# Displacement Sensing Using Bimodal Resonance in Over-Coupled Inductors

## TL;DR

This paper introduces a new method for measuring displacement using resonant phenomena in inductive sensors.

## Contribution

The novel contribution is using bimodal resonance in over-coupled inductors to measure separation and angular displacement.

## Key findings

- Co-planar separation can be predicted within ±1 mm using the proposed method.
- Angular displacement can be measured within ±1° using the same technique.
- Simulated and experimental results align well, validating the physics-based models.

## Abstract

This paper presents the theory and key experimental findings for investigating the generation of bimodal resonance (frequency-splitting) phenomena in mutually over-coupled inductive sensors and its exploitation to evaluate relative separation and angular displacement between coils. This innovative measurement technique explores the bimodal resonant phenomena observed between two coil designs—solenoid and planar coil geometries. The proposed sensors are evaluated against first-order analytical functions and finite element models, before experimentally validating the predicted phenomenon for the different sensor configurations. The simulated and experimental results show excellent agreement, and first-order best-fit functions are employed to predict displacement variables experimentally. Co-planar separation and angular displacement are shown to be experimentally predictable to within ±1 mm and ±1° using this approach. This study validates the first-order physics-based models employed and demonstrates the first proof of principle for using resonant phenomena in inductive array sensors for evaluating relative displacement between array elements.