Band-pass filter

A band-pass filter preferentially transmits signals within a range of frequencies and attenuates sufficiently lower and higher frequencies. Taking the output voltage across the resistor in a series RLC circuit gives one example: the resonant series RLC response selects a band around $1/\sqrt{LC}$. ^[ref].

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.