How to design an amplifier for a sensing liquid level using capacitive probes?
simulate this circuit &ndash; Schematic created using CircuitLab
The circuit diagram shows a positive integrator (DEBOO Integrator, NIC- intergrator). It has the advantage that the integrating capacitor is grounded (which may be important for the discussed application).
For R2=R4 and R1=R3 the opamps output voltage is Vout=Vin(2/jwT) with T=R1*C.
Therefore, the output voltage is inversely proportional to the capacitance of C and has - within certain limits, depending on the used opamp - a fixed phase shift of -90 deg (against Vin) .
If it is required that the output voltage is directly proportional to the capacitance you need another opamp with a feedback loop consisting of this integrator. However, in this case, specific stability considerations are to be taken.
EDIT: The working principle of the shown circuit is based on an IDEAL capacitor (resistive loses neglectable).