This paper aims at thoroughly analysing the dynamic behaviour of a droop-controlled dc-dc converter system. An insight into the constraints of the dynamics of the dc voltage droop controller imposed by the converter-level control loop is provided. The sensitivity of the eigenvalues to varying parameters of these control loops is analysed. The range of the control parameters is determined according to the converter model (plant transfer function) and the specifications of the target dynamic performance. To consider the interactions between the controllers of multiple converters in a dc microgrid, modal analysis is applied to a multi-terminal dc (MTdc) system. The participation factors for the dynamic modes of the system are derived and used to indicate the influence of the states on the modes. Influencing states are further investigated through parametric sensitivity analysis. Two cases of dc voltage droop control structures are investigated, namely proportional and proportional-derivative controllers. The analysis is supported by the simulation results of disturbance scenarios in the MTdc grid.