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GATE EC – 1998 Electronics and Communications Engineering Question Paper

SECTION – A
1.  For each of the following (1.1 œ 1.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or  D)  as  appropriate,  against  the  corresponding question  number in the answer book.

1.1  A network  has 7 nodes and  5 independent  loops. The number of branches in the network is
(a)  13  (b)  12  (c)  11  (d) 10

1.2  The eigen values of the matrix A =  0 1 are
(a)  1,1  (b)  -1,-1  (c)  j,-j  (d) 1,-1

f t s = +      ,  then the value of  1.3  If
(a)  cannot be determined   (b)  is zero
(c)  is unity      (d)  is infinite

1.4  The trigonometric Fourier series of a periodic time function can have only
(a)  cosine terms      (b)  sine terms
(c)  cosine and sine terms   (d)  d.c. and cosine terms

1.5  The nodal method of circuit analysis is based on
(a)  KVL and Ohm‘s law    (b)  KCL and Ohm‘s law
(c)  KCL and KVL      (d)  KCL, KVL and Ohm‘s law

1.6  Superposition theorem is NOT applicable to networks containing
(a)  nonlinear elements    (b)  dependent voltage sources
(c)  dependent current sources  (d)  transformers

1.7  The parallel RLC circuit shown in Fig.1.7 is in resonance. In this cicuit

1.8  A periodic signal x(t) of period  T is given by
The d.c. component of x(t) is

1.9  The  unit  impulse  response  of  a  linear  time  invariant  system  is  the  unit step function  u(t).  For  t>0,  the  response  of  the  system  ot  an  excitation

1.10  The short-circuit admittance matrix of a two-port network is …
The two port network is
(a)  non-reciprocal and passive  (b)  non-reciprocal and active
(c)  reciprocal and passive   (d)  reciprocal and active

1.11  The voltage across the terminals a and b in Fig.1.11 is
(a)  0.5 V
(b)  3.0 V
(c)  3.5 V
(d)  4.0 V
-
1.12   The  electron  and  hole  concentrations  in  a  intrinsic  semiconductor  are  n   and  p respectively.  When  doped  with  a  p-type  material,  these  change  to  n  and  p, respectively. Then

1.13  If   of BJT is related to its  ,  and       as follows:

1.14  The static characteristic of an adequately forward biased p-n junction is a straight line, if the plot is of
(a)  log I vs. log V  (b)  log I vs. V  (c)  I vs. log V  (d) I vs. V

1.15  A long specimen of p-type semiconductor material
(a)  is positively charged
(b)  is electrically neutral
(c)  has an electric field directed along its length
(d)  acts as a dipole

1.16  The Z-transform of the time function   n k  -  is

1.17  The number of roots of  s s s + + + = 5 7 3 0         in the left half of the s-plane is
(a)  zero  (b)  one  (c)  two  (d) three

1.18  The transfer function of a tachometer is of the form

1.19.  Consider  a  unity  feedback  control  system  with  open-loop  transfer  function. The steady state error of the system due to a unit step input is   G s s s = +      .

(a)  zero  (b)  K  (c)  1
K   (d) infinite

1.20.  The transfer function of a zero-order-hold system is

1.21.  In  the  Bode-plot  of a  unity feedback  control system, the  value of  phase  of G(j) at the gain cross over frequency is œ125°. The phase margin of the system is
(a)  -125°  (b)  -55°  (c)  55°    (d) 125°

1.22.  Consider a feedback control system with loop transfer fucntion
The type of the closed loop system is
(a)  zero  (b)  one  (c)  two  (d) three

1.23.  The transfer function of a phase lead controller is  1 3  . The maximum value of phase provided by this controller is
(a)  90°  (b)  60°  (c)  45°  (d) 30°

1.24.  The Nyquist plot of a phase transfer function g(j   ) H(j   ) of a system encloses the (-1,0) point. The gain margin of the system is
(a)  less than zero      (b)  zero
(c)  greater than zero     (d)  infinity

1.25  The transfer function of a system is
The characteristic equation of the system is

1.26  In  a  synchro error detector,  the output  voltage is  proportional to
t  is the rotor velocity and n equals
(a)  -2  (b)  -1  (c)  1  (d) 2

1.27  Two  identical  FETs,  each  characterissed  by  the  parameters   and  g r are connected in parallel. The composite FET is then characterized by the parameters

1.28  The circuit of Fig.1.28 is an example of feedback of the following type

(a)  current series
(b)  current shunt
(c)  voltage series
(d)  voltage shunt

1.29  In a differential amplifier, CMRR can be improved by using an increased
(a)  emitter resistance    (b)  collector resistance
(c)  power supply voltages  (d)  source resistance

1.30  From a  measurement  of  the  rise time of the output  pulse  of  an  amplifier whose input  is  a  small  amplitude  square  wave,  one  can  estimate the following parameter of the amplifier:
(a)  gain-bandwidth product  (b)  slow rate
(c)  upper 3-dB frequency   (d)  lower 3-dB frequency

1.31  A distorted sinusoidal has  the amplitudes  A A A > of the fundamental, second, harmonic, third harmonic, > respectively. The total harmonic distortion is

1.32  The emitter coupled pair of BJT‘s gives a linear transfer relation between the V differential output voltage and the differential input voltage   only when the a magnitude of   is less   times the thermal voltage, where   is
(a)  4  (b)  3  (c)  2  (d) 1

1.33  In a shunt-shunt negative feedback amplifier, as compared to the basic amplifier
(a)  both, input and output impedances, decrease
(b)  input impedance decreases but output impedance increases
(c)  input impedance increases but output impedance decreases
(d)  both, input and output impedances increase

1.34  A multistage  amplifier  has  a low-pass response with three  real poles  at s  =  – ,
and  . The approximate overall bandwidth B of the amplifier will be given by

1.35  A high Q-quartz crystal exhibits series resonance at the frequency   and parallel   resonance at the frequency  .   Then

1.36  One input  terminal of  high gain  comparator circuit is  connected to ground and a sinusoidal voltage is applied to the other input. The output of comparator will be
(a)  a sinusoid      (b)  a full rectified sinusoid
(c)  a half rectified sinusoid  (d)  a square wave

1.37  In  a  series  regulated  power  supply  circuit,  the  voltage  gain  A of  the  ”pass‘ transistor satisfies the condition:
(a)       A ‰  8   (b)  1          0   (c)  A  < 8            A =1    (d)  1            A 0

1.38  For  full  wave  rectification,  a  four  diode  bridge  rectifier  is  claimed  to have the following advantages over a two diode circuit:
(1)  less expensive transformer
(2)  smaller size transformer, and
(3)  suitability for higher voltage application.
Of these,
(a)  only (1) and (2) are true  (b)  only (1) and (3) are true
(c)  only (2) and (3) are true  (d)  (1), (2) as well as (3) are true

1.39  In  the  MOSFET  amplifier  of  Fig.1.39,  the  signal  outputs  V   and  V   obey the relationship

2.  For each of the following (2.1 œ 2.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or  D)  as  appropriate,  against  the  corresponding question  number in the answer book.

2.1  The minimum number of  2-input NAND gates required to implement the Boolean
function      , Z A B C =       assuming that A, B and C are available, is
(a)  two  (b)  three  (c)  five  (d) six

2.2  The noise margin of a TTL gate is about
(a)  0.2 V  (b)  0.4 V  (c)  0.6 V  (d) 0.8 V

2.3  In Fig.2.3, A = 1 and B =1, the input B is now replaced by a sequence 101010…. the outputs x and y will be
(a)  fixed at 0 and 1, respectively
(b)  x = 1010 …. while y = 0101 ….
(c)  x = 1010 …. and y = 0101 ….
(d)  fixed at 1 and 0, respectively

2.4  An  equivalent  2‘s  complement  representation  of  the  2‘s  complement  number 1101 is
(a)  110100  (b)  001101  (c)  110111    (d) 111101

2.5  The threshold voltage for each transistor in Fig.2.5, is 2V. For this circuit to work as an inverter, V  must take the values
(a)  -5 V and 0 V
(b)  -5 V and 5 V
(c)  -0 V and 3 V
(d)  3 V and 5 V

2.6  An I/O processor control the flow of information between
(a)  cache memory and I/O devices  (b)  main memory and I/O devices
(c)  two I/O devices      (d)  cache and main memories

2.7  Two 2‘s complement number having sign bits x and y are added and the sign bit of  the  result  is  z.  Then,  the  occurrence  of  overflow  is  indicated  by  the  Boolean function
(a)  x y z      (b)                                               x y z
(c)             x y z x y z +            (d)  xy + yz + zx

2.8  The advantage of using a dual slope ADC in a digital voltmeter is that
(a)  its conversion time is small  (b)  its accuracy is high
(c)  it gives output in BCD format  (d)  it does not require a comparator

2.9  For the identify  AB AC BC AB AC + + = +                 , the dual form is

2.10  An instruction used to set the carry Flag in a computer can be classified as
(a)  data transfer      (b)  arithmetic
(c)  logical      (d)  program control

2.11  Fig.2.11  shows  a  mod-K
counter, here K is equal to

2.12  The current I through resistance r in the circuit shown in Fig.2.12 is

2.13  The  K-map  for  a Boolean  function  is shown  in Fig.2.13. The number of essential prime implicants for this function is

2.14  For  small  signal  a.c. operation, a practical forward biased diode  can  be modeled as
(a)  a resistance and a capacitance in series
(b)  an ideal diode and resistance in parallel
(c)  a resistance and an ideal diode in series
(d)  a resistance

2.15  The amplitude spectrum of a Gaussian pulse is
(a)  uniform      (b)  a sine function
(c)  Gaussian      (d)  an impulse function

2.16  The ACF of a rectangular pulse of duration T is
(a)  a rectangular pulse of duration T
(b)  a rectangular pulse of duration 2T
(c)  a triangular pulse of duration T
(d)  a triangular pulse of duration 2T

2.17  The image channel selectivity of super heterodyne receiver depends upon
(a)  IF amplifiers only     (b)  RF and IF amplifiers only
(c)  Preselector, RF and IF amplifiers
(d)  Preselector, and RF amplifiers only

2.18  In a PCM system with uniform quantization, increasing the number of bits from 8 to 9 will reduce the quantization noise power by factor of
(a)  9  (b)  8  (c)  4  (d) 2

2.19  The  Fourier  transform  of  a  function  x(t)  is  X(f).  The  Fourier  transform  of

2.20  Flat top sampling of low pass signals
(a)  gives rise to aperture effect  (b)  implies over sampling
(c)  leads to aliasing      (d)  introduces delay distortion
2.21  A DSB-SC signal is generated using the carrier cos t +  and modulating singal
x(t). The envelope of the DSB-SC signal is
(a)  x(t)      (b)

(c)  only positive portion of x(t)  (d)  x(t) cos

(a)  the same as FDM     (b)  the same as TDM
(c)  a combination of FDM and TDM
(d)  quite different from FDM and TDM

2.23  The Fourier transform of a voltage signal x(t) is X(f). The unit of  X f is

(a)  volt  (b)  volt-sec  (c)  volt/sec  (d) volt

2.24  Compression in PCM refers to relative compression of
(a)  higher signal amplitudes  (b)  lower signal amplitudes
(c)  lower signal frequencies  (d)  higher signal frequencies

2.25  For a given data rate, the bandwidth  B of a BPSK signal and the bandwidth  B  of the OOK signal are related as

2.26  The spectral density of a real valued random process has
(a)  an even symmetry    (b)  an odd symmetry
(c)  a conjugate symmetry  (d)  no symmetry

2.27  The probability density function of the envelope of narrow band Gaussion noise is
(a)  Poisson  (b)  Gaussian  (c)  Rayleigh  (d) Rician

2.28  The intrinsic impedance of copper at high frequencies is
(a)  purely resistive      (b)  purely inductive
(c)  complex with a capacitive component
(d)  complex with an inductive component

2.29  The Maxwell equation  D V H J t × =         is based on

(a)  Ampere‘s law
(b)  Gauss‘ law
(d)  Coulomb‘s law

2.30  All  transmission  line  sections shown  in  Fig.2.30  have characteristic impedance R j + .  The  input  impedance
Z equals
i n

2.31  The  time  averages  Poynting  vector,  in  W/m         ,  for  a  wave  with  2

2.33  The depth of penetration of wave in a lossy dielectric increases with increasing
(a)  conductivity  (b)  permeability  (c)  wavelength  (d) permittivity

2.34  The polarization of wave with electric field vector  E E e a a = +                    is
(a)  linear      (b)  elliptical
(c)  left hand circular      (d)  right hand circular

2.35  The vector H in the far field of an antenna satisfies
(a)  . 0 and  0   =   × = H H                   (b)  . 0 and  0              ×   H H
(c)  . 0 and  0   =   ×   H H                   (d)  . 0 and  0               × = H H

2.36  The  radiation  resistance  of  a  circular  loop  of  one  turn  is  0.01   .  The  radiation resistance of five turns of such a loop will be
(a)  0.002          (b)  0.01             (c)  0.05               (d) 0.25

2.37  An antenna in free space receives 2 W of power when the incident electric field is 20 mV/m rms. The effective aperture of the antenna is
(a)  0.005 m          (b)  0.05 m          (c)  1.885 m             (d) 3.77 m

2.38  The maximum usable frequency of an ionospheric layer at 60° incidence and with 8 mHz critical frequency is

(a)  16 MHz  (b)  16                   MHz  (c)  8 MHz

2.39  A loop is  rotating  about  the y-axis in  a magnetic  field  E B t a T.            The voltage in the loop is
(a)  zero      (b)  due to rotation only
(c)  due to transformer action only
(d)  due to both rotation and transformer action

2.40  The far field of an antenna varies with distance r as
(a)  1                                    (c)                      (d)  1

3.  Determine the frequency of resonance and the resonant impedance of the parallel  circuit shown in Fig.3. What happens when L = CR ?

4.   A  voltage  source  of  internal  impedance  R jX +  supplies  power  to  a  load  of impedance  R jX +  in  which  only  R is  variable.  Determine  the  value  of  R for maximum  power  transfer  from  the  source  to  the  load.  Also,  find  the  numerical value of  R if the source impedance is 3.0    (purely resistive) and  X is 4.0   .

5.  (a)  Draw the transfer characteristic of the circuit of Fig.5, assuming both  D  and D  to be ideal.
(b)  How would the characteristic change if D  is ideal, but D   is non-ideal in that it has forward resistance of 10    and a reverse resistance of infinity?

6.  Given an irrotational vector field
gd gd gd gd  ( ) ( ) ( )

Find V.  F      at (1,1,-2).

SECTION B
(50 Marks)
Answer any TEN questions. Each question carries 5 marks.

7.  The loop transfer function of a single loop control system is given by

Using  the  Nyquist  criterion,  find  the  condition  for  the  closed  loop  system to be stable.

8.  The characteristic equation of a feedback control system is
4 3 2       s s s s K + + + + = 20 15 2 0
(i)  Determine the range of K for the system to be stable.
(ii)  Can the  system be marginally stable? If so, find the required value  of K and the frequency of sustained oscillation.

9.  Draw a signal flow graph for the following set of algebraic equations:

10.  Consider  the  system  shown  in  Fig.10.  Determine  the  value  of  such  that  the damping  ratio  is  0.5.  Also  obtain  the  values  of  the  rise  time  t and  maximum overshoot  M in its step response.

11.  Determine the input impedance of the circuit of Fig.11 and investigate if it can be inductive.

12.  Find  the  value of  R  in  the  circuit  of  Fig.12 for generating  sinusoidal oscillations. Find the frequency of oscillations.

13.  In  the  circuit  of  Fig.13,  determine  the  resistance  R   seen  by  the  output terminals. Ignore the effects of  R R    and  .

14.  The  JFET  in  the  circuit  of  Fig.14  is  characterized  by
the parameters  4  and  4 . I MA V V = = -
DSS p

15.  The  mod-5  counter  shown  in  Fig.15  counts  through  states
Q Q Q  =  000, 001, 010, 011 and 100
(a)  Will the counter lockout if it happen to be in any one of the unused states?
(b)  Find the maximum rate at which the counter will operate satisfactorily.
Assume  the  propagation  delays  of  flip-flop  and  AND  gate  to  be  t    and t
respectively.

16.  For  the  TTL  circuit  shown  in  Fig.16,  find  the  current  through  the  collector  of transistor Q  when V  = 0.2V.
ß   Assume     V V V V = = = 0.2 , 100 and  0.7 .                 The  a  of  Q in its inverse active
( ) ( )
CE sa t B E sa t
mode is 0.01.

17.  Write  a  short  assembly  language  program,  without  using  any  arithmetic instruction, to  store hexadecimal  5D in  the flag register of  8085 microprocessor.
Data  in  other  registers  of  the  processor  must  not  alter  upon  executing  this program.

18.  Implement  a  monostable  multivibrator  using  the  timer  circuit  shown  in  Fig.18.
Also determine an expression for ON time T of the output pulse.

19.  The  pulse  rate  in  a  DM  system  is  56,000  per  sec.  The  input  signal  is  5 cos(2 p 1000t)  +  2cos(2 p 2000t) V, with t  in sec.  Find  the minimum value  of  step size  which will  avoid slop  overload  distortion. What will  be the  disadvantages  of choosing a value of larger than the minimum?

20.  An  SSB  signal  is  demodulated  by  using  a  synchronous  demodulator.  However, the locally arranged carrier has a phase error    . Determine the effect of the error on  demodulation.  What  will  be  the  effect  of  this error  if  the  input is  DSB-SC  in place of SSB?

21.  White noise of two-sided spectral density 2  ×  10  V /Hz is applied to a simple R-C low  pass  filter  whose  3dB  cut  off  frequency  is  4  kHz.  Find  the  mean  squared value of the noise output.

22.  Consider  a  rectangular  pulse  g(t)  existing  between  t=   and t= . -               Find  and sketch the pulse obtained by convolving g(t) with itself. The Fourier transform of g(t)  is a sine function. Write down  to Fourier transform of  the pulse obtained by the above convolution.

23.  A rectangular wave  guide with inner dimensions  6 cm  ×  3 cm has been designed for a single mode operation. Find the possible frequency range of operations such that  the  lowest  frequency  is  5%   above  the  cut  off  and  the  highest  frequency  is 5%  below the cut off of the next higher mode.

( )   ß -  j t z 24.  A  plane  wave  with  E e a = 10         is  incident  normally  on  a  thick  plane
conductor  lying  in  the  x-y  plane.  Its  conductivity  is  6   ×   10   S/m  and  surface  impedance  is  5   ×   10     45°   . Determine the propagation  constant  and  the  skin  depth in the conductor.
25.  The electric field vector of a wave is given as

Its frequency is 10 GHz.
(i)  Investigate if this wave is a plane wave.
(ii)  Determine its propagation constant, and
(iii) Calculate the phase velocity in y-direction.

26.  The region between a pair of parallel perfectly conducting planes of infinite extent in the y- and œz directions is partially filled with a dielectric as shown in Fig.26. A 30  GHz  TE wave  is  incident  on  the  air  dielectric  interface  as  shown.  Find  the  10
x  VSWR at the interface.