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Question
Identify the mathematical expression for amplitude modulated wave ______.
Options
Ac sin [{ωc + k1vm (t)}t + φ].
Ac sin {ωct + φ + k2 vm (t)}.
(Ac + k2 vm (t)) sin (ωct + φ).
Ac vm (t) sin (ωct + φ).
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Solution
Identify the mathematical expression for amplitude modulated wave `underline((A_c + k_2 v_m (t)) sin (ω_ct + φ))`.
ω
Modulating signal m(t) = Am sin ωct
Carrier signal c(t) = Ac sin ωct
Modulated signal
`c_m (t) = (A_c + A_m sin ω_m t) sin ωt`
`c_m (t) = A_c [1 + A_m/A_c sin ω_m t] sin ω_mt`
`c_m (t) = (A_c + muA_c sin ω_ct)` as `k = muA_c`
`c_m (t) = (A_c + ksin ω_m t) sin ω_mt`
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