Efficient design of capacitive sensors using conformal maps

The electric field between relatively simply shaped electrode surfaces can be determined using conformal maps. For more complex electrode setups an approximation needs to be utilized to compute the parameters of the conformal map which introduces errors to the map. In this paper we show that while these errors do influence mapping of the geometry which represents an electrode configuration, the result for the electric field is correct for the warped geometry. Therefore the desired result can be obtained by prewarping the geometric parameters.