In today's state-of-the-art designs, bulky magnetic components pose major barriers to integrate a DC/DC converter into a single chip. One of the promising technologies to integrate the magnetic component with the active component is three-dimensional (3D) integration, using a low-profile inductor as the substrate. In order to optimize low-profile inductor design for high-frequency applications, the core loss of a low-profile inductor should be modeled. However, most low-profile planar inductors have very non-uniform flux distribution. Therefore, previous core loss models, which are based on uniform flux distribution, cannot be used. In addition to non-uniform flux distribution, some planar inductors, such as low-temperature co-fired ceramics (LTCC) inductors, also have non-linear permeability, which makes modeling the core loss for planar inductors even more unconventional and complicated. This paper proposes some analytical core loss models for different low-profile planar inductor structures with non-uniform flux distributions and non-linear permeability. These analytical models also consider non-sinusoidal excitations and the impact of dc bias on core loss. Based on LTCC technology, several low-profile planar inductors are fabricated to help verify these core loss models, and the measured core loss closely match the predicted results, which means the proposed analytical core loss models have very good accuracy.
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