Page 1
GATE EC  1999
SECTION  A
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 answers in the
boxes corresponding to the questions only on the FIRST sheet of the answer
book.
1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1
(a) begh
(b) defg
(c) adfg
(d) aegh
1.2 The ztransform F(z) of the function ( )
nT
f nT a = is
(a)
T
z
z a 
(b)
T
z
z a +
(c)
T
z
z a


(d)
T
z
z a

+
1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = 
? ? ? ?
is equal to
(a) ( )
sT
e F s (b) ( )
sT
e F s

(c)
( )
1
sT
F s
e +
(d)
( )
1
sT
F s
e


1.4 A 2port network is shown in Fig.P1.4. the parameter
21
h for this network can be
given by
(a)
1
2
 (b)
1
2
+ (c)
3
2
 (d)
3
2
+
1.5 The early effect in a bipolar junction transistor is caused by
(a) fast turnon
(b) fast turnoff
(c) large collectorbase reverse bias
(d) large emitterbase forward bias
1
2
3
4 5
a
b
c
d e f g
h
V 1 10µF
+
V 2
R
R
R I 1 I 2

+

Page 2
GATE EC  1999
SECTION  A
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 answers in the
boxes corresponding to the questions only on the FIRST sheet of the answer
book.
1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1
(a) begh
(b) defg
(c) adfg
(d) aegh
1.2 The ztransform F(z) of the function ( )
nT
f nT a = is
(a)
T
z
z a 
(b)
T
z
z a +
(c)
T
z
z a


(d)
T
z
z a

+
1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = 
? ? ? ?
is equal to
(a) ( )
sT
e F s (b) ( )
sT
e F s

(c)
( )
1
sT
F s
e +
(d)
( )
1
sT
F s
e


1.4 A 2port network is shown in Fig.P1.4. the parameter
21
h for this network can be
given by
(a)
1
2
 (b)
1
2
+ (c)
3
2
 (d)
3
2
+
1.5 The early effect in a bipolar junction transistor is caused by
(a) fast turnon
(b) fast turnoff
(c) large collectorbase reverse bias
(d) large emitterbase forward bias
1
2
3
4 5
a
b
c
d e f g
h
V 1 10µF
+
V 2
R
R
R I 1 I 2

+

GATE EC  1999
1.6 The first dominant pole encountered in the frequency response of a compensated
opamp is approximately at
(a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz
1.7 Negative feedback in an amplifier
(a) reduces gain
(b) increases frequency and phase distortions
(c) reduces bandwidth
(d) increase noise
1.8 In the cascade amplifier shown in
Fig.P1.8, if the commonemitter
stage(Q
1
) has a transconductance
1
,
m
g and the common base stage
(Q
2
) has a transconductance
2
,
m
g then the overall
transconductance
o
i
i
g
v
? ?
=
? ?
? ?
of the
cascade amplifier is
(a)
1 m
g (b)
2 m
g (c)
1
2
m
g
(d)
2
2
m
g
1.9 Crossover distortion behaviour is characteristic of
(a) Class A output stage (b) Class B output stage
(c) Class AB output stage (d) Commonbase output stage
1.10 The logical expression y A AB = + is equivalent to
(a) y AB = (b) y AB = (c) y A B = + (d) y A B = +
1.11 A Darlington emitterfollower circuit is sometimes used in the output stage of a
TTL gate in order to
(a) increase its I
OL
(b) reduces its I
OH
(c) increases its speed of operation (d) reduce power dissipation
1.12 Commercially available ECL gears use two ground lines and one negative supply
in order to
(a) reduce power dissipation
(b) increase fanout
(c) reduce loading effect
(d) eliminate the effect of power line glitches or the biasing circuit
V i
V o
Q 2
Q 1
R L
i o
Page 3
GATE EC  1999
SECTION  A
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 answers in the
boxes corresponding to the questions only on the FIRST sheet of the answer
book.
1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1
(a) begh
(b) defg
(c) adfg
(d) aegh
1.2 The ztransform F(z) of the function ( )
nT
f nT a = is
(a)
T
z
z a 
(b)
T
z
z a +
(c)
T
z
z a


(d)
T
z
z a

+
1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = 
? ? ? ?
is equal to
(a) ( )
sT
e F s (b) ( )
sT
e F s

(c)
( )
1
sT
F s
e +
(d)
( )
1
sT
F s
e


1.4 A 2port network is shown in Fig.P1.4. the parameter
21
h for this network can be
given by
(a)
1
2
 (b)
1
2
+ (c)
3
2
 (d)
3
2
+
1.5 The early effect in a bipolar junction transistor is caused by
(a) fast turnon
(b) fast turnoff
(c) large collectorbase reverse bias
(d) large emitterbase forward bias
1
2
3
4 5
a
b
c
d e f g
h
V 1 10µF
+
V 2
R
R
R I 1 I 2

+

GATE EC  1999
1.6 The first dominant pole encountered in the frequency response of a compensated
opamp is approximately at
(a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz
1.7 Negative feedback in an amplifier
(a) reduces gain
(b) increases frequency and phase distortions
(c) reduces bandwidth
(d) increase noise
1.8 In the cascade amplifier shown in
Fig.P1.8, if the commonemitter
stage(Q
1
) has a transconductance
1
,
m
g and the common base stage
(Q
2
) has a transconductance
2
,
m
g then the overall
transconductance
o
i
i
g
v
? ?
=
? ?
? ?
of the
cascade amplifier is
(a)
1 m
g (b)
2 m
g (c)
1
2
m
g
(d)
2
2
m
g
1.9 Crossover distortion behaviour is characteristic of
(a) Class A output stage (b) Class B output stage
(c) Class AB output stage (d) Commonbase output stage
1.10 The logical expression y A AB = + is equivalent to
(a) y AB = (b) y AB = (c) y A B = + (d) y A B = +
1.11 A Darlington emitterfollower circuit is sometimes used in the output stage of a
TTL gate in order to
(a) increase its I
OL
(b) reduces its I
OH
(c) increases its speed of operation (d) reduce power dissipation
1.12 Commercially available ECL gears use two ground lines and one negative supply
in order to
(a) reduce power dissipation
(b) increase fanout
(c) reduce loading effect
(d) eliminate the effect of power line glitches or the biasing circuit
V i
V o
Q 2
Q 1
R L
i o
GATE EC  1999
1.13 The resolution of a 4bit counting ADC is 0.5 volts. For an analog input of 6.6
volts, the digital output of the ADC will be
(a) 1011 (b) 1101 (c) 1100 (d) 1110
1.14 For a secondorder system with the closedloop transfer function
( )
2
9
4 9
T s
s s
=
+ +
The settling time for 2percent band, in seconds, is
(a) 1.5 (b) 2.0 (c) 3.0 (d) 4.0
1.15 The gain margin (in dB) of a system having the loop transfer function
( ) ( )
( )
2
1
G s H s
s s
=
+
is
(a) 0 (b) 3 (c) 6 (d) 8
1.16 The system mode described by the state equations
0 1 0
2 3 1
1 1
X x u
y x
? ? ? ?
= +
? ? ? ?

? ? ? ?
= ? ?
? ?
is:
(a) controllable and observable
(b) controllable, but not observable
(c) observable, but not controllable
(d) neither controllable nor observable
1.17 The phase margin (in degrees) of a system having the loop transfer function
( ) ( )
( )
2 3
1
G s H s
s s
=
+
is
(a) 45° (b) 30° (c) 60° (d) 30°
1.18 A signal x(t) has a Fourier transform X(?). If x(t) is a real and odd fucntion of t,
then X(?) is
(a) a real and even function of ?
(b) a imaginary and odd function of ?
(c) an imaginary and even function of ?
(d) a real and odd function of ?
Page 4
GATE EC  1999
SECTION  A
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 answers in the
boxes corresponding to the questions only on the FIRST sheet of the answer
book.
1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1
(a) begh
(b) defg
(c) adfg
(d) aegh
1.2 The ztransform F(z) of the function ( )
nT
f nT a = is
(a)
T
z
z a 
(b)
T
z
z a +
(c)
T
z
z a


(d)
T
z
z a

+
1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = 
? ? ? ?
is equal to
(a) ( )
sT
e F s (b) ( )
sT
e F s

(c)
( )
1
sT
F s
e +
(d)
( )
1
sT
F s
e


1.4 A 2port network is shown in Fig.P1.4. the parameter
21
h for this network can be
given by
(a)
1
2
 (b)
1
2
+ (c)
3
2
 (d)
3
2
+
1.5 The early effect in a bipolar junction transistor is caused by
(a) fast turnon
(b) fast turnoff
(c) large collectorbase reverse bias
(d) large emitterbase forward bias
1
2
3
4 5
a
b
c
d e f g
h
V 1 10µF
+
V 2
R
R
R I 1 I 2

+

GATE EC  1999
1.6 The first dominant pole encountered in the frequency response of a compensated
opamp is approximately at
(a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz
1.7 Negative feedback in an amplifier
(a) reduces gain
(b) increases frequency and phase distortions
(c) reduces bandwidth
(d) increase noise
1.8 In the cascade amplifier shown in
Fig.P1.8, if the commonemitter
stage(Q
1
) has a transconductance
1
,
m
g and the common base stage
(Q
2
) has a transconductance
2
,
m
g then the overall
transconductance
o
i
i
g
v
? ?
=
? ?
? ?
of the
cascade amplifier is
(a)
1 m
g (b)
2 m
g (c)
1
2
m
g
(d)
2
2
m
g
1.9 Crossover distortion behaviour is characteristic of
(a) Class A output stage (b) Class B output stage
(c) Class AB output stage (d) Commonbase output stage
1.10 The logical expression y A AB = + is equivalent to
(a) y AB = (b) y AB = (c) y A B = + (d) y A B = +
1.11 A Darlington emitterfollower circuit is sometimes used in the output stage of a
TTL gate in order to
(a) increase its I
OL
(b) reduces its I
OH
(c) increases its speed of operation (d) reduce power dissipation
1.12 Commercially available ECL gears use two ground lines and one negative supply
in order to
(a) reduce power dissipation
(b) increase fanout
(c) reduce loading effect
(d) eliminate the effect of power line glitches or the biasing circuit
V i
V o
Q 2
Q 1
R L
i o
GATE EC  1999
1.13 The resolution of a 4bit counting ADC is 0.5 volts. For an analog input of 6.6
volts, the digital output of the ADC will be
(a) 1011 (b) 1101 (c) 1100 (d) 1110
1.14 For a secondorder system with the closedloop transfer function
( )
2
9
4 9
T s
s s
=
+ +
The settling time for 2percent band, in seconds, is
(a) 1.5 (b) 2.0 (c) 3.0 (d) 4.0
1.15 The gain margin (in dB) of a system having the loop transfer function
( ) ( )
( )
2
1
G s H s
s s
=
+
is
(a) 0 (b) 3 (c) 6 (d) 8
1.16 The system mode described by the state equations
0 1 0
2 3 1
1 1
X x u
y x
? ? ? ?
= +
? ? ? ?

? ? ? ?
= ? ?
? ?
is:
(a) controllable and observable
(b) controllable, but not observable
(c) observable, but not controllable
(d) neither controllable nor observable
1.17 The phase margin (in degrees) of a system having the loop transfer function
( ) ( )
( )
2 3
1
G s H s
s s
=
+
is
(a) 45° (b) 30° (c) 60° (d) 30°
1.18 A signal x(t) has a Fourier transform X(?). If x(t) is a real and odd fucntion of t,
then X(?) is
(a) a real and even function of ?
(b) a imaginary and odd function of ?
(c) an imaginary and even function of ?
(d) a real and odd function of ?
GATE EC  1999
1.19. The input to a channel is a bandpass signal. It is obtained by linearly modulating
a sinusoidal carrier with a singletone signal. The output of the channel due to
this input is given by
( )
( ) ( )
6 6
1
cos 100 10 cos 10 1.56
100
y t t t

? ?
=  
? ?
? ?
The group delay
( )
g
t and the phase delay
( )
p
t in seconds, of the channel are
(a)
6
10 , 1.56
g p
t t

= = (b)
6
1.56, 10
g p
t t

= =
(c)
8 6
10 , 1.56 10
g p
t t

= = × (d)
8
10 , 1.56
g p
t t = =
1.20. A modulated signal is given by, ( ) ( ) ( ) ( ) ( )
1 2
cos 2 sin 2
c c
s t m t f t m t f t p p = + where
the baseband signal ( ) ( )
1 2
and m t m t have bandwidths of 10 kHz and 15 kHz,
respectively. The bandwidth of the modulated signal, in kHz, is
(a) 10 (b) 15 (c) 25 (d) 30
1.21. A modulated signal is given by ( ) ( ) ( ) cos ,
at
c
s t e t u t ? ?

? ? = + ?
? ?
where a,?
c
and
? ? are positive constants, and
c
? ? ? .
The complex envelope of s(t) is given by
(a) ( ) ( ) ( ) exp exp
c
at j t u t ? ? ? ?  + ?
? ?
(b) ( ) ( ) ( ) exp exp at j t u t ?  ?
(c) ( ) exp . j t u t ? ? ? ?
? ?
(d) ( ) exp
c
j t ? ? ? ? + ?
? ?
1.22. An electric field on a plane is described by its potential
( )
1 2
20 V r r
 
= + where r
is the distance from the source. The field is due to
(a) a monopole (b) a dipole
(c) both a monopole and a dipole (d) a quadrupole
1.23. Assuming perfect conductors of a transmission line, pure TEM propagation is NOT
possible in
(a) coaxial cable (b) airfilled cylindrical wave guide
(c) parallel twinwire line in air
(d) semiinfinite parallel plate wave guide
1.24. Indicate which one of the following will NOT exist in a rectangular resonant
cavity.
(a)
110
TE (b)
011
TE (c)
110
TM (d)
111
TM
Page 5
GATE EC  1999
SECTION  A
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 answers in the
boxes corresponding to the questions only on the FIRST sheet of the answer
book.
1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1
(a) begh
(b) defg
(c) adfg
(d) aegh
1.2 The ztransform F(z) of the function ( )
nT
f nT a = is
(a)
T
z
z a 
(b)
T
z
z a +
(c)
T
z
z a


(d)
T
z
z a

+
1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = 
? ? ? ?
is equal to
(a) ( )
sT
e F s (b) ( )
sT
e F s

(c)
( )
1
sT
F s
e +
(d)
( )
1
sT
F s
e


1.4 A 2port network is shown in Fig.P1.4. the parameter
21
h for this network can be
given by
(a)
1
2
 (b)
1
2
+ (c)
3
2
 (d)
3
2
+
1.5 The early effect in a bipolar junction transistor is caused by
(a) fast turnon
(b) fast turnoff
(c) large collectorbase reverse bias
(d) large emitterbase forward bias
1
2
3
4 5
a
b
c
d e f g
h
V 1 10µF
+
V 2
R
R
R I 1 I 2

+

GATE EC  1999
1.6 The first dominant pole encountered in the frequency response of a compensated
opamp is approximately at
(a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz
1.7 Negative feedback in an amplifier
(a) reduces gain
(b) increases frequency and phase distortions
(c) reduces bandwidth
(d) increase noise
1.8 In the cascade amplifier shown in
Fig.P1.8, if the commonemitter
stage(Q
1
) has a transconductance
1
,
m
g and the common base stage
(Q
2
) has a transconductance
2
,
m
g then the overall
transconductance
o
i
i
g
v
? ?
=
? ?
? ?
of the
cascade amplifier is
(a)
1 m
g (b)
2 m
g (c)
1
2
m
g
(d)
2
2
m
g
1.9 Crossover distortion behaviour is characteristic of
(a) Class A output stage (b) Class B output stage
(c) Class AB output stage (d) Commonbase output stage
1.10 The logical expression y A AB = + is equivalent to
(a) y AB = (b) y AB = (c) y A B = + (d) y A B = +
1.11 A Darlington emitterfollower circuit is sometimes used in the output stage of a
TTL gate in order to
(a) increase its I
OL
(b) reduces its I
OH
(c) increases its speed of operation (d) reduce power dissipation
1.12 Commercially available ECL gears use two ground lines and one negative supply
in order to
(a) reduce power dissipation
(b) increase fanout
(c) reduce loading effect
(d) eliminate the effect of power line glitches or the biasing circuit
V i
V o
Q 2
Q 1
R L
i o
GATE EC  1999
1.13 The resolution of a 4bit counting ADC is 0.5 volts. For an analog input of 6.6
volts, the digital output of the ADC will be
(a) 1011 (b) 1101 (c) 1100 (d) 1110
1.14 For a secondorder system with the closedloop transfer function
( )
2
9
4 9
T s
s s
=
+ +
The settling time for 2percent band, in seconds, is
(a) 1.5 (b) 2.0 (c) 3.0 (d) 4.0
1.15 The gain margin (in dB) of a system having the loop transfer function
( ) ( )
( )
2
1
G s H s
s s
=
+
is
(a) 0 (b) 3 (c) 6 (d) 8
1.16 The system mode described by the state equations
0 1 0
2 3 1
1 1
X x u
y x
? ? ? ?
= +
? ? ? ?

? ? ? ?
= ? ?
? ?
is:
(a) controllable and observable
(b) controllable, but not observable
(c) observable, but not controllable
(d) neither controllable nor observable
1.17 The phase margin (in degrees) of a system having the loop transfer function
( ) ( )
( )
2 3
1
G s H s
s s
=
+
is
(a) 45° (b) 30° (c) 60° (d) 30°
1.18 A signal x(t) has a Fourier transform X(?). If x(t) is a real and odd fucntion of t,
then X(?) is
(a) a real and even function of ?
(b) a imaginary and odd function of ?
(c) an imaginary and even function of ?
(d) a real and odd function of ?
GATE EC  1999
1.19. The input to a channel is a bandpass signal. It is obtained by linearly modulating
a sinusoidal carrier with a singletone signal. The output of the channel due to
this input is given by
( )
( ) ( )
6 6
1
cos 100 10 cos 10 1.56
100
y t t t

? ?
=  
? ?
? ?
The group delay
( )
g
t and the phase delay
( )
p
t in seconds, of the channel are
(a)
6
10 , 1.56
g p
t t

= = (b)
6
1.56, 10
g p
t t

= =
(c)
8 6
10 , 1.56 10
g p
t t

= = × (d)
8
10 , 1.56
g p
t t = =
1.20. A modulated signal is given by, ( ) ( ) ( ) ( ) ( )
1 2
cos 2 sin 2
c c
s t m t f t m t f t p p = + where
the baseband signal ( ) ( )
1 2
and m t m t have bandwidths of 10 kHz and 15 kHz,
respectively. The bandwidth of the modulated signal, in kHz, is
(a) 10 (b) 15 (c) 25 (d) 30
1.21. A modulated signal is given by ( ) ( ) ( ) cos ,
at
c
s t e t u t ? ?

? ? = + ?
? ?
where a,?
c
and
? ? are positive constants, and
c
? ? ? .
The complex envelope of s(t) is given by
(a) ( ) ( ) ( ) exp exp
c
at j t u t ? ? ? ?  + ?
? ?
(b) ( ) ( ) ( ) exp exp at j t u t ?  ?
(c) ( ) exp . j t u t ? ? ? ?
? ?
(d) ( ) exp
c
j t ? ? ? ? + ?
? ?
1.22. An electric field on a plane is described by its potential
( )
1 2
20 V r r
 
= + where r
is the distance from the source. The field is due to
(a) a monopole (b) a dipole
(c) both a monopole and a dipole (d) a quadrupole
1.23. Assuming perfect conductors of a transmission line, pure TEM propagation is NOT
possible in
(a) coaxial cable (b) airfilled cylindrical wave guide
(c) parallel twinwire line in air
(d) semiinfinite parallel plate wave guide
1.24. Indicate which one of the following will NOT exist in a rectangular resonant
cavity.
(a)
110
TE (b)
011
TE (c)
110
TM (d)
111
TM
GATE EC  1999
?
a
b
c
5O
30O
15O
a
b c
R 1
R 2 R 3
1.25 Identify which one of the following will NOT satisfy the wave equation.
(a)
( ) 3
50
j t z
e
? 
(b) ( ) sin 10 5 z t ? ? ? +
? ?
(c)
( )
2
cos 5 y t + (d) ( ) ( ) sin cos x t
2. This question consists of TWENTYFIVE subquestions (2.1 – 2.25) 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 answers in the
boxes corresponding to the questions only on the SECOND sheet of the answer
book.
2.1 The Fourier series representation of an impulses train denoted by
( ) ( )
0
n
s t d t nT
8
=8
= 
?
is given by
(a)
0 0
1 2
exp
n
j nt
T T
p
8
=8

?
(b)
0 0
1
exp
n
j nt
T T
p
8
=8

?
(c)
0 0
1
exp
n
j nt
T T
p
8
=8
?
(d)
0 0
1 2
exp
n
j nt
T T
p
8
=8
?
2.2. The Thevenin equivalent voltage
TH
V appearing between the terminals A and B of
the network shown in Fig.P2.2 is given by
(a) j16(3j4)
(b) j16(3+j4)
(c) 16(3+j4)
(d) 16(3j4)
2.3. The value of R (in ohms) required for maximum power transfer in the network
shown in Fig.P2.3 is
(a) 2
(b) 4
(c) 8
(d) 10
2.4. A Deltaconnected network with its Wyeequivalent is shown in Fig.P2.4. The
resistance R
1
, R
2
and R
3
(in ohms) are respectively
100?0°V
3O
V TH
j2
A
~
j6
j4
B
+

3A
5O
4O
25V
+

R
20O
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