Dual phase grating x-ray interferometry is compatible with common imaging detectors, and abandons the use of an absorption analyzer grating to reduce the radiation dose. When using x-ray tubes, an absorbing source grating must be introduced into the dual phase grating interferometer. In order to attain a high fringe visibility, in this work we conduct a quantitative coherence analysis of dual phase grating interferometry to find how the source grating affects the fringe visibility. Theoretical analysis shows that with the generalized Lau condition satisfied, the fringe visibility is influenced by the duty cycle of the source grating and the transmission through the grating bar. And the influence of the source grating profile on the fringe visibility is independent of the phase grating type. Numerical results illustrate that the maximum achievable fringe visibility decreases significantly with increasing transmission in the grating bar. Under a given transmission, one can always find an optimal duty cycle to maximize the fringe visibility. These results can be used as general guidelines for designing and optimizing dual phase grating x-ray interferometers for potential applications.