I have a problem finding the input impedance of a Butterworth filter. The circuit is shown in the figure below:
I have calculated the transfer function between input and output; but now I have to find the symbolic expression of the input impedance seen from the \$V_{\text{in}}\$ generator. I've tried a \$V_{\text{in}}/I_{\text{in}}\$ approach. Since
$$I_{\text{in}} = \frac{(V_{\text{in}} - V_{\text{x}})}{R_1} $$
and $$ V_{\text{x}} = -V_{\text{o}}(sC_2R_2) $$
I find that $$ Z_{\text{in}} = \frac{R_1}{1+ W(s) sC_2R_2} $$ Where \$W(s)\$ is the transfer function $$ W(s) = \frac{V_{\text{o}}}{V_{\text{in}}} $$ This sounds wrong to me, because the input impedance should decrease at high frequency, and in my case it's increasing. Where am I wrong? Thank for the precious help!
EDIT : I've checked it with SAPWIN, and it looks like the expression above is correct.
In the Picture there is the 1/Zin function.
Thanks to all for your help in solving the question!