Efficient algorithm for solving systems of circuit differential-algebraic equations with reliable divergence suppression in DC and time domains

Although many simulation tools contain advanced algorithms for the solution of the systems of differential-algebraic nonlinear equations, some classes of circuits still cause serious problems. These are typically the circuits with strong negative feedbacks, flip-flop circuits, the blocks that are characterized by macromodels with unusual elements, and large distributed amplifiers and oscillators. In the paper, a very efficient and reliable algorithm for solving the circuit differential-algebraic equations is characterized first, which is based on a sophisticated arrangement of the Newton interpolation polynomial. After that, a novel method is introduced for improving the convergence with four suggested criteria that are being compared. Unlike the similar algorithms focused on an operating point analysis only, the proposed method also works in a transient analysis. All the four criteria are thoroughly tested on nine problematic circuits - six of them often diverge in the operating point analysis, and three of them diverge at some points during the transient analysis. The results confirm extraordinary robustness of the proposed method, even circuits with a large memelement hysteresis can be solved.