Inverting RC high-pass amplifier ($H(\omega )=-i\omega R_{f}C/(1+i\omega R_{i}C)$)

An ideal operational amplifier with a series input resistor and capacitor, resistive feedback and a grounded noninverting terminal realizes the displayed high-pass filter. Virtual ground and Kirchhoff's current law give $H=-R_f/[R_i+1/(i\omega C)]$. Its phase is $-\pi /2-{\tan }^{-1}(\omega R_{i}C)$ in the $e^{i\omega t}$ convention. Equal resistances do not make its phase frequency independent.