As portable devices become smaller and thinner, an integrated voltage regulator (IVR) can save space and improve the efficiency of the whole system dramatically, thereby becoming a promising solution to power microprocessors. However, its high-frequency magnetic design is quite challenging and usually becomes the bottleneck. In previous work, a novel, two-phase coupled inductor structure with unsymmetrical through-core conductor distribution was demonstrated as a good candidate due to its small loss, footprint, and low profile. In this paper, the unique coupling mechanism of this specific structure is revealed, based on an equivalent circuit model to fully explore its benefits. Then, a four-phase integrated inductor is proposed to further improve inductor performance by utilizing flux cancellation. To realize a fully integrated three-dimensional IVR, PCB-embedded inductor samples are fabricated and tested experimentally. Compared with other state-of-art solutions, the proposed inductor structure integrates four inductors into one magnetic core with much smaller dc resistance and large inductance density.