$$ \text{In each case, $f_c$ varies with $| V_{ctrl} |$.} \\~\\ \text{$0.012V <= | V_{ctrl} | <= 3V$} \\~\\ \text{1st Order Lowpass} \\ \frac{V_{out}(s)}{V_{in}(s)} = - \frac{2\pi f_c}{s + 2\pi f_c} \\~\\ \text{1st Order Highpass} \\ \frac{V_{out}(s)}{V_{in}(s)} = - \frac{Gs}{s + 2\pi f_c} \\~\\ \text{1st Order Allpass} \\ \frac{V_{out}(s)}{V_{in}(s)} = - \frac{s - 2\pi f_c}{s + 2\pi f_c} \\~\\ \text{2nd Order Lowpass} \\ \frac{V_{out}(s)}{V_{in}(s)} = \bigg(\frac{2\pi f_c}{s + 2\pi f_c}\bigg)^2 \\~\\ \text{2nd Order Highpass} \\ \frac{V_{out}(s)}{V_{in}(s)} = \bigg(\frac{Gs}{s + 2\pi f_c}\bigg)^2 \\~\\ \text{2nd Order Allpass} \\ \frac{V_{out}(s)}{V_{in}(s)} = \bigg(\frac{s - 2\pi f_c}{s + 2\pi f_c}\bigg)^2 \\~\\ $$

$$ \text{1st Order:} \\ \begin{array}{|c|c|} \hline \text{Opamps} & \text{1 of 8} \\ \hline \text{Comparators} & \text{1 of 4} \\ \hline \text{Capacitors} & \text{5 of 32} \\ \hline \text{SAR} & \text{1 of 4} \\ \hline \end{array} \\~\\ \text{2nd Order:} \\ \begin{array}{|c|c|} \hline \text{Opamps} & \text{2 of 8} \\ \hline \text{Comparators} & \text{1 of 4} \\ \hline \text{Capacitors} & \text{8 of 32} \\ \hline \text{SAR} & \text{1 of 4} \\ \hline \end{array} $$