Transient Analysis of Lossy Transmission Lines: An Efficient Approach Based on the Method of Characteristics

Abstract

This paper is devoted to transient analysis of lossy transmission lines characterized by frequency-dependent parameters. A public dataset of parameters for three line examples (a module, a board, and a cable) is used, and a new example of on-chip interconnect is introduced. This dataset provides a well established and realistic benchmark for accuracy and timing analysis of interconnect analysis tools. Particular attention is devoted to the intrinsic consistency and causality of these parameters. Several implementations based on generalizations of the well-known method-of-characteristics are presented. The key feature of such techniques is the extraction of the line modal delays. Therefore, the method is highly optimized for long interconnects characterized by significant propagation delay. Nonetheless, the method is also successfully applied here to a short high/loss on-chip line, for which other approaches based on lumped matrix rational approximations can also be used with high efficiency. This paper shows that the efficiency of delay extraction techniques is strongly dependent on the particular circuit implementation and several practical issues including generation of rational approximations and time step control are discussed in detail.

Quantum Corrected Drift–Diffusion Modeling and Simulation of Tunneling Effects in Nanoscale Semiconductor Devices

“…∞ stands for the high-frequency limit, which may be evaluated from the physical model of the line or even from frequency-domain samples of the parameters provided by measurements, e.g., [10]. It is important to stress that Z r (s) and Y r (s) tends to zero as 1/s for s → ∞.…”

“…It is known in literature that the model adopted here is the most suitable to perform transient analysis of long transmission lines, i.e. lines for which the propagation delay plays a significant role, e.g., [10]. This is because such a model allows to extract analytically all the unbounded terms contained in the line impulse responses, which are then represented by simple resistive circuits and damped delayed sources.…”

Nonuniform Multiconductor Transmission Line Analysis by a Two-Step Perturbation Technique

“…Nevertheless, it requires very many data points to avoid aliasing errors when very fast signals are studied. The method of characteristics [5]- [8], which discretizes both time and distance, can also be applied to obtain transients. Unfortunately, the technique becomes inefficient to account for frequency-dependent p.u.l.…”

Optimized Waveform Relaxation Methods for Longitudinal Partitioning of Transmission Lines

“…Since then, continuous improvements have been made toward higher accuracy and larger frequency ranges of approximation, e.g. [8]- [10]. Hence, the quality of the multiconductor transmission line models has improved considerably over the years.…”