A carrier wave of peak voltage 12 V is used to transmit a message signal. What should be the pe

step 1 In this problem, peak voltage is equal to 12v. Modulation index is equal to 75 % which is equal

A carrier wave of peak voltage 12 V is used to transmit a...

A carrier wave of peak voltage $12 \mathrm{~V}$ 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\%?
(a) $7 \underline{\mathrm{V}}$
(b) $6 \mathrm{~V}$
(c) $9 \mathrm{~V}$
(d) $8 \mathrm{~V}$

Key Concepts

Amplitude Modulation (AM)

Amplitude Modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. In AM, the amplitude of the carrier wave is varied in proportion to the instantaneous amplitude of the message or modulating signal, while the frequency remains constant. This process allows the information contained in the modulating signal to be conveyed over long distances.

Carrier Wave

The carrier wave is a high-frequency sinusoidal signal that is used to carry the information signal in modulation. It serves as the basis for transmitting the modulated signal over a medium such as air. The properties of the carrier, especially its amplitude, frequency, and phase, are critical parameters that influence the performance and quality of the transmission.

Modulating Signal

The modulating signal (or message signal) is the original information signal that is used to modulate the carrier wave in amplitude modulation. It typically contains the audio, video, or other data that needs to be transmitted. Its amplitude variations directly affect the amplitude of the carrier wave, thereby encoding the information for transmission.

Modulation Index

The modulation index is a measure of the extent to which the carrier wave is modulated by the message signal in amplitude modulation. It is defined as the ratio of the peak amplitude of the modulating signal to the peak amplitude of the carrier wave. A modulation index of 100% corresponds to the maximum modulation without distortion, while values beyond this can lead to overmodulation and signal distortion.

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