Question

A carrier wave of peak voltage $14 V$ is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of $80%$ will be:
A. $11.2V$
B. $7V$
C. $22.4V$
D. $28V$

Answer 1

Hint: Modulation index is defined as the ratio of modulating signal voltage to the carrier signal peak voltage. The modulation index (or modulation depth) of a modulation scheme describes how much the modulated variable of the carrier signal varies around its unmodulated level.

Complete step by step answer:
Modulation index is the ratio of the peak variation actually used, to the maximum design variation in a given type of modulation. It is defined as the ratio of modulating signal voltage (${V_M}$) to the carrier signal peak voltage (${V_c}$).

Modulation index $ = \dfrac{{{V_m}}}{{{V_c}}}$ ----------(1)
Let the modulating signal voltage be ${V_m}$.
Given, carrier signal voltage$ = 14$
Modulation index$ = 80\% = \dfrac{{80}}{{100}} = 0.8$

Substituting these values in equation 1 we get,
$
0.8 = \dfrac{{{V_m}}}{{14}} \\
\therefore{V_m} = 14 \times 0.8 = 11.2V \\
$
The peak voltage of the modulating signal is 11.2V.

Note:One should know the standard definition of modulation index which is the ratio of modulating signal peak voltage to the carrier peak voltage to solve such questions.The modulation index (or modulation depth) of a modulation scheme describes how much the modulated variable of the carrier signal varies around its unmodulated level. In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform that is modulated with an information bearing signal for the purpose of conveying information. This carrier wave usually has a much higher frequency than the input signal does.