I am quite confused with this circuit. Most circuits I have seen don't have a capacitor between the op amp inputs. I tried to write out the differential equations using nodes, but I can't find enough equations to solve the system.
*The circuit showed in the picture is used for humidity measurement by measurement capacitance \$C_x\$, it is an old design but it still works for a range of humidity, i dont have the values of \$C_s\$ and \$C_x\$,but it seems that \$C_x\$ can range from \$0-20pF\$
My goal is understand how this circuit works, and find the mathematical relation between the output volatage of the op amp and \$C_x\$ , frequency and duty cycle of \$S_1\$, then calculate the values of each component in such a way that this relation more or less linear.
I didn't consider that the voltage between the inputs is zero, because I think capacitor \$C_9\$ takes time to be charged or the op amp takes time to make it zero. Do we have to always consider that the voltage between op amp inputs is zero?
Could someone suggest some steps to calculate the components of the circuit?, maybe I shoud remove \$C_9\$ at the beginning, calculate the component's values , and implement the circuit and then check which value of \$C_9\$ give a better performance.