1
EC/IN
Hinglish
WorkBook 02
Communication
Angle Modulation
Common Data for Q.1 to 4:
An angle modulated signal with carrier frequency
c = 2 106 is described by the equation
x(t )  20cos  c t  0.1sin(200t )
1.
The peak frequency deviation  f is ________ Hz.
frequency of 1 kHz. If the signal tone frequency is
increased to 2 kHz, assuming that phase deviation
remains unchanged, the bandwidth of the PM signal is
________ kHz.
10. A signal m(t) = 5 cos (2 100t) frequency modulates a
carrier. The resulting FM signal is 10 cos [2 10t + 15
2.
The peak phase deviation   is ________ rad.
sin (2 100t)]. the approximate bandwidth of the FM
would be ________ kHz.
3.
The power of modulated signal is ________ watt.
4.
What will be the bandwidth (in kHz) of modulated
signal?
5.
The signal m(t) = sinc (2 × 104 t) is frequency
modulated with kf = 103 Hz/V. If the carrier frequency
is 1 MHz, then the maximum instantaneous frequency
of the modulated signal is ________ MHz.
11. A device with input x(t) and output y(t) is
characterized by y(t) = x(t/2). An FM signal with
frequency deviation of 90 kHz and modulating signal
bandwidth of 5 kHz is applied to this device. The
bandwidth of the output signal is ________ kHz.
6.
The peak frequency deviation produced in a VHF
carrier by a signal of 100 Hz is 50 kHz. What is the
frequency modulation index?
12. A message signal with bandwidth 10 kHz is Lowerside Band SSB modulated with carrier frequency fc1 =
105 Hz. The resulting signal is then passed through a
Narrow-Band frequency Modulator with carrier
frequency fc2 = 109 Hz. What would be the bandwidth
(in MHz) of the output?
7.
An FM wave use a 2-5 V, 5000 Hz modulating
frequency and has a modulation index of 50. The peak
frequency deviation is ________ kHz.
13. An FM signal has a carrier swing of 100 kHz when the
modulating signal has a frequency of 8 kHz. The
modulation index is ________.
8.
A signal m(t) = 5 cos (2000 t) phase modulate the
14. An FM signal has a carrier frequency of 105 MHz and
upper frequency 105.007 MHz of modulated signal.
The carrier swing is ________ kHz.
carrier c(t) = 100 cos 2 fct. The PM signal has a peakphase deviation of /2. The carrier frequency is fc = 10
Hz. The approximate bandwidth (using Carson rule) is
________ Hz.
9.
A carrier is phase modulated (PM) with peak
frequency deviation of 10 kHz by a signal tone
Common Data for Q.15 and 16:
In a certain frequency-modulation experiment
conducted with fm = 1 kHz and increasing amplitude
(starting from 0 V), it is found that the carrier
2
component of the FM signal is reduced to zero for the
first time when Am = 2 V. Given that Bessel function
J0(x) is zero for x = 2.44, 5.52, 8.65, 11.8 and so on.
f1 = 200 kHz, fLO = 10.8 MHz,  f1 = 25 Hz, n1 = 64,
n2 = 48
15. What will be the frequency sensitivity (in kHz/V) of
the modulator?
16. The carrier components is reduced to zero for the
second time for the value of Am = ________ Volt.
22. What will be the maximum frequency deviation (in
kHz) at the output of the FM transmitter?
17. An angle modulated signal is expressed by
23. At output of the transmitter the carrier frequency is
________ MHz.
x(t )  cos[(2107 t )  75sin(2103 t )]
What is the peak frequency deviation (in kHz) of the
carrier?
18. A signal m(t )  100cos(2100t ) frequency modulates
a carrier. The resulting FM signal is
x(t )  20cos[2106 t  15sin(2100t )]
The approximate bandwidth of the FM would be
________ kHz.
19. An audio signal has a bandwidth of 25 kHz. The
maximum value of |m(t)| is 5 V. This signal frequency
modulates a carrier. If the frequency sensitivity
constant of the modulator is 20 kHz/V, then according
to Carson's rule, what will be the bandwidth (in kHz)
of the modulator output?
24. An FM signal with a peak frequency deviation of 10
kHz at a modulation frequency of 5 kHz is applied to
two multipliers connected in cascade. The first
multiplier doubles the frequency and the second
multiplier triples the frequency. the modulation index
of the FM signal obtained at the second multiplier
output is ________.
Common Data for Q.25 and 26:
An Armstrong indirect FM modulator is to be used to
generate an FM carrier with a carrier frequency of 98.1
MHz and frequency deviation  f = 75 kHz. A narrowband FM generator is available at a carrier frequency
of 100 kHz and a frequency deviation  f = 10 Hz. The
scheme utilized to accomplish this is shown in figure.
20. An FM modulator has fc = 1 kHz and frequency
sensitivity constant of the modulator kf = 12.5 Hz/V.
The modulator has input m(t) = 4 cos (2 10t). The
modulation index would be ________.
25. The center frequency of BPF is ________ MHz.
21. An AM transmitter radiates 4 kW with an
unmodulated carrier wave and 5 kW when it is
amplitude modulated. If the same carrier were
frequency modulated, then the radiated power will be
________ kW.
Common Data for Q.22 and 23:
A block diagram of an Armstrong FM transmitter is
shown in the figure. The parameter are as follows:
26. The frequency of local oscillator fLO would be
________ MHz.
27. The Fourier transformed M(f) of a signal m(t) is shown
in figure below. It is to be transmitted from a source to
destination. It is known that the signal is normalized,
meaning that –1  m(t)  1.
3
33. What will be the peak phase deviation (in radians) of
the signal?
34. At t 
If an FM signal with frequency sensitivity kf = 60 kHz
is used, then the bandwidth of the modulated signal is
________ kHz.
Common Data for Q.28 and 29:
An FM signal with a frequency deviation of 10 kHz at
a modulation frequency of 5 kHz is applied to two
frequency multiplier connected in cascade. The first
multiplier doubles the frequency and the second
multiplier triples the frequency.
28. What is the frequency deviation (in kHz) of the FM
signal obtained at the second multiplier output?
29. What will be the modulation index of the FM signal
obtained at the second multiplier output?
30. What is the maximum modulating frequency (in kHz)
that can be used to achieve a modulation index of 2.2
with a deviation of 7.48 kHz?
Common Data for Q.31 and 32:
The input to an FM receiver has signal to noise ratio
of 2.8. The modulating frequency is 1.5 kHz. The
maximum permitted deviation is 4 kHz.
1
second, the instantaneous frequency
30
deviation will be ________ Hz.
Common Data for Q.35 and 36:
An FM signal ranging from fmax = 100.02 MHz to
fmin = 99.98 MHz is modulated by a 3 kHz sine wave.
35. What is the carrier frequency (in MHz) of the signal?
36. What is the modulation index of FM signal?
37. The frequency range of a commercially broadcast FM
signal is 88 to 108 MHz with carrier swing of 125 kHz.
What will be the percentage modulation of signal?
(Assume that FCC standard for maximum frequency
deviation of FM broadcast signal is 75 kHz).
38. According to FCC (Federal Communications
Commission) regulations, the maximum allowable
frequency deviation of the TV signal is 25 kHz. For a
TV signal, given that the percentage modulation of the
audio portion is 80%. What is the frequency deviation
(in kHz) of the audio signal?
Common Data for Q.39 and 40:
Consider an FM signal represented by
s(t )  12cos[6 108  5sin(1250t )]
31. What is the frequency deviation (in Hz) caused by the
noise?
32. What is the output signal to noise ratio for the FM
receiver?
Common Data for Q.33 and 34:
An angle modulated signal s(t) is given as
s (t )  Ac cos[c t  2cos 60t  5cos 40t ]
where c is the carrier frequency.
39. What is the maximum frequency deviation (in Hz) in
the FM signal?
40. What power (in watt) will the FM wave dissipate in a
10 Ω resistor?
41. A video signal with bandwidth, W = 5 MHz is to be
transmitted via FM with frequency deviation  f = 25
4
MHz. What should the minimum carrier frequency (in
MHz) for the signal?
48. An FM signal s (t )  100cos  c t  2 k f

t

0 m() d 
is modulated by the waveform shown in figure below.
42. A commercial FM radio station alternates between
music and talk show call in formats. The broadcasted
CD music is bandlimited to 15 kHz based on
convention. If the bandwidth for voice signal is W = 5
kHz, and the deviation ratio for both music and voice
is D = 5, then the percentage of available transmission
bandwidth during the talk show is ________%.
43. An audio signal m(t) has a bandwidth of 25 kHz. The
maximum value of |m(t)| is 5 V. This signal frequency
modulates a carrier. If the deviation constant of
modulator is 20 Hz/V. What will be the bandwidth (in
kHz) of modulator output?
Common Data for Q.44 and 46:
A modulated signal is described by the equation,
s(t )  10cos[(2108 )t  10cos(2103 t )]
What should be the value of kf so that the peak to peak
frequency deviation is 25 kHz?
Common Data for Q.49 and 51:
An FM modulator has output,
s (t )  100cos  c t  2k f

t

0 m()d  
where, kf = 30 Hz/V. Assume that m(t) is the
rectangular pulse defined as
t  2
m(t )  8 rect 

 4 
44. What is the percentage of AM for the signal?
45. What is the maximum phase deviation (in radian) for
the signal?
49. What is the peak frequency deviation (in Hz) for the
FM signal?
50. What is the peak phase deviation in radians?
46. What is the maximum frequency deviation (in kHz)
for the signal?
47. A sinusoidal modulating waveform of amplitude 4V
and frequency 1 kHz is applied to an FM exciter that
has a modulator gain of 50 Hz/V. What is the
modulation index of the FM wave?
51. What is the average power (in watt) in modulator
output?
5
Answer Key
1.
(100)
27.
(140)
2.
(0.1)
28.
(60)
3.
(200)
29.
(12)
4.
(2.2)
30.
(3.4)
5.
(1.001)
31.
(0.5478)
6.
(500)
32.
(7.3)
7.
(25000)
33.
(7)
8.
(5142)
34.
(86.6025)
9.
(44)
35.
(100)
10.
(3.2)
36.
(6.67)
11.
(380)
37.
(83.3)
12.
(2)
38.
(20)
13.
(6.25)
39.
(995)
14.
(14)
40.
(7.2)
15.
(1.22)
41.
(600)
16.
(4.52)
42.
(33.3)
17.
(75)
43.
(50.2)
18.
(3.2)
44.
(0)
19.
(250)
45.
(10)
20.
(5)
46.
(10)
21.
(4)
47.
(0.2)
22.
(76.8)
48.
(1.67)
23.
(96)
49.
(240)
24.
(12)
50.
(1920 π)
25.
(1.635)
51.
(5000)
26.
(10.865)
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