Circuit simulations with uncertainties using affine arithmetic and piecewise affine statemodels

Especially in the field of safety critical applications the impact of process variations on the behavior of integrated circuits can not be neglected. Usually, simulation is costly due to the need for multiple simulation runs with different technology parameter settings. In the past, semi-symbolic-simulation applying affine arithmetic (AA), as a suitable range arithmetic, has produced very motivating results on netlistlevel. Using AA reduces the complexity without loosing generality of the simulation results. This paper covers the formulation of effective highlevel circuit models. We use piecewise affine functions to model the circuit and to provide fast simulations while simultaneously achieving good convergence. The equations are separated into matrices for linear mapping and matrices for the representation of the system¿s state. We formulate the uncertainties within the system with affine terms entered in the system matrices. Furthermore, we present the relevant solution algorithms for the semi symbolic simulation and their implementation.