Question

BPF Filter Bandpass Filter The following circuit acts as a C This filter has a center (resonance) frequency at Hz. 27-VLC and a 3-dB bandwidth of BW = Hz. 2RC 3l f, and a passband for which the signal is This means that the filter has 0 dB gain at attenuated less than 3 dB centered approximately at f, from f,-BW2 to f.+BW/2 (this passband is not exactly centered at f, but its total width is BW) 3l8 Input Signal Assume that the input to this filter is the following signal: cos(2070.9375) x)30.4746e -Ser Using your knowledge of FT pairs, find an expression for the frequency representation of your signal, i.e., find X()- S{r)}. Plot the magnitude (in dB) 1 and phase (in degrees) versus frequency in Hz (positive frequencies only). Design a filter that will pass the main energy lobe of X(f). That is, choose the center frequency of your filter to be the same as the frequency of maximum energy of x(f). Then, choose the BW of your filter to be as wide as the range between the -104B frequencies of x). To do so, determine the frequencies where X(f) has fallen 10 dB from its peak, and design your filter such that these frequencies are just within the 3 dB filter BW. Find R, L and C.

Answer 1

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