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In this paper we present an accurate physical model of discretization error in a 1-D perfectly matched layer (PML) using the finite-difference time-domain method. The model is based on the concept of the discrete wave impedance of the PML. This concept implies that the wave impedance in the discretized space changes, with respect to the continuous value, when absorption occurs. These changes depend on the absorption per unit length, as well as on the discretization step. In the discretized space, both, the magnitude and phase of wave impedance are modified. We employ numerical simulations obtained using a 1-D code to test the proposed model. We then compare the results with those obtained from coaxial wave guide geometry using a commercial 3-D software package. One important consequence of this modeling scheme is the feasibility of the PML without return losses due to discretization error. In practice, numerical results show that by correctly adjusting the electromagnetic parameters of the PML (electric permittivity and magnetic permeability), a significant improvement in the reflection characteristics is obtained. In some cases, it could be as much as 78 dB. The remaining return losses are successfully explained as second-order effects related to the discontinuity of electromagnetic parameters at the interface between the simulation space and PML.