Variability analysis of interconnect structures including general nonlinear elements in SPICE-type framework

Introduction: Over the past few decades, computer-aided simulation tools have become an important asset for the design, simulation and optimisation of complex electronic networks. Nonetheless, since large-scale integration and miniaturisation lead to an important impact of the manufacturing process on the system performance, appropriate instruments are needed to evaluate uncertainties of the circuit parameters. Typical tools to gather quantitative statistical information of the circuit response are based on the well-known Monte Carlo (MC) method. This is computationally demanding, especially when realistic, complex structures are analysed. Effective solutions to overcome these previous limitations have been proposed, leveraging the so-called polynomial chaos (PC) methods. In [1], a PC-based technique, called the stochastic Galerkin method (SGM), was developed in MATLAB for transmission lines terminated by linear loads. This technique for ‘distributed’ circuits including linear elements was modified in [2] to allow for implementation in a SPICE environment. A PC-method for lumped circuits consisting of discrete, linear and nonlinear elements was first reported in [3, 4], allowing the modelling of uncertainties in a small-signal regime or by approximating the nonlinearities by means of Taylor expansions. Recently, an improved PC-technique for ‘distributed’ circuit elements terminated by ‘general’ nonlinear loads was conceived by the authors of the present contribution [5]. Unfortunately, this technique could only be implemented in MATLAB, as it relies on a finite-difference timedomain solver for transmission lines, making it also cumbersome to deal with lossy, dispersive lines and arbitrary circuit topologies. Therefore, in the present Letter, a SPICE-compatible method is developed and implemented in a traditional environment allowing us for the first time to perform PC-based variability analyses of lossy, dispersive multiconductor transmission lines (MTLs) terminated by general nonlinear loads.