Physics Class 12 NCERT Solutions: Chapter 15 Communication System Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Amplitude Modulated Wave

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

Q_6_Modulated Square Wave

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.

Q_6_The Amplitude Modulated Waveform

(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.

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