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If a carrier wave  c(t)=A sin \omega _{c}t  gets amplitude modulated by a modulating signal m(t)=A sin \omega _{m}t .Then find the equation of modulated signal C_{m}(t) and its modulation index

Option: 1

C_m(t)=A(1+sin\omega _mt)sin\omega _ct \ \ \ \ and \ \ \ 2


Option: 2

C_m(t)=A(1+sin\omega _ct)sin\omega _mt \ \ \ \ and \ \ \ 1


Option: 3

C_m(t)=A(1+sin\omega _mt)sin\omega _ct \ \ \ \ and \ \ \ 1


Option: 4

C_m(t)=A(1+sin\omega _ct)sin\omega _mt \ \ \ \ and \ \ \ 2


Answers (1)

best_answer

 If the message signal is e_m = E_m \sin w_m t  and carrier waves e_c = E_c \sin w_c t

Then Amplitude modulated wave is given as

e = (E_c + E_m \sin w_mt ) \sin w_ct

So according to the question

carrier wave  c(t)=A sin \omega _{c}t 

and modulating signal m(t)=A sin \omega _{m}t

then the equation of modulated signal C_{m}(t) is given as 

C_{m}(t)=(A + A \sin w_m t ) \sin w_c

 

and 

Modulation Index

m_{a}= \frac{E_{m}}{E_{c}}=\frac{A}{A}=1

Posted by

shivangi.shekhar

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