AC resistance of planar power inductors and the quasidistributed gap technique

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.