Modular multilevel dc-dc converters (MMDCs) have attracted much interest in medium-voltage dc applications, but they have to face the main issue of balancing submodule (SM) capacitor voltages. Conventionally, the SM balancing demands monitoring and sorting the real-time SM capacitor voltages. It highly relies on the high-speed bidirectional communication between submodules and the central controller, which increases the implementation costs and decreases the system reliability. This paper proposes the optimal circulant modulation with inherent balancing capability as well as minimized SM capacitor voltage ripple. Firstly, the optimal SM switching pattern is derived according to the SM ripple expression cycle-by-cycle. Then the full-rank feature of the optimal switching matrix is proven, which promises the inherent balancing of SM capacitor voltages. Finally, the ripple optimization and inherent balancing capability of the proposed optimal circulant modulation are validated by experiments on an LLC-based MMDC prototype.