Modeling of an inductively coupled system

Purpose This paper aims to provide a flexible model for a system of inductively coupled loops in a quasi-static magnetic field. The outlined model is used for theoretical analyses on the magnetic field-based football goal detection system called as GoalRef, where a primary loop generates a magnetic field around the goal. The passive loops are integrated in the football, and a goal is deduced from induced voltages in loop antennas mounted on the goal frame. Design/methodology/approach Based on the law of Biot-Savart, the magnetic vector potential of a primary current loop is calculated. The induced voltages in secondary loops are derived by Faraday's Law. Expressions to calculate induced voltages in elliptically shaped loops and their magnetic field are also presented. Findings The induced voltages in secondary loops close to the primary loop are derived by either numerically integrating the primary magnetic flux density over the area of the secondary loop or by integrating the primary magnetic vector potential over the boundary of that loop. Both approaches are examined and compared with respect to accuracy and calculation time. It is shown that using the magnetic vector potential instead of the magnetic flux density can decrease the processing time by a factor of around 100. Research limitations/implications Environmental influences like conductive or permeable obstacles are not considered in the model. Practical implications The model can be used to investigate the theoretical behavior of inductively coupled systems. Originality/value The proposed model provides a flexible, fast and accurate tool for calculations of inductively coupled systems, where the loops can have arbitrary shape, position and orientation.