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GATE EC – 2003 Electronics and Communication Engineering Question Paper

Q.1 – Q.30 Carry One Mark Each
1.  The  minimum  number  of  equations  required  to  analyze  the  circuit  shown  in Fig.Q.1 is

(a)  3  (b)  4  (c)  6  (d) 7

2.  A source of angular frequency 1 rad/sec has a source impedance consisting of resistance in  series with 1 H  inductance. The load  that will obtain the  maximum power transfer is
(a)  1         resistance
(b)  1          resistance in parallel with 1 H inductance
(c)  1          resistance in series with 1 F capacitor
(d)  1         resistance in parallel with 1 F capacitor

3.  A series RLC circuit has  a resonance frequency of 1 kHz and a quality factor Q = 100. If each R, L and C is doubled from its original value, the new Q of the circuit is
(a)  25  (b)  50  (c)  100  (d) 200

4.  The Laplace transform of i(t) is given by I s s s   = +
As t ‰        8  , the value of i(t) tends to
(a)  0  (b)  1  (c)  2  (d)

5.  The differential equation for the current i(t) in the circuit of Figure Q.5 is

6.  n-type silicon is obtained by doping silicon with
(a)  Germanium  (b)  Aluminum  (c)  Boron  (d) Phosphorus

7.  The band gap of silicon at 300 K is
(a)  1.36 eV  (b)  1.10 eV  (c)  0.80 eV  (d) 0.67 eV

8.  The intrinsic  carrier  concentration of  silicon  sample of  300  K is  1.5   × 10 /m . If after doping,  the number of majority  carriers is  5  ×  10 /m , the minority carrier  density is
(a)  4.50       ×  10 /m       (b)  3.33                          ×  10 /m
(c)  5.00       ×  10 /m         (d)  3.00                   ×  10 /m

9.  Choose  proper  substitutes  for  X  and  Y  to  make  the  following  statement  correct Tunnel  diode  and  Avalanche  photodiode  are  operated  in  X  bias  and  Y  bias respectively.
(a)  X: reverse, Y: reverse   (b)  X: reverse, Y: forward
(c)  X: forward, Y: reverse  (d)  X: forward, Y: forward

10.  For  an  n-channel  enhancement  type  MOSFET,  if  the  source  is  connected  at  a higher  potential than  that  of  the bulk (i.e. V   > 0), the threshold  voltage V    of
the MOSFET will
(a)  remain unchanged    (b)  decrease
(c)  change polarity      (d)  increase

11.  Choose  the correct match for input resistance  of various amplifier configurations shown below.

Configuration  Input resistance
CB: Common Base  LO: Low
CC: Common Collector  MO: Moderate
CE: Common Emitter  HI: High
(a)  CB-LO, CC-MO, CE-HI   (b)  CB-LO, CC-HI, CE-MO
(c)  CB-MO, CC-HI, CE-LO   (d)  CB-HI, CC-LO, CE-MO

12.   The circuit shown in figure is best described as a
(a)  bridge rectifier
(b)  ring modulator
(c)  frequency discriminatory
(d)  voltage doubler

13.  If the input  to the ideal  comparator  shown  in  figure is  a  sinusoidal signal  of  8V (peak  to  peak)  without  any  DC  component,  then  the  output  of  the  comparator has a duty cycle of

(a)  1
2   (b)  1               3   (c)  1               6   (d)  12

14.  If  the  differential  voltage  gain  and  the  common  mode  voltage  gain  of  a differential  amplifier  are  48  dB  and  2  dB  respectively,  then  its  common  mode rejection ratio is
(a)  23 dB  (b)  25 dB  (c)  46 dB  (d) 50 dB

15.  Generally, the gain of a transistor amplifier falls at high frequencies due to the
(a)  internal capacitances of the device
(b)  coupling capacitor at the input
(c)  skin effect
(d)  coupling capacitor at the output

16.  The number of distinct Boolean expression of 4 variables is
(a)  16  (b)  256  (c)  1024  (d) 65536

17.  The minimum number of comparators required to build an 8 it flash ADC is
(a)  8  (b)  63  (c)  255  (d) 256

18.  The output of the 74 series of TTL gates is taken from a BJT in
(a)  totem pole and common collector configuration
(b)  either totem pole or open collector configuration
(c)  common base configuration
(d)  common collector configuration

19.  Without any additional circuitry, an 8:1 MUX can be used to obtain
(a)  some but not all Boolean functions of 3 variables
(b)  all function of 3 variables but none of 4 variables
(c)  all functions of 3 variables and some but not all of 4 variables
(d)  all functions of 4 variables

20.  A  0  to  6  counter  consists  of  3  flip  flops  and  a  combination  circuit  of  2  input gate(s). The combination circuit consists of
(a)  one AND gate      (b)  one OR gate
(c)  one AND gate and one OR gate  (d)  two AND gates

21.  The Fourier series expansion of a real periodic signal with fundamental frequency
ƒ 8  ( )               p j nf t  2 f is given by  g t c e =              it is given that C  = 3 + j5. Then C is
(a)  5+j3  (b)  -3-j5  (c)  -5+j3  (d) 3-j5

22.  Let  x(t)  be  the  input  to  a  linear,  time-invariant  system.  The  required  output  is
4x(t-2). The transfer function of the system should be

23.  A  sequence x(n)  with  the  z-transform X(z) =  z z z z + – + – 2 2 3        is  applied  as an  input  to  a  linear,  time-invariant  system  with  the  impulse  response  h(n)  =
2 d (n-3) where

24.  Figure  shows  the  Nyquist  plot  of  the  open-loop  transfer  function  G(s)H(s)  of  a system. If G(s)H(s) has one right hand pole, the closed loop system is
(a)  always stable
(b)  unstable with one closed loop right hand pole
(c)  unstable with two closed loop right hand poles
(d)  unstable with three closed loop right hand poles

25.  A  PD  controller  is  used  to  compensate  a  system.  Compared  to  the
uncompensated system, the compensated system has
(a)  a higher type number   (b)  reduced damping
(c)  higher noise amplification  (d)  larger transient overshoot

26.  The  input  to  a  coherent  detector  is  DSB-SC  signal  plus  noise.  The  noise  at  the detector output is
(a)  the in-phase component  (b)  the quadrature-component
(c)  zero      (d)  the envelope

27.  The  noise  at  the  input  to  an  ideal  frequency  detector  is  white.  The  detector  is operating above threshold. The  power spectral density of the noise at the output is
(a)  raised cosine  (b)  flat  (c)  parabolic  (d) Gaussian

28.  At a given probability of error, binary coherent FSK is inferior to binary coherent PSK by
(a)  6 dB  (b)  3 dB  (c)  2 dB  (d) 0 dB

29.  The unit of      ×  H is
(a)  Ampere      (b)  Ampere/meter
(c)  Ampere/meter              (d)  Ampere-meter  2

30.  The  depth  of  penetration  of  electromagnetic  wave  in  a  medium  having conductivity   s  at  a  frequency  of 1 MHz  is  25 cm. The depth  of  penetration at  a frequency of 4 MHz will be
(a)  6.25 cm  (b)  12.50 cm  (c)  50.00 cm  (d) 100.00 cm

Q.31 – Q.90 Carry Two Marks Each

31.  Twelve 1    resistances are used as edges to form a cube. The resistance between two diagonally opposite corners of the cube is

(a)  5            (b)  1                    (c)  6                    (d)  3

32.  The  current flowing through the resistance R in  the circuit in figure has the  form P cos 4t, where P is     M=0.75H
1/10.24F

(a)  (0.18+j0.72)
(b)  (0.46+j1.90)
(c)  -(0.18+j1.90)
(d)  -(0.192+j0.144)

The  circuit  for  Q.33-34  is  given  in  figure.  For  both  the  questions,  assume  that  the switch S is in position 1 for a long time and thrown to position 2 at t = 0.

Q.33-34, after the switch is brought from position 1 to position 2 at t = 0, are

35.  An  input  voltage  v(t)  =  10 2 cos 10 10 3 cos 2 10 t t V + ° + + °                         is  applied  to  a series combination of resistance R = 1    and an inductance L = 1H. The resulting steady state current i(t) in ampere is

36.  The  driving  point  impedance  Z(s)  of  a  network  has  the  pole-zero  locations  as shown in figure. If Z(0) =3, then Z(s) is

37.  The impedance parameters Z  and Z  of the two-port network in figure are
38.  An n-type silicon bar 0.1 cm long and  m  in cross-sectional area has a majority carrier  concentration  of  5   ×   10 /m   and  the  carrier  mobility  is  0.13m /V-s  at  300K. if the charge of an electron is 1.6 × 10  coulomb, then the resistance of the  bar is
(a)  10      ohm  (b)  10        ohm  (c)  10         ohm  (d) 10  ohm

39.   The electron concentration in a sample of uniformly doped n-type silicon at 300 K varies  linearly  from  10 /cm   at  x  =  0  to  6   ×   10 /cm   at  x  =  2 m.  Assume  situation that electrons are supplied to keep this concentration gradient constant with  time.  If  electronic  charge  is  1.6 × 10   coulomb  and  the  diffusion  constant
D  = 35 cm /s, the current density in the silicon, if no electric field is present, is
(a)  zero      (b)  -112 A/cm
(c)  +1120 A/cm            (d)  -1112 A/cm

40.  Match items in Group 1 with items in Group 2, most suitably.

Group 1  Group 2
P    LED  1   Heavy doping
Q   Avalanche photodiode  2   Coherent radiation
R   Tunnel diode  3   Spontaneous emission
S   LASER  4   Current gain

41.  At  300  K,  for  a  diode  current  of  1  mA,  a  certain  germanium  diode  requires  a forward  bias  of  0.1435V, whereas a  certain  silicon  diode requires  a forward  bias of  0.718V.  Under  the  conditions  stated  above,  the  closest  approximation  of  the ratio of reverse saturation current in germanium diode to that in silicon diode is
(a)  1  (b)  5  (c)  4                                        ×  10   (d) 8      ×  10

42.  A particular green LED emits light of wavelength 5490°A. The energy bandgap of the semiconductor material used there is (Planck‘s constant = 6.626 × 10 J-s)  – 34
(a)  2.26 eV  (b)  1.98 eV  (c)  1.17 eV  (d) 0.74 eV

43.  When  the  gate-to-source  voltage  (V  )  of  a  MOSFET  with  threshold  voltage  of GS
400mV,  working  in  saturation  is  900  mV,  the  drain current  in  observed to  be  1 mA.  Neglecting  the  channel  width  modulation  effect  and  assuming  that  the MOSFET  is  operating  at  saturation,  the  drain  current  for an applied V   of  1400 mV is
(a)  0.5 mA  (b)  2.0 mA  (c)  3.5 mA  (d) 4.0 mA

44.  If P  is  Passivation,  Q  is  n-well implant,  R  is  metallization  and  S  is  soruce/drain diffusion, then the order in which they are carried out in a standard n-well CMOS fabrication process, is
(a)  P-Q-R-S  (b)  Q-S-R-P  (c)  R-P-S-Q  (d) S-R-Q-P

45.  An  amplifier without feedback has a voltage gain of 50, input resistance of 1 K  and  output  resistance  of  2.5  K   .  The  input  resistance  of  the  current-shunt negative  feedback  amplifier  using  the  above  amplifier  with  a  feedback  factor  of 0.2, is
(a)  1              (b)  1                  (c)  5 K              (d) 11 K            K

46.  In  the amplifier circuit shown in figure, the values of R  and R   are such that the transistor  is  operating  at  V =  3V  and  I    =  1.5mA  when  its   ß   is  150.  For  a transistor with  ß  of 200, the operating point (V I  ) is
(a)  (2V, 2 mA)
(b)  (3V, 2 mA)
(c)  (4V, 2 mA)
(d)  (4V, 1 mA)

47.  The  oscillator  circuit  shown  in  figure  has  an  ideal  inverting  amplifier.  Its frequency of oscillation (in Hz) is

48.  The output voltage of the regulated power supply shown in figure is

(a)  3V  (b)  6V  (c)  9V  (d) 12V

49.  The action of a JFET in its equivalent circuit can best be represented as a
(a)  Current Controlled Current Source
(b)  Current Controlled Voltage Source
(c)  Voltage Controlled Voltage Source
(d)  Voltage Controlled Current Source

50.  If  the  op-amp  in  figure  is  ideal, the  output  voltage  V    will     (a)  1V

(b)  6V
(c)  14V
(d)  17V

51.  Three  identical  amplifiers  with  each  one  having  a  voltage  gain  of  50,  input resistance of 1 K    and output resistance of 250   , are cascaded. The open circuit voltage gain of the combined amplifier is
(a)  49 dB  (b)  51 dB  (c)  98 dB  (d) 102 dB

52.  An  ideal  sawtooth  voltage  waveform  of  frequency  500  Hz  and  amplitude  3V  is generated by charging a capacitor of 2  F in every cycle. The charging requires
(a)  constant voltage source of 3 V for 1 ms
(b)  constant voltage source of 3 V for 2 ms
(c)  constant current source of 3 mA for 1 ms
(d)  constant current source of 3 mA for 2 ms

53.  The  circuit  shown  in  figure  has  4  boxes  each  described  by  inputs  P,  Q,  R  and outputs Y, Z with
=     Y P Q R

The circuit acts as a
(a)  4 bit adder giving P + Q  (b)  4 bit subtractor-giving P – Q
(c)  4 bit subtractor-giving Q – P  (d)  4 bit adder giving P + Q + R

54.  If the functions W, X, Y and Z are as follows
Then
(a)  W  = Z, X =  Z   (b)  W = Z, X = Y  (c)  W = Y  (d) W = Y =  Z

55.  A 4 bit  ripple counter  and  a 4 bit  synchronous counter are  made using flip-flops having  a  propagation  delay  of  10  ns  each. If  the  worst  case  delay  in  the  ripple
counter and the synchronous counter be R and S respectively, then
(a)  R = 10 ns, S = 40 ns    (b)  R = 40 ns, S = 10 ns
(c)  R = 10 ns, S = 30 ns    (d)  R = 30 ns, S = 10 ns

56.  The DTL, TTL, ECL and CMOS families of digital ICs are compared in the following 4 columns

(P)  (Q)  (R)  (S)
Fanout is minimum  DTL  DTL  TTL  CMOS
Power consumption is minimum  TTL  CMOS  ECL  DTL
Propagation delay is minimum  CMOS  ECL  TTL  TTL
The correct column is
(a)  P  (b)  Q  (c)  R  (d) S

57.  The  circuit  shown  in  figure  is  a  4-bit DAC
The  input  bits 0  and 1 are represented by 0 and 5 V respectively. The OP AMP is ideal, but all the resistances and the 5V  inputs  have  a  tolerance  of   ± 10%. The  specification  (rounded  to  the nearest  multiple  of  5% )  for  the
tolerance of the DAC is
(a)       ± 35%   (b)              ± 20%   (c)              ± 10%   (d)         ± 5%

58.  The circuit shown in figure converts

(a)  BCD to binary code    (b)  Binary to excess œ 3 code
(c)  Excess œ 3 to Gray code  (d)  Gray to Binary code

59.  In  the circuit shown in Figure, A is a parallel in, parallel-out 4-bit register, which loads  at  the rising  edge  of  the  clock  C.  The  input  lines  are connected  to a  4-bit bus, W. Its output acts as the input to a 16 × 4 ROM whose output is floating when the enable input E is 0. A partial table of the contents of the ROM is as follows Address  0  2  4  6  8  10  11  14
Data  0011  1111  0100  1010  1011  1000  0010  1000

The clock to the register is shown, and the data on the W bus at time t  is 0110. The data on the bus at time t  is
(a)  1111  (b)  1011  (c)  1000  (d) 0010

60.  In  an  8085  microprocessor, the  instruction  CMP  B  has  been  executed  while  the content of the accumulator is less than that of register B. As a result
(a)  Carry flag will be set but Zero flag will be reset
(b)  Carry flag will be reset but Zero flag will be set
(c)  Both Carry flag and Zero flag will be reset
(d)  Both Carry flag and Zero flag will be set

61.  Let  X  and  Y  be  two  statistically  independent  random  variables  uniformly distributed in the ranges  (-1,1) and  (-2,1) respectively. Let  Z  = X + Y. then  the probability that [Z = -2] is

(a)  zero  (b)  1
(c)  1               3   (d)  1           12

62.  Let  P  be  linearity,  Q  be  time-invariance,  R  be  causality  and  S  be  stability.  A discrete time system has the input-output relationship,
where  x(n)  is  the  input  and  y(n)  is  the  output.  The  above  system  has  the properties
(a)  P, S but not Q, R      (b)  P, Q, S but not R
(c)  P, Q, R, S      (d)  Q, R, S but not P

Data for       are given below. Solve the problems and choose the correct answers.  Q.63-64
The  system under  consideration is an  RC low-pass filter  (RC-LPF) with R  =  1.0 k    and  C = 1.0 F.

63.  Let  H(f)  denote  the  frequency  response  of  the  RC-LPF.  Let  f   be  the  highest
(a)  327.8  (b)  163.9  (c)  52.2  (d) 104.4

64.  Let  t (f)  be the group  delay  function  of  the given RC-LPF and f   = 100  Hz. Then
(a)  0.717  (b)  7.17  (c)  71.7  (d) 4.505

Data  for are  given  below.  Solve  the  problems  and  choose  the  correct   Q.65  – 66 answers. X(t) is a random process with a constant mean value of 2 and the autocorrelation

65.  Let X be the Gaussian random variable obtained by sampling the process at t = t

66.  Let Y and Z be the random variables obtained by sampling X(t) at t =2 and t = 4 respectively. Let W = Y œ Z. The variance of W is
(a)  13.36  (b)  9.36  (c)  2.64  (d) 8.00

67.  Let  x(t) = 2cos(800 p t) + cos(1400 p t). x(t) is sampled with the rectangular pulse train  shown  in  figure.  The  only  spectral  components  (in  kHz)  present  in  the sampled signal in the frequency range 2.5 kHz to 3.5 kHz are

68.  The  signal  flow  graph  of  a  system  is  shown  in  figure.  The  transfer  function

69.  The root locus of the system  G s H s s s s =             has the break-away point located at
(a)  (-0.5,0)  (b)  (-2.548,0)  (c)  (-4,0)  (d) (-0.784,0)

70.  The  approximate  Bode  magnitude  plot  of a  minimum-phase  system is  shown  in figure. The transfer function of the system is

71.  A second-order system has the transfer function  =
with r(t) as the unit-step function, the response c(t) of the system is represented by

72.  The  gain  margin  and  the  phase  margin  of  a  feedback  system  with

73.  The zero-input response of a system given by the state-space equation

74.  A  DSB-SC  signal  is  to be generated  with  a  carrier  frequency f   =  1MHz  using  a nonlinear device with the input-output characteristic

where  a  and a   are constants.  The output of the nonlinear device can be filtered by an appropriate band-pass filter.

The  data  for  Q.75  œ  76  are  given  below.  Solve  the  problems  and  choose  the  correct answers.

75.  c(t)  and  m(t)  are  used  to  generate  an  AM  signal.  The  modulation  index  of  the generated AM signal is 0.5. Then the quantity  Total sideband power.
Carrier power is
(a)  1
2   (b)  1               4   (c)  1               3   (d)  1           8

76.  c(t) and m(t) are used to generate  an FM signal. If the peak frequency deviation of  the  generated  FM  signal  is three times the transmission bandwidth of the  AM

77.  Choose the correct one from among the alternatives A, B, C, D after matching an item in Group 1 with the most appropriate item in Group 2.

Group 1  Group 2
P  Ring modulator  1  Clock recovery
Q  VCO  2  Demodulation of FM
R  Foster-Seely discriminator  3  Frequency conversion
S  Mixer  4  Summing the two inputs
5  Generation of FM
6  Generation of DSB-Sc

78.  A super heterodyne receiver is to operate in the frequency  range 550 kHz œ  1650 kHz,  with  the  intermediate  frequency  of  450  kHz.  Let  R  =
required capacitance ratio of the local oscillator and I denote the image frequency
(in kHz) of the incoming signal. If the receiver is tuned to 700 kHz, then
(a)  R = 4.41, I = 1600    (b)  R = 2.10, I = 1150
(c)  R = 3.0, I = 1600    (d)  R = 9.0, I = 1150

79.  A sinusoidal signal  with peak-to-peak amplitude of 1.536 V is quantized into 128 levels using a mid-rise uniform quantizer. The quantization noise power is
(a)  0.768 V  (b)  48                   ×  10 V   (c)  12       ×  10 V     (d) 3.072 V

80.  If E ,  the energy per bit  of  a binary  digital signal,  is  10   watt-sec and the one-sided power spectral density of the white noise, N  = 10  W/Hz, then the output SNR of the matched filter is
(a)  26 dB  (b)  10 dB  (c)  20 dB  (d) 13 dB

81.  The input to a linear delta modulator having a step-size Í = 0.628 is a sine wave with frequency f   and peak amplitude E . If the sampling frequency f  = 40 kHz, the combination of the sine-wave frequency and the peak amplitude, where slope overload will take place is
(a)  0.3 V    8 kHz
(b)  1.5 V    4 kHz
(c)  1.5 V    2 kHz
(d)  3.0 V    1 kHz

82.  If  S  represents  the  carrier  synchronization  at  the  receiver  and       represents  the bandwidth efficiency, then the correct statement for the coherent binary PSK is
(a)          = 0.5, S is required   (b)                     = 1.0, S is required
(c)           = 0.5, S is not required  (d)                = 1.0, S is not required

83.  A  signal  is  sampled  at  8  kHz  and  is  quantized  using  8-bit  uniform  quantizer. Assuming SNR  for a  sinusoidal  signal, the correct statement for PCM signal with a bit rate of R is
(a)  R = 32 kbps, SNR     = 25.8 dB  (b)  R = 64 kbps, SNR         = 49.8 dB
(c)  R = 64 kbps, SNR      = 55.8 dB  (d)  R = 32 kbps, SNR        = 49.8 dB

84.  Medium 1 has the electrical permitivity  e =1.5  e  farad/m and occupies the region to  the  left  of  x  =  0  plane.  Medium  2  has  the  electrical  permitivity   e   =  2.5   e  farad/m and occupies the region to the right of x = 0 plane. If E  in medium 1 is E u u u = – +  2 3 1            volt/m, then E  in medium 2 is

85.  If the electric  field intensity is given by E xu yu zu =                 volt/m, the potential difference between X(20,0) and Y(1,2,3) is
(a)  +1 volt  (b)  -1 volt  (c)  +5 volt  (d) +6 volt

86.  A uniform plane wave traveling in air is incident  on the  plane boundary between air  and  another  dielectric  medium  with   e    =  4.  The  reflection  coefficient  for  the normal incidence, is
(a)  zero  (b)  0.5                      180°  (c)  0.333          0°  (d) 0.333      180°

87.  If  the  electric  field  intensity  associated  with  a  uniform  plane  electromagnetic wave traveling in a perfect dielectric medium is give by

88.  A  short-circuited  stub  is  shunt  connected  to  a  transmission  line  as  shown  in Figure. If Z  = 50 ohm, the admittance Y seen at the junction of the stub and the transmission line is

89.  A  rectangular  metal  wave-guide  filled  with  a  dielectric  material  of  relative permitivity   e   = 4 has  the inside  dimensions 3.0cm × 1.2cm. The cut-off  frequency for the dominant mode is
(a)  2.5 GHz  (b)  5.0 GHz  (c)  10.0 GHz  (d) 12.5 GHz

90.  Two  identical  antennas  are  placed  in  the       =  2  plane  as  shown  in  figure.  The elements have equal amplitude excitation with 180° polarity difference, operating at  wavelength     .  The  correct  value  of  the  magnitude  of  the  far-zone  resultant electric field strength normalized with that of a single element, both computed for f  = 0, is .