This paper provides an effective solution for the simulation of cables and interconnects with the inclusion of the effects of parameter uncertainties. The problem formulation is based on the telegraphers equations with stochastic coefficients, whose solution requires an expansion of the unknown parameters in terms of orthogonal polynomials of random variables. The proposed method offers accuracy and improved efficiency in computing the parameter variability effects on system responses with respect to the conventional Monte Carlo approach. The approach is validated against results available in the literature, and applied to the stochastic analysis of a commercial multiconductor flat cable.

This paper focuses on the derivation of an enhanced transmission-line model allowing the stochastic analysis of a realistic multiconductor interconnect. The proposed model, which is based on the expansion of the well-known telegraph equations in terms of orthogonal polynomials, includes the variability of geometrical or material properties of the interconnect due to uncertainties like fabrication process or temperature. A real application example involving the frequency-domain analysis of a coupled microstrip and the computation of the parameters variability effects on the transmission-line response concludes this paper.

This letter proposes a general and effective decoupled technique for the stochastic simulation of nonlinear circuits via polynomial chaos. According to the standard framework, stochastic circuit waveforms are still expressed as expansions of orthonormal polynomials. However, by using a point-matching approach instead of the traditional stochastic Galerkin method, a transformation is introduced that renders the polynomial chaos coefficients decoupled and therefore obtainable via repeated non-intrusive simulations and an inverse linear transformation. As discussed throughout the letter, the proposed technique overcomes several limitations of state-of-the-art methods. In particular, the scalability is hugely improved and tens of random parameters can be simultaneously treated within the polynomial chaos framework. Validating application examples are provided that concern the statistical analysis of microwave amplifiers with up to 25 random parameters.

In this paper, a novel stochastic modeling strategy is constructed that allows assessment of the parameter variability effects induced by the manufacturing process of on-chip interconnects. The strategy adopts a three-step approach. First, a very accurate electromagnetic modeling technique yields the per unit length (p.u.l.) transmission line parameters of the on-chip interconnect structures. Second, parameterized macromodels of these p.u.l. parameters are constructed. Third, a stochastic Galerkin method is implemented to solve the pertinent stochastic telegrapher's equations. The new methodology is illustrated with meaningful design examples, demonstrating its accuracy and efficiency. Improvements and advantages with respect to the state-of-the-art are clearly highlighted.

The aim of this article is to provide an overview of polynomial chaos (PC) based methods for the statistical analysis of transmission lines. The underlying idea of PC is to represent stochastic line voltages and currents as expansions of predefined orthogonal polynomials. The determination of the expansion coefficients allows obtaining pertinent statistical information and is generally much faster than running, e.g., a Monte Carlo (MC) analysis. There exist several approaches to calculate the PC expansion coefficients. The article briefly reviews virtually all existing methods, whilst focusing on the popular and accurate stochastic Galerkin (SG) method as well as on the recent, more efficient and non-intrusive formulation of the so-called stochastic testing (ST) method. These two techniques are introduced by way of a simple illustrative example, i.e., a single-wire line running above a ground plane. Numerical comparisons in terms of accuracy and efficiency are also provided for a four-wire line with nonlinear terminations.

This paper investigates the application of support vector machine to the modeling of high-speed interconnects with largely varying and/or highly uncertain design parameters. The proposed method relies on a robust and well-established mathematical framework, yielding accurate surrogates of complex dynamical systems. An identification procedure based on the observation of a small set of system responses allows generating compact parametric relations, which can be used for design optimization and/or stochastic analysis. The feasibility and strength of the method are demonstrated based on a benchmark function and on the statistical assessment of a realistic printed circuit board interconnect, highlighting the main features and benefits of this technique over state-of-the-art solutions. Emphasis is given to the effects of the initial sample size and of input noise on the model estimation.