InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Identify the mathematical expression for amplitude modulated wave:A. `A_(c )sin[{omega_(c )+k_(1)V_(m)(t)}t+phi]`B. `A_(c )sin{omega_(c )t+phi+k_(2)V_(m)(t)}`C. `{A_(c ) + k_(2)V_(m)(t)}sin(omega_(c )t +phi)`D. `A_(c) V_(m)(t) sin (omega_(c ) t+phi)` |
|
Answer» Correct Answer - C Consider a sinusoidal modulating signal represented by `A_(c) V_(m)(t) sin (omega_(c ) t+phi)` where, `A_(m)` = Amplitude of modulating signal `omega_(m)` = Angular frequency `= 2pi V_(m) = phi V_(m)` Also consider a sinusoidal carrier wave represented by `C(t) = A_(c ) sin omega_(c )t" .....(ii)"` Thus, modulated wave is given by `C_(m) (t) = (A_(c ) +A_(m)sin omega_(m)t)sin omega_(c ) t` `=A_(c)[1+(A_(m))/(A_(c))sin omega_(m)t)sinomega_(c)t` Here, `(A_(m))/(A_(c ))=M` `implies C_(m)(t) = (A_(c ) +A_(c)xxmusinomega_(m)t)sin omega_(c )t" .....(iii)"` Now, we know thta `A_(c) xx mu = K` [wave constant] and `sin omega_(m)t = V_(m)` [wave velocity] Thus, Eq. (iii) becomes `C_(m) (t) = (A_(c) +K xx V_(m))sin omega_(c ) t` Now, consider a change in phase angle by `phi` then `sin omega_(c ) t rarr sin (omega_(c ) t + phi)` Thus, `C_(m)(t) = (A_(c)+KV_(m))(sin omega_(c ) +phi)` |
|