Input impedance butterworth filter with multiple feedback
From my visual analysis,

Zin(dc)=R1+R2//R3

for f>>f-3dB

@ f = infinity Zin = R1







simulate this circuit &ndash; Schematic created using CircuitLab

DC gain is -R3/R1  where Vx(f=0)=0

For visual aid on Vx see Attenuation, phase shift of xy for VI plot
using Java with sweep. You can change any parameter