An adaptive time-step control method is proposed for the damped pseudo-transient analysis (DPTA) method. The new method is based on the idea of switched evolution/relaxation (SER), which can automatically adapt the step size for different circuit states. Considering the number of iterations needed for the convergence of Newton-Raphson (NR) method and the states in previous steps, the proposed method can automatically optimize the time-step size. Using numerical examples, the new method is proven to improve robustness, simulation efficiency, and the convergence of DPTA for solving nonlinear DC circuit equations.

An effective time-step control method is proposed for the damped pseudo-transient analysis (DPTA). This method is based on the idea of the switched evolution/relaxation method which can automatically adapt the step size for different circuit states. Considering the number of iterations needed for the convergence of the Newton-Raphson method, the new method adapts the suitable time-step size with the status of previous steps. By numerical examples, it is proved that this method can improve the simulation efficiency and convergence for the DPTA method to solve nonlinear DC circuits.

Recently, the compound element pseudo transient analysis, CEPTA, method is regarded as an efficient practical method to find DC operating points of nonlinear circuits when the Newton-Raphson method fails. In the previous CEPTA method, an effective SPICE3 implementation algorithm was proposed without expanding the Jacobian matrix. However the limitation of step size was not well considered. Thus, the non-convergence problem occurs and the simulation efficiency is still a big challenge for current LSI nonlinear cicuits, especially for some practical large-scale circuits. Therefore, in this paper, we propose a new SPICE3 implementation algorithm and an embedding algorithm, which is where to insert the pseudo capacitors, for the CEPTA method. The proposed implementation algorithm has no limitation for step size and can significantly improve simulation efficiency. Considering the existence of various types of circuits, we extend some possible embedding positions. Numerical examples demonstrate the improvement of simulation efficiency and convergence performance.

Finding DC operating points of nonlinear circuits is an important and difficult task. The Newton-Raphson method adopted in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. However, most previous studies are mainly focused on the bipolar transistor circuits and no paper presents the global convergence theorems of homotopy methods for MOS transistor circuits. Moreover, due to the improvements and advantages of MOS transistor technologies, extending the homotopy methods to MOS transistor circuits becomes more and more necessary and important. This paper proposes two nonlinear homotopy methods for MOS transistor circuits and proves the global convergence theorems for the proposed MOS nonlinear homotopy method II. Numerical examples show that both of the two proposed homotopy methods for MOS transistor circuits are more effective for finding DC operating points than the conventional MOS homotopy method and they are also capable of finding DC operating points for large-scale circuits.

The compound element pseudo-transient analysis (PTA) algorithm is an effective practical method for finding the DC operating point when the Newton-Raphson method fails. It is able to effectively prevent from the oscillation problems compared with conventional PTA algorithms. In this paper, an effective SPICE3 implementation method for the compound element PTA algorithm is proposed. It has the characteristic of not expanding the Jacobian matrix and not changing the Jacobian matrix structure when the pseudo-transient numerical simulation is being done. Thus a high simulation efficiency is guaranteed. The ability of the proposed SPICE3 implementation to avoid the oscillation problems and the simulation efficiency are demonstrated by examples.

Recently, an efficient homotopy method termed the variable gain Newton homotopy (VGNH) method has been proposed for finding DC operating points of nonlinear circuits. This method is not only very efficient but also globally convergent for any initial point. However, the programming of sophisticated homotopy methods is often difficult for non-experts or beginners. In this paper, we propose an effective method for implementing the VGNH method on SPICE. By this method, we can implement a "sophisticated VGNH method with various efficient techniques" "easily" "without programming," "although we do not know the homotopy method well."

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, we propose an improved version of the homotopy method that can find DC operating points of practical nonlinear circuits smoothly and efficiently. Numerical examples show the effectiveness of the proposed method.

In circuit simulation, dc operating points of nonlinear circuits are obtained by solving circuit equations. In this paper, we consider "hybrid equations" as the circuit equations and discuss the stability of dc operating points obtained by solving hybrid equations. We give a simple criterion for identifying unstable operating points from the information of the hybrid equations. We also give a useful criterion for identifying initial points from which homotopy methods coverge to stable operating points with high possibility. These results are derived from the theory of dc operating point stability developed by M. M. Green and A. N. Willson, Jr.

In this paper we study on the stability of an operating points of a nonlinear resistive circuits including transistors. A set of sufficient conditions for the operating point to be unstable are proposed. These conditions are a generalization of the well-known negative difference resistance (NDR) criteria.