## 1. Introduction

[2] The constant and rapid pace of technological innovation today has produced increasingly complex electronic devices to such an extent that they are often physically separated into several sub-devices and then connected together. The integrity of signals propagating on interconnections is then a fundamental point for the smooth functioning of the overall system. Cable bundles represent one of the most common means by which modern electronic systems and subsystems are interconnected. A large variety of examples exists, ranging from transportation vehicles (cars, aircrafts, ships) to Information Technology equipment and to industrial plants. The electromagnetic interaction among closely spaced individual wires induces disturbances in all other adjacent circuits. This crosstalk can cause functional degradation of the circuits at the ends of the cable. The magnitude of the electromagnetic interference varies significantly as a function of a number of factors including the wires geometries.

[3] The sensitivity of crosstalk to random wires position in the cable has led to several probabilistic models for the crosstalk according to the frequency ranges. Instead of using brute-force Monte Carlo (MC) method, some alternative solutions based on the derivation of pseudo-analytical expressions for the statistical parameters of the responses of distributed systems have been proposed so far [*Shiran et al.*, 1993; *Bellan et al.*, 2003]. However, their principal limitation is related to their scarce flexibility and restriction to the particular structures and output variables for which they have been derived. Possible complementary methods based on the optimal selection of the subset of model parameters in the whole design space [*Zhang et al.*, 2001] have also been proposed. However, these methods turn out to be extremely inefficient, since they require a large set of simulations with different samples of the random parameters and prevent us from applying them to the analysis of complex realistic structures.

[4] Recently, an effective solution based on the so-called polynomial chaos (PC) has been proposed to overcome the previous limitations. This methodology is based on the representation of the stochastic solution of a dynamical circuit in terms of orthogonal polynomials. For a comprehensive and formal discussion of PC theory, the reader is referred to *Ghanen and Spanos* [1991], *Xiu and Karniadakis* [2002], and *Debusschere et al.* [2004, and references therein]; also, it should be pointed out that the word chaos is used in the sense originally defined by *Wiener* [1938] as an approximation of a Gaussian random process by means of Hermite polynomials. This technique has been successfully applied to several problems in different domains, including the extension of the classical circuit analysis tools, like the modified nodal analysis (MNA), to the prediction of the stochastic behavior of circuits [*Strunz and Su*, 2008; *Zou et al.*, 2007; *Stievano and Canavero*, 2010]. However, so far, the application has been mainly focused on the gaussian variability of model parameters and limited to dynamical circuits consisting only of lumped elements. The authors of this contribution have recently proposed an extension of PC theory to distributed structures described by transmission-line equations [*Manfredi et al.*, 2010], also in presence of uniform random variables.

[5] The main drawback of PC is related to the reduction of its efficiency when the number of random variables increases. A possible solution consists in performing preliminary tests to identify the most influential variables to be included in the model [*Manfredi and Canavero*, 2011]. Yet, an approach based on the Response Surface Modeling (RSM) is also possible and presented in this paper as an alternative to PC, followed by a comparison between the two methods. The RSM is based on the fitting of a system response using polynomial terms, whose coefficients are computed in a least-square sense starting from a reduced set of samples.

[6] In order to be validated and compared, the advocated techniques are applied to the stochastic analysis of a commercial multiconductor flex-cable used for the communication between PCB cards.