Amplitude Modulation & Demodulation (DSB-SC, SSB-SC, and Standard AM)
Mathematical Operations & Communication Theory
1. Modulation Stage: The baseband message $m(t)$ is shifted to a higher frequency $f_c$ for efficient transmission. Depending on the scheme, the mathematical model changes:
Standard AM: s(t) = [A + m(t)] · cos(2Ï€fct)
SSB-SC: s(t) = m(t)cos(2Ï€fct) ∓ m̂(t)sin(2Ï€fct)
2. Coherent Detection (The Demodulator): To recover the signal, we use a Product Detector. The received signal $r(t)$ is multiplied by a local oscillator $cos(2πfct + φ)$.
Using trigonometric identities, this generates a baseband component and a high-frequency component at $2f_c$. By passing $v(t)$ through a Low Pass Filter (LPF), we extract the original message.
3. Effect of Phase Error (φ): If the local oscillator is not perfectly synchronized ($φ \neq 0$), the output amplitude is scaled by $cos(φ)$. At $φ = 90^\circ$ (Quadrature Null Effect), the output signal is completely lost in DSB systems.