Write the equation of Amplitude modulated wave, if the carrier volatge is 10 V, the modulaiton index , is 0.2 , the carrier and modulation frequenceis are 7 MHz and 2.5 KHz respectively .

Explanation

Modulating voltage `= E_(m) = 10 V`
Modulation index ` = m_(a) = 0.2`
`E_(c) = ?`
`E_(c) = (E_(m))/(m_(a)) = (10)/(0.2) = 50`
Carrier frequency `=v_(c) = 7 MHz`
` = 7 xx 10^(6) Hz`
`therefore " " w_(c) = 2pi v_(c) = 2 xx 7 xx 10^(6)`
`w_(c) = 14pi xx 10^(6)`
Modulating frequency `= v_(m) = 2.5 KHz`
` V_(m) = 2.5 xx 10^(3) Hz`
` w_(m) = 2 pi v_(m)`
` = 2pi xx 2.5 xx 10^(3)`
` = 5 pi xx 10^(3)`
We know `E = E_(c)` [ `1+ m_(a) sin w_(m)t] sin [w_(c)t]`
`E = 50 [ 1+ 0.2 sin 5 pi xx 10^(3) t] sin 4 pi xx 10^(6) t`
`E = 50 [ 1+ (1)/(5) sin (5pi xx 10^(3)) t] sin (14 pi xx 10^(6)) t `