The modularity of the modular multilevel dc-dc converters (MMDCs) makes it as a competitive candidate in medium voltage applications but brings the submodule (SM) voltage balancing issue. This paper proposes an optimal circulant modulation method for minimizing the SM voltage ripples with inherent balancing capability proven at the same time, which allows smaller SM capacitors and avoids the high-frequency communication for SM voltage balancing. Firstly, the optimal switching pattern is strictly derived providing a general method to theoretically minimize the SM capacitor voltage ripple. Then the switching matrix of the optimal circulant modulation is formulated by introducing the generalized-circulant matrix. It verifies the circularity and full-rank feature of the optimal switching matrix, which promises the uniformity of SM actions and the inherent balancing of SM voltages. Finally, full-scale simulations and down-scaled experiments are both provided with the isolated LLC -based MMDC model and prototype. The results show that the proposed optimal circulant modulation can reduce the SM capacitor voltage ripple by 37% compared with the existed method, and it also promises the inherent SM voltage balancing and the SM uniformity.