An improved refinable rational approximation to the ideal time delay

Time delays are an integral part of high-speed circuits and control-system applications. Rational approximations to the Laplace transform of a time de lay Td; i.e., e-(Tds) have been used in the past. These approximations incl ude Pade, Bessel, and other variations. The disadvantage of such approximat ions is that the quality of the response can only be improved by increasing the order of approximation. In some cases, this results in unstable system s, e,g., a fifth-order Pade approximation with no zeros and five poles is u nstable. In this paper, a neu rational approximation for the ideal time del ay is developed that offers a greater degree of precision and control over the type of response achievable within the same order. Comparisons of the e rrors between the step responses of the approximation developed here with t hat of Pade and Bessel shove that the new approximation can be tuned to res ult in a stable operation and the lowest error.