This work presents modeling and analysis techniques for low-profile transformers in power electronics. Based on the modeling and analysis, the design methodologies and design tools are provided. High frequency low-profile transformer 1-D winding loss, core loss and temperature rise models are derived in terms of the transformer geometry parameters. A 2-D FEA (Finite Element Analysis) is used to visualize the high frequency electromagnetic field and current density distribution, and to quantify high frequency power dissipation and energy storage in transformer by taking the skin effect, proximity effect, and edge effect into account. The characteristics of winding arrangements (interleaved or sandwiched, balanced or unbalanced) with different types of wire (solid wire, Litz wire, and printed wire) are accurately predicted. An algorithm is developed to design a low-profile transformer that has a maximum power density and meets a given set of specifications. The maximum achievable power density for a given power level and output voltage is computed based on only one fundamental constraint: temperature rise. A nonlinear optimization programming tool is developed based on the algorithm. Consequently, the maximum achievable power density and the required number of turns are determined, along with the optimum operating frequency and core geometry. / Ph. D.