This article presents a theoretical study of an absolute, ratiometric inductive position sensor (IPS) based on eddy currents. The aim is to describe the working principle of the sensor, having as key components a transmitting coil, the receiving coils and the conductive target, by introducing area-of-overlap functions. We show that each target–receiver pair needs the adoption of a different reconstruction formula for the identification of the target position, whereas in the literature the usual inverse tangent function is applied for every possible pair. Than, we seek the target–receiver pair that maximizes the amplitude of the induced voltages on the receivers. The results show that, to achieve the maximum value of the induced voltages, the best choice is to have rectangular target and rectangular receivers. In order to verify the theory, a simulation and optimization method has been applied to the rectangular receivers coils on two rotary IPS realized with Printed Circuit Board (PCB) technology. Measurements performed on the prototypes have shown an increment of the induced voltage of more than 57% with respect to the commonly used sinusoidal receivers. However, a linearity error of 1.5%FS is obtained by using the inverse tangent reconstruction formula. When using the formula provided from the theory, the linearity error becomes 0.6%FS for the non-optimized prototype and below 0.15%FS for the optimized one.
