In: Physics
1) A student wants to design a low-pass Butterworth filter for a data acquisition system that will not attenuate 2 Hz signal more than 4 dB but will have more than 80 dB of attenuation at 50 Hz signal.
(a) Determine the minimum number of filter stages required and the cutoff frequency (in Hz) that can be used (For the cutoff frequency, choose an integer number in the range)
(b) Assuming the source and load resistances are 50 Ω, draw the electric circuit of the designed low-pass Butterworth filter (in the above) and determine the values for the circuit components.
(c) With the designed filter, how much are the amplitudes of 20 Hz and 60 Hz attenuated? Specify the attenuation by dB unit.
(d) To test whether the designed filter produces anticipated response or not, the analog signal given below is used as an input signal to the filter. What is the average and rms values of the signal V(t)? Also, draw the frequency spectrums (amplitude (V) vs. frequency (Hz)) of the original signal before filtering and the signal after filtering. Specify the change in amplitude at each frequency, and briefly explain how the original signal changes by comparing the frequency spectrums.
?(?) = 4 + 2 sin(1??) + 8 sin(2??) + 2 sin (120??)