Low-Profile Inductor Design for High-Current Vertical Power Delivery Voltage Regulators

In high-current applications, vertical power delivery (VPD) architectures require highly compact inductors to maintain power integrity. However, the nonlinear relationship between magnetic reluctance and the three-dimensional geometry of the inductor under non-uniform flux distribution becomes complex, making it challenging to optimize inductance density and current density. This letter proposes a design method for low-profile inductor with air gaps under non-uniform flux distribution for high-current VPD voltage regulators, establishing an explicit mapping between inductance and core geometry with different structures. Using this method, a two-phase negative coupled inductor is designed, achieving a high continuous current density of 1.9 A/mm² within a compact 2.2 mm height. Experimental validation in a buck converter demonstrates that the inductor supports a continuous current of 110 A. Based on the proposed inductor, the height of the 12V-1V high current density voltage regulator module (VRM) can be reduced to 4.2mm.