Fast Simulation of Non-Linear Circuits using Semi-Analytical Solutions Based on the Matrix Exponential

This paper presents a new simulation method for fast evaluation of non-linear circuits. The proposed approach solves the non-linear ordinary differential equation (ODE) set of the system using a semi-analytical solution based on the matrix exponential. The method is fully general and suitable for different circuits, including switched-capacitor (SC) architectures, analog to digital converters (Pipeline, SAR, Sigma-Delta ADCs) or digital to analog converters. For illustration purpose in this paper, an analog signal processing front-end for discrete-time data acquisition system is considered as case study. The circuit comprises a Flip-Around Sample&Hold followed by a Programmable Gain Amplifier (PGA), based on a Correlated Double-Sampling amplifier, and a back-end ADC. The model includes non-linearity associated to switches, capacitive parasitics, finite nonlinear DC-gain and non-linear settling behavior including slew-rate. Comparison with traditional ODE numerical solvers shows a reduction of the computation time in almost two orders of magnitude with negligible difference in terms of accuracy.