# Butterworth filter design

#### Shakespeare

Joined Sep 12, 2022
16
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#### crutschow

Joined Mar 14, 2008
31,134
We don't do homework here, we help, so you need to show us you best effort to solve the problem.

#### Papabravo

Joined Feb 24, 2006
19,612
Well, you are given the bandwidth sort of. You know that the Butterworth response is maximally flat which means that the response never increases, and it must decrease monotonically. You also know there will be no ripple in the passband. Set the DC gain at 1.05 dB and the gain at 75 Hz. to 0.95 dB and take 5 times 75 Hz. = 375 Hz. as the point where the response is -40dB. That at least will give you the order of the filter required to achieve this goal. Technically this would be a lowpass filter, but I suppose you could call it a bandpass filter with a lower bound of 0Hz.

Also worth mentioning that this cannot be a passive Butterworth filter since there is no apparent insertion loss in the passband.

Now if there is also a specification for attenuation below 75 Hz. we can address that as well.

ETA: a lowpass Butterworth with these requirements may not be possible. Increasing the order to make the 5th Harmonic of 75 Hz @ 375 Hz be 40 dB down will strongly attenuate the response at 75 Hz. as well. Maybe that was the point of the exercise. I guess it doesn't matter much since the TS has apparently abandoned the thread.

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