A sinusoidal 10 cos ωct, ωc = 106 rad/sec is amplitude

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A sinusoidal 10 cos ωct, ωc = 106 rad/sec is amplitude

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A sinusoidal 10 cos ω_ct, ω_c = 10⁶ rad/sec is amplitude modulated using another sinusoidal A_m cos ω_mt, ω_m = 103 with 100% modulation, then the expression for AM modulated wave is expressed as—

1. 10 (1 + 0·1 cos 10³t) cos 10⁶t
2. 1·(1 cos 10³t) cos 10⁶t
3. 10(10 + 0·1 cos 10³t) cos 10⁶t
4. 10(1 + 1·cos 10³t) cos 10⁶t

Correct Option: D

AM modulated wave is expressed as
δ(t) = A_c[1 + μ cos ω_mt] cos ω_ct
given,
A_c = 10
μ = A_m = A_m = 1
A_c 10

(∴ 100% modulation)
or
A_m = 10
ω_m = 10³ rad/sec
ω_c = 10⁶ rad/sec
Hence, s(t) = 10[1 + 1.cos 10³t] cos 10⁶t