The paper proposes an Asymmetrical Modular Multilevel Converter (AMMC) suitable for low/medium-voltage dc-ac conversions with very high output quality. The modules' dc-links of the AMMC are charged to a binary exponential sequence to produce a large number of output levels using only a few modules.The concept of using asymmetrical dc-links for high-quality output is not entirely new. However, the practicality of existing approaches is relatively low and challenged by the difficulties in maintaining the required dc-link voltages as well as suppressing their interaction with the output, which often requires multiple isolated dc/dc converters. We solve this problem by aligning the modules in the Marquardt MMC inverter module configuration that offers more control freedom, hence the term AMMC. Furthermore, we introduce a highly effective switched-inductor charge transfer and balancing mode between modules and even across arms. We accordingly modify the underlying conventional chopper modules so that the dc-link voltage control can be completely sensorless. The proposed AMMC is tested in a lab setup with four modules per arm reaching 32 output levels. In contrast to the low benefit of an additional module in MMC due to only linear improvement of the output granularity, each further module halves the finest voltage step. The components to maintain the graded voltage sequence and the underlying inductive charge transfer only a fraction (< 10%) of the load current so that relatively low-power devices can be used.