Abstract
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.
Highlights
Circuit simulation is an important phase during the development of new electronic circuits
When a path has a high density of straight line segments, the Speed‐up hyperspheres path tracking method (SHPT) will tend to slow down, not as slow like the method proposed in Vazquez-Leal et al (2014)
This characteristic shows that SHPT, compared to Modified spheres algorithm (MSA), requires lower computation time (CP) or could perform almost identical if the homotopic curve exhibits a high number of break points
Summary
Circuit simulation is an important phase during the development of new electronic circuits. As shown in Vazquez-Leal et al (2014), the homotopic curves obtained with this formulation have a PWL nature, this will hold as long as all of the nonlinear devices in the circuit are PWL modelled This property allows to execute the following steps for the proposed path tracking method. The straight line path tracking does not need any correcting steps like those needed when using the NRM, this results in greatly reducing the computing resources and time required It avoids the calculation of different starting points when NRM fails. When a path has a high density of straight line segments, the SHPT will tend to slow down, not as slow like the method proposed in Vazquez-Leal et al (2014) This characteristic shows that SHPT, compared to MSA, requires lower computation time (CP) or could perform almost identical if the homotopic curve exhibits a high number of break points. 4.94280 3 −0.05719 −1.1418E−12 0.24268 2.10639 0.51159 2.37228 0.89835 −4.5210E−12 −0.00571 2.3965E−6 1.8000E−6 a 12
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