A switched AC to AC converter circuit comprises a rectifying circuit, which generates a rectified output signal from an alternating input voltage signal, and a switching circuit for controllably switching the polarity of the output from the rectifying circuit to generate a quasi-sine wave or a stepped wave output voltage signal. The switching circuit is included in the rectifying circuit to form a switched rectifier. The switched AC to AC converter controls the integral number of half input wave cycles comprising a half cycle of the quasi-sine wave output in order to maintain the frequency and root mean square (rms) voltage of the output signal between predetermined limits. The switched AC to AC converter further controls the shape of the output voltage wave output to provide instantaneous control over the maintenance of the rms output voltage.