Motivated by the recent commercialization of gallium-nitride (GaN) switches, an effort was initiated to determine whether it was feasible to switch the flyback converter at 5 MHz in order to improve the power density of this versatile isolated topology. Soft switching techniques have to be utilized to eliminate the switching loss to maintain high efficiency at multi-megahertz. Compared to the traditional modeling of zero-voltage-switching quasi-square-wave converters, a numerical methodology of parameters design is proposed based on the steady-state model of zero-voltage switching quasi-square-wave flyback converter. The magnetizing inductance is selected to guarantee zero-voltage switching for the entire input and load range with the trade-off design for conduction loss and turn-off loss. A design methodology is introduced to select a minimum core volume for an inductor or coupled inductors experiencing appreciable core loss. The geometric constant Kgac = MLT/(Ac2WA) is shown to be a power function of the core volume Ve, where Ac is the effective core area, WA is the area of the winding window, and MLT is the mean length per turn for commercial toroidal, ER, and PQ cores, permitting the total loss to be expressed as a direct function of the core volume. The inductor is designed to meet specific loss or thermal constraints. An iterative procedure is described in which two- or three-dimensional proximity effects are first neglected and then subsequently incorporated via finite-element simulation. Interleaved and non-interleaved planar PCB winding structures were also evaluated to minimize leakage inductance, self-capacitance and winding loss. The analysis on the trade-off between magnetic size, frequency, loss and temperature indicated the potential for a higher density flyback converter. A small-signal equivalent circuit of QSW converter was proposed to design the control loop and to understand the small-signal behavior. By adding a simple damping resistor on the traditional small-signal CCM model, it can predict the pole splitting phenomenon observed in QSW converter. With the analytical expressions of the transfer functions of QSW converters, the impact of key parameters including magnetizing inductance, dead time, input voltage and output power on the small-signal behavior can be analyzed. The closed-loop bandwidth can be pushed much higher with this modified model, and the transient performance is significantly improved. With the traditional fix dead-time control, a large amount of loss during dead time occurred, especially for the eGaN FETs with high reverse voltage drop. An adaptive dead time control scheme was implemented with simple combinational logic circuitries to adjust the turn on time of the power switches. A variable deadtime control was proposed to further improve the performance of adaptive dead-time control with simplified sensing circuit, and the extra conduction loss caused by propagation delay in adaptive dead-time control can be minimized at multi-megahertz frequency. / Ph. D.