The modular multilevel converter (MMC) based dc-dc converters (MMDC) are essential for voltage matching, galvanic isolation, renewable integration and other applications in high voltage direct current (HVdc) systems. The trapezoidal modulation in these converters has been a proven advantage owing to reduced capacitive requirement and high-power density. However, the existing short overlap (SO) trapezoidal modulation technique presents significant dc link current ripples requiring bulky dc link filter. This paper introduces an extended overlap (EO) modulation technique in MMDC to mitigate the need of dc link filters. The change in overlap angle alters the conduction states, component sizing, harmonic spectrum and other converter parameters. Therefore, a detailed mathematical analysis of MMDC with both SO and EO modes of trapezoidal modulation is carried out in this paper. The effect of change in overlap duration on size of sub-module (SM) capacitor, dc link filter is analyzed by simulation and analytical studies. A single stage three phase MMC experimental setup is built to verify the converter operation in both SO and EO modulations.