The principle of single-to-single phase matrix electric power conversioin is further studied and the conversioin switch function is introduced into conventional rectifier-inverter, thus a general character of the two conversion techniques is discovered. It is characteristic of the switch functiion to follow mains voltage distortion and mains frequency drift. By utilizing the merit, unidirectional switch duty-rations of the inverter follow the variation of DC-link voltage automatically, thus the size of DC-link electrolytic capacitor can be reduced considerably, bringing about improved mains side power factor. Corresponding topologies and theoretical and theoretical derivations are given, and so are the simulation results, based on which it is confirmed that the single-to-single phase matrix conversion technique is potentially useful in large scale production, and the introduction of switch function can yield good economic returns.