A single switch split dc-rail boost converter topology is described that uses a mutually coupled two winding inductor to balance the voltage drop across both of its capacitor smoothed split dc-rail input and output voltage terminals. The operation of the converter topology is described in discontinuous conduction with an unbalanced output load in steady-state. The resultant converter topology obtains balanced input and output voltages under extreme unbalanced load conditions without requiring extra converter control features. A current sharing action is described between the two coupled windings during both the switch on-time and off-time. This action is responsible for the voltage balancing feature of the converter when the converter load is unbalanced between the two output dc voltage rails. Simulations and experimental results are used to illustrate the nature of the winding current waveforms that produce this current sharing action. Load imbalances exceeding 3:1 can easily be compensated for, and simulations and experimental results show that typical deviations of the converter input and output voltages can be limited to within the range 1% to 8% for load imbalances of up to 2:1. The voltage imbalance experienced in the two dc rail output voltages is subject to design choices and linked to the winding leakage inductance and dc voltage gain.