High-Speed Interconnect Models with Stochastic Parameter Variability

In the process of design and fabrication of electronic products, numerical simulation plays a fundamental role for a preliminary electromagnetic compatibility (EMC) assessment of devices in the early design phase. Direct EMC measurements impact both cost and time-to-market as they require purchase and/or hiring of facilities and instruments, as well as fabrication of prototype devices, and need therefore to be minimized. Nowadays, designers can rely on several sophisticated modeling tools, helping them to perform right-the-first-time designs. Nonetheless, these simulation models are accurate as long as we are able to assign accurate values to each system parameter. In modern high-speed and high-density designs, process variations and uncertainties in operating conditions result in parameters which are hard to control or partially unavailable. The device response is thus no longer regarded as deterministic, but is more suitably interpreted as a random process. In this framework, the assessment of signal integrity requires a statistical analysis, which is traditionally based on the so-called Monte Carlo or other sampling-based methods. Yet, for practical applications, these approaches are often too time-consuming, as they are known to require a large number of samples to converge. In this thesis, we extend available literature results to the efficient analysis of high-speed interconnects, such as avionic and industrial cables or printed circuit board traces, affected by uncertainties, like process variations or unavailable operating conditions. Specifically, the framework of polynomial chaos theory is adopted to create stochastic models for transmission lines which are faster to be simulated compared to repeated Monte Carlo simulations. Such methodology is based on the expansion of random quantities in series of orthogonal polynomials, and has been already and successfully applied to the analysis of lumped circuits. In this work, the modeling of distributed components, which are key elements for modern high-frequency designs, is addressed. The advocated approach is general and overcomes the limitations of available literature models for the statistical analysis of the signal propagation over interconnects, which are based on simplified structures and approximate assumptions. Also, a SPICE-compatible implementation is presented, thus allowing the convenient use of SPICE-like circuit analysis tools for the simulation of complex stochastic network topologies, avoiding the creation of customized, ad hoc implementations. This thesis provides a comprehensive theoretical discussion together with several tutorial application examples, thus complementing the published material.