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The development of new converter systems with higher power density and/or efficiency offers many degrees of freedom for the design parameters as a large number of system component values have to be defined, where all of which are interdependent, to some extent, on another. Therefore, an automated optimization procedure, based on comprehensive analytical models and the resulting optimal design parameters, e.g., switching frequency or transformer design, to achieve the most compact and/or efficient design, is presented in this paper. In addition, the design of a volume-optimized 400/46–56-V phase-shift dc–dc converter with a current doubler rectifier and the underlying analytical models are also introduced. The power density of the converter is increased by integrating the output inductors in the transformer's core. A new lossless magnetic snubber circuit is introduced, which damps the intrinsic voltage ringing of the rectifier diodes and feeds the ringing energy to the output. The experimental results prove the analytical models and the design procedure. The 5-kW dc–dc converter prototype has a power density of 147 \W/in^3 (9 kW/L) and a maximum efficiency of 94.4% at 54-V output voltage and full load. [ABSTRACT FROM AUTHOR]