A square-law modulator for generating an AM wave relies on the useof a nonlinear device. The given figure depicts the simplest form of such amodulator. Ignoring the higher order terms, the input-output characteristics of thediode-load resistor combination in this figure are givenby: v2 (t) = a1*v1(t)+ a2* v12(t)
Where,v1(t)=Ac cos(2pfct )+m(t)
Where v1(t)is the input signal, v2(t) is the output signaldeveloped across the load
resistor, and a1 , a2 are constants.
a) Determine the spectral content of the output signal. FT
b) To extract the desired AM wave from v2(t) , we need a band-passfilter. If we were to insert this filter in the figure, determine the cut off frequencies of the required filter, assuming that the message signal is limited to the band: W= f =W .
c) To avoid spectral distortion by the presence of undesiredmodulation products in v2(t), the condition W= f = 3W must be satisfied;validate this condition.