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Explain amplitude modulation . |
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Answer» Solution :Amplitude modulation : In amplitude modulation , the amplitude of carrier wave VARIES , but frequency and phase remains constant . Here we can explain AM using a sinusoidal signal as a modulating signal . Let C(t) = `A_(c) sin omega_(c)t ` t represent carrier wave `m(t) = A_(m) sin omega_(m) t` represent modulating signal . The modulating `C_(m)` (t) can be written as `C_(m) (t) = (A_(c) + A_(m) sin omega_(m) t) sin omega_(C) t` `C_(m) (t) = A_(c) (1 + (A_(m))/(A_(c)) sin omega_(m)t) sin omega_(c) t "" ...(1)` Where `omega_(m) = 2 pi f_(m)` is the angular frequency of message signal . Note that the MODULATED signal now contains the message signal . `C_(m) (t) = A_(c) sin omega_(c) t + mu A_(c) sin omega_(m) t sin omega_(c) t "" ... (2)` Where `mu = (A_(m))/(A_(c)) = ` Modulation index . To avoid DISTORTION KEEP `mu le 1` `C_(m) (t) = A_(c) sin omega_(c) t + (muA_(c))/(2) "" cos(omega_(c) + omega_(m)) t - (muA_(c))/(2) ""cos (omega_(c) + omega_(m)) t "" ... (3)` Here `(omega_(c) - omega_(m))` and `(omega_(c) + omega_(m))` are lower side and upper side frequencies . As long as broadcast frequencies (carrier wave) are sufficiently spaced out the side bands donot over lap . |
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