GATE EC 2000 Electronics and Communication Engineering Question Paper
SECTION – A  (75 marks)
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 answers in the boxes  corresponding  to  the  questions  only  on  the  FIRST  sheet  of  the  answer book.

1.1  In the circuit of Fig.P.11, the voltage v(t) is

1.2  In the circuit of Fig.P1.2, the value of the voltage source E is                      0V +  2
-

1.4  In  the  differential  amplifier  of  Fig.P1.4,  if  the source  resistance  of  the  current  source I is infinite, then the common-mode gain is
(a)  zero
(b)  infinite
(c)  indeterminate

1.5  In the circuit of Fig.P.15,  V is
(a)  -1 V
(b)  2 V
(c)  +1 V
(d)  +15 V

1.6  Introducing  a  resistor  in  the  emitter  of  a  common  amplifier  stabilizes  the  dc operating point against variations in
(a)  only the temperature    (b)  only the                     ß  of the transistor
(c)  both temperature and  ß   (d)  none of the above

1.7  The current gain of a bipolar transistor drops at high frequencies because of
(a)  transistor capacitances  (b)  high current effects in the base
(c)  parasitic inductive elements  (d)  the Early effect

1.8  An  amplifier  with  resistive negative  feedback  has  two  left half-plane poles in  its open-loop transfer function. The amplifier
(a)  will always be unstable at high frequencies
(b)  will be stable for all frequencies
(c)  may be unstable, depending on the feedback factor
(d)  will oscillate at low frequencies

1.9  If the op-amp in Fig.P.1.9, is ideal, then  v , is

1.10  The configuration of Fig.P.1.10 is a
(a)  precision integrator
(b)  Hartley oscillator
(c)  Butterworth highpass filter

(d)  Wien-bridge oscillator

1.11  Assume  that  the  op-amp  of  Fig.P1.11  is  ideal.  If  v is  a  triangular  wave,  then  v will be
(a)  square wave
(b)  triangular wave
(c)  parabolic wave
(d)  sine wave

1.12  The  Fourier Transform of  the signal  x t e =  is  of the following form, where A and B are constants:

1.13  A  system  with  an  input  x t and  output  y t is  described  by  the  relation: y t tx t = .  This system is
(a)  linear and time-invariant  (b)  linear and time varying
(c)  non-linear and time-invariant  (d)  non-linear and time-varying

1.15  An  8  bit  successive  approximation  analog  to  digital  converter  has  full  scale reading of 2.55 V and its conversion  time for an  analog input of 1V is  20 s.  The conversion for a 2V input will be
(a)  10  s  (b)  20  s  (c)  40  s  (d) 50  s

1.16  The number of hardware interrupts (which require an external signal to interrupt) present in an 8085 microprocessor are
(a)  1  (b)  4  (c)  5  (d) 13

1.17  The most commonly used amplifier in sample and hold circuits is
(a)  a unity gain inverting amplifier
(b)  a unity gain non-inverting amplifier
(c)  an inverting amplifier with a gain of 10
(d)  an inverting amplifier with a gain of 100

1.18  The number of comparators in a 4 bit flash ADC is
(a)  4  (b)  5  (c)  15    (d) 16

1.19.  For  the  logic  circuit  shown  in  Fig.P1.19,  the  required  input  condition  (A,B,C)  to make the output (X)=1 is

(a)  1, 0, 1

(b)  0, 0, 1
(c)  1, 1, 1
(d)  0, 1, 1

1.20.  In  the  8085  microprocessor,  the  RST6  instruction  transfers  the  program execution to the following location
(a)  30 H  (b)  24 H  (c)  48 H    (d) 60 H

1.21.  The  magnitudes  of  the  open-circuit  and  short-circuit  input  impedances  of  a transmission line are 100    and 25    respectively. The characteristic impedance of the line is,
(a)  25          (b)  50                 (c)  75                  (d) 100

1.22.  A TEM wave is incident normally upon  a perfect conductor. The  E and H fields at the boundary will be, respectively.
(a)  minimum and minimum  (b)  maximum and maximum
(c)  minimum and maximum  (d)  maximum and minimum

1.23.  The frequency range for satellite communication is
(a)  1 KHz to 100 KHz     (b)  100 KHz to 10 KHz
(c)  10 MHz to 30 MHz    (d)  1 GHz to 30 GHz

1.24.  If the diameter of a  2  dipole antenna is increased from   to  ,     then its
(a)  bandwidth increases    (b)  bandwidth decreases
(c)  gain increases      (d)  gain decreases

1.25  The circuit of Fig.P1.25 represents a
(a)  low pass filter
(b)  high pass filter
(c)  band pass filter
(d)  band reject filter

2.  This question  consists of TWENTY-FIVE sub-questions  (2.1 œ 2.25) 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 answers in the
boxes  corresponding  to  the  questions  only  on  the  SECOND  sheet  of  the  answer book.
(a)  2, -2, 1, -1      (b)  2, 3, -2, 4
(c)  2, 3, 1, 4      (d)  None of the above

2.2.  Use the data of Fig.2(a). The current i in the circuit of Fig.(b) is

2.3.  For the circuit in Fig.P2.3, the voltage  v is
(a)  2V  (b)  1V
(c)  -1V                                                                         v   2
(d)  None of the above

2.4.  A  linear  time  invariant  system  has  an  impulse  response  e t  , 0  >  .  If  the  initial   2 t conditions are zero and the input is  e the output for t > 0 is   ,  3 t

(a)       e e -        (b)                                 e    3 2 t t                                                                     5t

(c)      e e +        (d)  None of the above   3 2 t t
15V

2.5.  In  the  circuit  of  Fig.P2.5,  assume  that  the  transistor  is  in
active region.  It has  a large   ß   and  its base-emitter  voltage  is
0.7V. The value of  I is
(a)  Indeterminate since      R is not given
(b)  1 mA
(c)  5 mA
(d)  10 mA

2.6.  If the op-amp in Fig.P2.6,  has  an input offset voltage of 5 mV and an open-loop voltage gain of 10,000, then  v will be
(a)  0V
(b)  5 mV
(d)  +50 V or œ50 V

2.7.  For the logic circuit shown in Fig.P2.7, the simplified Boolean expression for the output Y is
(a)  A+B+C
(b)  A
(c)  B
(d)  C

2.8.  For the 4 bit DAC shown in Fig.P2.8, the output voltage  v is
(a)  10 V  (b)  5 V  (c)  4 V  (d) 8 V

2.9.  A sequential circuit using D flip-flop and logic gates is shown in Fig.P2.9, where X and Y are the inputs and Z is the output. The circuit is

(a)  S œ R Flip-Flop with inputs X = R and Y = S
(b)  S œ R Flip-Flop with inputs X = S and Y = R
(c)  J œ K Flip-Flop with inputs X = J and Y = K
(d)  J œ K Flip-Flop with inputs X = K and Y = J

2.10.  The  contents  of  Register  (B)  and  Accumulator  (A)  of  8085  microprocessor are 49H and 3AH respectively. The contents of A and the status of carry flag (CY) and sign flag (S) after executing SUB B instructions are
(a)  A = F1, CY = 1, S =1   (b)  A = 0F, CY = 1, S =1
(c)  A = F0, CY = 0, S =0   (d)  A = 1F, CY = 1, S =1

2.11.  In  Fig.P2.11,  the  J  and  K  inputs  of  all  the  four  Flip-Flops  are  made  high.  The frequency of the signal at output Y is

(a)  0.833 KHz  (b)  1.0 KHz  (c)  0.91 KHz    (d) 0.77 KHz

2.12.  One  period  (0,T)  each  of  two  periodic  waveforms,  W   and  W   are  shown  in Fig.P2.12. The  magnitudes  of the n   Fourier series coefficients of W  and W , for  n  =  1, n odd, are respectively proportional to

2.13.  Let  u(t)  be  the  step  function.  Which  of  the  waveforms  in  Fig.P2.13(a)  œ  (d)
corresponds to the convolution of u(t) œ u(t œ 1) with u(t) œ u(t œ 2)?

2.14.   In Fig.P2.14, the steady state output voltage corresponding to the input voltage 3
+ 4 sin 100t V is

2.15.  In  a digital  communication  system employing  Frequency  Shift  Keying (FSK),  the 0  and  1  bit  are  represented  by  sine  waves  of  10  KHz  and  25  KHz  respectively.
These waveforms will be orthogonal for a bit interval of
(a)  45  sec  (b)  200  sec  (c)  50  sec  (d) 250  sec

2.16.  A message  m(t) band-limited to  the frequency  f has  a power  of  . P  The  power

2.17.  The Hilbert transform of  cos sin     t t       is  +

2.18.  A system has a phase response given by  ( ),  where   is  the angular frequency.  The phase delay and group delay at   =    are respectively given by

2.19.  A system described by the transfer function

2.20.  In  an  FM  system,  a  carrier  of  100  MHz  is modulated by  a  sinusoidal signal  of  5 KHz.  The  bandwidth  by  Carson‘s  approximation  is  1  MHz.  If  y(t)  =  (modulated 3 waveform) , than by using Carson‘s approximation, the bandwidth of y(t) around 300 MHz and the and the spacing of spectral components are, respectively.
(a)  3 MHz, 5 KHz      (b)  1 MHz, 15 KHz
(c)  3 MHz, 15 KHz      (d)  1 MHz, 5 KHz

2.21.  A  uniform  plane  wave  in  air  impinges  at  45°  angle  on  a  lossless  dielectric e material  with  dielectric  constant  .  The  transmitted  wave  propagates  in  a  30° e direction with respect to the normal. The value of   is
(a)  1.5  (b)  1.5   (c)  2  (d)  2

2.22.  For  an  8  feet  (2.4  m)  parabolic  disk  antenna  operating  at  4  GHz, the minimum distance required for far field measurement is closest to
(a)  7.5 cm  (b)  15 cm  (c)  15 m  (d) 150 m

2.23.  A rectangular wave guide has dimensions 1 cm   0.5 cm. Its cut-off frequency is
(a)  2 dB  (b)  5 dB  (c)  8 dB  (d) 12 dB

2.24.  A rectangular wave guide has dimensions 1 cm   0.5 cm. Its cut-off frequency is
(a)  5 GHz  (b)  10 GHz  (c)  15 GHz                                         (d) 20 GHz

2.25.  Two  coaxial  cables  1  and  2  are  filled  with  different  dielectric  constants
˜ ’
SECTION – B  (75 marks)
This  section  consists  of  TWENTY  questions  of  FIVE  marks  each.  Attempt  ANY  FIFTEEN questions  out  of  them.  If  more  number  of  questions  are  attempted,  score off the answers  not  be  evaluated,  else  only  the  first  fifteen  unscored  answers  will  be considered.
3.  For the circuit in Fig.P3
(a)  Find the  Thevenin equivalent of  the sub circuit faced by the  capacitor across the terminals a, b.
4.   For the circuit in Fig.P4, which is in steady state
(a)  Find  the  frequency         at  which  the  magnitude  of  the  impedance  across terminals a, b reaches a maximum.
(b)  Find the impedance across a, b at the frequency

5.  For  the  circuit  in  Fig.P5,  write  the  state  equations  using         and i  as  state

6.  The  network N  in  Fig.P6 consists  only  of  two  elements:  a resistor of  1  and  an inductor of L Henry. A 5 V source is connected at the input at t = 0 seconds. The inductor current is zero at t =0. The output voltage is found to be  5 ,  for   -
(a)  Find the voltage transfer function of the network.
(b)  Find L, and draw the configuration of the network.
(c)  Find the impulse response of the network.

7.  For the  linear,  time invariant system whose block  diagram is shown in Fig.P7(a), with input x(t) and output y(t),
(a)  Find the transfer function.
(b)  For the step response of the system [i.e. find y(t) when x(t) is a unit step
function and the initial conditions are zero]
(c)  Find y(t), if x(t) is as shown in Fig.P7(b), and the initial conditions are zero.

8.  A  certain  linear,  time-invariant  system  has  the  state  and  output  representation shown below:

(a)  Find the eigen values (natural frequencies) of the system.
(b)  If u(t) =      d (t) and  x x x t x t y t 0 0 0,  find  ,  and  , = =                                     for t > 0.
(c)  When the input is zero, choose initial conditions

9.  The block diagram of a feedback system is shown in Fig.P9(a).
(a)  Find the closed loop transfer function.
(b)  Find  the  minimum  value  of  G  for  which  the  step  response  of  the  system would exhibit an overshoot, as shown in Fig.P9(b).
(c)  For G  equal to twice  this minimum value, find the time period  T indicated in Fig.P9(b).

10.  (a)  For  Fig.P10(a),  Plot  v under  steady  state  conditions,  with  and  without  C. Assume that the diode is ideal.
(b)  Design a circuit using two ideal diodes, one resistor and two voltage sources that  would  convert  the  input  voltage  of  Fig.P10(b)  to  the  output  voltage  of Fig.P10(c). The resistor value need not be specified.

11.  For the amplifier of   Fig.P11,

(a)  What is the small-signal voltage gain,  ? A =
(b)  What is the approximate   if  A C  is removed?
(c)  What will   be if        C  is short-circuited?

12.  For a feedback amplifier, the open loop transfer function has three poles at 100k rad/s, 1 M  rad/s and 10  M rad/s. The low frequency open loop gain is  1000 and the feedback factor ( ß ) is 1. Use Bode plots to determine the phase margin of the amplifier. Is the amplifier stable?

13.  Fig.P13 shows a common base amplifier.
(a)  Write  expressions  for  the  time-constants  associated  with  the  capacitors,

(b)  What is the approximate lower cutoff frequency of the amplifier?

14.  For  the  CMOS  monostable  multi-vibrator  of  Fig.P14,  R  =  50  kW,  C  =  0.01 F, V V = 5 ,  and the CMOS NOR gates have a threshold voltage  V of 1.5 V.   is a trigger pulse  t  RC  as shown in the figure.
(a)  Plot           and   as functions of time.
(b)  Write the equation for     t ,  for t > 0.
(c)  Find the time period of the output pulse.

15.  The  operating  conditions  (ON  =  1,  OFF  =  0)  of  three  pumps  (x,y,z)  are  to  be monitored. x = 1 implies that pump X is on. It is required that the indicator (LED) on the panel should glow when a majority of the pumps fail.
(a)  Enter the logical values in the K-map in the format shown in Fig.15(a). derive the minimal Boolean sum  of  products expression whose output is  zero when a majority of the pumps fail.
(b)  The  above  expression  is  implemented  using  logic  gates,  and  point  P  is  the output  of this circuit, as shown in Fig.P15(b). P is at 0 V when a majority  of the  pumps  fails  and  is  at  5  V  otherwise.  Design  a  circuit  to  drive  the  LED using  this  output.  The  current  through  the  LED  should  be  10  mA  and  the voltage drop across it is 1V. Assume that P can source or sink 10 mA and a 5 V supply is available.

16.  A one-bit full adder is to be implemented using 8-to-1 multiplexers (MUX).
(a)  Write the truth table for sum (S) and carry to the next stage   in terms of  the  two  bits  (A, B)  and  carry  from the previous  stage  C The  truth  table  .
should be in the ascending order of (A,B, C ), i.e. (000,001,010,…etc.).
(b)  Implement S and      C using 8-to-1 multiplexers.

17.  (a)  The program and machine code for an 8085 microprocessor are given by

3E  MVI  A  C3
C3
00  NOP
80  ADD  B
3D  DEC  A
C2  JNZ  800A
0A
80
C3  JMP  800C
0C
80
D3  OUT  10
10
76  HLT
The starting address  of the above program is 7FFF H.  What would happen  if it is executed from 8000 H?
(b)  For the instructions given  below,  how many memory operations (read/write)
are performed during the execution in an 8085  P?
(c)  Write  an  instruction  which  takes  the  minimum  possible  time  to  clear  the accumulator of the 8085.

18.  A  band  limited  signal  x(t)  with  a       spectrum  X(f)  as  shown  in  Fig.P18(a)  is processed  as  shown  in  Fig.P18(b).  p(t)  is  a  periodic  train  of  impulses  as  in Fig.P18(c). The ideal bandpass filter has a passband from 26 KHz to 34 KHz.
(a)  Calculate the Fourier series coefficients  C in the Fourier expansion of p(t) in
(b)  Find the Fourier Transform of p(t).
(c)  Obtain and sketch the spectrum of  x t   .
(d)  Obtain and sketch the spectrum of  y t   .

19.  Zero  mean  white  Gaussian  noise  with  a  two-sided  power  spectral  density  of  4 W/Khz is passed through an ideal lowpass filter with a cut-off frequency of 2 KHz and a pass band gain of 1, to produce the noise output n(t).
(a)  Obtain the total power in n(t).
(b)  Find the  autocorrelation function  E[n(t)n(t+ t ) of the noise n(t)  as a function of  t .
(c)  Two  noise  samples  are  taken  at  times        t Find  the  spacing   and t
that the product  n t n t has the most negative expected value and obtain
this most negative expected value.

20.  Given  E e y V m = 10               in free space.
(a)  Write all the four Maxwell‘s equations in free space.
(b)  Find  .      × E
(c)  Find H.

21.  The three regions shown in Fig.P21 are all lossless and non-magnetic. Find
(a)  Wave impedance in mediums 2 and 3.
(b)  d such that medium 2 acts as a quarter wave  4      transformer.  ÷
(c)  Reflection  coefficient      G  and  voltage  standing  wave  ratio  (VSWR)  at  the interface of the medium 1 and 2, when d =  4    ÷

22.  Design  a  lossless  impedance  matching  network  shown  in  Fig.P22  to  transform Z j = +   10 10  to  50 . Z  =    Find the values  of  L,  C and quality  factor (Q)  of  the circuit at f = 1GHz