I'm looking at a guide by Texas Instruments on active filter design. In it are the following equations for a second order lowpass filter, verbatim:(adsbygoogle = window.adsbygoogle || []).push({});

The coefficient form of the denominator: [tex]s^2 + a_1s + a_0[/tex]

Normalized: [tex]P(s) = (\frac{s}{\sqrt{a_0}*\omega_c})^2 + \frac{a_1s}{a_0*\omega_c} + 1[/tex]

Substituting [tex] s = j2\pi f, \omega_c = 2\pi f_c, a_1 = \frac{1}{Q}, \sqrt{a_0} = FSF [/tex]

[tex]P(f) = -(\frac{f}{FSF*f_c})^2 + \frac{1}{Q}\frac{jf}{FSF*fc} + 1 [/tex]

Maybe I'm missing something obvious here, but why is it that it is not FSF^2 in the second term of the last equation, if [tex]\sqrt{a_0} = FSF[/tex]?

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# 2nd order filter transfer function normalization

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