Page 1
GATE EC  1991
1.1 An excitation is applied to a system at t = T and its response is zero for
. t T 8 < < Such a system is
(a) noncausal system
(b) stable system
(c) causal system
(d) unstable system
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency
(b) greater than the resonant frequency
(c) less than the resonant frequency
(d) none of the above
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = 
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two twoport networks are connected in cascade. The combination is to be
represented as a single twoport network. The parameters of the network are
obtained by multiplying the individual
(a) zparameter matrix (b) hparameter matrix
(c) yparameter matrix (d) ABCD parameter matrix
1.5 The polezero pattern of a certain filter is shown in the figure below. The filter
must be of the following type.
(a) low pass (b) high pass
(c) all pass (d) band pass
x(t)
t=T
t
×
×
×
jw
1
+1
j1
j2
+j1
+j2
Page 2
GATE EC  1991
1.1 An excitation is applied to a system at t = T and its response is zero for
. t T 8 < < Such a system is
(a) noncausal system
(b) stable system
(c) causal system
(d) unstable system
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency
(b) greater than the resonant frequency
(c) less than the resonant frequency
(d) none of the above
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = 
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two twoport networks are connected in cascade. The combination is to be
represented as a single twoport network. The parameters of the network are
obtained by multiplying the individual
(a) zparameter matrix (b) hparameter matrix
(c) yparameter matrix (d) ABCD parameter matrix
1.5 The polezero pattern of a certain filter is shown in the figure below. The filter
must be of the following type.
(a) low pass (b) high pass
(c) all pass (d) band pass
x(t)
t=T
t
×
×
×
jw
1
+1
j1
j2
+j1
+j2
GATE EC  1991
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be
driving point impedance of an RC network is that all poles and zeros should be
(a) simple and lie on the negative axis in the splane
(b) complex and lie in the left half of the splane
(c) complex and lie in the right half of the splane
(d) simple and lie on the positive real axis of the splane
1.7 In the signal flow graph of Figure, the gain c/r will be
(a)
11
9
(b)
22
15
(c)
24
23
(d)
44
23
1.8 A second order system has a transfer function given by
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the
second peak in response will occur at
(a) p sec (b) sec
3
p
(c)
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is:
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is:
(a) 2 (b) 4 (c) 8 (d) 16
1.10 A unity feedback control system has the open loop transfer function
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be
(a) 0 (b) 0.5 (c) 2 (d) infinity
1
1 1
1
1 C
5
T
2 3 4
Page 3
GATE EC  1991
1.1 An excitation is applied to a system at t = T and its response is zero for
. t T 8 < < Such a system is
(a) noncausal system
(b) stable system
(c) causal system
(d) unstable system
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency
(b) greater than the resonant frequency
(c) less than the resonant frequency
(d) none of the above
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = 
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two twoport networks are connected in cascade. The combination is to be
represented as a single twoport network. The parameters of the network are
obtained by multiplying the individual
(a) zparameter matrix (b) hparameter matrix
(c) yparameter matrix (d) ABCD parameter matrix
1.5 The polezero pattern of a certain filter is shown in the figure below. The filter
must be of the following type.
(a) low pass (b) high pass
(c) all pass (d) band pass
x(t)
t=T
t
×
×
×
jw
1
+1
j1
j2
+j1
+j2
GATE EC  1991
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be
driving point impedance of an RC network is that all poles and zeros should be
(a) simple and lie on the negative axis in the splane
(b) complex and lie in the left half of the splane
(c) complex and lie in the right half of the splane
(d) simple and lie on the positive real axis of the splane
1.7 In the signal flow graph of Figure, the gain c/r will be
(a)
11
9
(b)
22
15
(c)
24
23
(d)
44
23
1.8 A second order system has a transfer function given by
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the
second peak in response will occur at
(a) p sec (b) sec
3
p
(c)
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is:
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is:
(a) 2 (b) 4 (c) 8 (d) 16
1.10 A unity feedback control system has the open loop transfer function
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be
(a) 0 (b) 0.5 (c) 2 (d) infinity
1
1 1
1
1 C
5
T
2 3 4
GATE EC  1991
1.11 The characteristic equation of a feedback control system is given by
( )
3 2
5 6 0 s s K s K + + + + =
Where K > 0 is a scalar variable parameter. In the root loci diagram of the
system the asymptotes of the root locus for large values of K meet at a point in
the splane whose coordinates are
(a) (3,0) (b) (2,0) (c) (1,0) (d) (2,0)
1.12 A linear second order single input continuous time system is described by the
following set of differential equations
( ) ( ) ( )
( ) ( ) ( ) ( )
1 1 2
2 1 2
2 4
2
x t x t x t
x t x t x t u t
=  +
=  +
Where ( ) ( )
1 2
and x t x t are the state variables and ( ) u t is the control variable.
The system is:
(a) controllable and stable (b) controllable but unstable
(c) uncontrollable and unstable (d) uncontrollable and stable
1.13 A linear timeinvariant discretetime system is described by the vector matrix
difference equation
( ) ( ) ( ) 1 x k FX k Gu k + = +
Where ( ) X k is the state vector, F is an n × n constant matrix, G is a
( ) n r × constant matrix and ( ) u k is the control vector. The state transition matrix
of the system is given by inverse Ztransform of
(a) ZI  F (b) (ZI – F) Z (c) ( )
1
ZI F G

 (d) ( )
1
ZI F Z


1.14 A silicon sample is uniformly doped with
16
10 phosphorous atoms/cm
3
and
16
2 10 × boron atoms/cm
3
. If all the dopants are fully ionized, the material is
(a) ntype with carrier concentration of
16 3
10 /cm
(b) ptype with carrier concentration of
16 3
10 /cm
(c) ptype with carrier concentration of
16 3
2 10 /cm ×
(d)
2
T will get damaged and
1
T will be safe
1.15 An ntype silicon sample, having electron mobility
n
µ = twice the hole mobility
,
p
µ is subjected to a steady illumination such that the electron concentration
doubles from its thermal equilibrium value. As a result, the conductivity of the
sample increases by a factor of …
Page 4
GATE EC  1991
1.1 An excitation is applied to a system at t = T and its response is zero for
. t T 8 < < Such a system is
(a) noncausal system
(b) stable system
(c) causal system
(d) unstable system
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency
(b) greater than the resonant frequency
(c) less than the resonant frequency
(d) none of the above
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = 
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two twoport networks are connected in cascade. The combination is to be
represented as a single twoport network. The parameters of the network are
obtained by multiplying the individual
(a) zparameter matrix (b) hparameter matrix
(c) yparameter matrix (d) ABCD parameter matrix
1.5 The polezero pattern of a certain filter is shown in the figure below. The filter
must be of the following type.
(a) low pass (b) high pass
(c) all pass (d) band pass
x(t)
t=T
t
×
×
×
jw
1
+1
j1
j2
+j1
+j2
GATE EC  1991
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be
driving point impedance of an RC network is that all poles and zeros should be
(a) simple and lie on the negative axis in the splane
(b) complex and lie in the left half of the splane
(c) complex and lie in the right half of the splane
(d) simple and lie on the positive real axis of the splane
1.7 In the signal flow graph of Figure, the gain c/r will be
(a)
11
9
(b)
22
15
(c)
24
23
(d)
44
23
1.8 A second order system has a transfer function given by
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the
second peak in response will occur at
(a) p sec (b) sec
3
p
(c)
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is:
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is:
(a) 2 (b) 4 (c) 8 (d) 16
1.10 A unity feedback control system has the open loop transfer function
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be
(a) 0 (b) 0.5 (c) 2 (d) infinity
1
1 1
1
1 C
5
T
2 3 4
GATE EC  1991
1.11 The characteristic equation of a feedback control system is given by
( )
3 2
5 6 0 s s K s K + + + + =
Where K > 0 is a scalar variable parameter. In the root loci diagram of the
system the asymptotes of the root locus for large values of K meet at a point in
the splane whose coordinates are
(a) (3,0) (b) (2,0) (c) (1,0) (d) (2,0)
1.12 A linear second order single input continuous time system is described by the
following set of differential equations
( ) ( ) ( )
( ) ( ) ( ) ( )
1 1 2
2 1 2
2 4
2
x t x t x t
x t x t x t u t
=  +
=  +
Where ( ) ( )
1 2
and x t x t are the state variables and ( ) u t is the control variable.
The system is:
(a) controllable and stable (b) controllable but unstable
(c) uncontrollable and unstable (d) uncontrollable and stable
1.13 A linear timeinvariant discretetime system is described by the vector matrix
difference equation
( ) ( ) ( ) 1 x k FX k Gu k + = +
Where ( ) X k is the state vector, F is an n × n constant matrix, G is a
( ) n r × constant matrix and ( ) u k is the control vector. The state transition matrix
of the system is given by inverse Ztransform of
(a) ZI  F (b) (ZI – F) Z (c) ( )
1
ZI F G

 (d) ( )
1
ZI F Z


1.14 A silicon sample is uniformly doped with
16
10 phosphorous atoms/cm
3
and
16
2 10 × boron atoms/cm
3
. If all the dopants are fully ionized, the material is
(a) ntype with carrier concentration of
16 3
10 /cm
(b) ptype with carrier concentration of
16 3
10 /cm
(c) ptype with carrier concentration of
16 3
2 10 /cm ×
(d)
2
T will get damaged and
1
T will be safe
1.15 An ntype silicon sample, having electron mobility
n
µ = twice the hole mobility
,
p
µ is subjected to a steady illumination such that the electron concentration
doubles from its thermal equilibrium value. As a result, the conductivity of the
sample increases by a factor of …
GATE EC  1991
1.16 The small signal capacitances of an abrupt
1
P n  junction is
2
1 / nF Cm at zero
bias. If the built in voltage is 1 volt, the capacitance at a reverse bias voltage of
99 volts is equal to …
1.17 Referring to the figure. The switch S is in position 1 initially and steady state
conditions exist from time t = 0 to
0
. t t = The switch is suddenly thrown into
position 2. The current 1 through the 10K resistor as a function of time t from t =
0, is …. (Give the sketch showing the magnitudes of the current at t = 0,
0
and t t t = = 8 )
1.18 Discrete transistors
1 2
and T T having maximum collector current rating of 0.75
amps are connected in parallel as shown in the figure. This combination is treated
as a single transistor to carry a total current of 1 ampere, when biased with self
bias circuit. When the circuit is switched on,
1
T draws 0.55 amps and
2
T draws
0.45 amps. If the supply is kept on continuously, ultimately it is very likely that
(a) both
1 2
and T T get damaged (b) both
1 2
and T T will be safe
(c)
1
T will get damaged and
2
T will be safe
(d)
2
T will get damaged and
1
T will be safe
20V
20V
10K
1
S
2
T 1 T 2
Page 5
GATE EC  1991
1.1 An excitation is applied to a system at t = T and its response is zero for
. t T 8 < < Such a system is
(a) noncausal system
(b) stable system
(c) causal system
(d) unstable system
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency
(b) greater than the resonant frequency
(c) less than the resonant frequency
(d) none of the above
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = 
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two twoport networks are connected in cascade. The combination is to be
represented as a single twoport network. The parameters of the network are
obtained by multiplying the individual
(a) zparameter matrix (b) hparameter matrix
(c) yparameter matrix (d) ABCD parameter matrix
1.5 The polezero pattern of a certain filter is shown in the figure below. The filter
must be of the following type.
(a) low pass (b) high pass
(c) all pass (d) band pass
x(t)
t=T
t
×
×
×
jw
1
+1
j1
j2
+j1
+j2
GATE EC  1991
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be
driving point impedance of an RC network is that all poles and zeros should be
(a) simple and lie on the negative axis in the splane
(b) complex and lie in the left half of the splane
(c) complex and lie in the right half of the splane
(d) simple and lie on the positive real axis of the splane
1.7 In the signal flow graph of Figure, the gain c/r will be
(a)
11
9
(b)
22
15
(c)
24
23
(d)
44
23
1.8 A second order system has a transfer function given by
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the
second peak in response will occur at
(a) p sec (b) sec
3
p
(c)
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is:
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is:
(a) 2 (b) 4 (c) 8 (d) 16
1.10 A unity feedback control system has the open loop transfer function
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be
(a) 0 (b) 0.5 (c) 2 (d) infinity
1
1 1
1
1 C
5
T
2 3 4
GATE EC  1991
1.11 The characteristic equation of a feedback control system is given by
( )
3 2
5 6 0 s s K s K + + + + =
Where K > 0 is a scalar variable parameter. In the root loci diagram of the
system the asymptotes of the root locus for large values of K meet at a point in
the splane whose coordinates are
(a) (3,0) (b) (2,0) (c) (1,0) (d) (2,0)
1.12 A linear second order single input continuous time system is described by the
following set of differential equations
( ) ( ) ( )
( ) ( ) ( ) ( )
1 1 2
2 1 2
2 4
2
x t x t x t
x t x t x t u t
=  +
=  +
Where ( ) ( )
1 2
and x t x t are the state variables and ( ) u t is the control variable.
The system is:
(a) controllable and stable (b) controllable but unstable
(c) uncontrollable and unstable (d) uncontrollable and stable
1.13 A linear timeinvariant discretetime system is described by the vector matrix
difference equation
( ) ( ) ( ) 1 x k FX k Gu k + = +
Where ( ) X k is the state vector, F is an n × n constant matrix, G is a
( ) n r × constant matrix and ( ) u k is the control vector. The state transition matrix
of the system is given by inverse Ztransform of
(a) ZI  F (b) (ZI – F) Z (c) ( )
1
ZI F G

 (d) ( )
1
ZI F Z


1.14 A silicon sample is uniformly doped with
16
10 phosphorous atoms/cm
3
and
16
2 10 × boron atoms/cm
3
. If all the dopants are fully ionized, the material is
(a) ntype with carrier concentration of
16 3
10 /cm
(b) ptype with carrier concentration of
16 3
10 /cm
(c) ptype with carrier concentration of
16 3
2 10 /cm ×
(d)
2
T will get damaged and
1
T will be safe
1.15 An ntype silicon sample, having electron mobility
n
µ = twice the hole mobility
,
p
µ is subjected to a steady illumination such that the electron concentration
doubles from its thermal equilibrium value. As a result, the conductivity of the
sample increases by a factor of …
GATE EC  1991
1.16 The small signal capacitances of an abrupt
1
P n  junction is
2
1 / nF Cm at zero
bias. If the built in voltage is 1 volt, the capacitance at a reverse bias voltage of
99 volts is equal to …
1.17 Referring to the figure. The switch S is in position 1 initially and steady state
conditions exist from time t = 0 to
0
. t t = The switch is suddenly thrown into
position 2. The current 1 through the 10K resistor as a function of time t from t =
0, is …. (Give the sketch showing the magnitudes of the current at t = 0,
0
and t t t = = 8 )
1.18 Discrete transistors
1 2
and T T having maximum collector current rating of 0.75
amps are connected in parallel as shown in the figure. This combination is treated
as a single transistor to carry a total current of 1 ampere, when biased with self
bias circuit. When the circuit is switched on,
1
T draws 0.55 amps and
2
T draws
0.45 amps. If the supply is kept on continuously, ultimately it is very likely that
(a) both
1 2
and T T get damaged (b) both
1 2
and T T will be safe
(c)
1
T will get damaged and
2
T will be safe
(d)
2
T will get damaged and
1
T will be safe
20V
20V
10K
1
S
2
T 1 T 2
GATE EC  1991
1.19. The builtin potential of the gate junction of a nchannel JFET is 0.5 volts. The
drain current saturates at 4.0
DS
V = volts when 0.
GS
V = The pinch off voltage is
________.
1.20. In figure, all transistors are identical and have a high value of beta. The voltage
DC
V is equal to ______.
1.21. In figure, both transistors are identical and have a high value of beta. Take the
dc baseemitter voltage drop as 0.7 volt and KT/q = 25 mV. The small signal low
frequency voltage gain ( )
o i
V V is equal to _______
Q 1
Q 2 Q 3
Q 4
5mA 1kO
10 volts
V DC=?
V i
~
1kO
1.2kO
10 volts
5.7 volts
V O/V=?
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