We study both analytically and numerically the rate equations of a laser diode subject to a filtered phase-conjugate optical feedback (FPCF). We formulate dimensionless equations for the FPCF and determine the Hopf bifurcation conditions. The coalescence of different Hopf bifurcations as the filter width decreases suggests the disappearance of the external cavity modes for a narrow width. We confirm our analytical predictions with direct numerical simulations of the FPCF equations.