Question

(a) If A and B represent the maximum and minimum amplitudes of an amplitude modulated wave, write the expression for the modulation index in terms of A & B.
(b) A message signal of frequency 20 kHz and peak voltage 10 V is used to modulate a carrier of frequency 2 MHz and peak voltage of 15 V. Calculate the modulation index. Why the modulation index is generally kept less than one?

Answer 1

(a) In amplitude modulation, modulation index defines the degree of modulation. It determines the quality of transmitted signal. It is equal to the ratio of amplitude of modulating signal to the amplitude of carries wave, that is, ma = Em/Ec ... (1) Now maximum amplitude of modulated wave is A = Ec + Em ... (2) and maximum amplitude of modulated wave B = Ec - Em ... (3) From Eqs. (2) and (3), we get Substituting in Eq. (1), we get So, the modulation index in terms of A and B is (b) Given: Frequency of message signal is Fm = 20 kHz Peak voltage of message signal, Vm = 10 V frequency of carries wave, FC = 2 MHz peak voltage of carrier wave, Vc = 15 V. We know that the carrier voltage is ec = Ecsinωct where Ec is the amplitude of carrier wave and message signal voltage. em = Em sinωmt where Em is amplitude of message signal. So, from the relation ma = Em/Ec, The modulation index is generally kept less than one to avoid distortion.Read more on Sarthaks.com - https://www.sarthaks.com/544894/a-if-a-and-b-represent-the-maximum-and-minimum-amplitudes-of-an-amplitude-modulated-wave

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Answer 2

(a) Expression for the modulation index in terms of A & B:

Let maximum amplitude of A = A

Let maximum amplitude of A = B

Let amplitude of the message signal = Am

Let amplitude of the carrier wave = Ac

We know that,

$A_{c}+A_{m}=A_{m a x}=A \longrightarrow (1)$

$A_{c}-A_{m}=A_{m i n}=B \longrightarrow (2)$

On adding equation (1) and (2), we get,

$2 A_{c}=A+B$

$A_{c}=\frac{A+B}{2}$

On subtracting (2) from (1), we get,

$2 A_{m}=A-B$

$A_{m}=\frac{A-B}{2}$

(b) The modulation index is 2/3

Given:

Frequency of message signal = 20 kHz

Frequency of carrier wave = 2 MHz

To find:

Modulation index = ?

Formula:

Modulation index is given by the formula:

$\mu=\frac{E_{m}}{E_{c}}$

Solution:

On substituting the values in the above formula, we get,

$\mu=\frac{10 \ \mathrm{V}}{15 \ \mathrm{V}}=\frac{2}{3}$

The modulation index is generally kept less than one to avoid disturbances in the signal.