Physics Class 12 NCERT Solutions: Chapter 15 Communication System Part 2

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Q: 6. A modulating signal is a square wave, as shown in Figure.

The carrier wave is given by volts.

(i) Sketch the amplitude modulated waveform

(ii) What is the modulation index?

Answer:

It can be observed from the given modulating signal that the amplitude of the modulating signal,

It is given that the carrier wave

∴Amplitude of the carrier wave,

Time period of the modulating signal

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,

Q: 7. For an amplitude modulated wave, the maximum amplitude is found to be while the minimum amplitude is found to be. Determine the modulation index. What would be the value of if the minimum amplitude is zero volt?

Answer:

Maximum amplitude,

Minimum amplitude,

Modulation index , is given by the relation:

If

Then

Q: 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 and be the respective frequencies of the carrier and signal waves.

Signal received at the receiving station,

Instantaneous Voltage of the carrier wave,

At the receiving station, the low-pass filter allows only high frequency signals to pass through it. Obstructs the low frequency signal. Thus, at the receiving station, one can record the modulating signal , which is the signal frequency.