# Communications Systems of Frequency Downconverters

A frequency downconverter is implemented using a square-law device as follows.

The band-pass filter has a center frequency fi=|fc - ft| (also known as the intermediate frequency, IF). Assume that the message bandwidth of the input signal m(t) is equal to B Hz.

a) Determine the smallest possible IF frequency, so that there is no distortion in the output signal.

b) For a given IF frequency, what is the smallest bandwidth of the band-pass filter (BPF) so that there is no distortion in the output signal?

c) For a given IF frequency, what is the largest bandwidth of the BPF so that there is no distortion in the output signal?

Please see the diagram attached for a visual display of the frequency downconverter.

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#### Solution Summary

This answer provides the smallest possible frequency, smallest bandwidth, and largest bandwidth, given several parameters of centre frequency and the assumption that the message bandwidth of input signal is equal to BHz. Using the notion that this downconverter has used a Square-Law device, the calculations are determined by the Fourier Transform and trigonometric identities.