The design of power electronic converters is subject to extreme cost pressure, especially in the automotive sector. Consequently, each component needs to be optimized regarding material and manufacturing cost. The latter is especially important for magnetic components, as the expensive wire-wrapping process has a significant impact on the overall production costs. In this article, a new inductor concept is proposed, where the winding is directly integrated into the printed circuit board (PCB), while at the same time the usually large high-frequency conduction losses are mitigated. This is achieved by using the fringing field around a single air gap or several (distributed) air gaps for compensating the adverse magnetic skin and proximity fields within the winding. Consequently, low ac to dc resistance ratios are achieved and the required copper cross-section of the winding can effectively be reduced. Furthermore, a thermal model for the printed circuit board winding is derived, which allows for designing PCB-windings close to the thermal limit, and therefore inductors with very high power densities are obtained. Finally, the findings of this article are verified by experimental measurements and a simplified design sequence is described.