A process for supplying a polyphase motor with electronic switching (M) from a voltage supply source (A), includes a passive electric filter downstream of the supply source (A), a conversion of the voltage supplied by the source (A) to supply the phases of the motor (M), using an assembly of controllable switches having either a passing condition or blocking condition, where each combination of conditions of the switches defines a conversion configuration. The process regulates the supply current about a reference current (Iref), and a sequence of magnetization and de-magnetization cycles of the phases of the motor (M) initiated by magnetization or de-magnetization references of the phases. During at least one period of sequencing per cycle, several pairs of conversion configurations are selected so that the mean current conforms as close as possible to the reference current (Iref).