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A matrix converter is an ac-ac power converter topology that has received extensive research attention as an alternative to traditional ac-dc-ac converter. A matrix converter is able to convert energy from an ac source to an ac load without the need of a bulky and limited-lifetime energy-storage elements. The indirect three-level sparse matrix converter (I3SMC) is a new topology from this family that can synthesize three-level voltage in order to improve the output performance in terms of reduced harmonic content. This paper discusses the operating principles and a space-vector-modulation scheme for this topology. Simulation and experimental results are shown to prove the ability of this topology to generate multilevel output voltages as well as to maintain a set of sinusoidal balanced input currents. The performance of the converter is compared with the conventional matrix converter and an alternative multilevel matrix-converter topology in order to demonstrate the advantages and disadvantages of the I3SMC.