(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? 

 

 
 
 
 
 

Answers (1)

(a)  We have given that:-

Maximum amplitude,A_{max}=A

    Minimum Amplitude,A_{min}=B

Let, the amplitude of the carrier wave be A_{c} and

        the amplitude of the message signal be A_{m}

Now, we know that,

        A_{c}+A_{m}=A_{max}=A _____(1)

        A_{c}-A_{m}=A_{min}=B ______(2)

On adding(1) and (2), we have

        2\; A_{c}=A+B

            A_{c}=\frac{A+B}{2}

    and, On sunstracting (2) from (1), we have

            2\; A_{m}=A-B

                A_{m}=\frac{A-B}{2}

Hence, we know, the modulation index in terms of 

            A and B  can be given as ;

                \mu =\frac{A_{m}}{A_{c}}

              \mu =\frac{A-B}{A+B}

(b)     We know, the modulation index is given by :-

            \mu =\frac{A_{m}}{A_{c}}

       Hence, A_{m} is given as 10\; V and 

                    A_{c} is given as 15\; V  So,

            \mu =\frac{10\; V}{15\; V}

                \mu =\frac{2}{3}

To avoid the Distortion of the signal, the modulation index is generally kept less than one.

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