We derive the analytic equations for the transmission gain spectrum of a phase shift controlled (PSC) DFB filters with complexed coupled gratings considering both facet reflections and the phase of gratings using the transfer matrix method. The number of parameters of the equations is reduced by using the parameter of effective phase shift defined by the sum of the phase shift in a PSC region the effect of both facets reflections and the effective phase shift on the transmission gain spectrum and verify the validity of those equations from the computer simulation results. Computer simulation results show the PSC DFB filter with a pure index coupled grating has the widest tunable range and that with a pure gain grating has the largest side mode suppression ratio.