Saved Bookmarks
| 1. |
Due to economic reasons , only the upper sideband of an AM wave is transmitted , but at the receivingstation , there is a facility for generating the carrier . Show that if a device is available which can multiply two signals , then it is possible to recover the modulating signal at the receiver station . |
|
Answer» Solution :Let `omega_(c)` be the angular frequency of CARRIER waves & `omega_(m)`be the angular frequency of signal waves . Let the signal received at the receiving station be `e = E_(1)* cos(omega_(c) + omega_m)t` Let the instantaneous voltage of carrier WAVE `e_(c) = E_(0) cos omega_(c) t` is available at receiving station . Multiplying these two signals , we GET `e xx e_(c) = E_(1) E_(c)cos omega_(c) t . cos (omega_(c) + omega_(m))t` `E = (E_(1) E_(c))/(2)* 2 . cos omega_(c) t . cos (omega_(c) + omega_(m)) t "" ("Let" e xx e_(c) = E)` `=(E_(1)E_c)/(2) [ cos (omega_(c) + omega_(c) + omega_(m)) t + cos (omega_(c) + omega_(m)- omega_(c))t]` `because 2[ cos A cos B = cos (A + B) + cos (A - B)]` `(E_(1) E_(c))/(2) =[cos (2omega_(c) + omega_(m))t + cos omega_(m) t]` Now , at the receiving END as the signal passes through filter , it will PASS the high frequency `(2omega_(c) + omega_(m))` but obstract the frequency `omega_(m)` . so we can record the modulating signal `(E_(1) E_(c))/(2) ""cos omega_(m) t` which is a signal of angular frequency `omega_(m)`. |
|