Page No 531: - Chapter 15 - Communications - Exercise Solutions - Ncert Solutions class 12 - Physics

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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.