We present a method for improving the amplitude and angular error of inductive position sensors, by advancing the design of receiver coil systems with multiple windings on two layers of a printed circuit board. Multiple phase-shifted windings are connected in series, resulting in an increased amplitude of the induced voltage while decreasing the angular error of the sensor. The amplitude increase for a specific number of windings can be predicted in closed form. Windings are placed electrically in series by means of a differential connection structure, without adversely affecting the signal quality while requiring a minimal amount of space in the layout. Further, we introduce a receiver coil centerline function which specifically enables dense, space-constrained designs. It allows for maximization of the number of possible coil windings while minimizing the impact on angular error. This compromise can be fine-tuned freely with a shape parameter. The application to a typical rotary encoder design for motor control applications with five periods is presented as an example and analyzed in detail by 3D finite-element simulation of 18 different variants, varying both the number of windings and the type of centerline functions. The best peak-to-peak angular error achieved in the examples is smaller than 0.1° electrically (0.02° mechanically, periodicity 5) under nominal tolerance conditions, in addition to an amplitude increase of more than 170% compared to a conventional design which exhibits more than twice the angular error. Amplitude gains of more than 270% are achieved at the expense of increased angular error.