Transient Analysis of Lumped and Distributed Parameter Systems Using an Approximate Z-Transform Technique

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Abstract
An approximate Z-transform approach is presented to compute at discrete time intervals the time responses of lumped or distributed parameter systems which exhibit wave propagation or time delay effects. The approach was previously developed by Boxer and Thaler [R. Boxer and S. Thaler, Proc. IRE 44, 89–101 (1956)] as a numerical method of solving linear and nonlinear equations and is an extension of the more familiar Laplace transform technique which is used for the analysis of continuous linear systems. Rather than directly utilizing the inverse Laplace transformation to obtain the time function, a mapping of the Laplace transform of the function from the s domain to the z domain is performed via the transformation z = esT, where T is the desired sampling interval of the time function. Unlike the inverse Laplace transformation, which requires the pole-zero structure of the transform to obtain the continuous time function, the sampled time function is then obtained from its z domain representation without using the theory of residues. Numerical solutions to several problems are presented to illustrate the advantages of the approximate Z-transform approach.

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