Reliability of circuit-level simulation

Three issues affect the reliability of circuit-level simulation. They are numerical stability of integration, precision of results at each time step and convergence at each time step. The method underlying simulation is first the formulation of a coupled set of nonlinear first-order differential equations representing the behaviour of the interconnected set of devices comprising the circuit. Second, the replacement of the time derivatives in the differential equations by finite-difference approximations (known as integration formulae) which discretise time, in general, in a nonuniform way. This step transforms the nonlinear differential equations, at each discretised time point, into a time-independent set of nonlinear equations. The third step is to solve the nonlinear equations, at each discretised time, by the Newton-Raphson technique which approximates them with a linear set of equations based on an initial estimate of the solution. Repeated solution of the linear set, with appropriate adjustments to the linear equation set coefficients after each solution, is used to refine the solution estimate until it is deemed that adequate precision of solution has been achieved