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Time and Laplace‐domain methods for MTL transient and sensitivity analysis

Lubomír Brančík (Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic)



The purpose of this paper is to present the development and comparison of selected time‐domain and Laplace‐domain methods for the simulation of waves propagating along multiconductor transmission lines (MTLs), both uniform and nonuniform, and sensitivities with respect to distributed and lumped parameters of MTL systems.


A methodology is based on discrete, semidiscrete and continuous MTL models formulated and solved both in the time and Laplace domains, latter combined with a numerical inverse Laplace transform (NILT).


The most accurate method is that based on the MTL Laplace‐domain continuous model, processed via the MTL chain matrix and connected with an NILT. This method concurrently shows minimal RAM requirements, and in case of uniform MTLs, it runs fastest. For nonuniform MTLs, however, the implicit Wendroff formula is fastest, as long as the RAM is available.

Research limitations/implications

The research is limited to linear MTLs only and the methods suppose terminating circuits based on their generalized Thévenin equivalents. They can be, however, generalized for more complex systems via more sophisticated boundary conditions treatment. The time‐domain methods have further potential to be generalized towards nonlinear MTLs.

Practical implications

The methods considered can contribute to solving signal integrity issues in high‐speed electronic systems, the Matlab routines developed can serve in education process as well.


The implicit Wendroff formula has been adapted to enable simulation of voltage and/or current distributions and their sensitivities along the nonuniform MTLs' wires. Besides, semidiscrete and continuous nonuniform MTL models have been elaborated to enable sensitivities determination, both in the time and Laplace domains, latter connected with the NILT technique based on fast Fourier transform/inverse fast Fourier transform and quotient‐difference algorithms.



Brančík, L. (2011), "Time and Laplace‐domain methods for MTL transient and sensitivity analysis", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 4, pp. 1205-1223.



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