A sampling theorem in numerical integration [nonlinear circuit simulation]

A key issue in nonlinear circuit simulation is the determination of equilibrium points. Very often, sophisticated and computationally expensive integration methods are used in order to achieve highly accurate results. We show that for an important class of circuits whose dynamics are governed by a first-order nonlinear differential equation, the cellular neural networks (CNNs), a simple forward Euler integration method yields the exact equilibrium points with minimum computational effort, when the step size is chosen to be equal to the cell´s internal time constant. This allows a drastic acceleration of the simulation of continuous-time CNNs. Emphasis is put on the fact that numerical integration is a sampling process-a viewpoint that reveals that any forward Euler integrated CNN corresponds to a discrete-time CNN