A direct AC converter for converting a polyphase AC input supply into an output DC or single or polyphase AC supply of amplitude, phase, frequency or power factor which is different from the input supply using a matrix of bidirectional switches having contiguous width modulated conduction periods in cycles which synthesize the output supply voltage or voltages from samples of the input supply voltages taken cyclically at a much higher frequency than the supply frequency or frequencies. The switches are operated so that the or each output supply conductor is connected to only one of the input supply conductors at a time. The width modulation may be effected in response to phases of a sinusoidal oscillation to produce a frequency change. The output may have a "negative" frequency so that a phase displacement between current and voltage due to a reactive load appears in the opposite sense in the input supply. Width modulation may alternatively be effected by a combination of two sinusoidal oscillations so that the output frequency has equal positive and negative values to eliminate phase displacements in the input supply due to a reactive load. Motor speed control and generator output frequency control applications are described.