558 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 16, NO. 4, JULY 2001 AC Resistance of Planar Power Inductors and the Quasidistributed Gap Technique Jiankun Hu and Charles R. Sullivan, Member, IEEE Abstract—Low-ac-resistance planar or foil-wound inductors constructed using a quasidistributed gap comprising multiple small gaps that approximate a distributed gap are analyzed. Finite-element simulations are used systematically to develop a model broadly applicable to the design of such quasidistributed gap inductors. It is shown that a good approximation of a distributed gap is realized if the ratio of gap pitch to spacing between gap and conductor is less than four, or if the gap pitch is comparable to a skin depth or smaller. Large gaps can reduce ac resistance, but for most practical designs gap length has little effect. A closed-form expression, which closely approximates the ac resistance factor for a wide range of designs, is developed. The methods are illustrated with an inductor for a high-ripple-current fast-response voltage regulator module (VRM) for microprocessor power delivery. Fig. 1. Distributed-gap inductor: use of a low-permeability material to achieve low ac resistance. decaying exponentially with depth according to standard skin-effect behavior. IndexTerms—Airgaps,distributedgaps,eddycurrents,fringing effects, inductors, magnetic devices, power conversion, proximity effect, quasidistributed gaps, skin effect, voltage regulator mod-