A Two-Step Perturbation Technique for Nonuniform Single and Differential Lines

Abstract

Abstract-A novel two-step perturbation technique to analyze nonuniform single and differential transmission lines in the frequency domain is presented. Here, nonuniformities are considered as perturbations with respect to a nominal uniform line, allowing an interconnect designer to easily see what the effect of (unwanted) perturbations might be. Based on the Telegrapher's equations, the proposed approach yields second-order ordinary distributed differential equations with source terms. Solving these equations in conjunction with the pertinent boundary conditions leads to the sought-for currents and voltages along the lines. The accuracy and efficiency of the perturbation technique is demonstrated for a linearly tapered microstrip line and for a pair of coupled lines with random nonuniformities. Moreover, the necessity of adopting a two-step perturbation in order to get a good accuracy is also illustrated.

Analysis of Nonuniform Transmission Lines With an Iterative and Adaptive Perturbation Technique

“…parameters is limited by geometrical constraints, thus rendering the second-order perturbation sufficiently accurate [42]- [44]. On the contrary, the variations of wire positions in TWPs or in nonuniform cable harnesses, as considered in this paper, result in a more severe variation of the p.u.l.…”

“…Note that in [42] and [43], only the case K = 2 was considered, for which closedform expressions could be provided for V 1 , I 1 , V 2 and I 2 .…”

“…This method, originally presented for single lines, has been recently recast in terms of a two-step perturbation technique applied to single or differential [42] as well as to arbitrary multiconductor transmission lines [43]. The nonuniformity is in this case interpreted as a perturbation with respect to an average uniform line.…”

An Effective Modeling Framework for the Analysis of Interconnects Subject to Line-Edge Roughness

“…To overcome the aforementioned issues, a two-step PT for NUTLs [10], which was proven to be fast and accurate [13], is adopted here. The method is based on the representation of the actual voltages and currents as the sum of three contributions, i.e., V = V 0 +V 1 +V 2 and I = I 0 +I 1 +I 2 .…”

“…For further discussion on the accuracy of the PT, the reader is referred to [10] and [13]. The creation of the stochastic macromodel requires about 175 min instead.…”