Page 1
GATE EC  2002
V D
1mA
+

SECTION – A (75 marks)
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, 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
(c) delivers 40 W
(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
+ is
(a) 25 V
(b) 50 V
(c) 50 V
(d) 0 V
1.3 Convolution of x(t + 5) with impulse function d(t – 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 pt + 7 cos t
(c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt
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
D
is found to be 700 mV. If the temperature
rises to 40°C, V
D
becomes approximately equal to
(a) 740 mV
(b) 660 mV
(c) 680 mV
(d) 700 mV
5O
1
5
V
A
V 1=20V
I
5O
+

2.5A
5H
20O
20O
t=0
V x
+ 
Page 2
GATE EC  2002
V D
1mA
+

SECTION – A (75 marks)
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, 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
(c) delivers 40 W
(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
+ is
(a) 25 V
(b) 50 V
(c) 50 V
(d) 0 V
1.3 Convolution of x(t + 5) with impulse function d(t – 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 pt + 7 cos t
(c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt
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
D
is found to be 700 mV. If the temperature
rises to 40°C, V
D
becomes approximately equal to
(a) 740 mV
(b) 660 mV
(c) 680 mV
(d) 700 mV
5O
1
5
V
A
V 1=20V
I
5O
+

2.5A
5H
20O
20O
t=0
V x
+ 
GATE EC  2002
1.6 In a negative feedback amplifier using voltageseries (i.e. voltagesampling
series mixing) feedback. (R
i
and R
o
denote the input and output resistance
respectively)
(a) R
i
decreases and R
o
decreases (b) R
i
decreases and R
o
increases
(c) R
i
increases and R
o
decreases (d) R
i
increases and R
o
increases
1.7 A 741type opamp has a gainbandwidth product of 1 MHz. A noninverting
amplifier using this opamp and having a voltage gain of 20 dB will exhibit a 3dB
bandwidth of
(a) 50 KHz (b) 100 KHz (c)
1000
17
KHz (d)
1000
7.07
1.8 Three identical RCcoupled 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) (b)
(c) (d)
1.9 4bit 2’s complement representation of a decimal number is 1000. The number is
(a) +8 (b) 0 (c) 7 (d) 8
f
20Hz 1KHz
3
0
v
A dB
f
40Hz 0.5KHz
3
0
v
A dB
2
40Hz 1KHz
3
0
v
A dB
f
40Hz 2KHz
3
f
v
A dB
0
10Hz 0.5KHz
3
f
v
A dB
0
Page 3
GATE EC  2002
V D
1mA
+

SECTION – A (75 marks)
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, 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
(c) delivers 40 W
(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
+ is
(a) 25 V
(b) 50 V
(c) 50 V
(d) 0 V
1.3 Convolution of x(t + 5) with impulse function d(t – 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 pt + 7 cos t
(c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt
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
D
is found to be 700 mV. If the temperature
rises to 40°C, V
D
becomes approximately equal to
(a) 740 mV
(b) 660 mV
(c) 680 mV
(d) 700 mV
5O
1
5
V
A
V 1=20V
I
5O
+

2.5A
5H
20O
20O
t=0
V x
+ 
GATE EC  2002
1.6 In a negative feedback amplifier using voltageseries (i.e. voltagesampling
series mixing) feedback. (R
i
and R
o
denote the input and output resistance
respectively)
(a) R
i
decreases and R
o
decreases (b) R
i
decreases and R
o
increases
(c) R
i
increases and R
o
decreases (d) R
i
increases and R
o
increases
1.7 A 741type opamp has a gainbandwidth product of 1 MHz. A noninverting
amplifier using this opamp and having a voltage gain of 20 dB will exhibit a 3dB
bandwidth of
(a) 50 KHz (b) 100 KHz (c)
1000
17
KHz (d)
1000
7.07
1.8 Three identical RCcoupled 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) (b)
(c) (d)
1.9 4bit 2’s complement representation of a decimal number is 1000. The number is
(a) +8 (b) 0 (c) 7 (d) 8
f
20Hz 1KHz
3
0
v
A dB
f
40Hz 0.5KHz
3
0
v
A dB
2
40Hz 1KHz
3
0
v
A dB
f
40Hz 2KHz
3
f
v
A dB
0
10Hz 0.5KHz
3
f
v
A dB
0
GATE EC  2002
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 3bit 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
(a) I
C
is always equal to ß
dc
I
B
(b) I
C
is always equal to ß
dc
I
B
(c) I
C
is greater than or equal to ß
dc
I
B
(d) I
C
is less than or equal to ß
dc
I
B
1.13 Consider a system with the transfer function ( )
2
6
.
6
s
G s
ks s
+
=
+ +
Its damping ratio
will be 0.5 when the value of k is
(a)
2
6
(b) 3 (c)
1
6
(d) 6
1.14 Which of the following points is NOT on the root locus of a system with the open
loop transfer function ( ) ( )
( )( ) 1 3
k
G s H s
s s s
=
+ +
(a) s = 3 j  (b) s=  1.5 (c) s= 3 (d) s = 8
1
X
Y
C
ß dc denotes the dc
current gain
E
I C
I B
Page 4
GATE EC  2002
V D
1mA
+

SECTION – A (75 marks)
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, 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
(c) delivers 40 W
(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
+ is
(a) 25 V
(b) 50 V
(c) 50 V
(d) 0 V
1.3 Convolution of x(t + 5) with impulse function d(t – 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 pt + 7 cos t
(c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt
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
D
is found to be 700 mV. If the temperature
rises to 40°C, V
D
becomes approximately equal to
(a) 740 mV
(b) 660 mV
(c) 680 mV
(d) 700 mV
5O
1
5
V
A
V 1=20V
I
5O
+

2.5A
5H
20O
20O
t=0
V x
+ 
GATE EC  2002
1.6 In a negative feedback amplifier using voltageseries (i.e. voltagesampling
series mixing) feedback. (R
i
and R
o
denote the input and output resistance
respectively)
(a) R
i
decreases and R
o
decreases (b) R
i
decreases and R
o
increases
(c) R
i
increases and R
o
decreases (d) R
i
increases and R
o
increases
1.7 A 741type opamp has a gainbandwidth product of 1 MHz. A noninverting
amplifier using this opamp and having a voltage gain of 20 dB will exhibit a 3dB
bandwidth of
(a) 50 KHz (b) 100 KHz (c)
1000
17
KHz (d)
1000
7.07
1.8 Three identical RCcoupled 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) (b)
(c) (d)
1.9 4bit 2’s complement representation of a decimal number is 1000. The number is
(a) +8 (b) 0 (c) 7 (d) 8
f
20Hz 1KHz
3
0
v
A dB
f
40Hz 0.5KHz
3
0
v
A dB
2
40Hz 1KHz
3
0
v
A dB
f
40Hz 2KHz
3
f
v
A dB
0
10Hz 0.5KHz
3
f
v
A dB
0
GATE EC  2002
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 3bit 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
(a) I
C
is always equal to ß
dc
I
B
(b) I
C
is always equal to ß
dc
I
B
(c) I
C
is greater than or equal to ß
dc
I
B
(d) I
C
is less than or equal to ß
dc
I
B
1.13 Consider a system with the transfer function ( )
2
6
.
6
s
G s
ks s
+
=
+ +
Its damping ratio
will be 0.5 when the value of k is
(a)
2
6
(b) 3 (c)
1
6
(d) 6
1.14 Which of the following points is NOT on the root locus of a system with the open
loop transfer function ( ) ( )
( )( ) 1 3
k
G s H s
s s s
=
+ +
(a) s = 3 j  (b) s=  1.5 (c) s= 3 (d) s = 8
1
X
Y
C
ß dc denotes the dc
current gain
E
I C
I B
GATE EC  2002
1.15 The phase margin of a system with the openloop transfer function
( ) ( )
( )
( )( )
1
1 2
s
G s H s
s s

=
+ +
is
(a) 0° (b) 63.4° (c) 90° (d) 8
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
(a)
( )
0.5
2 s 
(b)
( )
1
2 s 
(c)
( )
0.5
2 s +
(d)
( )
1
2 s +
1.17 The Fourier transform ( )
{ }
1
F e u t

is equal to
1
.
1 2 j f p +
Therefore,
1
1 2
F
j t p
? ?
? ?
+
? ?
is
(a) ( )
f
e u f (b) ( )
f
e u f

(c) ( )
f
e u f  (d) ( )
f
e u f


1.18 A linear phase channel with phase delay T
P
and group delay T
g
must have
(a) T
P
= T
g
=constant (b) T
P
?f and T
g
?f
(c) T
P
= constant and T
g
?f (d) T
P
?f and T
g
=constant
1.19. A 1 MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave
of period 100µsec. 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
1.20. Consider a sampled signal ( ) ( ) ( )
6
5 10
s
n
y t x t t nT d
+8

=8
= × 
?
where x(t) =10
cos(8p×10
3
)t and T
s
=100µsec. When y(t) is passed through an ideal lowpass
filter with a cutoff frequency of 5KHz, the output of the filter is
(a)
( )
6 3
5 10 cos 8 10 t p

× × (b)
( )
5 3
5 10 cos 8 10 t p

× ×
(c)
( )
1 3
5 10 cos 8 10 t p

× × (d)
( )
3
10cos 8 10 t p ×
1.21. For a bitrate 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 lineofsight 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
Page 5
GATE EC  2002
V D
1mA
+

SECTION – A (75 marks)
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, 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
(c) delivers 40 W
(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
+ is
(a) 25 V
(b) 50 V
(c) 50 V
(d) 0 V
1.3 Convolution of x(t + 5) with impulse function d(t – 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 pt + 7 cos t
(c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt
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
D
is found to be 700 mV. If the temperature
rises to 40°C, V
D
becomes approximately equal to
(a) 740 mV
(b) 660 mV
(c) 680 mV
(d) 700 mV
5O
1
5
V
A
V 1=20V
I
5O
+

2.5A
5H
20O
20O
t=0
V x
+ 
GATE EC  2002
1.6 In a negative feedback amplifier using voltageseries (i.e. voltagesampling
series mixing) feedback. (R
i
and R
o
denote the input and output resistance
respectively)
(a) R
i
decreases and R
o
decreases (b) R
i
decreases and R
o
increases
(c) R
i
increases and R
o
decreases (d) R
i
increases and R
o
increases
1.7 A 741type opamp has a gainbandwidth product of 1 MHz. A noninverting
amplifier using this opamp and having a voltage gain of 20 dB will exhibit a 3dB
bandwidth of
(a) 50 KHz (b) 100 KHz (c)
1000
17
KHz (d)
1000
7.07
1.8 Three identical RCcoupled 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) (b)
(c) (d)
1.9 4bit 2’s complement representation of a decimal number is 1000. The number is
(a) +8 (b) 0 (c) 7 (d) 8
f
20Hz 1KHz
3
0
v
A dB
f
40Hz 0.5KHz
3
0
v
A dB
2
40Hz 1KHz
3
0
v
A dB
f
40Hz 2KHz
3
f
v
A dB
0
10Hz 0.5KHz
3
f
v
A dB
0
GATE EC  2002
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 3bit 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
(a) I
C
is always equal to ß
dc
I
B
(b) I
C
is always equal to ß
dc
I
B
(c) I
C
is greater than or equal to ß
dc
I
B
(d) I
C
is less than or equal to ß
dc
I
B
1.13 Consider a system with the transfer function ( )
2
6
.
6
s
G s
ks s
+
=
+ +
Its damping ratio
will be 0.5 when the value of k is
(a)
2
6
(b) 3 (c)
1
6
(d) 6
1.14 Which of the following points is NOT on the root locus of a system with the open
loop transfer function ( ) ( )
( )( ) 1 3
k
G s H s
s s s
=
+ +
(a) s = 3 j  (b) s=  1.5 (c) s= 3 (d) s = 8
1
X
Y
C
ß dc denotes the dc
current gain
E
I C
I B
GATE EC  2002
1.15 The phase margin of a system with the openloop transfer function
( ) ( )
( )
( )( )
1
1 2
s
G s H s
s s

=
+ +
is
(a) 0° (b) 63.4° (c) 90° (d) 8
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
(a)
( )
0.5
2 s 
(b)
( )
1
2 s 
(c)
( )
0.5
2 s +
(d)
( )
1
2 s +
1.17 The Fourier transform ( )
{ }
1
F e u t

is equal to
1
.
1 2 j f p +
Therefore,
1
1 2
F
j t p
? ?
? ?
+
? ?
is
(a) ( )
f
e u f (b) ( )
f
e u f

(c) ( )
f
e u f  (d) ( )
f
e u f


1.18 A linear phase channel with phase delay T
P
and group delay T
g
must have
(a) T
P
= T
g
=constant (b) T
P
?f and T
g
?f
(c) T
P
= constant and T
g
?f (d) T
P
?f and T
g
=constant
1.19. A 1 MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave
of period 100µsec. 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
1.20. Consider a sampled signal ( ) ( ) ( )
6
5 10
s
n
y t x t t nT d
+8

=8
= × 
?
where x(t) =10
cos(8p×10
3
)t and T
s
=100µsec. When y(t) is passed through an ideal lowpass
filter with a cutoff frequency of 5KHz, the output of the filter is
(a)
( )
6 3
5 10 cos 8 10 t p

× × (b)
( )
5 3
5 10 cos 8 10 t p

× ×
(c)
( )
1 3
5 10 cos 8 10 t p

× × (d)
( )
3
10cos 8 10 t p ×
1.21. For a bitrate 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 lineofsight 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
GATE EC  2002
(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
10
mode in an airfilled 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
2. This question consists of TWENTYFIVE subquestions (2.1 – 2.25) of TWO marks
each. For each of these subquestions, 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
L
if its value is
(a) 16O (b)
40
3
O (c) 60O (d) 20O
I 1
40O
50V
R L 20O
0.5I 1
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