Predictor/Corrector Newton-Raphson (PCNR): A Simple, Flexible, Scalable, Modular, and Consistent Replacement for Limiting in Circuit Simulation

Abstract

Modern circuit simulators predominantly use Newton-Raphson (NR) iteration to solve circuit equations. To improve NR convergence, circuit simulators use a practice called “limiting”. This ensures that sensitive circuit quantities (such as diode voltages) do not change too much between successive NR iterations. However, in most simulators, the implementation of limiting tends to be inflexible, non-modular, inconsistent, and confusing. We therefore propose Predictor/Corrector Newton-Raphson (PCNR), a replacement for limiting that overcomes these disadvantages while incurring modest computational overhead. The key ideas behind PCNR are, (1) to add each limited circuit quantity as an extra unknown to the circuit’s Modified Nodal Analysis (MNA) system of equations, (2) to split each NR iteration into a “prediction” phase followed by a “correction” phase, and (3) to mitigate the computational cost of the extra unknowns by eliminating them from all Ax = b solves using a Schur complement based technique.