Question 15.1:

 

Which of the following frequencies will be suitable for beyond-the-horizon communication using sky waves?

 

10 kHz

 

10 MHz

 

1 GHz

 

1000 GHz

 

Answer

 

 

 

 

 

 

 

 

(b)  Answer:

 

10 MHz

 

For beyond-the-horizon communication, it is necessary for the signal waves to travel a large distance. 10 KHz signals cannot be radiated efficiently because of the antenna size. The high energy signal waves (1GHz − 1000 GHz) penetrate the ionosphere. 10 MHz frequencies get reflected easily from the ionosphere. Hence, signal waves of such frequencies are suitable for beyond-the-horizon communication.

 

Question 15.2:

 

Frequencies in the UHF range normally propagate by means of:

 

Ground waves.

 

Sky waves.

 

Surface waves.

 

Space waves.

 

Answer

 

Answer:

 

Space waves

 

Owing to its high frequency, an ultra high frequency (UHF) wave can neither travel along the trajectory of the ground nor can it get reflected by the ionosphere. The signals having UHF are propagated through line-of-sight communication, which is nothing but space wave propagation.

 

Question 15.3:

 

Digital signals

 

Do not provide a continuous set of values,

 

Represent values as discrete steps,

 

Can utilize binary system, and

 

Can utilize decimal as well as binary systems.

 

Which of the above statements are true?

 

(i)  and (ii) only

 

(ii)  and (iii) only

 

(i) , (ii) and (iii) but not (iv)

 

All of (i), (ii), (iii) and (iv).

 

Answer

 

 

 

 

 

 

 

 

(c)  Answer:

 

A digital signal uses the binary (0 and 1) system for transferring message signals. Such a system cannot utilise the decimal system (which corresponds to analogue signals). Digital signals represent discontinuous values.

Question 15.4:

 

Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81m tall. How much service area can it cover if the receiving antenna is at the ground level?

 

Answer

 

 

 

 

 

 

 

 

Line-of-sight communication means that there is no physical obstruction between the transmitter and the receiver. In such communications it is not necessary for the 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, 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 15.5:

 

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 a modulation index of 75%?

 

Answer

 

Amplitude of the carrier wave, A_c = 12 V

 

Modulation index, m = 75% = 0.75

 

Amplitude of the modulating wave = A_m

 

Using the relation for modulation index:

 

Question 15.6:

 

A modulating signal is a square wave, as shown in Fig. 15.14.

 

The carrier wave is given by

 

Sketch the amplitude modulated waveform

 

What is the modulation index?

 

Answer

 

 

 

 

 

 

 

It can be observed from the given modulating signal that the amplitude of the modulating signal, A_m = 1 V

 

It is given that the carrier wave c (t) = 2 sin (8πt)

 

∴Amplitude of the carrier wave, A_c = 2 V

Time period of the modulating signal T_m = 1 s

 

The angular frequency of the modulating signal is calculated as:

 

The angular frequency of the carrier signal is calculated as:

 

From equations (i) and (ii), we get:

 

The amplitude modulated waveform of the modulating signal is shown in the following figure.

 

(ii) Modulation index,

 

 

Question 15.7:

 

For an amplitude modulated wave, the maximum amplitude is found to be 10 V while the minimum amplitude is found to be 2 V. Determine the modulation index μ. What would be the value of μ if the minimum amplitude is zero volt?

 

Answer

 

 

 

Maximum amplitude, A_max = 10 V Minimum amplitude, A_min = 2 V

Modulation index μ, is given by the relation:

 

 

Question 15.8:

 

Due to economic reasons, only the upper 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 is possible to recover the modulating signal at the receiver station.

 

Answer

 

 

 

 

 

 

 

Let ω_c and ω_s be the respective frequencies of the carrier and signal waves. Signal received at the receiving station, V = V₁ cos (ω_c + ω_s)t Instantaneous voltage of the carrier wave, V_in = V_c cos ω_ct

 

At the receiving station, the low-pass filter allows only high frequency signals to pass through it. It obstructs the low frequency signal ω_s. Thus, at the receiving station, one can

 

record the modulating signal                    , which is the signal frequency.