Circuit models for multiphase coupled inductors are summarized, compared, and unified. Multiwinding magnetic structures are classified into parallel-coupled structures and series-coupled structures. For parallel-coupled structures used for multiphase inductors, the relationships between a) inductance-matrix models, b) extended cantilever models, c) magnetic-circuit models, d) multiwinding transformer models, e) gyrator-capacitor models, and f) inductance-dual models are examined and discussed. These models represent identical physical relationships in the multiphase coupled inductors, but emphasize different physical aspects and offer distinct design insights. The circuit duality between the series-coupled structure and the parallel-coupled structure is explored. Design equations for interleaved multiphase buck converters based on these models are streamlined and summarized, and a simplified equation showing the relationships between current ripple with and without coupling is presented. The models and design equations are verified through theoretical derivation, SPICE simulation, and experimental measurements.

A basic procedure for designing a power inductor is presented. Many papers and textbook chapters offer more sophisticated methods, but it is harder to find a clear outline of a basic design process. Studying and practicing a basic design process is useful for beginners to understand the fundamental tradeoffs in design and to build intuition. For more advanced work, the basic design process is useful as it avoids relying on assumptions that might not be valid with, for example, high-frequency loss effects that are ignored in the development of some more sophisticated methods, or that constrain other methods to narrow, specific cases. Two options are outlined: starting with a saturation constraint, and then checking the core/winding loss balance; or, starting by optimizing the core/winding loss balance, and then checking the saturation constraint.