Question

The carrier wave is given by \[C(t)=2\sin (\omega t)volt\]. The modulating signal is a square wave as shown. Find the modulation index.

Answer 1

Hint: In the given question we have to find an amplitude modulation index for the given modulating signal wave. Here we will apply direct formula and direct values from the waveform and the given data. We will also discuss a few important things related to modulation and its significance.

Formula used:
\[\mu =\dfrac{{{A}_{M}}}{{{A}_{C}}}\]

Complete step by step answer:
Amplitude modulation index is the ratio of the amplitude of modulating signal to the amplitude of carrier wave, which is given as follows
\[\mu =\dfrac{{{A}_{M}}}{{{A}_{c}}}\]
Where, μ is modulating index.
The carrier wave is generally given as
 \[C(t)={{A}_{C}}\sin (\omega t)volt\]
Hence the value of \[{{A}_{C}}\] is 2 from the given data.
And from the waveform we can get the amplitude of modulating signal which is \[{{A}_{M}}=2\]
Hence the amplitude modulation index becomes
\[\mu =\dfrac{2}{2}=1\]
Hence the modulating index for the given data is 1.

Additional information:
Modulation is a process in which a low frequency signal is superimposed on a high frequency signal, such that it acts as a carrier wave to transmit the low frequency over a long distance. Modulation process can be done by controlling the amplitude or frequency or the phase of the carrier wave. Based on the quantity we are controlling, modulation is of three types: amplitude modulation (AM), frequency modulation (FM) and phase modulation (PM).
Modulation is necessary for transmitting the low frequency signal without any distortion or disturbance.

Note:
Modulation indexes are of three types which are amplitude modulation index, frequency modulation index, and phase modulation index. Here we have asked about modulating index which is taken as amplitude modulating index generally because in other cases it would be specified. Still I have used the terms amplitude modulation index to specify it.