Question

Evaluate the effect of a frequency error ∆f in the local carrier frequency of the detector, measured with respect to the carrier frequency of the incoming DSB- SC signal.

Answer 1

The coherent detector works properly only when Δω = 0.

Explanation:

• The DSB-SC modulated signal is s(t)  = Acm(t)cos ωct
• Suppose the local oscillator output in the coherent detector be cos(ωct + Δωt)

v(t) = {Acm(t)cos ωct} x cos (ωc t + Δωt) = Ac m (t) / 2 cosΔωt + Acm(t) / 2 cos (2ωct + Δωt)

We have  

s (t) = Acm(t)cos ωct  

vo(t) = Ac / 2 m(t) x cos Δωt

If Δω = 0  

Then  

vo(t) = Ac / 2 m(t)

The coherent detector works properly only when Δω = 0.