There is provided by this invention soft switching interleaved power converters that are suitable for high power and high voltage applications such as plasma processing. They have greatly reduced switching losses and diode reverse-recovery losses which allows operation at high switching frequencies. The peak values of the reverse-recovery currents of the diodes are substantially less then their peak forward operating currents. The power converters incorporate power converter cells that comprise a plurality of switching assemblies that are operated with an interleaved switching pattern, and that are each connected to an input terminal of an inductor assembly that also has a common terminal. The inductance between each pair of input terminals is less than the inductance between each input terminal and the common terminal of the inductor assembly.