Modular multilevel dc-ac-dc converters (MMDAC) have emergedrecently for high step-ratio connectionsin medium voltage distribution systems.Extended phase-shiftmodulation has been proposed and was found to create the opportunity for inherent balance of SM capacitor voltages. This letter presents fundamentalanalysis leading toclear criterion for the inherent balancecapability in MMDAC. A sufficient and necessary condition,with associated assumptions,to guarantee this capability isestablished. Using the mathematics of circulant matrices, this condition is simplified to a co-prime criterion which gives rise to practical guidance for the design of an MMDAC. Experimentson down-scaled prototypesand simulations on full-scale examples both provide verification of the analysis and criterion for the inherent balance capability of MMDAC.