CBSE Class 12 Physics 2019 Delhi Set 1 Paper

Question : 24 of 27

Marks: +1, -0

(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

and

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?

Solution:

(a) Obtaining the expression for modulation index in terms of

A

and

B

(b) Calculation of

µ

Reason
We are given that

A\;=A_c+A_m

\;\text " and "\; B\;=A_c-A_m

A_c\;=(A+B) \/ 2

A_m\;=(A-B) \/ 2

∴ µ\;=\;{A_m}/{A_c}

\;=\;{A-B}/{A+B}

(b) We have

µ\;=\;{A_m}/{A_c}

\;=\;{10}/{15}=\;{2}/{3}

µ

is kept less than one to avoid distortion.

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