A Quadrant-Based Capacitive Sensor for Simultaneous 2-D Displacement and Small-Angle Tilt Estimation With Minimal Cross-Sensitivity

We present a capacitive sensor capable of simultaneous two-dimensional (2D) displacement measurement and small-angle tilt estimation. The design features a symmetric parallel-plate quadrant electrode configuration and leverages differential capacitance to infer motion. A custom analog phase-shift-based readout circuit enables real-time voltage outputs, eliminating the need for digital signal processing or active demodulation. The sensor exhibits high linearity across both X and Y axes (R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> > 0.985), and accurately estimates tilt angles up to ±3°, with negligible cross-sensitivity—verified via phase-domain separation of displacement and tilt components. Experimental validation using an LCR meter and analog acquisition circuits confirms repeatability, minimal cross-axis interference, and sub-0.12 V root mean square error across the displacement range. Compared to existing solutions, the proposed system uniquely enables dual-mode sensing—displacement and tilt—using a fully passive analog framework, symmetric PCB electrodes, and low-complexity circuitry. This makes it ideally suited for embedded and low-power applications such as precision alignment and robotic feedback.