Question

A carrier voltage of peak voltage $12V$is used to transmit a message signal. What should be the peak voltage of the modulating signal to have a modulation index of \[75\% \]?

Answer 1

Hint: When we speak the range to which it will be audible is very less. So, to increase the range or to carry the message to large distances we use modulation. Modulation is a process by which we vary different properties of a waveform called carrier signal with a separate signal and modulating signal. Modulating signals can be an audio signal, video signal, etc. Modulation is widely used in communication and broadcasting.


Complete step by step solution:
Given: peak voltage of carrier = $12V$, we have to find peak voltage of modulating signal, modulation index =\[75\% \] .
The modulation index is defined as the ratio of the amplitude of modulating signal to the amplitude of carrier signal. Modulation index tells the amount of amplitude variation to about an unmodulated carrier.
Following is the formula of the modulation index.
$\mu = \dfrac{{{A_m}}}{{{A_c}}} = \dfrac{{{V_m}}}{{{V_c}}}$
Let us substitute the values.
$0.75 = \dfrac{{{V_m}}}{{12}} \Rightarrow {V_m} = 12 \times 0.75 = 9V$
Hence, the amplitude of modulating signal is $9V$.

Note:
Amplitude modulation is when the amplitude of the carrier is varied with modulating signal.
When the modulation index is one it is called perfect modulation.
When the modulation index is less than one it is called under-modulation.
When the modulation index is greater than one it is called over-modulation.
Depending on which property of the carrier wave is varied with the modulating wave, there are different types of modulation. For example. Amplitude modulation, frequency modulation, etc.. are the types of analog modulation.