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Power electronic converters are typically either step-down converters that take an input voltage and produce an output voltage of low amplitude or step-up converters that take an input voltage and produce an output voltage of higher amplitude. There are, however, applications where a converter that can step-up voltage or step-down voltage can be very useful, such as in applications where a converter needs to operate under a wide range of input and output voltage conditions such as a grid-connected solar inverter. Such converters, however, are not as common as converters that can only step down or step up voltage because most applications require converters that need to only step down voltage or only step up voltage and such converters have better performance within a limited voltage range than do converters that are designed for very wide voltage ranges. Nonetheless, there are applications where converters with step-down and step-up capability can be used advantageously. The main objectives of this thesis are to propose new power electronic converters that can step up voltage and step down voltage and to investigate their characteristics. This will be done for two specific converter types: AC/DC single-stage converters and DC-AC inverters. In this thesis, two new AC/DC single-stage converters and a new three-phase converter are proposed and their operation and steady-state characteristics are examined in detail. The feasibility of each new converter is confirmed with results obtained from an experimental prototype and the feasibility of a control method for the inverter is confirmed with simulation work using commercially available software such as MATLAB and PSIM.