Two new topologies of Buck-Boost single-phase ac-ac conversion are proposed. In one of the circuits a bi-directional switch with a single buck-boost inductor is used, whereas, in the other circuit a bi-directional switch with two separate buck-boost inductors are used. Both the circuits operate in buck-boost mode separately for positive and negative cycle of the supply. As a result the input current remains almost in phase with the supply voltage without any additional sensors and control circuit. It runs in free running mode. The input current becomes almost sinusoidal by the use of small input filter. Input current THD is very low and the input power factor is very high. The converters like other switch mode converters have variable efficiency with change in duty cycle. High efficiency is possible within a range of duty cycle.