This paper presents the design and implementation of patterned-magnetic-flux (PMF) coupled inductors for high-density voltage regulator modules (VRMs). The PMF structure enables the windings of a coupled inductor pair to conduct current straight through the inductor in the same direction while maintaining flux cancellation by patterning the flux to wrap around the conductors. Two PMF implementations are demonstrated: a variant for vertical power delivery (VPD) with 8 mm x 8 mm x 1.5 mm dimensions, and one for lateral power delivery (LPD) with 5 mm x 5 mm x 4 mm dimensions for direct stacking on power stages. The VPD PMF inductor is used in a two-phase module designed for 6 V input, with 3 mm total height, achieving 89.2% peak efficiency at 0.8 V output and 1 MHz switching frequency. The LPD PMF inductor is packaged with a dual-channel power stage to achieve a current density of 2-3 A/mm^2.
