The quality of laser wakefield accelerated electrons beams is strongly determined by the physical mechanism exploited to inject electrons in the wakefield. One of the techniques used to improve the beam quality is the density transition injection, where the electron trapping occurs as the laser pulse passes a sharp density transition created in the plasma. Although this technique has been widely demonstrated experimentally, the literature lacks theoretical and numerical studies on the effects of all the transition parameters. We thus report and discuss the results of a series of particle in cell (PIC) simulations where the density transition height and downramp length are systematically varied, to show how the electron beam parameters and the injection mechanism are affected by the density transition parameters.