In a two-stage power converter providing voltage regulation in a first stage, zero voltage switching (ZVS) is provided in switches in an unregulated, constant frequency second stage of a two-stage power converter by an inductor of a CLL resonant circuit connected in parallel with both a series connection of an external inductor and a primary winding of one or more transformers connected in series and an output of the switching circuit so that the output capacitances of the switches can be charged and discharged, respectively, by current in the parallel-connected inductor and independently of current in the magnetizing inductance of the transformer. Therefore, the magnetizing inductance of the transformer can be made sufficiently large to balance currents delivered to respective loads as is particularly desirable for driving a plurality of unbalanced LED strings independently of the value of the parallel-connected inductor which is desirably small.