The modular multilevel converter (MMC) is an attractive converter topology for medium-voltage multi-terminal flexible DC micro-grid. The capacitor voltage balancing is one of the key issues affecting the performance of the system. In this paper, the disturbance and unbalance mechanism of capacitor voltages in MMC with Carrier-Phase-Shift Pulse Width Modulation (CPS-PWM) is analyzed, extracted and quantified, by using a proposed non-synchronized switching period sampling method. The capacitor voltage disturbances are then extracted and compared under several commonly used sampling modes. Finally, based on the proposed sampling method, a metric of unbalance degree is also introduced to quantify the differences of the capacitor voltages among submodules (SM). These works will provide the foundation to further investigate, benchmark and deduct new ideas for the capacitor voltage balancing methods under various modulations, topologies and operations of the MMC.