= Selectivity bound for a two-real-pole band-pass
{title2=$Q=\sqrt{\tau_1\tau_2}/(\tau_1+\tau_2)\le1/2$}
For a response proportional to $s/[(1+s\tau_1)(1+s\tau_2)]$ with positive time constants, its half-power width is $1/\tau_1+1/\tau_2$. Combining with the geometric-mean centre <frequency> gives the displayed <quality factor>; the <arithmetic-geometric mean inequality> proves the bound. Equality requires matched time constants and gives half-power <frequencies> $(\sqrt2\pm1)\omega_0$. Adjusting gains does not make this topology a high-Q resonant filter.
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