Coupling Factor Between the Magnetic and Mechanical Energy Domains in Electromagnetic Power Harvesting Applications

Abstract

Micro-power generation is an area developing to support autonomous and battery-free wireless sensor networks and miniature electronic devices. Electromagnetic power harvesting is one of the main techniques for micro-power generation and it uses the relative motion between wire coils and miniature magnets to convert mechanical energy to electricity according to Faraday's law of induction. Crucial for the design and analysis of these power systems is the electromechanical coupling factor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> , which describes the coupling between the mechanical and electromagnetic energy domains. In current literature <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> is defined as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NBl</i> : the product between the number of turns in the coil ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ), the average magnetic induction field ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> ), and the length of a single coil turn ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> ) . This paper examines the validity of the current <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> definition and presents two case studies involving cylindrical permanent magnets and circular coil geometries to demonstrate its limitations. The case studies employ a numerical method for calculating <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> which uses the toroidal harmonics technique to determine the magnetic induction field in the vicinity of the cylindrical magnet.