Chapter 15 Communication Systems Solutions
Question - 1 : - Which of the followingfrequencies will be suitable for beyond-the-horizoncommunication using sky waves?
(a) 10 kHz
(b) 10 MHz
(c) 1 GHz
(d) 1000 GHz
Answer - 1 : -
(b)Answer:
10 MHz
For beyond-the-horizoncommunication, it is necessary for the signal waves to travel a large distance.10 KHz signals cannot be radiated efficiently because of the antenna size. Thehigh energy signal waves (1GHz − 1000 GHz) penetrate the ionosphere. 10 MHz frequenciesget reflected easily from the ionosphere. Hence, signal waves of suchfrequencies are suitable for beyond-the-horizon communication.
Question - 2 : - Frequencies in the UHF rangenormally propagate by means of:
(a) Ground waves.
(b) Skywaves.
(c) Surface waves.
(d) Spacewaves.
Answer - 2 : -
(d)Answer:
Space waves
Owing to its high frequency, an ultra high frequency (UHF) wave can neither travel along thetrajectory of the ground nor can it get reflected by the ionosphere. Thesignals having UHF are propagated through line-of-sight communication, which isnothing but space wave propagation.
Question - 3 : - Digital signals
(i) Donot provide a continuous set of values,
(ii)Represent values as discrete steps,
(iii) Canutilize binary system, and
(iv) Canutilize decimal as well as binary systems.
Which ofthe above statements are true?
(a) (i)and (ii) only
(b) (ii)and (iii) only
(c) (i),(ii) and (iii) but not (iv)
(d) Allof (i), (ii), (iii) and (iv).
Answer - 3 : -
(c)Answer:
A digital signal uses thebinary (0 and 1) system for transferring message signals. Such a system cannotutilise the decimal system (which corresponds to analogue signals). Digitalsignals represent discontinuous values.
Question - 4 : - Is it necessary for atransmitting antenna to be at the same height asthat of the receiving antenna for line-of-sight communication? A TVtransmitting antenna is 81m tall. How much service area can it cover if thereceiving antenna is at the ground level?
Answer - 4 : -
Line-of-sightcommunication means that there is no physical obstruction between thetransmitter and the receiver. In such communications it is not necessary forthe transmitting and receiving antennas to be at the same height.
Height of the given antenna, h =81 m
Radius of earth, R =6.4 × 106 m
For range, d = (2Rh)½,the service area of the antenna is given by the relation:
A = πd2
= π (2Rh)
= 3.14 × 2 × 6.4 × 106 × 81
= 3255.55 × 106 m2
= 3255.55
∼ 3256 km2
Question - 5 : - A carrier wave of peak voltage 12 V is used to transmit a message signal.What should be the peak voltage of the modulating signal in order to have amodulation index of 75%?
Answer - 5 : -
Amplitude of the carrier wave, Ac = 12 V
Modulation index, m =75% = 0.75
Amplitude of the modulating wave = Am
Using the relation formodulation index:
Question - 6 : - A modulating signal is a squarewave, as shown in Fig. 15.14.
The carrier wave is given by 
(i) Sketch the amplitude modulated waveform
(ii) What is the modulation index?
Answer - 6 : -
It can be observed from the givenmodulating signal that theamplitude of the modulating signal, Am = 1 V
It is given that the carrier wave c (t) = 2 sin (8πt)
∴Amplitudeof the carrier wave, Ac = 2 V
Time period of themodulating signal Tm = 1 s
The angular frequency of the modulating signal is calculated as:
The angular frequency of thecarrier signal is calculated as:
From equations (i)and (ii), we get:
The amplitude modulated waveform of the modulating signal is shown in thefollowing figure.
(ii)Modulation index, 
Question - 7 : - For an amplitude modulated wave,the maximum amplitude is foundto be 10 V while the minimum amplitude is found to be 2 V. Determine themodulation index μ.What would be the value of μ ifthe minimum amplitude is zero volt?
Answer - 7 : -
Maximum amplitude, Amax = 10 V
Minimum amplitude, Amin = 2 V
Modulation index μ,is given by the relation:
Question - 8 : - Due to economic reasons, only theupper sideband of an AM wave is transmitted,but at the receiving station, there is a facility for generating the carrier.Show that if a device is available which can multiply two signals, then it ispossible to recover the modulating signal at the receiver station.
Answer - 8 : -
Let ωc and ωs be the respective frequencies of thecarrier and signal waves.
Signal received at the receiving station, V = V1 cos (ωc + ωs)t
Instantaneous voltage of the carrier wave, Vin = Vc cos ωctAt thereceiving station, the low-pass filter allows only high frequency signals topass through it. It obstructs the low frequency signal ωs. Thus, at the receiving station, one can recordthe modulating signal 
, which is the signal frequency.