The prototype 2nd order low-pass type butterworth filter is given by

1
\(\frac{{\sqrt 2 }}{{{s^2} + \sqrt 2 s + 1}}\)
2
\(\frac{2}{{{s^2} + \sqrt 2 s + 2}}\)
3
\(\frac{1}{{{s^2} + \sqrt 2 s + 1}}\)
4
\({s^2} + \sqrt 2 s + 2\)

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