Consider a message signal 𝑚(𝑡) with bandwidth 𝑊 = 2 𝑘𝐻𝑧 , applied to a DSB-SC modulator, s.t., 𝑠(𝑡) = 𝐴𝑐𝑚(𝑡) cos(2𝜋𝑓𝑐 𝑡). Assuming perfect synchronism between the carrier waves in the modulator and detector. a. Determine (sketch) the spectrum of the detector output when 𝑓𝑐 = 1 𝑘𝐻𝑧. (Note: 𝑀(𝑓) is shown in the figure, and 𝑀(0) = 1.) b. Find the lowest 𝑓𝑐 for which each component of the modulated wave 𝑠(𝑡) is uniquely determined by 𝑚(𝑡). Sketch the spectrum of the detector output with the lowest 𝑓𝑐 that you have required.
Vc(t) = Ec sinωct – Vm(t) = Em sinωmt – VAM(t) = Ec sinωct + Em sinωmt . sinωct
We can express this as:
VAM(t) = [Ec + Em sinωmt ]. sinωct = [1+ m.sinωmt ]. Ec. sinωct