A given differential capacitive sensor is available that is based on the variation in plate distance and whose movable plate is grounded. In order to obtain a groundreferenced output signal proportional to the input displacement in the circuits shown. Assume that the op$-$amps are ideal. Determine the conditions to be fulfilled by resistors and capacitors in the circuit in order that the output voltage is directly proportional to the displacement and independent of oscillation frequency.

Note: for a variable plate separation:

$\backslash ($ C $1=\backslash$frac$\{$C o$\}\{1-$x$\}\backslash$quad $\backslash$& C $2=\backslash$frac$\{$C o$\}\{1+$x$\}\backslash$quad $\backslash )$ where x is the displacement