Synchronous Demodulation of Sinusoidal AM Hojo) 2 y(t) w(t) cos(ot+θ) Lowpass filter Local oscillator Y(o) Suppose 0=0 for now → Local oscillator is in phase with the carrier (c-oM) Wc(ac+OM Co (20c-aM2a
Synchronous Demodulation of Sinusoidal AM Suppose θ = 0 for now, ⇒ Local oscillator is in phase with the carrier
Synchronous demodulation in the Time domain w(t)=y(t)cos wct=a(t) cos wct=o(t)+ o(t)cos 2wct High-frequency signals Then t)= filtered out by the LPF Now suppose there is a phase difference, i.e. 0#0, then w(t)= y(t) cos(wct+0)=(t)cos wct cos(wct+8 a(t)cos 8+o(t)(cos(2wct+0)) OW (t)=a(t)cos g HF signal Two special cases 0=T/2, the local oscillator is 90o out of phase with the carrier or(o=0, signal unrecoverable 2)0=0(0)-slowly varying with time, =r(t=cos[0(o).x(o) → time-varying gain
Synchronous Demodulation in the Time Domain Two special cases: 1) θ = π/2, the local oscillator is 90 o out of phase with the carrier, ⇒ r ( t) = 0, signal unrecoverable. Now suppose there is a phase difference, i.e. θ ≠ 0, then 2) θ = θ ( t) — slowly varying with time, ⇒ r ( t) ≅ cos[ θ ( t)] • x ( t), ⇒ time-varying “gain