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This paper deals, both from the Fourier analysis and the circuit design point of view, with a large family of electronic power converters which synthesize the assigned slow-varying waveforms via highfrequency switching, thereby needing very little reactive elements. A general condition for high-frequency synthesis applicability is given, together with a method which allows direct converter design from the desired input-output characterizations. Furthermore, a general model is introduced for high-frequency synthesis converters; as a consequence, they are characterized as two-port, multipole, time varying, linear circuit elements. Finally, as a major application example, a new AC-AC, three-to-three phase converter is introduced. The new converter displays several attractive features: sinusoidal waveforms, bidirectionality, separate control over amplitude, frequency, phase, and power factor. Moreover, depending on which side is taken as an input, it can either step up or step down the voltage. For these reasons the new converter can be regarded to as a generalized transformer.