The phase sensitivity limit of Differential Phase Contrast (DPC) with partially coherent light is analyzed in details. The parameters to tune phase sensitivity, such as the diameter of illumination, the numerical aperture of the objective, and the noise of the camera are taken into account to determine the minimum phase contrast that can be detected. We found that a priori information about the sample can be used to fine-tune these parameters to increase phase contrast. Based on this information, we propose a simple algorithm to predict phase sensitivity of a DPC setup, which can be performed before the setup is built. Experiments confirm the theoretical findings.