Alternative SPICE implementation of circuit uncertainties based on orthogonal polynomials

The impact on circuit performance of parameters uncertainties due to possible tolerances or partial information on devices can be effectively evaluated by describing the resulting stochastic problem in terms of orthogonal polynomial expansions of electrical parameters and of circuit voltages and currents. This contribution formalizes a rule for the construction of an augmented instance of the original circuit, that provides a systematic solution approach for the unknown coefficients of the expanded electrical variables. The use of SPICE as a solution engine of the augmented circuit is straightforward, thus providing a convenient and efficient alternative to the conventional approach SPICE uses for uncertainty analysis. An application example involving the stochastic simulation of a digital link with variable substrate parameters demonstrates the potential of the proposed approach.