#### 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* = *V*_{1} cos (*ω*_{c} + *ω*_{s})*t*

Instantaneous voltage of the carrier wave, *V*_{in} = *V*_{c} cos *ω*_{c}*t*

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.