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GATE Electronics and Communications (EC) 2020 Solved Papers
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© examsnet.com
Question : 50
Total: 65
SPM(t) and SFM(t) as defined below, are the phase modulated and frequency modulated waveforms, respectively, corresponding to the message signal
m
(
t
)
shown in the figure.
S
P
M
(
t
)
=
cos
(
1000
π
t
+
K
p
m
(
t
)
and
S
F
M
(
t
)
=
cos
(
1000
π
t
+
K
f
∫
−
∞
t
m
(
τ
)
d
τ
)
Where
K
p
is the phase deviation constant in radians\/volt and
K
f
is the frequency deviation constant in radians\/second\/volt. If the highest instantaneous frequencies of
S
P
M
(
t
)
and
S
F
M
(
t
)
are same, then the value of the ratio
K
p
K
f
is ____________ seconds.
Your Answer:
Validate
Solution:
S
p
m
(
t
)
=
cos
[
1000
π
t
+
K
p
m
(
t
)
]
S
F
m
(
t
)
=
cos
[
1000
π
t
+
K
P
∫
∞
t
m
(
τ
)
d
τ
]
Maximum instantaneous frequency in FM.
f
i
=
1
2
π
[
d
d
t
θ
i
(
t
)
]
f
i
=
1
2
π
[
1000
π
t
+
K
f
m
(
t
)
]
........(i)
And maximum instantaneous frequency in PM
f
i
=
1
2
π
[
1000
π
+
d
d
t
k
p
m
(
t
)
]
d
d
t
m
(
t
)
f
i
=
1
2
π
[
1000
π
+
K
p
×
5
]
.......(ii)
Given maximum instantaneous frequency is same
1
2
π
[
1000
π
+
K
f
m
(
t
)
]
=
1000
π
2
π
+
5
K
P
2
π
K
f
×
10
=
5
K
P
K
p
K
f
=
2
© examsnet.com
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