(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)
S safeer

(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.

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions