Design Optimization of Integrated Magnetic Core Inductors

This paper presents a design study of novel geometrical configurations for miniaturized toroidal planar core thin-film inductors. A standard core with square-shaped toroidal geometry is compared with a new core with serpentine toroidal geometry. A design procedure is provided to maximize the inductance value of a square toroid in a certain footprint area. In addition, the mathematical model of the inductor demonstrates the possibility to further increase the maximum inductance value for closed or air-gap core inductors in a given footprint area (up to 35% in 16 mm²), by means of a more efficient use of the core surface area in the case of serpentine geometry, assuming the same coupling factor for both windings. Furthermore, the presented serpentine geometry increases performances in terms of magnetic energy density and quality factor, while retaining higher inductance values, at the cost of a limited increase of layout complexity. This paper also provides a more accurate estimation of the inductance of a square-shaped toroidal inductor based on the evaluation of the mean magnetic path length accounting for the non-uniformity of the magnetic flux density in the core cross section and for the corner effect.