If  the  input  X X X X to  the  ROM  in  figure  2.12  are  8-4-2-1  BCD  numbers,  , , ,then the outputs  YY YY are

(a)  gray code numbers    (b)  2-4-2-1 BCD numbers
(c)  excess 3 code numbers  (d)  none of the above

2.13.  Consider the following assembly language program.
MVI    B,87H
MOV    A,B
START:  JMP    NEXT
MVI    B,00H
XRA    B
OUT    PORT1
HLT
NEXT:  XRA    B
JP    START
OUT    PORT2
HLT
The execution of the above program in an 8085 microprocessor will result in
(a)  an output of 87H at PORT1
(b)  an output of 87H at PORT2
(c)  infinite looping of the program execution with accumulator data remaining at 00H
(d)  infinite  looping  of  the  program  execution  with accumulator  data  alternating between 00H and 87H

2.14.   The system shown in Figure 2.14 remains stable when

2.15.  The  transfer  function  of  a system is  G s s s = + +               For a  unit  step input to the system the approximate settling time for 2% criterion is
(a)  100 sec  (b)  4 sec  (c)  1 sec  (d) 0.01 sec

2.16.  The  characteristic  polynomial  of  a  system  is
The system is
(a)  stable  (b)  marginally stable (c)  unstable  (d) oscillatory

2.17.  The  system  with  the  open  loop  transfer  function  G s H s =             has  a gain margin of
(a)  – 6 dB  (b)  0 dB  (c)  3.5 dB  (d) 6 dB

2.18.  An angle modulated signal is given by

The maximum frequency and phase deviations of s(t) are
(a)  10.5 KHz, 140    p  rad    (b)  6 KHz, 80                 p  rad
(c)  10.5 KHz, 100     p  rad    (d)  7.5 KHz, 100                 p  rad

2.20.  A signal x(t) = 100 cos(24 p× 10 )t is ideally sampled with a sampling period of 50 sec and then passed through an ideal low-pass filter with cutoff frequency of 15 KHz. Which of the following frequencies is/are present at the filter output?
(a)  12 KHz only      (b)  8 KHz only
(c)  12 KHz and 9 KHz     (d)  12 KHz and 8 KHz

2.22.  A plane wave is characterized by  E x ye e = + 0.5 .      2           This wave is
(a)  linearly polarized     (b)  circularly polarized
(c)  elliptically polarized    (d)  unpolarized

2.23.  Distilled water at 25° C is characterized by  s  = 1.7  ×  10  mho/m and    =78    at  – 9 a frequency of 3 GHz. Its loss tangent tan  d  is (   = 10  /(36 p )F/m)

2.24.  The electric field on the surface of a perfect conductor is 2 V/m. The conductor is immersed in water with    =80    . The surface charge density on the conductor is
(a)  0 C/m            (b)  2 C/m                                    2                                                                     2
(c)  1.8       ×  10  C/m       (d)  1.14                   ×  10  C/m      – 11     2                                                             – 9     2

2.25.  A person with a receiver is 5 Km away from the transmitter. What is the distance that this person must move further to detect a 3-dB decrease in signal strength?
(a)  942 m  (b)  2070 m  (c)  4978 m  (d) 5320 m

SECTION  B     (75 Marks)
This section consists of TWENTY questions (EC3-EC22) of FIVE marks each. Attempt ANY FIFTEEN  questions.  Answers  must  be  given  in  the  answer  book  provided.  Answer  for each  question must start on  a fresh page and  must appear at one place only.  (Answers to all parts of a question must appear together).
3.  The switch in Figure 3 has been in position 1 for a long time and is then moved to position 2 at t = 0.

4.  For the network shown in Figure 4, R = 1 K   , L  = 2H, L = 5H, L  = 1H, L  = 4H and C = 0.2  F. The mutual inductances are M  = 3H and M  = 2H. Determine
(a)  the equivalent inductance for the combination of L  and L  .
(b)  the equivalent inductance across the points A and B in the network.
(c)  the resonant frequency of the network.
(a)  Find its short-circuit admittance parameters.
(b)  Find the open-circuit impedance Z .

6.  A  triangular  voltage  waveform  V  (t)  figure  6(a)  is  applied  at  the  input  to  the circuit of Figure 6(b). Assume the diodes to be ideal.
(a)  Determine the output V (t).
(b)  Neatly sketch the output waveform superimposed on the input V  (t) and label the key points.

7.  Figure  7  shows  a  2-stage amplifier.  The  transistors  Q1 and  Q2  are  identical  with current  gain   ß   =  100;  further ß   =   ß   =   ß .  The  Zener  diode D   has  a  break  down  voltage

V =  10.7  volt.  Assume  that  D is  in  breakdown region  and  its dynamic  resistance  r    is  zero.
The  capacitors  C1  and  C2  are large  and  provide  negligible impedance at  signal frequencies.

(a)  Identify  the  configuration in  each  of  the  amplifier stages  (i.e.,  whether  CE,
CC, CB etc.)
(b)  Determine the quiescent quantities I  and V .
(c)  Derive an expression for the voltage gain A  Í
V and determine its value.
(Assume V           = 0.7V, r = 8  and Thermal voltage V   = 25 mV)

8.  Consider the circuit of Figure 8. The op-amp used is ideal.
(a)  In which mode is  the BJT operating (i.e. active, saturation or cutoff)? Justify your answer.
(b)  Obtain an expression relating the output current I  and the input voltage V .
(c)  Determine I      and V   if V    = 2 Volt (V  utput of opamp)
(Assume         ß  = 99 and V  = 0.7 V)

9.  The  inputs to  a  digital circuit shown  in  Figure  9(a)  are the  external signals A, B and C.

,  and    (     A B Care  not  available).  The  +5V  power  supply  (logic  1)  and  the  ground (logic 0) are also available. The output of the circuit is      X AB A B C = +           .
(a)  Write down the output function in its canonical SOP and POS forms.
(b)  Implement  the circuit using only two 2:1 multiplexers shown in Figure  9(b), where  S  is the data-select  line,  D  and  D   are  the  input  data  lines  and  Y  is the output lines. The function table for the multiplexer is given in table 9.

10.  Each  transistor  in  Figure  10  has  dc  current  gain   ß   =  50,  cut-in  voltage = V V 0.65  and V ,    = 0.75 V. The output voltage V  for T  in saturation can be as  high  as  0.2  V.  Assume  0.7  V  drop  across  a  conducting  p-n  junction.
Determine?

(a)  the minimum value I  necessary to keep T  saturation.
(b)  the maximum permissible value for the resistance R  .
(c)  the worst-case high input (logic 1) and the worst-case low input (logic 0) for which T  will be either in saturation or in cut off.

11.  It  is  required to  design  a binary  mod-5  synchronous counter  using  AB flip-flops such  that  the  output  Q Q Q   changes  as  000  ‰  001  ‰ 010 …..  and  so  on.  The excitation table for the AB flip-flop is given in table 11.
(a)  Write down the state table for the mod-5 counter.
(b)  Obtain simplified SOP expressions  for  the  inputs A , B , A , B , A  and B   in terms of Q , Q , Q  and their complements.
(c)  Hence, complete the circuit diagram for the mod-5 counter given in Figure 11 using minimum number of 2-input NAND-gate only.

12.  An  8085  microprocessor  operating  at  5  MHz  clock  frequency  execute  the following routine.
START  MOVE  A,B
OUT                             55H
DCR  B
STA   FFF8H
JMP   START
(a)  Determine  the  total  number  of  machine  cycles  required  to  execute  this routine till the JMP instruction is executed for the first time.
(b)  Determine the time interval between two consecutive  MEMW signals.

(c)  If  the  external  logic  controls  the  READY  line  so  that  three  WAIT  states  are introduced  in  the  I/O  WRITE  machine  cycle,  determine  the  time  interval between two consecutive  MEMW signals.

13.  A unity feedback system has the plant transfer function

(a)  Determine the frequency at which the plant has a phase lag of 90°
(b)  An  integral  controller with  transfer  function  G s s     is  placed  in  the  feed-c forward  path  of  the  feedback  system.  Find  the  value  of  k  such  that  the compensated system has an open-loop gain margin of 2.5.
(c)  Determine  the  steady  state  errors  of  the  compensated  system  to  unit-step
and unit-ramp inputs.

14.  The Nyquist plot of an all-pole second order open-loop system is shown in Figure 14. Obtain the transfer function of the system.

15.  The block diagram of a linear time invariant system is given in Figure 15.

(a)  Write  down  the  state  variable  equations  for  the  system  in  matrix  form assuming the state vector to be  x t x t         .
(b)  Find out the state transition matrix.
=   (c)  Determine y(t), t      0, when the initial values of the state at time t = 0 are x

(0) =1, and x  (0) = 1.

16.  A deterministic signal x(t) = cos2 t is passed through a differentiator as shown in Figure 16.

(a)  Determine the autocorrelation R   (T) and the power spectral density S (f).
(b)  Find the output power spectral density S (f).
(c)  Evaluate R    (0) and R

17.  A  DSBSC  modulated  signal  s(t)  =  10  cos  (2     10 t+ )m(t  )  is  corrupted  by  an  6          -
additive white  Gaussian noise of  power spectral density 10  W/Hz. The message  f power  spectral  density  S (f)  is  as  shown  in  Figure  17  and    is  uniformly p distributed over the range 0 to 2 .

(a)  Express  the  signal  autocorrelation  function  R  (T)  in  terms  of  the  message autocorrelation function R  (T). Clearly state the necessary assumptions.
(b)  Determine the signal power spectral density S  (f).
(c)  Find  the  power  of  the  modulated  signal  and  the  noise  power  in  the
transmissions bandwidth.

18.  A continuous time signal with finite energy, band limited from 3 MHz to 5 MHz is ideally sampled, encoded by a fixed  length PCM coder and then transmitted over a digital channel of capacity 7 Mbps. The probability density function (pdf) at the output of the sampler is uniform over the range œ2V to +2V.
(a)  Determine the minimum sampling rate necessary for perfect reconstruction.
(b)  Determine the maximum SNR (in dB) that may be achieved.

19.  A discrete memory-less source generates either 0 or 1 at a rate of 160 Kbps; 0 is generated three  times more frequently than  1. A coherent binary  PSK  modulator is  employed  to  transmit  these  bits  over  a  noisy  channel.  The  received  bits  are detected in a correlator fed with the basis function of unit energy (for this binary PSK scheme) as  the reference signal. The  receiver  makes  a decision in favour  of 1  if the correlator  output  is  positive, else  decides  in  favour  of  0. If  0  and  1  are

(a)  determine the transmitted signal energy per bit.
(b)  determine the basis function of unit energy for this binary PSK scheme.
(c)  determine  the  probability  that  the  receiver  makes  a  decision  in  favour  of  1 when  the  channel  noise  is  characterized  as  zero-mean  AWGN  with  power

20.  Transmission line transformation of a load Z  and Z is given by

(a)  Show  that  the  above  transformation  implies  that  the  impedance  Z  gets  * transformed to  Z for real Z.
(b)  What is the importance of the result derived in (a)?

21.  Consider a  parallel  plate wave-guide  with  plate  separation  d  as shown  in  Figure 21 electric and magnetic fields for the TEM-mode are given by

(a)  Determine the surface charge  densities p  on the plates at x = 0 and x = d.
(b)  Determine the surface current densities  J  on the same plates.
(c)  Prove that p and  J  satisfy the current continuity condition.

22.  Consider a  linear array  of  two half-wave  dipoles A  and B  as shown in Figure  22.

The  dipoles  are  4  apart  and  are  excited  in  such  a  way  that  the  current  on element B legs that on element A by 90° in phase.
(a)  Obtain  the  expression  for  the  radiation  pattern  for  E in  the  XY  plane
(b)  Sketch the radiation pattern obtained in (a).