Effective properties of infinite periodic structures are governed by the dispersion law of the Bloch waves. A modeling of the dispersion law is proposed for all frequencies and wave vectors. This modeling is based on the complex analytic structure of the Bloch spectrum and on the Kramers-Kronig expression extended to spatially dispersive media. Several explicit formulas for effective parameters will be given for multilayer stacks, for all frequencies and wave vectors, in situations where a perturbation approach can be applied. The relevance of the obtained effective parameters will be discussed.