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We present an approximation by exponentials of the time-domain surface impedance of a lossy half space. Gauss-Chebyshev quadrature of order N-1 is employed to approximate an integral representation of the modified Bessel functions comprising the time-domain impedance kernel. An explicit error estimate is obtained in terms of the physical parameters, the computation time and the number of quadrature points N. We show that our approximation is as accurate as other approaches which do not come with such an error estimate. The paper investigates the conditions under which the derived error estimate also applies to the approximation of J.A. Roden and S.D. Gedney (see Trans. Microwave Theory Tech., vol.47, p.1954, 1999).