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

• Published in: 2020 IEEE International Symposium on Circuits and Systems (ISCAS) pp. 1 - 5
• Main Authors: Serrano, J. A., Gines, A. J., Peralias, E.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2020
• Subjects: Analog Front-End; C code; Capacitors; Computational modeling; Convergence; Differential equations; Electronics packaging; Fast Simulation of Non-linear Circuits; Mathematical model; Matrix Exponential; Non-linear Ordinary Differential Equation (ODE); Numerical models; Switched-Capacitor (SC) Simulations
• ISBN: 9781728133201; 1728133203
• ISSN: 2158-1525; 2158-1525
• DOI: 10.1109/ISCAS45731.2020.9180945

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.