Modular multilevel converter (MMC) has been employed for solid state transformer (SST) applications. For the MMC-based SSTs, ac-link excitation voltage waveforms are multilevel and controllable for energizing medium-frequency transformers. Different multilevel ac-link voltage waveforms have different performance and specification requirements in design and control. In this paper, power transfer characteristics and capacitor voltage ripple are investigated for the MMC-SSTs under different ac-link excitation voltage waveforms, i.e., sinusoidal and generalized non-sinusoidal voltages. Based on the analysis, capacitance and inductance sizing method is developed and verified. To address voltage balancing issue of the MMC under medium-frequency operating conditions, various capacitor voltage balancing methods are evaluated and compared based on phase-shift modulation and nearest-level modulation methods. The study is conducted in the PSCAD/EMTDC software environment. The study results show that, for the same design specifications, different ac-link excitation voltage waveforms have different capacitance requirements, which can be used for optimization design of the MMC-SSTs.