Energy distribution in a conventional magnetic component is generally not at a designer's disposal. In a conventional toroidal inductor, the energy density is inversely proportional to the square of the radius. Thus, a designer would be unable to prescribe uniform field distribution to fully utilize the inductor volume for storing magnetic energy. To address this problem a new inductor design, called a "constant-flux" inductor, is introduced in this thesis. This new inductor has the core and windings configured to distribute the magnetic flux and energy relatively uniformly throughout the core volume to achieve power density higher than that of a conventional toroidal inductor. The core of this new inductor design is made of concentric cells of magnetic material, and the windings are wound in the gaps between the cells. This structure is designed to avoid crowding of the flux, thus ensuring lower core energy losses. In addition, the windings are patterned for shorter length and larger area of cross-section to facilitate lower winding energy losses. Based on this approach, a set of new, constant flux inductor/transformer designs has been developed. This design set is based on specific input parameters are presented in this thesis. These parameters include the required inductance, peak and rms current, frequency of operation, permissible dc resistance, material properties of the core such as relative permeability, maximum permissible magnetic flux density for the allowed core loss, and Steinmetz parameters to compute the core loss. For each constant flux inductor/transformer design, the winding loss and core loss of the magnetic components are computed. In addition, the quality factor is used as the deciding criterion for selection of an optimized inductor/transformer design. The first design presented in this thesis shows that for the same maximum magnetic field intensity, height, total stored energy, and material, the footprint area of the new five-cell constant-flux inductor is 1.65 times less than that of an equivalent conventional toroidal inductor. The winding loss for the new inductor is at least 10% smaller, and core loss is at least 1% smaller than that in conventional inductors. For higher energy densities and taller inductors, an optimal field ratio of the dimensions of each cell (α = Rimin/Rimax) and a larger number of cells is desired. However, there is a practical difficulty in realizing this structure with a larger number of cells and higher field ratio α. To address this problem, an inductor design is presented that has a footprint area of a three-cell constant-flux inductor (α = 0.6) that is 1.48 times smaller in comparison to an equivalent conventional toroidal inductor. For the same maximum magnetic flux density, height, material, and winding loss, the energy stored in this new three-cell constant-flux inductor (α = 0.6) is four times larger than that of an equivalent conventional toroidal inductor. Finally, new designs for application-specific toroidal inductors are presented in this thesis. First, a constant-flux inductor is designed for high-current, high-power applications. An equivalent constant-flux inductor to a commercially available inductor (E70340-010) was designed. The height of this equivalent inductor is 20% less than the commercial product with the same inductance and dc resistance. Second, a constant-flux inductor design of inductance 1.2 µH was fabricated using Micrometal-8 for the core and flat wire of 0.97 mm x 0.25 mm for the conductor. The core material of this inductor has relative permeability < 28 and maximum allowed flux density of 3600 Gauss. The dc resistance of this new, constant flux inductor was measured to be 14.4 mΩ. / Master of Science