Comment on the original posting: There are various single phase converters, namely:
1. Single phase to three phase. These are essentially AC-DC-AC converters similar to 3phase AC-DC-AC converters except the AC-DC conversion (rectification) is single phase instead of three phase. The hardware for single phase to dc conversion is simpler than three-phase to dc conversion (rectification).
2. Another type of single phase converters are single phase converters, AC-DC-AC for single phase loads, e.g. single phase motor variable speed drives.
3. Another single phase converter AC-DC-AC is a frequency converter, e.g. 50Hz to 60Hz, 60Hz to 400Hz, etc.
To narrow down the topic, it would be nice if the original posting was elaborated on to become more specific.