Capacitance of Kelvin guard‐ring capacitors with modified edge geometry

摘要

An exact solution has been obtained for the capacitance of Kelvin guard‐ring capacitors with strongly limited radial dimensions compared with the distances between the electrodes. This is done by solving the three‐dimensional Laplace equation by means of separation of variables. From the achieved equations, formulas expressing the influences of several systematic errors are derived. Calculated capacitances, using these equations, are in full agreement with corresponding measured capacitances. This enables us to construct stable highly sensitive standard displacement transducers. Also small capacitors with low capacitance supplied with trim facilities can be easily constructed with this knowledge.