Point-of-load (POL) converters have been used extensively in IT products. Today, almost every microprocessor is powered by a multi-phase POL converter with high output current, which is also known as voltage regulator (VR). In the state-of-the-art VRs, the circuits are mostly constructed with discrete components and situated on the motherboard, where it can occupy more than 1/3 of the footprint of the motherboard. A compact POL is desirable to save precious space on motherboards to be used for some other critical functionalities. Recently, industry has released many modularized POL converters, in which the bulky inductor is integrated with the active components to increase the power density. This concept has been demonstrated at current levels less than 5A and power density around 600-1000W/in³. This might address the needs of small hand-held equipment such as smart phones, but it is far from meeting the needs for the applications such as laptops, desktops and servers, where tens and hundreds of amperes are needed. A 3D integrated POL module with an output current of tens of ampere has been successfully demonstrated at the Center for Power Electronic Systems (CPES), Virginia Tech. In this structure, the inductor is elaborated with low temperature co-fire ceramic (LTCC) ferrite, as a substrate where the active components are placed. The lateral flux inductor is proposed to achieve both a low profile and high power density. Generally, the size of the inductor can be continuously shrunk by raising the switching frequency. The emerging gallium-nitride (GaN) power devices enable the creation and use of a multi-MHz, high efficiency POL converter. This dissertation firstly explores the LTCC inductor substrate design in the multi-MHz range for a high-current POL module with GaN devices. The impacts of different frequencies and different LTCC ferrite materials on the inductor are also discussed. Thanks to the DC flux cancellation effect, the inverse coupled inductor further improves the power density of a 20A, 5MHz two-phase POL module to more than 1kW/in³. An FEA simulation model is developed to study the core loss of the lateral flux coupled inductor, which shows the inverse coupling is also beneficial for core loss reduction. The ceramic-based 3D integrated POL module, however, is not widely adopted in industrial products because of the relatively high cost of the LTCC ferrite material and complicated manufacturing process. To solve that problem, a printed circuit board (PCB) inductor substrate with embedded alloy flake composite core is proposed. The layerwise magnetic core is laminated into a multi-layer PCB, and the winding of the inductor then is formed by the copper layers and conventional PCB vias. As a demonstration of system integration, a 20A, 1.5MHz integrated POL module is designed and fabricated based on a 4-layer PCB with embedded flake core, which realizes more than 85% efficiency and 600W/in³ power density. The application of standardized PCB processes reduces the cost for manufacturing the integrated modules due to the easy automation and the low temperature manufacturing process. Combining the PCB-embedded coupled inductor substrate and advanced control strategy, the two-phase 40A POL modules are elaborated as a complete integrated laptop VR solution. The coupled inductor structure is slightly modified to improve its transient performance. The nonlinearity of the inductance is controlled by adding either air slots or low permeability magnetic slots into the leakage flux path of the coupled inductor. Then the leakage flux, which determines the transient response of the coupled inductor, can be well controlled. If we directly replace the discrete VR solution with the proposed integrated modules, more than 50% of the footprint on the motherboard can be saved. Although the benefits of the lateral flux inductor have been validated in terms of its high power density and low profile, the planar core is excited under very non-uniform flux. Some parts of the core are even pushed into the saturation region, which totally goes against the conventional sense of magnetic design. The final part of this dissertation focuses on evaluating the performance of the planar core with variable flux. The counterbalance between DC flux and AC flux is revealed, with which the AC flux and the core loss density are automatically limited in the saturated core. The saturation is essentially no longer detrimental in this special structure. Compared with the conventional uniform flux design, the variable flux structure extends the operating point into the saturation region, which gives better utilization of the core. In addition, the planar core with variable flux also provides better thermal management and more core loss reduction under light load. As conclusions, this research first challenges the conventional magnetic design rules, which always assumes uniform flux. The unique characteristics and benefits of the variable flux core are proved. As an example of taking advantages of the lateral flux inductor, the PCB integrated POL modules are proposed and demonstrated as a high-density VR solution. The integrated modules are cost-effective and ready to be commercialized, which could enable the next technological innovation for the whole computing and telecom industry. / Ph. D.