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A new finite-difference time-domain (FDTD) model for conductors coated with electrically thick frequency-dispersive coatings is developed. The model is based on first-order impedance boundary conditions. As the most important original feature of the model, the frequency dependence of the material parameters of the coating is very general: dispersive coatings of Lorentz-, Debye-, or Drude-type with multiple pole pairs and a fixed electrical conductivity can be modeled with the proposed technique. Another new property of the model is the use of rational approximation in a way that enables accurate approximation of the impedance function in a wide range, corresponding to several thickness resonances of the coating. The conductor losses in the metal backing that are neglected in many earlier models are accounted for in the proposed model. The model is formulated for planar interfaces in the general three-dimensional situation for the Yee algorithm and verified against analytical reference results with numerical examples in one-dimensional and two-dimensional problems.