Speed-up hyperspheres homotopic path tracking algorithm for PWL circuits simulations

In the present work, we introduce an improved version of the hyperspheres path tracking method adapted for piecewise linear (PWL) circuits. This enhanced version takes advantage of the PWL characteristics from the homotopic curve, achieving faster path tracking and improving the performance of the homotopy continuation method (HCM). Faster computing time allows the study of complex circuits with higher complexity; the proposed method also decrease, significantly, the probability of having a diverging problem when using the Newton-Raphson method because it is applied just twice per linear region on the homotopic path. Equilibrium equations of the studied circuits are obtained applying the modified nodal analysis; this method allows to propose an algorithm for nonlinear circuit analysis. Besides, a starting point criteria is proposed to obtain better performance of the HCM and a technique for avoiding the reversion phenomenon is also proposed. To prove the efficiency of the path tracking method, several cases study with bipolar (BJT) and CMOS transistors are provided. Simulation results show that the proposed approach can be up to twelve times faster than the original path tracking method and also helps to avoid several reversion cases that appears when original hyperspheres path tracking scheme was employed.