In this paper, a fundamental study of 3-dimensional pulse width modulation (3DPWM) is achieved. It depends on the DC linked capacitor center-split structure inverter. The mathematical model of 3DPWM for a 2-level system in rectangular, cylindrical and spherical coordinates is studied. The equivalent circuits in α,β and 0 frames are expressed independently. The conventional 2DPWM and this novel 3DPWM are compared. Generalized 3DPWM in multi-level systems is investigated. The 3D space vector modulation is also considered with simulation results. This paper forms the basic background for the further study of 3DPWM. The advantages and the disadvantages of this novel 3DPWM are also included.