Let the modulated wave be:
e = e’ cos ωc t ………. (1)
Where,
e’ = Ec + M Ec cos ωs t ………. (2)
Now substituting (2) in (1):
e = (Ec + M Ec cos ωs t) cos ωc t ………. (3)
Expanding the equation:
e = Ec cos ωc t + M Ec cos ωs t cos ωc t
We know that:
2 cos A cos B = cos(A + B) + cos(A – B)
Therefore,
e = Ec cos ωc t + (M Ec / 2) [cos(ωc + ωs)t + cos(ωc – ωs)t]
Hence, the Amplitude Modulated (AM) wave is:
e = Ec cos 2πfc t
(M Ec / 2) cos 2π(fc – fs)t
(M Ec / 2) cos 2π(fc + fs)t
Where:
- Ec = Carrier amplitude
- fc = Carrier frequency
- fs = Signal (modulating) frequency
- M = Modulation index
Writer : Saharear Ferdous
