FixedFrequencyActiveLp

$\begin{circuitikz} \draw (4, 4) node[op amp] (opamp) {} (opamp.+) node[anchor=south] {$v_+$} (opamp.-) node[anchor=south] {$v_-$} (opamp.out) node[anchor=south] {$v_o$} (2, 4.5) to (opamp.-) (2, 4.5) to (2,5.5) (2, 5.5) to[C, C=$C$] (6, 5.5) (6, 5.5) to[short] (6, 4) (2, 4.5) to (2, 7) (2, 7) to[R, R=$R$] (6, 7) (6, 7) to[short] (6, 4) (6, 4) to (opamp.out) (opamp.+) to (2, 3.5) (2, 3.5) to (2, 3) (2, 3) node[ground] {} (0, 4.5) node[anchor=east] {$v_i$} to[R, R=$R$] (2, 4.5);\end{circuitikz}$

Feedback impedance:

$\begin{eqnarray*} Z_{\mathrm{feedback}}(s) &=& R \parallel \frac{1}{Cs} \\ &=& \frac{1}{\frac{1}{R} + Cs} \end{eqnarray*}$

Transfer function:

$\begin{eqnarray*} H(s) &=& -\frac{Z_{\mathrm{feedback}}(s)}{Z_{\mathrm{input}}(s)} \\ &=& \frac{1}{\frac{1}{R} + Cs} \frac{1}{R} \\ &=& \frac{1}{1 + RCs} \end{eqnarray*}$

Low-pass, one pole at: $f = \frac{-1}{2 \pi R C}$