# capacitive displacement sensor calculation

while studying this certain types of problems with capacitive displacement sensors I came across one in particular that I am pretty much stuck. The whole problem is explained in following text and screenshots. I am looking for useful tips on how to approach this kind of problem. Thanks!

Capacitive displacement sensor is shown in the picture below. (picture a). It has surface area of S_0 and starting distance d_0. It is connected (integrated) in bridge circuit which are shown in the pictures b and c.

a) Find the expressions for the output voltage U_0 for pictures b and c

b) In the cases when the displacement is very small (Δd/d_0 << 1) you must calculate the effective value of output voltage when R(resistance) = d_0/(ωSε_0), and when the indicator resistance is very high.

• Ask a specific question please. If this is homework it needs an attempt at a solution – Voltage Spike Sep 4 '19 at 20:50
• Have you read any of the copious material on the Wheatstone Bridge? Are you aware of the capacitance equation, C = Ae/d for parallel plates. Are you aware than when a reciprocal is involved, and the denominator changes by a very small amount, the output is still essentially linear? – Neil_UK Sep 5 '19 at 4:52
• @Neil_UK yeah, that pretty much came to my mind when observing this situation but, the procedure of coming up with a reasonable expression for the output voltage is somewhat uclear to me. I am very gratefull that you pointed out the linearity of the output voltage since that very thing flew over my head. If you could give me any further advice on deriving the expresion for the output voltage i may be able to apply it to more of the problems of the same type. Thanks in advance! – Isnam Jukic Sep 5 '19 at 11:26