In the paper, the modified (compared to the classical asymmetric half-bridge) converter for a switched reluctance machine with an asymmetric rotor magnetic circuit was analysed. An analysis for two various structures of switched reluctance motors was conducted. The rotor shaping was used to obtain required start-up torque or/and to obtain less electromagnetic torque ripple. The discussed converter gives a possibility to turn a phase off much later while reduced time of a current flows in a negative slope of inductance. The results of the research in the form of waveforms of currents, voltages and electromagnetic torque were presented. Conclusions were formulated concerning the comparison of the characteristics of SRM supplied by the classic converter and by the one supplied by the analysed converter.