Selection of lumped element models for coupled lossy transmission lines

A practical method is developed for selecting the minimal number of lumped elements needed to represent a lossy transmission line if a certain accuracy is desired in a well-defined frequency range. This method, which uses dimensionless transmission line parameters, can be used in a wide range of applications and is also extended to hybrid equivalent circuits, consisting of ideal single lossless lines and resistors. For completeness, a lumped element model for coupled lossy lines is presented which uses the same dimensionless parameters and the same criteria as proposed for single lines. An example of coupled transmission line structure including skin-effect losses illustrates the approach.>