The dual active bridge (DAB) topology is ideally suited for high power dc-dc conversion. This paper presents a comprehensive analysis and experimental results with PWM control of the DAB. The PWM control is in addition to phase shift modulation between the two H-bridges. The analysis includes PWM of one bridge at a time and of both bridges simultaneously. In the latter, five distinct modes arise based on the choice of PWM and load condition. The possibilities are analyzed for optimizing power density and efficiency for low load operation. An optimum PWM scheme is proposed that extends the soft-switching range, reduces rms and peak currents at low loads, and results in significant size reduction of the transformer. Experimental results are presented with a 10kW prototype.