Series-fed parallel LC voltage response (source code)

= Series-fed parallel LC voltage response
{title2=$H(\omega)=\{1-iR[1/(\omega L)-\omega C]\}^{-1}$}

An ideal <voltage> source drives a series <resistor> feeding a parallel <inductor> and <capacitor>. In the $e^{i\omega t}$ convention, the branch <voltage> ratio is the title expression. It is a band-pass response with unit peak at $1/\sqrt{LC}$, phase from $+\pi/2$ through zero to $-\pi/2$, and half-power bandwidth $1/(RC)$. At <resonance> the input current vanishes while equal and opposite <inductor>/<capacitor> currents remain finite. Reactive branch-current magnitudes must be combined as <phasors>, not added as positive scalars.