Enhanced delay-rational Green´s method for cable time domain analysis

State-space models of multiconductor transmission lines can be generated by means of the Green´s function based method which allows to write the open-end impedance in a rational form as an infinite sum of “modal impedances”. It can be then embedded in a circuit simulation environment for efficient time domain analysis. The previous rational approach has been improved through a proper mathematical formulation, that makes use of explicit delay extraction and pole/residue asymptotic behavior. Nevertheless, the computation of the poles becomes computationally expensive when the number of conductors increases, since the zeros of high order polynomials have to be evaluated. A rational fitting over the “modal impedances” is proposed, which allows a fast identification of the poles that, together with the delays, model the high frequency behavior of the cable in terms of standard hyperbolic functions. The low-frequency behavior is captured by a reduced size state-space model, via rational fitting. Numerical results confirm the accuracy of the proposed modeling approach for electrically long cables, with a large number of conductors.