= Series-parallel RC band-pass filter
{title2=$H(\omega)=[3+i(\omega RC-1/(\omega RC))]^{-1}$}
A series <resistor> $R$ and <capacitor> $C$ feed a parallel pair with the same values. Measuring the parallel pair's <voltage> relative to the return gives this unloaded <transfer function> for <phasors> proportional to $e^{i\omega t}$. The <voltage divider> applied to $Z_s=R+1/(i\omega C)$ and $Z_p=R/(1+i\omega RC)$ proves the formula. The <amplitude> peaks at $\omega=1/(RC)$ with ratio $1/3$ and zero relative <phase>. At low and high positive <frequencies>, the <transfer function> tends respectively to $i\omega RC$ and $-i/(\omega RC)$. Reversing output polarity changes its sign, while loading changes the response itself.
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