Time delays are an integral part of high-speed circuits and control-system applications. Rational approximations to the Laplace transform of a time delay T d ; i.e., e 0T s have been used in the past.These approximations include Padê, Bessel, and other variations. The disadvantage of such approximations is that the quality of the response can only be improved by increasing the order of approximation. In some cases, this results in unstable systems, e.g., a fifth-order Padê approximation with no zeros and five poles is unstable. In this paper, a new rational approximation for the ideal time delay is developed that offers a greater degree of precision and control over the type of response achievable within the same order. Comparisons of the errors between the step responses of the approximation developed here with that of Padê and Bessel show that the new approximation can be tuned to result in a stable operation and the lowest error.

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