A　novel　circuit-topology　family　of　the　current-mode　ac/ac　converter　with　high-frequency　ac　link,　based　on　a　Flyback　converter,　is　proposed.　These　circuit　topologies,　which　can　transfer　one　unregulated　sinusoidal　voltage　with　high　total　harmonic　distortion　(THD)　into　another　regulated　constant-frequency　sinusoidal　voltage　with　low　THD,　are　composed　of　input　cycloconverter,　high-frequency　storage,　transformer,　and　output　cycloconverter.　The　circuit-topology　family　includes　single　four-quadrant　power　switch　mode,　push-pull　mode,　half-bridge　mode,　and　full-bridge　mode　circuits.　The　single　four-quadrant　power　switch　mode　and　push-pull　mode　converters　are　suitable　for　low　input　voltage　fields,　but　the　half-bridge　mode　and　full-bridge　mode　converters　are　suitable　for　high　input　voltage　fields.　The　operational　mode,　steady　principle,　and　transient　voltage　feedback　control　strategy　of　the　kind　of　converter　are　investigated.　The　output　characteristic　curve,　its　relation　to　internal　resistance,　and　the　design　criteria　for　the　key　circuit　parameters　are　given.　The　theoretical　analysis　and　the　test　result　of　the　500　VA　220　+/-　15%　50　HzAC/220　V　50　HzAC　prototype　have　shown　that　the　converters　have　advantages　such　as　high-frequency　galvanic　isolation,　simple　topology,　two-stage　power　conversion　[low　frequency　alternating　current　(LFAC)/high　frequency　alternating　current　(HFAC)/LFAC],　bidirectional　power　flow,　high　efficiency,　high　power　density,　low　THD　of　the　output　voltage,　strong　adaptability　to　various　loads,　higher　line　power　factor,　low　audio　noise,　etc.