A New Second Order Nonlinear Formulation for Fast-SPICE Circuit Simulation

A new second-order matrix formulation is proposed in this work to model any nonlinear electronic system. This new formulation is developed and implemented by using a recasting method that increases the number of variables but limits the non-linearity to a quadratic form. Nonlinearity is modeled without any approximation and can model complex nonlinearities such as exponential and Tanh-based models. The new quadratic method is applied to the extended tanh MOSFET model and an exponential diode model to illustrate the power and reliability of this method. The method also has the advantage of directly stamping transistors and diodes into matrix forms in ways similar to linear elements. To demonstrate the validity of the new formulation, several circuits are examined, and the results compare very well to SPICE simulations. The simulation time as well as numerical stability improve significantly when using time marching techniques with the quadratic formulation as compared to directly stamping transistor and diode exponential nonlinearities.