A Delay-Rational Model of Lossy Multiconductor Transmission Lines With Frequency-Independent Per-Unit-Length Parameters

Cables, printed circuit boards, and VLSI interconnects are commonly modeled as multiconductor transmission lines. Models of electrically long transmission lines are memory and time consuming. In this paper, a robust and efficient algorithm for the generation of a delay-based model is presented. The impedance representation via the open-end matrix Z is analyzed. In particular, the rational formulation of Z in terms of poles and residues is exploited for both lossless and lossy cases. The delays of the lines are identified, and explicitly incorporated into the model. A model order reduction of the system is automatically performed, since only a limited number of poles and residues are included in the rational part of the model, whereas the high-frequency behavior is captured by means of closed expressions that account for the delays. The proposed method is applied to two relevant examples and validated through the comparison with reference methods. The time-domain solver is found to be more accurate and significantly faster than the one obtained from a pure-rational model.