FPGA Modeling: Eddy Currents & Hysteresis

Publication: 2025 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), July 2025.
Partners: UQTR.

Introduction

In precision loudspeaker design, electromagnetic motor behavior is often oversimplified. However, eddy currents and magnetic hysteresis within the steel pole pieces introduce complex nonlinearities and frequency-dependent inductance.

This project presents an FPGA-based implementation of a “white-box” model capable of simulating these phenomena in real-time at a sampling frequency of 1 MHz.

Theoretical Approach: The Method of Lines (MoL)

To model flux diffusion within the axisymmetric core, we utilize the Method of Lines. Unlike conventional Finite Element Methods (FEM), MoL discretizes space while keeping time as a continuous variable.

1. Motor Geometry

Axisymmetric view of the transducer motor.

2. Lumped Model

Equivalent circuit representing magnetic branches.

Spatial Discretization

The radial domain of the core is divided into $N=128$ points. The diffusion equation derived from Maxwell’s equations is transformed into a system of Ordinary Differential Equations (ODEs):

FPGA Architecture & Resources

The implementation was carried out on a Xilinx Kintex-7 FPGA. The challenge was solving 128 ODEs in less than $1~\mu s$ using massive parallelism and pipelined Float32 arithmetic.

3. Diffusion Architecture

Hardware implementation of the MoL solver.

4. Hysteresis Architecture

Hardware implementation of the Tellinen model.

Resource Utilization (128 points)

Results & Virtual Instrumentation

5. Apparent Inductance

Measurement vs FEA vs FPGA

6. Current Distortion

Captured magnetic non-linearities.

References and Publications